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gregori [183]
2 years ago
7

A rectangle is drawn so the width is 97 inches longer than the height. If the rectangle's diagonal measurement is 113 inches, fi

nd the height. Give your answer rounded to 1 decimal place. Inches
Mathematics
1 answer:
inn [45]2 years ago
8 0

Step-by-step explanation:

h = height of rectangle (should be "length", but ok)

w = width of rectangle

w = h + 97

the diagonal of the rectangle is the Hypotenuse (baseline) of a right-angled triangle with the legs being one height and one width side of the rectangle.

so, we use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle).

diagonal² = h² + (h + 97)² = h² + h² + 2×97h + 97²

113² = 12769 = 2h² + 194h + 9409

3360 = 2h² + 194h

1680 = h² + 97h = (h + 97/2)² - 9409/4

(completing the square)

6720/4 + 9409/4 = (h + 97/2)²

16129/4 = (h + 97/2)²

127/2 = h + 97/2

30/2 = h = 15

the height is 15.0 in

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6 0
3 years ago
If g(x) =x^2 + 1, find g(4)
Papessa [141]

Answer:

17

Step-by-step explanation:

Since we are evaluating <em>g(x)</em> for g(4), we would substitute <em>x</em> in the equation with 4.

<em>x</em>² + 1

(4)²+ 1

16 + 1

17

I hope this helps

4 0
3 years ago
You begin the month with $5,550 of inventory. You purchase $13,000 of stock during the month. You end the month with $2,333 of i
Zanzabum

Answer:

The correct answer is $16217

Step-by-step explanation:

You do 5550 + 13000 and get that answer and subtract 2333

3 0
3 years ago
Tom opened a lemonade stand to earn money to buy a new bike for $200. He sells a cup of lemonade for $1.00. On the first day he
tia_tia [17]

1 - 8

2 - 16

3 - 32

x - +200

Each lemonade has a profit of $1, so the number of cups of lemonade he sells is the same as the amount of dollars he has. You just need to add each previous day's total to the next day's, doubling the amount of cups from the previous day's for each new day.

4 - (32 x 2 = ) 64

8 + 16 + 32 + 64 = 120. We need at least $80 dollars more, so we continue.

5 - (64 x 2 = ) 128

120 + 128 = $248.00 That's more than enough, so Tom will have enough money for his bike after the fifth day of selling lemonade.

6 0
3 years ago
Find the sum of the constants a, h, and k such that
ra1l [238]

Answer:

  3

Step-by-step explanation:

The value of "a" is the coefficient of x^2, so we know that is 2.

__

<u>Solve for h</u>

Now, we have ...

  2x^2 -8x +7 = 2(x -h)^2 +k

Expanding the right side gives us ...

  = 2(x^2 -2hx +h^2) +k

  = 2x^2 -4hx +2h^2 +k

Comparing x-terms, we see ...

  -4hx = -8x

  h = (-8x)/(-4x) = 2

__

<u>Solve for k</u>

Now, we're left with ...

  2h^2 +k = 7 = 2(2^2) +k = 8 +k

Subtracting 8 we find k to be ...

  k = 7 -8 = -1

__

And the sum of constants a, h, and k is ...

  a +h +k = 2 +2 -1 = 3

The sum of the constants is 3.

6 0
4 years ago
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