Which set of numbers has 21 as a common factor?

Changle. Show all work. Round each length to the nearest tenth and each angle to the

Sedaia [141]

Answer:

Part 1) $BC=12.2\ units$

Part 2) $m\angle A=55^o$

Part 3) $m\angle C=35^o$

Step-by-step explanation:

Part 1) Find AC

we know that

In the right triangle ABC of the figure

Applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=7^2+10^2$

$AC^2=149\\AC=12.2\ units$

Part 2) Find the measure of angle A

we know that

In the right triangle ABC

$tan(A)=\frac{BC}{AB}$ ----> by TOA (opposite side divided by the adjacent side)

substitute the values

$tan(A)=\frac{10}{7}$

using a calculator

$m\angle A=tan^{-1}(\frac{10}{7})=55^o$

Part 3) Find the measure of angle C

we know that

In the right triangle ABC

$m\angle A+m\angle C=90^o$ ----> by complementary angles

substitute the given value

$55^o+m\angle C=90^o$

$m\angle C=90^o-55^o=35^o$

8 0

3 years ago

5(x+4)= -2(-4-x)+3 what is the answer?

lianna [129]

Answer:

x = -3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Step-by-step explanation:

Step 1: Define equation

5(x + 4) = -2(-4 - x) + 3

Step 2: Solve for x

Distribute: 5x + 20 = 8 + 2x + 3
Combine like terms: 5x + 20 = 2x + 11
Subtract 2x on both sides: 3x + 20 = 11
Subtract 20 on both sides: 3x = -9
Divide 3 on both sides: x = -3

Step 3: Check

Plug in x to verify it's a solution.

Substitute: 5(-3 + 4) = -2(-4 - -3) + 3
Simplify: 5(-3 + 4) = -2(-4 + 3) + 3
Add: 5(1) = -2(-1) + 3
Multiply: 5 = 2 + 3
Add: 5 = 5

Here we see that 5 does indeed equal 5. ∴ x = -3 is a solution of the equation.

And we have our final answer!

5 0

3 years ago

Read 2 more answers

Make x the subject of: 2x + a = b (x - 2)

nlexa [21]

Answer:

no solution

Step-by-step explanation:

7 0

3 years ago

Jennifer wants to net $35,000 on her house. Her closing costs will be 7,500 plus a 7% commission. She owes $185,000 on her loan.

GenaCL600 [577]

7,500 plus the commision is 525 now you add it to the 7,500 that will leave you with 8,025 now you subtract it from 185,000 so the answer will be 176,975

I'm glad if it helps :)

3 0

4 years ago

Read 2 more answers

I will pick brainliest first come, first serve! I need help! Give me an answer that makes sense!

nordsb [41]

Step-by-step explanation:

Total amount of apples in one bag:

$x + y + z$

Hence, total amount of apples in two bags:

$2(x + y + z)$

or

$2x + 2y + 2z$

or

$x + x + y + y + z + z$

Hence, B, D and E are correct.

A is incorrect because you are adding 2 more apples on top of the total amount of apples in one bag, and you cannot assume that there are 2 apples in each bag.

C is incorrect because you are multiplying the apples together, but you are supposed to add them up to find the total.

F is incorrect because you are finding 1/2 a bag.

3 0

3 years ago