Given the trinomial, what is the value of the coefficient B in the factored form?
2x2 + 4xy − 48y2 = 2(x + By)(x − 4y)

Answers

Answer 1

Answer:

B = 6

Step-by-step explanation:

2x^2 + 4xy − 48y^2

Factor out 2

2(x^2 + 2xy − 24y^2)

What 2 numbers multiply to -24 and add to 2

-4 *6 = -24

-4+6 = 2

2 ( x+6y)( x-4y)

Answer 2

Answer:

[tex]\huge\boxed{B=6}[/tex]

Step-by-step explanation:

They are two way to solution.

METHOD 1:

Factor the polynomial on the left side of the equation:

[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]

Therefore:

[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]

METHOD 2:

Multiply everything on the right side of the equation using the distributive property and FOIL:

[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]

Compare polynomials:

[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]

From here we have two equations:

[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]

[tex]1)\\2B-8=4[/tex]        add 8 to both sides

[tex]2B=12[/tex]         divide both sides by 2

[tex]B=6[/tex]

[tex]2)\\-8B=-48[/tex]          divide both sides by (-8)

[tex]B=6[/tex]

The results are the same. Therefore B = 6.


Related Questions

Which equation will solve the following word problem? Jared has 13 cases of soda. He has 468 cans of soda. How many cans of soda are in each case? 13(468) = c 468c = 13 468/13 = c 13 = c/468

Answers

Answer:

c = 468 / 13

Step-by-step explanation:

If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.

Answer:

468/13 = c

Step-by-step explanation: Further explanation :

[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]

Find the area of the surface generated by revolving x=t + sqrt 2, y= (t^2)/2 + sqrt 2t+1, -sqrt 2 <= t <= sqrt about the y axis

Answers

The area is given by the integral

[tex]\displaystyle A=2\pi\int_Cx(t)\,\mathrm ds[/tex]

where C is the curve and [tex]dS[/tex] is the line element,

[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

We have

[tex]x(t)=t+\sqrt 2\implies\dfrac{\mathrm dx}{\mathrm dt}=1[/tex]

[tex]y(t)=\dfrac{t^2}2+\sqrt 2\,t+1\implies\dfrac{\mathrm dy}{\mathrm dt}=t+\sqrt 2[/tex]

[tex]\implies\mathrm ds=\sqrt{1^2+(t+\sqrt2)^2}\,\mathrm dt=\sqrt{t^2+2\sqrt2\,t+3}\,\mathrm dt[/tex]

So the area is

[tex]\displaystyle A=2\pi\int_{-\sqrt2}^{\sqrt2}(t+\sqrt 2)\sqrt{t^2+2\sqrt 2\,t+3}\,\mathrm dt[/tex]

Substitute [tex]u=t^2+2\sqrt2\,t+3[/tex] and [tex]\mathrm du=(2t+2\sqrt 2)\,\mathrm dt[/tex]:

[tex]\displaystyle A=\pi\int_1^9\sqrt u\,\mathrm du=\frac{2\pi}3u^{3/2}\bigg|_1^9=\frac{52\pi}3[/tex]

In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.

Answers

Answer:

40,000 populations

Step-by-step explanation:

Initial population in 2018 = 25,000

Annual growth rate (in %) = 4%

Yearly Increment in population = 4% of 25000

= 4/100 * 25000

= 250*4

= 1000

This means that the population increases by 1000 on yearly basis.

To determine what the  population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.

Amount of years we have between 2018 and 2033 = 2033-2018

= 15 years

After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.

Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.

Two charged particles, Q1, and Q2, are a distance r apart with Q2 = 5Q1 Compare the forces they exert on one another when F1 is the force Q2 exerts on Q1and F2 is the force Q1 exerts on Q2.
a) F2 = 5F1.
b) F2 =-5F1.
c) F2 = F1.
d) F2 = -F1.
e) 5F2 = F1.

Answers

Answer:

d) F2 = -F1.

Step-by-step explanation:

According to Coulomb's law of forces on electrostatic charges, the force of attraction is proportional to the product of their charges, and inversely proportional to the square of their distance apart.

What this law means is that both particles will experience an equal amount of force on them, due to the presence of the other particle. This force is not just as a result of their individual charges, but as a result of the product of their charges. Also, the force is a vector quantity that must have a direction alongside its magnitude, and the force on the two particles will always act in opposite direction, be it repulsive or attractive.

What is the name of a geometric figure that looks an orange


A. Cube

B. Sphere

C. Cylinder

D. Cone

Answers

Answer:

b . sphere

Step-by-step explanation:

Step 1: Subtract 3 from both sides of the inequality
Step 2
Step 3: Divide both sides of the inequality by the
coefficient of x.
What is the missing step in solving the inequality 5 -
8x < 2x + 3?
O Add 2x to both sides of the inequality
O Subtract 8x from both sides of the inequality
O Subtract 2x from both sides of the inequality
Add 8x to both sides of the inequality.
Mark this and return
Save and Exit
Intext
Submit

Answers

Answer:

add 8x to both sides

Step-by-step explanation:

5-8x<2x+3

first step, subtract 3 from both sides:

2-8x<2x

second step,?

2<?x

so you need to add 8x first

The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6 in./sec. At what rate is the volume of the cylinder changing when the radius is 20 in. and the height is 16 in.

Answers

Answer:

[tex]\approx \bold{6544\ in^3/sec}[/tex]

Step-by-step explanation:

Given:

Rate of change of radius of cylinder:

[tex]\dfrac{dr}{dt} = +7\ in/sec[/tex]

(This is increasing rate so positive)

Rate of change of height of cylinder:

[tex]\dfrac{dh}{dt} = -6\ in/sec[/tex]

(This is decreasing rate so negative)

To find:

Rate of change of volume when r = 20 inches and h = 16 inches.

Solution:

First of all, let us have a look at the formula for Volume:

[tex]V = \pi r^2h[/tex]

Differentiating it w.r.to 't':

[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)[/tex]

Let us have a look at the formula:

[tex]1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))[/tex]

[tex]3.\ \dfrac{dx^n}{dx} = nx^{n-1}[/tex]

Applying the two formula for the above differentiation:

[tex]\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}[/tex]

Now, putting the values:

[tex]\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}[/tex]

So, the answer is: [tex]\approx \bold{6544\ in^3/sec}[/tex]

PLEASE HELP WILL GIVE BRAINLIEST AND THX Which ratios have a unit rate of 3? Choose all that apply. 15/2 cups: 2 1/2 cups 1 cup: 1/4 cups 2/3 cups: 1 cup 3 3/4 cups: 2 cups 2 cups: 2/3 cups 2 1/2 cups: 5/6 cups

Answers

Answer:

15/2 cups: 2 1/2 cups

2 cups: 2/3 cups

2 1/2 cups: 5/6 cups

Step-by-step explanation:

Take and divide each by the smaller number

15/2 cups: 2 1/2 cups

First put in improper fraction form

15/2 : 5/2

Divide each by 5/2

15/2 ÷ 5/2  : 5/2 ÷5/2

15/2 * 2/5  : 1

3 :1   yes

1 cup: 1/4 cups

Divide each by 1/4 ( which is the same as multiplying by 4)

1*4  : 1/4 *1

4 : 1    no

2/3 cups: 1 cup

Divide each by 2/3  ( which is the same as multiplying by 3/2)

2/3 * 3/2  : 1 * 3/2

1 : 3/2   no

3 3/4 cups: 2 cups

Change to improper fraction

( 4*3+3)/4  : 2

15/4    : 2

Divide each side by 2

15/8  : 2/2

15/8   : 1    no

2 cups: 2/3 cups

Divide each side by 2/3 ( which is the same as multiplying by 3/2)

2 * 3/2 : 2/3 *3/2

3  : 1   yes

2 1/2 cups: 5/6 cups

Change to an improper fraction

( 2*2+1)/2 : 5/6

5/2  : 5/6

Divide each side by 5/6( which is the same as multiplying by 6/5)

5/2 * 6/5  : 5/6 * 6/5

3  : 1   yes

The 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3

What is the ratio?

It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign : between the numbers.

For checking: 15/2 cups: 2 1/2 cups

= (15/2)/(5/2)       [2(1/2) = 5/2]

= 3

For checking:  1 cup: 1/4 cups

= 1/(1/4)

= 4

For checking: 2/3 cups: 1 cup

=(2/3)/1

= 2/3

For checking: 3 3/4 cups: 2 cups

= (15/4)(2)

= 15/8

For checking: 2 cups: 2/3 cups

= (2)/(2/3)

= 3

For checking: 2 1/2 cups: 5/6 cups

= (5/2)/(5/6)

= 3

Thus, the 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ2

A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and standard deviation of 10. The professor has informed us that 6.3 percent of his students received A's while only 2.5 percent of his students failed the course and received F's.
a. What is the minimum score needed to make an A?
b. What is the maximum score among those who received an F?
c. If there were 5 students who did not pass the course, how many students took the course?

Answers

Answer:

a)  z (score) 1,53

b)  z ( score) - 1,96

c) 200 students

Step-by-step explanation:

Normal Distribution N ( 74;10)

a) From z-table, and for 6,3 %  ( 0,063 ) we find the z (score) 1,53

Note : 6,3 % or 0,063 is the area under the curve, the minimum score neded to get A

b) To fail   2,5 %  ( 0,025 ) from z-table  get - 1,96

c) If the group of  student who did not pass the course (5) correspond to 2,5 % then by simple rule of three

5                 2,5

x ?               100

x = 500/2,5

x = 200

(x-2) is a factor of x^2-3x^2+kx+14. The value of k is?​

Answers

Answer:

k = 5

Step-by-step explanation:

I will assume that your polynomial is

x^2 - 3x^2 + kx + 14

If x - a is a factor of this polynomial, then a is a root.

Use synthetic division to divide (x - 2) into x^2 - 3x^2 + kx + 14:

 2      /      1     -3     k     14

                        2     -2    2k - 4

         -------------------------------------

               1        -1    (k - 2)   2k - 10

If 2 is a root (if x - 2 is a factor), then the remainder must be zero.

Setting 2k - 10 = to zero, we get k = 5.

The value of k is 5 and the polynomial is x^2 - 3x^2 + 5x + 14

PLEASE HELP!!! TIMED QUESTION!!! FIRST CORRECT ANSWER WILL BE BRAINLIEST!!!

The bar graph shows the number or each item sold at a bake sale. Which statement about the graph is true?​

Answers

The answer is 2. You can see from the graph that 10 cookies were sold. If you take 1% of 10 and add it to 10, you get 11, which is exactly how many cupcakes were sold
Number 1 is correct.
Let me know if you need the working out. Hope it helps :)

What is the value of x to the nearest tenth?

Answers

Answer:

x=9.6

Step-by-step explanation:

The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.

The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.

Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:

[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]

What is the length of the arc on a circle with radius 16 inches intercepted by a 45° angle?

Answers

Find the circumference:

Circumference = 2 x PI x radius:

Circumference = 2 x 3.14 x 16 = 100.48 inches.

A full circle is 360 degrees, a 45 degree angle is 1/8 of a full circle.

Arc length = 100.48 / 8 = 12.56 inches.


[tex]4x - 2x = [/tex]

Answers

Answer:

2x

Step-by-step explanation:

These are like terms so we can combine them

4x-2x

2x

Answer:

2x

Explanation:

Since both terms in this equation are common, we can simply subtract them.

4x - 2x = ?

4x - 2x = 2x

Therefore, the correct answer should be 2x.

Choose the correct ray whose endpoint is B.

Answers

Answer:

The second option.

Step-by-step explanation:

The first option consists of a line that extends at both opposite sides to infinity, with no precise end.

The third option is a ray that has an endpoint of A, and extends to infinity towards B.

The fourth option is a line segment. It has two endpoints, B and A.

The second portion is a ray that has an endpoint B, and extends towards A in one direction, to infinity.

The answer is the 2nd option.

For the regression equation, Ŷ = +20X + 200 what can be determined about the correlation between X and Y?

Answers

Answer:

There is a positive correlation between X and Y.

Step-by-step explanation:

The estimated regression equation is:

[tex]\hat Y=20X+200[/tex]

The general form of a regression equation is:

[tex]\hat Y=b_{yx}X+a[/tex]

Here, [tex]b_{yx}[/tex] is the slope of a line of Y on X.

The formula of slope is:

[tex]b_{yx}=r(X,Y)\cdot \frac{\sigma_{y}}{\sigma_{x}}[/tex]

Here r (X, Y) is the correlation coefficient between X and Y.

The correlation coefficient is directly related to the slope.

And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.

Here the slope is positive.

This implies that the correlation coefficient must have been a positive values.

Thus, it can be concluded that there is a positive correlation between X and Y.

How many variable terms are in the expression 3x3y + 5x2 − 4y + z + 9?

Answers

Answer:

4

Step-by-step explanation:

"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.

Raul and his friends each way 1/20 of a ton are standing on a truck scale . The total weight shown by the scale is 3/4 of a ton . How can I find the total number of people on the scale when Raul and his friends are weighed?

Answers

Answer: There are 15 friends.

Step-by-step explanation:

We know that there is N friends (N is the number that we are looking for)

Each friend weights 1/20 ton.

Now, the weight of the N friends together is N times 1/20 ton.

Then we have:

N*(1/20) ton = 3/4 ton

We solve this for N.

First multiply both sides by 20.

20*N*(1/20) = N = 20*(3/4) = 60/4 = 15

Answer:

I can find the total number of people by dividing the total weight by the weight of one person.

Step-by-step explanation:

Triangle ABC has vertices A(0, 6) , B(−8, −2) , and C(8, −2) . A dilation with a scale factor of 12 and center at the origin is applied to this triangle. What are the coordinates of B′ in the dilated image? Enter your answer by filling in the boxes. B′ has a coordinate pair of ( , )

Answers

Answer:

[tex]B' = (-96,-24)[/tex]

Step-by-step explanation:

Given

[tex]A(0,6)[/tex]

[tex]B(-8,-2)[/tex]

[tex]C(8,-2)[/tex]

Required

Determine the coordinates of B' if dilated by a scale factor of 12

The new coordinates of a dilated coordinates can be calculated using the following formula;

New Coordinates = Old Coordinates * Scale Factor

So;

[tex]B' = B * 12[/tex]

Substitute (-8,-2) for B

[tex]B' = (-8,-2) * 12[/tex]

Open Bracket

[tex]B' = (-8 * 12,-2 * 12)[/tex]

[tex]B' = (-96,-24)[/tex]

Hence the coordinates of B' is [tex]B' = (-96,-24)[/tex]

Answer:

Bit late but the answer is (-4,-1)

Step-by-step explanation:

Took the test in k12

A company finds that the rate at which the quantity of a product that consumers demand changes with respect to price is given by the​ marginal-demand function Upper D prime (x )equals negative StartFraction 5000 Over x squared EndFraction where x is the price per​ unit, in dollars. Find the demand function if it is known that 1006 units of the product are demanded by consumers when the price is ​$5 per unit.

Answers

Answer:

q =  5000/x  + 6

Step-by-step explanation:

D´= dq/dx  =  - 5000/x²

dq = -( 5000/x²)*dx

Integrating on both sides of the equation we get:

q = -5000*∫ 1/x²) *dx

q = 5000/x + K   in this equation x is the price per unit and q demanded quantity and K integration constant

If when  1006 units are demanded when the rice is 5 then

x = 5     and   q = 1006

1006  =  5000/5 +K

1006 - 1000 = K

K = 6

Then the demand function is:

q =  5000/x  + 6

The dance team is selling headbands to raise
money for dance team jackets. They need
to sell 1,260 headbands. The headbands must
be divided equally among the three coaches.
Each coach is in charge of 10 dancers. If all
the headbands must be sold, how many
headbands will each dancer on the team
need to sell?

Answers

Answer:

42  headbands per dancer

Step-by-step explanation:

Selling 1260 headband

Divide by the three coaches

1260/3

420 per coach

Divide by each dancer under a coach

420/10 = 42

Each dancer must sell 42 headbands

For the following graph, state the polar coordinate with a positive r and positive q (in radians). Explain your steps as to how you determined the coordinate (in your own words). I'm looking for answers that involve π, not degrees for your angles. State the polar coordinate with (r, -q). Explain how you found the new angle. State the polar coordinate with (-r, q). Explain how you found the new angle. State the polar coordinate with (-r, -q). Explain how you found the new angle.

Answers

Answer:

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

Step-by-step explanation:

For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.

So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,

( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.

( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120

Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.

( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )

_________________________________

So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

The sequence below represents Marisa’s fine at the library for each day that she has an overdue book: $0.50, $0.65, $0.80, $0.95, $1.10, ... Which equation represents Marisa’s library fine as a function of a book that is n days overdue? f(n) = 0.15n f(n) = 0.50n f(n) = 0.15n + 0.35 f(n) = 0.50n + 0.15

Answers

Answer:

f(n) = 0.15n + 0.35

Step-by-step explanation:

The sequence of the problem above is an arithmetic sequence

For an nth term in an arithmetic sequence

F(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

To find the equation first find the common difference

0.65 - 0.5 = 0.15 or 0.80 - 0.65 = 0.15

The first term is 0.5

Substitute the values into the above formula

That's

f(n) = 0.5 + (n - 1)0.15

f(n) = 0.5 + 0.15n - 0.15

The final answer is

f(n) = 0.15n + 0.35

Hope this helps you

Answer:

The correct option is: f(n) = 0.15n + 0.35

Step-by-step explanation:

Took the math test on edge

Evaluate −x^2−5 y^3 when x = 4 and y = 1

Answers

Answer:

Simplify:

[tex]-4^2-5(1^3)[/tex]

So you get:

[tex]-21\\[/tex]

Answer:

[tex]\huge\boxed{-21}[/tex]

Step-by-step explanation:

-x²-5y³

Given that x = 4, y = 1

[tex]-(4)^2-5(1)^3[/tex]

[tex]-16-5(1)\\-16-5\\-21[/tex]

(x−1)(x−7)=0 PLEASE HELP

Answers

Answer:

1, 7

Step-by-step explanation:

Because the product is 0, either (x-1) or (x-7) is equal to 0. That means that x = 1, or 7

Need Help
Please Show Work​

Answers

Answer:

18 - 8 * n = -6 * n

The number is 9

Step-by-step explanation:

Let n equal the number

Look for key words such as is which means equals

minus is subtract

18 - 8 * n = -6 * n

18 -8n = -6n

Add 8n to each side

18-8n +8n = -6n+8n

18 =2n

Divide each side by 2

18/2 = 2n/2

9 =n

The number is 9

━━━━━━━☆☆━━━━━━━

▹ Answer

n = 9

▹ Step-by-Step Explanation

18 - 8 * n = -6 * n

Simple numerical terms are written last:

-8n + 18 = -6n

Group all variable terms on one side and all constant terms on the other side:

(-8n + 18) + 8n = -6n + 8n

n = 9

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

AB||CD. Find the measure of

Answers

Answer:

135 degrees

Step-by-step explanation:

3x+15 = 5x - 5 because of the alternate interior angles theorem.

20 = 2x

x = 10

3(10) + 15 = 30+15 = 45

Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.

180-45 = 135.

What is the x-value of point A?

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 5

▹ Step-by-Step Explanation

The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.

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Answer:

The x value is 5

Step-by-step explanation:

The x value is the value going across

Starting where the two axis meet, we go 5 units to the right

That is the x value

find the greatest common factor of 108d^2 and 216d

Answers

Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

Answer:

[tex]\boxed{108d}[/tex]

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The variables must have the same base.If one variable is raised to a power and the other is not, the GCF is the variable that does not have a power.If one variable is raised to a power and the other is raised to a power of lesser value, the GCF is the variable with the lesser value power.

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³.  Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is [tex]\boxed{108d}[/tex].

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

[tex]\frac{216}{108}=2[/tex]

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is [tex]\boxed{108d}[/tex].

A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain using the visual analog scale. Assume that both samples are independent simple random samples from populations having normal distributions. Use a significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.
n xbar s
Sham 20 0.41 1.26
Magnet 20 0.46 0.93

Answers

Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:

[tex]H_{0}: s_{1}^{2} = s_{2}^{2}[/tex]

[tex]H_{a}: s_{1}^{2} > s_{2}^{2}[/tex]

To test it, use F-test statistics and compare variances of each treatment.

Calculate F-value:

[tex]F=\frac{s^{2}_{1}}{s^{2}_{2}}[/tex]

[tex]F=\frac{1.26^{2}}{0.93^{2}}[/tex]

[tex]F=\frac{1.5876}{0.8649}[/tex]

F = 1.8356

The critical value of F is given by a F-distribution table with:

degree of freedom (row): 20 - 1 = 19

degree of freedom (column): 20 - 1 = 19

And a significance level: α = 0.05

[tex]F_{critical}[/tex] = 2.2341

Comparing both values of F:

1.856 < 2.2341

i.e. F-value calculated is less than F-value of the table.

Therefore, failed to reject [tex]H_{0}[/tex], meaning there is no sufficient data to support the claim that sham treatment have pain reductions which vary more than for those using magnets treatment.

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