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mrs_skeptik [129]
3 years ago
5

Y2 – 8y + 16 = 64 how would i factor this equation?

Mathematics
1 answer:
Talja [164]3 years ago
3 0

Answer: y= 4 or y= -12

Step-by-step explanation:

Y²-8y+16=64.

Rearrange

Y²-8y+16-64=0

Y²-8y-48=0

(Y²+12y)-(4y-48)=0

Y(y+12)-4(y+12)=0

(Y-4)=0 or (y+12)=0

Y-4=0 or y+12=0

Y=4 or y=-12

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Step-by-step explanation:

YOU NEED TO PUT THE M FIRST NOT THE X

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Solve the system by substitution.<br> [-2.5x+y = 13.5<br> 12.25x - y=-12.25
IrinaK [193]

Answer:

x = 5/39 , y = 539/39

Step-by-step explanation:

Solve the following system:

{y - 2.5 x = 13.5

12.25 x - y = -12.25

In the first equation, look to solve for y:

{y - 2.5 x = 13.5

12.25 x - y = -12.25

y - 2.5 x = y - (5 x)/2 and 13.5 = 27/2:

y - (5 x)/2 = 27/2

Add (5 x)/2 to both sides:

{y = 1/2 (5 x + 27)

12.25 x - y = -12.25

Substitute y = 1/2 (5 x + 27) into the second equation:

{y = 1/2 (5 x + 27)

1/2 (-5 x - 27) + 12.25 x = -12.25

(-5 x - 27)/2 + 12.25 x = 12.25 x + (-(5 x)/2 - 27/2) = 9.75 x - 27/2:

{y = 1/2 (5 x + 27)

9.75 x - 27/2 = -12.25

In the second equation, look to solve for x:

{y = 1/2 (5 x + 27)

9.75 x - 27/2 = -12.25

9.75 x - 27/2 = (39 x)/4 - 27/2 and -12.25 = -49/4:

(39 x)/4 - 27/2 = -49/4

Add 27/2 to both sides:

{y = 1/2 (5 x + 27)

(39 x)/4 = 5/4

Multiply both sides by 4/39:

{y = 1/2 (5 x + 27)

x = 5/39

Substitute x = 5/39 into the first equation:

{y = 539/39

x = 5/39

Collect results in alphabetical order:

Answer: {x = 5/39 , y = 539/39

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3 years ago
What is the slope of a line that goes through (0, 6) and (6, 0)?
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The slope of the line is -1
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UCF is a major Metropolitan University located in Orlando Florida. UCF is advertising their bachelor in Economics with the stati
ludmilkaskok [199]

Answer:

There is not enough evidence to suggest that mean starting salary of a graduate with a bachelor in economics is different from $48,500.

Step-by-step explanation:

In this case we need to test whether the mean starting salary of a graduate with a bachelor in economics is $48,500.

The information provided are:

\bar x=\$43350\\s=\$15000\\n=50\\\alpha =0.01

The hypothesis for the test can be defined as follows:

<em>H</em>₀: The mean starting salary of a graduate with a bachelor in economics is $48,500, i.e. <em>μ</em> = 48500.

<em>Hₐ</em>: The mean starting salary of a graduate with a bachelor in economics is different from $48,500, i.e. <em>μ</em> ≠ 48500.

As the population standard deviation is not known we will use a t-test for single mean.

Compute the test statistic value as follows:

 t=\frac{\bar x-\mu}{s/\sqrt{n}}

   =\frac{43350-48500}{15000/\sqrt{50}}\\\\=-2.42773\\\\\approx -2.43

Thus, the test statistic value is -2.43.

Compute the p-value of the test as follows:

 p-value=2\times P(t_{49}>-2.43)=0.0188

*Use a t-table.

Thus, the p-value of the test is 0.0188.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.0188 > α = 0.01

The null hypothesis will not be rejected at 1% level of significance.

Thus, concluding that there is not enough evidence to suggest that mean starting salary of a graduate with a bachelor in economics is different from $48,500.

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Answer:

$32.00

Step-by-step explanation:

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