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FrozenT [24]
3 years ago
6

Simplify. Write your answer using whole numbers and variables.

Mathematics
1 answer:
Andre45 [30]3 years ago
5 0

Answer:

q + 7

Step-by-step explanation:

(q² + 4q − 21) / (q − 3)

Factor the numerator:

(q + 7) (q − 3) / (q − 3)

Divide:

q + 7

You might be interested in
3х - 30 = у<br> 7y - 6 = 3х
mars1129 [50]

Answer:

Step-by-step explanation:

This one is simple substitution... at least, substitution is the easiest method. The first equation is 3<em>x</em> – 30 = <em>y</em>  and the second is 7<em>y</em> – 6 = 3<em>x</em>

As I look, I see 3 ways to use substitution to solve this:

  1. substitute 7<em>y</em> – 6 for 3<em>x</em>
  2. substitute 3<em>x</em> – 30 for <em>y</em>
  3. solve 3<em>x</em> – 30 = <em>y</em> for 3<em>x</em> and make it equal to 7<em>y</em> – 6

We're going to only use 1 method for the sake of time. Try the other two on your own. Assuming you don't make any mistakes, they will work.

<u>Method 1</u>:

3<em>x</em> – 30 = <em>y</em>

7<em>y</em> – 6 = 3<em>x</em>  — initial system of equations

7<em>y</em> – 6 – 30 = <em>y</em>  — substitute 7<em>y</em> – 6 for 3<em>x</em>

<u>7</u><u><em>y</em></u> – 6 – 30 = <u><em>y</em></u>  — marking like terms, bold for constants, <u>underlined</u> for variables

7<em>y</em> – 36 = <em>y</em>  — combining the constants and simplifying

Here, you could diverge into multiple paths: add 36 to both sides, subtract <em>y</em> from both sides, divide by 6 OR subtract 7<em>y</em> from both sides and divide by –6 . For the sake of time, I'm subtracting 7<em>y</em>, though I don't like dealing with negatives.

7<em>y</em> – 7<em>y</em> – 36 = <em>y</em> – 7<em>y</em>  — subtract 7<em>y</em> from both sides

–36 = –6<em>y</em>  — simplify

–36 ÷ –6 = –6<em>y</em> ÷ –6  — divide by –6 on both sides

<em>y</em> = 6  — simplify

Again, we can diverge here: substitute <em>y</em> into 3<em>x</em> – 30 = <em>y</em> or substitute <em>y</em> into 7<em>y</em> – 6 = 3<em>x</em>

I'm going to choose 3<em>x</em> – 30 = <em>y</em> but it will work either way, should you take the time (if you have it) to chase down every path this problem can take.

3<em>x</em> – 30 = <em>y</em>  — initial equation

3<em>x</em> – 30 = 6  — substitute 6 for <em>y</em>

3<em>x</em> – 30 + 30 = 6 + 30  — add 30 to both sides to isolate 3<em>x</em>

3<em>x</em> = 36  — simplify the expression

3<em>x</em> ÷ 3 = 36 ÷ 3  — divide both sides by 3 to isolate <em>x</em>

<em>x</em> = 12  — simplify

So, we have <em>x</em> = 12 and <em>y</em> = 6 . We know they work for 3<em>x</em> – 30 = <em>y</em>  but not if they work for 7<em>y</em> – 6 = 3<em>x</em> . Let's substitute those in to see if (12, 6) really is the solution point.

7<em>y</em> – 6 = 3<em>x</em>  — original equation

7(6) – 6 ≟ 3(12)  — substitute 6 for <em>y</em> and 12 for <em>x</em>

42 – 6 ≟ 36  — simplify by multiplying

36 = 36 ✔  — simplify by combining like terms on left side

Success! It works! We have found our solution!

I hope this helps increase your understanding of the concept. Have a great day!

8 0
3 years ago
What do i do here and plz help me answer this
stepladder [879]

Answer:

for number 1, you plug -3 in for x in the equation. and for number 2, you plug in 2 for y in the equation. you do this to find the missing values of the variables.

1. y= -10

2. x= -1

Step-by-step explanation:

i hope this helps :)

5 0
3 years ago
Read 2 more answers
Please help. Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact valu
o-na [289]

Answer:

Area = (18 + 4.5π) cm²

Perimeter = (6√2 + 12 + 3π) cm

Step-by-step explanation:

The shaded region given is made up of triangle ABC and a semicircle

AB = BC = 6 cm (note that the triangle is a portion of a square)

Diameter of semi-circle (d) = BC = 6cm

Radius (r) = ½*6 = 3 cm

==>Area of the shaded region in terms of π

Area of shaded region = area of triangle + area of semicircle

Area = ½*a*b + ½*πr²

Area = ½*6*6 + ½*π3²

Area = 18 + ½*π9

Area = 18 + 4.5π

<em>Area of the shaded portion = (18 + 4.5π) cm²</em>

==>Perimeter of shaded region in terms of π

Perimeter of shaded region = perimeter of triangle + perimeter of semicircle

= Sum of all sides of the triangle + ½πd

Sides of triangles are AB = 6 cm, BC = 6 cm

Use Pythagorean theorem to find side AC:

AC² = AB² + BC²

AC² = 6² + 6² = 36 + 36 = 72

AC = √72 cm

Perimeter of shaded triangle = √72 + 6 + 6 = √72 + 12 = (6√2 + 12) cm

Perimeter of semicircle = ½*πd = ½π6

= 3π

<em>Perimeter of the whole shaded region in terms of π = (6√2 + 12 + 3π) cm</em>

<em></em>

3 0
3 years ago
How many different 7-card hands include the ace and king of spades?
andrew-mc [135]
2118760 different 7 card hands

6 0
3 years ago
Pleaseeee helpppp !!!!!!!!! Will mark Brianliest !!!!!!!!!!!
Semenov [28]

Answer:

KL = 50

Step-by-step explanation:

∆JML is similar to ∆JNL. it follows that:

[tex] \frac{JM}{JN} = \frac{JL}{JK} [\tex]

JM = 4 + 20 = 24

JN = 4

JL = 10 + KL

JK = 10

Plug in the values

[tex] \frac{24}{4} = \frac{10 + KL}{10} [\tex]

[tex] 6 = \frac{10 + KL}{10} [\tex]

Multiply both sides by 10

[tex] 6*10 = \frac{10 + KL}{10}*10 [\tex]

[tex] 60 = 10 + KL [\tex]

Subtract 10 from each side

[tex] 60 - 10 = KL [\tex]

[tex] 50 = KL [\tex]

KL = 50

6 0
3 years ago
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