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3 years ago

10

Marla helped her mother and father fold invitations and put them into envelopes. If Marla can fill 36 envelopes in 30 minutes, h

ow long will it take her to fill 48 envelopes? (Only enter a numerical answer)

2 answers:

Rzqust [24]3 years ago

6 0

56 minutes hope this helped :)

statuscvo [17]3 years ago

3 0

Answer:

40 minutes

Step-by-step explanation:

12 envelopes every 10 minutes.

48 envelopes = 40 minutes

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How do I find surface area of a prism?

nlexa [21]

Answer:

Step-by-step explanation:

If you want the surface area of a rectangular prism, then you'll use a formula resembling this:

A = 2(area of end) + 2(area of top) + 2 (area of side).

Example: suppose the dimensions of the prism are 3 in by 5 in by 8 in.

Then the total surface area is:

A = 2(3*5) + 2(3*8) + 2(5*8) square inches, or 2(15) + 2(48) + 2(40) sq in, or

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The width of a rectangle is 6 kilometers less than twice its length. if the area of the rectangle is 176 square kilometers, find

trasher [3.6K]

Let w and 2w-6 be the width and length, respectively. Then:
w(2w-6)=176
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4 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csec%5Cleft%28x%5Cright%29%7D%7B%5Ccos%5Cleft%28x%5Cright%29%7D-%5Cfrac%7B%5Csin%5

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Answer:

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Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that $csc(x)=1/sin(x)$ and $sec(x)=1/cos(x)$ .

Thus:

$\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}$

$=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }$

Let's do the first part first: (Recall how to divide fractions)

$\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}$

For the second term:

$\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}$

So, all together: (same denominator; combine terms)

$\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}$

Note the numerator; it can be derived from the Pythagorean Identity:

$sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)$

Thus, we can substitute the numerator:

$\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1$

Everything simplifies to 1.

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