Ethan's car can travel 30 miles per gallon on gasoline. Gasoline costs $4 per gallon, including tax. Ethan drove his car 180 miles on the trip. What was the total cost, in dollars, of the gasoline that the car used for Ethan's trip?

180-40-60=80 degrees

ANSWER

The explicit rule is

[tex]f(n) = 45+9n [/tex]

EXPLANATION

The given sequence is :

54,63,72,81,...

The first term of this sequence is

[tex]a = 54[/tex]

The common difference is

[tex]d =63 - 54 = 9[/tex]

The explicit rule is given by:

[tex]f(n) = a + d(n - 1)[/tex][tex]f(n) = 54+9(n -1 )[/tex]

We expand to get:

[tex]f(n) = 54+9n -9[/tex]

[tex]f(n) = 45+9n [/tex]

None of them is correct .

Answer:Neither Maxim nor Salma

Step-by-step explanation:

i just answered ed the question

Answer:

probably 6////////////

Answer:

The answer is 6

Step-by-step explanation:

In a year there is 365 days.

From the first condition, 6x + 2 = to a unknown number of coins

From the second condition, 7x + 4 = to the same number of unknown coins.

The number which satisfies this given condition is 326 coins.

If we divide this number by 8 to share it among 8 students =

326 ÷ 8 = 40 coins/ student and 6 coins remaining. Therefore, the answer is

6 Coins

Answer:

Is needed [tex]452.32\ ft^{2}[/tex] of sheet metal to build this tank

Step-by-step explanation:

we know that

To find how much sheet metal is needed to build this tank including the top, calculate the lateral area of the cone plus the lateral area of the cylinder plus the area of the top of the cylinder

[tex]A=\pi rl+2\pi rh1+\pi r^{2}[/tex]

we have

[tex]r=5\ ft[/tex]

[tex]h1=8\ ft[/tex] ----> height of the cylinder

[tex]h2=6\ ft[/tex] ----> height of the cone

Find the slant height of the cone l

Applying Pythagoras Theorem

[tex]l^{2}=r^{2}+h2^{2}[/tex]

substitute

[tex]l^{2}=5^{2}+6^{2}[/tex]

[tex]l^{2}=61[/tex]

[tex]l=\sqrt{61}\ ft[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]A=(3.14)(5)(\sqrt{61})+2(3.14)(5)(8)+(3.14)(5)^{2}[/tex]

[tex]A=122.62+251.2+78.5=452.32\ ft^{2}[/tex]

Answer:

Jane had 20 stamps in the beginning

Step-by-step explanation:

* Lets study the information in the problem

- Jane has unknown numbers of stamps

- She gave 10 of them to her friend

- Her mom give her twice as many stamps as she had in the beginning

* To solve the problem let the unknown numbers of stamps = x

∵ Jane had at the beginning x stamps

- She gave her friend 10 of them

∴ The rest with her = x - 10 stamps

- Her mom gave her twice as many stamps as she had in the beginning

∵ She had at the beginning x stamps

∴ Her mom gave her 2 × x = 2x

∴ The number of stamps with her now = x - 10 + 2x stamps

- She has now 50 stamps

∴ x - 10 + 2x = 50 ⇒ add the like term

∴ 3x - 10 = 50 ⇒ add 10 to both sides

∴ 3x = 60 ⇒ divide both sides by 3

∴ x = 20

∴ Jane had 20 stamps in the beginning

Answer:

Monthly interest rate is r=0,004375

Monthly principal c=590,625

Step-by-step explanation:

Monthly interest payment rate :

[tex]r=\frac{5.25}{12}:100=0,0004375[/tex]

Now, we need to find monthly principal payment : [tex]c=\frac{rP}{1-(1+r)^{-N}}[/tex]

Use this rule : [tex]N=30*12=360[/tex]

P=108000

r=0,004375

[tex]c=\frac{0.004375*108000}{1-(1+0.004375)^{-360}} =\frac{472.5}{0.8}=590,625[/tex]

Answer: 596.38

Step-by-step explanation:

Answer:

a. the answer is incorrect

b. 1

Step-by-step explanation:

step 1) 6x=48

step 2) 48/6

step 3)x=3

Answer:

The parabola will become narrower.

Step-by-step explanation:

Because of the coefficient 2, every value of x² is doubled, which means higher value on the same X coordinate, compared to the y = x² function.

Answer: B) The parabola will become narrower

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a (x - h)² + k     where

In the given equation of y = 2x², the a-value has increased so it is stretched.  When the graph stretches, the sides will get closer together thus the parabola will become narrower.

total=147

a:m

1:6 =7

147÷7=21

21×1=21

alice recycled 21 bottles

Answer:

21

Step-by-step explanation:

We have an equation in the first sentence we are given.  Mike and Alice together recycled 147 bottles, so in equation form that looks like this:

M + A = 147.

That alone doesn't do us much good because we have 2 unknowns.  The next sentence gives us Mike's number of bottles based on Alice's.  If the number Mike recycles is 6 times as many as Alice, replace the word "is" with an "=" and "6 times as many as Alice" with 6A to get:

M = 6A

Now we can go back to the first equation and replace M with 6A:

6A + A = 147

Now we only have A's.  That's a good thing.  Solve for A:

7A = 147

A = 21

The area of rectangle ABCD is 18 square units.

Step 1: Calculate the length of the rectangle.

The length of the rectangle is the distance between points A and B (or C and D). Using the distance formula:

[tex]\[ \text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

For the points A(-5,2) and B(-5,4), the length is:

[tex]\[ \text{Length} = \sqrt{(-5 - (-5))^2 + (4 - 2)^2} \][/tex]

[tex]\[ \text{Length} = \sqrt{(0)^2 + (2)^2} \][/tex]

[tex]\[ \text{Length} = \sqrt{0 + 4} \][/tex]

[tex]\[ \text{Length} = \sqrt{4} \][/tex]

[tex]\[ \text{Length} = 2 \][/tex]

Step 2: Calculate the width of the rectangle.

The width of the rectangle is the distance between points B and C (or A and D).

For the points B(-5,4) and C(4,4), the width is:

[tex]\[ \text{Width} = \sqrt{(4 - (-5))^2 + (4 - 4)^2} \][/tex]

[tex]\[ \text{Width} = \sqrt{(4 + 5)^2 + (0)^2} \][/tex]

[tex]\[ \text{Width} = \sqrt{9^2 + 0} \][/tex]

[tex]\[ \text{Width} = \sqrt{81} \][/tex]

[tex]\[ \text{Width} = 9 \][/tex]

Step 3: Calculate the area using length and width.

Now that we have the length and width of the rectangle, we can use the formula:

[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]

[tex]\[ \text{Area} = 2 \times 9 \][/tex]

[tex]\[ \text{Area} = 18 \][/tex]

The length of the rectangle, calculated as the distance between points A and B (or C and D), is 2 units. The width of the rectangle, calculated as the distance between points B and C (or A and D), is 9 units. Multiplying the length and width together gives us the area of the rectangle, which is 18 square units. Therefore, the correct answer is that the area of rectangle ABCD is 18 square units.

Complete question :

RECTANGLE ABCD has vertices A(-5,2) B(-5,4) C(4,4) D(4,2) calculate the area.

so what is the question that u are asking. I'll help you out

Answer:

sheeewsh

Step-by-step explanation:

Answer:

-28

Step-by-step explanation:

(5+2) = 7

7 + 2 - 40 = -31

-31 + 3 = -28

An exponential expression refers to an expression where a base number is raised to a certain power or exponent. The exponent indicates how many times the base number is repeated as a factor. Exponential expressions can be simplified or evaluated using the rules of exponents.

In mathematics, an exponential expression refers to an expression where a base number is raised to a certain power, or exponent. The exponent indicates how many times the base number is repeated as a factor. For example, in the expression 23, 2 is the base and 3 is the exponent, so it means that 2 is repeated as a factor three times. Exponential expressions can be simplified or evaluated using the rules of exponents.

For example, in the expression 42, 4 is the base and 2 is the exponent, so it means that 4 is repeated as a factor two times. This can be evaluated as 42 = 4 x 4 = 16.

Exponential expressions are commonly used in various mathematical applications, such as in compound interest, population growth, and scientific calculations.

https://brainly.com/question/31870974

#SPJ3

Answer:

To complete the square move the non-x term to the right

2x^2 + 13x = -20 then divide equation by x^2 coefficient

x^2 + 6.5x = -10

then coefficient of x (which is 6.5) divide by 2 (3.25) square the number

=10.5625 Then add 10.5625 to both sides of the equation:

x^2 + 6.5x + 10.5625 = -10 + 10.5625

x^2 + 6.5x + 10.5625 = .5625

Take the square root of both sides

(x + 3.25)^2 = .75

Step-by-step explanation:

Answer:

910 bees

Step-by-step explanation:

There are 35 bees in a hive and we have 26 hives.

Take the number of hives and multiply by the number of bees per hive

26*35 =910

There are 910 bees total

If there are 26 hives and there are 35 bees in each hive we can do the simple math of 26x35=910

Answer:

The answer in the procedure

Step-by-step explanation:

Let

x ----> the dog walking hours

y ----> the car washing hours

we know that

The system of linear inequalities is equal to

[tex]x+y\leq20[/tex] -----> inequality A

[tex]9x+10y\geq 90[/tex] -----> inequality B

Solve the system of inequalities by graphing

The solution is the shaded area

see the attached figure

Two possible combinations of hours are

(10,10) and (0,9)

Verify

For (10,10)

Substitute the value of x and the value of y in both inequalities

Inequality A

[tex]10+10\leq20[/tex]

[tex]20\leq20[/tex]  -----> is true

Inequality B

[tex]9(10)+10(10)\geq 90[/tex]

[tex]190\geq 90[/tex] ----> is true

therefore

(10,10) is a possible solution

For (0.9)

Substitute the value of x and the value of y in both inequalities

Inequality A

[tex]0+9\leq20[/tex]

[tex]9\leq20[/tex]  -----> is true

Inequality B

[tex]9(0)+10(9)\geq 90[/tex]

[tex]90\geq 90[/tex] ----> is true

therefore

(0,9) is a possible solution

Final answer:

The situation can be described by two inequalities: x + y <= 20 and 9x + 10y >= 90. Two possible combinations of hours that meet these requirements are 0 hours of dog walking and 9 hours of car washing, or 8 hours of dog walking and 2 hours of car washing.

Explanation:

To represent this situation with a system of linear inequalities, we will let x be the number of hours working as a dog walker and y be the number of hours working as a car wash attendant. The two inequalities based on the constraints of the problem are:

x + y \<= 20 (because you can't work more than 20 hours).

9x + 10y >= 90 (because you need to earn at least $90).

Solving this system can be done graphically or algebraically. Let's see two possible solutions:

If you want to work at both jobs, you could work 8 hours dog walking (x=8) and 2 hours at the car wash (y=2). This means you would earn 8*$9 + 2*$10 = $92, which is also enough to cover the expenses.

[tex]\bf \cfrac{Melanie}{Jacob}\qquad \stackrel{ratio}{\cfrac{4.1}{20.5}}\qquad \qquad \cfrac{4.1}{20.5}=\cfrac{m}{5}\implies 20.5=20.5m \\\\\\ \cfrac{20.5}{20.5}=m\implies 1=m[/tex]

Answer:

  72°

Step-by-step explanation:

You correctly found x, but the measure of the angle is ...

  4x-22 = 4·23.5-22 = 72°

___

or (6x-69)° = (141-69)° = 72°

Answer:

its cos:48/80

Step-by-step explanation:

cos-1(48/80)=53.13

For this case we have by definition of trigonometric relations that the cosine of an angle is given by the leg adjacent to said angle on the hypotenuse of the triangle. So:

[tex]Cos (Y) = \frac {64} {80} = \frac {32} {40} = \frac {16} {20} = \frac {8} {10} = \frac {4} {5}[/tex]

After simplifying we have to:

[tex]Cos (Y) = \frac {4} {5}[/tex]

ANswer:

[tex]Cos (Y) = \frac {4} {5}=0.8[/tex]

Answer:

The first 6 terms are -7,-14,-28,-56,-112,-224

Step-by-step explanation:

The given sequence is defined recursively by:

[tex]a_1=-7[/tex] and [tex]a_n=2(a_{n-1})[/tex]

When n=2

[tex]a_2=2(a_{2-1})[/tex]

[tex]a_2=2(a_{1})[/tex]

[tex]a_2=2(-7)=-14[/tex]

When n=3

[tex]a_3=2(a_{3-1})[/tex]

[tex]a_3=2(a_{2})[/tex]

[tex]a_3=2(-14)=-28[/tex]

When n=4

[tex]a_4=2(a_{4-1})[/tex]

[tex]a_4=2(a_{3})[/tex]

[tex]a_4=2(-28)=-56[/tex]

When n=5

[tex]a_5=2(a_{5-1})[/tex]

[tex]a_5=2(a_{4})[/tex]

[tex]a_5=2(-56)=-112[/tex]

When n=6

[tex]a_6=2(a_{6-1})[/tex]

[tex]a_6=2(a_{5})[/tex]

[tex]a_6=2(-112)=-224[/tex]

The first 6 terms are -7,-14,-28,-56,-112,-224

Answer:

the monthly payment is $303.69

Step-by-step explanation:

this is how i got it:

9,550 divided by 100= 95.5

95.5 x 3.18= 303.69

so the monthly payment it $303.69

Final answer:

To find Chico's monthly car payment, divide the total loan amount by $100 to determine the number of units and multiply by the monthly payment per unit, resulting in a monthly payment of $303.69.

Explanation:

The student's question relates to calculating the monthly payment of a car financing plan. To determine Chico's monthly payment for his car loan, we can use the provided information that each $100 of the loan requires a $3.18 monthly payment at an APR of 8.9%. Since Chico is financing $9,550, we first divide this amount by $100 to find the number of 'units' of $100 in the total loan amount. We then multiply that number by the monthly payment per $100 to find the total monthly payment.

Calculate the number of $100 units in the total loan amount: $9,550 / $100 = 95.5 units.

Multiply the number of units by the monthly payment per unit: 95.5 units * $3.18/unit = $303.69.

Therefore, Chico's monthly payment for the car would be $303.69.

Answer: 2) Plant C is producing at a cost greater than the goal.

Explains which plant is achieving the goal set by the company regarding radio production costs.

Correct Statement: Plant B is at the goal of producing 20 radios for a cost of $2,500.

Explanation:

Plant A being farthest from the goal is inaccurate since the question mentions Plant B is producing at the goal cost.

Plant C producing at a cost greater than the goal is incorrect as Plant B is already reaching the goal cost.

Plant B is indeed at the goal, as stated in the question, producing 20 radios for a cost of $2,500.

neither even or odd, odd, even

Answer:

Odd, neither, neither

Step-by-step explanation:

A function is even if f(x) = f(-x).  That means that it passes through the origin and is symmetrical about the y-axis.

A function is odd if f(x) = -f(-x).  That means that it passes through the origin and is symmetrical about the origin.

The first graph, the line, passes through the origin and is symmetrical about the origin.  So it is odd.

The second graph does not pass through the origin, nor is it symmetrical.  So it is neither odd nor even.

The third graph does not pass through the origin, nor is it symmetrical about the y-axis.  So it is neither odd nor even.

Answer:

2.25π m²

Step-by-step explanation:

The area (A) of a circle is calculated using the formula

A = πr² ← r is the radius

here the diameter = 3

The radius is half the diameter, that is radius = 1.5, so

A = π × 1.5² = 2.25π m²

The answer is:

The correct option, is the second option:  

b || c ( b and c are parallel).

To solve the problem, let's remember the following relationship:

If:

[tex]a=b[/tex]

and

[tex]b=c[/tex]

Then:

[tex]a=c[/tex]

So, from the statement we know that a and b are parallel (a || b), so, if a and c are parallel ( a || c) it means that b and c are parallel ( b || c).

Hence, the correct option is:

The second option, b || c ( b and c are parallel)

Have a nice day!

Answer:

  12,897.69 ft

Step-by-step explanation:

The cable is assumed to be the hypotenuse of a right triangle with side lengths 11520 ft and 5800 ft. Then the length of it (in feet) is ...

  cable length = √(11520² +5800²) = √166,350,400 ≈ 12,897.69 . . . feet

_____

Comment on the question

A cable that long will have considerable sag, so even an answer rounded to the nearest 10 ft is probably in error by quite a bit.

Answer:

The minimum number of rolls to buy is 9

Step-by-step explanation:

step 1

Find the perimeter of the ceiling of Katie’s living room

The perimeter of a square is equal to

[tex]P=4b[/tex]

where

b is the length side of the square

we have

[tex]b=12\ ft[/tex]

so

[tex]P=4(12)=48\ ft[/tex]

step 2

Find the length side of the diagonals  of the ceiling

Applying Pythagoras theorem

[tex]d=\sqrt{12^{2} +12^{2}}\\ \\d=\sqrt{288}=16.97\ ft[/tex]

step 3

Find the total crepe paper needed

Sum the perimeter plus two times the length side of the diagonal

[tex]48\ ft+2*(16.97\ ft)=81.94\ ft[/tex]

step 4

Find the number of rolls needed

we know that

Each roll contain 10 ft of crepe paper

so

[tex]81.94/10=8.19\ rolls[/tex]

Round up

[tex]8.19=9\ rolls[/tex]

The minimum number of rolls to buy is 9

Final answer:

Katie needs to purchase 9 rolls of crepe paper to decorate her living room ceiling. The calculation includes both the perimeter and the diagonals of her square ceiling.

Explanation:

The ceiling of Katie’s living room is a square that is 12 ft long on each side. To calculate the amount of crepe paper she needs for the perimeter, we multiply the length of one side by 4, since a square has four equal sides: 12 ft × 4 = 48 ft. To calculate the length needed to hang crepe paper from corner to corner, we use the Pythagorean theorem for a square, which says the diagonal is equal to the side length multiplied by the square root of 2: 12 ft × √2 ≈ 12 ft × 1.414 ≈ 16.97 ft. Since there are two diagonals, we need twice this amount: 16.97 ft × 2 ≈ 33.94 ft. Adding the perimeter and diagonals, we get a total of 48 ft + 33.94 ft = 81.94 ft.

Each roll of crepe paper contains 10 ft. To find out the number of rolls needed, we divide the total footage by 10 ft per roll: 81.94 ft ÷ 10 ft/roll ≈ 8.194 rolls. Since Katie can't buy a fraction of a roll, she will need to purchase 9 rolls to have enough crepe paper to decorate her living room ceiling.

Answer:

h = 40 cm

Step-by-step explanation:

The volume (V) of a cylinder is calculated using the formula

V = πr²h ( r is the radius and h the height )

here V = 3240π, thus

π × 9² h = 3240π

81πh = 3240π ( divide both sides by 81π )

h = [tex]\frac{3240\pi }{81\pi }[/tex] = [tex]\frac{3240}{81}[/tex] = 40

Answer:

  51.3°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

  Tan = Opposite/Adjacent

For angle y, the opposite side is 10 cm, and the adjacent side is 8 cm. Then you have ...

  tan(y) = (10 cm)/(8 cm)

  y = arctan(1.25) ≈ 51.3402° ≈ 51.3°

Answer:

b= -1

Step-by-step explanation:

Step 1: Find out value of x

x-2 = 0

x= 2

Step 2: Substitute value of x in the equation

x^3 + bx^2-  4 = 0

(2)^3 + b (2)^2 - 4 = 0

8 + 4b - 4=0

4 - 4b = 0

4b = -4

b = -1