What is the solution to the system of polynomials graphed below?

Answer:

A.

Step-by-step explanation:

If the results are similar (A) should be your answer!

Option A is correct.

Generalization is a process which leads to something more general and whose product consequently refers refers to an actual or potential manifold  in a certain way.

According to the given question

"At the end of the first day, the store found that twice as many shoppers select an apple"

So, the generalization can be made from the above result is " from the given choice of a banana or an apple, twice as many shoppers will select an apple".

Hence, option A is correct.

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Answer:

See below for Part A.

Part B)

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

Step-by-step explanation:

Part A)

The parabola given by the equation:

[tex]y^2=4ax[/tex]

From 0 to h is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

[tex]y=f(x)=\sqrt{4ax}[/tex]

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]

Where r(x) is the distance between f and the axis of revolution.

From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:

[tex]r(x)=y(x)=\sqrt{4ax}[/tex]

Now, we will need to find f’(x). We know that:

[tex]f(x)=\sqrt{4ax}[/tex]

Then by the chain rule, f’(x) is:

[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]

For our limits of integration, we are going from 0 to h.

Hence, our integral becomes:

[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]

Combine roots;

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]

Integrate. We can consider using u-substitution. We will let:

[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]

We also need to change our limits of integration. So:

[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]

Hence, our new integral is:

[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]

Simplify and integrate:

[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

FTC:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]

Simplify each term. For the first term, we have:

[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]

We can factor out the 4a:

[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

For the second term, we have:

[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =(2a)^3[/tex]

Hence:

[tex]\displaystyle =8a^3[/tex]

Thus, our equation becomes:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]

We can factor out an 8a^(3/2). Hence:

[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Hence, we have verified the surface area generated by the function.

Part B)

We have:

[tex]y^2=36x[/tex]

We can rewrite this as:

[tex]y^2=4(9)x[/tex]

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

We can write:

[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]

Solve for h. Simplify:

[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]

Divide both sides by 8π:

[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]

Isolate term:

[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]

Raise both sides to 2/3:

[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]

Hence, the value of h is:

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

You seem to have left out that 0 ≤ x ≤ h.

From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is

[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]

We have

y(x) = 2√(ax)   →   y'(x) = 2 • a/(2√(ax)) = √(a/x)

so the integral is

[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]

[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]

[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]

[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]

Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :

[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]

[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]

[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]

[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]

[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]

Answer:

Mean=5

Median=6

Mode=2

Step-by-step explanation:

Answer:

Step-by-step explanation:

mode: 2

median: 6

mean: 8 + 2 + 7 + 2 + 6 = 17 + 8 = 25/5 = 5

Answer:

The correct answer is option 2: 32 cm

Step-by-step explanation:

Let l be the length of the picture frame and w be the width

Then according to given statements, the system of equations will be

[tex]2l+2w = 100\ \ \ Eqn\ 1\\w = 2l-4\ \ \ Eqn\ 2[/tex]

Putting w = 2l-4 in equation 1

[tex]2l+2(2l-4) = 100\\2l+4l-8=100\\6l-8 = 100\\6l = 100+8\\6l=108\\\frac{6l}{6}=\frac{108}{6}\\l = 18[/tex]

Putting the value of l in equation 2

[tex]w = 2(18)-4\\w = 36-4\\w = 32[/tex]

The width is 32 cm

Hence,

The correct answer is option 2: 32 cm

Answer:

δy

δx = 2x − 4 + δx;

and the limit as δx → 0 is

dy

dx = lim

δx→0

µδy

δx¶

= 2x − 4.

Step-by-step explanation:

dy/2d=(2-1)(2+3)

dy/2d=4+6-2-3

dy/2d=5

dy=5(2d)=10d

2d=5/dy

dy=5×(5/dy)= 25/dy

2d=5/dy

dy^2=25

dy=√25=5

2d=5/dy=5/5=1

d=1/2

dy=1/2×10=5 y=10

plug all of the values

5/(1/2×2)=5

=

4+6-2-3=5

so finally: 5=5

any questions?

Given:

The equation of parallel line is [tex]y=-\dfrac{1}{4}x+5[/tex].

Required line passes through (2,-3).

To find:

The equation of line.

Solution:

We have,

[tex]y=-\dfrac{1}{4}x+5[/tex]

On comparing this equation with [tex]y=mx+b[/tex], where m is slope, we get

[tex]m=-\dfrac{1}{4}[/tex]

Slope of two parallel lines are always same. So, slope of required line is [tex]m=-\dfrac{1}{4}[/tex].

The required line passes through the point (2,-3) having slope [tex]m=-\dfrac{1}{4}[/tex], so the equation of line is

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(-3)=-\dfrac{1}{4}(x-2)[/tex]

[tex]y+3=-\dfrac{1}{4}(x)-\dfrac{1}{4}(-2)[/tex]

[tex]y+3=-\dfrac{1}{4}(x)+\dfrac{1}{2}[/tex]

Subtracting 3 from both sides, we get

[tex]y=-\dfrac{1}{4}(x)+\dfrac{1}{2}-3[/tex]

[tex]y=-\dfrac{1}{4}(x)+\dfrac{1-6}{2}[/tex]

[tex]y=-\dfrac{1}{4}(x)-\dfrac{5}{2}[/tex]

Therefore, the equation of required line is [tex]y=-\dfrac{1}{4}(x)-\dfrac{5}{2}[/tex].

Answer:

18.5

Step-by-step explanation:

First we plug in the number

-1 1/2 is the same as -1.5

Plugging this in we will have:

15(-1.5) + 4 =

-22.5 + 4 =

-18.5

Answer:

To know what the answer is

Step-by-step explanation:

clearly I do not know, but I can say that we do need to know the mass bc in the future there will be more and more androids on the rising making human interaction bad.

Answer:

Step-by-step explanation:

Answer:

red balls = 5

blue balls = 5

total balls = 5 blue+5 red

= 10

[tex]p(first \: ball \: being \: red) = \frac{red \: balls}{total \: balls} [/tex]

[tex]p(first \: ball \: being \: red) = \frac{5}{10} = \frac{1}{2} [/tex]

Answer:

Step-by-step explanation:

Total number of red balls = 5

Total number of blue balls = 5

Total number of balls in jar = 5 + 5

                                             = 10

Probability of the first ball being red = total number of the red ball/total number of balls in the jar

                                                             = [tex]\frac{5}{10}[/tex]

                                                             = [tex]\frac{1}{2}[/tex]

Therefore, the probability of the first ball being red = [tex]\frac{1}{2}[/tex], 50% or 0.5 (in any way you are instructed to write it in)

Answer:

The last answer D

Step-by-step explanation:

Hope this helps. :) :D

The equation 3y + 1 = 3y + 1 has all real numbers as solutions becasuse 0 = 0 true for all real numbers option (D) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The first equation:

3y = 3y + 1

0 = 1 (false)

The second equation:

3y = 3

y = 1 (one real solution)

The third equation:

3y = 0

y = 0 (one real solution)

The fourth equation:

3y + 1 = 3y + 1

0 = 0 (infinitely solution)

Thus, the equation 3y + 1 = 3y + 1 has all real numbers as solutions becasuse 0 = 0 true for all real numbers option (D) is correct.

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Step-by-step explanation:

y = x2 + 12x.

x= y2 + 12x           would also be 12 y

y2 = x - 12x               would be -x

y2=-11x  

y=[tex]\sqrt{-11x}[/tex], for x > 0    negative  square root not possible

Describe the three errors?

The three errors made in finding the inverse of y = x² + 12x are,

⇒ First mistake to write 12y in place of 12x.

⇒ Second mistake to write the expression y² = x - 12x.

⇒ Third mistake because it never possible negative square root for x > 0.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = x² + 12x

Here, The process are,

⇒ y = x² + 12x.

⇒ x = y² + 12x

There is first mistake to write 12y in place of 12x.

⇒ y² = x - 12x

There is second mistake.

⇒ y² = -11x

⇒ y = √-11x, for x > 0

There is third mistake because it never possible negative square root for x > 0.

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Answer:

yes 40

Step-by-step explanation:

she got it correct

Answer:

The answer is 35%

Step-by-step explanation:

If we add together 35 and 65 we get 100.  This means altogether there are 100 kids in her school.  Out of those 100 kids, 35 like scary movies.  We can write this as the fraction 35/100.  This is equivalent to 0.35 or 35%.

Answer:

35%

Step-by-step explanation:

35+65

= 100

[tex]\frac{35}{100} * 100[/tex]

= 35%

Answer:

angle 5 will be 55 °

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Given

In JKL, we have:

[tex]\angle J = 27[/tex]

[tex]\angle K = 90[/tex]

In WXY, we have:

[tex]\angle Y = 63[/tex]

[tex]\angle X = 90[/tex]

Required

Is JKL ~ WXY?

In both triangles, we already have one similar angle (90)

Next, is to determine the third angles in both triangles.

In JKL

[tex]\angle J + \angle K + \angle L = 180[/tex]

We have that:

[tex]\angle J = 27[/tex] and [tex]\angle K = 90[/tex]

The expression becomes:

[tex]27 + 90 + \angle L = 180[/tex]

[tex]117 + \angle L = 180[/tex]

[tex]\angle L = 180-117[/tex]

[tex]\angle L = 63[/tex]

In WXY

[tex]\angle W + \angle X + \angle Y = 180[/tex]

We have that:

[tex]\angle Y = 63[/tex] and [tex]\angle X = 90[/tex]

The expression becomes:

[tex]\angle W + 63 + 90 = 180[/tex]

[tex]\angle W + 153 = 180[/tex]

[tex]\angle W = 180-153[/tex]

[tex]\angle W = 27[/tex]

The three angles in JKL are:

[tex]\angle J = 27[/tex]    [tex]\angle K = 90[/tex]   [tex]\angle L = 63[/tex]

The three angles in WXY are:

[tex]\angle W = 27[/tex]   [tex]\angle X = 90[/tex]   [tex]\angle Y = 63[/tex]

By comparing the angles, we can conclude that  both triangles are similar because of AAA postulate (Angle-Angle-Angle)

Answer:

x = -4

Step-by-step explanation:

A circle is 360 degrees.

Anyway, first add 85 + 35 + 115 and you will get 235.

Now subtract 235 from 360.

360 - 235 = 125 degrees

Now to find x, do

-32x - 3 = 125

-32x = 128

-32x/-32 = 128/-32

x = -4

Hope it helped! My answer is expert verified.

Answer:

sure easy man the carrot is blue and green and orange there naswer soled

Answer:

x=-5/2,0

Step-by-step explanation:

It is solved by first factorizing it

10x²+25x=5x(2x+5)=0

Finding the zeros

5x=0x=0/5=0

2x+5=0

x=-5/2

Therefore x is -5/2 or 0

Answer:

C.  G' (4,-7), R' (2,-3), T'(6,-4)

Step-by-step explanation:

Get a piece of paper and draw 2 intersecting lines, like how a graph looks like. Then get another paper that's transparent enough, and place a dot roughly where R would be. Rotate it 270* clockwise (3 times around 90 degrees), and R would be in the bottom right area. That means the figure would be around that area and you can base the coordinates from that.

Answer:

K = 56

Step-by-step explanation:

Subtract 9

k/2 = 28

multiply by 2

k = 56

Answer:

10 + w = -2.6

Step-by-step explanation:

Answer:

11 sqrt(2)

Step-by-step explanation:

We know that in a 45 45 90 triangle, the lengths of the sides are x, x ,x sqrt(2)

the length of x is 11

so the lengths of the sides are 11, 11, 11 sqrt(2)

The hypotenuse is 11 sqrt(2)

Step-by-step explanation:

We have,

[tex]f(x) = - 2 \sqrt[3]{x + 7} [/tex]

Taking limit,

[tex] \lim _{x \rarr \infty } f(x) \\ = \lim _{x \rarr \infty } - 2 \sqrt[3]{x + 7} [/tex]

If x approaches to positive infinity,

this implies f(x) approaches to negative infinity

Answer:

A) 6 Inches

Step-by-step explanation:

1/2=10 to find how many inches we need to get 120 miles, you have to find the conversion rate.

Conversion rate is 120 ÷ 10 which equals 12.

Now we multiply the conversion rate (12) times 1/2 to get an answer of 6 inches.

i'd appreciate a brainliest :)

Answer:

the GCF would be 22 this is because that is 88 and 66 greatest common factor (gcf)

Step-by-step explanation:

have a good day!!

Answer:

Step-by-step explanation:

85 + 50 + ? = 180

? = 180 - 85 - 50

? = 45

Answer:

pfft no lol

Step-by-step explanation:

yeah no

have a good day!  :)

plz give me brainliest

Answer:

yes

Step-by-step explanation:

i think,because it goes past the center it all

Answer:

6 LB 12 OZ

Step-by-step explanation:

16 OZ in a LB

9 LB - 2 LB = 7 LB

4 OZ - 12 OZ difference of 8 OZ

4 - 4 = 0 then 16 OZ in a LB

4 remaining - 16 = 12 dropping the 7 LB to 6 LB

Answer:

6lb 8oz

Step-by-step explanation:

9lb 4oz

+16

8lb 20 oz

-2 lb 12oz =