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Lera25 [3.4K]
3 years ago
9

In ΔCDE, the measure of ∠E=90°, the measure of ∠D=23°, and EC = 1.3 feet. Find the length of DE to the nearest tenth of a foot?

Mathematics
1 answer:
Rina8888 [55]3 years ago
5 0

Answer:

DE = 1.2ft

Step-by-step explanation:

It's actually a lot easier for someone to just draw a diagram. I recommend it in the future!

This is a right-angle triangle, so I'm guessing it's Sohcahtoa.

cos23° = DE/1.3

DE = 1.3cos 23°

DE = 1.1966...

Rounded:

DE = 1.2

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If f(x) = 3x22, evaluate afI: ()k=1
Korolek [52]

Step 1: Write out the function given

f(x)=3x^2-x

Step 2: Interprete the question given

\sum ^5_{k\mathop=1}f(\frac{k}{2})

The question requested we find the summation of the first five terms for f(k/2), when k is 1, 2, 3, 4, and 5

Step 3: Find the expression for f(k/2)

\begin{gathered} f(\frac{k}{2})=3(\frac{k}{2})^2-\frac{k}{2} \\ =\frac{3k^2}{4}-\frac{k}{2} \\ =\frac{3k^2-2k}{4} \end{gathered}\begin{gathered} =\frac{3(1)^2-2(1)}{4}+\frac{3(2)^2-2(2)}{4}+\frac{3(3)^2-2(3)}{4}+\frac{3(4)^2-2(4)}{4}+\frac{3(5)^2-2(5)}{4} \\ =\frac{1+8+21+40+65}{4} \\ =\frac{135}{4} \\ =33.75 \end{gathered}

Hence, the answer is 33.75

5 0
1 year ago
What is the answer to this question?<br> Y=x^2-1 with the input as 5
mixas84 [53]

We can see that, when the input is 5, the output is 24.

<h3>How to evaluate an equation?</h3>

Here we have the equation:

y = x^2 - 1

Where y is the output and x is the input.

We want to evaluate it with the input as 5, so we need to replace the variable x by the number 5, we will get:

y = 5^2 - 1 = 24

Then we can see that, when the input is 5, the output is 24.

If you want to learn more about evaluating functions:

brainly.com/question/1719822

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4 0
2 years ago
Joey has a beach ball with a radius of 20 cm. What volume of air will it hold when fully inflated? [Round to nearest tenth.]
nadya68 [22]
It would be D. because the volume of a sphere is 4/2 x pi x radius^3.
4 0
3 years ago
Read 2 more answers
PLEASE HELP I POSTED LIKE 2 HOURS AGO WITH THIS QUESTION AND I NEED HELP:)
garik1379 [7]

A system is inconsistent when there are no solutions between the two equations. Graphically, the lines will be parallel (they never meet!) and the slopes will be the same. But the y-intercepts will be different.

Let's look at the four equations, with each solved as needed, into y = mx + b form.

A: 2x + y = 5

y = 5 - 2x

y = -2x + 5

Compared to y = 2x + 5, the slopes are different, so this system won't be inconsistent. Not a good choice.

B: y = 2x + 5

Compared to y = 2x + 5, the slopes are the same and the y intercepts are the same. This system has infinitely many solutions. Not a good choice.

C: 2x - 4y = 10

-4y = 10 - 2x

-4y = -2x + 10

y = 2/4x -10/4

Here the slopes are different, so, like A this is not a good choice.

D: 2y - 4x = -10

2y = =10 + 4x

2y = 4x - 10

y = 2x - 5

Compared to y = 2x + 5 we have the same slopes and different y intercepts.  The lines will be parallel and the system is inconsistent.


Thus, D is the best choice.

7 0
3 years ago
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Westley and Buttercup are each saving money. Westley starts with $85 in in his savings and add $5 per week (y=85+5x)
love history [14]

Answer:

After 5 weeks.

Step-by-step explanation:

Westley starts with $85 and saves $5 per week. So:

y=85+5x

Buttercup starts with $10 and saves $20 per week. So:

y=10+20x

When they have the same amount of money, the two equations will be equal to each other. Therefore:

85+5x=10+20x

Solve for x. Subtract 10 from both sides:

75+5x=20x

Subtract 5x from both sides:

75=15x

Divide both sides by 15:

x=5

Westley and Buttercup will have the same amount of money after 5 weeks.

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3 years ago
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