**Answer:**

Nancy paid 2.98 per gallon of gasoline.

**Step-by-step explanation:**

The price of the gasoline is given by the total amount she paid for the gasoline divided by the amount of gasoline acquired with that money. The calculations for this are shown below:

ratio = total money / total gasoline

ratio = 10.43 / 3.5

ratio = 2.98 money / gallon

Nancy paid 2.98 per gallon of gasoline.

Find the surface area.

Any help will be appreciated thank you

**Answer:**

Find the area of the shape

First the two triangles

3 x 4 = 12 so the area of both triangles is twelve

Now it is only 1 big rectangle left

The side lengths can be added 3 + 4 + 5 = 12

12 x 11 = 132

132+12=144

144 is the surface area/area

If you have any questions please ask

**Step-by-step explanation:**

What is the equation of the following line? Be sure to scroll down first to see all answer options.

A. y = 3x

B. y = x

C. y = 2x

D. y = -1/3x

E. y = -3x

F. y = 1/3x

choice D: y=-1/3x

explanation:

explanation:

The owner of a car wash combines x gallons of a 2% liquid soap and 98% water mix with y gallons of a 7% liquid soap and 93% water mix to make 500 gallons of a 5% liquid soap and 95% water mix. Write a system of linear equations that represent the situation.

X(2+98) + y(7+93)= 500(5+95)

Not sure if it’s right or not!!!

Not sure if it’s right or not!!!

Directions: Identify the two integers which the square root lies between.

V48

5 and 6

7 and 8

6 and 7

8 and 9

I guess the answer is D!:( I hope u get it correct!

There is a unique positive real number x such that the three numbers

log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.

The number x can be written as m/n, where m and n are relatively prime positive integers.

Find m+n.

Step-by-step explanation:

If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.

Let a = log82x, b = log4x and c = log2x

If a = log8 2x; 8^a = 2x... (1)

If b = log4 x; 4^b = x ... (2)

If c = log2 x; 2^c = x...(3)

Since a, b c are in GP, then b/a = c/b

Cross multiplying:

b² = ac ...(4)

From eqn 1, x = 8^a/2

x = 2^3a/2

x = 2^(3a-1)

From eqn 2; x = 4^b

x = 2^2b

From eqn 3: x = 2^c

Equating all the values of x, we have;

2^(3a-1) = 2^2b = 2^c

3a-1 = 2b = c

3a-1 = c and 2b = c

a = c+1/3 and b = c/2

Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;

(c/2)² = c+1/3×c

c²/4 = c(c+1)/3

c/4 = c+1/3

Cross multiplying;

3c = 4(c+1)

3c = 4c+4

3c-4c = 4

-c = 4

c = -4

Substituting c = -4 into equation 3 to get the value of x we have;

2^c = x

2^-4 = x

x = 1/2^4

x = 1/16

Since the number x can be written as m/n, then x = 1/16 = m/n

This shows that m = 1, n = 16

m+n = 1+16

m+n = 17

The required answer is 17.

The value of **m+n** in which **m** and **n **are **relatively prime **positive **integers** is 17.

**Geometric **sequence is the **sequence **in which the next term is obtained by **multiplying **the previous term with the same number for the **whole **series.

There is a unique **positive **real number x such that the three **numbers** log82x, log4x and log2x, in that **order**, form a **geometric **progression with a positive common ratio. The **progression **is,

[tex]\log_82 x,\log_4x, \log_2x[/tex]

The above numbers are in **geometric **progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,

[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]

Using the **base **rule of **logarithmic **function,

[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]

Using the **Power **rule of **logarithmic **function,

[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]

The **number **x can be written as

[tex]\dfrac{m}{n}[/tex]

Here,* m* and* n* are **relatively **prime positive **integers**. Thus, the value of m+n is,

[tex]m+n=1+16=17[/tex]

Hence, the value of **m+n** in which **m** and **n **are **relatively prime **positive **integers** is 17.

Learn more about the **geometric sequence **here;

https://brainly.com/question/1509142

A ski run is 1000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski run to the bottom.

**Answer:**

angle of depression = -12 degrees

**Step-by-step explanation:**

Sin = opposite/hypotenuse

sin = -208/1000

inv sin 0.208 = -12

To solve this problem, we just need to use** trigonometric ratio **and use the** ratio **that best fits this problem. The **angle **of **depression** is equal to 76.23 degrees.

Using SOHCAHTOA, we can easily solve this problem, but we need to first know which** ratio** to use

Data;

opposite (ski run) = 1000 yardsadjacent (vertical drop) = 208 yardssince we have the value of **opposite** and **adjacent**, we can solve this using the** tangent** of the** angle**

[tex]tan\theta = \frac{opposite}{adjacent} \\tan \theta = \frac{1000}{208} \\tan\theta = 4.807\\\theta = sin^-^1 (4.0807)\\\theta = 76.23^0[/tex]

From the calculation above, the **angle **of **depression** is equal to 76.23 degrees.

Learn more on **angle of depression **here;

https://brainly.com/question/15580615

#SPJ2

I don’t understand this question. Can anyone help? I need answers ASAP. Thanks for all the help

There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)

There's **no solution** to this particular system because the two lines are parallel.

How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.

The line on the left passes through the points (-1, 0) and (0, -2), so it has slope

(-2 - 0)/(0 - (-1)) = -2/1 = -2

The line on the right passes through (0, 2) and (1, 0), so its slope is

(0 - 2)/(1 - 0) = -2/1 = -2

The slopes are equal, so the lines are parallel.

Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.

i think of a number multiply it by 3 and subract 2 . The result is 14

**Answer:**

5.3

**Step-by-step explanation:**

**Answer:**

The answer is 5.3

**Step-by-step explanation:**

5.3x3-2= 13.9 but when you round its 14

a rectangle has an area of 24m². its length is 5m longer than the width.

write an expression for the rectangle's length

**Answer:**

**2x+2(x+5)) = 24**

**Step-by-step explanation:**

**2x+ 2(x+5) = 24**

x is represented by the shorter side. Multiply by 2 because of the 2 sides. For the longer side, since it is 5m longer than the shorter side, you have to write (x+5). Multiply by 2 because of the 2 sides. Finally, add them both together since it is the area and set it equal to 24.

In parallelogram WXYZ, what is CY?

**Answer:**

The correct answer is 11 ft.

**Step-by-step explanation:**

The diagonals of a parallelogram bisect each other. This means that the portion marked x+4 is the same length as the portion marked 2x-7; this gives us the equation x+4=2x-7.

Subtract x from each side:

x+4-x=2x-7-x

4=x-7.

Add 7 to both sides:

4+7=x-7+7

11=x

Answer:

11

Step-by-step explanation:

On edge

What integer represents a drop in temperature of 12°

**Answer:**

*Integer; - 12*

**Step-by-step explanation:**

If we are considering a situation were there is a drop in temperature, this integer representation would contain a negative;

At the same time the temperature drops by 12 degrees ( ° ) such that this integer is;

*Answer; - 12*

what is m equal to.

4(m − 13) − 8 = 8

**Answer:**

m = 17

**Step-by-step explanation:**

[tex]4(m - 13) - 8 = 8 \\ 4(m - 13) = 8 + 8 \\ 4(m - 13) = 16 \\ (m - 13) = \frac{16}{4} \\ m - 13 = 4 \\ m = 4 + 13 \\ \huge \red { \boxed{m = 17}}[/tex]

Elaine and Sandy both like lemonade Elaine has a 16 tablesspoon box of lemonade Sandy has an 18 tablespoon box of lemonade mix he likes his lemoade stronger and uses 3 tablespoons of mix for each glass of lemonade who will run out of mix first Elaine or Sandy

**Answer:**

The answer is sandy

**Step-by-step explanation:**

18/3= 6 why? because each glass of lemonade he drink he puts 3 table spoons, and a table spoon is the big spoon

hope this helped <3

Caleb’s puppy weighs 2,250 grams. If the puppy weighed 600 grams at his last visit to the veterinarian’s office, what is the percent increase in the puppy’s weight rounded to the nearest whole number? Enter your answer in the box.

**Answer:**

[tex]73\%[/tex]

**Step-by-step explanation:**

Given: Present weight of Caleb’s puppy = 2,250 grams

Puppy weighed 600 grams at his last visit to the veterinarian’s office.

To find: percent increase in the puppy’s weight rounded to the nearest whole number

Solution:

Increase in puppy's weight = 2250 - 600 = 1650 grams

Percent increase in the puppy’s weight =( Increase in puppy's weight/Present weight of Caleb’s puppy) × 100 = [tex]\frac{1650}{2250}(100)=73.33 \%[/tex]

[tex]73.33\%[/tex] is rounded to [tex]73\%[/tex]

can someone help me with this question

**Answer:**

A 50

B 10

C 12/5

D 5

E 21

F 100

7. What is the value of the expression 3(2 - 7)

**Answer:**

-15

**Step-by-step explanation:**

3(2 - 7)

PEMDAS says parentheses first

Subtract

3 (-5)

Multiply

-15

The answer is -15 :)

hi!! <3 i attached a picture of a easy trigonometry question can you please help if you don’t mind <33

**Answer:**

Side AB has a length of 4, and side BC has a length of 11.7

I need this answer please tell me the answer

**Answer:**

less than

[tex]1 \frac{1}{2} [/tex]

I believe

Molly wants to put a fence around an area. The fence will follow the diagram of the triangle shown below. (Look at picture) About how much fencing does Molly need?

Answer:

Step-by-step explanation:

43feet

A trapezoid was broken into a triangle and rectangle. The base of the triangle b is ______cm.

B is 2 cm. Did you leave out some of the question

What is the difference between a rectangular prism and a triangular prism?

The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles.

A rectangular prism has two bases, while a triangular prism has one base,

A triangular prism has two bases, while a rectangular prism has one base.

A rectangular prism has two bases and three faces, while a triangular prism has two bases and four faces.

Dintro

Done

**Answer:**

The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles.

**Step-by-step explanation:**

**Any prism has two bases**. Since we are talking about a rectangular prism and a triangular prism both must have two bases.

For example, a square prism has two bases and they are both square.

In this case a rectangular prism has two bases that are rectangles and a triangular prism also has two bases and both bases are triangles.

Note: For the figure to have only one base it must be called a pyramid.

Thus, the answer is:

**The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles**

**Answer:**

a

**Step-by-step explanation:**

Select the expressions that are equivalent to 6(x + 7).

(7 + x) 6

6x + 42

(x + 7)6

42x + 6

**Answer:**

[tex]6x + 42[/tex]

**Step-by-step explanation:**

Apply the distributive property:

[tex]6x + 6 \times 7[/tex]

Multiply 6 by 7

[tex]6x + 42[/tex]

What happens to the parabola when a<1 compared to the parent function?

**Answer: The parabola is wider than the parent function**

Step-by-step explanation:

If "a" is a fraction less than one, then the parabola becomes wider.

See graph (attached)

Which expression has the same value as 5(4x+4)

**Answer: **20x + 20

**Step-by-step explanation: **In this problem, the 5 "**distributes**" through the parentheses, multiplying by each of the terms inside.

So we have 5(4x) + 5(4) which simplifies to **20x + 20**.

Solve the equation for x, and enter your answer below.

10x - 15x + 5= -45 + 40

**Answer: x = 2**

**Step-by-step explanation:**

[tex]10x - 15x + 5= -45 + 40[/tex]

subtract 5

[tex]10x - 15x= -45 + 40-5[/tex]

Combine like terms;

[tex]-5x=-10[/tex]

Divide by -5

[tex]x=\frac{-10}{-5}\\ x=2[/tex]

**Answer:**

[tex]x = 2[/tex]

**Step-by-step explanation:**

[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]

See question above

A) 7.2 cm

B) 9 cm

C) 10.6 cm

D) 12 cm

**Answer:**

B) 9 cm

**Step-by-step explanation:**

Just look at the triangle and use Pythagoras theoreum.

a² + b² = c²

a = 9 9 - 4.9 = 5

b = ?

c = 10

5² + b² = 10²

b² = 100 - 25

b² = 75

b = + - SQRT( 75 )

{Only the positive term has a meaning here.}

b = 8.66 rounded that is 9, which is answer B.

how many times does 6 go into 29

**Answer:**

4 times

**Step-by-step explanation:**

**Answer:**

4.8333333 or 4 5/6 times

**Step-by-step explanation:**

29/6 = 4.83333333

Please help I will give Brainliest please. Just tell what I need to do or solve I need help ASAP *image*

**Answer:**

**Step-by-step explanation:**

Hard to figure out huh

NEED HELP! ASAP PLEASE!

**Answer:**

(0,-41)

**Step-by-step explanation:**

You can see that for each 9 units that x goes up, y goes up by 19. If we continue this pattern, it will take 2 more jumps of 9 units for the x value to be 0 or to reach the y intercept. Adding 19 twice to -79 gives -41. Hope this helps!

Maria está en el piso 6 y quiere ir al sótano 2. Cuantos pisos bajará?

**Answer: 8 **

**Step-by-step explanation:**

Ella tiene que bajar los 6 pisos, mas 2.

6+2=8

In the figure angle a measures 41 degrees and angle d measures 32. What is the measurement of angle E?
Big ideas math 6th grade chapter 5 test
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I WILL GIVE BRAINLIEST!
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pls help it will mean alot!!due rn!!