5 Bruno buys 9.625 gallons of gasoline at a gas station.
Each gallon costs $3.40. Bruno also buys a bag of ice
for $3.99. How much in total does Bruno spend at the
gas station to the nearest cent?

Answer:

[tex]\textsf{1.} \quad f(x)+g(x) =8x^2+2x+3[/tex]

[tex]\textsf{2.} \quad f(x)-g(x)=-2x+1[/tex]

[tex]\textsf{3.} \quad h(x)+g(x)= 4x^2-x+5[/tex]

[tex]\textsf{4.} \quad h(x)-f(x)= -4x^2-3x+2[/tex]

[tex]\textsf{5.} \quad g(2)+f(x)= 4x^2+23[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=4x^2+2\\g(x)=4x^2+2x+1\\h(x)=-3x+4\end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

Question 1

Add function f(x) and function g(x) together:

[tex]\begin{aligned} \implies f(x)+g(x) & = (4x^2+2)+(4x^2+2x+1)\\& = 4x^2+2+4x^2+2x+1\\& = 4x^2+4x^2+2x+2+1\\& =8x^2+2x+3\end{aligned}[/tex]

Question 2

Subtract function g(x) from function f(x):

[tex]\begin{aligned} \implies f(x)-g(x) & = (4x^2+2)-(4x^2+2x+1)\\& = 4x^2+2-4x^2-2x-1\\& = 4x^2-4x^2-2x+2-1\\& =-2x+1\end{aligned}[/tex]

Question 3

Add function h(x) and function g(x) together:

[tex]\begin{aligned} \implies h(x)+g(x) & = (-3x+4)+(4x^2+2x+1)\\& = -3x+4+4x^2+2x+1\\& = 4x^2-3x+2x+4+1\\& = 4x^2-x+5\end{aligned}[/tex]

Question 4

Subtract function f(x) from function h(x):

[tex]\begin{aligned} \implies h(x)-f(x) & = (-3x+4)-(4x^2+2)\\ & = -3x+4-4x^2-2\\ & = -4x^2-3x+4-2\\ & = -4x^2-3x+2\end{aligned}[/tex]

Question 5

Add function g(x) when x = 2 to function f(x):

[tex]\begin{aligned} \implies g(2)+f(x) & = \left(4(2)^2+2(2)+1\right)+(4x^2+2)\\& = 4(4)+2(2)+1+4x^2+2\\& = 16+4+1+4x^2+2\\& = 4x^2+16+4+1+2\\& = 4x^2+23\end{aligned}[/tex]

Learn more about composite functions here:

https://brainly.com/question/24538829

Answer: wheres the answer choices

Step-by-step explanation: good for roderick

Step-by-step explanation:

f=ma

force=mass×acceleration

=32×2

=64N

Answer:

14

Step-by-step explanation:

Step-by-step explanation:

The coordinate of A is 0. It is given that AR = 17. AR represents the distance from point A to point R. Remember that distance is always positive. So, from here we have two possibilities.

Point R is on Right side of A i.e. at coordinate 17

Point R is on Left side of A i.e. at coordinate -17

In both of these cases AR which is the distance from A to R will be 17.

So, if R is on Right side of A, the midpoint of AR would be:

0+17

  ÷      =  17/2  = 8.5

  2

Or if R is on Left side of A, the midpoint of AR would be:

0-17

  ÷      =  -17/2  = -8.5

  2

Thus, the possible coordinates of the midpoint of AR are 8.5 and -8.5

Answer:

20

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

6x+15=27

6x=27-15

6x=12

x=2

2x+5=(2)(2)+5

= 4+5

= 9

Answer: C. 45°

Step-by-step explanation:

             These two given angles are corresponding angles. Corresponding angles are always equal to each other. In other words, they are congruent.

                                 x° = 45°

The length of line segment RT is 8 units

The given triangles are similar triangles

So, we have the following similarity ratio

RS : RT = QC : QY

Substitute the known values in the above equation

4 : RT = 3 : 6

Express as fractions

RT/4 = 6/3

Multiply through by 4

RT = 4 * 6/3

Evaluate

RT = 8

Hence, the length of RT is 8 units

Read more about similar triangles at

https://brainly.com/question/14285697

#SPJ1

Median for the number of sick days of the employees is 5

A statistical phrase that splits the data into four quarters is called a quartile. On the number line, it essentially separates the data points into a data set into four quarters. It essentially serves as an extended middle. Data is divided into two equal parts by the median, and into four parts by the quartiles.

Solution:

Stem and leaf plot from Minitab of the number of sick days of the employees is,

2, 3, 3, 5, 7, 10, 10, 7, 5, 3, 2

Arrange the numbers in the ascending order,

2, 2, 3, 3 ,3, 5, 5, 7, 7, 10, 10

Here,

[tex]number\;of\;data=10[/tex]

We know that the Quartile 2 is spilt the data in to two like median,

[tex]Q_{2}=(\frac{n+1}{2}) ^{th\;term}[/tex]

[tex]Q_{2}=(\frac{11+1}{2}) ^{th\;term}[/tex]

[tex]Q_{2}=(\frac{12}{2}) ^{th\;term}[/tex]

[tex]Q_{2}=6 ^{th\;term}[/tex]

Therefore, the 6th term is, 5

Median = 5

To learn more about Quartile, visit:

https://brainly.com/question/23444910

#SPJ4

Answer: A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven.

Step-by-step explanation:

Hope this helps you! :) have an amazing day! ^-^

Your original investment in a start-up company was $4200

Let you invested x dollars in a start-up company.

Now your investment has gained 60% and is worth $6,720.

We write above statement as a mathematical expression.

From given information, x + (60 percent of x) = 6720

So we get an equation,

x + (0.6 x) = 6720

We solve above equation for x.

1.6 x = 6720

x = 6720 / 1.6

x = 4200 dollars

This means, initially you invested $4,200

Therefore, your original investment in a start-up company was $4200

Learn more about the percentage here:

https://brainly.com/question/16797504

#SPJ4

The expression 3g in the numerator represent the total amount of money paid for the gallons of gas.

Given expression:3g / 4

where,

Therefore, the expression 3g in the numerator represent the total amount of money paid for the gallons of gas.

Learn more about fraction:

https://brainly.com/question/1622425

#SPJ4

Answer:

A

Step-by-step explanation:

A i tunk

I think that it is the 2nd one and the 5th one.

I hope that this helps! :)

Answer:

B

Step-by-step explanation:

Answer:

m

Step-by-step explanation:

Answer: x=59 1/10     x=59.1

Step-by-step explanation:

Answer:

He bought 3.8 pounds of streaks for 31.35$

Answer for steak cost per pound = 8.25$

Step-by-step explanation:

You have to divide 31.35 from 3.8.

31.35 ÷ 3.8

= 8.25

8.25 is how much the steak cost per pound.

If you multiply 8.25 x 3.8

It equals = 31.35.

Answer:

$8.25 per pound.  See attached image.

Step-by-step explanation:

How to Do Long Division with Decimals

If the number you're dividing by has a decimal, move the decimal point all the way to the right counting the number of places you've moved it to. Then move the decimal point in the number you're dividing the same number of places to the right.

Insert a decimal point in the quotient (answer) space, exactly above the decimal point in the number under the division bar.

Divide until the remainder is zero, or until you have enough decimal places in your answer. You can also stop if the remainder repeats because this indicates that your answer is a repeating decimal.

Water main valves should be located at frequent intervals in a grid system.

The flow and temperature in pipes and plumbing fittings are controlled by water valves. The valves regulate steady flow and volume when they are correctly placed and used. Water valves are made of brass, plastic, stainless steel, bronze, cast iron, and galvanised pipe, among other materials.

The master cutoff valve for the house will typically feature a wheel (a gate valve) or a straight handle (ball valve). The wheel on gate valves (seen on the right) is turned clockwise until the water is shut off. To turn off the water, turn the handle of a ball valve a quarter turn in the opposite direction. Every house has two main water shutoff valves: one inside and one near the intersection of your property and the street.

To know more about water valve, visit:

https://brainly.com/question/23755498

#SPJ4

The largest number of dress length that could be cut is 66.

The dressmaker measures a length of fabric as 600 meters correct to the nearest 5 meters.

He cuts this into dress lengths of 9cm correct to the nearest meters.

The largest number of complete dress length he could cut can be calculated as follows:

largest number of dress length cut = 600 / 9

largest number of dress length cut = 66.6666666667

largest number of dress length cut ≈ 66

Therefore, the largest number of dress length that could be cut is 66.  

learn more on length here: https://brainly.com/question/11727682

#SPJ1

The greatest number of medium squares that Talia can cut from this​ piece is 17. 89 centimeters

From the information given, we have that;

The area of the square piece is 320 square centimeters.

It is important to note that the formula for area of a square is expressed as;

Area = a ²

Where a is the length of it's side

Let's substitute the value of the area in the formula

320 = a²

Take the square root of both sides

a = √320

a = 17. 89 centimeters

Thus, the greatest number of medium squares that Talia can cut from this​ piece is 17. 89 centimeters

Learn more about squares here:

https://brainly.com/question/24487155

#SPJ1

Answer:

s = 4 m

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

given A = 16 m² , then

s² = 16 ( take square root of both sides )

s = [tex]\sqrt{16}[/tex] = 4 m

Answer:

4m

Step-by-step explanation:

All the sides of a square are equal lengths. So 2 numbers that are the same must equal 16m^2.

A number times itself is known as a square number. The value of this square number is 16 m².

It can be shown like this:

a²= 16 m² or a×a = 16 m²

The reverse of squaring numbers is square root. To find the value of one side you can do √16. √16 = 4. We can check this by substituting (replacing) 4 in the place of 'a' to see if the answer is 16.

a×a = 16 m²

4 × 4 = 16

Therefore, the length of one side of the square equals to 4m.

Approxiamtely 167 men will be there in a class if the percent of men is 58.6 of the total student.

According to the given question.

Total number of students in the class is 285.

And 58.6 percent of the total students are men.

As we know that, a relative value indicating hundredth parts of any quantity is called a percent.

Therefore,

the total number of men in the class

= 58.6 percent of 285

= (58.6/100) × 285

= 0.586 × 285

= 167.01

Hence, approxiamtely 167 men will be there in a class if the percent of men is 58.6 of the total student.

Find out more information about percent here:

https://brainly.com/question/16242050

#SPJ4

After the solution, the answer to the given fraction [tex]-3\frac{5}{6} *4\frac{1}{2}[/tex] is 9.75.

So, [tex]-3\frac{5}{6} *4\frac{1}{2}[/tex]:

Therefore, the solution of the given fraction is 9.75.

Know more about fractions here:

https://brainly.com/question/17220365

#SPJ1

Emmy's actual score in the exam is 64.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given,

class average =  76

standard deviation = 8

Z- score = -1.50

The formula of Z-score is -

z = (x-μ)/σ

Where x is the actual score,

μ is the mean,

σ is the standard deviation.

Now putting the values in the formula we get,

-1.50 = (x- 76) / 8

⇒ on solving, we get x = 64

So the actual score of Emmy = 64

To learn more about Z-score from given link

https://brainly.com/question/28000192

#SPJ4

For the given line segment, the value of variable d is 2 units and the value of YZ is 16 units.

Given that, Y is between X and Z.

We need to find the value of the variable and YZ.

A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.

Given that, XY=11d, YZ=9d-2, XZ=5d+28

Here, the line segment XZ is sum of XY and YZ

That is, XZ=XY+YZ (∵Y is between X and Z)

⇒5d+28=11d+9d-2

⇒5d+28=20d-2 (Add like terms that is 11d+9d=20d)

⇒20d-5d=28+2

⇒15d=30

⇒d=2

So, YZ=9d-2

=9×2-2=18-2

=16

Therefore, the value of variable d is 2 units and the value of YZ is 16 units.

To learn more about the line segment visit:

https://brainly.com/question/25727583.

#SPJ1

Answer: 830

Step-by-step explanation:

Answer:

The nearest whole number is 830

Step-by-step explanation:

Nora needs to visit at least 11 times in order to earn a free movie ticket .

Let the number of visit to the movie theater be " x " .

According to the question She earns 12.5 points for each visit to the movie theater .

Total number of points in " x " number of visit will be [tex]=12.5x[/tex]

She also receives 20 rewards points just for signing up.

Total points will be [tex]=20+12.5x[/tex]

She needs at least 155 points for a free movie ticket which means minimum to minimum she needs 155 points .

   [tex]20+12.5x\geq 155[/tex]

On simplifying the above inequality , we get

 [tex]12.5x\geq 155-20\\12.5x\geq135\\x\geq 10.8[/tex]

As , visits can't be in point so , on rounding off Nora needs to visit 11 times to the movie theater.

Learn more about inequality here :

https://brainly.com/question/25275758

#SPJ9