Mathematics High School

Convert this equation into standard form

Answers

Answer 1

The standard form of the linear function in this problem is given as follows:

-4x + 5y = -25.

How to convert the linear function in standard form?

The linear function for this problem is defined in point-slope form as follows:

y + 1 = 4/5(x - 5).

To convert to standard form, we leave the coefficients of x and y on the left side and the constant on the right side, hence:

y + 1 = 4x/5 - 4.

-4x/5 + y = -5.

Multiplying everything by 5, we have that:

-4x + 5y = -25.

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Related Questions

The typical pole for pole vaulting is 17 feet long. How fast would a pole vaulter have to run (in the direction of the pole) in order for a spectator sitting in the stands to see it 15 feet long

Answers

A pole vaulter have to run at 18m/s speed.

According to the statement

The typical pole for pole vaulting is 17 feet long

we use the formula

1/2 m(v)^2 = mgh

Now rearrange the terms

(v)^2 = 2gh

here g = 10 and h = 15 then

substitute the values

(v)^2 = 2*10*15

v = 17.32

So, A pole vaulter have to run at 18m/s speed.

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8. A company has 350 workers. The
president of the company wants to know
what percent increase in employment
would be necessary for the number of
workers to be greater than 375.
Help!

Answers

The percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%

How to determine the rates?

The given parameters are:

Initial = 350

Final = 375

The rate is calculated as:

Rate = Final/Initial - 1

So, we have:

Rate = 375/300 - 1

Evaluate

Rate = 1.25 - 1

This gives

Rate = 0.25

Express as percentage

Rate = 25%

Hence, the percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%

Answers

The population for this study is all registered voters from New York City.

What is the population for a study?

it is given that the poll has been carried out among 1000 registered voters from New York City. These 1000 people have been selected randomly from the population of the study.

The available study subset of the target population for a study, for instance, schizophrenics in the researcher's hometown, is known as the study population or population of the study. The sample chosen for the study is known as the study sample.

Study Population In This Case

In this case, out of all the New Yorkers, only the registered voters of the city are eligible for making the target subset. Hence, the registered voters of the New York city make the study population. Furthermore, since 1000 random registered voters are chosen for the poll, those 1000 registered voters make the study sample.

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What is 3x^3+5x^2-11x+3/x+3

Answers

The solution to the expression (3x³ + 5x² - 11x + 3)/(x + 3) is (x - 1/3)(x - 1)

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the expression:

(3x³ + 5x² - 11x + 3)/(x + 3)

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

= (x - 1/3)(x - 1)

The solution to the expression (3x³ + 5x² - 11x + 3)/(x + 3) is (x - 1/3)(x - 1)

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A canadian goose and a Great blue heron took off in opposite directions. The goose flew at 20 mph, and the heron flew at 10 mph. when they landed, they were 180 miles apart. Altogether, they flew for 14 hours. How long did each bird fly?

Answers

The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Let a represent the time flown by the goose and b represent the time flown by the heron. Hence:

a + b = 14 (1)

Also:

20a + 10b = 180 (2)

From equation 1 and 2:

a = 4, b = 10

The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours

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The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.01 level that the drug stays in the system for more than 377 minutes. After performing a hypothesis test, she decides to reject the null hypothesis. What is the conclusion

Answers

Here null hypothesis is rejected in this problem.

According to the statement

We have a given that the evidence at alpha level is 0.02, ANd the sample size n is 67. And mean time equal to 330 minutes and the variance that is the sigma square is equal to 529 point.

And We have to make the decision to reject or feel fail to reject the null hypothesis to solve this problem.

Firstly we solve alternative and null hypothesis

So, the null hypothesis h naught will be that mu is less than equal to 327 point and alternative hypothesis ha will be.

That mu is greater than 327 point now. This alternative hypothesis is claimed.

Next we will find the value of s which is given by sigma divided by under root n.

So, s = 67/ (529)^1/2

s = 2.8099.

Now we find the value of Z

So, Z = 327 - 330 / 2.8099

Z = 1.0677

Now the critical value of z is 2.05

Critical, we can say fail to reject the null hypothesis, and this is the result from the null hypothesis test.

With this test, we can conclude that the the data do not support that. There is evidence at 0.02 level that the drug stays in the system for more than 327 minutes. So this is the conclusion for the test for the hypothesis test and the answer to the problem.

So, Here null hypothesis is rejected in this problem.

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If 111 is divided into pieces that are each \dfrac19
9
1

start fraction, 1, divided by, 9, end fraction of a whole, how many pieces are there?
1\div\dfrac19=1÷
9
1

=1, divided by, start fraction, 1, divided by, 9, end fraction, equals

Answers

The results of dividing 1 into pieces that are each 1/9 of a whole is 9

Division of fraction

1 ÷ 1/9

multiply by the reciprocal of 1/9 which is 9/1

1 ÷ 1/9

= 1 × 9/1

= (1 × 9) / (1 × 1)

= 9/1

= 9

Complete question:

If 1 is divided into pieces that are each 1/9 of a whole, how many pieces are there

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What are the x-intercepts of the function y = 22 -x - 120? Check all that apply. O (-120. 0) O (-11.466, 0) O (-10.466, 0) O (0, -120) (10.466, 0) O (11.466, 0)

Answers

The x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)

How to determine the x-intercept?

The function is given as:

y = 2x^2 - x - 120

Set the function to 0

2x^2 - x - 120 = 0

Factor out 2

2(x^2 - 0.5x - 60) = 0

Divide by 2

x^2 - 0.5x - 60 = 0

Expand the function

x^2 + 7.5x - 8x - 60 = 0

Factorize the function

(x + 7.5)(x - 8) = 0

Split

x + 7.5 = 0 and x - 8 = 0

Solve for x

x = -7.5 and x = 8

Hence, the x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)

Answers

The equation representing the given situation is, 250 = 70x + 35, where x is the number of cars washed by the company.

In the question, we are given that Scarlett made a profit of $250.00 with her mobile car wash company. She charged $75.00 per car wash and received $35.00 in tips, but also had to pay $5.00 in cleaning supplies per car.

We are asked to represent the situation with an equation.

We assume the number of cars washed by the company to be x.

Charge for washing 1 car = $75.00.

Cost for cleaning supplies for 1 car = $5.00.

Thus the profit on the wash of 1 car = $75.00 - $5.00 = $70.00.

The total profit received by the company, on washing x number of cars = $70x.

The tips received = $35.00.

Thus, the total profit of the company = $(70x + 35).

But, the total profit is given to be $250.00.

Thus, we get an equation, 250 = 70x + 35.

Thus, the equation representing the given situation is, 250 = 70x + 35, where x is the number of cars washed by the company.

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Harriet earned $4,334 for the month. state and local taxes are 6.3% in her state and locality. how much state and local taxes were withheld from her check?

Answers

Total tax from state and local taxes were withheld from her check:

= $273.04

What is Percentage ?

A % is a number or ratio that, in mathematics, can be expressed as a fraction of 100. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "percent" is used to denote it.

Solution:

Harriet earned for the month = $4334

state and local taxes are = 6.3%

= [tex]\frac{4334}{100} *6.3%[/tex]

=$273.04

Total tax from state and local taxes were withheld from her check:

= $273.04

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The graph of Y= sin x--
= sin(x-3);
3%
O
units to the left
○ 3 units to the right
3x
2 units up
Зл
2
2 is the graph of the y = sin(x) shifted in which direction?
units down

Answers

direction of going upwards

The graph of y=sin(x-3π/2) is the graph of the y =sinx shifted right by 3π/2 units.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

If we have a parent function y = Sin(x), the function

y = Sin(x-b) would be the parent shifted b units right

y = Sin (x+b) would be the parent shifted b units left

The function given is y=sin(x-3π/2)

So from the rules, we can clearly say that it is parent function shifted right by 3π/2 units.

Hence, the graph of y=sin(x-3π/2) is the graph of the y =sinx shifted right by 3π/2 units.

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The potential energy p, in a spring is represented using the formula p=1/2kx^2. lupe uses and equivalent equation, which is solved for k to determine the answers to her homework

Answers

The value of [tex]k = 2P/x^2[/tex]

We are aware that an object's location might cause it to store energy. When a bow and arrow are used, the energy that is stored when the bow is pulled is what gives the arrow its kinetic energy when it is released.

when a spring is moved away from its equilibrium position, it gains some energy, which we can notice by the tension our hands experience as we stretch it. Potential energy is a type of energy that arises from a change in its position or condition, according to our definition

We know that P=1/2kx^2

Now solving for k

2P = kx^2

Therefore

k = 2P/x^2

Hence the value of k is 2P/kx^2

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Explain how you could use the dimensions of a reduced rectangle and one given measurement of an original rectangle to find a missing measure?

Answers

Using the dimensions of a reduced rectangle and one given measurement of an original rectangle:

Set up a proportion using the corresponding partsSolve the proportion to find the missing measure

What is Reduction?

Reduction is a type of dilation that reduces the size of an original figure to form a new figure that is similar to the original. The corresponding lengths of both figures are therefore proportional.

Assuming the dimensions of the reduced rectangle are 10 cm by 4 cm, and the length of the original rectangle is given as 8 cm, to find the missing measure (x), do the following:

Set up a proportion using the corresponding parts

10/8 = 4/x

Solve the proportion using cross products to find x:

10x = (8)(4)

10x = 32

x = 32/10

x = 3.2 cm

The missing length is 3.2 cm.

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Answer:

Using the given measurements of both figures, set up a proportion that has the corresponding parts in the same position. Then solve the proportion using cross products to find the value for the unknown.

Step-by-step explanation:

Set up a proportionCorresponding sides are in the same place in the proportion.Use cross products in the proportion to solve for the unknown.

In a binomial experiment, the probability of success is. 6. What is the probability of two successes in seven trials?.

Answers

The probability of two successes in seven trials is 0.0774144.

We can find the probability as shown below:

The probability can be found using the binomial formula.

The probability of success is given as 0.6.

Therefore, the probability of failure is 0.4.

We have to find the probability of two successes in seven trials.

It is given by:

[tex]P = nC_x p^{n} q^{n-x}\\=7C_{2} (0.6)^{2} (0.4)^{7-2} \\=7C_{2} (0.6)^{2} (0.4)^{5} \\=\frac{(7)(6)}{(1)(2)} (0.36)(0.01024)\\=0.0774144[/tex]

The probability of two successes in seven trials is found to be 0.0774144.

Therefore, we have found that the probability of two successes in seven trials is 0.0774144.

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If the range for a set of number is 8 and the maximum number is 2 what is the answer/

Answers

The range is -6.

What is a range?The range of a collection of data in statistics is the difference between the largest and lowest values. The difference here is that the range of a collection of data is determined by subtracting the sample maximum and minimum. In descriptive statistics, however, the concept of the range has a more nuanced meaning.

To find the answer, calculate as follows:

Range = Maximum - Minimum

Range = 8 and Maximum = 2

Let, the minimum be x.

Now, substitute values in the formula.

8 = 2 - x

x = 2 - 8

x = -6

Therefore, the answer is -6.

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[tex]x^{8}+x^{4}+1[/tex]

Answers

You did not provide directions. What do you want us to do with your 8th degree polynomial?

forty-seven marbles are shared between some children. each child receives six marbles and there are five marbles left over. how many children share the marbles?

Answers

The total number of children can be calculated using linear equation in one variable. The marbles are shared among 7children.

Solution

Total number of marbles = 47

The number of marbles received by each child = 6

Let the number of children be x

Then according to the question'

Total number of marbles received by all children + 5 = Total number of marbles

6x + 5 = 47

6x = 47- 5

6x = 42

x = 7

now, the number of children is 7.

What is linear equation in one variable?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.Here, the variables x and y, the coefficients A and B, and the constant C are all present.A linear equation's graph will always be a straight line.One-variable linear equations are fairly simple to solve. To determine the value of the unknown variable, the variables are divided and placed on one side of the equation, and the constants are combined and placed on the other side.

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Mr.Nguyen saves $120 of his income of 800.00 what percent of his income does Mr.Nguyen save?

Answers

Nguyen saves 15% of his income

How to determine the percentage?

The given parameters are:

Savings = $120

Income = $800

The percentage saved is calculated as:

Percentage = Savings/Income * 100%

This gives

Percentage = 120/800 * 100%

Evaluate

Percentage = 15%

Hence, Nguyen saves 15% of his income

Answers

3,471,738 this is the answer

What is the solution set to the following equation?

x4+2x−48=0

Select one:
a. { ±2i2–√,±6–√ }
b. { ±i6–√,±2–√ }
c. { ±2i2–√,±3 }
d. { ±i3–√,±22–√ }

Answers

The solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7

How to determine the solution set of the equation?

The equation is given as:

x^2 + 2x - 48 = 0

A quadratic equation is represented as:

ax^2 + bx + c = 0

By comparing both equations, we have

a = 1, b = 2 and c = -48

The solution of the quadratic equation is then calculated using

x = (-b ± √(b^2 - 4ac))/2a

Substitute values for a, b and c in the above equation

x = (-2 ± √(2^2 - 4 * 1 * -48))/2 * 1

This gives

x = (-2 ± √196)/2

Evaluate the square root of 196

x = (-2 ± 14)/2

Divide through by 2

x = -1 ± 7

Hence, the solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7

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A box of jerseys for a pick-up game of basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys. If you are first to the box and grab 2 jerseys, what is the probability that you randomly grab 2 extra-large jerseys

Answers

The probability that a randomly grab 2 extra large jerseys is 18.3%.

Given that a box of jerseys for a pick-up game of basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys.

The number of jerseys in the box is 8+6+4=18

To find the probability of picking 2-extra large jerseys by finding the probability of 1 extra large and probability of 2 extra large.

The probability of picking 1 extra large jersey is

P₁=8/18

P₁=4/9

The probability of picking 2 extra large jerseys is remaining jerseys

P₂=7/17

The total probability of getting 2 extra large jerseys is

P=P₁×P₂

P=(4/9)×(7/17)

P=28/153

P=0.183

P=18.3%

Hence, the probability that randomly grab 2 extra-large jerseys when basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys is 18.3%.

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A soccer team played 25 games last season. they won 16 games, lost 5 games, and tied the rest.

Answers

[tex]\frac{25}{4}[/tex] of the games was a tie.

What is a fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.

To find what fraction of the games was a tie:

Total game played = 25

Win 16 lose 5 total = 21

So, tie matches = 4

The fraction will be 25/4.

Therefore, [tex]\frac{25}{4}[/tex] of the game was a tie.

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Complete question:

A soccer team played 25 games last season they won 16 games, lost 5 games, and tied the rest what fraction of the games was a tie?

Simplify: x^3-1/x^2-1

Answers

Answer:(x-1)(x^2+x+1) / (x+1)(x-1)

Step-by-step explanation:

For x^3-「1」→ 1=1^3

For x^2-「1」→ 1=1^2. this way of thinking might help you understand better:)

You can just use a formula of factorizationヾ ^_^♪

slope:
y-intercept:
HELP

Answers

Answer:

Slope: 1

Y-intercept: -1

Step-by-step explanation:

The line touches the y-axis at -1, and using rise over run for the slope, it would be 1, since you go up 1 unit and move to the right 1 unit. 1/1 which is our rise/run would be 1 and that would make the slope 1.

I hope it helps! Have a great day!

bren~

x+y = 8 and 2x-y=7
Anyone can help

Answers

Step-by-step explanation:

x=8-y

2x-y=7

2(8-y)-y=7

16-2y-y=7

-3y=-9

y=3

x=8-y

x=8-3=5

Answer:

Hello

Step-by-step explanation:

Méthode par combinaisons linéaires:

[tex]\left\{ \begin{array}{ccc|c|c}x+y&=&8&1&-2\\2x-y&=&7&1&1\\\end {array} \right.\\\\\\\left\{ \begin{array}{ccc}3x&=&15\\-3y&=&-9\\\end {array} \right.\\\\\\\boxed{\left\{ \begin{array}{ccc}x&=&5\\y&=&3\\\end {array} \right. }\\[/tex]

Proof:

5+3=8 and 2*5-3=7

Write as an equation: The sum of -7 and a is equal to 37.
A. −7+a=37
B. −7+a=−37
C. −7−a=−37
D. −7−a=37

Answers

Answer is A. -7+a=37
Reason
Sum is to add (-7) and (a), and “is equal to” is to use the = sign.
So
-7+a = 37

CAN ANYONE HELP ME WITH QUESTION 7

Answers

Answer:

x = 4.

Step-by-step explanation:

Each angle in an equilateral triangle is 60 degrees, so we have:

10x + 20 = 60

10x = 40

x = 4.

Answer:

X = 4

Step-by-step explanation:

The angles of a triangle add up to 180 degrees and this is an equilateral triangle which means that all the angles are the same. which means you set up the equation:

10x + 20 + 10x + 20 + 10x + 20 = 180

Simplify: 30x + 60 = 180

- 60 - 60

You have : 30x = 120

(Divide by 30)

You end up with: X = 4

what is the result of 6 divided by 15

Answers

6/15, 0.4 as a decimal, it cannot be further simplified

Answer:

If you have 6 chocolate and you have to divide that into 15 people than the answer will be 2 upon 5 or 0.4 for each.

True or false: f(x) is a function.

Answers

A. True

Step by step explanation:

1. if we where given a graph and told to determine whether it's a function or not, we would have used a VERTICAL LINE TEST.

2. In this case we have points, and for every x value we have one corresponding y value which makes it a function that is a ONE-TO- ONE FUNCTION

There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players of 6 players can the coach make, if the position does not matter?

Answers

There are 5005 different groups

How to determine the number of groups?

The given parameters are:

Players, n = 15

Selected, r = 6

The number of groups is then calculated as:

[tex]Group = ^{n}C_r[/tex]

This gives

[tex]Group = ^{15}C_6[/tex]

Apply the combination formula

[tex]Group = \frac{15!}{9!6!}[/tex]

Evaluate the expression

Group = 5005

Hence, there are 5005 different groups