What is the length of LM?

The area of smaller square is 81

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

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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.

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.

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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:

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

Answer:

19,500 people

Step-by-step explanation:

20% of 25,000 is 5,000.

Add 5,000 to 25,000 - this will give you 30,000. That is a 20% increase.

65% of 30,000 is 19,500, thus there are 19,500 people in the stadium.

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:

-4<x≤5

Step-by-step explanation:

An open circle means 'less than' or 'greater than' while a closed cirlce means 'less than or equal to' or 'greater than or equal to'

Answer:

i dont know i tried really hard im not really good at math to be honest once again sorry

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

-4+4=0

If the temperature starts at -4 four and increases by 4, the temperature will be 0.

39°

Try harder to achieve success

Answer:

370×1850= 6,84,500

and then

56,950+6,84,500=7,41,450

the population will be 7,41,450

The population of bacteria after 1850 hrs in a colony, if the number of bacteria doubles every 370 hours, is 1822400.

Along with addition, subtraction, and division, multiplication is one of the four basic mathematical operations. In mathematics, multiply refers to the continuous addition of sets of the same size.

Given:

The population of bacteria, P = 56950,

If the number of bacteria doubles every 370 hours then in 1850 hrs = 1850 / 370 = 5,

So, the no doubles 5 times in 1850 hrs,

Now if it doubles 1 time it will be 56950 × 2, and

for 5 times double population will be = 56950 × 2 × 2 × 2 ×2 × 2

P = 1822400

Therefore, the population of bacteria after 1850 hrs in a colony, if the number of bacteria doubles every 370 hours, is 1822400.

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Answer:

11,520

Step-by-step explanation:

this should be the prism you're talking about if not i dont know which one

Answer:

B. 11,520 mm³

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]

[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.

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:

5 times as many should be your answer.

Answer:

d

Step-by-step explanation:

The answer must be a multiple of 4, because 4q⁵rs⁴ is divisible by 4. Only option d has this condition.

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:

60

Step-by-step explanation:

If we look at the picture, we can see that its a right angle having a 90 degree.

We can make a equation with this as we know that m1 and m2 has to equal 90

x + y = 90

Since we know that m2 = 30 we can plug 30 for x

(30) + y = 90

Now we simply moving the 30 to the 90

y = 90 - 30

y = 60

Answer:

the answer is .....true

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

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

:)

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: 5/8m-3/8

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

the quotient of m and 7 = m/7