I need an explanation on how to solve it!

The equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.

A function is truly equal to its graph in the modern mathematical foundations and typically in set theory. However, it is frequently helpful to think of functions as mappings, which include not just the relationship between input and output but also the sets that make up the domain and codomain. For instance, it is important to consider the codomain while determining whether a function is onto (surjective) or not.

For k=- 5, y=f(x) + k represents a vertical shift down.

For h=4, the horizontal shift left is y=f(x+h).

Therefore, the equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.

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Answer:

60 square inches

Step-by-step explanation:

The width of the second frame is 2 times the width of the first frame, or 2 * 5 inches = 10 inches.

The area of the second frame is its length multiplied by its width, or 6 inches * 10 inches = 60 square inches.

The function g(x) is a piecewise function For x 4, 1 g(x) = |x + 1| and for

x 1, 3 g(x) = 2.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

From the graph, we can conclude that g(x) is a piecewise function.

When x is - 4, 1 g(x) = |x + 1|.

And when x is 1, 3 g(x) = 2, A constant function.

Now, g(-2) = | - 2 + 1| = 1.

g(1) = | 1 + 1| = 2.

g(4) = 2.

The value of x when g(x) = 3 is - 4.

The value of x when g(x) = 1 is (0, - 2) as both satisfy g(x).

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Answer:

The rate of change is also called the slope.  The slope is -2

Step-by-step explanation:

Find 2 points on the line.  I am going to use the points (0,5) and (4, -3).  the rate is the change in y over the change in x.  From the two points, my values are -3 and 5.  The x values are 4 and 0.

To find the change, I subtract the y values and the x values.

[tex]\frac{-3-5}{4-0}[/tex] = [tex]\frac{-8}{4}[/tex] = -2

Answer: -2

Step-by-step explanation: The rate of change is also known as the slope!

To find the slope, you need to find the rise/run.

Let's pick two points ( 0,5) ( 4, -3)

You see that the y goes down by 8 and the x goes right by 4, so the rate of change is -8/4 = -2

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In linear equation,  { 2x + 3y = 7.20 ,   { 4x + 2y = 8.80 the price per pound for oranges.

 What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Product B performed worse in the study because 32% failed to get relief with this product, whereas only 28% failed to get relief with Product A.

Working through this, the percentage who failed to find relief from product A is (25 - 18) / 25 = 28%. Doing the same type of calculation for product B, we can determine the percentage who failed to find relief as (50 - 34) / 50 = 32%. The description statement asks for which offered less relief, which we can find using the less than operator:

28% < 32%

Product A offered relief to all but 28% of the people, while product B offered relief to all but 32% of the people. Given that fewer people failed to find relief on product 28%, we can argue that more people did find relief on product A.

Given that the tests are both on multiples of 25 people, we can also see the percentages by multiplying the numerators and denominators to bring both to a scale of 100:

7/25 * 4/4 = 28% of product A users failed to find relief.

16/50 * 2/2 = 32% of product B users failed to find relief.

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Answer:

Yup I think so to

Step-by-step explanation:

Answer:

Yes, it is an elimination problem.

x = -1.69230769

Step-by-step explanation:

You can eliminate 20y by adding both equations together.

Then, you will get 13x = -22.

Divide by 13 on both sides to get x= -1.69230769

That is a change in the hypotenuse's length of -2.6 inches per second.

What in math is a rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents

h = sqr(b^2 + a^2), b=30, a=40, b'=-5, a'=-7

h' = [(1/2)/sqr(b^2+a^2)](2bb' + 2aa') = sqr(30^2+40^2)(30(5)+40(-7)

= (150-280)/sqr2500 = (-130)/50 =-- -13/5 = -2.6 inches per second

2.6 inches are lost from the hypotenuse every second.

Check the response by observing what transpires in one second.

30 to 35 on the short leg

greater leg descends from 40 to 37

From 50 to 47.4 is the hypotenuse

In one second, 50-47.4 equals a 2.6 reduction. That is a change in the hypotenuse's length of -2.6 inches per second.

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The Rate of Tax for his state is 2.3%.

What is tax rate?

The ratio at which a business or individual is taxed in a tax system is known as the tax rate. Statutory, average, marginal, and effective tax rates are some of the ways that are used to present them. The terms inclusive and exclusive can be used to present these rates when applied to a tax base.

Annual Salary of Marcus Hatfield is = $43500

His Exemption from the tax is = $2000

He pays tax on the remaining amount i.e.

$43500 - $2000 = $41500.

His contribution toward the tax is $ 954.50,

Let the Rate of tax is x, thus

[tex](\frac{X}{100} *41500) = 954.50\\ x = \frac{95450}{41500} \\x = 2.3[/tex]

Thus, the rate of tax is 2.3% of his salary.

Hence, the Rate of Tax for his state is 2.3%.

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Answer:

as u can see the pattern is going up by 7.

Step-by-step explanation:

Answer:

His profit would be (-20)*3 or -60 $

Step-by-step explanation:

First month profit = -20 $

if the next three months will be the same, then:

(-20)*3

-60 $

The balance when the account went into overdraft was -48.61

An overdraft occurs when something is withdrawn in excess of what is in a current account. For financial systems, this can be funds in a bank account.

Let x be the balance when the account went into overdraft

To get back to a positive balance he deposited money at a steady rate of $31.97 per week.

Amount deposited per week = $31.97

Amount deposited 3 weeks = $95.91

Now amount in account after 3 weeks =x+95.91

We are given that After 3 weeks, he had $95.91 in the account.

So, x+95.91=47.3

x= 47.3-95.91

x= -48.61

Hence The balance when the account went into overdraft was -48.61

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The factored expression of 1/5c + 4/5 is 1/5(c + 4)

From the question, we have the following parameters that can be used in our computation:

1/5c + 4/5

From the above expression, we have the following highlights

In the above terms, we can see that the denominator of the terms is 5

When this denominator is removed, we have

Expression = c + 4

This means that

GCF =1/5

So, the factored expression is 1/5(c + 4)

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Answer:

Step-by-step explanation:

f −1 (x)= 3x−2

​

f, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis, equals, start fraction, x, minus, 2, divided by, 3, end fraction.

A) During the interval (0, 2) of the domain the water balloon's height is increasing.

B) During the interval (2, 4) of the domain the water balloon's height is staying the same.

C) During the interval (8, 10) of the domain, the water balloon's height is decreasing the fastest.

D) The height of the balloon will be zero since the height of the balloon has remained the same from the 10th interval.

What is an interval?

In mathematics, an interval is quantified in terms of numbers. Every number between two specific integers is considered to be an interval. Between those two values, this range encompasses all real numbers. Real numbers can be of any type you can imagine.

All the numbers between a pair of provided numbers are considered an interval. It is crucial to indicate if the start and end numbers are included. The Number Line, Inequalities, and Interval Notation are the three primary methods for displaying intervals.

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Answer:

∠ GFC = 70°

Step-by-step explanation:

∠ BFE and ∠ CBF are alternate angles and are congruent, that is

∠ BFE = 37°

∠ BFE , ∠ BFC and ∠ GFC lie on a straight line and sum to 180° , then

37° + 73° + ∠ GFC = 180°

110° + ∠ GFC = 180° ( subtract 110° from both sides )

∠ GFC = 70°

Answer: y = 10(x) + 56

Step-by-step explanation:

y=10(4) + 56

y = 40 + 56

y = 96

Answer:

1a. y = 10 x + 16

1b. 16

2a. y = 600x + 1500

2b. $8700

Step-by-step explanation:

1a. A linear model represents a relationship between two variables as a straight line. In this case, we want to represent the relationship between the number of hours a canoe is rented for and the total cost of the rental, including the deposit.

We can create a linear model by using the equation y = mx + b, where y is the total cost, x is the number of hours the canoe is rented for, m is the slope of the line (the rate at which the cost changes per hour), and b is the y-intercept (the total cost when x is 0).

Since the total cost includes a non-refundable deposit, we need to add this to the y-intercept. The deposit is not dependent on the number of hours the canoe is rented for, so it is not represented in the slope.

Based on the information given, the total cost is $56 when the canoe is rented for 4 hours, and the rental fee is $10 per hour. We can use these values to solve for the y-intercept and the slope:

y = mx + b

56 = (10) (4) + b

56 = 40 + b

b = 56 - 40

b = 16

So the linear model representing the relationship between the number of hours a canoe is rented for and the total cost of the rental, including the deposit, is: y = 10 x + 16

1b. We know that the total cost is $56 when the canoe is rented for 4 hours, and the rental fee is $10 per hour. We can use these values to solve for the y-intercept, which represents the non-refundable deposit:

y = (10) (4) + b

56 = 40 + b

b = 56 - 40

b = 16

So the non-refundable deposit is $16. This means that the total cost of the rental, including the deposit and the hourly fee, is $56.

2a. We can create a linear model by using the equation y = mx + b, where y is the total cost, x is the number of solar heaters produced, m is the slope of the line (the rate at which the cost changes per heater), and b is the y-intercept (the total cost when x is 0).

Based on the information given, it costs $7500 to produce 10 solar heaters, and it costs $13,500 to produce 20 solar heaters. We can use these values to solve for the y-intercept and the slope:

y = mx + b

7500 = m(10) + b

13500 = m(20) + b

Subtracting the second equation from the first equation gives:

-6000 = m(10) - m(20)

6000 = m(20) - m(10)

6000 = m(20 - 10)

6000 = m(10)

m = 6000/10

m = 600

Substituting this value for m in either of the original equations and solving for b gives:

7500 = (600)(10) + b

7500 = 6000 + b

b = 7500 - 6000

b = 1500

So the linear model representing the relationship between the number of solar heaters produced and the total cost of production is:

y = (600) x + 1500

According to this model, the total cost of producing 15 solar heaters would be $10,500.

2b. To find the total cost of producing 12 solar heaters, we can use the linear model that represents the relationship between the number of solar heaters produced and the total cost of production:

y = (600) x + 1500

Where y is the total cost, x is the number of solar heaters produced, m is the slope of the line (the rate at which the cost changes per heater), and b is the y-intercept (the total cost when x is 0).

To predict the total cost of producing 12 solar heaters, we can substitute 12 for x in the equation:

y = (600) (12) + 1500

y = 7200 + 1500

y = 8700

According to this model, the total cost of producing 12 solar heaters would be $8700.

Answer: for 35x+21 the answer is 7(5+3)

for the second one, the answer is 4x+2x+2

the 3rd one the answer is 5(6-3x)

for the fouth one the answer is 40x+50

for the fifth one the answer is 4x+4x+3

Step-by-step explanation:

Answer:8a<8b

Step-by-step explanation:

8a<8b

Answer:

0.62

Step-by-step explanation:

1.86 divided by 3 is 0.62

Kara erred when she answered the equation 2x + 6 = -8. Instead, she should have solved the equation 2x + 6 = 8 because it relates to the second situation (where -2x + 6 + 10 is smaller than 0).

Kara made a mistake when solving the equation |- 2x + 6 + 10| = 2. The correct steps to solve this equation are as follows:

First, we need to find the value of -2x + 6 + 10. To do this, we need to remove the absolute value bars by considering two cases:

a. If -2x + 6 + 10 is greater than or equal to 0, then the absolute value is equal to -2x + 6 + 10.

b. If -2x + 6 + 10 is less than 0, then the absolute value is equal to the negative of -2x + 6 + 10.

In the first case, we have -2x + 6 + 10 = 2. Solving this equation gives us x = -1.

In the second case, we have -(-2x + 6 + 10) = 2. Solving this equation gives us x = 7.

Therefore, the solution to the equation |- 2x + 6 + 10| = 2 is x = {7, -1}.

She made a mistake when she solved the equation 2x + 6 = -8. She should have solved the equation 2x + 6 = 8 instead, because this is the equation that corresponds to the second case (where -2x + 6 + 10 is less than 0).

As a result, Kara got the wrong value for x and included the incorrect solution {7, -1} in her final answer.

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Answer:

ok

Step-by-step explanation:

3x+1=4x-8= -6

x=-6

this is the x

I hope you have understand

Answer: 27.5, B

Step-by-step explanation:

      its a right angled trianalgle,

    ==> (30)^2= ((12)^2)+(x^2)

   ==> x^2= 900-144

==> x^2 = 765

==> x=(756)^(0.5)

==> x=27.49

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The required scale factor  for the given line segment is 2.

In math, a line segment  is limited by two unmistakable focuses on a line. Or on the other hand we can say a line portion is essential for the line that interfaces two focuses. A line has no endpoints and broadens endlessly in both the bearing yet a line fragment has two fixed or positive endpoints.

Scale factor is the number used to duplicate one item by to get another item that appears to be identical however is an alternate size. It makes a precise duplicate just bigger or more modest than the first. Scale Variable increases the image or item similarly as though you broadened or shrank it on a copier.

We have,

QS : QS' = 4 : 8 = QU : QU' = 5 : 10 = 1 : 2

Then the scale factor is of the dilation is 2 (magnification)

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Answer:

the answer to your question is 11

Step-by-step explanation:

1620÷180= 9

9+2=11

Answer:

72891

Step-by-step explanation:

150,000 is the base number

In the first year it will be the same, so it'll only count 13 years

the equation is: 150,000(0.946)^x

how:

150,000(100%-5.4%)^x

150,000(94.6%)^x

150,000(0.946)^x

*it's 100%-5.4% because that's that's remaining each year if it's decreasing by 5.4%. you would convert the percentage into decimals because it's decreasing by a percentage, not a whole number

150000(0.946)^13

*13 is the number of years, so it's x

72891.356467

The expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or (-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.

(-3 1/4d + 3/5) - (2 7/8d + 7/10)

⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10

⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10

⇒ (-13/4 - 23/8)d + 6/10 - 7/10

⇒ (-26/8 - 23/8)d - 1/10

⇒ -49/8 d - 1/10

Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

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To solve the given equation, t² - t = 12, by factoring, we will use (t + 3)(t - 4) = 0. The correct option is the first option

From the question, we are to determine how to solve the given equation by factoring

From the given information,

The given equation is

t² - t = 12

First, we will solve the equation by factoring

t² - t = 12

Transfer the constant to the other side

t² - t - 12 = 0

Factorize the expression

t² -4t + 3t - 12 = 0

t(t - 4) +3(t - 4) = 0

(t + 3)(t - 4) = 0

Then,

t + 3 = 0 OR t - 4 = 0

t = -3 OR t = 4

Hence, to solve the equation we will use (t + 3)(t - 4) = 0

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Using the distributive property we get 5y.

What is distributive property?

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical characteristics that is utilised the most. Commutative and associative qualities are the other two important features.

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

Using the distributive property

18y - 13y = (18 - 13)y

(18-13) y

Subtract the numbers: 18-13=5

=5 y

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Answer: 0.235

Step-by-step explanation:

To round up you need a number = 5 or > 5

So to round to 2 sig fig, the number will have to be 0.235