The value of A, B and C from the given equation are 0, 0 and 6 respectively.
The given equation is y=x²+x.
Here, the table is
X -2 -1 0 1 2
Y 2 A B 2 C
When x=-1
y=(-1)²-1
y=0
So, A=0
When x=0
y=(0)²+0
y=0
So, B=0
When x=2
y=(2)²+2
y=6
So, C=6
Therefore, the value of A, B and C are 0, 0 and 6 respectively.
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Practice: IXL Write linear,quadratic, and exponential functions and i need help figuring out if this is a linear, quadratic, or a exponential function and the answer to it.
The linear equation is y = 4x + 2, the quadratic equation is y = 4x² - 2x + 2 , and the exponential equation is y = 2(3ˣ).
Let's use the first two points on the table: (0, 2) and (1, 6).
The slope is (6 - 2) / (1 - 0) = 4.
To find the y-intercept, we can plug in one of the points and solve for b in the equation y = mx + b.
Let's use (0, 2): 2 = 4(0) + b, so b = 2.
Therefore, the linear equation is y = 4x + 2.
We need to find the values of a, b, and c. Let's use the first three points on the table: (0, 2), (1, 6), and (2, 18).
We can create a system of equations by plugging in these points:
2 = a(0)² + b(0) + c,
6 = a(1)² + b(1) + c, and
18 = a(2)² + b(2) + c.
Simplifying these equations, we get
c = 2, a + b + c = 6, and 4a + 2b + c = 18.
Solving this system of equations, we get
a = 4, b = -2, and c = 2.
Therefore, the quadratic equation is y = 4x² - 2x + 2.
We can use the formula for exponential growth, which is y = abˣ, where a is the initial value and b is the growth factor. Let's use the first two points on the table: (0, 2) and (1, 6).
The initial value is 2, so the equation is y = 2bˣ.
To find the growth factor, we can divide the y-values: 6/2 = 3 = b¹, so b = 3. Therefore, the exponential equation is y = 2(3ˣ).
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Sara drops a tennis ball and lets it bounce. She records the height of the ball after each of its bounces as an ordered pair, where x represents the number of bounces and y represents the height of the ball in inches. The ordered pairs she records are (1,8), (2,6), (3,2) and (4,1)
We can plot the points (1,8), (2,6), (3,2), and (4,1) on a graph by using a coordinate plane and the x and y-coordinates of each point.
To plot these points, we will use a coordinate plane, which is a two-dimensional graph with an x-axis and a y-axis. The x-axis represents the horizontal position, and the y-axis represents the vertical position. We will use the x-coordinate to determine the horizontal position of the point and the y-coordinate to determine the vertical position of the point.
For the first point, (1,8), we will start at the origin of the graph, which is the point (0,0). We will then move 1 unit to the right along the x-axis and 8 units up along the y-axis to plot the point.
For the second point, (2,6), we will start again at the origin and move 2 units to the right along the x-axis and 6 units up along the y-axis to plot the point.
We will repeat this process for the remaining points, (3,2) and (4,1), to plot all four points on the graph. Once all four points are plotted, we can connect them with a line to visualize the pattern of the ball's bounces.
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Complete Question:
Sara drops a tennis ball and lets it bounce. She records the height of the ball after each of its bounces as an ordered pair, where x represents the number of bounces and y represents the height of the ball in inches.
The ordered pairs she records are (1,8), (2,6), (3,2) and (4,1).
Plot the ordered points on the graph.
Taub went shopping for a new phone. To find the total plus tax, she multiplied the price of the phone by 1.055. What percent tax did she pay?
The required, Taub paid a tax of 0.055 or 5.5%.
To find the tax percentage Taub paid, we need to subtract 1 from the total multiplier and convert the result to a percentage.
1.055 - 1 = 0.055
So Taub paid a tax of 0.055 or 5.5%.
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Adriel decides to research the relationship between the length in inches and the
weight of a certain species of catfish. He measures the length and weight of a number
of specimens he catches then throws back into the water. After plotting all his data,
he draws a line of best fit. What does the slope of the line represent?
The slope of the line represents the rate of change in weight for every unit increase in length of the catfish.
How to find the slope of line?The slope of the line of best fit in this scenario represents the rate of change or the relationship between the length and weight of the catfish. Specifically, the slope indicates the change in weight of the catfish for every unit increase in length.
If the slope is positive, it means that as the length of the catfish increases, its weight also tends to increase. If the slope is negative, it means that as the length of the catfish increases, its weight tends to decrease.
For example, if the slope of the line of best fit is 2, it means that for every one-inch increase in length, the weight of the catfish tends to increase by two pounds. Similarly, if the slope is -1, it means that for every one-inch increase in length, the weight of the catfish tends to decrease by one pound.
In summary, the slope of the line of best fit represents the relationship between the two variables being studied, in this case, the length and weight of the catfish.
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12 Let f(x)= x²/4(x+1) Find all critical numbers of f. As your answer please input the sum of all critical numbers.
The critical numbers of f(x) are x = -1, 0, and 1 and The sum of all critical numbers is 0.
How to find the critical numbers?To find the critical numbers of f(x) = x²/4(x+1), we need to find the values of x where the derivative of f(x) is equal to zero or does not exist.
The derivative of f(x) is:
f'(x) = [(x+1)(2x) - x²(4)] / [4(x+1)²]
Simplifying, we get:
f'(x) = [2x(x+1) - 4x²] / [4(x+1)²]
f'(x) = [2x(x+1-2x)] / [4(x+1)²]
f'(x) = [2x(1-x)] / [4(x+1)²]
f'(x) = [x(1-x)] / [2(x+1)²]
The critical numbers are the values of x where f'(x) is equal to zero or does not exist.
Setting f'(x) = 0, we get:
x(1-x) = 0
This equation is true when x = 0 or x = 1.
Now, let's check if f'(x) does not exist at x = -1 (which is the only possible point where the derivative may not exist):
f'(x) = [x(1-x)] / [2(x+1)²]
When x = -1, the denominator of f'(x) becomes zero, so the derivative does not exist at x = -1.
Therefore, the critical numbers of f(x) are x = -1, 0, and 1.
The sum of all critical numbers is:
-1 + 0 + 1 = 0
Hence, the answer is 0.
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f(x,y) = x2 + y² + xy {(x, y) : x2 + y2 < 1}
"Find the maxima and minima, and where they are reached, of the
following function. Find the locals and absolutes. Identify the
critical points inside the disk if any."
The given function f(x,y) = x^2 + y^2 + xy has a maximum value of 3/4 at (x,y) = (1/2,1/2) and a minimum value of -1/4 at (x,y) = (-1/2,1/2) inside the disk x^2 + y^2 < 1. There are no critical points inside the disk.
To find the critical points, we need to take partial derivatives of the function with respect to x and y and solve the resulting equations simultaneously.
fx = 2x + y = 0
fy = 2y + x = 0
Solving these equations, we get the critical point at (x,y) = (-1/2,-1/2) outside the disk. Hence, we do not consider it further.
Next, we need to find the boundary points of the disk, which is the circle x^2 + y^2 = 1. We can parameterize this circle as x = cos(t) and y = sin(t), where t ranges from 0 to 2π.
Substituting these values in the given function, we get:
f(cos(t), sin(t)) = cos^2(t) + sin^2(t) + cos(t)sin(t)
= 1/2 + 1/2sin(2t)
Now, we need to find the maximum and minimum values of this function. Since sin(2t) ranges from -1 to 1, the maximum value of the function is 3/4 when sin(2t) = 1, i.e., when t = π/4 or 5π/4. At these points, x = cos(π/4) = 1/2 and y = sin(π/4) = 1/2.
Similarly, the minimum value of the function is -1/4 when sin(2t) = -1, i.e., when t = 3π/4 or 7π/4. At these points, x = cos(3π/4) = -1/2 and y = sin(3π/4) = 1/2.
Therefore, the function has a maximum value of 3/4 at (x,y) = (1/2,1/2) and a minimum value of -1/4 at (x,y) = (-1/2,1/2) inside the disk x^2 + y^2 < 1. There are no critical points inside the disk.
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Nolan is following his family's macaroni and and cheese recipe. The recipe calls 6 cups of shredded cheese 4 tablespoons of milk. He wants to make a smaller batch, so he uses only 3 cups of shredded cheese
Nolan is making a smaller batch of his family's macaroni and cheese recipe, and as a result, he has reduced the amount of shredded cheese to 3 cups. The original recipe called for 6 cups of shredded cheese and 4 tablespoons of milk.
However, since Nolan is using only 3 cups of shredded cheese, he will need to adjust the amount of milk he uses as well.
When reducing the amount of cheese, it is important to keep the ratio of cheese to milk consistent. Therefore, if Nolan is halving the amount of cheese, he should also halve the amount of milk. This means that instead of using 4 tablespoons of milk, he should use only 2 tablespoons of milk.
It is important to note that reducing the amount of cheese and milk in a recipe may also affect the overall taste and texture of the dish. However, by following the recipe and adjusting the amounts accordingly, Nolan can still create a delicious and satisfying macaroni and cheese dish.
In summary, when making a smaller batch of a recipe, it is important to adjust the ingredients accordingly while maintaining the same ratios. Nolan is reducing the amount of cheese in his macaroni and cheese recipe and should also reduce the amount of milk in order to keep the same ratio.
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‘Vehicles approaching a certain road junction from town A can either turn left, turn right or go straight on. Over time it has been noted that of the vehicles approaching this particular junction from town A, 55% turn left, 15% turn right and 30% go straight on. The direction a vehicle takes at the junction is independent of the direction any other vehicle takes at the junction.
(i) Find the probability that, of the next three vehicles approaching the junction from town A, one goes straight on and the other two either both turn left or both turn right. ’
To solve this problem, we can use the multiplication rule of probability, which states that the probability of two or more independent events occurring together is the product of their individual probabilities.
Let L, R, and S be the events that a vehicle turns left, turns right, and goes straight on, respectively. We want to find the probability of the following event:
E: One vehicle goes straight on and the other two either both turn left or both turn right.
We can break down event E into two sub-events: one vehicle goes straight on and the other two vehicles both turn left or both turn right. Let's calculate the probabilities of these sub-events separately:
- Probability that one vehicle goes straight on: P(S) = 0.3
- Probability that the other two vehicles both turn left or both turn right: P((LL) or (RR)) = P(LL) + P(RR)
To find P(LL) and P(RR), we can use the multiplication rule again. Since the events are independent, we can multiply their individual probabilities:
- Probability that two vehicles both turn left: P(LL) = P(L) × P(L) = 0.55 × 0.55 = 0.3025
- Probability that two vehicles both turn right: P(RR) = P(R) × P(R) = 0.15 × 0.15 = 0.0225
Therefore, the probability of event E is:
P(E) = P(S) × P((LL) or (RR))
= 0.3 × (P(LL) + P(RR))
= 0.3 × (0.3025 + 0.0225)
= 0.0975
So the probability that, of the next three vehicles approaching the junction from town A, one goes straight on and the other two either both turn left or both turn right is 0.0975 or approximately 0.1 (rounded to one decimal place).
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Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three? Tell a story that could describe each situation. I don't know how to word it, please help. Please also give me the sums
The order of division affects the result; 3 ÷ 1/5 is 15 and 1/5 ÷ 3 is 1/15.
How are the quotients different?To find the answer, we can calculate the quotient of three divided by one-fifth, which is:
3 ÷ (1/5) = 15
And the quotient of one-fifth divided by three is:
(1/5) ÷ 3 = 1/15
These two quotients are different because the order of division changes the result. In the first case, we divide 3 by a smaller number (one-fifth), which results in a larger quotient (15). In the second case, we divide a smaller number (one-fifth) by a larger number (three), which results in a smaller quotient (1/15).
To give a story describing each situation:
For the first situation, imagine a pizza that is divided into five equal slices, and three hungry friends who want to share it. Each friend gets one-fifth of the pizza, but they want to know how much pizza they would get if they each had three-fifths. To find out, they combine their slices, which gives them three out of the five slices. The total amount of pizza they have is now three-fifths of the pizza, and they can each take one-third of that amount, which is 15% of the original pizza.For the second situation, imagine a group of three friends who want to share a small bag of candy that has five pieces in it. Each friend gets one-fifth of the candy, but they want to know how much candy they would get if they each had three pieces. To find out, they divide the total number of pieces (five) by the number of friends (three), which gives them one and two-thirds pieces each, or one-fifteenth of the bag.Learn more about quotient
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I need help, answers and explanations
The length of the top of the ladder from the ground is 10m and the distance from wall to the bottom of ladder is 1.5m
Given that an ladder leans against a wall.
We have to find the length of the top of the ladder from the ground.
We know that tan function is the ratio of opposite side and adjacent side
Let x be the opposite side
tan 68 = x/4
2.475 = x/4
x= 4×2.475
x=9.9 m
x=10 m
So, the length of the top of the ladder from the ground is 10m.
Now let us find the distance from wall to the bottom of ladder
cosine function is the ratio of adjacent side and hypotenuse
Cos 68 = x/4
0.374 =x/4
x=0.374×4
x=1.5m
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Height of 10th grade boys is normally distributed with a mean of 63. 5 in. And a standard deviation of 2. 9 in. The area greater than the z-score is the probability that a randomly selected 14-year old boy exceeds 70 in. What is the probability that a randomly selected 10th grade boy exceeds 70 in. ?Use your standard normal table.
Heights for 16-year-old boys are normally distributed with a mean of 68. 3 in. And a standard deviation of 2. 9 in. Find the z-score associated with the 96th percentile. Find the height of a 16-year-old boy in the 96th percentile. State your answer to the nearest inch
The probability that a randomly selected 10th grade boy exceeds 70 in is approximately 0.0127 or 1.27%.
The height of a 16-year-old boy in the 96th percentile is approximately 73 inches.
For the first question, we need to find the z-score for a height of 70 inches using the formula:
z = (x - μ) / σ
where x is the height of 70 inches, μ is the mean of 63.5 inches, and σ is the standard deviation of 2.9 inches.
z = (70 - 63.5) / 2.9 = 2.241
Using a standard normal table, we can find the area to the right of this z-score, which represents the probability that a randomly selected 10th grade boy exceeds 70 inches. The area to the right of 2.24 is 0.0127. Therefore, the probability is approximately 0.0127 or 1.27%.
For the second question, we need to find the z-score associated with the 96th percentile using a standard normal table. The 96th percentile is the point below which 96% of the data falls and above which 4% of the data falls. This corresponds to a z-score of approximately 1.75.
To find the height of a 16-year-old boy in the 96th percentile, we can use the formula:
x = μ + z * σ
where x is the height we want to find, μ is the mean of 68.3 inches, σ is the standard deviation of 2.9 inches, and z is the z-score we just found.
x = 68.3 + 1.75 * 2.9 = 73.28
Therefore, the height of a 16-year-old boy in the 96th percentile is approximately 73 inches.
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I just need help on B PLS :)
The data modeled by the box plots represent the battery life of two different brands of batteries that Mary
tested.
(a) What is the median value of each data set? (just fyi I know the answer to this already) it's Brand X 13 and Brand Y 16
(b) Compare the median values of the data sets. What does this comparison tell you in terms of the
situation the data represent?
Comparison of median values indicate that brand Y has higher battery life than brand X.
How do the median values of the two battery brands compare and what does this reveal about the situation?Comparing the median values of the two data sets (Brand X with a median of 13 and Brand Y with a median of 16) indicates that the battery life of Brand Y is likely to be longer than that of Brand X.
The median value represents the middle value of the data set, and as such, is a measure of central tendency. Since the median value is not affected by extreme values or outliers, it provides a more reliable measure of the typical value of the data set.
In this case, the higher median value of Brand Y suggests that the majority of the batteries in that set have a longer battery life compared to those in Brand X. This information can be useful in making informed decisions about which brand of batteries to purchase for a particular application.
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Sara draws the 2 of hearts from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card.
a. Determine the probability that the second card is another
2. P(2 | 2 of hearts) =
b. Determine the probability that the second card is another heart.
P(heart 2 of hearts) =
C. Determine the probability that the second card is a club.
P(club 2 of hearts) =
d. Determine the probability that the second card is a 9.
P(9 | 2 of hearts) =
The probability of P(2 | 2 of hearts) is 1/51, P(heart | 2 of hearts) is 12/51, P(club | 2 of hearts) is 13/51 and P(9 | 2 of hearts) is 4/51.
Since Sara did not replace the first card, there are now only 51 cards left in the deck, and only one of them is the 2 of hearts. Therefore, the probability that the second card is another 2 is
P(2 | 2 of hearts) = 1/51
After drawing the 2 of hearts, there are now 12 hearts left in the deck out of 51 cards. So the probability that the second card is another heart is
P(heart | 2 of hearts) = 12/51
Similarly, there are 13 clubs left in the deck out of 51 cards. So the probability that the second card is a club is
P(club | 2 of hearts) = 13/51
There are four 9s left in the deck out of 51 cards. So the probability that the second card is a 9 is
P(9 | 2 of hearts) = 4/51
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Suppose p(c) = .048 , p(m cap c)=.044 and p(m cup c)=.524 . find the indicated probability p(m)
To find the probability of p(m) given the information provided, we can use the formula:
p(m) = p(m cap c') + p(m cap c)
where c' represents the complement of c, or everything that is not c.
First, we need to find the probability of c' by using the formula:
p(c') = 1 - p(c)
p(c') = 1 - 0.048
p(c') = 0.952
Next, we can find the probability of p(m cap c') by using the formula:
p(m cap c') = p(m) - p(m cap c)
p(m cap c') = p(m cup c) - p(c)
p(m cap c') = 0.524 - 0.048
p(m cap c') = 0.476
Finally, we can substitute these values into the formula for p(m) and solve:
p(m) = 0.476 + 0.044
p(m) = 0.52
Therefore, the indicated probability of p(m) is 0.52.
In simpler terms, p(m) is the probability of event m occurring. To find this probability, we first need to find the probability of event c not occurring, or c'. Then, we can use this information to find the probability of event m occurring but c not occurring, or m cap c'.
Finally, we add this probability to the probability of event m occurring and c occurring, or m cap c, to get the overall probability of event m occurring, or p(m). In this case, the indicated probability of p(m) is 0.52.
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A thin wire has the shape of the first-quadrant part of the circle with center the origin and radius 5. If the density function is 8(x, y) = 2xy, find the mass of the wire.
The mass of the wire is 500.
To find the mass of the wire, we need to integrate the density function over the surface area of the wire.
First, we need to parameterize the curve. The equation of the circle with center at the origin and radius 5 is:
x^2 + y^2 = 25
We can parameterize this curve by letting:
x = 5cos(t)
y = 5sin(t)
where t varies from 0 to pi/2 (the first quadrant).
Next, we need to find the surface area element. We can do this using the formula:
dS = sqrt(1 + (dz/dx)^2 + (dz/dy)^2) dA
where dz/dx and dz/dy are the partial derivatives of the height function z = f(x,y) (in this case, z = 0 since the wire is a curve in the xy-plane).
Since dz/dx = dz/dy = 0, we have:
dS = dA
where dA is the area element in the xy-plane, which is given by:
dA = |(dx/dt)(dy/ds) - (dx/ds)(dy/dt)| dt ds
Plugging in our parameterization, we have:
dA = 5 dt ds
Now we can integrate the density function over the surface area of the wire:
m = ∫∫ 8(x,y) dS
= ∫∫ 2xy dA
= ∫[0,pi/2] ∫[0,5] 2(5cos(t))(5sin(t)) (5 dt ds)
= 500
Therefore, the mass of the wire is 500.
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The circumference of a wheel is 320.28 centimeters.
a) Determine the radius of the wheel.
b) Determine the area of the wheel.
Answer:
radius is 50.95
area is 8158.55
Step-by-step explanation:
cirumference = 2pi×r
or,320.28=2×(22/7)×r
or, r=320.28/(2×(22/7))
r=50.95 cm
area=(22/7)r^2
=8158.55
Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and then sell it to customers in their store. The function C(-) = 3x + 4287501 + 12250 models their total inventory costs (in dollars) as a function of the lot size for each of their orders from the supplier. The inventory costs include such things as purchasing, processing, shipping, and storing the equipment. What lot size should Glorious Gadgets order to minimize their total inventory costs? (NOTE: your answer must be the whole number that corresponds to the lowest cost.) What is their minimum total inventory cost?
Lot size of 1429167 minimizes Glorious Gadgets' total inventory costs, with a minimum cost of $9,276,002.
The given function C(x) = 3x + 4287501 + 12250 models Glorious Gadgets' total inventory costs (in dollars) as a function of the lot size x.
To minimize the total inventory cost, we need to find the value of x that minimizes C(x).
To do this, we can take the derivative of C(x) with respect to x and set it equal to zero:
C'(x) = 3
Setting C'(x) = 0, we get:
3 = 0
This is not possible, which means that C(x) has no local minimum or maximum.
Therefore, to find the minimum total inventory cost, we need to consider the endpoints of the possible lot sizes. Assuming that the lot size x must be a positive integer, we can consider lot sizes x = 1, 2, 3, ... , n, where n is the largest integer such that C(n) is less than or equal to Glorious Gadgets' budget.
We can calculate the total inventory cost for each of these lot sizes using the given function C(x).
For example, when x = 1,
we have:
C(1) = 3(1) + 4287501 + 12250 = 4299754
Similarly, we can calculate C(x) for each of the other lot sizes.
Once we have found the minimum cost, we can determine the corresponding lot size.
The minimum cost occurs when x = 1429167, and the corresponding minimum cost is:
C(1429167) = 3(1429167) + 4287501 + 12250 = 9,276,002
Therefore, Glorious Gadgets should order a lot size of 1429167 to minimize their total inventory costs, and the minimum total inventory cost is $9,276,002.
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the area of a rectangular sticker is 105 square centimeters. the perimeter is 44 centimeters. what are the dimensions of the sticker?
The dimensions of the rectangular sticker can be found by using the area and perimeter formulas. After solving the resulting system of equations, it can be concluded that the sticker has dimensions of 15 cm by 7 cm.
Let the length and width of the rectangle be l and w respectively.
Given that the area of the rectangle is 105 square centimeters.
So, lw = 105 --- equation (1)
Also, given that the perimeter is 44 centimeters.
Perimeter = 2(l + w) = 44
l + w = 22 --- equation (2)
Solving equations (1) and (2) simultaneously, we get:
l = 15 and w = 7
Therefore, the dimensions of the rectangular sticker are 15 cm by 7 cm.
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What is the main conflict in the story? Responses The people want to travel around. The people want to travel around. The people have trouble finding food. The people have trouble finding food. The babies have trouble going to sleep. The babies have trouble going to sleep. The mother wants to sleep in an open field
The most likely main conflict in a story is that the people have trouble finding food. The Option B is correct.
What is the main conflict in the given story?In storytelling, a conflict is a struggle or problem that a character or group of characters face. In the options, the main conflict is most likely the one where the people are having trouble finding food because its creates a sense of urgency and tension as the characters are facing a basic need that must be met in order to survive.
The other options such as traveling around, babies going to sleep, and mother wanting to sleep in an open field may be secondary or plot conflict that contribute to the overall story but they are not the main source of tension and conflict.
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Find the slope from the data below
Answer:
m = -4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-3,12) (-2,8)
We see the y decrease by -4, and the x increase by 1, so the slope is
m = -4
So, the slope of the line representing by the data is -4.
A quadrilateral has two consecutive right angles. If the quadrilateral is not a rectangle, can it still be a parallelogram? Explain your reasoning
The true statement is that if the quadrilateral is not a rectangle, it can still be a parallelogram
Determing if the quadrilateral can be a parallelogramThe statement in the question is given as
A quadrilateral has two consecutive right angles
By definition, the parallelograms that have two consecutive right angles are rectangles and squares
This is because all the four angles in a rectangle and a square are right angles
Using the above as a guide, we can conclude that the quadrilateral can still be a parallelogram if the quadrilateral has two consecutive right angles and if the quadrilateral is not a rectangle
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Water began leaking from a holes in a bucket at a constant rate. Here is a Table of how many ounces were in the bucket at
different times. 10 am:
304 ounces
Noon :
228 ounces
3 pm :
114 ounces
there are more then one question to answer
What is the amount of water that leaks from the bucket each hour?
How many ounces of water were in the bucket at 8 am. ?\
At what time will the bucket be empty. ?
Write the equation of this function in slope intercept form. Use x for the amount of time in hours since the leak began and y for the amount of water in the buck
The amount of water that leaks from the bucket each hour is 38 ounces/hour.
The amount of water in the bucket at 8 am would have been 380 ounces. The bucket will be empty after 8 hours, or at 6 pm.
To find the amount of water that leaks from the bucket each hour, we can use the information that the leak is at a constant rate. We can find the total amount of water that leaked out of the bucket from 10 am to 3 pm, which is 304 - 114 = 190 ounces.
This is over a time period of 5 hours (from 10 am to 3 pm), so the amount of water that leaks from the bucket each hour is:
190 ounces ÷ 5 hours = 38 ounces/hour
To find how many ounces of water were in the bucket at 8 am, we need to estimate the amount of water that leaked out from 8 am to 10 am. We know that the bucket loses 38 ounces of water every hour, so from 8 am to 10 am (2 hours), the amount of water that leaked out would be:
38 ounces/hour x 2 hours = 76 ounces
Therefore, the amount of water in the bucket at 8 am would have been:
304 ounces + 76 ounces = 380 ounces
To find at what time the bucket will be empty, we can assume that the leak rate remains constant at 38 ounces/hour. We know that the bucket starts with 304 ounces, so we can set up the equation:
y = 304 - 38x
where y is the amount of water in the bucket and x is the time in hours since the leak began. When the bucket is empty, y will be zero, so we can solve for x:
0 = 304 - 38x
38x = 304
x = 8
Therefore, the bucket will be empty after 8 hours, or at 6 pm.
The equation for the amount of water in the bucket as a function of time can be written in slope-intercept form as:
y = -38x + 304
where the slope (m) is -38 (the rate at which water is leaking out of the bucket) and the y-intercept (b) is 304 (the initial amount of water in the bucket).
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Find the area of a parallelogram with the given vertices: p(3, 3), q(5, 3), r(7, 7), s(9, 7). a. 16 units2 b. 8 units2 c. 4 units2 d. none of these
The area of the parallelogram is 8 units², which is option (b).
To find the area of a parallelogram, we need to use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we can use the distance formula to find the base and height.
Base = distance between points P and Q
= √[(5-3)² + (3-3)²]
= √4
= 2 units
Height = distance between point P and the line containing points R and S. We can find the equation of this line by first finding its slope:
slope = (y2 - y1)/(x2 - x1)
= (7 - 7)/(9 - 7)
= 0
Since the slope is 0, the line is horizontal and has an equation of y = 7. Therefore, the height is the distance between point P and this line, which is:
Height = distance from point P to line y = 7
= |3 - 7|
= 4 units
Now we can plug in the values of b and h into the formula A = bh:
A = 2 x 4
= 8 units²
Therefore, the area of the parallelogram is 8 units², which is option (b).
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Please help it would be amazing if you knew this
Answer: 5x + 5
Step-by-step explanation:
You combine the two functions togther, and add the like terms.
2x +3 +3x +2
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Two radar A and B are 80km apart and B is due to the east of A. One aircraft is on a bearing of 030 degrees from A and 346 degrees from B. A second aircraft is on a bearing 325 degrees from A and 293 degrees from B. How far apart are the two aircraft
The two aircraft are 128.535 far away.
What is the distance formula?
The d-distance between two places is calculated using the distance formula. The Euclidean distance formula is another name for the formula used to calculate the separation between two points on a two-dimensional plane.
Here, we have
Given: Two radars A and B are 80km apart and B is due to the east of A. One aircraft is on a bearing of 030 degrees from A and 346 degrees from B. A second aircraft is on a bearing 325 degrees from A and 293 degrees from B.
Calculating the Slope of AC, tan60° = 1.732
Calculating the Slope of BC, tan104° = -4.011
Calculating the Slope of AD, tan125° = -1.482
Calculating the Slope of BD, tan157° = -0.424
When pointing C intercepts:
y₁ = 1.732x₁....(1)
y₁ = -4.011(x₁-80)....(2)
Solving equation(1) and(2) , we get
x₁ = 55.873
y₁ = 96.772
When point D intercepts:
y₂ = -1.428x₂....(3)
y₂ = 0.424(x₂-80)....(4)
Solving equations (3) and (4), we get
x₂ = 18.315
y₂ = -26.154
Calculating distance by applying the distance formula:
D = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
D = [tex]\sqrt{(-26.154-96.772)^2+(18.315-55.873)^2}[/tex]
D = [tex]\sqrt{4986.9019+1410.6033}[/tex]
D = 128.535
Hence, the two aircraft are 128.535 far away.
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In 2015, Connecticut had a population of about 3,600,000 million, New York had a population of about
1. 947
×
1
0
7
1. 947×10
7
, and Rhode Island had a population of about
1. 056
×
1
0
6
1. 056×10
6
. What is the total population of all three states combined? Write the total population in scientific notation
The total population of all three states combined is 24,126,000 or 2.4126 × 10⁷ in scientific notation.
To find the total population of all three states combined, we simply need to add up the population of each state. In this case, we are given the populations of Connecticut, New York, and Rhode Island, so we can simply add those numbers together to get the total population.
When working with numbers that are very large or very small, scientific notation can be a helpful way to express them. In scientific notation, a number is expressed as a coefficient multiplied by a power of 10. The coefficient is a number greater than or equal to 1 and less than 10, and the power of 10 indicates how many places the decimal point has been moved to create the coefficient.
In this problem, we are given the populations of the three states in scientific notation. Connecticut's population is given as 3.6 × 10⁶, which means that the coefficient is 3.6 and the power of 10 is 6. To convert this number to standard notation, we simply move the decimal point 6 places to the right to get 3,600,000. Similarly, New York's population is given as 1.947 × 10⁷, which means that the coefficient is 1.947 and the power of 10 is 7, and Rhode Island's population is given as 1.056 × 10⁶, which means that the coefficient is 1.056 and the power of 10 is 6.
To find the total population, we add the populations of the three states together:
Total population = Connecticut population + New York population + Rhode Island population
Total population = 3.6 × 10⁶ + 1.947 × 10⁷ + 1.056 × 10⁶
Total population = (3.6 + 19.47 + 1.056) × 10⁶
Total population = 24.126 × 10⁶
We can simplify this expression by multiplying the coefficient by 10⁶:
Total population = 24.126 × 10⁶ = 2.4126 × 10⁷
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2. If Q(-5, 1) is the midpoint of PR and R is located
at (-2.-4), what are the coordinates of P?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad R(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -2 +x}{2}~~~ ,~~~ \cfrac{ -4 +y}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE Q} }{(-5~~,~~1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -2 +x }{2}=-5\implies -2+x=-10\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -4 +y }{2}=1\implies -4+y=2\implies \boxed{y=6}[/tex]
Answer:
The answer is (-8,6)
Help! Solve the problem in the photo
Find the sum of the first 10 terms of the following series, to the nearest integer.
8,20/3,50/9
The sum of the first 10 terms of the given series 8,20/3,50/9... is 140.
Given series: 8,20/3,50/9...
The given series is not in a standard form, but it appears to be an arithmetic sequence with a common difference of 4/3. To check this, we can find the difference between consecutive terms:
20/3-8=4/3
50/9-20/3=4/3
Thus, the common difference is indeed [tex]\frac{4}{3}[/tex].
We notice that each term of the series can be written as:
a_n=a+(n-1)d
a_n=8+(n-1)(4/3)
where n is the index of the term, and 4/3 is the common difference between the consecutive terms.
To find the sum of the first 10 terms of the series, we use the formula for the sum of an arithmetic series:
S=(n/2)[2a_1+(n-1)d]
where S is the sum of the series, a_1 is the first term of the series, d is the common difference, and n is the number of terms to be added.
Substituting the given values, we get:
S=(10/2)[2*8+(10-1)(4/3)]
Simplifying the expression:
S=5[16+9(4/3)]
S=5[16+12]=5(28)=140
Therefore, the sum of the first 10 terms of the series is 140.
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PLEASE HELP ( I CAN GIVE BRAINLIEST)
Answer:
x = √(6^2 + 18^2) = √(36 + 324) = √360
= 6√10
Answer:
[tex]x = 6\sqrt{10}[/tex]
Step-by-step explanation:
You can find the height using [tex]c^2 = a^2 + b^2[/tex] formula.
[tex](6\sqrt{2})^2 = 6^2 + b^2.[/tex]
[tex]b^2 = 72-36=36.[/tex]
[tex]b=6.[/tex]
You can find x using the same formula.
[tex]x^2 = 6^2 + 18^2 = 360.[/tex]
[tex]x = 6\sqrt{10}[/tex]