Is this function continuous or discrete? How far can you get on 20 gallons? What is the domain and range of this function? How many gallons to get 500 miles? Where do the labels on the graph go?

The graph of the linear function 5x + 3y = 20 is given at the end of the answer.

To build the graph of a linear function, we identify two points on the line, and then plot a line passing through them.

In this problem, the function is:

5x + 3y = 20.

The points that we are going to choose are the intercepts. The x-intercept is the value of x when y = 0, hence:

5x = 20

x = 20/5

x = 4.

Meaning that point (4,0) is on the graph of the function.

The y-intercept is the value of y when x = 0, hence:

3y = 20

y = 20/3

y = 6.67.

Meaning that point (0, 6.67) is on the graph of the function.

The graph is plotted with a line passing through the points (4,0) and (0, 6.67).

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part 1 of the question is asking us to evaluate expressions to the power of 2. To do that let's remember the following:

Ther is, when a number is elevated to second power it means we have to multiply that number by itself. For example:

In the second part of this question, we are asked to evaluate the square root of a number. Let's remember that the square root is the inverse operation of elevating a number to the second power. That is if we have:

it means:

For example:

The third part of the questions asks us to solve for "x" the following equation:

To do that we take square root on both sides:

Since the square root of a number to the second power is the same number and the square root of 9 is 3, we get:

Answer:18

Step-by-step explanation:

$128,000 represents 100%

To find how much is 4% we can use the next proportion:

Solving for x:

Her commission is $5,120

Answer:

x intercept is -3

Step-by-step explanation:

We need to find the equation for the line First we find the slope m = (y2-y1)/(x2-x1)     = (2- -4)/(6- -3)     = (2+4)/(6+3)     =6/9     = 2/3 The we can write the equation y= mx+b y = 2/3x +b We can substitute in (6,2) 2 = 2/3(6) +b 2 =4+b Subtract 4 from each side 2-4 =b b =-2 y = 2/3 x-2 We want to find the x intercept, so set y =0 and solve for x 0 = 2/3x -2 Add 2 to each side 0-2 = 2/3x  Multiply each side by 3/2 to isolate x -2 *3/2 = 2/3x * 3/2 -3 =x The x intercept is -3  

Answer:

D y < 8

Step-by-step explanation:

the range is the interval or set of all valid y (functional result) values.

we can see the y values start at +8, and as the curve is only going down, clearly endlessly, every value smaller than 8 is valid.

8 itself is the be excluded, as there is a hollow point (a filled point would indicate "include").

and therefore we cannot say y <= 8.

we have to use y < 8.

SOLUTION

From the image above

Considering the bigger right angle triangle,

We can obtain the expression of y from the smaller right angle triangle,

Using pythagora's rule, we have

Then, recall

Substite the expression for y², we have

Expand the paranthesis, we have

subtract 9 from both sides, we have

Divide both sides by 6, we obtain

Therefore

Answer: x= 12

Answer:

d. y= 2x³

Step-by-step explanation:

All of the other equations represent linear functions, and are in the form y = mx + b. D on the other hand contains an exponent, making it a non-linear (in this case cubic) function.

The inverse of the function y = 4ˣ is f⁻¹(x) = ㏑x / ㏑4.

For the given question;

The function is given as;

y=4ˣ

Interchange the variables of the function.

x = 4∧y

Taking log both side.

㏑ x =  ㏑(4∧y)

Using the power rule of log function.

㏑ x =  y㏑(4)

y = ㏑ x/㏑(4)

Now, replace y with f⁻¹(x).

f⁻¹(x) = ㏑ x/㏑(4)

Thus, the inverse of the function y = 4ˣ is found to be f⁻¹(x) = ㏑x / ㏑4.

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The correct question is-

Evaluate the inverse when y=4ˣ. Show all of your work.

Answer:

183 miles per hour.

Explanation:

The estimated velocity(v) at the end of a drag race is modeled using the formula below:

Given:

• The horsepower, p = 1311

• The weight (in pounds), w = 2744 pounds.

Substitute into the formula above:

The velocity is approximately 183 miles per hour.

If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.

Total number of registered voters in Central city = 29791 voters

Total number of voting centers = 93 voting centers

The number of population serves by each center = Total number of registered voters in Central city ÷ Total number of voting centers

Substitute the values in the equation

The number of population serves by each center = 29791/93

= 320.33

≈ 320

Hence, If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.

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Total 250 adult tickets are sold.

Let a = number of adult tickets sold

Let s = number of student tickets sold

a + s = 553

s = a + 53

From above equations;

a + a + 53 = 553

2a = 553 - 53

2a = 500

a = 250

Total 250 adult tickets are sold.

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The solution of the system of linear equations 2x + 3y = 6 and -3x + 5y = 10 is (0, 2).

Linear equation:

Linear equation refers an equation in which the highest power of the variable is always 1. It is also called as a one-degree equation.

Given,

Here we have the following system of linear equations.

2x + 3y = 6

-3x + 5y = 10

Now, we need to find the solution for the equations.

Here we have to use the substitution method to solve this one,

To do the substitution method we have to follow the following steps:

Step 1) Solve anyone of the equations either for the variable x or y

Step 2) Now, substitute the value obtained from step 1 to the other equation

Step 3) Finally, solve the equation to find the value of the remaining variable.

Here we have to take the equation (2), and we have to solve it for the value of y,

For that we have to rewrite the equation as,

5y = 10 + 3x

y = (10 + 3x)/5

Apply the value of y on the equation (1), in order to get the value of x,

So,

2x + 3(10 +3x)/5 = 6

2x + (30 + 9x)/5 = 6

(10x + 9x + 30)/5 = 6

19x + 30 = 30

19x = 0

x = 0

Now, apply the value of x on the equation in order to get the value of y,

y = (10 + 3(0))/5

y = 10/5

y = 2.

Therefore, the resulting ordered pairs for the system of linear equation is (0, 2).

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AS per the order of operations, the value of the expression 3.2+2(-1.5)-3.4 is -3.2

Order of operations:

Order of operations states the rule that tells the correct sequence of steps for evaluating a math expression.

The order using PEMDAS:

Parentheses,

Exponents,

Multiplication and Division (from left to right),

Addition and Subtraction (from left to right).

Given,

Here we have the expression. 3.2+2(-1.5)-3.4

Now, we have to use the order of operations concept in order to solve it.

The highest priority for the order of operation is brackets and the next priority is for division and multiplication,

So, here we have to solve those things first, then we get,

=> 3.2 + (-3) - 3.4

We know that (+) x (-) = -, so, the expression is rewritten as,

=> 3.2 - 3 - 3.4

The next priority is for addition and subtraction,

So, the result is,

=> 3.2 - 6.4

=> -3.2

Therefore, the resulting number is -3.2

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Answer:

6.5625 gal per hour

Step-by-step explanation:

Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour. Combining these: 14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr) = 6.5625 gal per hour. Written as a mixed fraction: 6 9/16 gal per hour.

Amira's age is 12 years when Amira is younger than Marques and their ages are consecutive integers and the sum of Amira's age and 2 times Marques's age is 38.

According to the question,

We have the following information:

Amira is younger than Marques.

Their ages are consecutive integers.

The sum of Amira's age and 2 times Marques's age is 38.

Now, let's take Amira's age to be x years.

Then, Marques's age will be (x+1) years.

So, we have:

x + 2(x+1) = 38

x + 2x + 2 = 38

3x+2 = 38

3x = 38-2 (Moving 2 from the left hand side to the right hand side will result in the change of the sign from plus to minus.)

3x = 36

x = 36/3

x = 12 years

Hence, Amira's age is 12 years.

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The sum of 12 and P can be written as 12 + P

Then, f decreased by the sum of 12 and P can be written as:

f - (12 + P)

Answer: it isn't correct, the correct answer is f - (12 + P)

Answer:

4x3+6x6=48

Step-by-step explanation:

PEMDAS

4x3=12

6x6=36

12+36=48

therefore, the answer is 48

Answer:

Length in inches → 11

1 inch = 2.5 centimeters

Length in Centimetres → 11 × 2.5 → 27.5 cm

Answer: 93°

Step-by-step explanation:

[tex]\angle A \ and\ \angle B\ are\ vertical\ angles.\ Hence,\ \angle A \ = \ \angle B\\\\2x+19=3x-18\\\\2x+19+18=3x-18+18\\\\2x+37=3x\\\\2x+37-2x=3x-2x\\\\37=x\\\\Thus,\ x=37\\\\m\angle A=(2(37)+19)^0\\\\m\angle A=(74+19)^0\\\\m\angle A=93^0\\\\[/tex]

The system of inequalities that can be used to determine the number of each type of plant to be sold are :

x + y  ≥ 15

$150x + $125y  ≥  $2000

The first step is to determine the inequality signs that would be used in the system of inequalities:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is the greater than or equal to sign, ≥.

Two system of inequalities would be formed using the information provided in the question. The form of the system of inequalities would be:

number of Mediterranean palms sold + number of palmetto sold  ≥ least number of plants

(number of Mediterranean palms sold x cost of Mediterranean palms) + (number of palmetto sold x cost of palmetto sold   ≥ least number of sales

x + y  ≥ 15

$150x + $125y  ≥  $2000

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the answer would be (0,5)

We were told that the salary, t years after 2015 is given by the function,

S(t) = 3100t + 56000

When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2

We would substitute t = 2 into the function and find S(2)

Thus,

S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200

When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5

We would substitute t = 2 into the function and find S(2)

Thus,

S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500

Thus, we can say that

when

x1 = 2, y1 = 62200

when x2 = 5, y2 = 71500

Recall,

slope or average rate of change = (y2 - y1)/(x2 - x1)

average rate of change = (71500 - 62200)/(5 - 2) = 9300/3

average rate of change = 3100

The last option is correct

Answer:

x = 10

Step-by-step explanation:

-3x - 6 = -7x + 34

+7x

4x - 6 = 34

+6

4x = 40

/4

x = 10

Answer:

x = 10

Step-by-step explanation:

-3x - 6 = -7x + 34  Add 7x to both sides

4x - 6 = 34  Add 6 to both sides

4x = 40  Divide both sides by 4

x = 10

Answer:

There is no dot plot below

Step-by-step explanation:

Answer:

16%.

Explanation:

In a recent math test:

• The average score = 75

• Standard Deviation = 10

To find: The percentage of people who scored an 85 or higher, P(X>85).

First, find the z-score when X=85.

Substitute the given values:

The people who scored an 85 or higher are 1 standard deviation away from the mean.

The percentage of people who scored an 85 or higher is 16%.

The measure of ∠C in the given triangle is 58°.

According to the question,

We have the following information:

ACD is a triangle where we have BD as an altitude on the side AC.

Now, we know that the altitude on any side makes an angle of 90° or in other words, it can be said that it makes a right angle.

Now, we have two right-angled triangle: ABD and CBD.

We have ∠ADB = 32°.

Now, ∠CDB will also be equal to 32° because the altitude bisects the angle (in two equal parts).

We know that the sum of the three angles in a triangle is 180°.

In ΔCBD, we have:

∠B + ∠C + ∠CDB = 180°

90° + ∠C + 32° = 180°

∠C + 122° = 180°

∠C = (180-122)°

(Moving 122 from the left hand side to right hand side will result in the change of sign.)

∠C = 58°

Hence, the measurement of ∠C in the given triangle is 58°.

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The equations of the lines are:

7. y = 3/2x - 3/2

8. y = -1/3x - 8/3

The equation that represents a line, in slope-intercept form is, y = mx + b.

7. Find the slope (m) between (5, 6) and (1, 0):

Slope (m) = (6 - 0)/(5 - 1) = 6/4

Slope (m) = 3/2

Find the y-intercept of the line, b, by substituting m = 3/2 and (x, y) = (1, 0) into y = mx + b:

0 = 3/2(1) + b

-3/2 = b

b = -3/2

To write the equation, substitute m = 3/2 and b = -3/2 into y = mx + b:

y = 3/2x - 3/2

8. Find the slope (m) between (-5, -1) and (1, -3):

Slope (m) = (-1 -(-3))/(-5 - 1) = 2/-6

Slope (m) = -1/3

Find the y-intercept of the line, b, by substituting m = -1/3 and (x, y) = (1, -3) into y = mx + b:

-3 = -1/3(1) + b

-3 = -1/3 + b

-3 + 1/3 = b

-8/3 = b

b = -8/3

To write the equation, substitute m = -1/3 and b = -8/3 into y = mx + b:

y = -1/3x - 8/3

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