The volume of a triangular prism is increased by a factor of 8. By what factor is the surface area of the figure increased?

HURRY PLEASE!!!

Answer:

D.

Step-by-step explanation:

The conclusion that can be drawn from the given statements is that " events E and F are independent".

Two events such as A and B are said to be independent if the occurrence of event A does not affect the occurrence of event B. I.e.,

P(A ∩ B) = P(A)×P(B)

If A and B are two events in a sample space S, then the probability of event B after event A has occurred is called the conditional probability and it is denoted by P(B|A) = [P(A ∩ B)]/P(A).

Given that E and F are two events.

P(E|F) = 0.3

P(E) = 0.3

So, the conditional probability is written as,

P(E|F) = P(E ∩ F)/P(F)

If E and F are independent events, then the probability P(E ∩ F) = P(E) × P(F).

On substituting,

P(E|F) = P(E) × P(F)/P(F)

          = P(E)

Therefore, P(E|F) = P(E) = 0.3

Hence, events E and F are independent.

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Answer:

The height of the trapezoid is [tex]4.5\ ft[/tex]

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

[tex]A=\frac{1}{2}(b1+b2)h[/tex]

In this problem we have

[tex]A=33.75\ ft^{2}[/tex]

[tex]b1=5\ ft[/tex]

[tex]b2=10\ ft[/tex]

substitute in the formula and solve for h

[tex]33.75=\frac{1}{2}(5+10)h[/tex]

[tex]67.5=15h[/tex]

[tex]h=67.5/15=4.5\ ft[/tex]

Answer:

[tex]h=4.5\text{ feet}[/tex]

Step-by-step explanation:

We have been given that a plot of land has an area 33.75 square feet. Jackson wants to put a 4-foot by 4 foot shed on the land. Jackson wants to put a 4-foot by 4 foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet.

We will use area of trapezoid to find the height of trapezoid.

[tex]\text{Area of trapezoid}=\frac{1}{2}(a_1+a_2)\times h[/tex], where,

[tex]a_1\text{ and }a_2=\text{ Parallel sides or bases of trapezoid}[/tex],

[tex]h=\text{Height}[/tex].

We can see that parallel sides are 5 feet and 10 feet. We have been given that area of trapezoid is 33.75 square feet.

[tex]33.75\text{ feet}^2=\frac{1}{2}(\text{ 5 feet + 10 feet})\times h[/tex]

[tex]33.75\text{ feet}^2=\frac{1}{2}(\text{ 15 feet})\times h[/tex]

Switch sides:

[tex]2\times\frac{1}{2}(\text{ 15 feet})\times h=2\times 33.75\text{ feet}^2[/tex]

[tex]\text{ 15 feet}\times h=67.50\text{ feet}^2[/tex]

[tex]\frac{\text{ 15 feet}\times h}{\text{ 15 feet}}=\frac{67.50\text{ feet}^2}{\text{ 15 feet}}[/tex]

[tex]h=4.5\text{ feet}[/tex]

Since the height of trapezoid is 4.5 feet, therefore, Jackson can put a 4 foot by 4 foot shed on the land.

Answer:

supplementary angle sum = 180°

EOG + EOF = 180°

71° +EOF = 180°  

EOF = 180° -71°

EOF = 109°

Step-by-step explanation:

Answer:

m<EOF = 109 deg

Step-by-step explanation:

Definition of supplementary angles:

Two angles are supplementary if the sum of their measures is 180 degrees.

Angles EOF and EOG are supplementary, so the sum of their measures is 180 degrees.

m<EOF + m<EOG = 180

We are given the measure of <EOG: m<EOG = 71 deg.

We substitute that measure in our equation and solve the equation for m<EOF.

m<EOF + 71 deg = 180 deg

Subtract 71 deg from both sides.

m<EOF = 109 deg

[tex]2x+7x=747\\9x=747\\x=83\\\\2x=166\\7x=581[/tex]

Tom - [tex]\pounds166[/tex]

Ben - [tex]\pounds581[/tex]

Answer:

B AND C

Step-by-step explanation:

Collinear Points: points that lie on the same line.

Coplanar Points: points that lie in the same plane.

Answer:

Step-by-step explanation:

Givens

Let Phoebe = P

Let Andy = A

Let Polly = Po

Total = 270

Equations

P = 3*A

A = 2*Po

P + A + Po = 270

Solution

P + 2Po + Po = 270

P = 3*A                                       But A = 2Po. Substitue 2Po for A

P = 3(2*Po)                                 Combine the right

P = 6Po                                      Substitute 6Po for P  

6Po + 2Po + Po = 270               Combine the left

9*Po = 270                                 Divide by 9

9Po/9 = 270/9                           Do the division

Po = 30

==========================

A = 2*Po = 2* 30 = 60

A = 60

==========================

P = 3*A

P = 3*60

P = 180

Answer

Phoebe gets 180

Andy gets       60

Polly gets        30

Answer:

Segment JK is a chord in circle H

Line LM is a secant to circle H

Step-by-step explanation:

* Lets revise some definition in the circle

- The radius of the circle is a line segment drawn from the center of  

 the circle to a point on the circumference of the circle

- The chord of a circle is a line segment whose endpoints lie on the

 circumference of the circle

- The secant is a line intersect the circle in two points

- The tangent is a line touch or intersect the circle in one point

* Now lets solve the problem

- In circle H

∵ JK is a segment in circle H

∵ Point J lies on the circumference of circle H

∵ Point K lies on the circumference of circle H

∴ Segment JK is a chord in circle H

∵ LM is a line

∵ LM intersect circle H in two points L and M

∴ Line LM is a secant to circle H

Answer:

-12-14i

Step-by-step explanation:

subtract real from real number and imaginary from imaginary number

Answer:

-12 -14i

Step-by-step explanation:

(2 + 2i) - (14+ 16i)

Distribute the negative sign

2+2i -14-16i

Subtract the real part

2-14 = -12

Subtract the imaginary part

2-16 = -14

Put them back together in the form a + bi where a is the real part and b is the imaginary part

-12 -14i

Answer:

x=6

x=2

Step-by-step explanation:

Fortunately for us, the function is written in factorized terms, so it is easier to find its roots.

The roots are the values for the 'x' variables that makes the functions goes to zero.

They are x=6 and x=2, any of those value make the function equals zero, or in other words, they are the points of interception with the 'y' axis.

To obtain these value

lets study the following condition

(x-6) * (x-2)=0

The above is accomplish when (x-6)=0 or (x-2)=0

We have two independent equations from where we obtain that x=6 and x=2

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}1&26&7\end{array}\right] }[/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}-1&2&4\end{array}\right] \times\left[\begin{array}{ccc}3&6&1\\2&4&0\\0&6&2\end{array}\right]\\\\=\left[\begin{array}{ccc}(-1)(3)+(2)(2)+(4)(0)&(-1)(6)+(2)(4)+(4)(6)&(-1)(1)+(2)(0)+(4)(2)\end{array}\right]\\\\=\left[\begin{array}{ccc}-3+4+0&-6+8+24&-1+0+8\end{array}\right] \\\\=\left[\begin{array}{ccc}1&26&7\end{array}\right][/tex]

Option B [1 26 7] is the product of given matrix.

What is matrix multiplication formula?

Consider matrix A which is a × b matrix and matrix B, which is a b ×c matrix.

Then, matrix C = AB is defined as the A × B matrix.

An element in matrix C, Cxy is defined as Cxy = Ax1By1 +….. + AxbBby =

AxkBky  for x = 1…… a  and y= 1…….c

How to multiply given matrix?

[tex]\left[\begin{array}{ccc}-1&2&4\end{array}\right][/tex]×[tex]\left[\begin{array}{ccc}3&6&1\\2&4&0\\0&6&2\end{array}\right][/tex]

=[ -1×3+2×2+4×0   -1×6+2×4+4×6   -1×1+2×0+4×2  ]

=[-3+4+0   -6+8+24   -1+0+8]

=[1  26 7 ]

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Answer:

f(x)=(x-12)^2

Step-by-step explanation:

We know that the function f(x+m) equals to the function f(x) translated 'm' times to the left. Therefore, to translate the function f(x) = x^2 twelve units to the right, we have to:

f(x-12) = (x-12)^2

Therefore, the new function is: f(x)=(x-12)^2

Answer:

You multiply

Step-by-step explanation:

The base: 12 in times 12 in

Each side (There are four, so multiply by 4!): 10 in times 12 in divided by 2

Answer:

there was an increase and it increased by 6.9%

Answer:

F(x)=4x and g(x) =3x

Step-by-step explanation:

We will have to check each pair of functions one by one

So,

For f(x)=3-4x and g(x)=16x-3

For composition we have to put g(x) in place of x in f(x)

(fog)(x)=3-4(g(x))

= 3-4(16x-3)

=3-64x+12

=-64x+15

So first pair doesn't give 12x.

Now for,

F(x)=6x2 and g(x)= 2/x

(fog)(x)= 6(g(x))^2

=6(2/x)^2

=6*(4/x^2)

=24/x^2

For the last pair:

F(x)=4x and g(x) =3x

(fog)(x)=4(g(x))

=4(3x)=12x

So for the last pair of functions (fog)(x) is 12x ..

Answer:

d

Step-by-step explanation:

on edge

Answer:

1st, 3rd, and 6th

Step-by-step explanation:

Let's look at each statment...

1.) Correct

Explanation: 10 percent of the students at the school participate in soccer. If 140 is 10% of the number of students at the school, there is more than 140 students at this school.

2.) Incorrect

Explanation: We've already established that the # of students at the school is more than 140.

3.) Correct

Explanation: 10% as a decimal is 0.1 Divide 140 by 0.1 and you get 1,400. So, the total number of students is 1,400.

4.) Incorrect

Explanation: We've already established that the number of students is 1,400, not 290.

5.) Incorrect

Explanation: We've already established that the number of students is 1,400, not 150.

6.) Incorrect

Explanation: If the percent was a ratio, it would be 10:100 or 10/100. This is because a whole percent is 100% and the percent of students who play soccer is 10%.

7.) Correct

Explanation: We've already established that the ratio would be 10:100 or 10/100. Thus, this is correct.

I hope this helps! :)

Answer:

29/50 is the same as 0.580

Step-by-step explanation:

0.580 is the same as 0.58

.58=58/100

I knew to put 58 over 100

because the decimal terminates in the hundredths spot

58/100 can be reduced

58 and 100 are both even so they are both divisible by 2

58/2=29

while

100/2=50

so 58/100 is the same as saying 29/50

Answer:

29/50

Step-by-step explanation:

0.58 = 58/100 = 29/50

Answer:

y=-4x

Step-by-step explanation:

You can graph it.. It might be easier for you to count than to use the formula for slope. We are counting from (0,0) to (2,-8)... I'm doing rise/run... I have to go down from (0,0) 8 units so the rise is -8 and the run is 2. So the slope is -8/2=-4.

We know the y-intercept is (0,0)... so the equation is y=-4x+0 or just y=-4x

Maybe you seen that this was proportional because it was a straight diagonal line going through the origin which we knew then that the line was already in the form of y=kx

Then you can look at the point (2,-8) and see what you need to do 2 to get -8 multiplication-wise.

2(-4)=-8

so

x(-4)=y

or

y=-4x

Answer:

3:2

Step-by-step explanation:

To answer questions like this I would makeup an age for Alan

Like say Alan is 10 years old

John is 3 times the age of 10 so he is 30

Ralph is twice the age of 10 so he is 20

so 30/20 can be simplified to 3/2

There are other ways to solve it but that is how I would solve it

I hope it helped you

Answer:

3:2 or 3/2

Step-by-step explanation:

Let Alan's age be x

So according to the assumed variable, John's age will be three times of Alan's age

John's Age = 3x

Similarly,

Twice of Alan's age = 2x

so, Ralph's age = 2x

Since we have to find the ratio of John's age to Ralph's age that will be equal to

3x : 2x

which can also be written as:

3:2 or 3/2 ..

Answer:

-55

Step-by-step explanation:

A debt is a negative value

-55

Answer:

[tex]-55[/tex].

Step-by-step explanation:

We are asked to write an integer for the given situation.

Situation: Greg has a debt of $55.

As Greg has a debt of $55, this means that Greg owes $55 to someone.

So the balance of Greg's account would be [tex]-55[/tex].

Therefore, our required integer would be [tex]-55[/tex].

Answer:

the answer is no solutions

Step-by-step explanation:

the solution is found at the point in which the two lines intersect.

in this case they do not intersect because the lines are parallel. if you rearrange  2x – y = 7   you will get y = 2x - 7.  the slope is 2x

the slope of the second equation is 2x as well. when slopes are the same they are parallel and therefore never cross.

For this case we have the following system of equations:

[tex]2x-y = 7\\y = 2x + 3[/tex]

To solve, we substitute the second equation in the first:

[tex]2x- (2x + 3) = 7\\2x-2x-3 = 7\\-3 = 7[/tex]

As noted, equality is not fulfilled. Thus, the system has no solution.

It can also be observed that the equations are:

[tex]y = 2x + 3\\y = 2x-7[/tex]

That is, they have the same slope, [tex]m = 2[/tex], so the lines are parallel. If the lines are parallel, they never intersect.

Answer:

The system has no solution

Answer: w = 4

Step-by-step explanation:

Subtract 1w from each side of the equation to get 5w = 20.

Divide both sides of the equation by 5 to get w = 4.

Hello!

Answer:

[tex]\boxed{w=4}\checkmark[/tex]

Answer should be positive sign.

Step-by-step explanation:

First, you subtract by w both sides of an equation.

[tex]6w-w=w+20-w[/tex]

Simplify.

[tex]5w=20[/tex]

Then, you divide by 5 both sides of an equation.

[tex]\frac{5w}{5}=\frac{20}{5}[/tex]

Finally, simplify and then solve.

[tex]20\div 5 = 4[/tex]

[tex]\boxed{w=4}[/tex], which is our final answer.

Hope this helps!

Thanks!

Have a nice day! :)

Answer:

Answer: A (first option)

Step-by-step explanation:

E2020

The angles formed by the diagonals and sides of the rhombus are

x + y = z.

Option A is correct.

As, When the diagonals of a rhombus are perpendicular, the angle z must be exactly 90 degrees (z=90).

Any triangle's interior angles must add up to 180 degrees.

Using Angle Sum Property

x + y + z = 180°

(x+y+z)=180°

x+y+z=180

As, z=90

x + y + 90 = 180

x + y = 90

So, the angles formed by diagonals is x + y = z.

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Answer:

Step-by-step explanation:

Use the half angle identity for cosine:

cos(x/2)=+ or - sqrt(1+cos(x))/sqrt(2)

I'm going to figure out the sign part first for cos(x/2)...

so x is in third quadrant which puts x between 180 and 270

if we half x, x/2 this puts us between 90 and 135 (that's the second quadrant)

cosine is negative in the second quadrant

so we know that

cos(x/2)=-sqrt(1+cos(x))/sqrt(2)

Now we need cos(x)... since we are in the third quadrant cos(x) is negative...

If you draw a reference triangle sin(x)=3/5 you should see that cos(x)=4/5 ... but again cos(x)=-4/5 since we are in the third quadrant.

So let's plug it in:

cos(x/2)=-sqrt(1+4/5)/sqrt(2)

No one likes compound fractions (mini-fractions inside bigger fractions)

Multiply top and bottom inside the square roots by 5.

cos(x/2)=-sqrt(5+4)/sqrt(10)

cos(x/2)=-sqrt(9)/sqrt(10)

cos(x/2)=-3/sqrt(10)

Rationalize the denominator

cos(x/2)=-3sqrt(10)/10

Answer:

b and c

Step-by-step explanation:

i think its b and c

Answer:

A, D, and E

Step-by-step explanation:

They all have ten 0.1 square which equals 1.

To solve this you must use a proportion like so...

[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]

65 is a percent and percents are always taken out of the 100. This means that one proportion will have 65 as the part and 100 as the whole

We want to know out of what number is 78 65%. This means 78 is the part and the unknown (let's make this x) is the whole

[tex]\frac{78}{x} =\frac{65}{100}[/tex]

Now you must cross multiply

78*100 = 65*x

7800 = 65x

To isolate x divide 65 to both sides

7800/65 = 65x/65

120 = x

This means that 65% of 120 is 78

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: 120

It is because google said so

To find the x-intercepts of a parabola with given vertex and y-intercept, we can use the vertex form of the equation. Substituting the given values, we find the value of a, and then substitute the values again to find the x-intercepts. The x-intercepts of this parabola are approximately (0.55, 0) and (1.45, 0).

To find the x-intercepts of a parabola, we need to find the values of x when y is equal to zero. Starting with the equation of the parabola in vertex form, y = a(x-h)^2 + k, where (h,k) is the vertex, we can substitute the given values for the vertex (1,1) into the equation. This gives us y = a(x-1)^2 + 1. Next, we substitute the y-intercept (-3) into the equation, so we have -3 = a(0-1)^2 + 1. Solving for a, we get a = -2.

Now we can substitute a and the given values into the equation again to find the x-intercepts. Plugging in a = -2, we have 0 = -2(x-1)^2 + 1. Simplifying this equation and solving for x, we get x = 1 ± √(3/2). Rounding to the nearest hundredth, the x-intercepts are approximately (0.55, 0) and (1.45, 0).

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Answer:

X=1

Step-by-step explanation:

Subtract by 2 from both sides of equation.

6x+2-2=9x-1-2

Simplify.

1-2=-3

6x=9x-3

Then subtract by 9x from both sides of equation.

6x-9x=9x-3-9x

Simplify.

-3x=-3

Divide by -3 from both sides of equation.

-3x/3=-3/-3

Simplify, to find the answer.

-3/-3=1

X=1 is the correct answer.

Answer:

x=1

Step-by-step explanation:

Answer:

y = 4x + b, where b is any number

Step-by-step explanation:

Adrian, you need to share the possible answer choices.

Every line parallel to y = 4x + 1 has the slope 4.

This is true for any y-intercept, that is, for any b in y = mx + b.

Final answer:

An equation of a line parallel to y=4x+1 would have the same slope of 4 and can be expressed as y=4x+b, where b is any y-intercept not equal to 1.

Explanation:

An equation of a line parallel to the line represented by y=4x+1 would have the same slope as the given equation. This is because parallel lines have identical slopes. In the equation y=4x+1, the slope is 4, as this is the coefficient of x. Therefore, any line that has a slope of 4 will be parallel to y=4x+1. The general form for such a parallel line would be y=4x+b, where b is the y-intercept, which can be any number different than 1 to ensure the lines are not the same.

Answer:

C. 4x+5y

Step-by-step explanation:

Lets start by factorizing the expression 16x²+40xy+25y²

Consider the expression ax²+bx+c

During factorization, two numbers picked should add up to b while the product should be=ac

We find two numbers that when added give 40 and when multiplied = 16×25=400

These numbers are 20 and 20

Therefore the expression will be broken into:

16x²+20xy+20xy+25y²

4x(4x+5y)+5y(4x+5y)

(4x+5y)(4x+5y)

The expression is a perfect square.

Answer:

c

Step-by-step explanation:

a p e x

Answer:

(x + 5)=0 or (x - 17)=0

x=-5 or x=17

Discard the negative value

x=17 is considered.

Michael is 17yrs old

Answer:

Step-by-step explanation:

          Let x = Michael's age.

     Then x² = the square of his age

and x² - 12x = the square of his age – 12 times his age

and x² - 12x = 85

We must solve the quadratic for x.

1. Subtract 85 from each side.

x² - 12x - 85 = 0

2. Multiply the leading coefficient and the constant

1 × 85 = 85

3. Find two numbers that multiply to give -85 and add to give -12.

Possible pairs are 1, 85; 5, 17

Start with the numbers near the end of the list.

By trial and error, you will find that 5 and -17 work:

5 ×(-17) = -85  

and 5 -  17 = -12

4. Rewrite -12x as 5x -17x

x² + 5x – 17x - 85 =0

5. Factor by grouping the first two and the last two terms

x(x + 5) - 17(x + 5) =0

(x  + 5)(x - 17) = 0

6. Find the zeroe

[tex](x + 5)(x - 17) = 0\\\\\begin{array}{rlrl}x + 5 & = 0 &  x - 17 & =0\\x & = -5 & x & = 17\\\end{array}\\\text{Michael can't have a negative age, so } \boxed{\textbf{he is 17 years old.}}[/tex]

Check:

[tex]\begin{array}{rcl}(-17)^{2} + 12(-17) & = & 85\\289 - 204 & = & 85\\85 & = & 85\\\end{array}[/tex]

OK.