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o-na [289]
3 years ago
7

The sum of three numbers is 72 the second number is three times the third the third number is eight more than the first what are

the numbers
Mathematics
1 answer:
Rina8888 [55]3 years ago
6 0

Answer:

Our three numbers are 8, 48, and 16.

Step-by-step explanation:

Let the first, second, and third numbers be <em>x</em>, <em>y</em>, and <em>z</em>, respectively.

The sum of them is 72. In other words:

x + y + z = 72

The second number <em>y</em> is three times the third number <em>z</em>. So:

y = 3z

And the third number <em>z</em> is eight more than the first number <em>x</em>. So:

z = x + 8

To find the numbers, solve for the system. We can substitute the last two equations into the first:

x + (3z) + ( x + 8) = 72

Substitute again:

\displaystyle x + 3(x+8) + x+8 = 72

Solve for <em>x</em>. Distribute:

x+3x+24+x+8=72

Combine like term:

5x + 32 = 72

Subtract:

5x = 40

And divide:

x=8

Thus, the first number is eight.

And since the third number is eight more than the first, the third number <em>z</em> is 16.

The second number is three times the third. Thus, the second number <em>y</em> is 3(16) or 48.

Our three numbers are 8, 48, and 16.

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Answer:

25\pi

Step-by-step explanation:

The formula for the area of a circle is A=\pi r^{2}, r is your radius, A is your area, and π is pi (3.1415...). You plug in your radius, or 5 into r, square it, 25, and multiply it by pi. You may be asked to use a certain number of digits of pi, and in that case you multiply for example 3.14 by 25, however 25\pi is the exact answer.

6 0
2 years ago
PLEASE HELP! find (1,2) obtained by translating 2 units down followed by a rotation of 180 counterclockwise.
N76 [4]

Answer:

Please check the explanation.

Step-by-step explanation:

Translating two units down means we need to subtract two units from the y-coordinate. i.e

(x, y) → (x, y-2)

We are given that the original point is (1, 2), and we have to find the image of (2, 4) obtained by translating 2 units down followed by a rotation of 180 counterclockwise.

                                                FOR (1, 2)

Given

  • P(1, 2)

First translation: Translating two units down

(x, y) → (x, y-2)

P(1, 2) → P'(1, 2-2) → P'(1, 0)

Second transformation: Rotation of 180 counterclockwise.

Rotation of 180 counterclockwise will make both 'x' and 'y' coordinates negative. i.e

(x, y) → (-x, -y)

Thus, after second transformation

P'(1, 0) → (-1, 0)

Thus, the image of (1, 2) obtained by translating 2 units down followed by a rotation of 180 counterclockwise will be: (-1, 0)

                                                    FOR (2, 4)

Given

  • P(2, 4)

First translation: Translating two units down

(x, y) → (x, y-2)

P(2, 4) → P'(2, 4-2) → P'(2, 2)

Second transformation: Rotation of 180 counterclockwise.

Rotation of 180 counterclockwise will make both 'x' and 'y' coordinates negative. i.e

(x, y) → (-x, -y)

Thus, after the second transformation

P'(2, 2) → (-2, -2)

Thus, the image of (2, 4) obtained by translating 2 units down followed by a rotation of 180 counterclockwise will be: (-2, -2)                                        

6 0
2 years ago
Determine the slope and y intercept of the line represented by the linear equation 1/2y+2=0
sleet_krkn [62]
Hope the diagrams help

3 0
2 years ago
LK is tangent to circle J at point K. Circle J is shown. Line segment J K is a radius. Line segment K L is a tangent that inters
Evgen [1.6K]

Answer:

(B)r=\dfrac{85}{12}

Step-by-step explanation:

Given a circle centre J

Let the radius of the circle =r

LK is tangent to circle J at point K

From the diagram attached

  • LX=6
  • Radius, XJ=JK=r
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Theorem: The angle between a tangent and a radius is 90 degrees.

By the theorem above, Triangle JLK forms a right triangle with LJ as the hypotenuse.

Using Pythagoras Theorem:

(6+r)^2=r^2+11^2\\(6+r)(6+r)=r^2+121\\36+6r+6r+r^2=r^2+121\\12r=121-36\\12r=85\\r=\dfrac{85}{12}

The length of the radius, r=\dfrac{85}{12}

8 0
3 years ago
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