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3 years ago

What is the solution to -4(8 – 3x) >_ 6x – 8?

Mathematics

1 answer:

Vsevolod [243]3 years ago

3 0

Answer:

x ≥ 4

General Formulas and Concepts:

<u>Pre-Algebra</u>

Equality Properties

Step-by-step explanation:

<u>Step 1: Define inequality</u>

-4(8 - 3x) ≥ 6x - 8

<u>Step 2: Solve for </u><em><u>x</u></em>

Distribute -4: -32 + 12x ≥ 6x - 8
Subtract 6x on both sides: -32 + 6x ≥ -8
Add 32 on both sides: 6x ≥ 24
Divide 6 on both sides: x ≥ 4

Here we see that <em>x</em> can be any value greater than or equal to 4.

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Please help me with this

Brums [2.3K]

Answer:

match the boxes to the parts of the equations shown below

Step-by-step explanation:

$\text{slope}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{50-34}{5-3}=\dfrac{16}{2}=8$

<h3>Right</h3>

$\text{slope}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-31}{30-1}=\dfrac{-29}{29}=-1$

3 0

3 years ago

The gear is one of the oldest mechanical devices. It has been used since ancient times for its ability to increase or decrease r

eduard

The large gear attached to the pedals connected to the smaller gear

attached to the wheel allows the bicycle to travel further per rotation.

Correct responses:

Part A: Approximately 10.47 inches

Part B: 300°The d

Part C: Approximately 125.66 inches

Part D: The distance traveled increases by approximately 62.83 inches

<h3 /><h3>Methods used to calculate the above values</h3>

Given:

The radius of the large central gear, <em>r</em> = 4 inches

Radius of the small gear = 2 inches

Part A:

The distance travelled by the larger gear when the angle of rotation is 150° is given as follows;

$\displaystyle Distance \ travelled \ by \ larger \ gear = \mathbf{\frac{150^{\circ}}{360^{\circ}} \times 2 \times \pi \times 4 \, inches} = \frac{10}{3} \cdot \pi \ inches$

$\displaystyle Distance \ traveled \ by \ the \ outer \ edge = \frac{10}{3} \cdot \pi \ inches \approx \underline{ 10.47 \ inches}$

Part B:

When the small gear travels the same linear distance as the large gear in part A, we have;

$\displaystyle Degree \ of \ rotation = \frac{\frac{10}{3} \cdot \pi }{2 \times \pi \times 2 } \times 360^{\circ}= 300^{\circ}$

The degree of rotation of the small gear = <u>300°</u>

Part C:

The distance travelled, <em>C</em>, by a single rotation of the large gear is given as follows;

C = 2 × π × 4 inches = 8·π inches

The degree of rotation of the smaller gear following one rotation of the large gear is therefore;

$Degree \ of \ rotation = \displaystyle \frac{8\cdot \pi \ inches}{4 \cdot \pi \ inches } \times 360^{\circ} = \mathbf{ 720^{\circ}}$

720° = 2 × 360°

1 complete rotation is equivalent to 360°.

Therefore'

720° is equivalent to two complete rotation.

Therefore, the smaller gear and the wheel rotates twice for each rotation of the large gear

The distance the bicycle travels = 2 × The circumference of the wheel

Therefore;

Distance traveled by the bicycle = 2 × 2 × π × 10 inches = 40·π inches

Distance traveled by the bicycle = 40·π inches ≈ <u>125.66 inches</u>

Part D:

If the radius of the small gear is 1.5 inches and the radius of the large gear is 4.5 inches, we have;

Number of rotation of the small gear for each rotation of the large gear = 3 rotations

Therefore, number of rotation of the wheel = 3

Distance the bicycle travels = 3 × 2 × π × 10 inches = 60·π inches

The difference in distance traveled = 60·π inches - 40·π inches = 20·π inches

The distance traveled by the bicycle increases by 20·π inches ≈ <u>62.83 inches</u>

Learn more about gear transmission here:

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8 0

3 years ago

Melanie had two $10 bills one$5 bill,four dimes, and six pennies. Then she bought a fruit cup for $2.19

irga5000 [103]

Answer:

$23.27

Step-by-step explanation:

yes

7 0

4 years ago

What fraction of 9 is 3

Alex Ar [27]

Answer:

1/3

Step-by-step explanation:

Take the part over the whole

3/9

We can simplify

Divide the top and bottom by 3

1/3

4 0

3 years ago

Read 2 more answers

Julie has 5 times as many red beads as green beads. She has half as many yellow beads as red beads. She has 12 green beads.

ANEK [815]

12 green beads
60 red beads
30 yellow beads.
102 beads in all.

I hope this helped:)

8 0

3 years ago