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4 years ago

10

Connor and Maria are doing yard work for a neighbor. They make a total of $503.56 . Since Maria works fewer hours than Connor

, Maria gets 31 % of the money. About how much (in whole dollars) does Maria make?

1 answer:

Evgen [1.6K]4 years ago

7 0

Maria would have made a total of $156

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Fine length of BC on the following photo.

MrMuchimi

Answer:

$BC=4\sqrt{5}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

$AC^2=AD^2+DC^2$

substitute the given values

$AC^2=16^2+8^2$

$AC^2=320$

$AC=\sqrt{320}\ units$

simplify

$AC=8\sqrt{5}\ units$

step 2

In the right triangle ACD

Find the cosine of angle CAD

$cos(\angle CAD)=\frac{AD}{AC}$

substitute the given values

$cos(\angle CAD)=\frac{16}{8\sqrt{5}}$

$cos(\angle CAD)=\frac{2}{\sqrt{5}}$ ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

$cos(\angle BAC)=\frac{AC}{AB}$

substitute the given values

$cos(\angle BAC)=\frac{8\sqrt{5}}{16+x}$ ----> equation B

step 4

Find the value of x

In this problem

$\angle CAD=\angle BAC$ ----> is the same angle

so

equate equation A and equation B

$\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}$

solve for x

Multiply in cross

$(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units$

$DB=4\ units$

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

$BC^2=DC^2+DB^2$

substitute the given values

$BC^2=8^2+4^2$

$BC^2=80$

$BC=\sqrt{80}\ units$

simplify

$BC=4\sqrt{5}\ units$

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3 years ago

Simplify 3/4 - 1 1/4

lbvjy [14]

I think the answer is -7/4.

4 0

3 years ago

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The pollutant PCB (polychlorinated biphenyl) can affect the thickness of pelican eggshells. Thinking of the thickness, T, of the

gayaneshka [121]

Answer:

The expression f(200) depicts the value of the concentration of the pollutant, which when substituted in the expression T = f(P) will give the value of the thickness of the pelican eggs.

Step-by-step explanation:

Since we are given that T = f(P)

Where T = thickness of the eggs

P = concentration in ppm ((parts per million))

Considering f(200) comparing to f(P)

The expression f(200) depicts the value of the concentration of the pollutant, which when substiuted in the expression T = f(P) will give the value of the thickness of the pelican eggs.

i.e substituted the value of the concentration in ppm to get the thickness of the pelican eggs in mm. since the expression shows thickness of pelican eggs as a function of the concentration. for every 200ppm of concentration, the numerical value of the thickness of pelican eggs can be gotten.

6 0

3 years ago

A recipe calls for 3 cups of sugar for every 5 cups of water. How many cups of sugar are needed for 25 cups of water?

nasty-shy [4]

The answer is 15 cups

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3 years ago

What is the value of p?

kenny6666 [7]

Answer:

35

Step-by-step explanation:

All angles of a triangle add up to 180 degrees, so you can add the other two angles, then subtract by 180.

4 0

3 years ago

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