Answer:
BD = 35
Step-by-step explanation:
Calculate CD in right triangle ABC, then BD in right triangle BCD
Using Pythagoras' identity in both triangles.
The square on the hypotenuse is equal to the sum of the squares on the other two sides.
In Δ ADC
CD² + AD² = AC² , substitute values
CD² + 9² = 15²
CD² + 81 = 225 ( subtract 81 from both sides )
CD = 144 ( take the square root of both sides )
CD = 
= 12
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In Δ BCD
BD² + CD² = BC² , substitute values
BD² + 12² = 37²
BD² + 144 = 1369 ( subtract 144 from both sides )
BD² = 1225 ( take the square root of both sides )
BD = 
= 35
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Answer:
The function r(x)=(2+.25x)(240-20x) reveals that the revenue earned by the cafe from coffee sales will be $500 after 2 $0.25 price increases.
Step-by-step explanation:
The revenue from sales is the product of the price per cup and the number of cups sold.
For x increases of $0.25 each, the price per cup is (2 +0.25x).
For x increases of $0.25 each, the number of cups sold is (240 -20x).
Then the revenue as a function of x is ...
r(x) = (2 +0.25x)(240 -20x)
The revenue function can be simplified to better show its zeros.
r(x) = 5(8 +x)(12 -x)
The maximum is halfway between the zeros, so is at x = (-8 +12)/2 = 2.
When x=2, the revenue is ...
r(2) = 5(8+2)(12-2) = 5(10)(10) = 500
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The function <u>r(x)=(2+.25x)(240-20x)</u> reveals that the revenue earned by the cafe from coffee sales will be <u>$500</u> after <u>2</u> $0.25 price increases.
We conclude that the solution to the given linear equation is x = 15/13.
<h3>
How to solve that equation for x?</h3>
Here we have the linear equation:
13x - 4 = 11
And we want to solve this for x. To do so, we need to isolate x in one side of the equation.
We can start by adding 4 in both sides, so we get:
13x - 4 + 4 = 11 + 4
13x = 15
Now we can divide both sides by 13, so we get:
13x/3 = 15/13
x = 15/13
We conclude that the solution to the given linear equation is x = 15/13.
If you want to learn more about linear equations:
brainly.com/question/1884491
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