Plz help with A and D!​

The correct equations in the question are:

(a) [tex]\dfrac{x}{x^2+x-2}[/tex]   (b) [tex]\dfrac{6-x}{x^2-3x-54}[/tex]

Answer:

Step-by-step explanation:

From above:

a) [tex]\dfrac{x}{x^2+x-2}[/tex]  

We are to find the roots of the quadratic equation at the denominator.

i.e.

x²+x-2 =  x² + 2x - x - 2

= x(x+2) - 1(x+2)

= (x -1 ) (x + 2)

Thus;

[tex]\mathbf{\dfrac{x}{x^2+x-2} = \dfrac{A}{x-1} + \dfrac{B}{x+2}}[/tex]

b) [tex]\dfrac{6-x}{x^2-3x-54}[/tex]

The quadratic equation roots can be calculated by finding two numbers that if we multiply then, we will get -54 and if we add or subtract them, we will get -3

x²-3x -54 =  x² - 9x +6x - 54

=  x(x-9) + 6(x-9)

= (x + 6) (x - 9)

[tex]\mathbf{\dfrac{6-x}{x^2-3x-54} = \dfrac{A}{x+6} + \dfrac{B}{x-9}}[/tex]

Answer: D. 30

Step-by-step explanation:

Given that:

63 have a car,

27 have a bike,

12 have a skateboard,

20 have a car and a bike,

8 have a car and a skateboard,

9 have a bike and a skateboard, and

5 have a car, a bike, and a skateboard.

Car and bike only :(20 - 5) = 15

Car and skateboard only = (8 - 5) = 3

Car only = 63 - (15 + 3 + 5) = 40

Bike and skateboard only = (9 - 5) = 4

Bike only = 27 - (15 + 5 + 4) = 3

Skateboard only = 12 - (3 + 5 + 4) = 0

Number of people in the survey do not own a car, a bike, or a skateboard: = x

(40+0+3+15+3+5+4+x) = 100

70 + x = 100

x = 100 - 70

x = 30

Answer:

b

Step-by-step explanation:

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[tex]h(x) = 4 {x}^{2} + 4x + 1 [/tex]

[tex]h(x) = ({2x + 1})^{2} [/tex]

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Answer:

21

Step-by-step explanation:

they both have 21

Answer:

2

Step-by-step explanation:

The x-coordinate of point (2, 9) is 2.

The distance from 0 to 2 on a number line is 2.

Answer: 2

Answer: 5/12

Step-by-step explanation:

Answer:

[tex]1.75[/tex] × [tex]10^{-15}[/tex]  

I hope this helps!

Answer:

smaller number = - 12

larger number = -2

Step-by-step explanation:

x + y = - 14

x - y =    10                Add

2x = - 4                     Divide by 2

x = -4/2 = - 2

-2 + y = - 14               Substitute - 2 = x in x + y = - 14

y = - 14 + 2                Combine

y = - 12

Answer:

The sample size 'n' = 26

Step-by-step explanation:

Explanation:-

Given a researcher wishes to estimate within $5 the average repair cost of for a refrigerator

Given estimate "E" = $5

The  estimate within  the average is determined by

                [tex]E = \frac{Z_{0.10}S.D }{\sqrt{n} }[/tex]

 Level of significance    ∝ = 90 % or 10%

                                            = 0.90 or o.10

Z₀.₁₀ = 1.645

                                 [tex]E = \frac{Z_{0.10}S.D }{\sqrt{n} }[/tex]

                             [tex]5 = \frac{1.645 X15.50 }{\sqrt{n} }[/tex]

                        √n =  [tex]\frac{25.49}{5} = 5.099[/tex]

Squaring on both sides , we get

                        n = 26

Conclusion:-

The sample size 'n' = 26

Answer:

0.0520833333 is the answer

Answer:

0.05208333333 (reoccurring)

Step-by-step explanation:

Simple bus stop division (:

Answer:

2 1/2

Step-by-step explanation:

6/4=3/2=1 1/2

Answer:

6/4= 3/2

so you now divide 2 by the 3 which will give you;

1.5

Answer:

6,000  ft

Step-by-step explanation:

3,000 x 2 = 6,000

6,000 feet

Step-by-step explanation:

in 5 minutes she jogs 3,000 feet

in 10 minutes she jogs 6,000 feet

10/2= 5 minutes or 5 minutes ×2 =10 minutes

3,000×2 = 6,000 feets

24,10 and 16,5 have slope of a 5/8.

Answer:

90%

Step-by-step explanation:

We know that

9/10

is the same as

9÷10

Then using

Long Division for 9 divided by 10

gives us

0.9

Converting our number to a percentage:

0.9×100

=90%

(Note this isnt rounded up.)

Answer: Three-8 ounce containers

Step-by-step explanation: 3 x 1.29 divided by 0.6= $6.45 for three 8-ounce containers

4 x 3.77 divided by 0.6= $15.08

Answer:

a = 68deg b = 112deg c = 68deg

Step-by-step explanation:

angle opposite 112deg is 112deg (vertically opp angels)

since the 2 angles are same, a = 180deg - 112deg = 68deg (angles on a straight line are supplementary)

b = 112 deg (vertically opp angles)

c = a (vertically opp angles)

Answer:2 2/9

Step-by-step explanation: 4/3 x 5/3= 20/9= 2 2/9

Answer:

sarah makes 10 cupcakes

Step-by-step explanation:

baker makes 30 cupcakes.

30/3=10

Answer:

Range is 44

mean is 29.7

variance is 289.56

standard deviation is 17.016

Step-by-step explanation:

The data given as follows

3, 24, 30, 47, 43, 7, 47,13, 44, 39

Range = maximum - minimum

             = 47 -3 = 44

mean = [tex]\frac{3+24+30+47+43+7+47+13+44+39}{10}[/tex] = 297/10 = 29.7

variance = [tex]\frac{sum xi^2 }{N} - mean^2 }[/tex]

              = 289.56

SD = [tex]\sqrt{variance}[/tex]  = 17.016

The standard deviation of the given data is not a good measure as the range and standard deviation are far apart. The standard deviation gives how the given data is dispersed from the mean or expected value, while the range gives a rough idea of variability of the data.

Answer:

-3.8

Step-by-step explanation:

I used my calculator.

Answer:

-3.8            

Step-by-step explanation:

Answer:

Put x then y u get x+y=15*2

Answer:

can you show me the data so i can see the temperature

Answer: Graph C

Step-by-step explanation: The answer is C (Took the quiz)- Khan Academy

Answer: x=60

Step-by-step explanation:

x+22+x+6+x−28=180

Step 1: Simplify both sides of the equation.

x+22+x+6+x−28=180

x+22+x+6+x+−28=180

(x+x+x)+(22+6+−28)=180(Combine Like Terms)  22+6=28 and then 28-28=0

3x=180  

3x=180

Step 2: Divide both sides by 3.

3x/3 = 180/3

x=60

hope this was helpful.

Answer:

25

Step-by-step explanation:

16+9

Answer:

The correct should be 25.

Step-by-step explanation:

If this is incorrect let me know and I will correct it.

Answer:

The percentage of people that chose relaxation was equal for each age-group.

Step-by-step explanation:

Answer:

5 or E- The percentage of people that chose relaxation was equal for each age group

Step-by-step explanation:

You can use the process of elimination where every other answer choice is correct except for the last one. Otherwise, the percentages for each group of age group are all different as shown on the margins, which is why it is incorrect. Therefore, that is the correct answer for this problem.  

Answer:

0.5

Step-by-step explanation:

Answer:

Step 2 shows Emily's first mistake.

Step-by-step explanation:

3(2) = 6

But instead of this Emily wrote 3(2) = 9.