Suppose ∠A and ∠B are complementary angles, m∠A = (3x + 5)°, and

2 answers:

8 0

M∠A + m∠B = 90

$(3x + 5) + (2x - 15) = 90$

$
(3x + 2x) + (5 - 15) = 90$

$5x - 10 = 90$

$5x - 10 +10 = 90+10$

$5x = 100$

$5x/5 = 100/5$ $Divide \ both \ sides \ by \ 5$

$x = 20$    $Solutions$

m∠A = $3x + 5$    $(x=20)$

m∠A = $3(20) + 5$ $Substitute \ x \ for \ 20$

m∠A = $60 + 5$    $Simplify$

m∠A = $65$

m∠B = $2x - 15$

m∠B = $2(20) - 15$

m∠B = $40 - 15$

<span>m∠B = </span> $25$

mario62 [17]3 years ago

6 0

m∠A + m∠B = 90
(3x + 5) + (2x - 15) = 90
(3x + 2x) + (5 - 15) = 90
5x - 10 = 90
+ 10 + 10
5x = 100
5 5
x = 20

m∠A = 3x + 5
m∠A = 3(20) + 5
m∠A = 60 + 5
m∠A = 65

m∠B = 2x - 15
m∠B = 2(20) - 15
m∠B = 40 - 15
m∠B = 25

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For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a

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Answer:

The radius of the new cheese ball formed is approximately 6.603 inches.

Step-by-step explanation:

We are given the following in the question:

Radius of three cheese ball = 2 inches, 4 inches, and 6 inches

They were combined to form a new cheese ball.

Thus, we can write

Volume of three cheese balls = Volume of new cheese ball.

Let r be the radius of new cheese ball.

Volume of sphere =

$\displaystyle\frac{4}{3}\pi r^3$

Putting values, we get:

$\displaystyle\frac{4}{3}\pi r_1^3 + \displaystyle\frac{4}{3}\pi r_2^3 +\displaystyle\frac{4}{3}\pi r_3^3 =\displaystyle\frac{4}{3}\pi r^3\\\\\frac{4}{3}\pi(2^3 + 4^3 + 6^3) = \displaystyle\frac{4}{3}\pi r^3\\\\2^3 + 4^3 + 6^3 = r^3\\\Rightarrow 288 = r^3\\\Rightarrow r = (288)^{\frac{1}{3}}\\\Rightarrow r \approx 6.603$