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2 years ago

Which number line represents the solution of 4x - 9 ≥ -21? what would the number line look like ?

Mathematics

2 answers:

elixir [45]2 years ago

8 0

Steps to solve:

4x - 9 ≥ -21

~Add 9 to both sides

4x - 9 + 9 ≥ -21 + 9

~Simplify

4x ≥ -12

~Divide 4 to both sides

4x/4 ≥ -12/4

~Simplify

x ≥ 3

The number line will be in the picture below.

Best of Luck!

Fittoniya [83]2 years ago

5 0

Solve for x:

4x-9 >= -21

Add 9 to both sides:

4x >= -12

Divide both sides by 4:

X >= -3

The number line would have a solid dot on -3 with a line and arrow pointing to the right of -3

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1 year ago

Quadrilateral ABDE is a rectangle. DE = 4 in. and BD = 6 in. If the rectangle is rotated about a line through CF, cylinder Y is

postnew [5]

Answer:

1 in. is the answer.

Step-by-step explanation:

Solution: A Rectangle ABDE in which DE=4 inches and BD= 6 inches

There are two kinds of rotations

1. one along the Breadth, side having length 6 inches,i.e rotated along line GH, Cylinder Z is created.

Radius of cylinder Z=6/2= 3 inches

2. Second along the Length, Side having length 4 inches,i.e rotated about a line CF, cylinder Y is created.

Radius of cylinder Y= 4/2= 2 inches

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Diagram shown below of both the cases:

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2 years ago

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Susan works as a hostess where she makes $8.75 per hour. She also babysits and earns $10.00 per hour. Last week she made $165.00

True [87]

Answer:

6 hours as a babysitter and 12 hours as a hostess

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2 years ago

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Mark has three 4 1/2 oz cans and five 8 1/4 oz cans. How many ounces of tomatoes does Mark need?

Mashutka [201]

Answer:

54.74 ounces of tomatoes mark need.

Step-by-step explanation:

Given : Mark has three $4\frac{1}{2}$ oz cans and five $8\frac{1}{4}$ oz cans.

To find : How many ounces of tomatoes does Mark need?

Solution :

Mark has three $4\frac{1}{2}$ oz cans.

i.e. $3\times 4\frac{1}{2}=3\times \frac{9}{2}=\frac{27}{2}$

Mark has five $8\frac{1}{4}$ oz cans.

i.e. $5\times 8\frac{1}{4}=5\times \frac{33}{4}=\frac{165}{4}$

Total ounces of tomatoes does Mark need is

$T=\frac{27}{2}+\frac{165}{4}$

$T=\frac{54+165}{4}$

$T=\frac{219}{4}$

$T=54.75$

Therefore, 54.74 ounces of tomatoes mark need.

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2 years ago

The formula T= 2pi sqrt(L/32) relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing

tester [92]

The length of pendulum is 2.485 feet

<h3><u><em>Solution:</em></u></h3>

Given that,

The formula T= 2pi sqrt(L/32) relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing back and forth

<u><em>Therefore, the given formula is:</em></u>

$T=2\pi \sqrt{\frac{L}{32} }$

We have to find the length of pendulum that makes one full swing in 1.75 seconds

So the modify the given equation to find "L"

$T=2\pi \sqrt{\frac{L}{32} }\\\\ \sqrt{\frac{L}{32} }=\frac{T}{2 \pi}\\\\\text{Taking square root on both sides }\\\\\frac{L}{32} = \frac{T^2}{4 \pi^2}\\\\L = \frac{T^2}{4 \pi^2} \times 32\\\\L = \frac{T^2}{\pi^2 } \times 8$

Substitute T = 1.75 seconds and $\pi = 3.14$

$L = \frac{1.75^2}{3.14 \times 3.14} \times 8\\\\L = \frac{3.0625}{9.8596} \times 8\\\\L = 2.485$

Thus length of pendulum is 2.485 feet approximately

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2 years ago