Which of the following equations correctly represents the law of cosines?

A gardener buys a rake and a pair of gloves for each of the 12 volunteers in the gardening club. Each pair of gloves

matrenka [14]

Let unit cost of one rake be : r

Given : Total number of volunteers = 12

Given : Each pair of gloves cost $8.00

⇒ Cost of 12 pair of gloves for 12 volunteers = (12 × 8) = $96

Given : The gardener spends a total of $300 on both rakes and gloves

⇒ Cost of 12 rakes + Cost of 12 pair of gloves = $300

⇒ 12r + 96 = 300

⇒ 12r = 204

⇒ r = 17

<u>Answer</u> : Cost of one rake is $17

4 0

3 years ago

What percent of 18.75 is 27?

Olin [163]

The answer is 144%

Your welcome

4 0

3 years ago

Please help me out<br><br><br><br> Find the area .

Gemiola [76]

Answer:

its27.54 8.1×3.4 =27.54 base×height

7 0

3 years ago

Im confused and i need help please help

denis23 [38]

Answer:

C

Step-by-step explanation:

8 0

3 years ago

Which set of numbers could represent the lengths of the sides of a right triangle?

DiKsa [7]

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

By the pythagorean theorem, a triangle is a right triangle if and only if

$\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2$ .

In this case,

$\text{longest side}^2 = 17^2 = 289$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}$ .

In other words, indeed $\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2$ . Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

Factor out the common factor $2$ to simplify the calculations.

$\text{longest side}^2 = 20^2 = 400$

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = 11^2 = 121$ .

<h3> $\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}$ .</h3>

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

6 0

3 years ago