On solving the provided question we can say that So, we have two solutions: t = (9/2) or t = (-6/2) = -3
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a single variable quadratic polynomial. a 0. Because this polynomial is of second order, the Basic Theorem of Algebra implies that it has at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic equation. This means it has at least one word that must be squared. One of the most common solutions for quadratic equations is "ax2 + bx + c = 0." where a, b, and c are numerical coefficients or constants. where the variable "X" is unnamed.
So, we can set h(t) = 0 and solve for t:
[tex]0 = t^2 + 3t - 18\\t = (-3 + \sqrt (3^2 - 4(1)(-18))) / (2(1))\\t = (-3 + \sqrt (81)) / 2\\t = (-3 + 9) / 2\\[/tex]
So, we have two solutions:
t = (9/2) or t = (-6/2) = -3
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distributive property
7(r+3)+2(r-2)?
1. 7r+3+2r-2
2. 7r+21+2r-4
3. 7r+21-2r-2
4. 7r+3+2r-4
Step-by-step explanation:
ans is 2 nd option
first bracket multiply with 7 and second multiply with 2 multiply the sign also carefully.
hey guyz what is 65 x 340 +3000
i will giv branlist
Answer:
217,100
Step-by-step explanation:
in this equation first you would want to add together 3000 + 340 which is 3340 then multiply that by 65. Remember to do addition and subtraction steps in multi-step equations first
(2x+3)(3x+6) as a trinomiol
Answer: [tex]6x^{2}[/tex] + 24x + 18
Step-by-step explanation: To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
Write the equation of the line of reflection between the points (-9, 12) and (17, -78) in point-slope form
The equation of the line of reflection is y = (−13 / 45)x − (1376 / 45) in point-slope form.
EquationsTo find the equation of the line of reflection between the points (-9, 12) and (17, -78), we first need to find the midpoint of the line segment joining these two points, which will lie on the line of reflection. The midpoint formula is:
[(x₁ + x₂) / 2, (y₁ + y₂) / 2]
Using the coordinates of the two given points, we get:
[(−9 + 17) / 2, (12 − 78) / 2] = [4, −33]
So, the midpoint is (4, −33).
Next, we need to find the slope of the line of reflection. This is equal to the negative reciprocal of the slope of the line passing through the two given points, since the line of reflection is perpendicular to this line. The slope of the line passing through the two given points is
m = (y₂ − y₁) / (x₂ − x₁) = (−78 − 12) / (17 − (−9)) = −90 / 26 = −45 / 13
So, the slope of the line of reflection is:
m' = −1 / m = −13 / 45
Finally, we can use the point-slope form of the equation of a line, with the midpoint we found as the point and the slope we calculated as the slope which is
y − (−33) = (−13 / 45)(x − 4)
y + 33 = (−13 / 45)x + (52 / 45)
or
y = (−13 / 45)x − (1376 / 45)
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Please help me with this question TT. I really don’t understand…
Answer:
Step-by-step explanation:
i)
(x+1)(7-x) = (x+1)(-x+7) = -x² + 6x + 7
standard form: y = -x² + 6x + 7
for the vertex form you have to find the coordinates of the vertex (h, k):
a = -1, b = 6, c = 7
h = -b/2a = -6/2(-1) = 3
k = ah² + bh + c = -1(3)² + 6(3) + 7 = 16
vertex form: y = a(x-h) + k
y = -1(x - 3) + 16
ii)
Dimensions of the largest rectangle that can be made are:
Plug in maximum value of x, x = 3
x + 1 = 3 + 1 = 4
7 - x = 7 - 3 = 4
largest rectangle is 4 x 4 = 16
Make p the subject of m=3n+2p
Answer:
[tex]n = \frac{m - 2p}{3} \\ \\ p = \frac{m - 3n}{2} [/tex]
Step-by-step explanation:
[tex]1. \: m - 2p = 3n \\ 2. \: \frac{m - 2p}{3} \\ 3. \: n = m - 2p \\ \\ 1. \: m - 3n = 2p \\ 2. \: \frac{m - 3n}{2} = p \\ 3. \: p = \frac{m - 3n}{2} [/tex]
1. Find the length of the missing side:
8m
7
12m
2. Is the triangle a right triangle?
11
9
The graph of quadratic function g is shown on the grid.
Which statements are best supported by the graph of g?
Select THREE correct answers.
The correct option for the quadratic function g are-
The x-intercept are- (-4,0) and (2,0)The coordinates of y-intercept are (0, -8)The coordinates of the vertex are (-1, -9).Explain about the quadratic function?Mathematical expressions with a two as the highest power are called quadratic functions. A function or numerical statement of degree two is a quadratic function. This indicates that two is the function's highest power.
The examples are all of degree 2. Hence, two is their highest power. A quadratic function must have a highest power of two.The correct option for the given quadratic function g from the graph are-
The x-intercept are- (-4,0) and (2,0)The coordinates of y-intercept are (0, -8)The coordinates of the vertex are (-1, -9).Correction for the incorrect statements:
The axis of symmetry is (x = -1)The function has the minimum value of -9.Know more about the quadratic function
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Bridget is creating a new board game called Tri-Tri-Again to enter a contest at the local game shop. She is making the game board in the shape of a triangle. The base of the triangle is 1
1
4
feet long, and its height is 2
1
2
feet.
What is the area of the game board?
Write your answer as a whole number, proper fraction, or mixed number.
The area of the Tri-Tri-Again board game is 3 1/8 square feet.
To calculate the area of a triangle, we need to know the length of its base and its height. In this case, Bridget's Tri-Tri-Again board game is in the shape of a triangle with a base of 1 1/4 feet and a height of 2 1/2 feet. To find the area of the triangle, we can use the formula for the area of a triangle, which is 1/2 x base x height.
We first convert the mixed numbers to improper fractions. The base is 5/4 feet and the height is 5/2 feet. We can then substitute these values into the formula to get:
Area of triangle = 1/2 x 5/4 feet x 5/2 feet
Area of triangle = 25/8 square feet
We can simplify the answer by dividing the numerator and denominator by the greatest common factor of 25 and 8, which is 1. This gives us:
Area of triangle = 25/8 square feet
Area of triangle = 3 1/8 square feet
Therefore, the area of the Tri-Tri-Again board game is 3 1/8 square feet.
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Express as a trinomial (2x+3)(3x+6)
Answer:
[tex]6 {x}^{2} + 21x + 18 [/tex]
Step-by-step explanation:
[tex](2x + 3)(3x + 6)[/tex]
[tex]6 {x}^{2} + 12x + 9x + 18[/tex]
[tex]6 {x}^{2} + 21x + 18[/tex]
Can someone help me, pls
Answer is attached
hope it helps you ⬆️
a student's grades in a history class are shown in the histogram. which statement best describes the spread and distribution of the data? the data is almost symmetric, with a maximum range of 59. this might be because the topic is easily understood by the students. the data is skewed, with a maximum range of 59. this might be because the teacher offered extra credit, and most of the students did that to increase their grades above 70. the data is bimodal, with a maximum range of 59. this might be because students either did not understand and earned less than 51, or they knew the topic well and earned higher than 90. the data is symmetric, with a maximum range of 59. this might be because the topic was very difficult for the students and most of them earned lower grades.
The data is bimodal, with a maximum range of 59.
This might be because students either did not understand and earned less than 51, or they knew the topic well and earned higher than 90.
Using the following terms: a student's grades in a history class are shown in the histogram.
Which statement best describes the spread and distribution of the data:
The data is almost symmetric, with a maximum range of 59.
This might be because the topic is easily understood by the students.
The data is skewed, with a maximum range of 59.
This might be because the teacher offered extra credit, and most of the students did that to increase their grades above 70.
The data is bimodal, with a maximum range of 59.
This might be because students either did not understand and earned less than 51, or they knew the topic well and earned higher than 90.
The data is symmetric, with a maximum range of 59.
This might be because the topic was very difficult for the students, and most of them earned lower grades.
The correct answer to this question is the data is skewed, with a maximum range of 59.
This might be because the teacher offered extra credit, and most of the students did that to increase their grades above 70.
Skewness refers to a condition in which the data is not symmetrical.
When data is skewed, it indicates that the majority of the data lies on one side of the graph, while the other side is either empty or has a small amount of data.
A histogram with a peak and a long tail is referred to as a positively skewed histogram, indicating that most of the data is on the left side of the graph.
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Lola has 4 1/2 cups of rice. She uses 3/4 of the rice to make sushi rolls for dinner. She uses the rest of the rice to make rice pudding for dessert. How much rice does Lola use for the rice pudding?
Lola has 9/8 cups of rice left to use for the rice pudding.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
To find out how much rice Lola uses for the rice pudding, we need to first determine how much rice she used for the sushi rolls.
Lola used 3/4 of the 4 1/2 cups of rice for the sushi rolls. To calculate this, we can multiply:
4 1/2 cups x 3/4 = (9/2) x (3/4) = 27/8 cups
So Lola used 27/8 cups of rice for the sushi rolls.
To find out how much rice Lola has left for the rice pudding, we need to subtract the amount she used for the sushi rolls from the original amount of rice she had:
4 1/2 cups - 27/8 cups = 36/8 cups - 27/8 cups = 9/8 cups
Therefore, Lola has 9/8 cups of rice left to use for the rice pudding.
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By the definition of a parallelogram, ab∥dc. ad is a transversal between these sides, so ∠a and ∠d are angles. because ab and dc are , the same-side interior angles must be by the same-side interior angles theorem. therefore, ∠a and ∠d are supplementary.
In a parallelogram, The statement "angle A and angle D are supplementary" is not correct.
The same-side interior angles theorem states that if a transversal intersects two parallel lines, then the same-side interior angles are supplementary. However, in this case, we are dealing with a parallelogram, which has two pairs of parallel sides.
When we say that "ab||dc", we are stating that side AB is parallel to side DC. We cannot assume that side AD is a transversal between these two sides, as it could intersect the sides at some other angle. Therefore, we cannot conclude that angle A and angle D are angles.
However, we do know that opposite angles in a parallelogram are congruent. Therefore, we can conclude that angle A is congruent to angle C, and angle B is congruent to angle D.
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The length of a rectangle is equal to
three times its width. If the perimeter of
the shape is equal to 56 feet, what is the
length and what is the width?
Answer:
the length of the rectangle is 21 feet.
Step-by-step explanation:
Let's use "w" to represent the width of the rectangle. According to the problem, the length is three times the width, so we can use "3w" to represent the length.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
Substituting the expressions for length and width, we get:
56 = 2(3w + w)
Simplifying the right side, we get:
56 = 2(4w)
56 = 8w
w = 7
So the width of the rectangle is 7 feet. To find the length, we can use the expression we derived earlier:
length = 3w = 3(7) = 21
Therefore, the length of the rectangle is 21 feet.
PLEASE HELP!
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds:
Part A: During what interval(s) of the domain is the water balloon's height increasing?
Part B: During what interval(s) of the domain is the water balloon's height staying the same?
Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer.
Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds. Use complete sentences to support your answer.
step-by-step explanation:
Part A. We can see that within only for a 0-2 second interval, the height of the water balloon increases from 60ft to approximately 80ft.
Part B. In two intervals, 2-4 seconds to approximately 80 ft and 10-14 seconds to 0 ft.
Part C. Between 4 and 6 seconds, the water balloon height changes from approximately 80ft to 40ft, whereas between 6-8 seconds and 8-10 seconds, the height only changes by 20ft.
Part D. According to the graph, we can suppose that the water balloon was thrown up, and after beginning to fall, at 10 seconds touched the floor, so in 16 seconds kept staying on the floor, at 0ft.
Hope it helps.
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
Geometry Homework
Please help
The measure of angle x is 90°
How to find the measure of angle x?In a semicircle, an angle that has its vertex at the center of the circle will always be a right angle, which is 90 degrees.
This is because a semicircle is defined as half of a full circle, and the diameter of a circle forms a right angle with any chord that it intersects.
Therefore, any angle in a semicircle that has its vertex at the center of the circle will be 90 degrees.
Thus, the measure of angle x is 90°.
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a continuous random variable x has the following sample frequency distribution: value frequency 0 73 between 0 and 70 37 between 70 and 200 182 between 200 and 500 232 what is the mean from this sample?
As per the mentioned informations and values provided, the mean from this sample frequency distribution is calculated to be approximately 160.50.
To find the mean from the given sample frequency distribution, we need to first calculate the midpoint for each class interval, then multiply it by the corresponding frequency, sum all of these products, and finally divide by the total frequency.
Using the formula: mean = (sum of midpoint x frequency) / (sum of frequency)
Midpoint for the first interval = (0 + 70) / 2 = 35
Midpoint for the second interval = (70 + 200) / 2 = 135
Midpoint for the third interval = (200 + 500) / 2 = 350
Now we can calculate the sum of midpoint x frequency:
35 x 73 + 135 x 37 + 350 x 182 + 232 x 500 = 84,166
The total frequency is the sum of all frequencies: 73 + 37 + 182 + 232 = 524
Finally, we can calculate the mean:
mean = (sum of midpoint x frequency) / (sum of frequency) = 84,166 / 524 ≈ 160.50
Therefore, the mean from this sample frequency distribution is approximately 160.50.
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Paula invited some friends to dinner, and she plans to make fajitas. At the grocery store, she spends $2.56 on red bell peppers and $1.92 on green bell peppers. If both types of bell peppers cost $1.60 per pound, how many total pounds of bell peppers does she buy?
We must first determine the total price of the bell peppers in order to determine the number of pounds Paula purchased. Paula bought a total of [tex]2.8[/tex] pounds of bell peppers.
What is the total cost?To determine the total pounds of bell peppers Paula bought, we first need to find the total cost of the bell peppers.
The cost of the red bell peppers is $2.56 and the cost of the green bell peppers is $ [tex]1.92[/tex] , so the total cost of both types of bell peppers is:
$ [tex]2.56[/tex] + $ [tex]1.92 =[/tex]$ [tex]4.48[/tex]
Since both types of bell peppers cost $[tex]1.60[/tex] per pound, we can use this information to find the total weight of the bell peppers.
Let x be the total weight of the bell peppers. Then we can set up the following equation:
$ [tex]1.60\times =[/tex]$[tex]4.48[/tex]
To solve for x, we divide both sides by $[tex]1.60[/tex]:
[tex]x = $4.48 / $1.60[/tex]
[tex]x = 2.8[/tex]
Therefore, Paula bought a total of [tex]2.8[/tex] pounds of bell peppers.
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Answer: 2.8 pounds of bell pepper bought by Paula
Step-by-step explanation:
Given that :
At the grocery store, the amount spent by Paula :
The amount spent on red bell pepper = $2.56
The amount spent on green bell pepper = $1.92
the total amount spent = $2.56+$1.92 = $4.48
If both the bell peppers are at $1.60 per pound, then the total pounds of bell pepper Paula bought
= $4.48/ $1.60
= 2.8 pounds
Solution:
Therefore the number of pounds of bell pepper bought by Paula is 2.8.
Given rectangle JKLM below, JN = 44.
If MN = -2x + 2, solve for x.
The solution for x is -21 when rectangle JKLM below, JN = 44.
If MN = -2x + 2,
What is the rectangle?
A rectangle is a geometric shape with four sides and four right angles. It is a quadrilateral in which opposite sides are equal in length and parallel to each other, and adjacent sides are perpendicular to each other.
To solve for x, we can use the given information that JN = 44 and MN = -2x + 2 in the rectangle JKLM.
Since JN is a side of the rectangle and is equal to 44, and MN is also a side of the rectangle and is equal to -2x + 2, we can set up the equation:
JN = MN
44 = -2x + 2
Now we can solve for x:
Add 2x to both sides:
44 + 2x = 2
Subtract 2 from both sides:
44 + 2x - 2 = 0
42 + 2x = 0
Subtract 42 from both sides:
42 + 2x - 42 = 0 - 42
2x = -42
Finally, divide both sides by 2 to isolate x:
2x / 2 = -42 / 2
x = -21
Hence, the solution for x is -21.
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A brother and a sister are in the same math class. There are 9 boys and 8 girls in the class. One boy and one girl are randomly chosen. What is the probability that the brother and sister are chosen? Write your answer as a fraction in simplest form.
The probability is ?
Answer:
1/72
Step-by-step explanation:
There are a total of 17 students in the class, and we want to choose one boy from 9 and one girl from 8 without replacement. The total number of ways to choose two students from the class is:
17C2 = (17!)/(2!15!) = (1716)/(21) = 136
To choose a boy and a girl, we can choose the boy in 9 ways and the girl in 8 ways, for a total of 9*8 = 72 ways.
Now, since the brother and sister are both in the class, there is only one way to choose them together. Therefore, the probability of choosing the brother and sister is:
1/72
So the probability is 1/72, written as a fraction in simplest form.
Help me solve this please.
a gift card for a coffee shop has a starting balance of $50. you buy a coffee everyday for $3.35 and some days you buy a bagel with cream cheese for $2.95. After 10 days, the remaining balance is $1.75. How many bagels did you buy
Answer:
5
Step-by-step explanation:
Cost of bagels = 50 - 1.75 - 33.5 = 14.75
No. of bagels = 14.75/2.95 = 5
Answer:
You bought 5 bagels.
Step-by-step explanation:
Since you buy a coffee every day and it says "after 10 days" you multiply the price of the coffee by 10: $3.35 * 10 = $33.5
It also says that the remaining balance on the gift card is $1.75. So you need to subtract that from the original balance, 50: $50- $1.75 = $48.25 - this is the amount of money you spent.
Next, you subtract the price of all the coffees you bought from the amount of total money you spent over the course of 10 days. $48.25 - $33.5 = $14.75
This remaining money is for the bagels that you bought on some days. The last step should be to divide $14.75 by the price of one single bagel:
$14.75 / 2.95 = 5
You bought 5 bagels.
Hope this helps!!!!
Question 5(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions MC)
Rewrite x^² - 2x³y³ using a common factor.
Ox²y(xy-2xy²)
Ox²²(x²-2xy)
O 2xy²(x²-x²y)
O 2xy(x³y-x²y)
[tex]x^4y^2-2x^3y^3\\\\x^2y^2(x^2-2xy)[/tex]
Answer is the second one.
a probability distribution is: group of answer choices the average value that a random variable is expected to assume over a large number of trials. a summary of data into classes along with the number of occurrences in each class. a listing of all possible outcomes along with their likelihood of occurrence. a listing of the successes and failures from a given experiment.
A probability distribution is a listing of all possible outcomes along with their likelihood of occurrence.
It is a way of describing the likelihood of different outcomes in a statistical experiment or random event. It is used to calculate the probability of different events or outcomes in situations where there is uncertainty or variability. There are two types of probability distributions: discrete and continuous.
Discrete probability distributions are used when the possible outcomes of a statistical experiment are discrete or countable, such as the number of heads obtained in flipping a coin. Continuous probability distributions are used when the possible outcomes of a statistical experiment are continuous or uncountable, such as the height of people in a population.
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explain clearly why we cannot have the combination of a yes to practical significance, and a no to statistical significance.
It is not possible for a study to have practical significance without statistical significance because statistical significance provides evidence that the observed effect is unlikely to have occurred by chance.
The Practical significance and statistical significance are two different concepts that are often used in hypothesis testing.
The Statistical significance refers to the probability that the observed results of a study occurred by chance, given a particular level of significance or alpha.
The Practical significance refers to whether the observed effect size is large enough to be meaningful in a real-world context.
It is possible for a study to have statistical significance without practical significance. For example, a study may find a statistically significant difference between two groups, but the difference may be so small that it is not meaningful in practice.
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explain the reasons that someone would create either a bar chart or a histogram in order to explore a single column of data
A bar chart or a histogram are visual representations of data that can be used to explore a single column of data.
A bar chart is used to compare different categories of data, and a histogram is used to measure the frequency of data within a given range. Bar charts allow a user to compare the differences between the categories of data, while histograms provide a better indication of how the data is distributed within the range.
Both bar charts and histograms are useful for identifying patterns, outliers, and trends in the data. By using a bar chart or a histogram, a user can quickly and easily identify where the data is concentrated, as well as identify any outliers or trends in the data.
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what is the median and range of the data
The median and the range of the given data above would be =5 and 11 respectively.
How to calculate the median and range of a given data?The range of a data set can be calculated by the subtraction of the largest variable form the smallest variable of a data set.
That is;
Data set = 1,1,1,1,2,2,2,5,6,6,6,8,9,10,12
largest variable = 12
smallest variable = 1
range = 12-1 = 11
The median of the data set is the figure that fall at the middle of the data set after being arranged either in ascending or descending order.
The median of the data = 5
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If something is $125 with a sale for $87.50, what percent off was the sale?
well, the amount off from the original 125 is just 125 - 87.50 = 37.50.
now, if we take 125(origin amount) as the 100%, what's 37.50 off of it as a percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 125 & 100\\ 37.50& x \end{array} \implies \cfrac{125}{37.50}~~=~~\cfrac{100}{x} \\\\\\ 125x=3750\implies x=\cfrac{3750}{125}\implies x=30[/tex]
To determine what percent off the sale for something was, we need to use the formula for percent off calculation.
What is percent off? The percent off is used to refer to the reduction in price or value of something. The percent off calculation is used to determine the amount of discount in percentage of the original price or value.
What is the formula for percent off calculation? The formula for percent off calculation is as follows:
percent off = (discount / original price) x 100, where,discount = original price - sale price
original price = $125 sale price = $87.50
Substitute the given values into the formula and simplify.
percent off = (discount / original price) x 100percent off =
(($125 - $87.50) / $125) x 100percent off
(37.50 / 125) x 100percent off
⇒ 0.3 x 100percent off = 30%
Therefore, the percent off the sale was 30%.
Sylvia is 56 3/4 inches tall Bill is 1/3 8 inches taller than Sylvia and Jane is 1 1/5 inches taller than bill how tall is Jane
The required Jane is approximately 59.28 inches tall.
How to find the height of the jane?Height is a measurement of vertical distance, either in terms of vertical extent (how tall an object or person is) or in terms of vertical position (how high a point is). "The height of that building is 50 meters" or "The height of an airplane in flight is approximately 10,000 meters" are two examples.
Sylvia's height can be represented as:
Sylvia’s height =56[tex]\frac{3}{4}[/tex] inches
Bill is [tex]\frac{1}{3}$[/tex] of 8 inches taller than Sylvia, which means that Bill's height is:
[tex]$\begin{align*}\text{Bill's height} &= \text{Sylvia's height} + \frac{1}{3} \times 8\ \text{inches} \&= 56 \frac{3}{4}\ \text{inches} + \frac{8}{3}\ \text{inches} \&= 58 \frac{7}{12}\ \text{inches}\end{align*}[/tex]
Jane is [tex]1 \frac{1}{5}$[/tex] inches taller than Bill, which means that Jane's height is:
[tex]$\begin{align*}\text{Jane's height} &= \text{Bill's height} + 1 \frac{1}{5}\ \text{inches} \&= 58 \frac{7}{12}\ \text{inches} + 1 \frac{1}{5}\ \text{inches} \&= 59 \frac{17}{60}\ \text{inches}\end{align*}[/tex]
Therefore, Jane is approximately 59.28 inches tall.
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