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3 years ago

In a right triangle, the acute angles measure 2x + 50 and 3x degrees. What is the measure of the smallest angle of the triangle?

1 answer:

4 0

Since this is a right triangle the two acute angles must sum to 90 degrees because a triangle's angles must sum to 180 degrees.

2x+50+3x=90

5x+50=90

5x=40

x=8

So the smallest angle is 3x=3*8=24°

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A triangle with vertices at (0,4), (3,5), and (2, -l) is rotated 90 degree counterclockwise about the origin. What are the verti

Ksenya-84 [330]

Answer:

$(0,4) \implies (-4, 0)\\(3,5) \implies (-5,3)\\(2,-1) \implies (1,2)$

Step-by-step explanation:

A 90° counterclockwise rotation is defined as

$(x,y) \implies (-y,x)$

The given coordinates are

$(0,4)\\(3,5)\\(2,-1)$

Applying the 90° counterclockwise rotation, we have

$(0,4) \implies (-4, 0)\\(3,5) \implies (-5,3)\\(2,-1) \implies (1,2)$

The image attached show both figures.

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3 years ago

Why do we use variables, and what is the significance of using them in expressions and equations?

n200080 [17]

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7 0

3 years ago

-1 3/7 • (-3 2/3) = ? A: 3 2/7 B: 5 5/21 C: 11 D: -5 5/21

Anna35 [415]

[|] Answer [|]

$\boxed{5 \ \frac{5}{21}}$

[|] Explanation [|]

$-1 \ \frac{3}{7}$ * $-3 \frac{2}{3}$

-----------

Convert Fractions To Mixed Numbers:

$-1 \ \frac{3}{7}$ = $\frac{-10}{7}$

$-3 \ \frac{2}{3}$ = $\frac{-11}{3}$

Multiply Across:

$\frac{-10 \ * \ -11}{7 * 3}$

= $\frac{110}{21}$

Simplify:

= $5 \ \frac{5}{21}$

$\boxed{[|] \ Eclipsed \ [|]}$

8 0

3 years ago

Ellen drove 357.3 miles.for each gallon of gas,the car can travel 21 miles.select a reasonable estimate of the number of gallons

kari74 [83]

Just a little over 17 gallons was used

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3 years ago

What is 10 squared plus b squared equals 22 squared

klio [65]

I'm pretty sure you are asking for the value of b. Let's actually write it and then solve it:
$10^2 + b^2 = 22^2$

Solving for b yields:
$b = \sqrt{22^2-10^2} = \sqrt{484-100} = \sqrt{384} = 19.59$

So, b = 19.59. If you want the answer in simplified radical form, we can also do that:
$\sqrt{384} = \sqrt{16*24} = 4 \sqrt{24} = 4 \sqrt{4*6} = 8 \sqrt{6}$

So, b = 8√6 = 19.59

4 0

3 years ago