Mathematics High School

Given the function f(x) = x - 4, find f(-2).

Answers

Answer 1

Answer: f(-2) = -6

Step-by-step explanation: f(-2) = -2 -4

f(-2) = -6

Related Questions

Find the distance between the two points in simplest radical form.

(−5,−4) and (−2,−6)

Answers

Answer: $\sqrt{13}$ units

Work Shown:

$(x_1,y_1) = (-5,-4) \text{ and } (x_2, y_2) = (-2,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-5-(-2))^2 + (-4-(-6))^2}\\\\d = \sqrt{(-5+2)^2 + (-4+6)^2}\\\\d = \sqrt{(-3)^2 + (2)^2}\\\\d = \sqrt{9 + 4}\\\\d = \sqrt{13}\\\\d \approx 3.6056\\\\$

I used the distance formula.

A slightly alternate method is to form a right triangle and use the pythagorean theorem. The hypotenuse will have the endpoints (-5,-4) and (-2,-6).

Question 8 of 10
If f(x) = 3x - 2 and g(x) = 2x + 1, find (f- g)(x).
OA. x-3
B. 5x - 1
OC. 5x-3
OD. 3-x
SUB

Answers

Answer:

Step-by-step explanation:

when adding or subtracting (or multiplying or dividing) functions, we do this by applying the same operation to the functional expressions.

(f-g)(x) = (3x - 2) - (2x + 1) = 3x - 2 - 2x - 1 = x - 3

so, A is the correct answer.

Answer:

a) x - 3

Step-by-step explanation:

Given:

a) (f)(x) = 3x - 2

b) (g)(x) = 2x + 1

Find (f - g)(x):

(f - g)(x) = f(x) - g(x)

(f - g)(x) = (3x - 2) - (2x + 1) [subtract]

(f - g)(x) = 3x - 2x - 2 - 1 [combine like terms]

(f - g)(x) = x - 3

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The functions f(x) and g(x) are shown on the graph.
f(x) = |x|
What is g(x)?
10
107
-10%
g(x) = ?
f(x) = |x|

Answers

g(x) is a translation to the left of 5 units, this is written as:

g(x) = f(x + 5)

How to find the rule for function g(x)?

We can see that g(x) is a transformation of the parent absolute value function f(x) = |x|

We can see that the slopes are the same ones (in the graphs) then we only have a translation, we can see that the graph of g(x) is 5 units at the left of f(x), then we have a horizontal translation of 5 units to the left.

This is written as:

g(x) = f(x + 5)

Replacing f(x) by the actual function we will get:

g(x) = |x + 5|

That is the rule for g(x).

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If an investment of $8,000 in 1965 had a value of $49,000 in 1990, how many years did it take for the investment to double? (Round to the nearest tenth of a year)

Answers

Answer:

it took 5 years

Step-by-step explanation:

1965,1970,1975,1980,1985,1990

Hamburgers can be purchased from two different popular fast food restaurants. restaurant a sells 11 burgers for $14.19, and restaurant b sells 2 burgers for $2.64. which restaurant offers the best value per hamburger, and what is its amount? restaurant a for $1.29 restaurant b for $1.29 restaurant a for $1.32 restaurant b for $1.32

Answers

Restaurant A offers the best value as one hamburger is $1.29

How to calculate the Restaurant with the best value ?

The first step is to calculate the price of one burger in restaurant A

11= 14.19

1= x

cross multiply

11x= 14.19

x= 14.19/11

x= 1.29

The next step is to calculate the price on one burger in restaurant B

2= 2.64

1= x

Cross multiply

2x= 2.64

x= 2.64/2

x= 1.32

Hence the price of the hamburger at Restaurant A is $1.29 and the price at Restaurant B is $1.32.

Answers

The number of paychecks Jalen will have to save until he can purchase the laptop is 6

How many paychecks will Jalen have to save until he can purchase the laptop?

Define your variable

To do this, we use the following variables

x represents the number of paychecksy represents the cost of the laptop

Set up an equation, and solve it.

In (a), we have:

x represents the number of paychecksy represents the cost of the laptop

Using the above variables, the equation is:

y = 200 + 50x

The cost of the laptop is $500.

So, we have:

200 + 50x = 500

Evaluate the like terms

50x = 300

Divide by 50

x = 6

Hence, the number of paychecks Jalen will have to save until he can purchase the laptop is 6

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hi please HELP ME I really need it

Answers

Answer:

? = 14

Step-by-step explanation:

let us say that ? = x

7^x * 7^5^4 = 7^34

When you have a power to a power you multiply

7^x * 7^20 = 7^34

when you multiply common bases you add the power. since all the bases aer the same just look at the power

7^34-20 = 7^x

7^14 = 7^x

CAN SOMEONE HELP ME PLEASEEEEEEE

Answers

Answer:

Step-by-step explanation:

Because all of the other sides are equal so it makes that equal

Show that there exist a rational number a and an irrational number b such that a^b is irrational.

Answers

Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

7) The value of a piece of office equipment is changing at a rate of $175 per year
How long will it take for the change in value to be $1,050?

Answers

Answer:

6 days

Step-by-step explanation:

1050 divided by 175 is 6

Answer:

6 times 175 equals 1050

Bern is flying a kite directly over his friend Frank. Bern lets out string which makes an angle of 28°
with the ground. If the kite is 175 feet above Frank, how far are Bern and Frank?
Help ASAP!!

Answers

orayt so 28 degree and 175 feet is about...the fox jumps into the lazy dog and say "c'mon barbie let's go party! ah ah ah yeah"....but i dont know the answer as well so thank you.

Answer:

Approximately $329\; \rm ft$, assuming that the ground between Bern and Frank is level.

Step-by-step explanation:

Refer to the diagram attached.

The kite is right above Frank. Therefore, the imaginary line segment (the dashed line segment in the diagram) would form a right angle with the ground under Frank. Bern, Frank, and the Kite would be the three vertices of a right triangle.

The question states that from the perspective of Bern, the angle of elevation of the kite is $28^\circ$. In this right triangle, the side opposite to this angle would be the imaginary line segment between Frank and the kite over him. The question states that the length of this imaginary line segment is $175\; \rm ft$.

The question is asking for the length of the line segment between Bern and Frank. In the right triangle pictured in this diagram, that line segment would be the side adjacent to the $28^\circ$ angle.

The cotangent of $28^\circ$ would be the ratio between the length of these two sides:

$\displaystyle \cot (28^\circ) = \frac{\text{adjacent}}{\text{opposite}}$.

$\begin{aligned}\text{adjacent} &= \text{opposite} \cdot \cot(28^\circ) \\ &= (175\; \rm ft) \cdot \cot(28^\circ) \approx 329\; \rm ft\end{aligned}$.

Bern is flying a kite directly over his friend Frank. Bern lets out string which makes an angle of 28with

You have been commissioned to perform a study of the relationship between class size and academic performance in elementary school, and you have a chance to take a survey in either one of two comparable cities. The hypothesis is that kids in smaller classes do better. In the first city, you will have permission to gather a random sample of 100 pupils from a wide variety of class sizes, ranging from only 7 all the way up to 45. In the second city you would be able to gather a much larger sample, but the range in class size from which you would be able to gather observations would be much narrower. Are there tradeoffs involved in deciding which city to use? Or is the decision straightforward? Explain

Answers

The decision between the two cities involves tradeoffs: the first city offers a wide range of class sizes but a smaller sample, while the second city has a larger sample but a narrower class size range.

The decision of which city to choose for the study involves tradeoffs. The first city allows for a wide range of class sizes, providing a comprehensive analysis of the relationship between class size and academic performance. However, the smaller sample size limits generalizability.

The second city offers a larger sample size, increasing generalizability, but with a narrower range of class sizes. Researchers should consider their specific research objectives, available resources, and constraints. If the goal is to assess the impact of extreme variations in class size, the first city is suitable. If obtaining highly generalizable results is paramount, the second city, despite the narrower range, should be chosen.

Therefore, The decision between the two cities involves tradeoffs: the first city offers a wide range of class sizes but a smaller sample, while the second city has a larger sample but a narrower class size range.

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Solve the system of equations using the substitution method. Show your work and be sure to include the solution to the system.

Answers

Answer:

Is that simultaneous equation

You can ask if something is not clear or you don't understand

The solution of system of equations y=x-1 , 2x+y=8 are x=3 and y=2 which we get by substitution method.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The given system of equations are

y=x-1 ...(1)

2x+y=8...(2)

By using substitution method we solve the value of x and y.

Substitute y value in equation (2)

2x+x-1=8

Combine the like terms

3x-1=8

Add 1 on both sides

3x=9

Divide both sides by 3

x=3

Now plug in x value in y equation.

y=3-1

y=2

Hence, the solution of system of equations y=x-1 , 2x+y=8 are x=3 and y=2 which we get by substitution method.

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What is an equation of the line that passes through the points (7,-3) and
(-8,-3)?

Answers

Answer:

Step-by-step explanation:

m= [ -3-(-3)] ÷ [-8-7} = 0

Therefore, the slope of the line is 0.

Now use the slope and either of the two points to find the y-intercept.

y= mx+b

-3= (0)(7)+b

b=-3

Write the equation in slope intercept form as:

y= mx+b

y= (0)x-3

y= -3

Hence, the equation of the line is y= -3.

If integral from negative 2 to 3 of the quantity 2 times f of x plus 2 end quantity dx equals 18 and integral from 1 to negative 2 of f of x dx equals negative 10 comma then integral from 1 to 3 of f of x dx is equal to which of the following? a 4b 0c −6d −8

Answers

For an integral value of $I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ $ and

$I_2 = \int_{ 1}^{-2} f(x)dx = -10 \\ $, the computed value of integral $\int_{ 1}^{3} f(x)dx$ is equals to the -6. So, option(c) is right one.

In mathematics, an integral is the continuous process of a sum, which is used to calculate areas, volumes, and their properties. Integration is a way to sum up parts to the whole.

We have an integral say $I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ $

$I_2 = \int_{ 1}^{-2} f(x)dx = 10 \\ $

We have to determine value of $\int_{ 1}^{3} f(x)dx$.

Using the properties of integral, consider integral $I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18\\ $

from distribution property, $I_1 = \int_{ -2}^{3} 2f(x) dx + \int_{ -2}^{3} 2 dx = 18 \\ $

$2 \int_{ -2}^{3} f(x) dx + [ 2x]_{ -2}^{3} = 18$

$2 \int_{ -2}^{3} f(x) dx + 10 = 18$

$2 \int_{ -2}^{3} f(x) dx = 8$

$\int_{ -2}^{3} f(x) dx = 4$

Now, consider the required integral and rewrite, $\int_{ 1}^{3} f(x)dx = \int_{ 1}^{-2} f(x)dx + \int_{ -2}^{3} f(x)dx \\ $

Substitute all known values of integrals

$\int_{ 1}^{3} f(x)dx = 10 + 4 = 14 $

Hence, required value is 14.

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for the following exercise, consider the following scenario: a town has an intial population of 50000 . it grows at a constant rate of 5000 per year. find the linear function that model's the town's population p as a function of the year, t , where t is the number of years since the model began.

Answers

The required function is P(t)=50000 + 5000t.

In this problem we need to form the function of the population in a town.

Here it is given that the initial population of the town is 50000.

the rate at which the population increases is 5000 per year.

So, the increase for the first year will be 5000. And the population will be 55000.

Then again for the next year the growth will be 5000 and the population will be 50000 + (5000×2)

= 60000

So we can see clearly that the population is varying with time and we can write the function as P(t)=50000 + 5000t where t is the time in years.

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Under what circumstances is a score that is located 5 points above the mean a central value, relatively close to the mean?

a. When the population standard deviation is much less than 5

b. When the population mean is much less than 5

c. When the population mean is much greater than 5

d. When the population standard deviation is much greater than 5

Answers

The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

What is the standard deviation?

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

The circumstance is a score that is 5 points above the mean considered a central value.

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

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Use the standard potential values from the data sheet to calculate the equilibrium constant for the reaction of solid tin with copper(II) ion:
Sn(s) + 2 Cu2+ ⇄ Sn2+(aq) + 2 Cu+(aq)
A. 5.8 x 10⁹
B. 1.0
C. 2.0 x 10⁻¹⁰
D. 1.3
E. 0.29

Answers

The value of the equilibrium constant from the calculation is 5.8 x 10⁹

What is electrode potential?

The value of the equilibrium constant can be obtained from the standard electrode potential of the cell as we can see in the solution that have been shown below us here.

We know that;

E cell = E cathode - E anode

Thus we have that;

E cell = 0.15 - (-0.14)

Ecell = 0.29 V

Then;

Ecell = 0.0592/nlog K

Where n = 2 and Ecell = 0.29 V

We have that;

log K = Ecell * n/0.0592

K = Antilog (Ecell * n/0.0592)

K = Antilog(0.29 * 2/0.0592)

K = 5.8 x 10⁹

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PLEASE SHOW WORK!!!!!!!!!

Answers

The fifth term of the given sequence is: a₅ = 63

How to find the nth term of a sequence?

We are told the formula for the nth term of the sequence is given as:

aₙ = aₙ₋₁ + 6(n - 1) for n ≥ 2

We are given:

a₁ = 3

a₂ = 9

a₃ = 21

a₄ = 39

Thus:

a₅ = a₅₋₁ + 6(5 - 1)

a₅ = a₄ + (6 * 4)

a₅ = 39 + 24

a₅ = 63

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suppose that your younger sister is applying for entrance to college and has taken the sat. she scored at the 77th percentile on the verbal section of the test and at the 94th percentile on the math section of the test. because you have been studying statistics, she asks you for an interpretation of these values. what would you tell her?

Answers

I would tell her that out of all the people who took the verbal section, 23% scored higher than she did and 77% scored at or below her score. For the math section, 94% of those who took the exam scored at or below her score and 6% scored higher than she did.

Here's the complete question:

Suppose that your younger sister is applying for entrance to college and has taken the sat. she scored at the 77th percentile on the verbal section of the test and at the 94th percentile on the math section of the test. because you have been studying statistics, she asks you for an interpretation of these values. what would you tell her?

I would tell her that out of all the people who took the verbal section, ___% scored higher than she did and ___ % scored at or below her score. For the math section, ___ % of those who took the exam scored at or below her score and ____ % scored higher than she did.

For the Verbal section: 100 - 77 = 23

For the Maths section: 100 - 94 = 6

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What is infinite algebra 1?

Answers

Infinite Algebra 1 is a software program developed by the company Kuta Software that provides an online resource for teaching and learning algebra 1.

It offers a comprehensive collection of algebra 1 problems and exercises that cover a wide range of topics such as linear equations, systems of equations, inequalities, polynomials, factoring, and graphing.

The program includes features such as an interactive equation editor, step-by-step solutions, and the ability to generate customized worksheets and assessments.

It is designed to provide students with a self-paced and adaptive learning experience that allows them to practice and reinforce their understanding of algebraic concepts. Infinite Algebra 1 is widely used in schools and educational institutions as a tool for teaching and practicing algebra 1.

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please help, will mark brainliest!! thanks

Answers

Answer:

39.43 for each dog

Step-by-step explanation:

d = 2c (given)

164 c + 23 d = 4140 sub in the above equation for d

164 c + 23 (2c) = 4140

210c = 4140

c =19.71

d = 2c = 39.43

If f(x)= x^2-25 and g(x)=x-5, what is the domain of (f/g)(x)?

Answers

Answer:

B) all real values of x except x=5

Step-by-step explanation:

If $f(x)=x^2-25$ and $g(x)=x-5$, then $\bigr(\frac{f}{g}\bigr)(x)=\frac{f(x)}{g(x)}=\frac{x^2-25}{x-5}=\frac{(x-5)(x+5)}{(x-5)}$.

Given that $x-5$ exists in both the numerator and denominator, this creates a hole on the graph of the function where $x=5$ since $5-5=0$all real values of x except x=5 is correct.

Review the attached graph for more information

The original yield of the recipe is 8 servings, you need to serve 32. Using the factor method what would your conversion fa 1cup cake flour 3/4 cup sugar 2tablespoons sugar 12large egg whites, MUST be room temperature 1 teaspoons cream of tartar 1/4teaspoon salt 3/4 cup sugar 1 teaspoons vanilla 1/2 teaspoon almond extract Conversion Factor = 4; 1 teaspoon of salt Conversion Factor= 25; 0625 teaspoon of salt Conversion Factor 25; 1 teaspoon of salt Conversion Factor= 4:1 tablespoon of salt

Answers

Please note that this is a proportional adjustment based on the serving size, and you may need to consider other factors such as cooking time and pan size when scaling up a recipe.

To convert the recipe to serve 32 servings instead of 8, we need to determine the conversion factor and apply it to each ingredient. The conversion factor is the ratio of the desired serving size to the original serving size.

Let's calculate the conversion factors for each ingredient:

1 cup cake flour: