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denpristay [2]
3 years ago
14

Which of the following expressions are equivalent to 48a^3-75a? Select all that apply. Answer 1) 3(48a^3-75a). Answer 2) 3a(16a^

2-25) Answer 3)3a(4a+5)(4a+5) Answer 4) 3a(4a+5)(4a-5) Answer 5) -3a(25-16a^2) Answer 6) -3a(5-4a)(5+4a)
Mathematics
2 answers:
Ainat [17]3 years ago
8 0
The answer is 4) 3a(4a+5)(4a-5)
lapo4ka [179]3 years ago
7 0

Answer: The answer is (2), (4), (5) and (6).

Step-by-step explanation: The given expression is

E=48a^3-75a.

We are to select the correct expressions from the given options that are equivalent to the above expression.

We have the following forms of the give expressipn:

E\\\\=48a^3-75a\\\\=3a(16a^2-25)\\\\=3a\left((4a)^2-5^2\right)\\\\=3(4a+5)(4a-5)\\\\=-3a(5+4a)(5-4a)\\\\=-3a(25-16a^2).

Thus, (2), (4), (5) and (6) are the correct options.

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A cylinder has a volume 1200 cubic inches and radius 5 inches. What is the height of the cone to the nearest tenth inch
mihalych1998 [28]

Answer: 15.3 in

Step-by-step explanation:

First, the formula for the volume is: V=\pi r^2h

If you solve for h,

h=\frac{V}{\pi r^2}

h=\frac{1200in^3}{(3.14)(5in)^2}

h=15.3in

3 0
3 years ago
What is the slope of a line perpendicular to the line whose equation is 2x−10y=100. Fully reduce your answer.
Aliun [14]

Answer:

2x-10y=100

-8xy=100

xy=12

3 0
2 years ago
9x-8(x-6)=52 what is the answer
Effectus [21]

Answer:

x = 4

Step-by-step explanation:

Step 1: Write equation

9x - 8(x - 6) = 52

Step 2: Solve for <em>x</em>

  1. Distribute -8: 9x - 8x + 48 = 52
  2. Combine like terms: x + 48 = 52
  3. Subtract 48 on both sides: x = 4

Step 3: Check

<em>Plug in x to verify it's a solution.</em>

9(4) - 8(4 - 6) = 52

36 - 8(-2) = 52

36 + 16 = 52

52 = 52

7 0
3 years ago
A crossover trial is a type of experiment used to compare two drugs. Subjects take one drug for a period of time and then switch
zysi [14]

Answer:

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-0.714 -0}{\frac{1.38}{\sqrt{7}}}=-1.369

df=n-1=7-1=6

p_v =2*P(t_{(6)}

We see that the p value is higher than the ususal significance levels commonly used of 1% or 5% so then we can conclude that we FAIL to reject the null hypothesis, and there is not enough evidence to conclude that we have a different response between the two drugs

Step-by-step explanation:

We have the following info given by the problem

Subject  1 2 3 4 5 6 7

Drug A  6 3 4 5 7 1 4

Drug B  5 1 5 5 5 2 2

x=value for drug A , y = value for drug B

x: 6 3 4 5 7 1 4  

y: 5 1 5 5 5 2 2

We want to verify if the mean response differs between the two drugs then  the system of hypothesis for this case are:

Null hypothesis: \mu_y- \mu_x = 0

Alternative hypothesis: \mu_y -\mu_x \neq 0

We can begin calculating the difference d_i=y_i-x_i and we obtain this:

d: -1, -2, 1, 0, -2, 1, -2

Now we can calculate the mean difference  

\bar d= \frac{\sum_{i=1}^n d_i}{n}=-0.714

Now we can find the the standard deviation for the differences, and we got:

s_d =\sqrt{\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}}=1.38

And now we can calculate the statistic given by :

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-0.714 -0}{\frac{1.38}{\sqrt{7}}}=-1.369

Now we can find the degrees of freedom given by:

df=n-1=7-1=6

We can calculate the p value, since we have a two tailed test the p value is given by:

p_v =2*P(t_{(6)}

We see that the p value is higher than the ususal significance levels commonly used of 1% or 5% so then we can conclude that we FAIL to reject the null hypothesis, and there is not enough evidence to conclude that we have a different response between the two drugs

7 0
3 years ago
Which of these systems of linear equations has no solution?
Alika [10]

Answer:

A is correct

Step-by-step explanation:

A has no solution because since the slopes are the same, setting both equations equal to each other will cancel out the slopes and result in 8=16, meaning no solution will make both sides equal to each other.

B does have a solution because of different slopes

C does have a solution because of different slopes

D does have a solution because of different slopes

7 0
3 years ago
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