Mathematics College

If you answer first with the correct answers ill mark you brainlist:)

Answers

Answer 1

All the correct values are,

a)⇒ f (0) = - 1

b)⇒ f (1) = 1

c)⇒ f (-1) = - 3

d)⇒ f (a) = 2a - 1

e)⇒ g (0) = - 4

f)⇒ g (-2) = 0

g)⇒ g (3) = 5

h)⇒ g (t) = t² - 4

i)⇒ f (a+5) = 2a + 9

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The function are,

⇒ f (x) = 2x - 1

⇒ g (x) = x² - 4

Now, We can find all the values by substituting as;

a) f (0)

⇒ f (x) = 2x - 1

Put x = 0;

⇒ f (0) = 2×0 - 1

⇒ f (0) = - 1

b) f (1)

⇒ f (x) = 2x - 1

Put x = 1;

⇒ f (1) = 2×1 - 1

⇒ f (1) = 1

c) f (-1)

⇒ f (x) = 2x - 1

Put x = -1;

⇒ f (-1) = 2×-1 - 1

⇒ f (-1) = - 2 - 1

⇒ f (-1) = - 3

d) f (a)

⇒ f (x) = 2x - 1

Put x = a;

⇒ f (a) = 2×a - 1

⇒ f (a) = 2a - 1

e) g (0)

⇒ g (x) = x² - 4

Put x = 0;

⇒ g (0) = 0² - 4

⇒ g (0) = - 4

f) g (-2)

⇒ g (x) = x² - 4

Put x = -2;

⇒ g (-2) = -2² - 4

⇒ g (-2) = 4 - 4

⇒ g (-2) = 0

g) g (3)

⇒ g (x) = x² - 4

Put x = 3;

⇒ g (3) = 3² - 4

⇒ g (3) = 5

h) g (t)

⇒ g (x) = x² - 4

Put x = t;

⇒ g (t) = t² - 4

i) f (a+5)

⇒ f (x) = 2x - 1

Put x = a + 5;

⇒ f (a+5) = 2×(a + 5) - 1

⇒ f (a+5) = 2a + 10 - 1

⇒ f (a+5) = 2a + 9

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Related Questions

A quantity with an initial value of 4400 grows continuously at a rate of 0.5% per year. What is the value of the quantity after 46 years, to the nearest hundredth?

Answers

Answer:

To find the value of the quantity after 46 years, we can use the formula for continuous compound interest:

A = P(1 + r)^t

Where:

A = final amount

P = initial amount (4400)

r = rate of growth (0.5%)

t = number of years (46)

We need to convert the percentage rate to decimal form, so we divide the rate by 100

0.5/100 = 0.005

Now we can substitute the values into the formula:

A = 4400(1 + 0.005)^46

A = 4400(1.005)^46

A = 4400 * 1.294624

A = 5685.89

Therefore, the value of the quantity after 46 years is 5685.89, to the nearest hundredth.

Step-by-step explanation:

Jean joined a gym. It costs $60 per month and $2 per hour of boxing classes. Write an expression to represent the total cost of his gym, including the boxing classes for a month. Then determine how much it would cost him, if he spent 19.5 hours in gym class that month.

Answers

Answer:

y= 60+ 2x and if he spent 19.5 hours then he would pay $99 for that month

Step-by-step explanation:

$60 PER MONTH + $2 per hour of boxing classes

X represents the total hours he had the boxing classes

equation: y= 60+ 2x

if he spent 19.5 hours in boxing class

plug in 19.5 hours to X

99 = 60+ 2(19.5) = 60 + 39

Holly needs to buy some cloth to make masks. The following deals are available at various stores. Choose the best deal.

Answers

The best deal that Holly can choose, would be Store A.

How to find the best deal ?

The best deal that Holly can get from the various stores would be the deals that leads to a lower price per yard.

The store with the best deal would therefore be:

Store A :

= Cost of yards / Number of yards

= 16. 52 / 6

= $ 2.75 per yard

Store B :

= 13. 85 / 5

= $ 2.77

The cheaper store is therefore Store A.

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The deals are:

$16.52 per 6 yd

$13.85 per 5 yd

A car is purchased for $22,500. After each year, the resale value decreases by 30%. What will the resale value be after 4 years?
Use the calculator provided and round your answer to the nearest dollar.

Answers

On solving the provided question, exponents, resale value be $5339 after 4 years.

Exponents in math: what are they?

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) means 2 x 2 x 2 = 8. and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.

y = cn^x

y is the new price, c is the starting price, n is the rate of increase (or decrease), and x is the number of years. I won't bore you with the various names this exponent use has in calculus and economics.

In our instance:

By calculating how much of the price will remain, we can determine n.

1.00 — 0.25 = 0.75

f(x) = (22500)(0.75)^x

f(5) = (22500)(0.75)^5

=5339.35

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What is the Y value of the function of the table when the X value is zero

Answers

Answer:

Step-by-step explanation:

the difference between 76 and 52 is 24

and the difference between 52 and 28 is 24

the difference between 28 and 24 is 4

PLSSS HELP due at 9:00

Answers

Answer: 39.5

Step-by-step explanation: 47.5 + 93 = 140.5

180 - 140.5 = 39.5

I HOPE YOU TURN IT IN BEFORE THE DUE DATE !! GOOD LUCK!

Ms. Rios wants to store her son’s old clothes in a box. She believes the clothes will fit in a box that has a volume of 12 cubic feet³. What could be the dimensions of Ms. Rios' box?
Is it
6 ft x 4 ft x 2 ft
4 ft x 4 ft x 4 ft
4 ft x 2 ft x 2 ft
3 ft x 2 ft x 2 ft

Please Help

Answers

Answer:

the fourth one

Step-by-step explanation:

3x2x2 = 12

Answer:Last one,

Step-by-step explanation:

it equals 12, making it the only one that works.

In a basket there are 20 apples and 10 oranges. Find the percentage

Answers

Answer:

0.2% apples & 0.1 oranges resp

need help with questions 6-15 only with all work shown.

Answers

Consequently, the square root of the [tex]\sqrt{25}[/tex] is 5 and square root of [tex]\sqrt{4}[/tex] is 2 . The square root and nth root .

what is square root ?

The square root or nth root is represented by the radical sign. Square roots are a component of root expressions. There is a radical's radicand—a number or word that appears. Radicals like 7 and 2y+1 serve as examples. Additional terms that describe radicals include: Radical equations are those equations that include radicals. A "root expression" is the phrase used to describe the expression contained within the square root. To demonstrate radical representations, consider the numbers 2, 372, 2x+7, and 41p. The phrase "root expression" refers to the expression contained within the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.

given

square root of (a) [tex]\sqrt{25}[/tex] because 5 is the square root, square root of

as b ) square root of [tex]\sqrt{4}[/tex] s2's square root

Consequently, the square root of the [tex]\sqrt{25}[/tex] is 5 and square root of [tex]\sqrt{4}[/tex] is 2 .

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Determine f –1(x) if f of x is equal to the quantity x plus 1 end quantity over the quantity x minus 2 end quantity where x ≠ 2. (5 points)
f inverse of x is equal to the quantity x minus 1 end quantity over the quantity 2 times x plus 1 end quantity
f inverse of x is equal to the quantity x minus 2 end quantity over the quantity x plus 1 end quantity
f inverse of x is equal to the quantity x minus 1 end quantity over the quantity x plus 2 end quantity
f inverse of x is equal to the quantity 2 times x plus 1 end quantity over the quantity x minus 1 end quantity

Answers

The inverse of the function, f⁻¹(x), if f(x) = [tex]\dfrac{x + 1}{x - 2}[/tex] is the option;

f inverse of x is equal to the quantity 2 times x plus 1 end quantity over the quantity x minus 1 end quantity.

Mathematically, the inverse is; [tex]f^{-1}(x) = \dfrac{2\cdot x + 1}{x - 1}[/tex]

What is the inverse of a function?

The inverse of a function is another function that undoes the operations of another function, such that when the output of the function is the input of the inverse function, the input of the function is obtained.

The specified function is presented as follows;

f(x) = (x + 1)/(x - 2) and x ≠ 2

The inverse of the above function is found as follows;

Let y represent f(x);

y = (x + 1)/(x - 2)

x·y - 2·y = x + 1

x·y - x = 1 + 2·y

x·(y - 1) = 1 + 2·y

x = (1 + 2·y)/(y - 1) = (2·y + 1)/(y - 1)

Plugging in y = x, and x = f⁻¹(x), we get;

f⁻¹(x) = (2·x + 1)/(x - 1)

[tex]f^{-1}(x) = \dfrac{2\cdot x + 1}{x - 1}[/tex]

The correct option is therefore;

f inverse of x is equal to the quantity 2 times x plus 1 end quantity over the quantity x minus 1 end quantity

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please help me i would be happy if you helped me

Answers

The function to represent the arithmetic sequence is y = 0.17x + 0.71, and an envelop weighing 8 ounces cost $2.07

What is an equation?

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

An arithmetic sequence is in the form:

[tex]a_n=a_1+(n-1)d\\\\where\ a_1=first\ term,d=common\ difference[/tex]

Let y represent the price to send an envelop of x ounces. The arithmetic sequence is:

y = a₁ + (x - 1)d

Given that the first ounce is 88 cents($0.88), hence a₁ = 0.88. Eadh additional ounce is 17 cents (0.17), hence d = 0.17. Therefore:

y = 0.88 + (x - 1)(0.17)

y = 0.17x + 0.71

For a cost of $2.07:

2.07 = 0.17x + 0.71

x = 8 ounces

The function to represent the arithmetic sequence is y = 0.17x + 0.71

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I need help ASAP

Look at the image below

Answers

Answer:

2 only

Step-by-step explanation:

Answer:2 and 4

Step-by-step explanation:

if you divide 164 by all the numbers you only get whole numbers when you divide it by 2 and 4 not 3 and 6

Given a specific value of x and confidence level, which of the following statements is correct?
A. The confidence interval estimate of the expected value of y will be wider than the prediction interval.
B. The prediction interval of y for the given value of x can be calculated but the confidence interval estimate of the expected value of y cannot be calculated.
C. The confidence interval estimate of the expected value of y can be calculated but the prediction interval of y for the given value of x cannot be calculated.
D. The confidence interval estimate of the expected value of y will be narrower than the prediction interval.

Answers

A. The confidence interval estimate of the expected value of y will be wider than the prediction interval is correct.

A confidence interval gives an estimated range of a population parameter based on a sample. It is calculated by taking a sample of the population and using statistical methods to estimate the range in which the true population parameter would fall, with a certain level of confidence.

On the other hand, a prediction interval gives an estimated range of a future observation based on a sample. It is calculated by taking a sample of the population and using statistical methods to estimate the range in which a future observation would fall, with a certain level of confidence.

Since a prediction interval includes the uncertainty of an unobserved future value, it will typically be wider than the confidence interval estimate of the expected value of y which is based on the sample and the estimation of the population parameter.

Therefore Option A is the correct answer.

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Please, someone help

Answers

Answer: 10 in just squash, 7 in just onions, Intersection is 4, Union is 21

Step-by-step explanation: 10 are by themselves in the squash circle. 7 are alone in onion circle. Intersection is where the circles cross and Union is all of them.

Solve the following literal equation for y. -5x+8y=15

Answers

Here is the answer. In order to solve for y you have to move over the 5x. Then you divide and you get your answer.

Sara has a 30-gallon fish tank.The tank already has 24 gallons of water in it.Sara adds more water at a rate of 0.5 gallons per minute.

Answers

Solving a linear equation we can see that the tank will be filled in 12 minutes.

How long will take Sara to fill the tank?

We know that the fish tank has a volume of 30 gallons, and it already has 24 gallons of wate on it.

Sara is adding more water at a rate of 0.5 gallons per minute, so after x minutes, the volume of water on the tank is modeled by the linear equation:

V(x) = 24gal + 0.5gal*x

The tank will be full when the volume is equal to 30 gallons, then we can solve the equation:

30 gal = 24 gal + 0.5gal*x

30 gal - 24gal = 0.5gal*x

6 gal = 0.5gal*x

6gal/0.5gal = x

12 = x

The tank will be full after 12 minutes.

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Determine if the scenario involves mutually exclusive events.

A box of chocolates contains five milk chocolates, five dark chocolates, and three
white chocolates. You randomly select a chocolate. It is a milk chocolate or a dark chocolate.
A) Not mutually exclusive
B) Mutually exclusive

Answers

The given question where we randomly select a chocolate. It is a milk chocolate or dark chocolate is a mutually exclusive chocolate

How do you calculate probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. Probability is a measure of how likely something is to occur. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur.

In the given question

we see

Selecting a milk chocolate or dark chocolate is mutually exclusive event as they are not related to each other

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Suppose that for a graduating class of seniors at a local high school, the average GPA is 3.21. If a sampling distribution of size n = 20 is created from this population of seniors, what would be the expected mean of the sampling distribution?

0.72

1.67

0.161

3.21

Answers

Suppose that for a graduating class of seniors at a local high school, the average GPA is 3.21. The expected mean of the sampling distribution would be 3.21.

What is the average GPA?

Generally, This is because the sampling distribution of the mean is a probability distribution of the means of all possible samples of the same size from the same population.

The mean of the sampling distribution is equal to the population mean, in this case, 3.21.

Answers

Haley lives with her sister Emily, and together they care for their parents' home, who have been traveling the world for the past two years.

What does Haley do as a wife in Stardew Valley?Haley moves in with you after the wedding (obviously) and spends most of her time around the house and farm. She could be. On Mondays, though, she does have unusual schedules. Due to the fact that Haley comes across as rude when first spoken to, she is one of the least liked NPCs in Stardew Valley. But as you get to know her better and she starts to show you her softer side, she'll become much more endearing. Haley's favorite gifts can be harder to find early on, making her not the most straightforward marriage candidate to woo. However, she is worth the effort because she is a kind and caring person, just like the others.

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Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42? l'll give brainiest

Answers

Answer: x3 +y3 20

Step-by-step explanation:

jim's auto shop will tow your vehicle for $15 plus $.50 per mile. dannys wrecker serices charges $ 10 for the tow and $.075per mile

Answers

Answer:

Step-by-step explanation:

The flat cost of Jim's Auto Shop is $15 dollars.

The flat cost of Danny's Wrecker Services is $10.

The per-mile cost for Jim's Auto Shop is .50

The per-mile cost for Danny's Wrecker Services is .75

Let's say that your vehicle needs to be towed for x number of miles.

The equation for the total cost would be:

flat cost x (per-mile cost × number of miles)

_____________________________________________________

Just use the above equation and substitute it with the information given to you in your question. Hopefully, this helps. If you need further help, please elaborate on your question and comment.

The total cost would be equal to ;75 dolar.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that the flat cost of Jim's Auto Shop is $15 dollars.

The flat cost of Danny's Wrecker Services = $10.

The per-mile cost for Jim's Auto Shop = 0.50

The per-mile cost for Danny's Wrecker Services = 0.75

Let's say that vehicle needs to be towed for x number of miles.

The equation for the total cost would be as;

flat cost x (per-mile cost × number of miles)

10 x 0.50 x 15

= 75

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Listed below are the lead concentrations (in mg/g) measured in different samples of a medicine. What do the results suggest about the safety of this medicine? What do the decimal values of the listed amounts suggest about the precision of themeasurements?
O 18.5
O 14.5
O 20.5
O 7.5
O 18
O 8.5
O 8
O 9.5
O 15

Answers

The results suggest that the lead concentrations in the medicine samples are relatively low, as all of the values are below 20 mg/g. However, it would be necessary to compare these values to a standard, such as the acceptable limit of lead in medicine set by a regulatory body, in order to determine if the medicine is considered safe.

The decimal values of the listed amounts suggest that the measurements were precise, as they are all reported to one decimal place. It means that the measurement was done with a precision of 0.1. In addition to that, the measurements are consistent and close to each other, which also indicates that the measurements were precise.

It's important to keep in mind that precision and accuracy are different things. Precision refers to the degree of reproducibility of a measurement, while accuracy refers to the degree of closeness of a measurement to the true value. In this case, the measurements are precise but it's not specified if the measurements are accurate or not.

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which of the following could be an example of a function with a domain [a, infinity) and a range (-infinity, b] where a>0 and b>0

Answers

f(x) = √x ⇒ f(x) = -√(x -a) +b . . . . . . matches choice B

What is function ?

Function is the relationship between the input or domain and the output. A relation is a function if and only if there exists one value in the range for every domain value. A function is written as f x , where x is the input value. The general form of a function is y = f x

Function transformations

To move the domain from [0, ∞) to [a, ∞) requires the function be translated 'a' units to the right. That transformation is accomplished by replacing x with (x-a) in the function definition.

To move the range from [0, ∞) to [b, ∞) requires the function be translated upward by 'b' units. This is accomplished by adding 'b' to every function value.

Therefore, the range of the function will be (-∞,b] i.e. y ≤ b.

Hence, the required function is f(x) = √x ⇒ f(x) = - √(x -a) +b . . . . . . matches choice B

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Prove that if parallel lines are crossed by a transversal, then the alternate interior angles are congruent. That is, use rigid transformations to map ∠CFG onto ∠BCF. Explain.

Answers

Alternate interior angles are congruent if parallel lines are crossed by a transversal.

What is congruent geometry?

In congruent geometry, the shapes that are so identical. can be superimposed on themselves.

Here,
A figure has been shown below,
Where there is 2 parallel line intersected by a transversal line.
The measure of the alternate angle [besides interior and exterior angle], their measure are equal to corresponding angles as well as with alternate angles. As shown in the figure.

Thus, alternate interior angles are congruent if parallel lines are crossed by a transversal.

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Use perfect squares to find two consecutive integers to complete each inequality.
1) ? < √13 < ?
2) ? < √78 < ?
3) ? <√181 < ?
(Please hurry)

Answers

Following are the required perfect squares of each of the following.

A square number, sometimes known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, 9 is a square number since it equals 32 and is represented by the symbols 3×3.

Use perfect squares to find two consecutive integers to complete each inequality -

1. ? < √13 < ?

⇒ 9 < 13 < 16

⇒ 3 < √13 < 4

2. ? < √78 < ?

⇒ 64 < 78 < 81

⇒ 8 < √78 < 9

3. ? <√181 < ?

⇒ 169 < 181 < 196

⇒ 13 < √181 < 14

Comparing values -

π/2 < √34 5/6 √22 ⇒ 29/6 > √22-√29 = -5 2/5

Arranging from least to greatest -

9/2 < √10 < 22/7 < 5/3

5 2/5 < 5.3 < 3√3 < √25

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Zahara rides with her to her grandmother's house. They travel 159 miles in 3 hours. Her uncle Jorge drives there separately from his home.
a. At what speed does Zahara's dad drive in miles per hour
b. Jorge's trip takes the same time as Zahara's, but he travels a shorter distance. Does Jorge drive faster or slower than Zahara's dada

Answers

Answer: a. To find the speed at which Zahara's dad drives, we need to divide the distance traveled by the time it took to travel that distance. The formula is: speed = distance/time.

So, speed = 159 miles / 3 hours = 53 miles per hour

b. Since Zahara's trip and Jorge's trip took the same amount of time, the only way that Jorge could have traveled a shorter distance than Zahara is if he drove slower. So, it can be inferred that Jorge drives slower than Zahara's dad.

Step-by-step explanation:

f(x) = 2x² - 2x - 12
g(x)=x+2
What is the value of f(x),
g(x)
A. x-6
B. x-3
OC. 2x-6
OD. 2x+4

Answers

Answer:

Step-by-step explanation:

Answer:b

Step-by-step explanation:

carlos borrowed 26,000 for 5 years at an APR 5.25% what will his monthly payment be?

Answers

Answer:

$568.75.

Step-by-step explanation:

Please help I don’t understand!

Answers

From the curve in the graph the function values are

h(3) = 2

h(5) = 6

h(6) = 5

What is parabolic curve?

A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line.

The quadratic equation represents a parabolic curve on a graph

Examining the graph the function values can be deduced noting that the values 3 5 6 and in h(3), h(5) and h(6) are points in the x axis or the domain

The function values are points on the y axis corresponding to tracing the x values to the curve

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Theresa is an article writer who is paid 3 cents per word that she writes. If it takes her 2 hours to write a 3,000-word article, what is her rate of payment dollars per hour?

A. $20/hr
B. $30/hr
C. $45hr
D. $50/hr

Answers

As Theresa write a 3,000-word article in 2 hours, her rate of payment dollars per hour is $45 per hour. The Option C is correct.

What does rate of payment mean?

The payment rate relates to the amount of money paid to someone or the act of paying this money. The rate of pay of an employee is the amount of money they are paid over a period of time. Some employees who work more than 40 hours per week may be eligible for $30per hour.

Data

She is paid 3 cents per word

For 3,000-word article, she will be paid:

= 3,000 * 3

= 9,000 cent or $90.

Because it will take her 2 hours to write 3,000-word article, then, her her rate of payment dollars per hour equals to $45 ($90 / 2 hours).