terry ran around a circular track . if the radius of the track is 200 feet how far did tarry run​

The two given angles are vertical angles and equal each other:

3x + 50 = 6x -10

Now solve for x:

Subtract 3x from both sides:

50 = 3x -10

Add 10 to both sides:

60 = 3x

Divide both sides by 3

X = 20

The radius of the circle is approximately 7.5 cm, and the corresponding area is approximately 56.25π cm², as calculated using the formulas for circumference and area. Here option C is correct.

1: Find the radius using the circumference formula

We know the circumference C = 157 cm.

We also know the formula for circumference of a circle: C = 2πr, where r is the radius.

Rearranging the formula to solve for r, we get: r = C / (2π).

Substituting C with 157, we get: r = 157 / (2π) ≈ 7.5 cm.

2: Calculate the area using the area formula

Now that we know the radius, we can use the formula for the area of a circle: A = πr², where A is the area.

Substituting r with 7.5, we get: A = π * (7.5)² ≈ 56.25π cm².

Therefore, the area of the circle is 56.25π cm². Here option C is correct.

Complete question:

The circumference of a circle is 157 centimeters. What is the area of the circle in terms of t?

A - 7.570 cm?

B - 157 cm

C - 56.251 cm

D - 2257 cm

Answer:

1/4 2/5 4x5=20

Step-by-step explanation:

Step-by-step explanation:

First, you recognize the algorithm for the equation: A=P(1+r)^n. This is the algorithm for interest. P is the amount of initial money (in this case, 6500), r is the interest rate (6%, or 0.06), and n is the number of times it is being compounded. Since half a year is given to me, 6 months is what I will be using, or just 6.

Next, plug in the numbers. The equation is now: A=6500(1+0.06)^6.

Now time to solve. First add what's in the parenthesis, and put it to the power of 6, for 6 months. Then multiply that amount to the initial dollar amount; 6500. This will leave you with 9,220.37.

Your answer would be 4000.

The only step needed:

Multiply 400 by 10.

400 ---> 400×10 ---> 4000

Hope this helps, :)

it is 3r.75 it totally right

Answer:

6

Step-by-step explanation:

Just remember the order of operations (PEMDAS)

5 - 2 + 12 / 4, first divide

5 - 2 + 3, then proceed from left to right

3 + 3 = 6

Answer:

25.4 feet tall

Step-by-step explanation:

254 divided by 10 equals 25.4

The height of the apple tree that you expect an apple tree to be ​25.4 feet.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A coast redwood tree is about 10 times as tall as an apple tree.

Let 'x' and 'y' be the height of redwood and apple trees. Then the equation is given as,

y = x / 10

One of the tallest coast redwoods even measured 254 feet tall. Then we have

y = 254 / 10

y = 25.4 feet

The height of the apple tree that you expect an apple tree to be ​25.4 feet.

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Answer:

16[tex]\pi[/tex]

Step-by-step explanation:

we know that the formula for finding area of circle is A=[tex]\pi[/tex]r^2. and circumference of circle can be calculated by c=2[tex]\pi[/tex]r.

first we need find radius from circumference formula and put in area formula to get the desired result.

for radius, r=c/2[tex]\pi[/tex] =8[tex]\pi[/tex]/2[tex]\pi[/tex] we get 4. now put in area formula as shown above.

we get , A=[tex]\pi[/tex]*(4)^2 =[tex]\pi[/tex]*4*4 =16[tex]\pi[/tex]

Answer:

The answer is B 16

Step-by-step

There are quite a few possible combinations that are minimum 8 sodas, and under $20.

1. 4 Dr. Peppers and 4 Sprites. $2.98 times 4 = $11.92. $1.99 times 4 = $7.96. $7.96 + $11.92 = $19.88.

2. 3 Dr. Peppers and 5 Sprites. $2.98 times 3 = $8.94. $1.99 times 5 = $9.95. $9.95 + $8.94 = $18.89.

3. 2 Dr. Peppers and 6 Sprites. $2.98 times 2 = $5.96. $1.99 times 6 = $11.94. $11.94 + $5.96 = $17.90.

4. 2 Dr. Peppers and 7 Sprites. $2.98 times 2 = $5.96. $1.99 times 7 = $13.93. $5.96 + $13.93 = $19.89.

5. 1 Dr. Pepper and 7 Sprites. $2.98 times 1 = $2.98. $1.99 times 7 = $13.93. $2.98 + $13.93 = $16.91.

6. 1 Dr. Pepper and 8 Sprites. $2.98 times 1 = $2.98. $1.99 times 8 = $15.92. $15.92 + $2.98 = $18.90.

I hope this helps!

Mean: 175/5 = 35.

Median: 0, 25, 25, 25, 100 - 25 is in the middle.

Mode: 25, it appears the most.

The outlier 100 affects the data, because the number 100 still farthest from the main cluster. (Sorry if this is wrong)

2 x 7 x 7 or in exponential form, 2 x 7². 98 turns into 2 times 49, then 49 turns into 7 times 7.

The prime factorization of 98 is equal to 2 x 7².

The prime factorization of 98 involves breaking it down into prime numbers that multiply together to give the original number, 98.

The process for finding the prime factors of 98 is as follows:

Start with the smallest prime number, 2.

Since 98 is an even number, it is divisible by 2. So, divide 98 by 2 to get 49.

Now, 49 is not divisible by 2, so we try the next prime number, which is 3.

Since 49 is not divisible by 3 either, we move to the next prime number, 5, and so on until we reach 7, which does divide 49.

Divide 49 by 7 to get 7. So, 49 is 7 multiplied by 7, both of which are prime numbers.

Putting it all together, the prime factorization of 98 is 2 × 7 × 7 or 2 × 7².

Answer:

3

Step-by-step explanation:

I think you misses attaching the photo, so please have a look at my photo for your better understanding.

We know the formula for rate of change of the  parabola line:

[tex]\frac{f(b)- f(a)}{b-a}[/tex]

Given here:

a= 2 => f(a) = 2

b=6 => f(b) = 2

Substitute all the values into the function, we have:

[tex]\frac{14-2}{6-2} = 3[/tex]

So the rate of change is 3

Answer:

D.) 3

Step-by-step explanation:

Got it right on the assignment

Width of the rectangle is 4 units

Step-by-step explanation:

Area of the rectangle = length × width

⇒ 20 = x (x + 1)

⇒ 20 = x² + x

⇒ x² + x - 20 = 0

⇒ x² + 5x - 4x - 20 = 0 (Using Product Sum rule to factorize)

⇒ x(x + 5) - 4(x + 5) = 0

⇒ (x + 5)(x - 4) = 0

⇒ x = -5, 4 (negative value is neglected)

x = 4

Final answer:

The solution reveals that the width of the rectangle is 4 units.

Explanation:

The student is asking to find the width of the rectangle when the length is given as the sum of the width and 1 unit, and the area of the rectangle is 20 square units.

To solve this, we can set up an equation using the area formula for a rectangle, A = length * width, where the area (A) is 20 square units.

Let's denote the width as w units.

Then the length can be expressed as w + 1 units. Substituting these expressions into the area formula gives us:

20 = w * (w + 1)

Expanding the right side, we get:

20 = w² + w

This is a quadratic equation, which we can solve by setting it equal to zero:

w² + w - 20 = 0

Factoring the quadratic equation, we find:

(w + 5)(w - 4) = 0

Therefore, w could be -5 or +4. Since a width cannot be negative, the only reasonable solution is w = 4 units.

Thus, the width of the rectangle is 4 units.

Answer:

we can write

3 as a percent of 5 as

as is = to sign

percent is 100

and of is multiplication sign that gives us

3=x/100×5

x=(3×100)/5

x=300/5

x=60

so 3 is 60% of 5

Answer:

The answers would be 60%

Step-by-step explanation:

Answer:

{ - 9, - 7, - 3, - 1 }

Step-by-step explanation:

To obtain the range substitute the values of x from the domain into f(x)

f(- 2) = - 2(- 2) - 5 = 4 - 5 = - 1

f(- 1) = - 2(- 1) - 5 = 2 - 5 = - 3

f(1) = - 2(1) - 5 = - 2 - 5 = - 7

f(2) = - 2(2) - 5 = - 4 - 5 = - 9

range is { - 9, - 7, - 3, - 1 }

Answer:

4(4)= 16

4(5)= 20

4(6)=24

4(7)= 28

4(8)= 32

4(9)= 36

4(10)= 40

Step-by-step explanation:

Answer:

b. 4

Step-by-step explanation:

Given f(x) = 4x - 4 and g(x) = x - 1, we can find (f/g)(x) by dividing f(x) by g(x):

(f/g)(x) = (4x - 4)/(x - 1)

Now, substituting x = -4 into the expression

(f/g)(-4) = (4*(-4) - 4)/((-4) - 1) = (-16 - 4)/(-5) = -20/-5 = 4

Therefore, the correct answer is b. 4.

Given the function g(x) = x - 1, let's solve (f/g)(-4) using the function f(x) = 4x - 4.

To find (f/g)(-4), we need to evaluate the expression (f(x)/g(x)) at x = -4.

First, let's find the value of f(x)/g(x) for any x:

(f/g)(x) = f(x)/g(x) = (4x - 4)/(x - 1)

Now, substituting x = -4 into the expression:

(f/g)(-4) = (4(-4) - 4)/((-4) - 1) = (-16 - 4)/(-5) = -20/-5 = 4

Therefore, the correct answer is b. 4.

Step-by-step explanation:

x=k/y------(1)

k=xy

k= 7×3

k=21

from equation 1

x=k/y

y=k/x

y=21/9

y = 2.33

Answer:

3.85714285714

Step-by-step explanation:

7 = 3

9 = y

9*3=27

27/7 = 3.85714285714

To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothegm. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothegm = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x<33

Interval Notation:

(−∞,33)

Solution:

Given that we have to factor -3y - 18

Use the distributive property,

a(b + c) = ab + bc

From given,

-3y - 18

Factor out the greatest common factor of 3 and 18

The factors of 3 are: 1, 3

The factors of 18 are: 1, 2, 3, 6, 9, 18

Then the greatest common factor is 3

Factot out 3 from given expression

-3y - 18 = 3( - y - 6)

Or else we can rewrite as,

-3y - 18 = -3(y + 6)

Thus the given expression is factored

Answer:

od=2(13)

Step-by-step explanation:

Diameter of a circle is two times of its radius.

Answer: It wouldn’t be 13 to the second power you have to divide 13 by 2 then do that by the second power 13/2=6.5 than 6.5 to the second power so it would be 13x3.14=40.82

Step-by-step explanation:

Step-by-step explanation:

√17= 4.12

Therefore, we need to find an irrational no. between 4.1 and 4.12

So, the correct option is a

4.1001000100001000001....

Answer:

[tex] {f}^{ - 1} (x) = 3 {x}^{2} - 3[/tex]

Step-by-step explanation:

We want to find the inverse of

[tex] y = \sqrt[3]{ \frac{x}{3} + 1} [/tex]

We interchange x and y to get:

[tex]x= \sqrt[3]{ \frac{y}{3} + 1} [/tex]

We solve for y;

[tex] {x}^{2} = \frac{y}{3} + 1[/tex]

Multiply through by 3

[tex]3 {x}^{2} = y + 3[/tex]

Subtract 1 from both sides:

[tex]y = 3 {x}^{2} - 3[/tex]

Therefore the inverse is

[tex] {f}^{ - 1} (x) = 3 {x}^{2} - 3[/tex]

Answer:

2

Step-by-step explanation:

1/4 times 8 = 2

Answer: She jogged 2 miles

Step-by-step explanation: 1\4 x 8 which will give you 8\4, then you simplify it and you get 2.

The height of an object off the ground h after t seconds is [tex]h(t)=-16t^2+128t[/tex] and the rate of change of h is 192.

Given data:

The average rate of change of a function over an interval [a,b] is given by the formula:

[tex]R=\frac{f(b)-f(a)}{b-a}[/tex]

Now, the function [tex]h(t)=-16t^2+128t[/tex] represents the height of an object off the ground at time t seconds. We are asked to find the average rate of change of h over the interval [4,8].

So, the value of a = 4 and b = 8.

[tex]h(8)=-16(8)^2+128(8)[/tex]

[tex]h(4)=-16(4)^2+128(4)[/tex]

On simplifying the equation:

[tex]R=\frac{h(8)-h(4)}{8-4}[/tex]

[tex]R=\frac{768}{4}[/tex]

[tex]R=192[/tex]

Hence, the average rate of change of h over the interval is 192 feet per second.

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The average rate of change of h over the interval [4,8] is -64 feet per second. This is found by substituting the values of a = 4 and b = 8 into the equation h(t) = -16t² + 128t and into the formula for average rate of change.

To find the average rate of change of h over the interval [4, 8], we use the formula for the average rate of change: (h(b) - h(a)) / (b - a). Here, a = 4 and b = 8.

First, calculate h(a) and h(b) using the given equation h(t) = -16t² + 128t:

Substitute h(a) and h(b) into the formula to get:
(0 - 256) / (8 - 4) =-256/4 = -64.

So, the average rate of change of h over the interval [4, 8] is -64 feet per second.

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Answer:the slope is 3/9

Step-by-step explanation:use the y intercept form

Answer:

3

Step-by-step explanation:

Slope = change in y/change in x

That’s y2 - y1 /x2 - x1

Given

x1 = 2

y1 = 5

x2 = -1

y2 = -4

Slope = -4 - 5 /-1 - 2

= -9/-3

= 3