Given the function f , evaluate f(−1) , f(0) , f(2) , and f(4) .



f(x)={x2−14+|x−6|if x<2if x≥2

37.68 cm³ is the volume of the given figure.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

We need to find the volume of the cone which has radius 3 cm and slant height 5 cm

Volume of cone=1/3πr²√S²-r²

S=5 cm and r is 3 cm

Substitute S and r value in formula

=1/3×3.14×(3)²√5²-3²

=1/3×3.14×9√25-9

=1/3×3.14×9√16

=1/3×3.14×9×4

=37.68 cm³

Hence, 37.68 cm³ is the volume of the given figure.

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ1

Brad needs to rent the scaffolding for 6 hours for the cost to be the same from each rental company.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Handy Rentals

C = $15 + $12.50h ---------- 1

EZ Rental Company

$7.50 + $13.75h ------------ 2

where h is number of hours

Equating both equations

$15 + $12.50h = $7.50 + $13.75h

$15 - $7.50 = $13.75h - $12.50h

$7.5 = $1.25h

h = $7.5/$1.25

h = 6 hours

Learn more about linear equations here: https://brainly.com/question/12788590

#SPJ1

The line 5 = 3X - Y or3X minus Y equals five is the same line of  Y equals 3X -5. The correct option is A.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given line:

Y equals 3X -5

Simplifying,

Y = 3X - 5

This is a linear equation.

To find the same line:

Y = 3X - 5

Taking constant to one side and variable to one side,

That means,

5 = 3X - Y

3X minus Y equals five

Therefore, 3X minus Y equals five or 5 = 3X - Y is the required line.

To learn more about the linear equation;

https://brainly.com/question/29739212

#SPJ1

By function composition, f(x) and g(x) are inverse functions

A function is a relationship between inputs where each input is related to exactly one output.

f(x)= ∛(x-1) and g(x)=x³+1

To confirm the inverse relationship using composition.

If f(g(x)) = g(f(x)) then they are inverse functions

Let's confirm:

f(g(x)) = f(∛(x³+1))

         = ( ∛((x³+1)-1 )

        = ∛(x³)

       = x

g(x)=x³+1

g(f(x)) = g(∛(x-1) )

        = (∛(x-1))³ + 1

        = x-1+1

        = x

Since  f(g(x)) = g(f(x)) then they are inverse functions

Learn more about function composition on:

brainly.com/question/29363352

#SPJ1

Answer:

4

Step-by-step explanation:

To find f(-1), we can plug -1 into the equation in place of x and simplify:

f(-1) = 4(-1)² + 9(-1) + 9

f(-1) = 4 + (-9) + 9

f(-1) = 4 - 9 + 9

f(-1) = 4 - 0

f(-1) = 4

Therefore, f(-1) = 4.

There are approximately 13.38 ounces of chips in the bag.

What is division?

Division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. It is the inverse operation of multiplication, and it is used to find out how many times one number is contained within another number.

To find out how many ounces of chips are in the bag, you can use the formula:

cost of bag / cost per ounce = number of ounces

In this case, you know that the cost of the bag is $3.91 and the cost per ounce of chips is 29.5 cents per ounce.

First, you need to convert the cost per ounce from cents to dollars. 29.5 cents is equal to 0.295 dollars (29.5 cents / 100 cents = 0.295 dollars)

So, you can substitute these values into the formula:

3.91 / 0.295 = 13.38

Hence, there are approximately 13.38 ounces of chips in the bag.

To learn more about division, Visit

https://brainly.com/question/25289437

#SPJ1

The integral of f(x) on the interval [0, 6] is equal to 8.

Here we have the graph of f(x), and we want to find the integral:

[tex]\int\limits^6_0 {f(x)} \, dx[/tex]

Remember that the integral is the area under the curve, so we only need to find the areas of the "blocks" on the image.

Betwen 0 and 2 we can see that f(x) = 2, there the area is:

A = 2*(2 - 0) = 4

Between 2 and 4 we have f(x) = -3, then:

A' = -3*(4 - 2) = -3*2 = -6

And between 4 and 6 we have f(x) = 5, then:

A'' = 5*(6 -4) = 5*2 = 10

Then the integral is:

[tex]\int\limits^6_0 {f(x)} \, dx = 4 - 6 + 10 = 8[/tex]

Learn more about integrals by reading:

https://brainly.com/question/22008756

#SPJ1

Answer:

----------------------------------------

Identify two points on the line:

Find the slope using these two points:

The answer is NO.

Answer:

1,449

Step-by-step explanation:

Answer:

1449

Step-by-step explanation:

when you multiply equations like this you have to cross multiply. you go from right to left.

7x7=49

you would carry your 4 over the 0.

7x0=0 plus the 4 you carried so 4.

last you would do 7x2=14

your answer is 1,449

[tex]A=e^2[/tex], where e is the side length of the square and A is the area of the square.

Answer:

The answer is D, y=0.25t + 9.5

Step-by-step explanation:

Since the crew has been painting at a rate of 0.25 per hour continuosly, it will be 0.25 times the number of hours (t), plus the already completed road, which is 9.5.

Answer: 8

Step-by-step explanation: make it x = 1/3 times 24.

Also, try inserting 8 in the blank.

Answer: LCM(6,8)

Step-by-step explanation: Each of six slices of the first pasta has the area 1%2F6 of the entire pan.

Each of eight slices of the second pasta has the area 1%2F8 of the original pan.

David will cut each 1%2F6 in 4 equal pieces to get 1%2F24.

he also will cut each 1%2F8 in 3 equal pieces to get 1%2F24.

Then he will meet his goal.

Notice that the number 24 is the Less Common Multiple of the numbers 6 and 8: 24 = LCM(6,8).

Answer:

There would be six pieces in each pan.

Step-by-step explanation:

1. To make the number of pieces in each pan equal, the total number must be the same.

2. 8 pieces from the first pan + 6 pieces from the second pan = 14 pieces.

3. Divide 14 by 2 to get the same number of pieces in each pan:

14/2 = 7

4. Round down 7 to get six pieces in each pan.

Answer:

(A)

Step-by-step explanation:

SOS: Here is The correct answer, Brainly would not allow me to type it, so I took a screenshot instead. Hope this helps!! :D

The correct expression to represent this situation through inequality is "p + n ≥ 17"

In mathematics, inequalities are mathematical expressions that compare two values without using the symbol = (equal). Instead, in inequalities, one value is greater than, less than, etc. Due to this, the most common symbols used to write an inequality are:

< = This means less than

> = This means greater than

≥ = This means equal or greater than

≤ = This means equal or less than

Considering, the amoung of pennies and nickels is minimum 17, the correct symbol to use is ≥, which means the amoung of coins is either 17 or more than 70. Moreover, the letters p and n can be used to represent the pennies and nickels. Based on this, the correct expression is:

p + n ≥ 17

Learn more about inequality in: https://brainly.com/question/20383699

#SPJ1

Events A and B are dependent, because P(A)≠P(B|A). The correct option is A.

From the information, the experiment consists of rolling a standard six-sided die once. Event A is "rolling a 5 and event B is "rolling an odd number."

Events A and B are dependent because the outcome of event A (rolling a 5) affects the probability of event B (rolling an odd number). The probability of rolling a 5 is 1/6, while the probability of rolling an odd number given that you have already rolled a 5 is 0. The probability of rolling an odd number is 1/2, and thus P(A) ≠ P(B|A)

In simple terms, Events A and B are dependent because outcome of event A affects the probability of event B happening.

Learn more about dependent events on'

https://brainly.com/question/14106505

#SPJ1

The graph that shows the solution set of the inequality t > 4 or t < -1 is given by the image presented at the end of the answer.

The inequality for this problem is defined as follows:

t > 4 or t < -1.

It is a compound inequality, as it has two conditions.

The first condition is given as follows:

t > 4.

Which means that numbers to the right of t = 4 are graphed, with an open circle representing an open interval.

The second condition is given as follows:

t < -1.

Which means that numbers to the left of t = -1 are graphed, with an open circle also representing an open interval.

The open intervals are because none of the conditions contain the equal symbol.

More can be learned about inequalities at https://brainly.com/question/9290436

#SPJ1

Therefore , When the side lengths are (2x-1) and (4x + 5), the smartboard's perimeter is expression is  as 12x2 - 8.

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

Here,

Given :

smartboard of side length is ( 2x-1) and ( 4x + 5 )

perimeter of small board = 2( l+ b)

2( 2x-1 + 4x + 5  )

2( 6x - 4)

When the side lengths are (2x-1) and (4x + 5), the smartboard's perimeter is expressed as 12x2 - 8.

The diagram can be imagined as a big whiteboard of shape of rectangle.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

The number of solutions in the equation x + 5x + 4 = 3(2x - 1) is 0

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

x + 5x + 4 = 3(2x - 1)

Open the brackets

This gives

x + 5x + 4 = 6x - 3

Subtract 6x from both sides of the equation

So, we have the following representation

4 = -3

Subtract -3 from both sides of the equation

So, we have the following representation

7 = 0

The above equation is false

Hence, the equation has no solution

Read more about equations at

https://brainly.com/question/2476251

#SPJ1

The time required for the baseball to reach the given height is 2 and 5/3 units respectively.

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

The equation for the height of baseball can be written as,

h(t) = -12t² + 44t + 6

It is a quadratic equation.

At h = 46 ft, the value of t can be found as,

Plug h(t) = 46 in  h(t) = -12t² + 44t + 6 as,

⇒ -12t² + 44t + 6 = 46

⇒ -12t² + 44t - 40 = 0

⇒ t = 2, 5/3

Hence, the time at which the height is 46 ft are given as 2 and 5/3 units respectively.

To know more about quadratic equation click on,

https://brainly.com/question/17177510

#SPJ1

According to this postulate, two triangles are congruent if their two angles and included sides are congruent with each other.

If the sides and angles of one triangle are the same as the sides and angles of another triangle, then two or more triangles are said to be congruent. Three postulates—ASA (angle-side-angle), SAS (side-angle-side), and SSS—that are demonstrated in the lesson can also be used to assess for congruency.

If, for example, triangle ABC has a hypotenuse of 5 cm and a leg of 4 cm and triangle PQR has a hypotenuse of 5 cm and a leg of 4 cm, then these two triangles have the same dimensions and, according to the HL theorem, are congruent to one another.

Triangle congruence can be implied in some situations by SSA, but not always. It differs from the other triangle congruence postulates/criteria because of this.

To learn more about Congruence Postulate refer to:

https://brainly.com/question/29268421

#SPJ1

The relationship between the slopes of the parallel sides is m₁ = m₂.

The relationship between the lengths of the non-parallel sides is perpendicular or intersecting.

The slope of a line can be calculated by taking the tangent ratio of the angle formed by it with the x axis.

The angle between two parallel lines is zero.

This implies that they form same angle with the x-axis.

The slopes of two parallel lines are always equal to each other.

Since, the slope of a line is the tangent of the angle made by it with x axis.

Then, it can be written as m₁ = m₂.

Hence, the relationship between the lengths of the non-parallel sides;

perpendicular or intersecting.

To know more about slope click on,

brainly.com/question/3605446

#SPJ1

Answer:

-----------------------------------

The slopes of the parallel sides are equal. We can prove this by finding the slopes:

We can see the non-parallel sides have same length. Let us  prove this by finding their length:

The formula for the arithmetic sequence is aₙ = 2 + (n - 1)(-4)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The arithmetic sequence is a sequence in which the difference between successive numbers is constant. It is given by:

aₙ = a₁ + (n - 1)d

where a₁ is the first term and d is the common difference

Given the sequence:

2,-2,-6,-10

The first term (a₁) = 2, the common difference (d) = -2 - 2 = -4

The formula is:

aₙ = 2 + (n - 1)(-4)

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

98,329.16 is the Growing Ordinary Annuity's Future Value (FV). Given a predetermined rate of return or discount rate, the present value of an annuity is the entire cash worth of all of your future annuity payments.

A sequence of equal-spaced payments constitutes an annuity. There are a lot of real-world examples of financial transactions involving annuities, including. • an automobile loan with a set repayment schedule of equal monthly payments.

Calculating the present value of an annuity is done by multiplying the dollar amount of each payment by the following formula:[tex]P = PMT \times [1- [ (1 / 1+r)^n] / r][/tex]  where P is the present value of your annuity stream. PMT is short for payment method type.

A set of periodic payments that will be received in the future at the start of each period or at its conclusion is referred to as a "annuity." The formula used to determine annuity payments and annuities due is based on the PV of annuities due, the effective interest rate, and the number of periods.

To learn more about annuity refer to :

https://brainly.com/question/19131462

#SPJ1

The paper company shipped 10 small boxes and 8 large boxes.

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

Let x represent the number of small boxes shipped and y represent the number of large boxes shipped.

Each small box of paper weighs 30 pounds and each large box of paper weighs 75 pounds.

A total of 18 boxes of paper were shipped, hence:

x + y = 18

y = 18 - x    (1)

Also, they weighed 900 pounds, hence:

30x + 75y = 900

but y = 18 - x, hence:

30x + 75(18 - x) = 900

30x - 75x + 1350 = 900

x = 10

y = 18 - x = 18 - 10 = 8

The company had 10 small boxes and 8 large boxes.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: yes

Step-by-step explanation: yesterday

The first step is to determine the appropriate inequality sign that would be used.

Here are inequality signs and what they mean:

The inequality sign that would be used is ≤.

The form of the inequality is:

(weight of each math book x number of maths book that can be shipped) + (weight of each workbook x number of workbooks that can be shipped)  

≤ total weight that can be shipped

(3.2x + 0.8y)  ≤ 50

To learn more about inequality, please check: https://brainly.com/question/5031619

#SPJ

Answer:

B

Step-by-step explanation:

The duration of the game was 3¹/₄ hours

To convert, multiply your number of hours by 60 to get time in minutes. Whenever we have given conversion from higher unit to lower unit then always use multiply and divide the number of minutes by 60 to get the number of hours.

Given here, game started at 8:39 PM and ended at 11:54 PM.

Therefore the duration of the game is in minutes = 21+60+60+54

                                                                                  = 195 minutes

And thus duration of the game in hours is = 195/6

                                                                      =  3¹/₄

Hence, The duration of the game was 3¹/₄ hours

Learn more about minutes and hours here:

https://brainly.com/question/1376612

#SPJ1

Answer:

Sure, here is a more casual and friendly way to explain how to calculate the weighted dollar amount of the savings account:

"Hey there! To find out the weighted dollar amount of the savings account, you just need to do a little math. First, multiply the amount invested in the savings account by the return on investment (ROR). Then, divide that number by the total ROR for all investments.

So, if you have $2,700 invested in the savings account and it has an ROR of 3.6%, the weighted dollar amount of the savings account would be:

($2,700 * 3.6%) / (3.6% + 1.8% + 13.6% - 1.2%) = $104.04

Easy peasy! Let me know if you have any other questions!