Evaluate the following expression. 3^-2

In a right triangle one leg measures a quarter of the other, how much do its acute angles measure? with procedure please

KATRIN_1 [288]

Answer:

The answer to your question is 14° and 76°

Step-by-step explanation:

Data

leg 1 = x

leg 2 = x/4

angle 1 = ?

angle 2 = ?

Process

To solve problem use trigonometric functions. We must use the trigonometric function that relates both legs (tangent).

tangent Ф = Opposite side / Adjacent side

-Substitution

tan Ф = (x/4) / x

-Simplification

tan Ф = x / 4x

tan Ф = 1/4

- Find Ф

Ф = tan⁻¹(1/4) = 14°

- Find the other acute angle

The sum of the internal angles in a triangles equals 180°

Ф + Ф₁ + 90° = 180

-Solve for Ф₁

Ф₁ = 180 - 90 - 14

-Result

Ф₁ = 76°

3 0

3 years ago

The variables x and y vary inversely If x=5 when y=12, then find the value of x when y=32

Vilka [71]

Answer:

x=15/8

Step-by-step explanation:

Inverse variation is given by

xy = k

Substituting x=5 and y=12

5*12 = k

60 =k

Our original equation is xy = 60

Now let y=32

x*32 = 60

Divide each side by 32

32x/32 = 60/32

Divide top and bottom by 4

x = 15/8

4 0

4 years ago

I need an answer! NO LINKS PLS! il give brainlist

cricket20 [7]

Answer:

D. The company's chocolate bars weigh 3.2 ounces on average.

Step-by-step explanation:

We are given that a company claims that its chocolate bars weigh 3.2 ounces on average.

The company took many large samples, and each time the mean weight of the sample was within the 95% confidence interval.

Definition of 95% confidence level: 95% confidence level means a range of values that you can be 95% certain contains the true mean of the population.

Thus by considering definition we can conclude that The company's chocolate bars weigh 3.2 ounces on average.

Thus Option D is correct.

D. The company's chocolate bars weigh 3.2 ounces on average.

4 0

3 years ago

James delivered 3/8 of the newspaper his route in the first hour and 4/5 of the rest in the second hour. What fraction of the ne

Soloha48 [4]

Answer:

1/2

Step-by-step explanation:

Remaining fraction will be (1-3/8)=5/8

Given that in the second hour he delivered 4/5 of 5/8, then the fraction delivered in the second hour will be:

4/5 of 5/8

=4/5×5/8

=1/2

He delivered 1/2 (in fraction)

7 0

3 years ago

Hannah and Corrine are playing a game by rolling two cubes, each numbered 1 through 6. If the sum of the numbers on the cubes is

Katarina [22]

Answer:

D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

Step-by-step explanation:

To get a sum of 7 by rolling two cubes, we need to get one of the combinations from the list below:

1 on the first cube, 6 on the second cube

or

6 on the first cube, 1 on the second cube

2 on the first cube, 5 on the second cube

or

5 on the first cube, 2 on the second cube

3 on the first cube, 4 on the second cube

or

4 on the first cube, 3 on the second cube

Therefore, the correct answer option is D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

7 0

3 years ago