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3 years ago

Find the measure of one interior angle of a regular pentagon

1 answer:

5 0

Use (n - 2)180.
n is the number of sides.

There are 5 sides in a pentagon.
Plug in 5 for n.

(5 - 2)180 = 540

Divide 540 by 5 = 108

The measure of one interior angle of a regular pentagon is 108°.

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What is the missing constant term in the perfect square that starts with x^2+10x?

natulia [17]

Answer:

+ 25

Step-by-step explanation:

To complete the square

add ( half the coefficient of the x- term )²

the coefficient of the x- term is 5 and 5² = 25, hence

x² + 10x + 25 = (x + 5)² ← perfect square

7 0

3 years ago

At a basketball game, an air cannon launches T-shirts into the crowd. The function y=−1/8x^2 + 4x represents the path of a T-shi

Juliette [100K]

Answer:

The T-shirt lands in the bleachers at a height of 14 feet.

Step-by-step explanation:

The point where they meet is the solution of the simultaneous system of equations:

$y = -\frac{1}{8}x^2+4x$ ...........................................(1)

$3y = 2x - 14$ ..............................................(2)

From (2),

$y = \frac{2}{3}x-\frac{14}{3}$ .................................................(3)

Substituting (3) in (1),

$\frac{2}{3}x-\frac{14}{3} = -\frac{1}{8}x^2+4x$

Multiply through by 24 (the LCM of 3 and 8, the denominators of the fractions)

$(24\times\frac{2}{3}x)-(24\times\frac{14}{3}) = (-24\times \frac{1}{8}x^2)+(24\times4x)$

$16x - 112 = -3x^2+96x$

$3x^2-80x -112 = 0$

$(x-28)(3x+4) = 0$

$x-28 = 0$ OR $3x+4=0$

$x=28$ OR $x = -\frac{4}{3}$

The value of y represents the height.

Substituting for x in (3)

$y = \frac{2}{3}\times28-\frac{14}{3} = \frac{56}{3} - \frac{14}{3} = 14$

$y = \frac{2}{3}\times(-\frac{4}{3})-\frac{14}{3} = -\frac{8}{9} - \frac{14}{3} = -\frac{50}{9}$

We discard the negative answer.

Hence, the T-shirt lands in the bleachers at a height of 14 feet.

6 0

3 years ago

I have 7 hundreds blocks, 5 tens blocks, and 8 ones blocks. I use my blocks to model two 3-digit numbers. What could my two numb

lawyer [7]

There 7 blocks of hundreds which means each such block is equivalent to 100.
There are 5 blocks of tens, which means each such block is equivalent to 10.
There are 8 blocks of ones, which means each such block is equivalent to 1.

The total of these blocks will be = 7(100) + 5(10) + 8(10) = 758

We can make several two 3-digit numbers from these blocks. An example is listed below:

Example:
Using 3 hundred block, 2 tens blocks and 4 ones block to make one number and remaining blocks to make the other number. The remaining blocks will be 4 hundred blocks, 3 tens blocks and 4 ones blocks
The two numbers we will make in this case are:

1st number = 3(100) + 2(10) + 4(1) = 324
2nd number = 4(100) + 3(10) + 4(1) = 434

The sum of these two numbers is = 324 + 434 = 758
i.e. equal to the original sum of all blocks.

This way changing the number of blocks in each place value, different 3 digit numbers can be generated.

5 0

3 years ago

In a casino, the chance of winning a certain game is 14.5%. If you play the game 20 times, what’s your best estimate for the num

EleoNora [17]

Expected number of wins=number of plays times the probability of winning

w=20(14.5/100)

w=20(0.145)

w=2.9

w≈3

So you would expect to win 3 times out of 20 attempts (rounded to the nearest whole number of wins)

7 0

4 years ago

Jaleia borrows $1500 from the bank. To pay back the loan this year, she will pay the bank the amount she borrowed plus 12% simpl

sineoko [7]

Answer:

$1860

Step-by-step explanation:

12% of 1500 = 180

180 x 2 = 360

1500 + 360=1860

4 0

3 years ago

Read 2 more answers