Graph −4 < x < 2 on the number line. Write −4 < x < 2 in interval notation.

We can find the percentage of increase in the number of Magikarps that Jose captured in the lake by taking the initial number of them and subtracting it from the number that he had by the end of the day, like this:

16 - 8 = 8

Now, we just have to divide 8 by 16 and then multiply by 100, like this:

Then, his number of Magikarps increased a 50%

We must graph the line with the equation:

Plotting this line, we get the following graph:

From the graph, we see that:

• the x-intercept is (-2, 0),

• the y-intercept is (0, -1).

• The x-intercept is ,(-2,0) ✓

• The y-intercept is not (0, -4) ,✖,, the correct y-intercept is ,(0, -1), ,✓,.

When we have an inverse function, the domain and range are switched.

All x-coordinates become y-coordinates and vice-versa.

So, if the point (-7, -5) is a solution of h(x), the point (-5, -7) is a solution of h^-1(x)

If the point (-1, -2) is a solution of h(x), the point (-2, -1) is a solution of h^-1(x).

Therefore, the endpoints of the segment that represents the inverse function are the points (-5, -7) and (-2, -1).

The graph that matches the given linear inequality is (B) .

In the question ,

it is given that

the linear inequality is y [tex]>[/tex] -x + 4

on rewriting the inequality

we get

x + y [tex]>[/tex] 4

to plot the inequality , we need points to plot .

So ,when x = 0 , we have y = 4

and when y = 0 , we have x = 4

so the two points are (0,4) and (4,0) .

For shading the inequality , we put x = 0 and y = 0 ,

and get 0+0 > 4

0>4 , the result is False , So , the shaded region will be away from the origin which is shown in option (b) .

Therefore , The graph that matches the given linear inequality is (B) .

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Answer:

x=75

Step-by-step explanation:

Answer:

x = 75

Step-by-step explanation:

x/5 = 15

Multiply 5 on both sides

x = 75

The meaning of 13*pi/6 is as if you made 13 complete revolutions around the point pi/6.

therefore, is the same calculate the sin of 13pi/6 than the sin of pi/6.

Substituing:

The answer is: csc(13pi/6)=2.

Notice that the expression for h(x) uses an absolute value. The absolute value is the basic function related to h(x).

Recall the following function transformations:

Horizontal shift by c units:

Vertical shift by c units:

Reflection across the X axis:

Starting with the absolute value function, notice that the function h can be obtained by applying a reflection across the X-axis, a horizontal shift by 1 unit and a vertical shift by 4 units:

The rocket arrives at its most extreme level at 1.5 seconds after send-off will be 39 feet.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

A toy rocket is shot upward up high from a take-off platform 3 feet over the ground with an underlying speed of 48 feet each second. The level h, in feet, of the rocket over the ground at t seconds after send-off is given by the capability h(t) = - 16t² + 48t + 3.

Differentiate the function and put it equal to zero.

h'(t) = 0

-32t + 48 = 0

32t = 48

t = 1.5 seconds

Then the maximum height is given as,

h(1.5) = - 16(1.5)² + 48(1.5) + 3

h(1.5) = 39 feet

The rocket reaches its maximum height at 1.5 seconds after launch will be 39 feet.

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Answer:

  $15.27

Step-by-step explanation:

You want to know how much more profit Kevin made on Saturday than on Friday, if his revenue and expenses for the two days were ...

The profit each day is the difference between revenue and expenses:

  Saturday profit = $807.31 -289.00 = $518.31

  Friday profit = $735.90 -232.86 = $503.04

The profit on Saturday exceeded the profit on Friday by ...

  $518.31 -503.04 = $15.27

Kevin made $15.27 more on Saturday than Friday.

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Although it is true that only the x-axis is affected, that is, on the horizontal, when multiplying by a number less than 1, there would not be a stretch but a narrowing.

That is, the horizontal part would be smaller, which contradicts what Richard says.

It is a pictorial representation that shows a logical relations between sets.

The centre portion of the set is the intersection between the two sets. This will represent your experience from the start until this day. ​

The other portion of school starts will represent expectation while for school emds will represents your experience as shown

Answer:

SAS (Both sides share common angle n, and the sides, 40 : 65 and 32 : 52 have the same ratio)

▲LMN ~ ▲GHN

The area of a rectangle is the product of its length and breadth. The maximum area enclosed by the fence is 36800 square meter  and the dimensions of the enclosed area are 115 meter and 320 meter. The width is given as 115 meter.

A rectangle is a kind of parallelogram that has equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

The dimensions of the given rectangle is (650 - 2x) and x.

Then, the area of the given rectangle is A(x)  = x(650 - 2x)

In order to find the maximum area enclosed take the derivative of A(x) and equate it to zero as follows,

(660 - 2x) - 2x = 0

=> 4x = 660

=> x = 660 / 4

=> x = 115

Now, the maximum area is the value of A(x) at x = 115 as below,

= 115 × (650 - 2×115)

= 115 × 320

= 36800

The dimensions for the maximum area are 115 and (650 - 2 × 115) = 320.

Hence, the largest area enclosed is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter. The width is given as 115 meter.

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SOLUTION

Dependent events influence the probability of other events or their probability of occurring is affected by other events. Independent events do not affect one another and do not increase or decrease the probability of another event happening.

PART A

Since the flip of a coin would not affect the spin of the spinner, therefore these events are independent events.

The answer is 'I'

PART B

To find the probability that the coin lands tails-up and the spinner lands on 1, we would need to find the probability of getting a tail, then we find the probability of getting a 1

Therefore,

When we flip a coin, the favourable outcome for a tail is 1 since a tail can only occur once in one flip. The total possible outcomes are 2, since we can have either a tail or head occurring in one flip.

Then,

When we spin the spinner, the favourable outcome for one is 1, since we have only one slot for one on the spinner. The total possible outcome is 4 since we have 4 different number

slots on the spinner.

Then,

To get the probability of getting a tail, then we find the probability of getting a 1 we multiply the probability of getting a one on the spinner and a tail on the flip.

We will have the following:

So, the value of k will be 14.

According to the statement given in Part a, there is one table for 10 people and many tables for 4 and in total there are tables for 200 people. Taking x as the number of tables for 4 people, the inequality that represents this situation is:

It means that there must be less than or 47.5 tables in the cafeteria.

According to the statement given in Part b, there are 4 barrels that are the same size, and one that is 10 liters, in total they can hold 200 liters. Taking x as the volume hold by the 4 barrels , the inequality that represents this situation is:

It means that each barrel must hold less than or 47.5 liters of water.

These problems are similar because of the inequality used to find the solution is the same, they are different because of the variable that is found is completely different, the first one is the number of tables and the second one is the volume that can be hold by the barrels.

Rational number will be 1/4, 2/3, √4 and Irrational number will be √8, √90, π/2, π as "Any whole number, fraction, or decimal that ends or repeats is a rational number. Any number that cannot be divided into a fraction and thus does not meet the definition of a rational number is considered to be irrational."

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so forth. P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers (terminating decimals and recurring decimals).

Any real number that cannot be expressed as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number. For instance, the square root of 2 cannot be expressed as an integer or a fraction. A real number that cannot be expressed as a straightforward fraction is referred to as an irrational number. It cannot be described using a ratio. When p and q are integers and q is not equal to 0, N is not equal to p/q if N is irrational. Example: The numbers 2, 3, 5, 11, 21, and (Pi) are all illogical.

Here,

Rational number=1/4, 2/3, √4

Irrational number=√8, √90, π/2, π

As "Any whole number, fraction, or decimal that ends or repeats is a rational number. Any number that cannot be divided into a fraction and thus does not meet the definition of a rational number is considered to be irrational." so Rational number will be 1/4, 2/3, √4 and Irrational number will be √8, √90, π/2, π.

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Answer:

I think the answer would be 88

Given that:

Diameter of the circle, EG = 22

To find EQ, take the half of the diameter.

The third option is correct.

Answer:

Step-by-step explanation:

14x + 11

The value of 16 ft is the diameter of the semicircle.

That means the radius is 8 ft, and this is also the measure of the smaller side of the rectangle.

First, let's calculate the area of the rectangle:

Now, let's calculate the area of the semicircle:

So the area of the shaded region is:

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given ratios

STEP 2: Add the ratios

STEP 3: Calculate the earnings of each of them

Erin's

Kim's

Megans's

Hence, the earnings are given as:

Erin's: $1099.34

Kim's: $12825.62

Megan's: $855.04

The functional value of f(-3a + 7) is  24a - 56

What is a function?

A rule that assigns a specific element of B to each element of A is known as a function from A to B. Both A and B are referred to as the function's domain and codomain, respectively. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

There are different operations on functions like addition, subtraction, multiplication, division, and composition of functions.

Here we have,

the given function is

f(b) = -8b

f(-3a + 7) =  -8(-3a + 7)

               = 24a - 56

Hence,  the functional value of f(-3a + 7) is  24a - 56        

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Given:

The graph shows the prices of the current year for the number of bushels.

And the table shows the prices of the previous year.

Part A: We will find the rate of change of bushels of corn in the current year.

As the graph shows a line, so, the rate of change will be the slope of the line

We will find the slope using two points.

As shown the line passes through the points (0,0) and (3,24)

So, the slope will be as follows:

So, the rate of change = $8 per Bushel.

Part B: How many dollars more in the price of a bushel of corn in the current year than the previous year.

From the table: the price of the previous year = 21/3 = $7

And form the graph, the price of the current year = $8

So, the differnce = 8 - 7 = $1

So, the answer will be:

$1 more is the price of the current year than the price of the previous year.

The graph of the polynomial function shows the factored form of the

related polynomial, the factored form is (x+2)(x-2).

The factored from of a polynomial can be found from the zeros or x-intercepts of the graph.

The x-intercepts here are x= -2 and x= 2.

Then the factors are x+2 and x-2.

So the factored form is (x+2)(x-2).

Therefore, The graph of the polynomial function shows the factored form of the related polynomial, the factored form is (x+2)(x-2).

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In (x+3)(x+2)=0, we use zero product property

And in [tex]x^{2}[/tex]+6=31, we use square root property

What is square root property and zero product property?

It is a property that can be used to solve the quadratic equations. It is used to solve an equation that can be put into one of the following two forms.

zero product property states the product of two non-zero elements is non-zero. The principle of zero-product property states that if there is any product of two numbers, that is equivalent to zero.

(x + 3) (x + 2) = 0

The most appropriate technique used to solve this equation is,

1.) zero product property

The solutions are:

(x + 3) = 0

x = -3

(x + 2) = 0

x = -2

x² + 6 = 31

The most appropriate technique used to solve this equation is,

2.) square root property

x² = 31-6

x² = 25

x = +/- root (25)

x = +/- 5

The solutions are:

x = 5, x=-5

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Answer:

−13w − 6.8

Step-by-step explanation:

Let's simplify step-by-step.

−6w − 8.3 + 1.5 − 7w

−6w + −8.3 + 1.5 + −7w

Combine Like Terms:

−6w + −8.3 + 1.5 + −7w

(−6w + −7w) + (−8.3 + 1.5)

−13w + −6.8

The answer is -13w+9.8

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.

Given here: -6w + (-8.3) + 1.5 + (-7w) = -13w+9.8

Hence, The answer is -13w+9.8

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Recall that:

Then, if:

Now, notice that:

Therefore:

Answer: True.

9(5 - y)

EXPLANATION

Difference means subtraction.

This implies that the difference of 5 and y can be expressed as 5 - y.

Hence, nine times the difference of 5 and y can be represented as:

9(5 - y)

Using the perimeter concept, the measures are given as follows:

a) Perimeter when the missing box is of -7: -6x² + 8x + 4.

b) Coefficient missing when the perimeter is of 5x² + 8x + 4: a = 4.

c) Perimeter from part B when x = 3: 73 inches.

The perimeter of a figure is obtained by the sum of their outer side lengths.

For this shape, these lengths are given as follows:

With a missing coefficient of a = -7, we have that:

ax² + x = -7x² + x.

Hence the perimeter is:

3x + x² + 5 - 7x² + x + 4x - 1 = -6x² + 8x + 4.

In symbolic terms, the perimeter is:

(1 + a)x² + 8x + 4.

When the perimeter is of 5x²+8x + 4, the coefficient is:

1 + a = 5

a = 5 - 1

a = 4.

When x = 3 and a = 4, the perimeter is given as follows:

P = 5(3)² + 8(3) + 4 = 73 inches.

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