Marcy is making a hooked circle-shaped rug for her mother. The circumference of the circle-shaped rug is 69.08 inches.

The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

What is the scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2. The new figure we receive will resemble the first figure, but every dimension will be double that of the first rectangle. The scale factor in this case will be denoted by the number 2.

Let us take the radius of the circle to be r

We know that circumference = 2πr and the area of a circle is πr²

As, Scale factor = Original circle / Scaled circle

From the question, scale factor = 2

Thus,

2 = Circumference of the Original circle / Circumference of the Scaled circle.

⇒ Circumference of the Scaled circle = (1/2) * Circumference of the Original circle

For the area as well, scale factor = 2

2 = Area of the Original circle / Area of the Scaled circle

⇒ Area of the scaled circle = (1/2) * Area of the original circle

Thus,

The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

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The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

What is the scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2. The new figure we receive will resemble the first figure, but every dimension will be double that of the first rectangle. The scale factor in this case will be denoted by the number 2.

Let us take the radius of the circle to be r

We know that circumference = 2πr and the area of a circle is πr²

As, Scale factor = Original circle / Scaled circle

From the question, scale factor = 2

Thus,

2 = Circumference of the Original circle / Circumference of the Scaled circle.

⇒ Circumference of the Scaled circle = (1/2) * Circumference of the Original circle

For the area as well, scale factor = 2

2 = Area of the Original circle / Area of the Scaled circle

⇒ Area of the scaled circle = (1/2) * Area of the original circle

Thus,

The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.

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The graph has 2 x-intercepts.

What is the quadratic function?

In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. A quadratic polynomial defines the polynomial function known as a quadratic function.

We have,

f(x) = -3(x-3)² + 1

by simplifying the equation above

-3(x² -6x + 9) + 1 = 0

-3x² + 18x - 27 + 1 = 0

-3x² + 18x - 26 = 0

By calculating the quadratic equation we get

[tex]x=\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

[tex]x=\frac{ -18 \pm \sqrt{18^2 - 4(-3)(-26)} }{2(-3)}[/tex]

[tex]x= 3 \pm \frac{\sqrt{3} }{3}[/tex]

x = 2.42265,      x = 3.57735

so the points are (0, 0) and (2.4, 3.6)

The graph crosses the x-axis at (2.4, 3.6)

Hence, the graph has 2 x-intercepts.

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Answer:

[tex]60=4x\\\\15=x[/tex]

I hope this helped.

Answer: y = -4x+60

y is -4 times x plus 60

For the function, y = log₄ (x + 16) - 1, it has x-intercept of -12 and y-intercept of 1.

Logarithmic functions are functions expressed in another way for exponential functions. It is the power to which any number should be raised to yield other values.

Logₐ x = n can be written in exponential form as x = aⁿ.

y = log₄ (x + 16) - 1

x-intercept is the x-coordinate of the point when y = 0.

0 = log₄ (x + 16) - 1

For the left hand side to be equal to 0, the term log₄ (x + 16) must be equal to 1.

log₄ (x + 16) = 1  

⇒ x + 16 = 4       (∵ logₐ a = 1)

⇒ x = -12

y-intercept is the y-coordinate of the point where x = 0.

y = log₄ (0 + 16) - 1

y =  log₄ (16) - 1

y =  log₄ (4²) - 1

logₐ mⁿ = n logₐ m

⇒ y = 2 log₄ (4) - 1

⇒ y = 2 - 1     (∵ log₄ (4) = 1)

⇒ y = 1

Hence, the function y = log₄ (x + 16) - 1 has x-intercept of -12 and y-intercept of 1.

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Answer:

Is the question written correctly?  As written, the answer is 4.16 x [tex]10^{-8}[/tex].

Step-by-step explanation:

1+3+5+8+7+7+8= 39

39 = 937392920x

x = 39/(937392920)

x = 4.16 x [tex]10^{-8}[/tex]

Answer:

[tex]122.5[/tex]

Step-by-step explanation:

[tex]circumference \: = 2\pi \:r[/tex]

[tex]\pi = 3.14[/tex]

[tex]r = 19.5[/tex]

Replacing:

[tex]2 \times 3.14 \times 19.5 = 122.46[/tex]

Therefore, final answer[tex] = 122.5[/tex](to the nearest tenth)

The answer is 122.5

In the given question, we have given the radius of the circle and we need to find the circumference of the same.

To need to find the circumference, we must recall this formula

Circumference of circle = [tex]2\pi r[/tex]

Now, according to the question

Radius = 19.5 cm

Circumference = 2 * [tex]\pi[/tex] * 19.5

                         = 2 * 3.14 * 19.5       (Taking [tex]\pi[/tex] = 3.14)

                         = 122.5 cm

Therefore, the circumference of a circle with radius 19.5 cm is 122.5 cm

On rounding off the answer to the nearest tenth, it remains the same.

Hence, the final answer to the question is 122.5 cm.

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We can conclude there is an association between age group of the viewer and amount of violence watched and its  55+ year-olds are likely to be categorized as low-violence.

What is segmented bar graph?

In a stacked (or segmented) bar graph:

The horizontal axis still represents one variable, with every bar representing one in every of the catgories of the variable.

Each bar is segmented in step with the classes of the second variable. or else, every bar will be seen as being created from smaller bars stacked on high of every different.

Main body:

We can know from the graph The older the age, the more the Tow-violence, 55+ year-olds are likely to be categorized as low-violence"

so there is an association Choose D

Hence ,  we can conclude there is an association between age group of the viewer and amount of violence watched and its  55+ year-olds are likely to be categorized as low-violence.

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The rate at which the distance from the plane to the station is increasing when it has a total distance of 3 mi away from the station is 313.05 mi/h .

Given :

a plane flying horizontally at an altitude of 2 mi and a speed of 420 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it has a total distance of 3 mi away from the station .

Here ,

h = 2

d = 3

we know that ,

x = [tex]\sqrt{d^2 - h^2}[/tex]

= [tex]\sqrt{3^2 - 2^2}[/tex]

= [tex]\sqrt{9 -4}[/tex]

= [tex]\sqrt{5}[/tex]

d = [tex]\sqrt{5}[/tex] * 420 / 3

= [tex]\sqrt{5}[/tex] * 140

= 313.05 mi/h

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The equation that used to determine the dimension is 2(2x+10) = 300 and the dimensions of the rectangular yard is 80 foot and 70 foot

Total length of the fence = 300 foot

Consider the width of the rectangular yard = x

The length of the rectangular yard = x + 10

The perimeter of the rectangle = 2(l + w)

Where l is the length and w is the width

Substitute the values in the equation

300 = 2(x+10 + x)

300 = 2(2x + 10)

4x + 20 = 300

4x = 300 - 20

4x = 280

x = 280/4

x = 70 foot

The length = x + 10

= 70 + 10

= 80 foot

Therefore, the equation is 2(2x+10) = 300 and dimensions are 80 foot and 70 foot

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Answer: 150+30n ≤ p

Step-by-step explanation:

150 is your starting amount, and you add 30 lbs of how many ever boxes (n) onto your plane. So far, you have 150 + 30n. Because there is a limit of p amount that you can't exceed, you need a less than or equal to sign because it can be p amount but not over p amount. So your answer is 150 +30n ≤ p

To test the null hypothesis that there is no difference in parents' wealth for the different levels of schooling, a one-way ANOVA (analysis of variance) test should be used.

To compare the means of two or more groups, statisticians employ the analysis of variance (ANOVA) test. It is used to assess whether there are any significant variations in the means of the groups and to pinpoint which group or groups have significantly different means. The null hypothesis, according to which there is no difference between the group means, is evaluated using the ANOVA test using the F-statistic. If the F-statistic is significant, at least one of the groups has a mean that differs from the others in a meaningful way. To examine how several treatments or circumstances affect a response variable, investigations frequently utilize an ANOVA. It can also be used in non-experimental research to compare the means of different groups.

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From the given picture of a triangle, we have come to find that variable x = 7 and y = 4

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

3x - 5 = y + 12  (if two angles of a triangle are equal, the sides opposite                    

                          them are also equal)   ------------(1)

Also, 3x - 5 = 5y - 4     (sides of a equilateral  triangle are equal)

So,  5y - 4 = y + 12

       5y - y = 12 + 4

         4y = 16

           y = 4

Now,

Put value of y in equation (1)

3x - 5 = y + 12

3x = 4 +12 + 5

3x = 21

x = 7

Hence, x = 7 and y = 4

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Answer:

Function • Quadratic Function •

Absolute Value Inequalities • Linear Function

A small airplane can fly about 124.8 miles in one hour.

In this question, we have been given a small airplane flew 104 miles in 50 minutes.

We need to find the distance the airplane would cover in an hour.

Let a small airplane can fly 'x' miles in one hour.

We know that 1 hour = 60 minutes

Using proportionality we get an equation,

x/104 = 60/50

We solve above equation.

50x = 60 * 104

x = 6240/50

x = 124.8

So, the distance would be 124.8 miles

Therefore, an airplane can fly 124.8 miles in an hour.

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Answer:

i think it is the bottom one

Step-by-step explanation:

Answer:q<-6.87

Step-by-step explanation:

isolate q by adding 2.01 to both sides

-q>6.87

divide by side by -1, and since it is negative flip the sign

q<-6.87

When Akbar is 9 years older than Yasir and Hamid is 2 years younger than Yasir then, the expression for their sum of ages is 3x+7

A linear equation is a mathematical equation that describes a straight line. It is a first-degree polynomial equation, which means that the largest exponent of the variables is 1. Since a and b are constants and x and y are variables, linear equations have the general form ax+by=c. A straight line forms on a coordinate plane when the values of x and y fulfil the expression. The connection between two variables or the price of a product are two examples of real-world events that are frequently modelled using linear equations. Solving a linear equation entails determining the values of the variables that make the equation true. Different techniques, such graphing, substitution, or elimination, can be used to accomplish this.

How to solve?

Let x be Yasir's age

Akbar is x+9

Hamid is x-2

The sum of their ages is x+(x+9)+(x-2)

=3x+7

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Answer:

3/4>2/3

Explanation:

3/4 is the same as 3*3/4*3, which equals 9/12.

2/3 is the same as 2*4/3*4, which equals 8/12.

Thus, 3/4=9/12 and 2/3=8/12.

9/12 > 8/12, and since 3/4=9/12 and 2/3=8/12, 3/4>2/3.

Hope this helps.

Answer: 56

Step-by-step explanation: 23+5=56

The required number solutions of given quadratic equation is -1 or 5/2.

A quadratic equation in math is a second-degree condition of the structure ax^2 + bx + c = 0. Here a, b, are the coefficients, c is the steady term, and x is the variable. Since the variable x is of the subsequent degree, there are two roots or deals with this quadratic condition.

We have,

x-1/x+1=3/2x+2

(x - 1)(2x + 2) = 3(x + 1)

2x^2+2x-2x-2 = 3x+3

2x^2-3x-5 = 0

2x^2-5x+2x-5 = 0

x(2x-5)+(2x-5)

(x+1)(2x-5) = 0

x = -1 or x = 5/2

Thus, solution of equation is -1 or 5/2.

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Answer: 178.25

Step-by-step explanation:

124.25 + 223.56 - 89.56 - 80.00

Answer: $178.25

Step-by-step explanation: Your balance on May 15 is $124.25. On May 20, you deposit $223.56, which increases your balance to $124.25 + $223.56 = $347.81. You then write a check for $89.56, which decreases your balance to $347.81 - $89.56 = $258.25. Finally, you withdraw $80.00 from an ATM on May 25, which decreases your balance to $258.25 - $80.00 = $178.25. Therefore, your current balance is $178.25.

Answer:

135

Step-by-step explanation:

The solution to the system of equations is (d) (-2, 1)

From the question, we have the following parameters that can be used in our computation:

y = 2x + 5

y = -1/4x + 0.5

Substitute y = 2x + 5  in the equation y = -1/4x + 0.5

So, we have the following representation

-1/4x + 0.5 = 2x + 5

Collect the like terms

So, the equation becomes

2x + 1/4x = 0.5- 5

So, we have

2.25x = -4.5

Divide by 2.25

x = -2

Substitute x = -2 in y = 2x + 5

y = 2 x -2 + 5

y = 1

Hence, the solution is (d) (-2, 1)

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The area of the resulting shape if a circle with a 12-inch diameter is folded in half and then folded in half again is 28.26 square inches

If a circle with a 12-inch diameter is folded into half and then folded into half again the circle will become a quadrant.

So,

The area of a quadrant is area of a circle divided by 4

Area of a quadrant = πr² / 4

Diameter of a circle = 2r

12 = 2r

divide both sides by 2

r = 6 inch

Area of the quadrant = 3.14 × (6)²/4

Area of the quadrant = (3.14 × 36) /4

Area of the quadrant = 113.04 / 4

Area of the quadrant = 28.26 square inches

In conclusion, the area of the quadrant is 28.26 square inches

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Answer:

----------------------------------------

The perimeter is:

If the perimeter is less than 20, then the inequality is:

Answer:

x < 4

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Therefore, from inspection of the triangle:

⇒ Perimeter = 4 + 9 + x + 3

⇒ Perimeter = x + 16

If the perimeter is less than 20 meters then:

⇒ x + 16 < 20

Solve the inequality:

⇒ x + 16 - 16 < 20 - 16

⇒ x < 4

Students will board the bus at 1350 even though it is not totally full.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few cmmon units for measuring area

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

723+685

1408-58

1350

Hence, Students will board the bus at 1350 even though it is not totally full.

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Answer: 34.5

Step-by-step explanation:

50 + 10 = 60 (birthday and dog walking)

60 - 7.50 = 53.5 (paid what she owed)

52.5 - 18 = 34.5 (bought a shirt)

Since 3 | 1+3 | = 3 |4|

                      = 3·4

                      = 12

and

since 3 | -7+3 | = 3 |-4|

                        = 3·4

                        = 12,

both 1 and -7 check as solutions,

so C: x = 1 or x = -7

The number of students who drive to school is 125.

What is  number ?

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of expressing numbers that uses digits or symbols to represent them.

At Jefferson High School, there are 250 students who drive to school and 375 students who ride the bus to school. The number of students who drive to school is

=375-250

=125

Hence, the number of students who drive to school is 125.

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