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3 years ago

What is the length of x? What is the length of EF? Only enter numbers in the answer boxes below:

Mathematics

1 answer:

dimaraw [331]3 years ago

7 0

Focus on triangles DFC and DFE:

They are both right triangles because DF is perpendicular to EC
DC=DE
DF is a common side

So, the two triangles are congruent. It follows that CF=FE, and in particular

$8x=3x+15 \iff 5x=15 \iff x=3$

And since x=3, the length of EF is

$EF=3x+15=3\cdot 3+15=24$

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And one season the top four players on one major league team had batting averages of 0.332, 0.361, 0.343 and 0.360 which is the

DanielleElmas [232]

ANSWER: 0.361

This is as:

0.361 > 0.332

0.361 > 0.343

0.361 > 0.36

Therefore, as 0.361 is greater than all the other averages, it must be the highest average.

Hope this helps! :)
Have a lovely day! <3

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3 years ago

the school newspaper has a circulation of 500 and sells for $.035 a copy. the students decide to raise the price to increase the

Alik [6]

Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is

$.35+.05x$

Let y be the newspaper they sell, then the income will be

$y(.35+.05x)$

Now, we know that the circulation is of 500, assuming that they sold every newspaper at the original price now the number the will sell will be

$y=500-20x$

Plugging the value of y in the first expression we have that the income will be

$\begin{gathered} f(x)=(500-20x)(.35+\text{0}.5x)=175+25x-7x-x^2 \\ =-x^2+18x+175 \end{gathered}$

Then the income is given by the function

$f(x)=-x^2+18x+175$

To find the maximum value of this functions (thus the maximum income) we need to take the derivative of the function,

$\begin{gathered} \frac{df}{dx}=\frac{d}{dx}(-x^2+18x+175) \\ =-2x+18 \end{gathered}$

no we equate the derivative to zero and solve for x.

$\begin{gathered} \frac{df}{dx}=0 \\ -2x+18=0 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}$

This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then

$\begin{gathered} \frac{d^2f}{dx^2}=\frac{d}{dx}(\frac{df}{dx}) \\ =\frac{d}{dx}(-2x+18) \\ =-2 \end{gathered}$

Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.

With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.

Therefore the price to maximize the income is $0.35+$0.45=$0.80.

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1 year ago

The average price of a 30 second commercial for the 2002 Super Bowl was $1,900,000. What was the price per second?

Tanzania [10]

Answer:

$63,333.33

Step-by-step explanation:

Divide 1,900,000 by 30 to get $63333.3333....which technically just rounds to $63333.33, and if you want to go further, $63333.

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2 years ago

Marley picked 18 bananas, which is 6 timies as many bananas as Julans picked. The equation 6x?=18 can be used to find the number

ivann1987 [24]

Answer:

1. 6x = 18 (Divide by six on both sides

2. $\frac{6x}{6} =\frac{18}{6}$ (the6 on the right side cancels out, you are left with 18/6)

3. x = 3

Step-by-step explanation:

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2 years ago

Mrs.Anderson bought party favors for the 24 students in her class. Each favor cost $2.27. How much did all the party favors cost

laiz [17]

$54.48 because 24 x 2.27 = 54.48

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3 years ago