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jenyasd209 [6]
3 years ago
14

What is the quotient of the rational expression shown below? Make sure your answer is in reduced form x^2-4/x+3 divided x^2-4x+4

/4x+2
Mathematics
1 answer:
natita [175]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

Given

\frac{x^2-4}{x+3} ÷ \frac{x^2-4x+4}{4x+2}

The first step is to factor numerators/denominators, if possible

x² - 4 = (x - 2)(x + 2) ← difference of squares

x² - 4x + 4 = (x - 2)(x - 2) ← perfect square

4x + 2 = 2(2x + 1)

To divide the expressions follow the steps

• Leave the first fraction

• Change division to multiplication

• Turn the second fraction upside down

We now have

\frac{(x-2)(x+2)}{x+3} × \frac{2(2x+1)}{(x-2)(x-2)}

Final step is to cancel common factors from the numerators/denominators

= \frac{2(2x+1)(x+2)}{(x+3)(x-2)} ← quotient


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Solve the inequalities -150x ≥ − 2,400 and -336 ≥ − 21y.
astra-53 [7]
Ok so easy peasy
remember that when divide or multiply by negative, reverse the inequality symbol example
2>3 times -1=
-2<-3 so

-150x<u>></u>-2400
divide both sides by -150
flip sign
<u />x<u><</u>16



-336<u>></u>-21y
divide both sides by -21
flip sign
16<u><</u>y

they seem to have the same solution

x=y<u>></u>16
4 0
3 years ago
Read 2 more answers
Which statements are true about a rectangular pyramid with a height of 9 centimeters and a base with the dimensions of 4
tigry1 [53]

Answer:

- The area of the base of the pyramid, B, is 24 cm

- A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.

Step-by-step explanation:

Volume of a rectangular based pyramid = 1/3{Base area × Height}

Base Area = Length × Breadth

Volume = 1/3{(Length × Breadth) × Height}

Given a rectangular pyramid with a height of 9 centimeters and a base with the dimensions of 4

centimeters by 6 centimeters

Base Area = 4cm × 6cm

Base area = 24cm²

If Height =9cm

Volume of the pyramid = 1/3 × 24 × 9

Volume = 24 × 3

Volume of the pyramid = 72cm³

If the shape is a prism, the volume will be base area × height

= 24 × 9

= 216cm³

It can be seen that volume of rectangular prism = 3 × volume of rectangular pyramid.

6 0
3 years ago
Read 2 more answers
Se
Diano4ka-milaya [45]
X+y=7 and 16x+25y=148
8 0
3 years ago
F(x) = –3x² - 6x +1<br><br> Find f(8)
MAXImum [283]

Answer:

-239

Step-by-step explanation:

6 0
3 years ago
How do I order rational and irrational numbers from least to greatest
gizmo_the_mogwai [7]

Answer: Rational numbers are any numbers that can be expressed by a fraction with integers in both the numerator and the denominator. The amount of time and paper it takes to put them into an increasing line depends on how many numbers there are and how big of a range they have.

1.Rewrite improper fractions

An improper fraction is a fraction with a bigger numerator than denominator. These numbers can be difficult to compare. For example, numbers such as 26/7, 31/9, 12/5, 8/3 and 22/13 do not have an obvious highest or lowest term. Rewrite improper fractions as mixed numbers or as numbers with decimals. To turn an improper fraction into a decimal, divide the numerator by the denominator. If the denominator is large or a prime number greater than five, use a calculator. For example, divide the numbers 26/7, 31/9, 12/5, 8/3 and 22/13 to create 3.71, 3.44, 2.4, 2.67 and 1.69.

2.Find the highest and lowest terms

Figure out where your number line starts and ends. Put the lowest term on the far left and the highest term on the far right. Remember, negative numbers are lower than positive numbers, and the greater a negative number's distance from zero, the lower it is.

3.Mark benchmark terms

Draw a line extending through your lowest and highest points. Figure out some major points between these values and mark them on your line. For example, if your lowest number is negative 25 and your highest number is 50, find where zero and 25 would be. Mark these as benchmarks or guides.

4.Fill in the remaining numbers

Using your guides, fill in the rest of the numbers. Start with the lowest values on the left and work your way up.  


4 0
3 years ago
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