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PolarNik [594]
3 years ago
15

Using SET NOTATION, what is the solution set for the following equation? a² - 3 = 22

Mathematics
1 answer:
mixas84 [53]3 years ago
7 0

Answer:

a = 5 or  a = -5

Step-by-step explanation:

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What is 2,520 divided by 16?
maw [93]

Answer:

157.5 is the answer

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Please show the steps​
notka56 [123]

Answer:

  x = -3, 0, or 7

Step-by-step explanation:

After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.

__

<h3>Step 1</h3>

Write the equation in standard form.

  4x³ -16x² -84x = 0

<h3>Step 2</h3>

Factor out the common factor from all terms.

  = 4x(x² -4x -21) = 0

<h3>Step 3</h3>

Compare to the factored form of a quadratic:

  (x +a)(x +b) = x² +(a+b)x +ab

This tells you the constants 'a' and 'b' in the factors can be found by considering ...

  (a+b) = -4 . . . . the coefficient of the x term of the quadratic

  ab = -21 . . . . . the constant term of the quadratic

It is often helpful to list factor pairs of the constant:

  -21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum

The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...

  a = -7, b = 3

<h3>Step 4</h3>

Put it all together.

  4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation

<h3>Step 5</h3>

Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:

  4x = 0   ⇒   x = 0

  x -7 = 0   ⇒   x = 7

  x +3 = 0   ⇒   x = -3

Solutions to the equation are x ∈ {-3, 0, 7}.

_____

<em>Additional comment</em>

What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.

A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.

3 0
2 years ago
Mrs. Terrace cut a small birthday cake into 6 equal pieces for 6 children. One child was not hungry, so she gave the birthday bo
ELEN [110]

Missing part of question:

Draw a tape diagram to show how much cake each of the five children received.

Answer:

See attachment

Step-by-step explanation:

Given

Equal\ Pieces = 6

Children = 5

Required

Tape diagram to represent the scenario

Because one child is not hungry, the number of children to share the cake becomes 6.

So, first we calculate the share of each child.

Share = \frac{Pieces}{Children}

Share = \frac{6}{5}

Share = 1.2

See attachment for tape diagram

The tape diagram implies that:

5 * 1.2 = 6

or

\frac{6}{1.2} = 5

or

\frac{6}{5} = 1.2

4 0
3 years ago
A swimming pool is 50 meters long,15 meters wide,and 3 meters deep. What is the volume of the pool
steposvetlana [31]

Answer: 2,250m^{3}

Step-by-step explanation:

Volume of the pool is given by : Length X breadth X height

V = 50 X 15 X 3

V = 2,250

5 0
3 years ago
A digital camera for 249.99 at 4% sales tax
spin [16.1K]
First round up 249.99 to 250.00

Then change the 4% into a decimal= 1.04 

Now multiply so the equation is= 250 x 1.04 =

$260 as your answer!

4 0
3 years ago
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