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3 years ago

Is it possible that for every right triangle, it has two complementary angles?

1 answer:

Montano1993 [528]3 years ago

3 0

Yes, every right triangle has two complementary angles.

This is because you know that the interior angles of a triangle have to add up to 180 degrees.

A right angle is 90 degrees, so the remaining two angles have to add up to (180-90) degrees, or 90 degrees.

Two angles whose sum is 90 degrees are complementary.

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the area of a rectangle is 90 in2^. the ratio of the length to the width is 5:2. find the length and the width

-BARSIC- [3]

Length and width of rectangle is 15 inches and 6 inches respectively

<h3><u>Solution:</u></h3>

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

<em><u>The formula for area of rectangle is given as:</u></em>

$\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}$

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

$\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}$

On solving the above expression for x we get

$\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}$

$\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}$

Hence length and width of rectangle is 15 inches and 6 inches.

4 0

3 years ago

12(3w+8)=25 what is the w

Mashcka [7]

12(3w+8)=25
36w+96=25 ( I used the distributive property)
-96 . -96
36w=-71
w=-1.972222.... ( I divided both sides by 36)

7 0

3 years ago

Elaine scored 19 out of 24 on her science test.

kozerog [31]

Answer:

Addison scored a better score on the test.

Step-by-step explanation:

Elaine's score can be found by dividing 19 by 24, which yields a result of 0.7916, which means her score is a 79 out of 100 (79%). Her score can also be found by doing 100/24 = 4.16666 repeating and multiplying that by 19, which also yields 79.6. Hope this helps!

4 0

3 years ago

Read 2 more answers

A rock falls off a balcony. It's height (in feet) is given by the formula f(x)=-16t^2+13.4t+120, where t is measured in seconds.

pantera1 [17]

Answer:

3.189 seconds

Step-by-step explanation:

You want f(t) = 0, so ...

0 = -16t^2 +13.4t +120

0 = t^2 -0.8375t -7.5 . . . . divide by -16

0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*

0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square

√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root

t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875

It will take the rock about 3.189 seconds to hit the ground.

_____

* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...

(t^2 -2at +a^2) = (t -a)^2

Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.

_____

<em>Comment on the question</em>

We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...

8 0

2 years ago

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.Refer to

Dafna11 [192]

Given that

the weight of football players is distributed with a mean of 200 pounds and a standard deviation of 25 pounds.

And we need to find What is the minimum weight of the middle 95% of the players?

Explanation -

Using the Empirical Rule, 95% of the distribution will fall within 2 times of the standard deviation from the mean.

Two standard deviations = 2 x 25 pounds = 50 pounds

So the minimum weight = 200 pounds - 50 pounds = 150 pounds

Hence the final answer is 150 pounds.

3 0

1 year ago