Factor out the GCF of the three terms, then complete the factorization of 6x3 + 6x2 – 1202.

Answer:

this is the answer

681,474

Answer:

B. 20 Units

Step-by-step explanation:

unit test review edge 2021

The area of rhombus WXYZ as shown in the diagram given with the given vertices is: 24 units².

Area of a rhombus = pq/2, where p and q are the diagonals of the rhombus.

Find the lengths of diagonals XZ and WY:

XZ = |4 -(-2)| = 6 units

WY = |-3 - 5| = 8 units

Area of rhombus WXYZ = 1/2(XZ × WY) = 1/2(6 × 8)

Area of rhombus WXYZ = 24 units².

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Answer:

7x - 6 = -2x + 2

Step-by-step explanation:

Hi! First we are going to distribute our "2" and "-2" values to the values in parenthesis.

5x + 2x - 6 = -2x + 2

Now, we can combine our like terms, "5x" and "2x".

7x - 6 = -2x + 2

Since our problem's answers are left in this form, not completely combined our answer is 7x - 6 = -2x + 2.

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

Hypothenus = 22

Step-by-step explanation:

From the question given above, we were told that the triangles are congruent (i.e same size). Thus,

AC = EF

BC = DE

To obtain the length of each Hypothenus, we shall determine the value of y and x. This can be obtained as follow:

For y:

AC = y + 3

EF = 2y + 1

AC = EF

y + 3 = 2y + 1

Collect like terms

3 – 1 = 2y – y

2 = y

y = 2

For x:

BC = 5x + 7

DE = 6x + 2y

y = 2

DE = 6x + 2(2)

DE = 6x + 4

BC = DE

5x + 7 = 6x + 4

Collect like terms

7 – 4 = 6x – 5x

3 = x

x = 3

Finally, we shall determine the length of each Hypothenus. This can be obtained as follow:

Hypothenus = BC

Hypothenus = 5x + 7

x = 3

Hypothenus = 5x + 7

Hypothenus = 5(3) + 7

Hypothenus = 15 + 7

Hypothenus = 22

OR

Hypothenus = DE

DE = 6x + 2y

y = 2

x = 3

Hypothenus = 6(3) + 2(2)

Hypothenus = 18 + 4

Hypothenus = 22

Answer:

The Answer of the above question is 30.25

Step-by-step explanation:

Hope it helps you.

Answer:

Step-by-step explanation:

Hope this helps :)!

Hi there!  

»»————-　★　————-««

I believe your answer is:  

18in³

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

Assuming that the figure is a rectangular prism:

⸻⸻⸻⸻

[tex]\boxed{\text{Volume of a rectangular prism is:}}\\\\V = l * w * h\\-----------\\V = 2 * 2.25 * 4\\\\\boxed{V = 18}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.    

Answer:

[tex]x^{7}[/tex]

Step-by-step explanation:

When multiplying exponents, you add them together.

x^12

Step-by-step explanation:

x^5*x^7

x^5+7

=x^12

Complete Question

Complete Question is attached below

Answer:

[tex]UCL= 0.25[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size[tex]n=150[/tex]

Sample Variants [tex]s=7[/tex]

Sigma control limits  [tex]Z = 3[/tex]

Therefore

Total number of observations is Given as

[tex]T_o=n*s[/tex]

[tex]T_o=150 *7[/tex]

[tex]T_0=1050[/tex]

Generally

Summation of defectivee

[tex]\sum np=23+34+15+30+25+22+18[/tex]

[tex]\sum np= 167[/tex]

Generally the equation for P-bar is mathematically given by

[tex]P-bar=\frac{\sum np}{T_o}[/tex]

[tex]P-bar=\frac{167}{1050}[/tex]

[tex]P-bar=0.16[/tex]

Therefore

[tex]Sp=\sqrt{\frac{P-bar(1-P-bar)]}{ n}}[/tex]

[tex]Sp=\sqrt{\frac{[0.159(1-0.159)]}{150}}[/tex]

[tex]Sp=0.03[/tex]

Generally the equation for 3-sigma upper control limit of the process is mathematically given by

[tex]UCL = P-bar + Z*Sp[/tex]

[tex]UCL= 0.16 + 3*0.03[/tex]

[tex]UCL= 0.25[/tex]

Answer:

(×:x is a natural number up to 10) just an example

Answer:

Step-by-step explanation:

Given,

Radius = 30 in

So,

Circumference

[tex] = 2\pi r[/tex]

[tex] = 2 \times \pi \times 30in.[/tex]

[tex] = 60\pi \: in.(ans)[/tex]

[tex] \sf \: r \: = 30 \: in. \\ \sf \: C \: = 2\pi r \\ \\ \sf \: C \: = 2\pi(30) \\ \sf \: C = 2 \times 30\pi \\ \sf \: C = \boxed{\underline{ \bf c. \: 60\pi \: in.}}[/tex]

Answer:

im so confused

Step-by-step explanation:

Answer:

what is this goat saying

Answer:

y"-6y'+18y=0

Second order

Step-by-step explanation:

Since there are 2 constants, the order of the differential equation will be 2. This means we will need to differentiate twice.

y = e^(3x) (acos3x +bsin3x)​

y'=3e^(3x) (acos3x+bsin3x)

+e^(3x) (-3asin3x+3bcos3x)

Simplifying a bit by reordering and regrouping:

y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)

y"=

3e^(3x) cos3x (3a+3b)+-3e^(3x) sin(3x) (3a+3b)

+3e^(3x) sin3x (3b-3a)+3e^(3x) cos(3x) (3b-3a)

Simplifying a bit by reordering and regrouping:

y"=

e^(3x) cos3x (9a+9b+9b-9a)

+e^(3x) sin3x (-9a-9b+9b-9a)

Combining like terms:

y"=

e^(3x) cos3x (18b)

+e^(3x) sin3x (-18a)

Let's reorder y like we did y' and y".

y = e^(3x) (acos3x +bsin3x)

y=e^(3x) cos3x (a) + e^(3x) sin3x (b)

Objective is to find a way to combine or combine constant multiples of y, y', and y" so that a and b are not appearing.

Let's start with the highest order derivative and work down

y"=

e^(3x) cos3x (18b)

+e^(3x) sin3x (-18a)

We need to get rid of the 18b and 18a.

This is what we had for y':

y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)

Multiplying this by -6 would get rid of the 18b and 18a in y" if we add them.

So we have y"-6y'=

e^(3x) cos3x (-18a)+e^(3x) sin3x (-18b)

Now multiplying

y=e^(3x) cos3x (a) + e^(3x) sin3x (b)

by 18 and then adding that result to the y"-6y' will eliminate the -18a and -18b

y"-6y'+18y=0

Also the characteristic equation is:

r^2-6r+18=0

This can be solved with completing square or quadratic formula.

I will do completing the square:

r^2-6r+18=0

Subtract 9 on both sides:

r^2-6r+9=-9

Factor left side:

(r-3)^2=-9

Take square root of both sides:

r-3=-3i or r-3=3i

Add 3 on both sides for each:

r=3-3i or r=3+3i

This confirms our solution.

Another way to think about the problem:

Any differential equation whose solution winds up in the form y=e^(px) (acos(qx)+bsin(qx)) will be second order and you can go to trying to figure out the quadratic to solve that leads to solution r=p +/- qi

Note: +/- means plus or minus

So we would be looking for a quadratic equation whose solution was r=3 ×/- 3i

Subtracting 3 on both sides gives:

r-3= +/- 3i

Squaring both sides gives:

(r-3)^2=-9

Applying the exponent on the binomial gives:

r^2-6r+9=-9

Adding 9 on both sides gives:

r^2-6r+18=0

Answer:

Rate of slower bus; 90 km/h

Rate of faster bus; 102 km/b

Step-by-step explanation:

We know that formula do distance is;

Distance = speed/time

We are told that One bus travels 12h slower than the other.

Let speed of slower bus be x.

Thus;

Speed of faster bus = x + 12

Speed of slower bus = x

After 3 hours, distance by faster bus = 3(x + 12)

Speed of slower bus = 3x

Since the towns are 576 km apart, then;

3(x + 12) + 3x = 576

Divide through by 3 to get;

x + 12 + x = 192

2x + 12 = 192

2x = 192 - 12

2x = 180

x = 180/2

x = 90 km/h

Faster bus speed = 90 + 12 = 102 km/h

Answer:

a) The sample mean is of 49 and the sample standard deviation is of 11.7.

b) The range of the true mean at 90% confidence level is of 9.62 hours.

c) The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.

Step-by-step explanation:

Question a:

Sample mean:

[tex]\overline{x} = \frac{34+40+46+49+61+64}{6} = 49[/tex]

Sample standard deviation:

[tex]s = sqrt{\frac{(34-49)^2+(40-49)^2+(46-49)^2+(49-49)^2+(61-49)^2+(64-49)^2}{5}} = 11.7[/tex]

The sample mean is of 49 and the sample standard deviation is of 11.7.

b)Determine the range of the true mean at 90% confidence level.

We have to find the margin of error of the confidence interval. Since we have the standard deviation for the sample, the t-distribution is used.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0.150

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample. So

[tex]M = 2.0150\frac{11.7}{\sqrt{6}} = 9.62[/tex]

The range of the true mean at 90% confidence level is of 9.62 hours.

(c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time.

This is the confidence interval, so:

The lower end of the interval is the sample mean subtracted by M. So it is 49 - 9.62 = 39.38 hours.

The upper end of the interval is the sample mean added to M. So it is 49 + 9.62 = 58.62 hours.

The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.

9514 1404 393

Answer:

  B) f(1)=7, f(n+1)= f(n)-3; for n >= 1

Step-by-step explanation:

The first term of the sequence is 7 and the next (4) is found by adding -3 to that: 4 = 7-3. This is described in answer choice B.

Answer:

The p-value of the test if 0.0131, which is less than the standard significance level of 0.05, meaning that these data indicates that the self-worth of heroin addicts is less than that of the general population.

Step-by-step explanation:

On a test designed to measure self-worth, the mean for the general population is 48.6.

At the null hypothesis, we test if the mean is of 48.6, that is:

[tex]H_0: \mu = 48.6[/tex]

A psychologist suspects that heroin addicts have a different assessment of self-worth than others in the general population. Test if it is lower.

At the alternative hypothesis, we test if the mean is lower, that is:

[tex]H_1: \mu < 48.6[/tex]

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

48.6 is tested at the null hypothesis:

This means that [tex]\mu = 48.6[/tex]

The psychologist obtains a random sample of 40 test scores produced by heroin addicts and found the sample mean and the sample standard deviations are 45.5 and 8.5, respectively.

This means that [tex]n = 40, X = 45.5, s = 8.5[/tex]

Value of the test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{45.5 - 48.6}{\frac{8.5}{\sqrt{40}}}[/tex]

[tex]t = -2.31[/tex]

P-value of the test:

The p-value of the test is a one-tailed test(mean lower than a value), with t = -2.31 and 40 - 1 = 39 df.

Using a t-distribution calculator, this p-value is of 0.0131.

The p-value of the test if 0.0131, which is less than the standard significance level of 0.05, meaning that these data indicates that the self-worth of heroin addicts is less than that of the general population.

Hello!

$52 ..... 800kWh

$x ..... 650kWh

_____________

52/x = 800/650 <=>

<=> 52 × 650 = 800x <=>

<=> 33800 = 800x <=>

<=> 800x = 33800 <=>

<=> x = 33800/800 <=>

<=> x = 338/8 <=>

<=> x = 169/4 <=>

<=> x = 42,25$

Good luck! :)

Answer:

f(x) = 2.25x + 5

Step-by-step explanation:

The cost from the weight in pounds of the box can be represented by 2.25x, since the charge is $2.25 per pound.

The flat fee of $5 can be represented in the function by adding 5 to 2.25x.

Put these together in function notation:

f(x) = 2.25x + 5

So, the equation is f(x) = 2.25x + 5

Answer:

1. purple graph

2. orange graph

3. green graph

4. blue graph

The equation of the graph is : x = -2

A graph is a pictorial representation of the locus of a certain point.

A graph can be drawn by picking some fixed points from the locus of the point.

Here, the straight line passes through the points are : (-2,1); (-2,2); (-2,-5);(-2,-5).

Hence, the straight line is to be parallel to the x-axis and the equation of the graph is x= -2.

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Answer:

N = 50 +4d

Step-by-step explanation:

Take the original number of stamps and add the stamps per days times the number of days

N = 50 +4d

Answer:

C. 5

Step-by-step explanation:

To find the degree of the polynomial, all you have to do is find the largest degree. (aka the largest lil number above the x)

In this case, it's 5.

Answer:

exponential decay

Step-by-step explanation:

The function is in the form

y = ab^x  where a is the initial value and b is the growth or decay rate

If b >1 then it is growth

b < 1 then it is decay

f(x) = 5(2/3)^x

a = 5

b = 2/3

2/3 <1 so it is decay

Answer:

28

Step-by-step explanation:

10/14 mph no wind

20 wind

14 x 2 = 28

28 mph with wind

Answer:

38 divided by 10 equals 3.8

Answer:

Step-by-step explanation:

the answer is 2250 percent is = 22.5

Answer:

18% discount

Step-by-step explanation:

Percent discount is found by the following formula:

[tex]\frac{original-discount}{original}[/tex]

In this scenario, the original is 12500 and the discount, or special is 10250.

We can plug this into the formula to get

[tex]\frac{12500-10250}{12500}[/tex]

We can simplify the numerator by subtracting, and we get that answer as 2250.

We get the remainder of the answer as 2250 divided by 12500. We divide that, and get the answer as 0.18, which can be rewritten as 18%.

Answer:

19 bags of peanuts and 31 bags of pistachios were sold.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

x is the number of bags of peanuts sold.

y is the number of bags of pistachios sold.

50 bags of  peanuts and pistachios were sold

This means that [tex]x + y = 50[/tex], that is: [tex]x = 50 - y[/tex]

A grocery store recently sold a  bag of peanuts for $0.76 and a bag of pistachios for $3.68. Were sold for a total of $128.52.

This means that:

[tex]0.76x + 3.68y = 128.52[/tex]

Since [tex]x = 50 - y[/tex]

[tex]0.76(50 - y) + 3.68y = 128.52[/tex]

[tex]2.92y = 90.5[/tex]

[tex]y = \frac{90.5}{2.92}[/tex]

[tex]y = 31[/tex]

[tex]x = 50 - y = 50 - 31 = 19[/tex]

19 bags of peanuts and 31 bags of pistachios were sold.

Answer:

2, x, 2x

Step-by-step explanation:

A) 2

They are even numbers, so it is going to be 2.

B) x

It is going to only be x because the exponents are even and odd.

C) 2x

It is going to be 2x because the numbers are even but the exponents are even and odd.

Hope this helps.