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Nuetrik [128]
4 years ago
10

2. Solve each given location and show your work. Tell whether each equation has one solution, an infinite number of solutions, o

r no solutions. Explain your answers. (a) 4x + 2(x – 1) = 10 + 2x (b) 30 – x = 10 – (6 + 10) (c) 8x = 4x + 4x + 10(x-x) Answers:
Mathematics
1 answer:
solniwko [45]4 years ago
4 0

Answer:

a  one solutions x=3

b  one solution x=36

c  infinite solutions

Step-by-step explanation:

(a) 4x + 2(x – 1) = 10 + 2x

Distribute

4x+2x-2 = 10+2x

Combine like terms

6x-2 = 10+2x

Subtract 2x from each side

6x-2x-2 = 10+2x-2x

4x-2 = 10

Add 2 to each side

4x-2+2 =10+2

4x=12

Divide by 4

4x/4 = 12/4

x=3

There is one solution


(b) 30 – x = 10 – (6 + 10)

Distribute the minus sign

30-x = 10-6-10

30-x=-6

Subtract 30 from each side

30-x-30 = -6-30

-x = -36

Multiply by -1

x = 36


(c) 8x = 4x + 4x + 10(x-x)

Parentheses first

8x = 4x+4x+10(0)

8x=4x+4x

Combine like terms

8x=8x

Subtract 8x from each side

8x-8x=8x-8x

0=0

This is always a true statement

x =all real numbers

infinite solutions

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3 years ago
What smallest prime factor of 12?
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3 years ago
Nadia is investigating rotations about the center of regular polygons that carry the regular polygon onto itself. She claims tha
GalinKa [24]

Answer:

\theta_1 \ n\ \theta_2 = 120, 240

Step-by-step explanation:

The question is incomplete, as the angles of rotation are not stated.

However, I will list the angles less than 360 degrees that will carry the hexagon and the nonagon onto itself

We have:

Nonagon = 9\ sides

Hexagon = 6\ sides

Divide 360 degrees by the number of sides in each angle, then find the multiples.

<u>Nonagon</u>

\theta = \frac{360}{9} =40

List the multiples of 40

\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320

<u>Hexagon</u>

\theta = \frac{360}{6} =60

List the multiples of 60

\theta_2 = 60, 120, 180, 240, 300

List out the common angles

\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320

\theta_2 = 60, 120, 180, 240, 300

\theta_1 \ n\ \theta_2 = 120, 240

This means that, only a rotation of 120, 240 will lift both shapes onto themselves, when applied to both shapes.

The other angles will only work on one of the shapes, but not both at the same time.

7 0
3 years ago
Plz help I’ll pay I promise this is timed
Wewaii [24]

Answer:

you can say u are mutiplying them by two each times see

2:16

4:32

6:48

8:64

10:80

12:96

Step-by-step explanation:

mark brainlyest

4 0
3 years ago
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