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gregori [183]
3 years ago
7

9x – 5 < –41 or 3x + 13 > 7

Mathematics
2 answers:
aev [14]3 years ago
5 0
9x - 5 < -41
    +5      +5
9x < -36
x < -4

3x + 13 > 7
       -13   -13
3x      > -6
x > -2

x < -4 OR x >2
Elis [28]3 years ago
4 0
9x-5<-41                  or          3x+13>7
9x-5+5<-41+5                        3x+13-13>7-13 
9x/9<-36/9                             3x/3>-6 /3 
x<-4                                      x>-2
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A community is planning to build a rectangular garden.the width of the garden is 27/4 feet and the perimeter of the garden is 37
Crank

We know that the width of the garden is = \frac{27}{4} feet = 6.75 feet

and Perimeter of the garden is = 37.5 feet

Also, we know that for a rectangular space perimeter = 2 * (l + w)

⇒ 37.5 = 2 * (l + 6.75)

⇒ 37.5 = 13.5 + 2*l

⇒ 24 = 2*l

⇒ l = 12 feet

Now, we need to determine how much square feet of mulch is required, hence we need to calculate the area of the garden

Area = l * w

⇒ Area = 12 * 6.75

⇒ Area = 81 square feet

Hence, they require 81 square feet of mulch

7 0
3 years ago
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Answer:

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Step-by-step explanation:

4 0
3 years ago
You get paid ​​\$14.50$14.50​ an hour at your job and the newest video game costs ​\$85.00$85.00​. Find the inequality that repr
Zielflug [23.3K]

Answer:

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Step-by-step explanation:

14.50x > 85

divide both sides by 14.5

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3 0
2 years ago
Write the polynomial in factored form as a product of linear factors f(r)=r^3-9r^2+17r-9
adelina 88 [10]

Answer:

  f(r) = (x -1)(x -4+√7)(x -4-√7)

Step-by-step explanation:

The signs of the terms are + - + -. There are 3 changes in sign, so Descartes' rule of signs tells you there are 3 or 1 positive real roots.

The rational roots, if any, will be factors of 9, the constant term. The sum of coefficients is 1 -9 +17 -9 = 0, so you know that r=1 is one solution to f(r) = 0. That means (r -1) is a factor of the function.

Using polynomial long division, synthetic division (2nd attachment), or other means, you can find the remaining quadratic factor to be r^2 -8r +9. The roots of this can be found by various means, including completing the square:

  r^2 -8r +9 = (r^2 -8r +16) +9 -16 = (r -4)^2 -7

This is zero when ...

  (r -4)^2 = 7

  r -4 = ±√7

  r = 4±√7

Now, we know the zeros are {1, 4+√7, 4-√7), so we can write the linear factorization as ...

  f(r) = (r -1)(r -4 -√7)(r -4 +√7)

_____

<em>Comment on the graph</em>

I like to find the roots of higher-degree polynomials using a graphing calculator. The red curve is the cubic. Its only rational root is r=1. By dividing the function by the known factor, we have a quadratic. The graphing calculator shows its vertex, so we know immediately what the vertex form of the quadratic factor is. The linear factors are easily found from that, as we show above. (This is the "other means" we used to find the quadratic roots.)

7 0
3 years ago
Solve for x and y: x+y=5 x−y=a
9966 [12]

Answer:

x=5/2 + a/2,  y= 5/2 - a/2

Step-by-step explanation:

We can solve this system using addition of the equations

x+y=5

<u>x-y=a</u>

2x  =(5+a)

x=(5+a)/2= 5/2 +a/2

x=5/2 +a/2

x-y=a

y = x - a , x=5/2 + a/2

y= 5/2 + a/2-a

y= 5/2 - a/2

5 0
3 years ago
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