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3 years ago

Which graph represents the solution of the inequality 24x – 17x ≥ 13x + 15?

Mathematics

1 answer:

Taya2010 [7]3 years ago

5 0

Answer:

See below ~

Step-by-step explanation:

Solving the inequality :

24x - 17x ≥ 13x + 15
7x ≥ 13x + 15
-6x ≥ 15
<u>x ≤ -2/5</u>

<u />

Plotted graph :

Kindly note the line drawn should be a solid line for the inequality to be true
When you draw on a graph, kindly remember this and don't directly copy from the attached graph

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labwork [276]

Hello!

The figure is made up of a cone and a hemisphere. To the nearest whole number, what is the approximate volume of this figure? Use 3.14 to approximate π . Enter your answer in the box. cm³

A 12 cm cone with a dome on top of it that has an 8 cm diameter

Data: (Cone)

h (height) = 12 cm

r (radius) = 4 cm (The diameter is 8 being twice the radius)

Adopting: $\pi \approx 3.14$

V (volume) = ?

Solving: (Cone volume)

$V = \dfrac{ \pi *r^2*h}{3}$

$V = \dfrac{ 3.14 *4^2*\diagup\!\!\!\!\!12^4}{\diagup\!\!\!\!3}$

$V = 3.14*16*4$

$\boxed{V = 200.96\:cm^3}$

Note: Now, let's find the volume of a hemisphere.

Data: (hemisphere volume)

V (volume) = ?

r (radius) = 4 cm

Adopting: $\pi \approx 3.14$

If: We know that the volume of a sphere is $V = 4* \pi * \dfrac{r^3}{3}$ , but we have a hemisphere, so the formula will be half the volume of the hemisphere $V = \dfrac{1}{2}* 4* \pi * \dfrac{r^3}{3} \to \boxed{V = 2* \pi * \dfrac{r^3}{3}}$

Formula: (Volume of the hemisphere)

$V = 2* \pi * \dfrac{r^3}{3}$

Solving:

$V = 2* \pi * \dfrac{r^3}{3}$

$V = 2*3.14 * \dfrac{4^3}{3}$

$V = 2*3.14 * \dfrac{64}{3}$

$V = \dfrac{401.92}{3}$

$\boxed{ V_{hemisphere} \approx 133.97\:cm^3}$

Now, to find the total volume of the figure, add the values: (cone volume + hemisphere volume)

Volume of the figure = cone volume + hemisphere volume

Volume of the figure = 200.96 cm³ + 133.97 cm³

$\boxed{\boxed{\boxed{Volume\:of\:the\:figure = 334.93\:cm^3}}}\end{array}}\qquad\quad\checkmark$

_______________________

I Hope this helps, greetings ... Dexteright02! =)

6 0

3 years ago

Tracey paid $145 for an item that was originally priced at $460. What percent of the original price did Tracey pay?

Elena L [17]

It is given in the question that

Tracey paid $145 for an item that was originally priced at $460.

And we have to find what percent of the original price did Tracey pay.

So we have to find the percentage of 145 out of 460, and for that, we have to divide 145 by 460 and multiply the result by 100. THat is

$\frac{145}{460}*100=31.52 percentage$

And that's the required answer .

5 0

3 years ago

Trapezoid A and trapezoid B as shown on the coordinate grid.

mixer [17]

Answer:

Step-by-step explanation:

The missing diagram showing the trapezoids is attached in the diagram below.

There are three stages by which trapezoid A must be transformed into trapezoid B.

We can see three fundamental differences as follows:

rotation
size
location

As a result, we will perform the following transformations:

Right off the bat, carry out an anticlockwise rotation of Trapezoid A 90 degrees from the origin.
Then, to balance the size of the dimension, elongate by a scale factor of 1/3. (As can be shown, each side is three times larger after this move, and its base is at y = -2)
Finally, a three-unit down translation is carried out.