Use the given values to write an equation that relates x and y.

45 represents the slope while -900 is the y-intercept of the function

Here, we want to write the slope and y-intercept of the function that represents Patrick's elevation during his climbing

From the question, we are told that he averaged an elevation of 45 meters per hour

What the slope basically does is to measure a rate of change. As we can see from here, the change represents a rate and thus, we have this as our slope

To get the y-intercept of the function, we can see this as a distance of -900 meters

The reason for this is that we can see the summit of the mountain as 0 m

So we can represent the equation as;

The absolute value inequality is given by | x-130745 | > 10000

and the possibility of Car B is  x < 120745  or  x > 140745

What is absolute value inequality?

Absolute value inequality are inequalities in algebra that involve algebraic expressions with absolute value symbols and inequality symbols. In simple words, we can say that an absolute value inequality is an inequality with an absolute value symbol in it. It can be solved using two methods of either the number line or the formulas.

x = price of car B

x-130745 = difference in price from car A to car B

If x is the larger price, then x-130745 will be positive. If x is the smaller price, then x-130745 is negative.

In short,

x-130745 > 0 when x > 130745

x-130745 < 0 when x < 130745

Using absolute value will give us

|x-130745| = positive difference in price

The result of an absolute value is never negative

We write the |x-130745| > 10000 to indicate that the difference in price is more than 10000 dollar

 | x-130645 | > 10000

Part b.

We'll use the idea that if |x| > k, then x < -k or x > k

to get the following

|x-130745| > 10000

x-130745 < -10000 or x-130745 > 10000

x < -10000+130745  or  x > 10000+130745

x < 120745  or  x > 140745

Car B has a price less than $120,745

OR

Car B has a price greater than $140,745

So basically anything that is not between 120745 and 140745. The price has to be positive of course.

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Given

Jessie has 5 dogs

2 are male

3 are female

Procedure

What percent of the dogs are male?

Male dogs

40 % of dogs are male

Many graduate schools require applicants to take a certain test. Those taking the test receive three scores:

a verbal reasoning score,

a quantitative reasoning score,

an analytical writing score.

Let average verbal reasoning score represent by v

Let average quantitative reasoning score represent by q

Let average analytical writing score represent by a

In 2013, the average quantitative reasoning score exceeded the average verbal reasoning score by 1.3 points

i.e.,

Average quantitative reasoning score - average verbal reasoning = 1.3

q - v = 1.3 ...(1)

The average verbal reasoning score exceeded the analytical writing score by 150.5 points.

i.e.,

Average Reasoning score - average analytical writing = 150.5

v - a = 150.5 ...(2)

The sum of the three average scores was 305.9.

i.e.,

v + q + a = 305.9 ...(3)

Simplify the equation (1), (2) and (3) to get the value of q,v and a;

Add equation (1) and (2)

(q-v) + (v-a) = 1.3 + 150.5

q + a = 151.8 ....(4)

Substitute the value of (q+a=151.8) in the equation (3);

v + q + a = 305.9

v + 151.8 = 305.9

v = 305.9 - 151.8

v = 154.1

Substitute the value of v = 154.1 in the equation (2);

v - a = 150.5

154.1 -a = 150.5

a = 154.1 - 150.5

a = 3.6

Now, substitute the value of a = 3.6 in the equation (4)

q + a = 151.8

q + 3.6 = 151.8

q = 151.8 - 3.6

q = 148.2

Answer :

The average verbal reasoning score was 154.1

The average quantitative reasoning score was 148.2

The average analytical writing score was 3.6

The answer for this process of long division is, therefore:

To find the result for this long division, we needed to divide the first term of the polynomial by the x in the divisor. Then, if we see the first graph, we have:

Then, we need to multiply this term by the divisor (x - 3), and then, subtract the result from the first two terms of the dividend. We can see as follows:

The smaller number = 27

The larger number = 119

Let the smaller number be x

Let the larger number be y

The sum of the two numbers is 146

x + y = 146..............(1)

The larger number is 16 less than five times the smaller number

y = 5x - 16.............(2)

Substitute equation (2) into equation (1)

x + (5x - 16) = 146

x + 5x - 16 = 146

6x = 146 + 16

6x = 162

x = 162/6

x = 27

Substitute the value of x into equation (2)

y = 5(27) - 16

y = 135 - 16

y = 119

The smaller number = 27

The larger number = 119

To find h(-6), replace x = -6 into the function, as follows:

h(x) = -x - 3

h(-6) = -(-6) - 3

h(-6) = 6 - 3

h(-6) = 3

Answer:

C

Step-by-step explanation:

- 2 = 5x + 3 ( subtract 3 from both sides )

- 5 = 5x ( divide both sides by 5 )

- 1 = x

Given:

The equation is:

Find-:

Restrictions for this equation

Explanation:

The equation is:

The denominator is not equal to zero. If the denominator is zero, then the function is undefined.

Then the restriction is:

For the function value of x is:

The value of "x" is:

So above function value of x is possible only -6 and -1 then the restriction value is all real numbers except only -6 and -1

Answer:

g(x) + 4 = x

g(x) = x - 4 which is probably the answer you should submit.

Step-by-step explanation:

Givens

f(x) = x

g(x) +4 = f(x)  

Comment

f(x) and g(x) are forms of y or z. What they mean is that whatever x is on the left, it will be make the same on the right. It is just a short hand to help you in defining the y value.

If you want to move down, The y value is the one to notice. Notice that it is not intuitive. If you want to go down the sign on y + 4 = x is the equation you use. It is the exact opposite of what you think it should be. The graph below should help you.

The red line is f(x)  = x

The blue line is g(x) + 4 = x.

The blue line can be written as g(x) = x - 4 which would be more inetuitive.

Hello!

First, let me explain the difference between discrete and continuous.

Discrete: only some numbers of the interval are on the input. For example, in the interval 1 - 10, consider only the integers.

Continuous: all the numbers of the interval are on the input. For example: in the interval 1 - 10, all values are considered (integers and decimals).

Knowing it, let's analyze your exercise:

The function D = 25 + 0.3x represents the daily rental charge D (in dollars) for x miles driven.

We can represent miles as integers and also decimals, right?

• 2 miles

• 5.750 miles

So, it means that all values can be considered.

So, this is a continuous domain.

Please provide the question.

We are asked to select the mathematical expressions that represent 40% of 84

We then recall that the mathematical form of 40% is in fact 40 / 100 = 0.4

Then, 40% of 84 can be written in math terms as:

40/100 times 84 = 40/100 * 84

or also

0.4 times 84 = 0.4 * 84

Therefore there are TWO options we can select in the list of possible answers:

Answer C and answer E

Given: The figure shown

To Determine: The value of EF

Solution

Using intersecting chord theorem that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.

Applying the theorem to the given would give us

Therefore

2. Let us label the the image given

The most appropriate choice for pattern will be given by

Option E is the correct option

What is pattern?

Repeated arrangement of number or shape is called pattern.

Here,

Let the boxes be counted row wise

The question is all about filling all the blank boxes with orange colour.

Let the pattern be solved column wise

In the first column,

In first figure

The 2nd, 3rd and 4th boxes are filled with orange colour

Then in the second figure 5th box is filled with orange colour

To complete filling all the boxes with orange colour, 1st, 6th, 7th, 8th and 9th boxes are left. That is shown in the third figure.

In the third column

In first figure

The 5th, 6th and 9th boxes are filled with orange colour

Then in the second figure

1st, 2nd, 4th, 7th and 8th boxes are filled with orange colour

To complete filling all the boxes with orange colour, only the 3rd box is left

That is shown in third figure

Now, in the second column,

In the first figure,

1st, 7th and 8th boxes are  filled with orange colour.

Then in the second figure 3rd, 6th and 9th are filled with orange colour

To complete filling all the boxes with orange colour, 2nd, 4th and 5th boxes are left.

That is shown in option E

So option E is correct

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Answer:

Result of [tex] \tt{}(3 {x}^{2} + 2x - 5) - ( {5x}^{2} - 4x + 1)[/tex] is [tex]\tt{} - {2x}^{2} + 6x - 6.[/tex]

Step-by-step explanation:

[tex] \tt{}(3 {x}^{2} + 2x - 5) - ( {5x}^{2} - 4x + 1)[/tex]

[tex]\tt{} {3x}^{2} + 2x - 5 - {5x}^{2} + 4x - 1[/tex]

[tex]\tt{} - {2x}^{2} + 6x - 6[/tex]

This will be his initial investment. The amount for 8% will be 84000, and the amount for 12% will be 204000.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the

value of the variable x is 7.

let x = the money invested at 8%

y = the money invested at 12%

an actor invests some money at 8% and 36,000 more than four times the amount at 12%

x = 36000 + 2y

total annual interest earned from the investment is 26400

0.08*x + 0.12*y = 26400

by solving the system of equations

x = 36000 + 2y

0.08*x + 0.12*y = 26400

solving the equations,

0.08(36000+2y)+0.12y=26400

2880+0.16y+0.12y=26400

y=84000

x=204000

The amount for 8% will be 84000, and the amount for 12% will be 204000.

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The second expression 1/(x^2 - 4x + 3) is equivalent to the given expression.

What are the equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Consider the given expression,

((x + 3) / (x^2 - 2x - 3)) / ((x^2 + 2x -3)/ (x + 1))

We can write the expression as,

((x + 3) / (x^2 - 2x - 3)) x ((x + 1) / (x^2 + 2x -3))        

Rewrite the equation x^2 - 2x - 3 and x^2 + 2x -3 as,

x^2 - 2x - 3 = x^2 - 3x + x - 3 = (x - 3)(x + 1)

x^2 + 2x - 3 = x^2 + 3x - x - 3 = (x + 3)(x - 1)

plug these values in the above expression, we get

((x + 3) / ((x - 3)(x + 1)) x ((x + 1) / ((x + 3)(x - 1))

After solving this, we get

1 / ((x - 3)(x - 1) = 1 / (x^2 - 4x + 3)

Therefore, the second expression is equivalent to the given expression.

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Answer:

Step-by-step explanation:

Jenny is 20 years old

Lynn is 14 years old

Kim is 23 years old

Given:

The distance between two stations in map, D= 9cm.

The distance between two stations in real life, d=3 km.

Now, to find the scale of the map take the ratio of D/d .

So, the scale of the map is 1 km=3 cm.

The height is 9.875 feet from which the goalkeeper catches the ball.

The player kicks soccer from a height of 2 feet

x = 0 and y = 2

Maximum height of 20 feet after traveling 40 feet

x = 40, y = 20

So let y = a(x - 40)² + 20  ( the path of parabola)

Since x = 0 , y = 2

So, 2 = a(0 - 40)² + 20

2 = 1600a + 20

-18 = 1600a

a = - 9/800

Thus, y = -9/800(x - 40)² + 20

Since the soccer is caught by the goalkeeper 70 feet from where it was kicked

x = 70

So at this time,

y = -9/800 ( 70 - 40)² + 20

  = -9/800 × 900 + 20

  = - 81/8 + 20

  = 79/ 8

  = 9.875 feet

Therefore the height at which the goalkeeper catches the ball is 9.875 feet.

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The given inequalities are :

2x + 8 > 18

2c + 8 < 18

Inequality 1 : 2x + 8 > 18

Simplify

Subtract 8 from both side :

2x + 8 - 8> 18 - 8

2x > 10

Divide both side by 2

x > 5

Inequality : 2c + 8 < 18

2c + 8 < 18

Subtract 8 from both side:

2c + 8 - 8 < 18 - 8

2c < 10

Divide both side by 2:

2c/2 < 10/2

c < 5

So, the solution is x > 5 and c < 5

So, equation will be : c < x < 5

Answer:

Step-by-step explanation:

If I did the math right! The bill should be $400.00

How I did it, was I did 175+5x45.

seeing, it is $5 per mile! And the total miles you got was 45.

If I missed something, please let me know

P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.

An Independent Event is defined as if the outcome of one event has no bearing on the outcome of the other, the two events are said to be independent events. Or, we may say that an event is considered independent if it does not affect the probability of another event. Probability-independent events mirror actual occurrences.

Let B and C be two events such that P(B) = 0.25 and P(C) = 0.67.

To determine P (B U C),

Given that B and C are independent.

Since B and C are independent events, we can just multiply the probabilities together, 0.25 × 0.67 = 0.1675

To determine P (B U C),

Given that B and C are mutually exclusive.

Since B and C cannot both occur at the same moment by definition because they are mutually exclusive, the answer is 0.

Therefore, P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.

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(a) 250000 of this revenue was sales and $11250 much was sales tax. (b) $11250 of sales tax should be sent to the city and $3750 sales tax should be sent to the state.

Let us assume that the total sales are $X.

According to the given situation, 7% is the sales tax and an additional state sales tax of 1.5% will be charges on the sales.

The total revenue including sales tax is $271250.

(a) Total revenue = sales + total sales tax

So, we can write,

X + X(7+1.5)% = 271250

Solving further,

X + X(8.5%) = 271250

X + 8.5X/100 = 271250

108.5X = 271250×100

X = 250000

Total sales is $250000.

Total sales tax is $(2710250-250000)

Total sales tax is $21250.

(b) Total sales is $250000.

Tax charges by city is 7%.

Using percentage formula,

Percentage of tax = Total tax amount/Total sales amount × 100

Putting all the values,

7 = Total tax amount/250000 × 100

Total tax amount = 7 × 2500

Total tax amount = 17500 dollars.

Total amount to be sent to the city is 175000$.

(c) Total sales is $250000.

Tax charges by city is 1.5%.

Using percentage formula,

Percentage of tax = Total tax amount/Total sales amount × 100

Putting all the values,

1.5 = Total tax amount/250000 × 100

Total tax amount = 1.5 × 2500

Total tax amount = 3750 dollars.

Total amount to be sent to the city is 175000$.

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Determine the equation of line passing through two points.

So equation of line is,

Answer:

Find the following probabilities if you are dealt cards from a standard 52-card deck. Round your answers to three decimal places.

a. If a card is randomly selected, what is the probability that the card is a heart?

13/52 = 1/4

b. If a card is randomly selected, what is the probability that the card is either a club or a spade?

26/52 = 1/2

c. If a cards is randomly selected, what is the probability that the card is both a club and a spade?

0

d. If two cards are randomly selected, what is the probability of drawing a three first, then drawing a jack?

4/52·4/51 = 4/663 = 0.006033182503

e. If two cards are randomly selected, what is the probability of drawing a heart first, then drawing a diamond?

13/52·13/51 = 13/204 = 0.06372549019

f. If two cards are randomly selected, what is the probability of drawing a face card followed by drawing an ace?

12/52·4/51 = 4/221 = 0.01809954751

g. If two cards are randomly selected, what is the probability of drawing a diamond first, then drawing an eight?

12/52·4/51 + 1/52·3/51 = 1/52 = 0.01923076923

The current area of Mr. Milstein's kitchen table is:

The new width of Mr. Milstein's kitchen table = 5 feet

The area of the new kitchen table if the length is l is given by

Note that the area of the proposed kitchen table should be larger than the current one.

Therefore,

The correct option is F