Simplify (x²y³) to the power of 5​

Answer:

B

Step-by-step explanation:

The given equation y = 2x^2 -12x - 32 can be factored as follows:

y = 2(x^2 - 6x - 16) = 2(x - 8)(x + 2).  Then its roots are x = -2 and x = 8.

Since d > e and 8 > -2, we conclude that d = 8 and e = -2.

We need to find the minimum of y = 2x^2 -12x - 32.

We can do this by finding the vertex:                  b

The equation of the axis of symmetry is x = - ----------

                                                                                2a

                                 -12

which here is x = - --------- = 3

                                 2(2)

so f = 3.

Answer choice B is correct.

Answer:

Tama sya Ayan yung lumabas na sagot

Answer:

Step-by-step explanation:

A) The equation for the volume of a sphere is [tex]V=\frac{4}{3} \pi r^{3}[/tex]

As the diameter of each ball is 3 inches, that would mean that the radius of each is 1.5 inches.

Now we can plug our value into the equation

[tex]V=\frac{4}{3} \pi (1.5)^{3}[/tex]

This would simplify to

V = 14.12716694 [tex] in^{3}[/tex]

B) The equation for the volume of a cylinder is [tex]V=d\pi h[/tex]

As there are 3 balls in a container and the diameter of each is 3, that would mean that the height is 9 inches

Now we can plug in our values into the equation

[tex]V = (3)(9)\pi[/tex]

This would mean that this equation would simplify to

[tex]V = [/tex] 27\pi [tex]in^{3}[/tex]

C) To find the empty space, we must take the total volume, the volume of the cylinder, and subtract the volume of the tennis balls

This would mean that the equation would look like this

[tex](27\pi)-(3(\frac{4}{3} \pi (1.5)^{3})) [/tex]

This would simplify to

42.41150082 [tex]in^{3}[/tex] of empty space.

Answer:

Step-by-step explanation:

Givens

First, we find the volum of each tennis ball.

Notice that they have spherical form, so their volume is defined by

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

Where [tex]r=\frac{d}{2}=\frac{3 in }{2}=1.5in[/tex]

Replacing the radius and using [tex]\pi \approx 3.14[/tex], we have

[tex]V=\frac{4}{3}(3.14)(1.5in)^{3}=14.13 \ in^{3}[/tex]

Therefore, the volume of each tennis vall is 14.13 cubic inches, approximately.

Assuming that the diameter of each ball is congruent with the diameter of the can, we have the volume of a cylinder defined by

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

Where, [tex]r=1.5in[/tex] and [tex]h= 3(3in)=9in[/tex], because each can has three balls, and the height is the sum of all three diameters.

Replacing, we have

[tex]V=3.14(1.5in)^{2} (9in)=63.59 in^{3}[/tex]

Therefore, the volume of each can is 63.59 cubic inches, approximately.

Now, notice that between the can and the tennis balls thereis empty space, because balls are spherical and cans are cylindric.

Let's find the difference between their volumes:

[tex]V_{empy}=63.59-14.13= 49.46 in^{3}[/tex]

Therefore, there are 49.46 cubic inches of empty space between the tennis balls and the cans.

Number 2 is the answer

7 rollercoasters because 4 shows plus 3 more rollercoasters equal 7 and 4 shows .

It takes 5 minutes to ride on the rollercoaster plus the estimated 30 minute wait equals 35 and 35*7=245 and it takes 25 minutes to watch show and 25*4=100 and 245+100=345 so he can ride 7 rollercoasters and 4 shows in 345 minutes.

Hence function 's graph is option D .

Cos function is ration of adjacent side to hypotheses.

Range of function lies between [-1,1]

Cos x = 2 n [tex]\pi[/tex]

where x is angle

Hence option D where y=3cos ([tex]\frac{\pi }{2}[/tex]X) is function

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Answer: 3cos(4x)

Step-by-step explanation:

Answer:

Unfortunately, your picture doesn't show all the graphs of the possible answers.

However, the graph should look like the one I attached, passing by the (5,0) point.  Which is logic since a value of 5 for x would make the y the cubic root of 0... which is 0.

When trying to identify a graph of a formula, always try to see which values of x could make y = 0 or what would happen to y if x = 0, that will always give you a pretty good idea of which graph to choose from.

Answer:D

Step-by-step explanation:

Answer: 2.66 hours

Step-by-step explanation:

Shawana can paint a fence in 8hours which means in one hour she can paint 1/8 of a fence.

Kevin can paint the same fence in 4 hours, so in one hour he can paint 1/4 of the fence.

Together in 1 hour they can paint 1/8 + 1/4 = 3/8

Total hours for painting is 3/8 or 2.66 hours

The answer is:

The will paint the same fence at the same time in 2.67 hours.

From the statement we know that Shawna can paint a fence in 8 hours while Kevin can paint the same in 4 hours, and we are asked to calculate how long will it take them to paint the fence working together, so, calculating we have:

For Shawna, we have:

[tex]ShawnaRate=\frac{FencePainted}{TimeToPaint}\\\\ShawnaRate=\frac{1fence}{8hours}[/tex]

For Kevin, we have:

[tex]KevinRate=\frac{FencePainted}{TimeToPaint}\\\\KevinRate=\frac{1fence}{4hours}[/tex]

So, the combined work for both Shawna and Kevin will be:

[tex]CombinedWorkRate=\frac{1fence}{8hours} +\frac{1fence}{4hours}\\\\CombinedWorkRate=\frac{4fence.hours+8fence.hours}{32hours^{2}}\\ \\CombinedWorkRate=\frac{12fence.hours}{32hours^{2}}\\\\CombinedWorkRate=\frac{12fence.hours}{32hours^{2}}=\frac{3fence}{8hours}[/tex]

Now, if the want to paint the same fence at the same time, we can calculate it by the following way:

[tex]\frac{3fence}{8hours}=\frac{1fence}{x(hours)}\\\\x=1fence*\frac{8hours}{3fence}=2.67hours[/tex]

Hence, the will paint the same fence at the same time in 2.67 hours.

Have a nice day!

Answer:

C. 1/4

Step-by-step explanation:

There are in total 12 marbles in the bag.  So the probability of picking a red marble is 3/12.  If you simplify that, you get 1/4.

Odd numbers take the form [tex]2n-1[/tex], where [tex]n\ge1[/tex] is an integer. When [tex]n=400[/tex], the last odd number would be 799. So we're adding

[tex]S=1+3+5+\cdots+795+797+799[/tex]

By reversing the order of terms, we have

[tex]S=799+797+795+\cdots+5+3+1[/tex]

and we can pair up terms in both sums at the same position to write

[tex]2S=(1+799)+(3+797)+(5+795)+\cdots(795+5)+(797+3)+(799+1)[/tex]

so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:

[tex]2S=400\cdot800\implies S=160,000[/tex]

###

We could also make use of the formulas,

[tex]\displaystyle\sum_{i=1}^n1=n[/tex]

[tex]\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2[/tex]

We have

[tex]S=\displaystyle\sum_{i=1}^{400}(2i-1)=2\sum_{i=1}^{400}i-\sum_{i=1}^{400}1=400(400+1)-400=400^2=160,000[/tex]

Answer:

c

Step-by-step explanation:

a and b ar out because suplementry angels are 180 so its just c and d

When parallel line are cut by a traversal line,

Then corresponding angles are congruent.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

The parallel lines are cut by a traversal line.

(A) The sum of the degree measure of complementary angles is 180 degrees.

This is a contradictory statement.

Because, the sum of the degree measure of supplementary angles is 180 degrees.

(B) The sum of the degree measure of corresponding angles is 180 degrees.

This is a contradictory statement.

Because, the sum of the degree measure of supplementary angles is 180 degrees.

(C) Corresponding angles are congruent.

This is a true statement.

(D) The angles in a vertical pair are acute

This is also ca contradictory statement.

Therefore, corresponding angles are congruent.

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Answer:

Option D : 86.7% is the answer.

Step-by-step explanation:

Given information is :

A farmer grows vegetables on 7 acres of land.

He grows fruit on 6 acres of land.

And he grows flowers on 2 acres of land.

Total farming acres are = [tex]7+6+2=15[/tex] acres.

Now, we have to find what the theoretical probability that the ladybug was not found within the acres of flowers. This means it was not found in 2 acres of land. It must have been in 13 acres of land.

So, probability will be : [tex]\frac{13}{15} \times100[/tex] = 86.66% ≈86.7%

Therefore, option D is the answer.

Answer: d

Step-by-step explanation:

The probability that Jase makes an A given that he studies for the geometry test is [tex]\(\frac{68}{75}\)[/tex].

Let's denote the event that Jase studies for the geometry test as [tex]\(S\)[/tex] and the event that he makes an A as [tex]\(A\)[/tex].

The probability that Jase studies for his geometry test is given as [tex]\(P(S) = \frac{15}{16}\)[/tex].

The probability that Jase studies and makes an A is given as [tex]\(P(S \cap A) = \frac{17}{20}\).[/tex]

To find the probability that he makes an A given that he studies [tex](\(P(A|S)\))[/tex], we use the conditional probability formula:

[tex]\[ P(A|S) = \frac{P(S \cap A)}{P(S)} \][/tex]

Substitute the given values:

[tex]\[ P(A|S) = \frac{\frac{17}{20}}{\frac{15}{16}} \][/tex]

To divide by a fraction, multiply by its reciprocal:

[tex]\[ P(A|S) = \frac{17}{20} \times \frac{16}{15} \][/tex]

Simplify the expression:

[tex]\[ P(A|S) = \frac{17 \times 16}{20 \times 15} \][/tex]

[tex]\[ P(A|S) = \frac{272}{300} \][/tex]

Now, simplify the fraction:

[tex]\[ P(A|S) = \frac{68}{75} \][/tex]

So, the probability that Jase makes an A given that he studies for the geometry test is [tex]\(\frac{68}{75}\)[/tex].

Answer:

Step-by-step explanation:

The density of maple trees per square kilometer for the cosidered rectangular patch of land is 283 maple trees/sq. km approximately.

Density is like rate. It tells you how much of a thing is available for each unit other thing which contains the first thing.

Density = (Total amount available)/(total space which contains that amount)

For this case, we're specified that:

Density of trees will be expressed in terms of number of trees per unit area

Area of the considered land = [tex]3 \times 4 = 12 \: \rm km^2[/tex]

Thus, the density of the maple trees in terms of maple trees per sq. kilometers is:

[tex]D = \dfrac{3400}{12} = 283.3\overline{3} \approx 283 \: \rm \text{maple trees/sq. km}[/tex] (approximated to integers as trees cannot be in decimal).

Thus, the density of maple trees per square kilometer for the cosidered rectangular patch of land is 283 maple trees/sq. km approximately.

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The question is not perfectly clear, but I assume you're asking something like this:

in a rectangle, the area is given by [tex]A=wl[/tex]

where A is the area, w is the width and l is the length.

So, if we know that the width is 7 and we let x be the length of the rectangle, we have

[tex]A=7x[/tex]

If you need to solve this for x, divide both sides by 7:

[tex]x=\dfrac{A}{7}[/tex]

The length of a rectangular computer screen can be determined by the equation x = A / 7.

To find the length of a rectangular computer screen given its area (A) and width (7 inches), you can use the formula for the area of a rectangle:

Area = Length × Width

Given:

Area = A square inches

Width = 7 inches

We need to find the length, denoted by x. By rearranging the area formula, we get:

x = Area / Width

Substitute the given values:

x = A / 7

Therefore, the length of the computer screen in inches can be found using the equation x = A / 7.

Answer:

[tex]x=37[/tex]

Step-by-step explanation:

Use the alternating interior angles theorem.

It states that alternating interior angles are congruent.

Therefore,

[tex]3x+4=115 \\ \\ 3x=111 \\ \\ x=37[/tex]

Answer:

[tex]m=\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

we know that

In the diagram

[tex]tan(\theta)=\frac{m}{1/2}=2m[/tex]

[tex]tan(\theta)=\sqrt{3}[/tex]

Equate

[tex]2m=\sqrt{3}[/tex]

[tex]m=\frac{\sqrt{3}}{2}[/tex]

Answer:

B

Step-by-step explanation:

Option B on edge

Answer: Last Option

[tex]y> | x + 1 | +3[/tex]

Step-by-step explanation:

First we must identify the function shown in the graph.

It is a function of absolute value whose vertex is in the point (-1, 3)

The absolute value parent function is:

[tex]h(x) = | x |[/tex]. And it has its vertex in (0, 0)

The function shown in the graph is the function h(x) displaced 1 unit to the left and 3 units to the top.

Therefore the function shown in the graph [tex]f(x) = h (x + 1) +3[/tex]

[tex]f (x) = | x + 1 | +3[/tex].

Then, the region shaded in the graph are all the values of y that are above the graph of [tex]f (x) = | x + 1 | +3[/tex]

That is, the region is formed by all values where y is greater than [tex]f (x) = | x + 1 | +3[/tex]

Then the inequality is:

[tex]y> | x + 1 | +3[/tex]

Answer:

Final answer is Volume = 60 cubic centimeters.

Step-by-step explanation:

Given that area of the base of the given picture = 10 square centimeters.

Given that height of the given picture = 6 centimeters.

Now we need to find the volume of the given solid.

So we just need to multiply the base area with the height to get the volume.

Volume = (Area of base) ( height)

Volume = (10 square centimeters) ( 6 centimeters)

Volume = 60 cubic centimeters

Hence final answer is Volume = 60 cubic centimeters.

Answer:

0.36

Step-by-step explanation:

Percentage of boys = 60%

Percentage of girls = 100 - 60 = 40%

Percentage of boys that arrive by car

= 20% of 60%

= 0.2 x 60 = 12%

Percentage of girls that arrive by car

= 60% of 40%

= 0.6 x 40

= 24%

Total Percentage of children arrive by car

= 12 + 24

= 36%

P(Arrive by car)

= 36%

= 0.36

Answer:

n = 62 + x

Step-by-step explanation:

From the problem given, it is clear that the orange has LESS calories than a nectarine. HOW much less? "x" less.

Also, orange has 62 calories. So, nectarine MUST HAVE 62 + x calories.

If we let nectarine's calories be n, we can write:

n = 62 + x

27 multiplied by 8 is 216 so she would need a total of 216 cans. If each of the 23 students brings nine cans (multiple 23 by 9) then she has a total of 207. The difference is 9... so she needs 9 more cans

Answer:

What are the options?

Answer:

-17y+16x

Step-by-step explanation:

-3(3y -2x) +2(5x-4y)

Distribute

-9y +6x +10x -8y

Combine like terms

-9y -8y+ 6x+10x

-17y+16x

Answer:

-17y+16x

Step-by-step explanation:

Answer:

  0.5 < t < 2

Step-by-step explanation:

The function reaches its maximum height at ...

  t = -b/(2a) = -16/(2(-16)) = 1/2 . . . . . . where a=-16, b=16, c=32 are the coefficients of f(t)

The function can be factored to find the zeros.

  f(t) = -16(t^2 -1 -2) = -16(t -2)(t +1)

The factors are zero for ...

  x = -1 and x = +2

The ball is falling from its maximum height during the period (0.5, 2), so that is a reasonable domain if you're only interested in the period when the ball is falling.

Answer:

1.44 pi meters squared

Step-by-step explanation:

Area of circle form: pi r squared

pi is there so we need to find radius

2.4/2 is 1.2

1.2 squared is 1.44

I set up an equal proportion [tex]\frac{100}{0.25} = \frac{80}{x}[/tex]

cross multiply to get 80 * 0.25 = 100x

20 = 100x; divide both sides by 100

0.2 = x so the answer is choice B

Answer:

B. 0.2 meters.

Step-by-step explanation:

Let x represent meters of spring stretched by 80 newtons.

We have been given that a force of 100 newtons will stretch a spring 0.25 meters.

We will use Hooke's law, which states that the force needed to compress or extend a spring is directly proportional to the distance we stretch it.[tex]N=kx[/tex], where,

N = Force in Newtons,

k = The spring constant,

x = Amount of extension in meters.

Let us find spring constant by substituting [tex]N=100[/tex] and [tex]x=0.25[/tex].

[tex]100=k*0.25[/tex]

[tex]\frac{100}{0.25}=\frac{k*0.25}{0.25}[/tex]

[tex]400=k[/tex]

So, our equation would be [tex]N=400x[/tex].

Now, we will substitute [tex]N=80[/tex] in our equation to find x.

[tex]80=400x[/tex]

Upon dividing both sides of our equation by 400 we will get,

[tex]\frac{80}{400}=\frac{400x}{400}[/tex]

[tex]\frac{1}{5}=x[/tex]

[tex]0.2=x[/tex]

Therefore, the force of 80 newtons will stretch the spring 0.2 meters and option B is the correct choice.

Answer:

The graph in the bottom right (The circle) is not a function

Step-by-step explanation:

As the circle has multiple y values for each x value, it is not a function. In other words, that graph fails the vertical line test.

Answer:

IV graph

Step-by-step explanation:

Function: It is relation between x and y.For each x, there is  a unique value of y.

Only one output for one input.

One value of x cannot have more than one images.

Vertical line test:

When we draw a vertical line passing through any given  value of x and cut the curve more than one  points then, the curve does not represents the function.

When a vertical line cuts the curve at one point then, the curve represents the function.

In I graph, We can see that

Image of 1 is 2.

Image of 2 is 1.

Image of -2 is 1.

There is only one output for input.

Hence, it represents the function.

In II graph,

By vertical line test, when we draw a vertical line x=1 then it cuts the graph at one point only.

Hence, it represents the function.

In III graph,

Image of 1 is 1.

Image of 0 is 2.

Image of -1 is 3.

Image of -2 is 4.

There is only one output for 1 input.

Hence, it represents the function.

In IV graph,

When we draw a vertical line x=1 then , it cuts the curve at two points.

Therefore, given circle does not represents the function.

Answer:

-4y -7

Step-by-step explanation:

−4y−4+(−3)

The terms -4 and -3 are the like terms.  When we add them together we get

-4 +-3 = -7

-4y + -7

or -4y -7

Final answer:

To combine like terms in the expression −4y−4+(−3), you combine the constants −4 and −3 to get −4y - 7.

Explanation:

To combine the like terms in the expression −4y−4+(−3), let's first identify the like terms. Here, since we only have one variable term −4y, it doesn't combine with any other, but we do have constant terms that we can combine: −4 and (−3).

When combining these constants, we treat the parentheses as a multiplication by -1 due to the negative sign in front of the 3. Thus, the expression becomes:

−4y − 4 − 3

Now we simply combine the constants:

−4y - 7

So the equivalent expression after combining like terms is −4y - 7.

Answer:

L=4a which means a = 36/4 = 9

The other vertices could be: (12, 5), (3, 14), (12, 14)

Step-by-step explanation: