Remark: What might be confusing you is the the given expression must add up to 90o. You know this because <B = 90 so the other two angles must be 90o.

Equation

5x - 10 + 6x - 21 = 90 Combine like terms on the left

11x - 31 = 90 Add 31 to both sides.

11x - 31 + 31 = 90 + 31

11x = 121 Divide by 11

x = 121/11 = 11.

Find the value of 6x - 21

6*11 - 21 = 66 - 21= 45

Comment

The central angle for arc AB (which is double ADB = 2*45 =90) is 90. So arc AB = 90

5 0

2 years ago

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Two quantities vary inversely. If the value of the first is 15 when the value of the second is 18, find the value of the second

vovikov84 [41]

Answer:

The value of second quantity is 27

Step-by-step explanation:

Inverse variation can be represented by the equation xy=k or $y = \frac{k}{x}$ i.e,

y varies inversely as x , if there is some nonzero constant k such that, xy =k or $y = \frac{k}{x}$ where x≠0 and y≠0.

Given: Two quantities vary inversely.

Let x be the first quantity and y be the second quantity if they vary inversely.

then, by definition of inverse variation;

$y = \frac{k}{x}$ .....[1]

Substitute the value of x=15 and y=18 to solve for k;

$18= \frac{k}{15}$

Multiply both sides by 15 we have;

$15\times 18=15 \times \frac{k}{15}$

Simplify:

k=270

now, find the second quantity y using same method when x=10.

then;

after substituting the value of x=10 and k=270 in [1] ;

$y = \frac{270}{10}$

Simplify:

y= 27

Therefore, the second quantity value i.e,y = 27

7 0

3 years ago

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