A rope is 72 feet long. What is the length of the rope in yards

Answer:

1. option A is correct i.e., [tex]\(90^{\circ}[/tex].

2. option B is correct.

3. the coordinates of the car after a rotation of [tex]\(270^{\circ}[/tex] is (0,-30).

Step-by-step explanation:

1. The angle of rotation is [tex]\(90^{\circ}[/tex].

To calculate the angle of rotation we can use a protractor and measure the angle between two corresponding angles, using point C as a center.

2. Given: ΔPRS with coordinates P(-3,2), R(2,5) and S(0,0) is rotated through an angle of 270°, the new image will be as follows;

The formula for rotation through 270° is: (x,y) → (y,-x)

hence our image will be at point:

P(-3,2)→P'(2,3)

R(2,5)→R'(5,-2)

S(0,0)→S'(0,0)

from the above, the approximate image will be option B.

3. Given: Ferris wheel is drawn on a coordinate plane at the point P(30,0). The coordinates of the car after a rotation of [tex]\(270^{\circ}[/tex] is (0,-30).

Because the formula for rotation through 270° is: (x,y) → (y,-x).

So, point P(30,0)→P'(0,-30).

Follow below steps:

The problem involves finding the radius of a quarter circle given its perimeter. The perimeter of a full circle is known as its circumference, represented by the formula C = 2πr for a circle of radius r. However, for a quarter circle, only 1/4 of this circumference plus twice the radius (the straight sides of the quarter circle) constitutes the perimeter. Therefore, the perimeter (P) can be expressed as P = (πr)/2 + 2r.

Given that the perimeter is 32.13, we use the formula to set up the equation 32.13 = (πr)/2 + 2r. To solve for r, combine the like terms to get (2 + π/2)r = 32.13 and then isolate r by dividing both sides of the equation by (2 + π/2). Using the approximate value of π = 3.14159, you continue with the arithmetic to find the exact value of the radius.

Remember that precision is important in mathematics. When providing an answer, consider the number of significant figures supplied in the given data and maintain the same level of precision in the final answer.

The radius of the quarter circle is 20.48 units.

To find the radius of a quarter circle given its perimeter, we can start by understanding the formula for the perimeter of a circle.

The perimeter of a full circle is given by [tex]\( P = 2\pi r \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle. Since we are dealing with a quarter circle, the perimeter would be one-fourth of the perimeter of a full circle.

The radius of the quarter circle as [tex]\( R \)[/tex]. Then, the perimeter of the quarter circle is [tex]\( \frac{1}{4} \times 2\pi R = \frac{\pi R}{2} \)[/tex].

The perimeter of the quarter circle is 32.13 units, we can set up the equation:

[tex]\[ \frac{\pi R}{2} = 32.13 \][/tex]

To solve for [tex]\( R \)[/tex], isolate it by multiplying both sides of the equation by [tex]\( \frac{2}{\pi} \)[/tex]:

[tex]\[ R = 2 \times \frac{32.13}{\pi} \][/tex]

[tex]\[ R \approx 20.48 \][/tex]

Final answer:

Abigail will need to use 0.8 cup of flour to make 60% more pancakes than the original recipe.

Explanation:

To determine how much flour Abigail needs to use, we can set up a proportion based on the increase in the number of pancakes. If her mother's recipe calls for 1/2 cup of flour for a certain number of pancakes, and Abigail wants to make 60% more pancakes, then she will need 60% more flour. To calculate the amount of flour, we can multiply the original amount by 1.6 (which is 100% + 60%).

Flour needed = 1/2 cup * 1.6 = 0.8 cup

Therefore, Abigail will need to use 0.8 cup of flour to make 60% more pancakes than the original recipe.

Answer:

D is the answer

Step-by-step explanation:

yw :)

The solution to the equation is 6 if equation is 6(2x - 11) + 15 = 21 the answer is 6.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a mathematical equation:

6(2x - 11) + 15 = 21

DIstributive property:

12x - 66 + 15 = 21

Subtraction property:

12x -51 = 21

Add 51 on both side:

12x -51 + 51 = 21 + 51

12x = 72   (adding like terms)

x = 6 (divide by 12 on both side)

Thus, the solution to the equation is 6 if equation is 6(2x - 11) + 15 = 21 the answer is 6.

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Answer:  The correct option is

(D) 17.5.

Step-by-step explanation:  Given that in the diagram shown, AC is perpendicular to BD, where

[tex]m\angle BEC=(6x-15)^\circ,\\\\m\angle AED=(3y+12)^\circ.[/tex]

We are to find the value of x.

Since AC is perpendicular to BD and they are intersecting each other at the point E.

So, all the four angles made by this intersection are right angles.

That is, angle BEC is also a right angle.

Therefore, we get

[tex]m\angle BEC=90^circ\\\\\Rightarrow (6x-15)^\circ=90^\circ\\\\\Rightarrow 6x-15=90\\\\\Rightarrow 6x=105\\\\\Rightarrow x=\dfrac{105}{6}\\\\\Rightarrow x=17.5.[/tex]

Thus, the required value of x is 17.5.

Option (D) is CORRECT.

To rewrite 1/2^5 in exponential notation, remember that 1/2^5 is the same as 2^-5. Therefore, 1/2^5 = 2^-5.

Rewrite the given expression in the form 2u where u is a constant or an algebraic expression.

To rewrite 1/25 in exponential notation, we need to understand that 1/25 is the same as (2-1)5. Using the property of exponents, we can rewrite this as 2-5, where -5 is the new exponent.

Therefore, 1/25 = 2-5, where u = -5.

The distance from the edge of Frank's garden to the center of the garden is about 2.815 feet.

To find the approximate distance from the edge of Frank's garden to the center, we first need to determine the radius of the circular garden. We are given the area (A) of the garden, which is 100 square feet. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

We can rearrange the formula to solve for the radius:

r² = A / π

Now, plug in the given area:

r² = 100 ft² / π

Calculate the square of π (approximately 3.1416):

r² = 100 / 3.1416

r² = 31.8309

Now, find the square root of r² to get the radius:

r ≈ √31.8309

r = 5.63 ft

Now that we have the radius, we can find the distance from the edge to the center. In a circle, the distance from the edge to the center is half the radius. So, we can calculate this as follows:

Distance from edge to center ≈ (1/2) * radius

Distance from edge to center ≈ (1/2) * 5.63 ft

Distance from edge to center ≈ 2.815 ft

Answer   236 square millimeters      

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The expression (x+a)(x+b) can not be written as a(x+b) + x(x+b). Therefore, option A is the correct answer.

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

Using distributive property, we get

x(x+b)+a(x+b)

= x²+bx+ax+ab

= x²+x(a+b)+ab

The expression (x+a)(x+b) can not be written as a(x+b) + x(x+b). Therefore, option A is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

The expression (x+a)(x+b) can not be written as

a) a(x+b) + x(x+b)

b) x² + (a+b)x + ab

c) x² + abx + ab

d) x(x+a) + b (x+a)

the general rule for estimating is to look at the digit to the right of the digit you want to estimate. Estimating or rounding to the nearest whole number means looking at the digit to the right of the decimal. if you see a digit greater than 5,round up, an if it's less than 5, round down. we would go to the right of 18.3 which would be (6.37), so we're going to to round that to the nearest whole number which would be 7 because it's more than 5. this shows how you estimate 18.3 an (6.37) hope this helps have a good day♡