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1 year ago

A secretary can type 12 pages per hour. There are a total of 152 pages to type. How many pages remain to be typed after 9 hours?

1 answer:

4 0

So, she can type 12 pages in 1 hour, how many would she type in 9 hours then? let's check,

$\bf \begin{array}{ccll}
pages&hours\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
12&1\\
p&9
\end{array}\implies \cfrac{12}{p}=\cfrac{1}{9}\implies \cfrac{12\cdot 9}{1}=p$

so in 9 hours, she has that typed that many pages, how many pages remain from the 152? well 152 - p.

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Find the area of the shaded portion in the equilateral triangle with sides 6. Show all work for full credit. (Hint: Assume that

Vadim26 [7]

So... if you notice the picture below

each circle, has their central angle at the vertex of the triangle
that simply means, 3 circles with a radius of 3, overlapping the triangle

now, the area in the middle, the shaded one, will be, the whole area of the triangle MINUS those 3 circle sectors

hmmmm each sector has 60°, that means, all three of them will then be 60+60+60 or 180°, so the area of those three sectors, can be combined into a 180° sector, well, hell, 180° is really half a circle

so.... the area of those three sectors of 60° each, all three combined, is the same area of half a circle with a radius of 3

so $\bf \textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}\qquad s=\textit{length of one side}\\\\
-----------------------------\\\\
\textit{area of a circle}\\\\
A=\pi r^2\qquad r=radius\\\\
\textit{area of half a circle}\\\\
A=\cfrac{\pi r^2}{2}\\\\
-----------------------------\\\\$

$\bf \textit{now, let us use the side of 6, and radius of 3}
\\\\\\

\begin{array}{clclll}
\cfrac{6^2\sqrt{3}}{4}&-&\cfrac{\pi 3^2}{2}\\
\uparrow &&\uparrow \\
triangle's&&semi-circle's
\end{array}\impliedby \textit{area of shaded area}\\\\
-----------------------------\\\\
\boxed{\cfrac{36\sqrt{3}}{4}-\cfrac{9\pi }{2}}$

you can, add the fractions if you want, or leave them like that, or get their difference by using their decimal format

8 0

2 years ago

Read 2 more answers

A slide has an angle of elevation of 25°. It is 60 feet from the end of the slide to the stairway beneath the top of the slide.

Valentin [98]

Cos 25=0.90631
cos 25=(the end of the slide to the stairway beneath the top of the slide)/( length of the slide)
length of the slide=60/0.90631=66.2
the length of the slide = 66.2 feet

3 0

1 year ago

A village wishes to measure the quantity of water that is piped to a factory during a typical morning. A gauge on the water line

nignag [31]

122 is the
answer. i think this help

4 0

2 years ago

Nick billups is paid a salary of $ 900 a month, a 2 % commission on all sales, and 1.8 % more on monthly sales over $ 17,500. In

Trava [24]

June :
900 + 0.02(48,500) + 0.018(48500 - 17500) =
900 + 970 + 558 = 2428 <==

July :
900 + .02(50,200) + 0.018(50200 - 17500) =
900 + 1004 + 588.60 = 2492.60 <===

5 0

1 year ago

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According to the synthetic division below, which of the following statements are true?

makkiz [27]

Answer:

Correct options are A and D

Step-by-step explanation:

According to the synthetic division in the diagram you can write down the result of division:

$2x^2+9x-7=(x-(-6))(2x-3)+11,\\ \\2x^2+9x-7=(x+6)(2x-3)+11.$

Therefore,

when $2x^2+9x-7$ is divided by $x+6,$ the remainder is 11 (option D is correct). To find the remainder after division by $x-6,$ you have to use another synthetic division. Actually, $2x^+9x-7=(x-6)(2x+21)+119,$ then the remainder is 119 (option C is false).
when $x=-6,$ the expression $x+6$ is $-6+6=0$ and $2x^2+9x-7=0\cdot (2x-3)+11=11$ (option A is correct). You cannot state the same when $x=6$ (option B is false).
neither $x-6$ nor $x+6$ is a factor of $2x^2+9x-7,$ because the remainders in both cases are not equal to 0 (options E and F are false).

4 0

2 years ago

Read 2 more answers