A ninja star, or shuriken, is usually constructed using four congruent isosceles triangles that are placed along the sides of a square. What is the value of x?

a.) 46
b.) 56
c.) 62
d.) 118

A Ninja Star, Or Shuriken, Is Usually Constructed Using Four Congruent Isosceles Triangles That Are Placed

Answers

Answer 1

The measure of angle x of the ninja star is given by x = 56°

Given data ,

Let the ninja star be represented as an isosceles triangle

Now , it is constructed using four congruent isosceles triangles that are placed along the sides of a square

And , the vertex angle of the triangle is x

In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle

So , the measure of x = 180° - ( 62° + 62° )

On simplifying , we get

x = 56°

Hence , the angle of triangle is x = 56°

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Related Questions

HELP DUE TOMORROW!!!

Answers

The equation of the attached graph is

y = 1 cos (1x) + 0

How to write the equation of the graph

The equation is written by the general formula

y = A cos (Bx + C) + D

where:

A = amplitude.

B = 2π/T

where T = period

C = phase shift.

D = vertical shift.

A = amplitude

A = (maximum - minimum) / 2

Using the graph,

maximum = 1

minimum = -1

A = [1 - (-1)] / 2 = 2/2 = 1

B = 2π/T

where T = 2π

B = 2π/(2π) = 1

C = phase shift = 0

D = vertical shift

D = 1 - 1 = 0

substituting results to

y = 1 cos (1x + 0) + 0

this is written as

y = 1 cos (1x) + 0

y = cos (x)

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the line whose equation is 3x-5y=4 is dilated by a scale factor of 5/3 centered at the origin. Which statement is correct?

Answers

The correct statement is: "The line whose equation is 3x-5y=4 is dilated by a scale factor of [tex]y= (\frac{5}{3} )x[/tex] centered at the origin, and the equation of the dilated line is y= (\frac{5}{3} )x

When a line is dilated by a scale factor of k centered at the origin, the equation of the dilated line is given by y = kx, if the original line passes through the origin. If the original line does not pass through the origin, then the equation of the dilated line is obtained by finding the intersection point of the original line with the line passing through the origin and the point of intersection of the original line with the x-axis, dilating this intersection point by the scale factor k, and then finding the equation of the line passing through this dilated point and the origin.

In this case, the equation of the original line is 3x - 5y = 4. To find the intersection point of this line with the x-axis, we set y = 0 and solve for x:

3x - 5(0) = 4
3x = 4
[tex]x = \frac{4}{3}[/tex]

Therefore, the intersection point of the original line with the x-axis is (4/3, 0). Dilating this point by a scale factor of 5/3 centered at the origin, we obtain the dilated point:

[tex](\frac{5}{3} ) (\frac{4}{3},0) = (\frac{20}{9},0)[/tex]

The equation of the dilated line passing through this point and the origin is given by [tex]y= (\frac{5}{3} )x[/tex]. Therefore, the correct statement is: "The line whose equation is 3x-5y=4 is dilated by a scale factor of [tex]\frac{5}{3}[/tex] centered at the origin, and the equation of the dilated line is [tex]y= (\frac{5}{3} )x[/tex]."

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Pls help quickly i’ll give brainlyist

Answers

Answer:

Angle Q measures 55°, so angle M measures 55°.

39 + 55 + x = 180

94 + x = 180

x = 86

In triangle ABC, the length of side AB is 12 inches and the length of side BC is 20 inches. Which of the following could be the length of side AC?

Answers

Applying the triangle inequality theorem, the possible length of side AC is: C. 18 inches.

How to Determine the Length of a Triangle Using Triangle Inequality Theorem?

The triangle inequality theorem states that lengths of the two sides of a triangle, when added together must be greater than the third side of any given triangle.

Therefore, to determine the possible length of side AC, we can use the triangle inequality theorem, stated above and applying this to triangle ABC, we have the following:

AC < AB + BC

AC < 12 + 20

AC < 32

This implies that, length of side AC must be less than 32 inches. Thus, the answer is: C. 18 inches.

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Tamekia and Marsha mow lawns during the summer to earn money. Tamekia determined that she can earn between $6. 00 and $6. 25 per hour. Marsha estimates that she earns between $7. 50 and $8. 00 per hour. About how much more money will Marsha earn than Tamekia if they each work 22 hours?

Answers

If they each work 22 hours, Marsha will earn about $35.75 more than Tamekia.

To compare how much more money Marsha will earn than Tamekia, we can use the averages of their respective hourly rates and then multiply by the number of hours worked.

Tamekia's average hourly rate: ($6.00 + $6.25) / 2 = $6.125
Marsha's average hourly rate: ($7.50 + $8.00) / 2 = $7.75

Now, we'll multiply their average hourly rates by the number of hours worked, which is 22 hours.

Tamekia's total earnings: $6.125 x 22 = $134.75
Marsha's total earnings: $7.75 x 22 = $170.50

Finally, we'll subtract Tamekia's earnings from Marsha's earnings to find the difference:

$170.50 - $134.75 = $35.75

So, Marsha will earn about $35.75 more than Tamekia if they each work 22 hours.

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Marsha will earn $38.50 more than Tamekia if they each work 22 hours.

determine whether the function f(x) = a^x-a^(-x)+sinx is even or odd.

Answers

To determine whether the function f(x) = a^x-a^(-x)+sinx is even or odd, we need to check if it satisfies the properties of even and odd functions.

An even function is a function that satisfies the property f(x) = f(-x) for all x in the domain of the function. This means that if we reflect the graph of the function across the y-axis, we get the same graph.

An odd function is a function that satisfies the property f(x) = -f(-x) for all x in the domain of the function. This means that if we reflect the graph of the function across the origin (both x and y-axis), we get the same graph.

Let's start by checking whether f(x) is even:

f(-x) = a^(-x)-a^(x)+sin(-x)  (since sin(-x) = -sin(x))

       = -a^x+a^(-x)-sin(x)

Comparing f(-x) with f(x), we can see that f(-x) = -f(x) only when sin(x) = 0.

This means that f(x) is an even function only when sin(x) = 0, which occurs when x = nπ (where n is an integer).

Now, let's check whether f(x) is odd:

f(-x) = a^(-x)-a^(x)+sin(-x)  (since sin(-x) = -sin(x))

       = -a^x+a^(-x)-sin(x)

Comparing f(-x) with -f(x), we can see that f(-x) = -f(x) only when a^x = -a^x, which is not possible for any real value of a.

Therefore, f(x) is neither an even nor an odd function.
To determine whether the function f(x) = a^x - a^(-x) + sin(x) is even or odd, we can evaluate f(-x) and compare it to f(x).

An even function satisfies the condition f(-x) = f(x), while an odd function satisfies the condition f(-x) = -f(x).

Let's evaluate f(-x):
f(-x) = a^(-x) - a^(-(-x)) + sin(-x)
f(-x) = a^(-x) - a^x - sin(x)

Now, let's compare f(-x) to f(x):
f(-x) ≠ f(x) because f(x) = a^x - a^(-x) + sin(x)
f(-x) ≠ -f(x) because -f(x) = -a^x + a^(-x) - sin(x)

Since f(-x) is neither equal to f(x) nor -f(x), the function f(x) = a^x - a^(-x) + sin(x) is neither even nor odd.

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66. Which value of m makes the inequality true?
A. 4
B. 5
3m-4 < 11
C. 6
D. 7

Answers

Answer:

The answer to the question provided is choice A, 4.

The value of m which makes the inequality true is, 4

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 3m - 4 < 11

Now,. We can simplify as;

⇒ 3m - 4 < 11

⇒ 3m < 11 + 4

⇒ 3m < 15

⇒ m < 5

Thus, The value of m which makes the inequality true is, 4

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Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth.

Answers

1. The probability that the point chosen is in the triangle is 0.1 (nearest tenth)

2. The probability that the point is in the square is 0.2( nearest tenth)

What is probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty for an event is 1 which is equivalent to 100%.

Probability = sample space / total outcome

total outcome is the area of rectangle , which is

A = l× w

= 12 × 8

= 96

area of the rectangle = 1/2 bh

= 1/2 × 4 × 5

= 2 × 5

= 10

Area of the square = 4×4

= 16

1. Probability the the point will be in the triangle= 10/96 = 5/48

= 0.1( nearest tenth)

2. probability the the point will be in the square =

16/96 = 1/6

= 0.2 ( nearest tenth)

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what value of x is y/z

a-13
b-77
c-103
d-154

Answers

Answer:

I got you

Step-by-step explanation:

it's c -103 cause you first have to get 180 degrees

Grams of


Peanuts


Grams of


Raisins


14


4


21


6


35


10


Enter the number of grams of peanuts in a bag for every 1 gram of raisins.

Answers

For every 1 gram of raisins, there are 3.5 grams of peanuts in a bag.

To find the number of grams of peanuts for every 1 gram of raisins, you need to set up a ratio and solve for the missing value.

1. Set up the ratio: grams of peanuts / grams of raisins.
2. You are given three sets of values: (14, 4), (21, 6), and (35, 10).

For the first set (14, 4):
3. Calculate the ratio: 14 grams of peanuts / 4 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.

For the second set (21, 6):
4. Calculate the ratio: 21 grams of peanuts / 6 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.

For the third set (35, 10):
5. Calculate the ratio: 35 grams of peanuts / 10 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.

Your answer: For every 1 gram of raisins, there are 3.5 grams of peanuts in a bag.

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The model q(t) = 2. 5.00E+00. 0168t predicts the world population, in billions, t years after 1955. What was the population of the world in 1955 based


on this model?

Answers

The population of the world in 1955 based on the model q(t) = 2.500[tex]e^{0.0168t}[/tex] is 2.54 billion.

The model q(t) = 2.500[tex]e^{0.0168t}[/tex] represents the world population in billions

Here, t represents the years after 1955 and e is exponential constant its value is approximately 2.718.

Here the population is growing exponentially means population is growing at faster rate.

To find the population of the world in 1955 we will take

t = 1

on putting the value of t in the given function q(t)

q(t) = 2.500e[tex]e^{0.0168(1)[/tex]

on solving the function q(t) we get

q(t) ≈ 2.54

so, the population of the world in 1955 is 2.54 billion

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Lucy’s dog weighs nine and seventy-five hundredths kilograms. what is the weight, in kilograms, of lucy’s dog written in expanded notation?

Answers

The weight of Lucy's dog, written in expanded notation, is 9 kilograms and 0.75 kilograms.

Expanded notation is a way of writing a number as the sum of each digit multiplied by its place value. In this case, the number is 9.75. The digit 9 is in the tens place, so it represents 9 tens or 90. The digit 7 is in the ones place, so it represents 7 ones or 7.

The digit 5 is in the tenths place, so it represents 5 tenths or 0.5. The digit 7 is in the hundredths place, so it represents 7 hundredths or 0.07. Therefore, the weight of Lucy's dog in expanded notation is 90 kilograms plus 7 kilograms plus 0.5 kilograms plus 0.07 kilograms, which simplifies to 9 kilograms and 0.75 kilograms.

Mathematically, we can represent the given number as 9.75 = 9 x 10 + 7 x 1 + 5 x 0.1 + 7 x 0.01 = 90 + 7 + 0.5 + 0.07 = 9.57. Thus, the weight of Lucy's dog written in expanded notation is 9 kilograms and 0.75 kilograms.

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How much paint will you need to paint all sides of the box shown below? 4m 13m 4m 4m 11m​

Answers

To paint all sides of the box, you would need approximately 344 square meters of paint.

To calculate the amount of paint needed to paint all sides of the box, we first need to find the total surface area of the box.

The box has five sides: top, bottom, front, back, and two sides.

Given the dimensions:

Top: 4m x 13m

Bottom: 4m x 13m

Front: 4m x 4m

Back: 4m x 4m

Sides (2): 4m x 11m.

To calculate the surface area, we sum the areas of all the sides:

Surface Area = (4m x 13m) + (4m x 13m) + (4m x 4m) + (4m x 4m) + (4m x 11m) + (4m x 11m)

Surface Area = 52m² + 52m² + 16m² + 16m² + 44m² + 44m²

Surface Area = 224m² + 32m² + 88m²

Surface Area = 344m²

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Americans consume on average 32. 3 lbs of cheese per year with a standard deviation of 8. 7 lbs. Assume that the amount of cheese consumed each year by an American is normally distributed. An American in the middle 70% of cheese consumption consumes per year how much cheese?

Answers

An American in the middle 70% of cheese consumption consumes per year between 23.252 and 41.348 lbs of cheese.

To find the amount of cheese consumed by an American in the middle 70%, we need to find the range of values that contain the middle 70% of the distribution.

First, we need to find the z-scores corresponding to the lower and upper boundaries of the middle 70% of the distribution. We can use the standard normal distribution for this, by converting the raw score of 32.3 lbs to a z-score:

z = (x - μ) / σ = (32.3 - 32.3) / 8.7 = 0

The z-score for the mean is zero, which means the mean is the midpoint of the normal distribution.

Next, we need to find the z-scores that correspond to the lower and upper boundaries of the middle 70% of the distribution. We can use the standard normal distribution table or calculator to find the z-scores. For a middle 70% range, the z-scores are approximately -1.04 and 1.04.

Finally, we can use the z-scores and the formula z = (x - μ) / σ to find the corresponding values of x, which represent the range of cheese consumption that contains the middle 70% of the distribution:

Lower boundary: z = -1.04

-1.04 = (x - 32.3) / 8.7

x - 32.3 = -9.048

x = 23.252 lbs

Upper boundary: z = 1.04

1.04 = (x - 32.3) / 8.7

x - 32.3 = 9.048

x = 41.348 lbs

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A tree farm has begun to harvest a section of trees that was planted a number of years ago. the table shows the number of trees remaining for each of 8 years of harvesting.

a) find the regression equation for the relationship between time and trees remaining. (round values for a and b to two decimal places.)

b) the owners of the farm intend to stop harvesting when only 1000 trees remain. during which year will this occur?

Answers

The owners of the farm will stop harvesting when only 1000 trees remain during the fifth year of harvesting.

a) To get the regression equation for the relationship between time and trees remaining, we need to use linear regression. We can use the data given in the table to create a scatterplot and then find the line of best fit. Using a calculator or Excel, we can find that the regression equation is:
Trees remaining = 1177.38 - 36.25(time)
where "Trees remaining" is the number of trees remaining and "time" is the number of years since harvesting began.
b) To find during which year the owners of the farm will stop harvesting when only 1000 trees remain, we can substitute "1000" for "Trees remaining" in the regression equation and solve for "time":
1000 = 1177.38 - 36.25(time)
Solving for "time", we get:
time = (1177.38 - 1000) / 36.25
time ≈ 4.89 years
Therefore, the owners of the farm will stop harvesting when only 1000 trees remain during the fifth year of harvesting.

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A UPS driver need to drive 600 miles. The drivers average speed for the first 160 miles is b miles per hour. The drivers average speed for the rest of the trip is c miles per hour. Write an equation for the total time, t, in hours it took the UPS driver to complete the trip.

Answers

The answer is : 600 /b + c=t

Bob earns $60,000 a year at an accounting firm. Each year, he receives a raise. Bob


has determined that the probability that he receives a 10% raise is 0. 7, the probability that he earns


a 3% raise is 0. 2, and the probability that he earns a 2% raise is 0. 1.


A competing company has offered Bob a similar position for $65,000 a year. Bob wonders if he


should take the new job or take his chances with his current job. SHOW ALL WORK!


A) Find the mathematical expectation of the dollar amount of his raise at his current job

Answers

The mathematical expectation of the dollar amount of Bob's raise at his current accounting firm is $4,680. Therefore, Bob should take the new job at the competing company.

To find the mathematical expectation of the dollar amount of Bob's raise at his current accounting firm, we'll first calculate the expected raise percentages using the given probabilities. Then, we will multiply those percentages by his current salary to determine the expected dollar amount.

A) Step 1: Calculate the expected raise percentages using probabilities
- 10% raise with a probability of 0.7: (0.1 * 0.7) = 0.07
- 3% raise with a probability of 0.2: (0.03 * 0.2) = 0.006
- 2% raise with a probability of 0.1: (0.02 * 0.1) = 0.002

Step 2: Add up the expected raise percentages
0.07 + 0.006 + 0.002 = 0.078

Step 3: Multiply the expected raise percentage by Bob's current salary
Expected dollar amount of raise = $60,000 * 0.078 = $4,680

The mathematical expectation of the dollar amount of Bob's raise at his current accounting firm is $4,680.

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Grace and Kelly can create math problems for a particular course in 20 hours. Alone, Grace can do write all of the problems 4 hours faster than Kelly could if she were to work alone. How long would it take each person to write the problems if they worked alone?

Answers

From the word problem given, it will take Grace 0.05 hours and Kelly 4.05 to complete the task

How long will it take for each person to write the problem if they worked alone?

To solve this problem, we need to write an equation for the word problem.

Let x = time it takes for Kelly

let y = time it takes for Grace

From the problem;

y = x - 4 ...eq(i)

Since they can complete the work in 20 hours;

1/x + 1/y = 20 ...eq(ii)

Solving for both equations

From equ(ii)

1/x + 1/(x - 4) = 20

Solving for x;

x = 4.05 or x = 0.049

Put the value in and solve for y

y = x - 4

y = 4.05 - 4 = 0.05 or y = 0.0049 - 4 = insignificant

The value of y = 0.5 hours

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8x + 19 -28 + 8x
what is the solution?

Answers

the answer is 16x - 9

Ink pens and pencils are substitutes. If demand of pen falls,what happens to demand, supply, quantity

Answers

Pen demand decrease reduces pen price, quantity supplied; increases pencil demand, price, and quantity supplied as a substitute.

How do pen demand changes affect supply?

If the demand for ink pens falls, this would likely result in a decrease in the demand for pens and an increase in the demand for pencils, since they are substitutes.

As a result, the price of pens would likely fall, as producers try to entice buyers to purchase pens over pencils. This decrease in the price of pens would, in turn, lead to a decrease in the quantity supplied of pens, as producers shift their focus to producing other goods that are more in demand.

However, the quantity demanded of pencils would increase, leading to an increase in the price of pencils and an increase in the quantity supplied of pencils. Ultimately, the market for ink pens and pencils would adjust to reflect the changes in demand, resulting in changes in both price and quantity.

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A car accelerates away from the starting line at 3. 6 m/s2 and has the mass of


2400 kg. What is the net force acting on the vehicle?

Answers

If A car accelerates away from the starting line at 3. 6 m/s2 and has a mass of 2400 kg, Therefore, the net force acting on the vehicle is 8640 N.

The net force acting on the vehicle can be calculated using Newton's second law of motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration:

Net force = mass x acceleration

In this case, the mass of the car is 2400 kg and the acceleration is 3.6 m/s^2. Thus, we can calculate the net force as:

Net force = 2400 kg x 3.6 m/s^2

Net force = 8640 N

Therefore, the net force acting on the vehicle is 8640 N.

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students in mr gonzales class are researching situations of exponitial decay and creating their graphs mr gonzales asked his students what the situations have in common and their responses are shown below

Answers

Therefore , the solution of the given problem of unitary method comes out to be  it is consistently a constant proportion or percentage of the preceding value.

A unitary method is what?

The task can be completed using the well-known minimalist technique, actual variables, and any essential components from the very first Diocesan specialised question. In response, customers can be given another opportunity to use the item. If not, significant effects on our comprehension of algorithms will disappear.

Here,

According to the students' responses, all instances of exponential decay share the following characteristics:

They begin with a baseline value. (y-intercept).

They get smaller with time. (or successive periods).

They get closer to a horizontal asymptote, which stands for the function's minimum or limit value.

The graphs also demonstrate that, although the rate of decay—or the rate at which values decrease—can vary from circumstance to circumstance,

it is consistently a constant proportion or percentage of the preceding value.

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Please answer the question correctly and neatly. Please find the
exact answer. Will upvote if correct.
Find the volume of the solid obtailed by rotating the region bounded by the given curves about the specified axis. y= x, y = 1 about y = 3

Answers

The region bounded by the given curves is a triangle with vertices at (0,0), (1,1), and (1,0). When this region is revolved around the line y=3, we obtain a solid with a hole in the middle.
To find the volume of this solid, we can use the method of cylindrical shells. Imagine slicing the solid into thin cylindrical shells with radius r and height Δy. The volume of each shell is approximately 2πrΔy times the thickness of the shell.

The distance between the axis of rotation (y=3) and the line y=1 is 2 units. Therefore, the radius of each cylindrical shell is r = 3 - y. The height of each shell is Δy = dx, where x is the distance from the y-axis.

To set up the integral, we need to express x in terms of y. Since the region is bounded by y=x and y=1, we have x=y for 0<=y<=1. Therefore, the integral for the volume of the solid is:
V = ∫[0,1] 2π(3-y)x dx
 = 2π ∫[0,1] (3-y)y dx

Evaluating this integral, we get:
V = 2π [3y^2/2 - y^3/3] from 0 to 1
 = 2π (3/2 - 1/3)
 = 2π/3

Therefore, the volume of the solid obtained by rotating the region bounded by y=x, y=1 about y=3 is (2/3)π cubic units.

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Select all the correct answers.
Isosceles trapezoid ABCD is shown.
Which three statements are correct?

Answers

In the given Isosceles trapezoid ABCD, the following three statements are correct:

∠ADC ≅ ∠BCD

AD ≅ BC

AC ≅ BD

An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths. Non-parallel sides on isosceles trapezoids have the same lengths. Hence, AD ≅ BC

A triangle with two equal sides is said to be isosceles. The two angles facing the two equal sides are also equal. Hence, ∠ADC ≅ ∠BCD.

The diagonals of the isosceles trapezoid are also equal. Hence, AC ≅ BD.

Thus, three correct statements in the given question are:

∠ADC ≅ ∠BCD

AD ≅ BC

AC ≅ BD

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Which equation defines a linear
function?
A y = 2/4x + 12
B y = x2 + 4x - 6
C x2 + y2 =16
D 1/x2 + 1/y2 = 4

Answers

The equation defines a linear function is A y = 2x/4 + 12

Which equation defines a linear function?

A y = 2x/4 + 12 is the equation that defines a linear function because it can be simplified to y = 1/2x + 12,

Which has a constant slope of 1/2 and a constant rate of change.

The other options are not linear functions because they involve exponents or do not have a constant slope.

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Find the critical numbers of the function. (Enter your answers as a comma-separated list.) h(x) = sin^2 x + cos x, 0 < x < 2π x =

Answers

To find the critical numbers of h(x) = sin^2(x) + cos(x) in 0 < x < 2π steps are first to find the derivative h'(x), set h'(x) equal to zero and solve for x and check if solutions are within the given interval. The critical numbers are x = π, π/3, and 5π/3.

To find the critical numbers of the function h(x) = sin^2(x) + cos(x) in the interval 0 < x < 2π, we will follow these steps:

Find the derivative of the function, Set the derivative equal to zero and solve for x, Set h'(x) equal to zero and solve for x, Check if the solutions are within the given interval.
1: Differentiate h(x) with respect to x.
h'(x) = d(sin^2(x) + cos(x))/dx
Using chain rule, we get:
h'(x) = 2sin(x)cos(x) - sin(x)
2: Set h'(x) equal to zero and solve for x.
0 = 2sin(x)cos(x) - sin(x)
Factor out sin(x):
0 = sin(x)(2cos(x) - 1)
So, either sin(x) = 0 or 2cos(x) - 1 = 0.
3: Solve for x and check if the solutions are within the interval 0 < x < 2π.
For sin(x) = 0, x = π (since 0 < π < 2π).
For 2cos(x) - 1 = 0, cos(x) = 1/2.
x = π/3 and 5π/3 (since 0 < π/3 < 2π and 0 < 5π/3 < 2π).
Therefore, the critical numbers of the function h(x) = sin^2(x) + cos(x) in the interval 0 < x < 2π are x = π, π/3, and 5π/3.

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Amita, Monica and Rita are three sisters.
Monica is x years old.
Amita is 3 years older than Monica.
Rita is twice the age of Amita.
If the mean age of the three sisters is 15, how old is Amita?

Answers

Answer:

So Monica is 9 years old.

To find Amita's age, we substitute x into the expression for Amita's age:

Amita's age = 9 + 3 = 12

Therefore, Amita is 12 years old.

Her age is 12 year old

Solve the following pair of equations by substitution method:
0.2x + 0.3y − 1.1 = 0, 0.7x − 0.5y + 0.8 = 0

Answers

Answer:

  (x, y) = (1, 3)

Step-by-step explanation:

You want to solve this system of equations by substitution:

0.2x +0.3y -1.1 = 00.7x -0.5y +0.8 = 0

Expression for x

We can solve the first equation for an expression in x:

  x = (1.1 -0.3y)/0.2 = (11 -3y)/2

Substitution

Substituting for x in the second equation gives ...

  0.7(11 -3y)/2 -0.5y +0.8 = 0

  7.7 -2.1y -y +1.6 = 0 . . . . . . . . . multiply by 2, eliminate parentheses

  -3.1y +9.3 = 0 . . . . . . . . . . . . collect terms

  y -3 = 0 . . . . . . . . . . . . . . . divide by -3.1

  y = 3 . . . . . . . . . . . . . . . add 3

  x = (11 -3(3))/2 = 2/2 = 1 . . . . . find x

The solution is (x, y) = (1, 3).

__

Additional comment

A graphing calculator confirms the solution.

Tickets for the school basketball game cost $4 each. Spencer plans to


make a table relating the number of people (x) to the money made from


ticket sales (y).


What is the most appropriate domain for Spencer's table?


A.


all integers


B.


all rational numbers


C.


all real numbers


D


all whole numbers

Answers

The most appropriate domain for Spencer's table would be D. all whole numbers.

To explain this, let's first understand the terms involved. In this context, the domain refers to the set of possible input values (x) for the function, which in this case, represents the number of people attending the school basketball game.

Option A, all integers, includes negative numbers, which are not suitable as you cannot have a negative number of people. Option B, all rational numbers, comprises fractions, which are also not applicable because you cannot have a fraction of a person attending the game. Option C, all real numbers, consists of all numbers including irrational numbers like π, which are not relevant in this context as well.

Option D, all whole numbers, represents the most suitable domain as it includes all non-negative integers (0, 1, 2, 3, ...). This set accurately represents the possible number of people attending the game, since you can have zero or a whole number of people attending but not negative or fractional values.

Therefore, Spencer should use whole numbers as the domain for his table to relate the number of people (x) to the money made from ticket sales (y).

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Find the length of the curve. y = ∫√25sin^2t - 1 dt, 0 < x < т/2

Answers

I apologize, but there seems to be some confusion in your question. The function given, y = ∫√25sin^2t - 1 dt, is not a curve but rather an indefinite integral expression. In order to find the length of a curve, we need a function defined explicitly in terms of x (or y) and its bounds. Could you please provide more information or clarify your question?
To find the length of the curve given by y = ∫√(25sin^2(t) - 1) dt from 0 to π/2, we need to calculate the definite integral.

First, let's set up the integral:

Length = ∫√(25sin^2(t) - 1) dt, with bounds from 0 to π/2

Unfortunately, this integral cannot be solved analytically using elementary functions. You will need to use a numerical method, such as the Trapezoidal Rule or Simpson's Rule, to approximate the value of the integral, and thus find the length of the curve.

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