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3 years ago

Factor the quadratic expression

Mathematics

1 answer:

Ber [7]3 years ago

3 0

(x - 6)(x - 2) the answer to the question

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Monic and Rachel purchased a tv for $378. Monica paid $36 less then Rachel. How many did each person pay for the tv? Solve using

topjm [15]

Answer:

Monica paid $171 while Rachel paid $207

Step-by-step explanation:

We are told that Monic and Rachel purchased a tv for $378.

Let the amount spent by Monica be X and the amount spent by Rachel be Y.

Thus;

x + y = 378 - - - - (eq 1)

We are told that Monica paid $36 less then Rachel. Thus;

y = x + 36

Or y - x = 36 - - - (eq 2)

Add eq 1 & eq 2 together to give;

2y = 378 + 36

2y = 414

y = 414/2

y = $207

Put 207 for x in eq 1 to get;

x + 207 = 378

x = 378 - 207

x = $171

Thus;

Monica paid $171 while Rachel paid $207

8 0

2 years ago

Keira goes shopping at a supermarket

Damm [24]

What is the rest of it

6 0

3 years ago

Can you plz help me answer this question?

Hatshy [7]

Answer:

50km/h is 13.89m/s

and the lorry is only going 13.5m/s

Step-by-step explanation:

4 0

3 years ago

The volume of a sphere whose diameter is 18 centimeters is _ cubic centimeters. If it’s diameter we’re reduced by half, it’s vol

kaheart [24]

<h2>Answer:</h2>

<u>First Part</u>

Given that

$Volume = \frac{4}{3} \pi r^{3}$

We have that

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{Diameter}{2})^{3} = \frac{4}{3} \pi 9^{3} = 972\pi cm^{3} \approx 3053.63 cm^{3}$

<u>Second Part</u>

Given that

$Volume = \frac{4}{3} \pi r^{3}$

If the Diameter were reduced by half we have that

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{r}{2}) ^{3} = \frac{\frac{4}{3} \pi r^{3}}{8}$

This shows that the volume would be $\frac{1}{8}$ of its original volume

<h2>Step-by-step explanation:</h2>

<u>First Part</u>

Gather Information

$Diameter = 18cm$

$Volume = \frac{4}{3} \pi r^{3}$

Calculate Radius from Diameter

$Radius = \frac{Diameter}{2} = \frac{18}{2} = 9$

Use the Radius on the Volume formula

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi 9^{3}$

Before starting any calculation, we try to simplify everything we can by expanding the exponent and then factoring one of the 9s

$Volume = \frac{4}{3} \pi 9^{3} = \frac{4}{3} \pi 9 * 9 * 9 = \frac{4}{3} \pi 9 * 9 * 3 * 3$

We can see now that one of the 3s can be already divided by the 3 in the denominator

$Volume = \frac{4}{3} \pi 9 * 9 * 3 * 3 = 4 \pi 9 * 9 * 3$

Finally, since we can't simplify anymore we just calculate it's volume

$Volume = 4 \pi 9 * 9 * 3 = 12 \pi * 9 * 9 = 12 * 81 \pi = 972 \pi cm^{3}$

$Volume \approx 3053.63 cm^{3}$

<u>Second Part</u>

Understanding how the Diameter reduced by half would change the Radius

$Radius =\frac{Diameter}{2}\\\\If \\\\Diameter = \frac{Diameter}{2}\\\\Then\\\\Radius = \frac{\frac{Diameter}{2} }{2} = \frac{\frac{Diameter}{2}}{\frac{2}{1}} = \frac{Diameter}{2} * \frac{1}{2} = \frac{Diameter}{4}$

Understanding how the Radius now changes the Volume

$Volume = \frac{4}{3}\pi r^{3}$

With the original Diameter, we have that

$Volume = \frac{4}{3}\pi (\frac{Diameter}{2}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{2^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{2 * 2 * 2} = \frac{4}{3}\pi \frac{Diameter^{3}}{8}\\\\$

If the Diameter were reduced by half, we have that

$Volume = \frac{4}{3}\pi (\frac{Diameter}{4}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{4^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 4 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 2 * 2 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{8 * 8} = \frac{\frac{4}{3}\pi\frac{Diameter^{3}}{8}}{8}$

But we can see that the numerator is exactly the original Volume!

This shows us that the Volume would be $\frac{1}{8}$ of the original Volume if the Diameter were reduced by half.

3 0

2 years ago

When x increases from a to a + 2, y increases by a difference of 8. For which functions is this statement true?

lord [1]

Answer:

That would be Option C.

Step-by-step explanation:

Lets look at y = 4x + 2:-

Let x = a then y = 4a + 2

Now if x in creases to a +2, y = 4(a +2) + 2 = 4a + 8 + 2

= 4a + 10.

(4a + 10) - (4a + 2) = 8 , so this is the required expression, y = 4x + 2.

6 0

3 years ago