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3 years ago

The registrar's office at ACC predicts that 30% of the 6,950 spaces open in various math classes will be filled

Mathematics

1 answer:

Nesterboy [21]3 years ago

7 0

Answer:

a) 70%

b) 4865

Step-by-step explanation:

a) We assume that 100% of spaces are available prior to the first week of registration, so filling 30% will leave 70% available.

b) 70% of 6950 is ...

0.70×6950 = 4865 . . . spaces available after the first week

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Given: PRST is a square

xxTIMURxx [149]

Answer:

$(1-\sqrt{2})a^2$

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

$PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a$

Thus,

$MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a$

Consider isosceles triangle MSC. In this triangle

$MS=MC=(\sqrt{2}-1)a.$

The area of this triangle is

$A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}$

Consider right triangle PTS. The area of this triangle is

$A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}$

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

$A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2$

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Please help! The expressions 3x - 9 and 23 - 5x represent the lengths (in feet) of two sides of an equilateral triangle. Find th

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An equilateral triangle has 3 congruent sides so the 2 expressions above are equal
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And then you solve for x
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