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3 years ago

Find the supplement of the complement of a 51 degree angle

1 answer:

5 0

Complimentary = 90 degrees
Supplementary = 180 degrees

Compliment of 51:
90 - 51 = 39 degrees

Supplement of 39:
180 - 39 = 141 degrees

The supplement of the compliment of a 51 degree angle is 141 degrees.

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HELPPP!! which of the following could be the ratio between the lengths of two legs of a 30,60,90 triangle

sp2606 [1]

Answer:

$\sqrt{3}:3\\1:\sqrt{3}$

Step-by-step explanation:

<u>Trigonometric Ratios</u>

The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant, and cotangent.

The longest side of the triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The tangent ratio is defined as:

$\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}$

The cotangent ratio is defined as:

$\displaystyle \cot\theta=\frac{\text{adjacent leg}}{\text{opposite leg}}$

As shown above, the tangent and the cotangent are the ratios of the two legs in any possible order.

If the triangle has angles of 30°, 60°, and 90°, then we can take one of the acute angles and find the tangent and cotangent to know the required ratios:

Let's take for example the 30° angle:

$\displaystyle \text{ratio of legs: }\tan 30^\circ=\frac{\sqrt{3}}{3}$

$\displaystyle \text{ratio of legs: }\cot 30^\circ=\sqrt{3}$

Thus the possible ratios from the list are:

$\sqrt{3}:3\\1:\sqrt{3}$

The reciprocals of those ratios are also applicable

6 0

3 years ago

A travel company is selling two different suitcases, each in the shape of a rectangular prism. Which statement is true?

9966 [12]

Answer:

Suitcase 2 is the better deal because it is less expensive than Suitcase 1 by approximately $0.01 per cubic inch ⇒ C

Step-by-step explanation:

Let us find the volume of each suitcase and find the price per cubic inch to chose the better deal

The formula of the volume of a rectangular prism is V = L × W × H, where

L is the length of it
W is the width of it
H is the height of it

Suitcase 1:

∵ Its length is 14 inches

∵ Its width is 9 inches

∵ Its height is 22 inches

- Substitute them in the formula of the volume above

∵ V = 14 × 9 × 22

∴ V = 2772 inches³

∵ The cost of it is $139.99

- Divide the cost by the volume to find the cost per cubic inch

∵ The cost per cubic inch = 139.99 ÷ 2772

∴ The cost per cubic inch ≅ 0.05

∴ The cost per cubic inch is approximately $0.05

Suitcase 2:

∵ Its length is 18 inches

∵ Its width is 10 inches

∵ Its height is 22 inches

- Substitute them in the formula of the volume above

∵ V = 18 × 10 × 22

∴ V = 3960 inches³

∵ The cost of it is $158.99

- Divide the cost by the volume to find the cost per cubic inch

∵ The cost per cubic inch = 158.99 ÷ 3960

∴ The cost per cubic inch ≅ 0.04

∴ The cost per cubic inch is approximately $0.04

∵ 0.04 is less than 0.05

∵ 0.05 - 0.04 = 0.01

∴ Suitcase 2 is less expensive than suitcase 1 by $0.01

∴ Suitcase 2 is the better deal

Suitcase 2 is the better deal because it is less expensive than Suitcase 1 by approximately $0.01 per cubic inch

6 0

3 years ago

⎩

kifflom [539]

Answer:

the explicit formula for h(n) is, -65-10n

Step-by-step explanation:

Given that:

h(1) = -75

h(n) = h(n-1)-10 ......[1]

Put n =2 in [1] we have;

$h(2) = h(1)-10 = -75-10 = -85$

Similarly for n = 3

$h(3) = h(3)-10 = -85-10 = -95$ and so on...

The series we get;

$-75, -85, -95, ....$

This is an arithmetic sequence series with common difference(d) = -10

Since,

-85-(-75) = -85+75 = -10,

-95-(-85) = -95+85 = -10 and so on

First term(a) = -75

the Explicit formula for arithmetic sequence is given by:

$a_n = a+(n-1)d$

where a is the first term,

d is the common difference and

n is the number of terms.

We have to find the explicit formula for h(n);

$h(n) = a+(n-1)d$

Substitute the given values we have;

$h(n) = -75+(n-1)(-10)$

$h(n) = -75-10n+10 = -65-10n$

Therefore, the explicit formula for h(n) is, -65-10n

5 0

3 years ago

Read 2 more answers

Solve the inequality for u<br>-5u+27 [less than or equal to] 2

baherus [9]

Answer:

5≤u

Step-by-step explanation:

Put the words and numbers into an equation:

-5u+27≤2

Put all like terms on one side:

27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)

Simplify:

25≤5u

Solve:

5≤u

6 0

3 years ago

A. B. C. D. E. Which expressions listed on the left are equivalent to ? Check all that apply. (Assume that a ≠ 0.) A B C D E

Neko [114]

The Answer Is .A,B,AND E

4 0

3 years ago

Read 2 more answers