Please Help! In a proof to show two triangles are congruent if a given is PR ⟂ CK, which of the following statements most likely will be used within the proof?

Answer:

the answer is 8 units

Step-by-step explanation:

The radius of a circle given by the equation [tex]\rm x^2+y^2-2x+8y-47=0[/tex] is 8 units.

It is given that the circle equation is given by  [tex]\rm x^2+y^2-2x+8y-47=0[/tex]

It is required to find the radius of the circle.

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We circle the equation:

[tex]\rm x^2+y^2-2x+8y-47=0[/tex]

Converting this equation into the standard form of the circle:

[tex]\rm (x-a)^2+(y-b)^2=r^2[/tex]

[tex]\rm x^2+y^2-2x+8y-47=0[/tex]

[tex]\rm x^2+y^2-2x+8y-47+1-1+16-16=0[/tex]  (by adding and subtracting by                  

                                                                         1 and 16)

[tex]\rm x^2-2x+1+y^2+8y+16-1-16-47=0\\\\\rm (x-1)^2+(y-(-4))^2-64=0\\\\\rm (x-1)^2+(y-(-4))^2=64\\\\\rm (x-2)^2+(y-(-4))^2=8^2 \\\\[/tex]

By comparing with the standard circle equation, we get:

r = 8

Thus, the radius of a circle given by the equation [tex]\rm x^2+y^2-2x+8y-47=0[/tex]  is 8 units

Learn more about circle here:

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Answer:

4.6cm

Step-by-step explanation:

5.4 is the length of one side and if you have 2 sides that are equal you double that

5.4 x 2 = 10.8

15.4 - 10.8 = 4.6cm

Answer:

77

Step-by-step explanation:

The area of a rectangle is A = lw. 'A', the area, is 3927, and 'w', the width, is 51. By substituting the values in, we get that 3927 = 51L. Dividing both sides by 51, we get that L, the length, is 77.

Answer:

length= 52 feet,

width= 15 feet

Step-by-step explanation:

[tex]\textcolor{steelblue}{\text{\textcircled{1} Define the variables}}[/tex]

Let the length and the width of the rectangle bs L and W feet respectively.

L= 4W -8 -----(1)

Perimeter of rectangle= 2(length +width)

2(L +W)= 134

Divide both sides by 2:

L +W= 67 -----(2)

[tex]\textcolor{steelblue}{\text{\textcircled{2} Solve for one variable}}[/tex]

Substitute (1) into (2):

4W -8 +W= 67

5W -8= 66

5W= 67 +8

5W= 75

W= 75 ÷5

W= 15

[tex]\textcolor{steelblue}{\text{\textcircled{3} Solve for the other variable}}[/tex]

Substitute W= 15 into (1):

L= 4(15) -8

L= 60 -8

L= 52

[tex]\textcolor{steelblue}{\text{\textcircled{4} Write concluding statement}}[/tex]

Thus, the rectangle's length is 52 feet, and its width is 15 feet.

Answer:

The measure of each angle will be 10° and 170°.

Step-by-step explanation:

A supplementary angle refers to an angle that has the sum to be equal to 180°.

Let the small angle be represented by x

Therefore, the big angle will be: = 17 × x = 17x

Therefore, the value of both angles will be:

x + 17x = 180

18x = 180

Divide both side by 18

18x/18 = 180/18

x = 10

Therefore, the bigger angle will be:

17x = 17 × 10 = 170

Therefore, the angles are 10° and 170°

Answer:

10 and 170 degrees.

Step-by-step explanation:

If the angle is x degrees then its supplementary angle = 180-x degrees.

So x + 17x = 180

18x = 180

x = 10 degrees.

Answer:

Step-by-step explanation:

Answer: 120

Step-by-step explanation:

x/6 + 5 =25, subtract 5 on both sides

-5 -5

x/6 = 20, multiply both sides by 6

6(x/6) = 20(6)

x = 120

Answer:

The answer to your question is D 64

Step-by-step explanation:

hope this helps you have a wonderful day.

Answer:

Jenna is correct.

Step-by-step explanation:

See attached image.

Answer:

use a kittykat proportion

Step-by-step explanation:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \sin(37 \degree) = \frac{0.6}{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \frac{3}{5} = \frac{0.6}{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x = 5 \times 0.6[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 3 \div 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 1[/tex]

Therefore, the required value of x is 1

Answer:

[tex]\displaystyle 1[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x}{0,6} = csc\:37 \hookrightarrow 0,6csc\:37 = x \hookrightarrow 0,9969840846... = x \\ \\ 1 ≈ x[/tex]

OR

[tex]\displaystyle \frac{0,6}{x} = sin\:37 \hookrightarrow xsin\:37 = 0,6 \hookrightarrow \frac{0,6}{sin\:37} = x \hookrightarrow 0,9969840846... = x \\ \\ 1 ≈ x[/tex]

Information on trigonometric ratios

[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]

I am joyous to assist you at any time.

The nth term of the sequence whose integers are between 1 -7 such that there is the permission of repetition but no two consecutive digits must be even is 1.254 × 10¹¹

Consecutive numbers are those numbers that succeed each other in increasing order from least to greatest. The numbers that are given:

Now, suppose a (n) denotes the number of n-digit positive integers as stated in the question, thereby using:

Then, the number of n can be computed as n!

= (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)

= 1.254 × 10¹¹

Learn more about consecutive numbers here:
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The nth term of the series of integers is between 1 -7 such that there is the permission of repetition but no two consecutive digits must be even is 1.254 × 10¹¹

Consecutive numbers are those numbers that succeed by each other in increasing order from lowest to greatest such are 1, 2, 3, 4, 5, 6, or 7.

Now, suppose n represents the number of n-digit positive integers.

1, 2, 3, 4, 5, 6, or 7 with the permission of repetition no two consecutive digits are even.

Then, the number of n can be calculated as n!

= (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)

= 1.254 × 10¹¹

Learn more about consecutive numbers here:

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#SPJ4

Answer:

The answer is b. 979,000

Step-by-step explanation:

If you move the decimal right five time from 9.79 you would get 979,000

Answer:

x=4, perimeter is 30.

Step-by-step explanation:

Let's calcualte the perimeter of the two figures. I'm assuming the pentagon is regular else the problem lacks information.

[tex]5(x+2) = 3x+(2x-1)+(x+7)\\5x+10=6x+6\\4=x[/tex]

At this point the easiest to compute is the pentagon, one side is 6, the whole perimeter is 30.

Answer:

C

Step-by-step explanation:

sqrt(2 - 3x)/sqrt(4x) = 2

sqrt(2 - 3x) = 2×sqrt(4x)

now let's just square both sides

2 - 3x = 4×4x = 16x

2 = 19x

x = 2/19

Answer: 14%

Step-by-step explanation:

Answer:

w

Step-by-step explanation:

The number of pairs of shoes in the factory is approximately 2 × 10⁶  in 10 years.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

A shoe factory produces 1.81 × 10⁴ pairs of shoes each month.

Estimate the number of pairs of shoes the factory will produce if it maintains that rate for 10 years.

There are 1.2 × 10² months in 10 years.

1.81 ≈ 2 and 1.2 ≈ 1

The number of shoes in 10 years will be

→ (2 × 10⁴)(1 × 10²)

→ 2 × 10⁶

The number of pairs of shoes in the factory is approximately 2 × 10⁶  in 10 years.

More about the multiplication link is given below.

https://brainly.com/question/19943359

Answer: (-√(3) /2, 1/2)

Step-by-step explanation:

The triangle created is a 30 60 90 triangle, and thus the opposite side of the angle equals the y-coordinate which equals 1/2, and the adjacent side of the angle equals the x-coordinate which equals -√(3) /2

Answer:

[tex]\frac{ \sqrt{3} }{2} [/tex]

Step-by-step explanation:

[tex] \cos \bigg( \frac{11\pi}{6} \bigg) \\ \\ = \cos \bigg( 2\pi - \frac{\pi}{6} \bigg) \\ \\ = \cos \bigg(\frac{\pi}{6} \bigg) \\ \\ = \frac{ \sqrt{3} }{2} [/tex]

720000 liter

[tex]Known:\ a=10\ m,b=9\ m,h=8\ m.[/tex]

[tex]Because:\ V=abh\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (Volume\ caculation\ formula)[/tex]

[tex]Thus:\ V=10\times9\times8=720\ m^3[/tex]

[tex]Because\ 1\ m^3=1000\ L\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (unit\ conversion)[/tex]

[tex]Thus\ 720\ m^3=720000\ L[/tex]

I hope this helps you

:)

Step-by-step explanation:

[tex]70 \times \frac{35}{100} = 24 .5 [/tex]

Answer:

24.5

Step-by-step explanation:

35% can be broken down into 10% + 10% + 10% + 5%

To find 10% of 70, divide 70 by 10.

To divide a number by 10, move the decimal point 1 place to the left.

⇒ 70 ÷ 10 = 7

So 10% = 7

5% is half of 10%

⇒ 5% = 7 ÷ 2 = 3.5

Therefore,

10% + 10% + 10% + 5% = 7 + 7 + 7 + 3.5

                                    = 21 + 3.5

                                    = 24.5

Answer: 1/6

Step-by-step explanation: I think you multiply 3 times 3 because the other circle circle has an option the first doesn't have have.

Answer:

Wrong

Step-by-step explanation:

Eva must subtract 4*3/2=6 from each side to get 4x=2, the divide by 4 to get x=1/2

Another way:

First, divide both sides with 4 to get x+3/2=2. Then subtract 3/2 from each side and we will have x= 2-3/2= 1/2

39°

Try harder to achieve success

4 years

[tex]per\ year\ earn:2000\times 5\%=100[/tex]

[tex]years\ needed:\ \ \ \ \ 400\div 100=4[/tex]

I hope this helps you

:)

Answer:

4 years

Step-by-step explanation:

Given data

Simple interest= $400

Principal= $2000

Rate= 5%

The simple interest formula is given as

SI=PRT/100

substitute and solve for T

400=2000*5*T/100

cross multiply

400*100= 10000*T

40000=10000T

T= 40000/10000

T= 4 years

Hence the time taken is 4 years

Answer:

(y-4) = 2(X+1)

Step-by-step explanation:

The given eqaution is; y = 2x-5.......(i)

Now; the equation is in the form of y= mx+b.

Slope(m1) = 2.

As per the condition of parallel lines, the slope of the 1st equation (m1) = the slope of the 2nd equation (m2).

Therefore, m1= m2= 2

Now, use one point formula for finding the equation of the line which passes through the point.

(y-y1) = m2(x-x1)

~ Put all values.

(y-4) = 2(X+1)

You can simply write up here. But if you want to make it simplified form then, (look below)

~ simplify it.

y = 2x +2+4

The eqaution of the line which is parallel to y = 2x -5 and point (-1,4) is y = 2x + 6.

The expression which represents the volume of the prism, in cubic units, is one-half x³+ x².

Volume of prism is the amount of quantity, which is obtained in it in the 3 dimensional space. The volume of a prism is the product of the area of its base and height.

[tex]V=A_b\times h[/tex]

Here, ([tex]A_b[/tex]) is the area of the base and (h) is the height of the prism.

The side of the base of the triangular prism is x units. Thus the area of the base is,

[tex]A_b=\dfrac{x\times x}{2}\\A_b=\dfrac{x^2}{2}[/tex]

The height of this prism is (x+2) units long. Thus, the volume of the prism is,

[tex]V=\dfrac{x^2}{2}\times (x+2)\\V=\dfrac{1}{2}x^3+x^2[/tex]

Thus, the expression which represents the volume of the prism, in cubic units, is one-half x³+ x².

Learn more about the volume of a prism here;

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Answer:

1. A- 1/2x^3

2. 168

3. 927

4A. 48

4B. 336

5. A D

6. 1 3 3

7. 12 cm

8. 8 , 4

9. B

10. A C D

Step-by-step explanation:

whole thing right on edge

Answer:

6 feet

Step-by-step explanation:

8×8+x×x=10×10

x×x=100-64

x=6