Answers
The circumference of the given circle with TQ = 8 units is given by approximately 50.26 units.
We know that the formula for the circumference of a circle with radius of 'r' units is given by,
P = 2πr
Here in the given figure we can see that the length TQ is a radius for the given circle with center at point Q.
Given the value of TQ = 8 units.
So, radius = 8 units.
So the circumference of the circle is given by
= 2πr
= 2π*8
= 16π
= 50.26 units [taking π = 3.14 and approximating the value to the two decimal places]
Hence the circumference of circle is 50.26 units approximately.
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Related Questions
whats the answer!???????
Answers
Which expression is equivalent to 3x – (2x + 4) + 5?
Responses
Answers
The expression that is equivalent to 3x – (2x + 4) + 5 is x+1 ( optionB)
What is equivalent of expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.
For example , 2a+6a is equivalent to 2a( 1+3) and they will surely have the same value when a value is replaced with a
3x – (2x + 4) + 5 = 3x-2x-4+5
= x-4+5
= x +1
therefore the equivalent of 3x – (2x + 4) + 5 is x+1
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Can anyone help? i need to solve these using the completing the square method
Answers
Using the completing the square method, the quadratic equation x²-5x=9 can be simplified to (x-2.5)²=15.25, and the solutions are x=2.5+√15.25 and x=2.5-√15.25.
To solve this quadratic equation using the completing the square method. Here are the steps
Move the constant term (in this case, 9) to the right-hand side of the equation
x² - 5x = 9 becomes x² - 5x - 9 = 0
To complete the square, we need to add and subtract a constant term inside the parentheses. The constant term we add is half of the coefficient of the x-term, squared. In this case, the coefficient of the x-term is -5, so we need to add and subtract (5/2)² = 6.25.
x² - 5x - 9 + 6.25 - 6.25 = 0
Rearrange the terms inside the parentheses to group the perfect square with the x-term
(x² - 5x + 6.25) - 15.25 = 0
Factor the perfect square trinomial inside the parentheses
(x - 2.5)² - 15.25 = 0
Add 15.25 to both sides of the equation
(x - 2.5)² = 15.25
Take the square root of both sides
x - 2.5 = ±√15.25
Add 2.5 to both sides
x = 2.5 ±√15.25
So the solutions to the equation x² - 5x = 9, using the completing the square method, are x = 2.5 + √15.25 and x = 2.5 - √15.25.
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--The given question is incomplete, the complete question is given
"Can anyone help? i need to solve these using the completing the square method
x²-5x = 9"--
The point (7,8) in the coordinate plane represents a ratio. adela claims that you can find equivalent ratio by adding the same number to both coordinate of the point. is adela correct? explain.
Answers
For the point (7,8) in the coordinate plane which represents a ratio, Adela claims that you can find equivalent ratio by adding the same number to both coordinate of the point is incorrect.
Adela claim is not correct. To find an equivalent ratio, you should multiply (or divide) both coordinates by the same nonzero number instead of adding the same number.
1. The point (7,8) represents the ratio 7:8.
2. If we add the same number to both coordinates, let's say 2, we get the point (9,10), which represents the ratio 9:10.
3. We can check if 7:8 and 9:10 are equivalent ratios by cross-multiplying:
7 * 10 = 70 and 8 * 9 = 72. Since 70 ≠ 72, these ratios are not equivalent.
Therefore, Adela's claim is incorrect because adding the same number to both coordinates of the point does not result in an equivalent ratio. To find equivalent ratios, you should multiply (or divide) both coordinates by the same nonzero number.
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Scores at a local high school on the Algebra 1 Midterm are extremely skewed left with a mean of 65 and a standard deviation of 8. A guidance counselor takes a random sample of 10 students and calculates the mean score, x¯¯¯.
(a) Calculate the mean and standard deviation of the sampling distribution of x¯¯¯
(b) Would it be appropriate to use a normal distribution to model the sampling distribution? Justify your answer
Answers
The standard deviation of the sampling distribution is 2.53. It would not be appropriate to use a normal distribution to model the sampling distribution.
(a) When dealing with a sampling distribution, the mean of the sampling distribution (μ_x) is equal to the mean of the population (μ). In this case, the mean of the population is 65. Therefore, the mean of the sampling distribution is also 65.
To calculate the standard deviation of the sampling distribution (σ_x), you will use the following formula: σ_x = σ / √n, where σ is the standard deviation of the population and n is the sample size. In this case, the standard deviation of the population is 8 and the sample size is 10. So the standard deviation of the sampling distribution is:
σ_x = 8 / √10 ≈ 2.53
(b) The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution, provided that the population is not heavily skewed or has extreme outliers. Since the scores are extremely skewed left and the sample size is only 10, it would not be appropriate to use a normal distribution to model the sampling distribution. A larger sample size would be needed to use a normal distribution model.
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After simplifying, which expressions are equivalent? select three options. (3.4a – 1.7b) (2.5a – 3.9b) (2.5a 1.6b) (3.4a 4b) (–3.9b a) (–1.7b 4.9a) –0.4b (6b – 5.9a) 5.9a – 5.6b
Answers
(3.4a – 1.7b) and (–1.7b 4.9a) and (5.9a – 5.6b) are equivalent expressions.
Which expressions are equivalent after simplification?
The question presents a list of six expressions. We need to select three expressions that are equivalent after simplifying them.
One of the expressions is (3.4a - 1.7b), and another is (-1.7b + 4.9a). These two expressions can be simplified to 2.4a - 1.7b.
Another expression is (2.5a - 3.9b), and another is (-3.9b + a). These two expressions can be simplified to 3.5a - 3.9b.
The third expression is 5.9a - 5.6b, which cannot be simplified further.
The three expressions that are equivalent after simplifying are (3.4a - 1.7b) and (-1.7b + 4.9a), (2.5a - 3.9b) and (-3.9b + a), and 5.9a - 5.6b.
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1. Mrs. Zimmerman is interested in learning about how much time seventh grade students at our school spend outdoors on a typical school day.
Select all the samples that are a part of the population. Justify your reasoning.
. The 20 students in a seventh grade math class.
B. The first 20 students to arrive at school on a particular day.
C. The seventh grade students participating in a science fair put on by the four middle schools in a school district.
D. The 10 seventh graders on the school soccer team.
E. The students on the school debate team.
Answers
A, c, D
Step-by-step explanation:
A) we can sample these 7th graders as we are looking to study 7th graders.
b) The first 20 students could be from any grade and so this option wouldn't work.
c) Involves 7th graders.
d) involves 7th graders
E) The students could be any grade level on the debate team so, this option wouldn't work.
The school budget for e-readers was $40,000 in 2014. The budget for 2015 was 20% less than the budget for 2014. What was the school budget for e-readers in 2015?
Answers
Answer: 32000
Step-by-step explanation: 40000 x 80% because you still have 80 percent of that budget so you minus 20 for 100.
to
Mrs. James, a sixth grade teacher, recorded how many minutes
each student reported reading over winter break.
Time spent reading (min.)
0
H
200.
What was the upper quartile of the time spent reading?
minutes
Submit
100
H
300.
400
+
500
Answers
The upper quartile of the time spent reading is 300.
We have,
The upper quartile, also known as the third quartile, is a measure of central tendency that divides a data set into four equal parts.
It represents the data point that separates the top 25% of the data from the bottom 75%.
Now,
From the box pot.
Median = 250
Lower quartile = 100
Upper quartile = 300
Thus,
The upper quartile is 300.
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A particle moves along the x-axis so that its position at time t>0 is given by
X(t) = (t^2 - 9)/(3t^2 + 8)
A) show that the velocity of the particle at time this given by v(t) = 70t/(3t^2 + 8)^2
B) is the particle moving toward the origin or away from the originator time t = 2? Give a reason for your answer.
C) The acceleration of the particle is given by £(t). Write an expression for £(t), and find the value of £(2).
D) What position does the particle approach as t approaches infinity?
Answers
The velocity of the particle at time t is given by [tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]
The expression for the acceleration of the particle is a(t) [tex]= (210t^2 + 1120)/(3t^2+8)^3.[/tex]
A) To find the velocity of the particle, we need to take the derivative of its position with respect to time:
[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]
[tex]v(t) = dX/dt = [(2t)(3t^2+8) - (t^2-9)(6t)]/(3t^2+8)^2[/tex]
[tex]v(t) = (6t^3 + 16t - 6t^3 + 54t)/(3t^2 + 8)^2[/tex]
[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]
Therefore, the velocity of the particle at time t is given by[tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]
B) To determine whether the particle is moving toward or away from the origin at time t = 2, we need to examine the sign of the velocity v(2). Plugging t = 2 into the expression for v(t), we get:
[tex]v(2) = 70(2)/((3(2)^2 + 8)^2) = 280/169[/tex]
Since v(2) is positive, the particle is moving away from the origin at time t = 2.
C) The acceleration of the particle is given by the derivative of its velocity with respect to time:
[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]
[tex]a(t) = dv/dt = (70(3t^2+8)^2 - 2(70t)(2t)(3t^2+8))/(3t^2+8)^4[/tex]
[tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]
Therefore, the expression for the acceleration of the particle is [tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]. To find the value of a(2), we plug in [tex]t = 2:a(2) = (210(2)^2 + 1120)/(3(2)^2+8)^3 = 175/677[/tex]
D) To find the position that the particle approaches as t approaches infinity, we examine the behavior of X(t) as t gets very large. We can do this by looking at the leading term of the numerator and denominator of X(t) as t approaches infinity:
[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]
As t approaches infinity, the numerator is dominated by the t^2 term, and the denominator is dominated by the 3t^2 term. Therefore, as t approaches infinity, X(t) approaches:
[tex]X(infinity) = t^2/3t^2 = 1/3[/tex]
So the particle approaches the point x = 1/3 as t approaches infinity.
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If R is the unbounded region between the graph of [tex]y=\frac{1}{x(ln(x))^2}[/tex] and the x-axis for [tex]x\geq 3[/tex] then what is the area of R?
will give brainliest to answer with good explanation please i'm desperate
Answers
The area of the unbounded region R between the graph of y=1/(xln(x))² and the x-axis for x≥3 is 1/ln(3) square units. The integral was found by substitution and evaluated at the interval limits.
To find the area of the region R, we need to integrate the function y = 1/(x ln(x))² with respect to x over the interval x≥3.
Let's first find the indefinite integral
∫ 1/(x ln(x))₂ dx = ∫ u₂ du [where u = ln(x)]
= - u⁻¹ + C
= - ln(x)⁻¹ + C
Now, to find the definite integral, we need to evaluate this expression at the upper and lower bounds of the interval x≥3
[tex]\int\limits^ \infty} _3[/tex]1/(x ln(x))² dx = [- ln(x)⁻¹[tex]]^ \infty} _3[/tex]
= [- ln(∞)⁻¹] - [- ln(3)⁻¹]
= 0 - (-1/ln(3))
= 1/ln(3)
Therefore, the area of the region R is 1/ln(3) square units.
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In a game of chance players spin the pointer of a spinner with six equal sized sections Anna 1 John 4 Carrie 4 Steve 1 Ethan 2 Liz 4 Jane 1 which outcome has a frequency closest to its expected frequency A (1) B (2) C (3) D (4)
Answers
The outcome with a frequency closest to its expected frequency is C (3).
Which outcome in a spinner game has a frequency closest to its expected frequency?In a spinner game where the pointer spins on a wheel with six equal-sized sections, the expected frequency of each section is 1/6 or 16.67%. Based on the given spinner, section A has an expected frequency of 1/6, section B has an expected frequency of 4/6, section C has an expected frequency of 4/6, section D has an expected frequency of 1/6, section E has an expected frequency of 2/6, and section F has an expected frequency of 4/6.
To determine the outcome with a frequency closest to its expected frequency, we need to compare the expected frequency to the actual frequency for each section.
Based on the given spinner, section A has an actual frequency of 1/18, section B has an actual frequency of 4/18, section C has an actual frequency of 4/18, section D has an actual frequency of 1/18, section E has an actual frequency of 2/18, and section F has an actual frequency of 4/18.
Calculating the difference between the expected and actual frequency for each section, we find that section C has the smallest difference, making it the outcome with a frequency closest to its expected frequency.
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Need help asap. (See photo below)
Angles Formed by Chords, Tangents, Secants
Answers
The value of m∠MGA between the tangent and the diameter is 90 degrees.
How to find the angle between tangent?A line that touches the circle at one point is known as a tangent to a circle.
Therefore, MU is tangent to the circle O at the point G. The diameter of the
circle is GA.
Therefore, let's find the angle m∠MGA in the circle.
If a tangent and a diameter meet at the point of tangency, then they are perpendicular to one another. Therefore, the point where they meets form a right angle(90 degrees).
Hence,
m∠MGA = 90 degrees
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how many times can 2 go into 1742? please its for my homework due tomorrow
Answers
I’m confused math has never really been my strong suit
Answers
Thus, 25.13 cubic inches is the closest estimate for the ice cream's overall volume.
what is volume ?Volume is a mathematical concept that describes how much space a three-dimensional object occupies. It is frequently expressed in terms of cubic units like cubic metres (m3), cubic feet (ft3), or cubic centimetres (cm3). Depending on the shape of the object, different formulas can be used to determine its volume. Consider this: The formula V = l w h, where l has been the length, w is the broad, and h corresponds to the height of the rectangular prism (box), gives the volume of the object. A sphere's volume can be calculated using the method V = (4/3)r3, where r is the sphere's radius.
given
The formula for a cone's volume is as follows, assuming that the ice cream has the correct circular cone shape with radius r = 2 in and height h = 6 in:
[tex]V = (1/3) * \pi * r^2 * h[/tex]
Inputting the values provided yields:
[tex]V = (1/3) * \pi * (2 in) * (2 in) * (6 in)[/tex] = 25.13 cubic inches
Thus, 25.13 cubic inches is the closest estimate for the ice cream's overall volume.
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The complete question is:-
r = 2 in.
h = 6 in.
Which is closest to the total volume of the ice
cream?
Write 23.4571 correct to
b) the nearest 10
Answers
Answer:
20
Step-by-step explanation:
Answer:
23.50
Step-by-step explanation:
23.4571 rounded of to the nearest tenth 23.4+1
Sara collects beads in a jar she weighs the jar every week to see how many grams of beads she has. she as 2.5 grams if blue beads. 4.9 grams of pink beads, 7.1 grams of yellow beads and the rest are white beads
if sara weighs her jar this week and finds out that she has 1.8 grams of beads, how many grams of white beads does she have?
Answers
Therefore, Sara has 3.5 grams of white beads in her jar.
Based on the information provided, Sara has 2.5 grams of blue beads, 4.9 grams of pink beads, and 7.1 grams of yellow beads. If she weighs her jar this week and finds out she has a total of 18 grams of beads, we can determine the number of grams of white beads she has by following these steps:
Step 1: Add the weights of the blue, pink, and yellow beads together.
2.5 grams (blue) + 4.9 grams (pink) + 7.1 grams (yellow) = 14.5 grams
Step 2: Subtract the total weight of the blue, pink, and yellow beads from the total weight of the jar (18 grams).
18 grams (total weight) - 14.5 grams (blue, pink, and yellow beads) = 3.5 grams
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Find the area of triangle ABC given that AB= 8cm , AC = 6cm , ∠ = 55° ∠ = 35°.
a) 48cm*2 b) 12cm*2 c) 24cm*2 d) 5cm*2
Answers
Area = (1/2) * a * b * sin(C)
where a and b are the side lengths, and C is the angle between them. In our case, a = 8 cm, b = 6 cm, and ∠C = 180° - (∠A + ∠B) = 180° - (55° + 35°) = 90°.
Now, we can plug in the values:
Area = (1/2) * 8 cm * 6 cm * sin(90°)
Since sin(90°) = 1, the area becomes:
Area = (1/2) * 8 cm * 6 cm = 24 cm²
So, the correct answer is c) 24 cm².
Step-by-step explanation:
so like you use sine rule to find line BC and i got 7.3 the you have to split the triangle in half to get a right angle triangle then divide 7.3 by two to get 3.7 and then use .pythagoras theorem to find the height and then use the area of a triangle formula to get your answer as option (C)
please hurry A 4-column table with 3 rows. Column 1 has entries boys, girls, total. Column 2 is labeled less than 8 pounds with entries a, c, e. Column 3 is labeled greater-than-or-equal-to 8 pounds with entries 50, d, 70. Column 4 is labeled Total with entries b, 96, 160.
Last July, 160 babies were born in a hospital in Maine; 3
5
of the babies were girls. Seventy babies weighed 8 pounds or more. Fifty boys weighed 8 pounds or more.
a = 64, b = 14, c = 76, d = 20, e = 90
a = 14, b = 64, c = 90 d = 20, e = 76
a = 14, b = 76, c = 64, d = 90, e = 20
a = 14, b = 64, c = 76, d = 20, e = 90
Answers
Answer: the correct answer is:
a = 14, b = 64, c = 76, d = 20, e = 90
Step-by-step explanation: can i get brainliest :D
Emilio draws an example of an obtuse triangle. Which triangle could be Emilio's drawing?
A.
Triangle with three angles less than 90 degrees.
B.
Triangle with one 90 degree angle and two angles less than 90 degrees.
C.
Triangle with two angles less than 90 degrees and one angle greater than 90 degrees.
D.
Triangle with three angles less than 90 degrees.
Answers
Answer:
C. An obtuse triangle has two angles less than 90 degrees and one angle greater than 90 degrees.
Jack plus 1/3 pound of birdseed into his birthday. Every time he sells it how many times can jack sell his bird feeder with 4 lb of birdseed
Answers
Jack can sell 12 bird feeders with 4 lb of birdseed. We can use Proportion method to calculate this :
Assuming that Jack mixes 1/3 pound of birdseed for each bird feeder, we can find out how many bird feeders he can sell with 4 pounds of birdseed by using a proportion.
Let x be the number of bird feeders Jack can make with 4 pounds of birdseed. We can set up the proportion:
1/3 pounds of birdseed per bird feeder = 4 pounds of birdseed / x bird feeders.
Simplifying this equation, we get:
1/3 = 4/x
To solve for x, we can cross-multiply:
1x = 12
x = 12
Therefore, Jack can make and sell 12 bird feeders with 4 pounds of birdseed.
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Select the statement that correctly describes the relationship for angles of an inscribed quadrilateral. (10pts pls help)
Answers
The opposite angles in an inscribed quadrilateral are supplementary, meaning their sum is 180 degrees.
What is the relationship between the angles of an inscribed quadrilateral, and how related to each other?An inscribed quadrilateral is a quadrilateral whose vertices all lie on a circle. Let's label the vertices of the quadrilateral as A, B, C, and D, in clockwise order.
Draw the circle that contains all four vertices, and label the center of the circle as O.
Now, draw chords AC and BD that cross at point P. Each chord divides the quadrilateral into two triangles. Notice that angle AOC and angle BOD are both central angles that subtend the same arc, CD.
Therefore, these angles have the same measure, and we can write:
angle AOC = angle BOD = x
Similarly, we can show that angle AOB = angle COD = y.
Now, consider the two triangles APC and BPD. These triangles share the side P D and have the same angle APD, which is equal to angle AOC + angle BOD, or 2x.
Therefore, by the angle-sum property of triangles, the other angles in each triangle must also be equal. We can write:
angle APC = angle BPD = (180 - 2x)/2 = 90 - x
Similarly, consider the two triangles APB and CPD. These triangles share the side P C and have the same angle APC, which we just found to be 90 - x.
Therefore, by the angle-sum property of triangles, the other angles in each triangle must also be equal. We can write:
angle APB = angle CPD = (180 - (90 - x))/2 = 90 + x/2
Finally, notice that angle APB + angle CPD = (90 + x/2) + (90 - x/2) = 180, so the opposite angles in the quadrilateral are indeed supplementary.
Therefore, the main answer is: The opposite angles in an inscribed quadrilateral are supplementary, meaning their sum is 180 degrees.
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Aaden is driving to a concert and needs to pay for parking. There is an automatic fee of $9 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour he had his car in the lot. How much total money would Aaden have to pay for parking if he left his car in the lot for 3 hours? How much would Aaden have to pay if he left his car in the lot for
�
t hours?
Answers
Answer:
$15.
Step-by-step explanation:
9 + 3*2
= $15.
3. The table below shows the relationship between the amount of electricity used by a customer in different months and the cost shown on the customer's electric bill. Month 1 2 3 4 Monthly Electric Bills for a Customer Amount of Electricity Used (kilowatt-hours) A 0.095x < 65.00 B. 0.095x> 65.00 C. 0.92x < 65.00 D. 0.92x> 65.00 290 350 460 500 Cost of Electricity Used ($) 27.55 33.25 43.70 47.50 Based on the information shown in the table, which inequality could be used to determine all the numbers of kilowatt-hours (x) of electricity a customer could use in a month for the cost to be less than $65.00?
Answers
The correct inequality is:
A. 0.095x < 65.00.
To determine the inequality that represents the numbers of kilowatt-hours a customer could use in a month for the cost to be less than $65.00, we need to look for the rate at which the cost of electricity changes with the amount of electricity used.
From the table, we can see that the cost of electricity increases as the amount of electricity used increases.
We can also see that the cost per kilowatt-hour (the rate) is not constant. For example, the cost per kilowatt-hour for the first month is:
27.55 / 290 ≈ 0.095
But for the fourth month, it is:
47.50 / 500 ≈ 0.095
This means that the rate is not constant, and we cannot simply use a proportion to determine the numbers of kilowatt-hours that will result in a cost of less than $65.00.
However, we can use the data to create an inequality that represents the numbers of kilowatt-hours that will result in a cost less than $65.00. We can start by finding the highest cost per kilowatt-hour:
43.70 / 460 ≈ 0.095
This means that the cost per kilowatt-hour is always less than or equal to 0.095.
Next, we can set up the inequality:
0.095x < 65.00
This inequality represents the numbers of kilowatt-hours that will result in a cost less than $65.00, because if the cost per kilowatt-hour is always less than or equal to 0.095, then the total cost will be less than $65.00 if and only if the number of kilowatt-hours used is less than 684.21 (which is the result of dividing $65.00 by 0.095).
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Please answer 1-9, i really need help tysm
Answers
Answer:
the answer is 8
Step-by-step explanation:
it is because if you take your 9 fingers and remove 1 finger it will be 8
Use similar triangles to calculate the height, h cm, of triangle ABE. 10 cm 36 cm D B 20 cm E Optional working I h = Answ cm Search
Answers
Answer:
h=24
Step-by-step explanation:
Since the traingles are similar we can calculate the scale factor
20/10 = 2
So the Linear Scale Factor is 2
We can use that to figure out the ratio between the 2 triangles
Since DC = 10 and AE = 20
We cans say that the ratio between DBC and ABE is 2:1
Using this we can see that the ratio of the height is split into 2:1 and the total is 3
Knowing this we can calculate the the heights of both triangles
36 / 3 = 12
Height of small traingle = 1*12 = 12
Height of large triangle = 2*12 = 24
A school’s art teacher designs a circular flower bed inside a rectangular sandbox. The sandbox is 6 feet wide and 10 feet long. How many square feet will there be for sand after the flower bed is installed? Use 3.14 for pi. ROUND the answer to the NEAREST SQUARE FOOT.
A. 22 square feet
B. 28 square feet
C. 32 square feet
D. 41 square feet
Answers
Solve the system of equations.
6x – y = 6
6x2 – y = 6
A (0, 6) and (0, –6)
B (1, 0) and (0, –6)
C (2, 6) and (1, –11)
D (3, 12) and (2, 19)
Answers
sin^2(x) + sin(x) = 0
Answers
If both are multiples it means one must equal 0
Sinx=0
X= pi
Sinx+1=0
X=3pi/2 or 180°
Imagine that the price per gallon of gas with a $7 car wash is $3. 19 and the price without the car wash is $3. 39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?
Answers
If we plan to buy more than 10 gallons of gas, it is worth it to buy the car wash, assuming that the cost of the car wash is $2.
The car wash costs $7, and the price per gallon of gas with the car wash is $3.19, while the price per gallon of gas without the car wash is $3.39. Let's assume that we buy x gallons of gas, then the total cost of buying gas with the car wash would be:
Total cost with car wash = 7 + 3.19x
The total cost of buying gas without the car wash would be:
Total cost without car wash = 3.39x
To determine when it is worth it to buy the car wash, we need to find when the total cost with the car wash is less than the total cost without the car wash:
7 + 3.19x < 3.39x
Solving for x:
7 < 0.2x
x > 35
This means that if we plan to buy more than 35 gallons of gas, it is worth it to buy the car wash.
Now, let's consider the scenario where the car wash costs $2. The total cost of buying gas with the car wash would be:
Total cost with car wash = 2 + 3.19x
To determine when it is worth it to buy the car wash in this scenario, we need to find when the total cost with the car wash is less than the total cost without the car wash:
2 + 3.19x < 3.39x
Solving for x:
2 < 0.2x
x > 10
This means that if we plan to buy more than 10 gallons of gas, it is worth it to buy the car wash, assuming that the cost of the car wash is $2.
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