Which set shows a subset of the set of natural numbers?

Select all correct statements about the related properties of triangleABC and triangle A'B'C'. CHOOSE ALL ANSWERS THAT APPLY.

Mariana [72]

I believe the correct answer is

D.) None of the above.

5 0

3 years ago

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What is the point of intersection of the lines represented by these equations

Marizza181 [45]

<h2>Points of Intersection</h2>

To find the point of intersection of two lines, we can use substitution to find the <em>x</em> and <em>y</em> coordinates.

<h2>Solving the Question</h2>

We're given:

$y = -2x + 2$
$y = x - 4$

Use substitution to find <em>x</em>:

$-2x + 2=x-4\\-2x=x-6\\-3x=-6\\x=2$

Use substitution to find <em>y</em>:

$y=x-4\\y=2-4\\y=-2$

<h2>Answer</h2>

The point of intersection is (2,-2).

3 0

2 years ago

A student performed the following steps to find the solution to the question x^2 - 2x - 15 = 0. Where did the student go wrong?

nataly862011 [7]

Answer:

D In step 3

Step-by-step explanation:

Given polynomial: x² - 2x - 15 = 0

Step 1: factor the polynomial ⇒ (x + 3)(x - 5) = 0

Step 2: x + 3 = 0 and x - 5 = 0

Step 3: x = -3 and x = 5

x - 5 = 0

Add 5 to both sides:

⇒ x - 5 + 5 = 0 + 5

⇒ x = 5

7 0

2 years ago

What is the greatest common factor (GCF) of 12 and 54?

Ahat [919]

The greatest common factor is six

5 0

3 years ago

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The radius of the large sphere is double the radius of the small sphere. How many times does the volume of the large sphere than

pshichka [43]

Answer:

8 times larger.

Step-by-step explanation:

The radius of the large sphere is double the radius of the small sphere.

Question asked:

How many times does the volume of the large sphere than the small sphere

Solution:

<u>Let radius of the small sphere = </u> $x$ <u />

<u>As the radius of the large sphere is double the radius of the small sphere:</u>

Then, radius of the large sphere = $2x$

To find that how many times is the volume of the large sphere than the small sphere, we will <em><u>divide the volume of large sphere by volume of small sphere:-</u></em>

For smaller sphere: $Radius = x$

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

$=\frac{4}{3} \pi x^{3}$

For larger sphere: $Radius = 2x$

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

$=\frac{4}{3} \pi (2x)^{3}$

Now, we will divide volume of the larger by the smaller one:

$=\frac{4}{3} \pi (2x)^{3}\div\frac{4}{3} \times\frac{\pi }{1 } \times x^{3}\\ \\ =\frac{4}{3} \pi\times8x^{3} \times\frac{3}{4\pi }\ \times\frac{1}{x^{3} }$

$\frac{4}{3}\pi\ is \ canceled\ by\ \frac{3}{4\pi } \ and\ also\ x^{3} is\ canceled\ by \ \frac{1}{x^{3} }$

= $\frac{8}{1}$

Therefore, the volume of the large sphere is 8 times larger than the smaller sphere.

7 0

4 years ago

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