For f(x)=4x+1 and g(x)=x^2-5, find (f-g)(x).

Answer:

18+12.125π units²

Step-by-step explanation:

The diameter of the semicircle can be found by the use Pythagoras theorem.

Δx²+Δy²=d²

Δx=3--1=4

Δy=3--6=9

d²=4²+9²

d=√(16+81)

Area=πr²/2

=π×(√(16+81)/2)²÷2

=[π×(97)/4]/2

=97π/8

=18+12.125π units²

97π/8 is equivalent to 18+12.125π units²

Answer:

18+12.125π units²

I tooked the test (●'◡'●)

Step-by-step explanation:

Let's solve for g.

gx=x4−3x2+4x−5

Step 1: Divide both sides by x.

gx

x

=

x4−3x2+4x−5

x

g=

x4−3x2+4x−5

x

Answer:

g=

x4−3x2+4x−5

x

Answer:

x = 5

Step-by-step explanation:

the expression is "undefined"  when the denominator is equal to zero

denominator =  25 - x²

Values of x where the equation is "undefined"

0 = 25 - x²

x² = 25

√x² = √25

x = ± 5

Nonnegative value of x where the equation is "undefined"

x = 5

An expression is said to be undefined, if it has 0 as its denominator. For [tex]\frac{5 + x}{25 - x^2}[/tex] to be undefined, x must be 5.

Given that:

[tex]\frac{5 + x}{25 - x^2}[/tex]

For the expression to be undefined, the denominator must equal 0.

i.e.

[tex]25 - x^2 = 0[/tex]

Collect like terms

[tex]-x^2 = 0 - 25[/tex]

[tex]-x^2 = - 25[/tex]

Cancel out negatives

[tex]x^2 = 25[/tex]

Take positive square root

[tex]x = 5[/tex]

This means that when [tex]x = 5[/tex],  [tex]\frac{5 + x}{25 - x^2}[/tex] is undefined.

Read more about undefined expressions at:

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Answer:

9.10 km to the nearest hundredth.

Step-by-step explanation:

We have a triangle whose adjacent side is 25 km and angle  20 degrees.

If h is the height we have the equation:

tan 20 = h / 25

h = 25 tan 20

= 9.099 km.

Answer:

1.97 hours to land in New York

Step-by-step explanation:

We know that the number of hours it takes to complete the flight is: 5 [tex]\frac{1}{4}[/tex] hours

This is the same as [tex]5 + \frac{1}{4} = 5.25\ hours[/tex]

If we have traveled [tex]\frac{5}{8}[/tex] of the way, then [tex]\frac{3}{8}[/tex] more of the way to get to New York is missing, therefore the number of hours remaining is:

[tex]\frac{3}{8}*5.25\ hours = 1.97\ hours[/tex]

1.97 hours to land in New York

The time left for the flight from Seattle to New York, after travelling 5/8 of the way, is approximately 2 hours.

The flight from Seattle to New York takes 5 1/4 hours. If you've travelled 5/8 of the way, it means you've covered a significant portion of the total flight time. Here's how you would figure out how much time you have left:

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A nominal has three terms.

Only B and D have three terms.

A constant term would be a number without a variable.

All the terms in B have variables ( x , y are part of each term).

The last term in D is the number 12, with no variable associated with it.

The answer would be D.

Answer:

it's d y^5+13x+12. you feel me you gon get it right

Answer: A

Step-by-step explanation:

360°-50°=310°

Answer:it’s actually 260

Step-by-step explanation:

I just did the test

Answer:

True.

Step-by-step explanation:

This is  'less than' so the area below the line is shaded.

It is a dotted line  because the solution does not contain points on the line as the inequality sign is < NOT ≤.

Answer:

First option: True.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Given this inequality:

[tex]y<2x -5[/tex]

We know that the line is:

[tex]y=2x -5[/tex]

Whose slope is 2 and the y-intercept is -5

The symbol "<" provided in the inequalty, indicates that the shaded region must be below the line and the line must be dotted. Therefore, the answer is: TRUE.

Answer:

Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..

Step-by-step explanation:

Given function is:

3[|x-1|+2]

Can also be written as:

3|x-1|+6

As we can see that the -1 is grouped with x which means it is a horizontal shift of 1 unit to the right.

Now, 6 is added to the function and it is not grouped with x which means that there is a vertical shift of 6 units upward.

Lastly, 3 is multiplied with the term containing x which means that there is a vertical stretch of 3 units.

Hence, the correct option is:

Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..

Answer:

Horizontal shift of [tex]1[/tex] unit to the right, a vertical shift upward of [tex]6[/tex] units, and a vertical stretch by a factor of [tex]3[/tex].

Step-by-step explanation:

First we re write the equation by multiplying the number [tex]3[/tex] in this way we will see much better the solution

[tex]g(x)=3[|x-1|+2]=3|x-1|+6[/tex]

we will start from the inside to the outside

[tex]|x-1|[/tex] this [tex]-1[/tex]is grouped with the x and this means there is a horizontal shift of [tex]1[/tex] unit to the right (because of the sign)

[tex]3|x-1|[/tex] this [tex]3[/tex] is multiplying the x which means the function will be stretching by a factor of [tex]3[/tex] ([tex]g(x)[/tex] will be [tex]3[/tex] times bigger)

[tex]3|x-1|+6[/tex] this [tex]6[/tex] is not goruped with x and moves the entire function 6 units upwards.

We can see it more clearly in the graph attached.

Finding the slope using two points:

The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =-7\\y_{1} =2\\x_{2} =4\\x_{1} =-3[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{-7 - 2}{4 - (-3)}[/tex]

[tex]\frac{-9}{6}[/tex]

^^^Reduce this fraction

[tex]\frac{-3}{2}[/tex]

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

c

Step-by-step explanation:

x=180-100=80

The value of x is [tex]80^{o}[/tex].

The opposite angles in a quadrilateral are those angles that are located diagonally opposite to each other.

The sum of the opposite angles of a cyclic quadrilateral is 180 degrees.

According to the given question.

We have a quadrilateral ABCD which is inscribed in a circle.

Also, m ∠ABC = 100 degrees

Since, we know that the sum of the opposite angles of a cyclic quadrilateral is 180 degrees.

Therefore,

[tex]m\angle ABC +m\angle CDA = 180^{o} \\\implies 100^{o} + x = 180^{o} \\\implies x = 180^{o} -100^{o} \\\implies x = 80^{o}[/tex]

Hence, the value of x is [tex]80^{o}[/tex].

Find out more information about sum of the opposite angles of a cyclic quadrilateral here:

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Answer:

Part A) The system of inequalities is

[tex]x\geq2[/tex]  and  [tex]y\geq2[/tex]

Part B) In the procedure

Part C) The schools that Natalie is allowed to attend are A,B and D

Step-by-step explanation:

Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions

we have

Points C(2,2), F(3,4)

The system of inequalities could be

[tex]x\geq2[/tex] -----> inequality A

The solution of the inequality A is the shaded area at the right of the solid line x=2

[tex]y\geq2[/tex] -----> inequality B

The solution of the inequality B is the shaded area above of the solid line y=2

see the attached figure N 1

Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify point C

C(2,2)    

Inequality A

[tex]x\geq2[/tex] -----> [tex]2\geq2[/tex] ----> is true

Inequality B

[tex]y\geq2[/tex] ------> [tex]2\geq2[/tex] ----> is true

therefore

Point C is a solution of the system of inequalities

Verify point D

F(3,4)    

Inequality A

[tex]x\geq2[/tex] -----> [tex]3\geq2[/tex] ----> is true

Inequality B

[tex]y\geq2[/tex] ------> [tex]4\geq2[/tex] ----> is true

therefore

Point D is a solution of the system of inequalities

Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.

we have

[tex]y < -2x+2[/tex]

The solution of the inequality is the shaded area below the dotted line [tex]y=-2x+2[/tex]

The y-intercept of the dotted line is the point (0,2)

The x-intercept of the dotted line is the point (1,0)

To graph the inequality, plot the intercepts and shade the area below the dotted line

see the attached figure N 2

therefore

The schools that Natalie is allowed to attend are A,B and D

Answer:

Construct a square of side length 4 cm

Step-by-step explanation:

* Lets explain how to construct a square polygon with side length 4 cm

- Use your straightedge to draw a horizontal line

- Measure on the horizontal line a segment of 4 cm

- Label its endpoints by A and B (AB = 4 cm)

- Open your compass at a distance greater then half AB (3 cm)

- Put the pin of the compass at point B and draw an arc intersects AB

 at point E and the horizontal line at point F

- Open the compass at a distance greater than the length of the side

 of the square (6 cm) and put its pin on the point E and draw an arc

- Put the pin of the compass on the point F without changing the open

 of the compass and draw another arc

- The two arcs intersect each other at point G

- Join BG and measure 4 cm from point B and label the end point of

 the 4 cm by C

- Open your compass at a distance 4 cm and put the pin on point C

 and draw an arc and put it on point A with the same distance 4 cm

 and draw another arc, the two arc intersect each other at point D

∴ ABCD is a square of side length 4 cm

# Look to the attached figure to more understand

As you can see from the image in the picture all the sides of the triangle are equal to each other (25). This means that this is an equilateral triangle.

The definition of an equilateral triangle is:

A triangle that has all sides equal to each other. The angles are also equal to each other. Since it is known that the sum of all the angles of a triangle equals 180, one angle of an equilateral triangle is always 60 degrees ( 180 / 3 = 60).

That means angle B has the measure of 60 degrees

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

F(-7,3)  -> F'(-7,-3)

G(2,6) -> G'(2,-6)

H(3,5) ->H'(3,-5)

Step-by-step explanation:

If you are taking point (a,b) and reflecting it across the x-axis (the horizontal axis), your x value is going to stay the same because you want the point on the same vertical line as (a,b).  The y-coordinate is going to be opposite because you want a reflection and the opposite of b will this give you the same distance from the x-axis as b.

So the transformation is this: (a,b)  -> (a,-b).

All this means is leave x the same and take the opposite of y.

F(-7,3)  -> F'(-7,-3)

G(2,6) -> G'(2,-6)

H(3,5) ->H'(3,-5)

The coordinates of each vertex if the triangle is reflected over the x-axis are [tex]F'(-7,-3),G'(2,-6),H'(3,-5)[/tex].

Given:

The vertices of a triangle are [tex]F(-7,3),G(2,6),H(3,5)[/tex].

To find:

The coordinates of each vertex if the triangle is reflected over the x-axis.

Explanation:

If a triangle is reflected over the x-axis, then the rule of reflection is defined as:

[tex](x,y)\to (x,-y)[/tex]

Using this rule, we get

[tex]F(-7,3)\to F'(-7,-3)[/tex]

[tex]G(2,6)\to G'(2,-6)[/tex]

[tex]H(3,5)\to H'(3,-5)[/tex]

Therefore, the coordinates of each vertex if the triangle is reflected over the x-axis are [tex]F'(-7,-3),G'(2,-6),H'(3,-5)[/tex].

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Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

See attached reference

For this case we must find the roots of the following equation:

[tex]x ^ 2-7x-4 = 0[/tex]

We have to:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 1\\b = -7\\c = -4[/tex]

Substituting the values:

[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {7 \pm \sqrt {49 + 16}} {2}\\x = \frac {7\pm\sqrt {65}} {2}[/tex]

We have two roots:

[tex]x_ {1} = \frac {7+ \sqrt {65}} {2} = 7.53\\x_ {2} = \frac {7- \sqrt {65}} {2} = - 0.53[/tex]

Answer:

[tex]x_ {1} = \frac {7+ \sqrt {65}} {2} = 7.53\\x_ {2} = \frac {7- \sqrt {65}} {2} = - 0.53[/tex]

Answer:

(C)

Step-by-step explanation:

♥☺

Answer:

5=.25, 3=.30, 2=.50

Step-by-step explanation:

5×5=.25

Answer: 25%

Step-by-step explanation: A nickel is worth 5 cents. There are 5 nickels. Multiply 5 by 5. 5 x 5 = 25. You have 25 cents in nickels. There are 100 cents in a dollar, so divide 25 by 100. 25/100 = 0.25. To get the percent, multiply 0.25 by 100. 0.25 x 100 = 25%.

Answer:

(x+1+i)(x+1-i) goes with x^2+2x+2

(x+2i)(x-2i) goes with x^2+4

(x-2+2i)(x-2-2i) goes with x^2-4x+8

Step-by-step explanation:

(x+1+i)(x+1-i)

(x+[1+i])(x+[1-i])

Use foil.

First: x(x)=x^2

Outer: x(1+i)=x+ix

Inner: x(1-i)=x-ix

Last: (1+i)(1-i)=1-i^2 since 1+i and 1-i are conjugates

__Add together to get: x^2+2x+1-i^2

We can actually simplify this because i^2=-1

So x^2+2x+1-i^2=x^2+2x+1-(-1)=x^2+2x+2

(x+2i)(x-2i)

These are conjugates so just do first and last of foil.

First: x(x)=x^2

Last: 2i(-2i)=-4i^2=-4(-1)=4

==Adding together gives x^2+4

(x-2+2i)(x-2-2i)

(x+[-2+2i])(x+[-2-2i])

This is similar to first.

Foil time!

First: x(x)=x^2

Outer: x(-2-2i)=-2x-2ix

Inner: x(-2+2i)=-2x+2ix

Last: (-2-2i)(-2+2i)=4-4i^2 (multiplying conjugates again)

==Add together giving us x^2-4x+4-4i^2

This can be simplified since i^2=-1.

So applying this gives us x^2-4x+4-4(-1)

=x^2-4x+4+4

=x^2-4x+8

Answer:

1. The first expression is equivalent to [tex]x^2+2x+2[/tex].

2. The second expression is equivalent to [tex]x^2+4[/tex].

3. The third expression is equivalent to  [tex]x^2-4x+8[/tex].

Step-by-step explanation:

(1).

The given expression is

[tex](x+1+i)(x+1-i)[/tex]

[tex][(x+1)+i][(x+1)-i][/tex]

Using the algebraic properties, we get

[tex](x+1)^2-(i)^2[/tex]                 [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]x^2+2x+1-(i)^2[/tex]               [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]

[tex]x^2+2x+1-(-1)[/tex]             [tex][\because i^2=-1][/tex]

[tex]x^2+2x+2[/tex]

Therefore the first expression is equivalent to [tex]x^2+2x+2[/tex].

(2).

The given expression is

[tex](x+2i)(x-2i)[/tex]

Using the algebraic properties, we get

[tex](x)^2-(2i)^2[/tex]                [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]x^2-4i^2[/tex]

[tex]x^2-4(-1)[/tex]            [tex][\because i^2=-1][/tex

[tex]x^2+4[/tex]

Therefore the second expression is equivalent to  

[tex]x^2+4[/tex].

(3)

The given expression is

[tex](x-2+2i)(x-2-2i)[/tex]

[tex][(x-2)+2i][(x-2)-2i][/tex]

Using the algebraic properties, we get

[tex](x-2)^2-(2i)^2[/tex]           [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]x^2-4x+4-4i^2[/tex]               [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]

[tex]x^2-4x+4-4(-1)[/tex]             [tex][\because i^2=-1][/tex]

[tex]x^2-4x+4+4[/tex]

[tex]x^2-4x+8[/tex]

Therefore the third expression is equivalent to  [tex]x^2-4x+8[/tex].

Answer:

B

Step-by-step explanation:

Given

5x + y = 14 ( subtract 5x from both sides )

y = 14 - 5x

Substituting values of x into the right side allows the corresponding value of y to be found.

x = - 1 : y = 14 - 5( - 1) = 14 + 5 = 19

x = 0 : y = 14 - 5(0) = 14 - 0 = 14

x = 1 : y = 14 - 5(1) = 14 - 5 = 9

Hence the corresponding values of x and y are

x    y

- 1   19

0     14

1       9

Answer:

12 miles per hour

Step-by-step explanation:

Answer:

41 units

Step-by-step explanation:

The diagonal forms a right triangle with the sides, so we can use Pythagorean theorem.

c² = a² + b²

d² = 9² + 40²

d = 41

The diagonal is 41 units long.

Answer:

The value of 27, because it’s greater than 26.7 and less than 29.3.

Step-by-step explanation:

You should find the confidence Interval at 95%

The formula to apply is;

C.I= x±z*δ/√n

where C.I is the confidence interval, x is the mean of the sample, z is the z* value from the standard normal distribution for 95% confidence interval, δ is the standard deviation and n is the sample size

Substitute values in the formula

[tex]z*=1.96\\\\[/tex]

Find δ/√n

[tex]=\frac{5}{\sqrt{60} } =0.64549722436\\\\\\[/tex]

Calculate z*δ/√n

[tex]=1.96*0.64549722436=1.2652\\\\\\[/tex]

C.I= 28±1.2652

Upper limit is = 28+1.2652=29.2625

Lower limit is =28-1.2652=26.7348

Solution

The value 27 is within 95% confidence interval because it is greater than 26.7 and less than 29.3

Answer:

B.The value of 27, because it’s greater than 26.7 and less than 29.3.Step-by-step explanation:

Answer:

[tex]\frac{3\pi}{4}[/tex]

(Assuming you want your answer in radians)

If you want the answer in degrees just multiply your answer in radians by [tex]\frac{180^\circ}{\pi}[/tex] giving you:

[tex]\frac{3\pi}{4} \cdot \frac{180^\circ}{\pi}=\frac{3(180)}{4}=135^{\circ}[/tex].

We can do this since [tex]\pi \text{ rad }=180^\circ[/tex] (half the circumference of the unit circle is equivalent to 180 degree rotation).

Step-by-step explanation:

[tex]\cos^{-1}(x)[/tex] is going to output an angle measurement in [tex][0,\pi][/tex].

So we are looking to solve the following equation in that interval:

[tex]\cos(x)=-\frac{\sqrt{2}}{2}[/tex].

This happens in the second quadrant on the given interval.

The solution to the equation is [tex]\frac{3\pi}{4}[/tex].

So we are saying that [tex]\cos(\frac{3\pi}{4})=\frac{-\sqrt{2}}{2}[/tex] implies [tex]\cos^{-1}(\frac{-\sqrt{2}}{2})=\frac{3\pi}{4}[/tex] since [tex]\frac{3\pi}{4} \in [0,\pi][/tex].

Answer is [tex]\frac{3\pi}{4}[/tex].

Answer:

The number of toys that Kevin can make per hour is equal to [tex]60\frac{c}{m}\ toys[/tex]

Step-by-step explanation:

we know that

Kevin makes c toys in m minutes

Remember that

1 hour=60 minutes

so

Using proportion find out how many toys can be make in 60 minutes (one hour)

Let

x -----> the  number of toys that Kevin can make per hour

so

[tex]\frac{c}{m}=\frac{x}{60}\\ \\x=60\frac{c}{m}\ toys[/tex]

therefore

The number of toys that Kevin can make per hour is equal to [tex]60\frac{c}{m}\ toys[/tex]

Answer:

8a.

Step-by-step explanation:

32 = 2*2*2*2*2

40 = 2*2*2* 5

Thus the GCF of 32 and 40 is 2*2*2 = 8.

The GCF of a and ab = a.

For this case we must find the GCF of the following expressions:

[tex]32ab ^ 3\\40a ^ 2[/tex]

By definition, the GCF is given by the largest factor that divides both numbers without leaving residue.

We look for the factors of 32 and 40:

32: 1,2,4,8,16

40: 1,2,4,5,8,10,20

Thus, the GCF is 8.

On the other hand, the GCF of [tex]ab ^ 3[/tex]and [tex]a ^ 2[/tex] is a.

Finally, the GFC of the expressions is:

[tex]8a[/tex]

Answer:

[tex]8a[/tex]

The equation (x+5)^2 + (y+7)^2=81 is a variation of a circles standard formula (x - h)^2 + (y - k)^2 = r^2

To find the diameter you must first know the radius.

In this question the radius is 9.

9^2 = 81

The diameter is composed of the length of two radii, this means that the equation to find the diameter when the radius is known is (let diameter be D and radius be r): D = 2r

D = 9 * 2

D = 18

The diameter is 18 units

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: First and last option

The birds began 1320 miles from the equator.

The birds are flying toward the equator at a rate of 60 mph.

Step-by-step explanation:

Note that the function f(x) is a linear function.

[tex]f (x) = - 60x + 1320[/tex]

If x represents the number of hours and f(x) represents the distance from the equator, then x = 0 means that the first hour has not yet elapsed.

When x = 0 then:

[tex]f (0) = -60 * 0 +1320\\f (0) = 1320[/tex].

This means that the initial distance at which the birds of the equator are located is 1320 miles.

Then when x = 1 then:

[tex]f (x) = -60 * 1 + 1320\\f (x) = -60 +1320[/tex]

When x = 2 then:

[tex]f (x) = -60 * 2 + 1320\\f (x) = -120 +1320[/tex]

As x increases by one unit then the distance of the birds to the equator decreases by 60 miles. This means that birds travel at a speed of 60 miles per hour

Answer:

The birds began 1320 miles from the equator.

The birds are flying toward the equator at a rate of 60 mph.

Step-by-step explanation:

Answer:

P(10)=0

Step-by-step explanation:

As per factor theorem:

If x-10 is factor of polynomial p(x), then the remainder after division by x-10 should be zero. i.e.  If we synthetic-divide a p(x) by x = 10 and get zero remainder as following

P(10)=0

it is reverse of remainder theorem!

Answer:

Option A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.

Step-by-step explanation:

step 1

Find the volume of the original pyramid

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the pyramid

we have

[tex]B=16^{2}=256\ m^{2}[/tex] ----> is the area of a square

[tex]h=12\ m[/tex]

substitute

[tex]V=\frac{1}{3}(256)(12)[/tex]

[tex]V=1,024\ m^{3}[/tex]

step 2

Find the volume of the new pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z -------> the scale factor

x ------> the volume of the new pyramid

y -----> the volume of the original pyramid

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{1}{4}[/tex]

[tex]y=1,024\ m^{3}[/tex]

substitute and solve for x

[tex](\frac{1}{4})^{3}=\frac{x}{1,024}[/tex]

[tex]x=(1,024)\frac{1}{64}=16\ m^{3}[/tex]

therefore

The volume of the new pyramid is the volume of the original pyramid times 1/64

Answer:

The answer is A

Step-by-step explanation: