Initially, Ernie does not like a book that he is reading, so he reads very few pages. Then, the story becomes interesting, and he reads more pages. The more Ernie reads, the more he enjoys, so he reads faster and faster until he finishes the book. Choose the graph that best corresponds to the situation.

The two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.

Hence, option C is the correct answer.

Given the equation; 9x² + 4 = 0

First, we subtract 4 from both sides.

9x² + 4 = 0

9x² = -4

x² = -4/9

Take the square roots of both sides

x = ±√(-4/9)

Rewrite -4/9 as (2i/3)²

x = ±√(2i/3)²

x = ±(2i/3)

Hence,

x = 2i/3, -2i/3

Therefore the two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.

Hence, option C is the correct answer.

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Answer:

but it says ill get 10 only

Step-by-step explanation:

The value of the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex] after substituting y = 7 is 108

The given expression is:

[tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex]

Simplifying the expression, we have:

[tex]2+4+y^2+4+y^2\\\\2y^2+10[/tex]

Substitute y = 7 into the simplified expression

[tex]2(7)^2+10\\\\=2(49)+10\\\\=98+10\\\\=108[/tex]

Therefore, after substituting y = 7, into the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex], the resulting value is 108

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Answer: -1

Step-by-step explanation: khan academy

The list price of the house is $260,869.57

What is a list price?

This is the price the property is valued to sell at in an arm's length transaction in a transaction that occurs between independent parties.

In this case, the property was sold for 92% of its list price, which means the sales price is 92% multiplied by the list price.

sales price=92%* list price

sales price=$240,000

list price=unknown(assume it is X)

$240,000=92%*X

X=$240,000/92%

X=$260,869.57

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Answer:

B. ABCD is a trapezoid because it has at least

one pair of parallel sides.  

Step-by-step explanation:

the two points A(-3,-1) and D(5,-1) have the same y-coordinates

Then

The line AD is parallel to the x-axis

On the other hand,

the two points B(1,5) and C(5,5) have the same y-coordinates

Then

The line BC is parallel to the x-axis.

We obtain :

• AD is parallel to the x-axis

• BC is parallel to the x-axis.

Therefore

AD // BC

Conclusion:

ABCD is a trapezoid because it has at least

one pair of parallel sides. 

Answer:

b

Step-by-step explanation:

plato

Answer:  [tex]\frac{\sqrt{7}}{7}[/tex]

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

Explanation:

The reciprocal of x is 1/x where x is nonzero. Multiplying x with 1/x leads to 1. For example, the numbers 9 and 1/9 are multiplicative inverses of each other.

We'll stick 1 over the given square root expression. Then follow these steps to rationalize the denominator.

[tex]\frac{1}{\sqrt{7}}\\\\\\\frac{1*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\\\frac{\sqrt{7}}{(\sqrt{7})^2}\\\\\\\frac{\sqrt{7}}{7}\\\\[/tex]

In short, [tex]\frac{1}{\sqrt{7}}=\frac{\sqrt{7}}{7}[/tex]

The volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.

To find the volume of the solid generated, we use the shell method since the cross-sections are parallel to the axis of rotation.

So, [tex]V = 2\pi\int\limits^a_b {xy} \, dx[/tex]

Now given that  the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis.

So, we integrate from x = 0 to x = 2.

[tex]V = 2\pi\int\limits^a_b {xy} \, dx\\= 2\pi\int\limits^2_0 {x(x^{2} + x)} \, dx\\= 2\pi\int\limits^2_0 {(x^{3} + x^{2} )} \, dx\\= 2\pi\int\limits^2_0 {x^{3} + 2\pi\int\limits^2_0 x^{2} } \, dx\\= 2\pi[\frac{x^{4} }{4}]_{0}^{2} + 2\pi[\frac{x^{3} }{3}]_{0}^{2} \\= 2\pi[\frac{2^{4} - 0^{4} }{4}}]+ 2\pi[\frac{2^{3} - 0^{3} }{3}]\\= 2\pi[\frac{16 - 0}{4}}]+ 2\pi[\frac{8 - 0}{3}]\\= 2\pi[\frac{16}{4}}]+ 2\pi[\frac{8}{3}]\\= 2\pi (4)+ [\frac{16\pi}{3}]\\= 8\pi + [\frac{16\pi}{3}]\\[/tex]

[tex]= \frac{24\pi + 16\pi}{3} \\= \frac{40\pi}{3}[/tex]

So, the volume of the solid generated by rotating the region bounded by the curves y = 0, y = x² + x, x = 2 and x = 0 about the y-axis is 40π/3 cubic units.

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The inequality graphed is the one in the first option.

On the graph we can see a solid parabola, the parabola opens downwards, and we can see that the vertex of the parabola is on the point (-1, 5).

And the shaded region is above the parabola.

Then the inequality is of the form:

y  ≥  parabola.

By knowing where is the vertex, we know that:

parabola = -a*(x + 1)^2 + 5

Then the correct option is the first one.

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[tex]f(x) = \sqrt{1 - 4{ x}^{2} } [/tex]

[tex]1 - 4x {}^{2} \geqslant 0[/tex]

[tex] - \infty \: \: \: \: \: \: \: \: - 0.5 \: \: \: \: \: \: \: \: \: 0.5 \: \: \: \: \: \: \: \: \infty \\ - \: \: \: \: \: \: \: \: \: \: \: \: \: \:0 \: \: \: \: \: + \: \: \: \:0 \: \: \: \: \: - [/tex]

[tex]domain \\ [ \: -0.5 \: , \: 0.5 \: ][/tex]

[tex]g(x) = 1 - 4x {}^{2} \\ g'(x) = - 8x \\ g'(x) = 0 \\ x = 0 \\ g(0) = 1 - 4(0) = 1 \\ maximum \: = 1[/tex]

[tex]range \\ [ \: 0 \: , \: 1 \: ][/tex]

Answer:

[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]

[tex]\textsf{Range}: \quad [0, 1][/tex]

Step-by-step explanation:

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

Given function:

[tex]f(x)=\sqrt{1-4x^2}[/tex]

As negative numbers don't have real square roots:

[tex]\implies 1-4x^2\geq 0[/tex]

Therefore, to find the domain, solve the inequality.

Subtract 1 from both sides:

[tex]\implies -4x^2\geq -1[/tex]

Divide both sides by -1 (reverse the inequality):

[tex]\implies 4x^2 \leq 1[/tex]

Divide both sides by 4:

[tex]\implies x^2\leq \dfrac{1}{4}[/tex]

[tex]\textsf{For }\:a^n \leq b,\:\:\textsf{if }n\textsf{ is even then }-\sqrt[n]{b} \leq a \leq \sqrt[n]{b}:[/tex]

[tex]\implies -\sqrt[2]{\dfrac{1}{4}} \leq x \leq \sqrt[2]{\dfrac{1}{4}}[/tex]

[tex]\implies -\sqrt{\dfrac{1}{4}} \leq x \leq \sqrt{\dfrac{1}{4}}[/tex]

[tex]\implies -\dfrac{1}{2} \leq x \leq \dfrac{1}{2}[/tex]

Therefore:

[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]

To find the range, input the endpoints of the domain into the function:

[tex]\implies f\left(-\dfrac{1}{2}\right)=\sqrt{1-4\left(-\dfrac{1}{2}\right)^2}=0[/tex]

[tex]\implies f\left(\dfrac{1}{2}\right)=\sqrt{1-4\left(\dfrac{1}{2}\right)^2}=0[/tex]

To find the limit of the range, find the extreme point(s) of the function by differentiating the function and setting it to zero.

[tex]\implies f(x)=(1-4x^2)^{\frac{1}{2}}[/tex]

[tex]\implies f'(x)=\dfrac{1}{2}(1-4x^2)^{-\frac{1}{2}} \cdot -8x[/tex]

[tex]\implies f'(x)=-\dfrac{4x}{\sqrt{1-4x^2}}[/tex]

Setting it to zero and solving for x:

[tex]\implies -\dfrac{4x}{\sqrt{1-4x^2}}=0[/tex]

[tex]\implies -4x=0[/tex]

[tex]\implies x=0[/tex]

Substitute x = 0 into the function:

[tex]\implies f(0)=\sqrt{1-4(0)^2}=1[/tex]

Therefore, the range is [0, 1]

Answer: -5

Step-by-step explanation:

[tex]h(4)=\frac{1}{2}(4)-5=-3\\\\f(4)=3h(4)+4=3(-3)+4=-5[/tex]

The general-form equation of the circle is:

A. [tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

This circle has center at (4,4), hence:

[tex]x_0 = 4, y_0 = 4[/tex]

The radius is of 3 units(distance of A and B from the center), hence the equation is:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - 4)^2 + (y - 4)^2 = 3^2[/tex]

We expand the equation to find the general form, hence:

[tex]x^2 - 8x + 16 + y^2 - 8y + 16 = 9[/tex]

[tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]

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Using the interpretation of the confidence interval, it is found that:

It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.

Considering the mean and the standard error, the bounds of the interval are:

Hence:

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See below for the missing terms of the sequences

The given parameters are:

T4 = 30

T5 = 49

Calculate the third term as follows:

T3 = T5 - T4

T3 = 49 - 30

T3 = 19

Calculate the second term as follows:

T2 = T4 - T3

T2 = 30 - 19

T2 = 11

Calculate the first term as follows:

T1 = T3 - T2

T1 = 19 - 11

T1 = 8

Hence, the first term of the sequence is 8

The given parameters are:

T2 = x

T3 = y

Calculate the first term as follows:

T1 = T3 - T2

T1 = y - x

Calculate the fourth term as follows:

T4 = T2 + T3

T4 = x + y

Calculate the fifth term as follows:

T5 = T3 + T4

T5 = y + x + y

T5 = x + 2y

Hence, the missing terms of the sequence are y - x, x + y and x + 2y

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Based on the width of the aluminum sheets and the angle of the edges, the depth that allows maximum cross-sectional area is 4 inches.

Assuming that the depth is x, the area would be:

= x (16 - 2x)

= 16x - 2x²

The maximum of the parabola is:

x = -b / 2a

= - 16 / (2 x -2)

= -16 / -4

= 4 inches

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The graph of function f is shifted right 3 units and up 4 units.

Let f(x) be the parent function

Now use the Rule : f(x)→f(x-b) to find the shifting of graph

The graph shifts right by b units

So, shift the graph by 3 unit

So, f(x)→f(x-3)

So, the graph shifted right by 3 units

2nd rule used is Rule : f(x)→f(x)+b to find the another shifting of graph

The graph shifts up by b units

Now shift the obtained graph up by 4 units

So,  f(x-3)→f(x-3)+4

So, the graph shifts up by 4 units

Thus, The graph of function f is shifted right 3 units and up 4 units.

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Answer:

f(x)⁻¹ = (x - 11)²

Step-by-step explanation:

To find the inverse of the function, you need to (1) swap the places of the "x" and "y" variables and then (2) solve for "y". Remember, f(x) is another way of writing "y".

y = √x + 11                                        <----- Original equation

x = √y + 11                                        <----- Swap variables

x - 11 = √y                                         <----- Subtract 11 from both sides

(x - 11)² = (√y)²                                  <----- Square both sides

(x - 11)² = y                                        <----- Simplify

Another way of writing the output of an inverse function is with f(x)⁻¹.

The reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.

For any function f(x), the reflection across the line y = x, gives the inverse of the function f(x).

In the question, we are asked for the equation, representing the reflection of f(x) = x⁴, across the line y = x.

The function can be shown as:

y = f(x) = x⁴,

or, x⁴ = y,

or, [tex]x = \pm\sqrt[4]{y}[/tex]

Changing the variables to general form, that is, y as the dependent variable and x as the independent variable, we get the inverse function as, [tex]y = F(x) = \pm \sqrt[4]x[/tex].

Thus, the reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.

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The complete question is:

"Which of the following equations represents F(x) = x⁴ reflected across the line y = x?

A. [tex]F(x)= \pm\sqrt[4]{x}[/tex]

B. [tex]F(x)= \sqrt[4]{x}[/tex]

C. [tex]F(x)= \pm x^4[/tex]

D. [tex]F(x)=- \sqrt[4]{x}[/tex] "

The equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]

The expression is given as:

7x^2 sqrt 2x^4 times 6 sqrt 2x^12

Rewrite properly as:

[tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex]

Evaluate the product

[tex]7 * 6x^2 \sqrt{2x^4*2x^{12 }[/tex]

This gives

[tex]42x^2 \sqrt{4x^{16}[/tex]

Take the square root of 4

[tex]2*42x^2 \sqrt{x^{16}[/tex]

Take the square root of x^16

[tex]2*42x^2 *x^8[/tex]

So, we have:

[tex]84x^{10[/tex]

Hence, the equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]

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Answer:

Step-by-step explanation:

The equivalent expression of  is

How to determine the equivalent expression?

The expression is given as:

7x^2 sqrt 2x^4 times 6 sqrt 2x^12

Rewrite properly as:

Evaluate the product

This gives

Take the square root of 4

Take the square root of x^16

So, we have:

Hence, the equivalent expression of is

All the angles required to complete each sentence are:

In this question we must take advantage of definitions and theorems of Euclidean geometry to complete the three sentences seen in the figure. Now we proceed to present each sentence completed in detail:

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The following expressions set up as an equation to solve for the unknown numbers in the cases given below:

let

5x + 6 = 46

5x = 46 - 6

5x = 40

x = 40/5

x = 8

2/3x - 5 = 11

2/3x = 11 + 5

2/3x = 16

x = 16 ÷ 2/3

x = 16 × 3/2

x = 48/2

x = 24

1/3x + 4 = 45

1/3x = 45 - 4

1/3x = 41

x = 41 ÷ 1/3

x = 41 × 3/1

x = 123

3x - 12 = 18

3x = 18 + 12

3x = 30

x = 30/3

x = 10

40 - 2x = 16

-2x = 16 - 40

-2x = -24

x = -24/-2

x = 12

(x + 18) / 6 = 7

(x + 18) = 7 × 6

x + 18 = 42

x = 42 - 18

x = 24

2/3x - 8 = 6

2/3x = 6 + 8

2/3x = 14

x = 14 ÷ 2/3

x = 14 × 3/2

= 42/2

x = 21

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The attached image shows the image of A"B"C" after the transformation

The transformation rule states:

A"B"C" = Ro90° (T(-4,3)(ABC))

This implies that one need to rotate the triangle in a 90⁰ clockwise direction, and then one need to translate the triangle.

Using the image shown, the coordinates of ABC are;

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The 90⁰ rule clockwise rotation  will be:

(x,y) -- (y,-x)

So, when translated, it will be:

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

Then the translation of the triangle using T(-4,3):

(x, y) -  (x - 4, y + 3)

So, there is:

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

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The height of the ramp above the ground is 1.55 meters.

The difference between the height of the tree is 33.20 meters

The situation forms a right angle triangle.

Therefore, the height the ramp above the ground can be calculated as follows:

Using Pythagoras theorem,

sin 15  = opposite / hypotenuse

sin 15 = x / 6

cross multiply

x = 6 sin 15

x = 6 × 0.2588190451

x = 1.55291427062

x = 1.55

Therefore, the height of the ramp above the ground is 1.55 meters

tan 36  = opposite / adjacent

tan 36 = x / 60

x = 60 tan 36

x = 43.5925516803

x = 43.60 meters

tan 52 = y / 60

60 tan 52 = y

y = 76.7964979316

y = 76.79 meters

The difference between the height of the tree = 76.79 - 43.60 = 33.20 meters

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Given z = -1 - i, the expression for [tex]z^3[/tex] is 2 - 2i

The given complex number is z = -1 - i

[tex]z^3[/tex] means to raise z to the power of 3

[tex]z^3=(-1-i)^3[/tex]

Expand and simplify the expression:

[tex]z^3=(-1)^3+3(-1)^2(-i)+3(-1)(-i)^2+(-i)^3\\\\z^3=-1-3i-3i^2-i^3[/tex]

Note that:

[tex]i^2=-1\\\\i^3=-i[/tex]

Substitute these into the resulting expression

[tex]z^3=-1-3i-3(-1)-(-i)\\\\z^3=-1+3-3i+i\\\\z^3=2-2i[/tex]

Therefore, given z = -1 - i, the expression for [tex]z^3[/tex] is 2 - 2i

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Answer:

Six Serving Men is a team exercise that examines an issue from twelve different viewpoints. It is based on the words of the poem by Rudyard Kipling: I keep six honest serving men, they taught me all I knew. Their names are What and Why and When and How and Where and Who. To use this technique in a meeting, provide 12 areas for answering questions related to the central topic

Step-by-step explanation:

The proof that the diagram is a square is that; D: slopes are perpendicular where the sides meet

We know that a square is a quadrilateral that has 4 sides. Now, the 4 sides of a square are all equal and at right angles.

Since all sides of the square are equal, then it means that 2 consecutive sides must be perpendicular to each other. Thus, this means that the slope of 2 consecutive sides must be perpendicular to each other.

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The fraction computed shows that the total inches the infant grew over the three months is 3 3/4 inches.

First month = 2/4 inches

Second month = 1 inch

Third month = 7/4 inches.

The total inches the infant grew over the three months will be;

= 2/4 + 1 + 7/4

= 3 1/4 inches.

The difference in the infants from the second month to the third month will be:

= 7/4 - 1

= 3/4 inches.

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The solutions to the given quadratic equations are x = -25/16 and x = 1

From the question, we are to determine the solutions to the given quadratic equation

The given quadratic equation is

16x² + 9 = 25

The equation can be solved as follows

16x² + 9 = 25

16x² + 9 - 25 = 0

16x² -16x +25x -25 = 0

16x(x -1) +25(x -1) = 0

(16x +25)(x -1) = 0

16x + 25 = 0 OR x - 1 = 0

16x = -25 OR x = 1

x = -25/16 OR x = 1

Hence, the solutions to the given quadratic equations are x = -25/16 and x = 1

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Answer:

2-2 goes with 1 - 1

10 - 7 goes with 8 - 5

4 - 3 goes with 7 - 6

8 - 2 goes with 9 - 3

9 - 5 goes with 5 - 1

Have a nice day.

I am Clara btw.

Step-by-step explanation:

The probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.9

Standard deviation = 0.2

Calculate the z-score at x = 0.92 using

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

z = (0.92 - 0.9)/0.02

Evaluate the numerator; subtract 0.9 from 0.92

z = 0.02/0.02

Divide 0.02 by 0.02. This gives

z = 1

The probability is then represented as:

P(x > 0.92) = P(z > 1)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.92) = 0.841

Hence, the probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

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Answer: 36

Step-by-step explanation:

As this is a two-digit number, it will have a digit in its 10's place and a digit in its 1's place. We can represent the 10's digit using x and the 1's digit using y.

Since the ones is twice the number of tens, this means that y is equal to 2*x. Let's put this into an equation.

[tex]y=2x[/tex]

If the 10's digit is x and the 1's digit is y, the original number would be [tex]10x + y[/tex], as x must be multiplied by 10 to get it to the 10's place. Similarly, the reversed number would be [tex]10y + x[/tex], as y must be multiplied by 10 to get it to the 10's place.

Twice the original number (10x+y) is equal to 9 more than (i.e. 9 plus) the reversed number. We can put this into an equation to help us answer the question.

[tex]2(10x+y)=9+10y+x\\20x+2y=9+10y+x\\19x+2y=9+10y\\19x=9+8y[/tex]

Now we have a system of two equations.

[tex]y=2x\\19x=9+8y[/tex]

We can solve this system by substituting y for 2x in the second equation. Then, we can isolate and get the value of x.

[tex]19x=9+8(2x)\\19x=9+16x\\3x=9\\x=3[/tex]

Now that we have the value of x, let's put it back into the first equation and solve for y.

[tex]y=2(3)\\y=6[/tex]

Remember that x is the 10's digit and y is the one's digit of our answer. Since x is 3 and y is 6, our answer is 36.

We can quickly check if our answer is right by making sure both conditions in the question are met.

6 (the one's digit) is twice the value of 3 (the ten's digit), making the first condition true. Twice of 36 is 72, which is 9 more than the reversed number, which is 63.