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2 years ago

6x+18y=18 find y and z

Mathematics

1 answer:

Masja [62]2 years ago

3 0

6x + 18y = 18. Let us take x = 0

6(0) + 18y = 18

0 + 18y = 18

18y = 18

y = 18/18

y = 1

(0, 1) [x = 0, y = 1]

6x + 18y = 18. Let us take y = 0

6x + 18(0) = 18

6x + 0 = 18

6x = 18

x = 18/6

x = 3

(3, 0) [x = 3, y =0]

Infinite solutions can be found for x and y

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hichkok12 [17]

Answer:

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Part b) $AC=13.66\ units$

Step-by-step explanation:

step 1

Find the length side BC

Applying the law of sines

we know that

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

we have

$AB=5\sqrt{2}\ units$

$A=45^o$

$C=30^o$

substitute

$\frac{5\sqrt{2}}{sin(30^o)}=\frac{BC}{sin(45^o)}$

solve for BC

$BC=\frac{5\sqrt{2}}{sin(30^o)}(sin(45^o))$

$BC=10\ units$

step 2

Find the measure of angle B

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

$m\angle A+m\angle B+m\angle C=180^o$

substitute the given values

$45^o+m\angle B+30^o=180^o$

$75^o+m\angle B=180^o$

$m\angle B=180^o-75^o$

$m\angle B=105^o$

step 3

Find the length side AC

Applying the law of sines

we know that

$\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

we have

$AB=5\sqrt{2}\ units$

$A=45^o$

$B=105^o$

substitute

$\frac{5\sqrt{2}}{sin(30^o)}=\frac{AC}{sin(105^o)}$

solve for AC

$AC=\frac{5\sqrt{2}}{sin(30^o)}(sin(105^o))$

$AC=13.66\ units$

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2 years ago

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Step-by-step explanation:

Given: Selling price of each hat = $12

Profit on each hat = $3

To find: The percent of the selling price of each hat is the profit.

Ratio of profit to selling price = $\dfrac3{12}=\dfrac14$

The required percentage = Ratio of profit to selling price x 100

$=\dfrac14\times100=25\%$

The profit is 25% of the selling price.

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