Simplify the expression (x^2+3x-28)/(x^2+10x+ 21). Show your work.
NOTE: Must show your factoring work using either the big X strategy covered in class, or the quadratic formula method. Must show how you get factors. Not just give me factors.

Sum of three terms in a GP = 7

Product of the numbers = 8

G.P

Let the three numbers be a/r , a , ar where a is the first term and r is the common ratio.

So,

⟹ a/r + a + ar = 7 -- equation (1)

And,

⟹ (a/r) * a * ar = 8

⟹ a³ = 8

⟹ a = ³√8

⟹ a = 2

Substitute the value a in equation (1).

⟹ 2/r + 2 + 2r = 7

⟹ (2 + 2r + 2r²)/r = 7

⟹ 2 + 2r + 2r² = 7r

⟹ 2r² + 2r - 7r + 2 = 0

⟹ 2r² - 5r + 2 = 0

⟹ 2r² - 4r - r + 2 = 0

⟹ 2r(r - 2) - 1 (r - 2) = 0

⟹ (2r - 1)(r - 2) = 0

★ 2r - 1 = 0

⟹ 2r = 1

⟹ r = 1/2

★ r - 2 = 0

⟹ r = 2

If r = 1/2 ;

a/r = 2/(1/2) = 2 * 2 = 4

a = 2

ar = 2 * 1/2 = 1

If r = 2 ;

a/r = 2/2 = 1

a = 2

ar = 2 * 2 = 4

∴ Required GP is 4 , 2 , 1 or 1 , 2 , 4.

I hope it will help you.

Regards.

Step-by-step explanation:

Assume that the 4 terms are a/r, a , ar, ar2.

Product of first 3 terms = a3 =8

=> a=2

Sum of last 3 terms :

a(1 + r + r2) = 14

=> r2 + r - 6 = 0

Solving the above equation r= -3 or 2

So the terms are

-2/3, 2, -6, 18

Or

1, 2, 4, 8

Answer:

1/11x

Step-by-step explanation:

Answer: it is [tex]\frac{1}{11}x[/tex] or [tex]\frac{x}{11}[/tex]

She earns if she does not make any sales on a given day $0.

We have given that,

A salesperson earns 25% of her total sales in addition to base pay. The graph below represents her total pay for a given day.

We have to determine what she earns if she does not make any sales on a given day.

The line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G.

From the observation of the graph, we can say that she earns if she does not make any sales on a given day none.

Therefore option A is correct.

she earns if she does not make any sales on a given day $0.

To learn more about the linear graph visit:

https://brainly.com/question/4025726

#SPJ2

Answer:

x = 8 and y = 8

Step-by-step explanation:

Giving equations:

     x + y  = 16

     x - y = 0

Unknown:

Find the values of x and y= ?

Solution:

      x + y  = 16  ---- (i)

      x - y = 0   ------(ii)

Add i and ii:

      2x  = 16

         x = 8

Subtract i and ii;

         2y = 16

            y = 8

Answer: y=1/5x -8

Step-by-step explanation:

Step-by-step explanation:

The next cup will always have 2 more than the previous one. Continue the pattern of adding two seeds to each cup until you reach the 24th cup like so:

#s on left side = # of seed , #s on right side = # cup

6 | 3    8 | 4      10 | 5      12 | 6     14 | 7    16 | 8     18 | 9          20 | 10        22 | 11

24 | 12     26 | 13       28 | 14      30 | 15     32 | 16    34 | 17    36 | 18     38 | 19

40 | 20      42 | 21         44 | 22     46 | 23    48 | 24

What you want to know is the number of TOTAL SEEDS NEEDED TO PLAY THIS GAME. NOT how many seeds will be in the 24th cup. To find the TOTAL you need to add 2 + 4 + 6 and so on like so:

2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = 600 TOTAL SEEDS TO PLAY THIS GAME. (this is your answer)

Answer:

12 species

Step-by-step explanation:

37-N=25

working backwards

25-37=N

=25-37=12

Answer:

x=5

Step-by-step explanation:

4x-9=29

4x=29-9

4x=20

x=20/4

x=5

Answer:

0

Step-by-step explanation:

Answer: WE create 0

Step-by-step explanation: SINCE 5 and -5 are opposites they cancel out to 0.

Answer:

$430

Step-by-step explanation:

Total hours worked by Michael = 42 hours

hours worked by Michael in excess of 40 hour = 42 - 40 = 2 hour

thus,

Michael worked 2 hours overtime.

money paid for working 1 hour in regular pay = $10.00

money paid for working 40 hour in regular pay = $10.00*40 = $400

lets calculate money paid to him for over time

given

Michael is paid 1 1/2 times his regular pay for overtime hours

Money paid for overtime for 1 hour =  1 1/2 *money paid for working 1 hour in regular pay

Money paid for overtime for 1 hour = 3/2 *$10 = $15

Money paid for 2 hours work overtime = $15*2 = $30

Thus,

gross pay for 42 hours work for Michael = $400 + $30 = $430

Answer:

3/2

Step-by-step explanation:

opposite inverse

Answer

25,20,15,10,5,0

Answer:

10-4x

Step-by-step explanation:

Answer:

[tex]2 \sqrt{5} [/tex]

decimal form: 4.47213595

Answer: 395 km

lol they want it to be 200 characters long what I look like ? Lol

Answer:

I currently have $-68

Step-by-step explanation:

Answer: m< MIH is 34°

M< AVM is 70°

And the angle of the obtuse angle formed at the intersection of AV and HI is 104°

Step-by-step explanation: starting with m<MIH, AH is parallel to MI, so that would make the same angle H has the same for I. (34°)

Next is m<AVM. The angle of m<LAH is 110°. So the angle of m<HAV (because it's supplementary of it) is 70 (110+70=180). Which makes m<AVM 70° since it's vertical to each other.

Since we got those answers, the next one you just plug it in, and the answer would be 104°

Answer:

We want to write the cost equation for the company.

First, we know that:

It cost $20 per box.

There is a fixed cost of $2300.

Then the only variable will be the number of boxes that they make.

Where the number of boxes is the independent variable (the company can decide the number of boxes that they make) and the dependent variable will be the cost (the cost changes as the number of boxes change).

Then we can write the cost equation as:

C(x) = $20*x + $2300.

Where x is our variable, the number of boxes made by the company.

Answer:

1.59

Step-by-step explanation:

Divide 2,787 by 1,750

Answer:I think it’s 75

Step-by-step explanation:

Answer: C

i hope this helps

Answer:

120 centimeters cubed

Step-by-step explanation:

you dont even need to know the last part. multiply length x width x height=volume (6x4x5) to get 120. the volume is 120 centimeters cubed :)

Answer:

120

Step-by-step explanation:

I know this question is old but why not

Answer: Answer: 98

6(3) + 10(8) = 98

Step-by-step explanation:

Answer:

I can't see the options

Step-by-step explanation:

Answer:

0.75 or 3/4

Step-by-step explanation:

multiply each by 3 equal full cup of milk and 3/4 of water

Answer the answer is 83

Step-by-step explanation:

Answer:

the answer is in the link

Step-by-step explanation:

https

      bxaha zshkkkvxxxkvvvvwuqgceuuuegieg   DONT KNO

Answer:

7x - 5 = 42

Step-by-step explanation: Hope this helps you!

Answer:

y=[tex]\frac{-7}{2}[/tex]x-7

Step-by-step explanation:

you didnt put a graph so this is the linear equation

Answer:

y = -5x + 35.

Step-by-step explanation:

y = -5x + 7

The slope for that y = -5x+7 is -5. Parallel lines have the same slopes which means the line parallel to that one will also have a slope of -5.

So now let's use the slope intercept form to create the equation that is parallel to the above equation.

y = mx + b

Since slope (m) is -5, we can plug it into the equation.

y = -5x + b

Now let's use the point (7,0) to find the y-intercept (b). We can do that by plugging the numbers in (7 for x and 0 for y).

y = -5x + b

0 = -5(7) + b

0 = -35 + b

b = 35

Now let's plug the y-intercept back into the equation.

y = -5x + 35

Therefore, the equation is y = -5x + 35.

Hope this helped! If not, please let me know! <3