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3 years ago

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

Mathematics

1 answer:

timofeeve [1]3 years ago

4 0

Answer: Choice B

Open circle at 3. Shading to the right

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Work Shown:

3(8 - 4x) < 6(x - 5)

24 - 12x < 6x - 30

24 + 30 < 6x + 12x

54 < 18x

18x > 54

x > 54/18

x > 3

We use an open circle at 3 to indicate we don't include this endpoint as part of the solution. The solution set is everything larger than 3, so we shade to the right of this open circle.

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The circumference of a circle is 30t. What is its area?

labwork [276]

Answer:

$A=\frac{225t^2}{\pi}$ given the circumference is 30t.

Step-by-step explanation:

The circumference of a circle is $C=2\pi r$ and the area of a circle is $A=\pi r^2$ assuming the radius is $r$ for the circle in question.

We are given the circumference of our circle is $2 \pi r=30t$ .

If we solve this for r we get: $r=\frac{30t}{2\pi}$ . To get this I just divided both sides by $2\pi$ since this was the thing being multiplied to $r$ .

So now the area is $A=\pi r^2=\pi (\frac{30t}{2 \pi})^2$ .

Simplifying this:

$A=\pi (\frac{30t}{2 \pi})^2$ .

30/2=15 so:

$A=\pi (\frac{15t}{\pi})^2$ .

Squaring the numerator and the denominator:

$A=\pi (\frac{(15t)^2}{(\pi)^2}$

Using law of exponents or seeing that a factor of $\pi$ cancels:

$A=\frac{(15t)^2}{\pi}$

$A=\frac{15^2t^2}{\pi}$

$A=\frac{225t^2}{\pi}$

4 0

3 years ago

Charlie runs at the speed of 3 yards per second.. About how many miles per hour does charlie run?

mariarad [96]

Charlie can run at the speed of 6.13636 miles per hour.

I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

8 0

3 years ago

17. Tiana deposited $500 into an

Ivahew [28]

Answer:

In 50 years the amount will be $ 2000.

Step-by-step explanation:

Tiana deposited $500 into a account at 6 % simple interest per Year .

Therefore, Principal (P) is $500

Amount (Principal + Interest) = $2000

Interest (I) = $2000 - $500 = $1500

Rate percentage (R) = 6% per Year

Let, The time be T years

Now, I = $\frac{P . R . T}{100}$

Or, T = $\frac{100. I }{P . R}$

Or, T = (100×1500 ) ÷ ( 500× 6 )

∴ T = 50 Years

3 0

3 years ago

Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 136.

vagabundo [1.1K]

Answer:

A=20 C=19

Step-by-step explanation:

3A+4C=136

2A+3C=97

4 0

3 years ago

4,336 is 10 times as much as?

algol13

Answer:

433.6

Step-by-step explanation:

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4 years ago