Carl's new car gets 27 miles per gallon. What is the equation that represents y, the total miles driven on x gallons of gas?

x = 27y
y = 27 + x
x = 27 + y
y = 27x

Answer:

588 should be the answer :)

Answer:

300

Step-by-step explanation:

Solve for x.

x+(2/5*x)=420

x=300

Answer:

$285

Step-by-step explanation:

Blueberries:

B = number of pounds of blueberries bought

$5.50 = price of blueberries per pound

$5.50B = total price of B pounds of blueberries

Blueberries:

R = number of pounds of raspberries bought

$4 = price of raspberries per pound

$4R = total price of R pounds of raspberries

Total:

$5.5B + $4R

Since 5.5B+4R=285, then Amit spends in total on both types of berries $285

Complete question:

5B+4R=28

The above equation is true if Amit buys B pounds of blueberries and R pounds of raspberries at a farm where blueberries cost $5.50 per pound and raspberries cost $4.00 per pound. According to the equation, how much does Amit spend in total on both types of berries?

Answer:

In total Amits spends $28 in both types of berries.

Step-by-step explanation:

The equation is

5B+4R=28

B represent the weight in pounds of the blueberries and R represent the weight in pounds of the raspberries.

B =  weight in pounds of blueberries

R = weight in pounds of raspberries

The price per pound of blue berries is $5.50. The amount of blueberries he takes depending on the number of pounds Amit buys which is equals to 5B.

Cost of blueberries depending on the number of pounds = 5.5B

The price per pound of the blue berries is $4.00 .The cost of raspberries he takes depend on the number of pounds Amit buys which is equal to 4R.

Cost of raspberries depending on the number of pounds = 4R

The total cost of both blueberries and raspberries depending on the number of pounds is equals to 5B+4R=28

Total cost

5B+4R=28

In total Amits spends $28 in both types of berries.

Answer: 39.76

Step-by-step explanation: To find 56% of 71, first write 56% as a decimal by moving the decimal point two places to the left to get .56.

Next, the word "of" means multiply so we have .56 × 71.

(.56) (71) = 39.76

Therefore, 56% of 71 is 39.76.

a. (3,4) is only the solution to Equation 1.

(4, 2.5) is the solution to both equations

(5,5) is the solution to Equation 2

(3,2) is not the solution to any equation.

b. No, it is not possible to have more than one (x,y) pair that is solution to both equations

Step-by-step explanation:

a. Decide whether each neither of the equations,

i (3,4)

ii. (4,2.5)

ill. (5,5)

iv. (3,2)

To decide whether each point is solution to equations or not we will put the point in the equations

Equations are:

Equation 1: 6x + 4y = 34

Equation 2: 5x – 2y = 15

i (3,4)

Putting in Equation 1:

[tex]6(3) + 4(4) = 34\\18+16=34\\34=34\\[/tex]

Putting in Equation 2:

[tex]5(3) - 2(4) = 15\\15-8 = 15\\7\neq 15[/tex]

ii. (4,2.5)

Putting in Equation 1:

[tex]6(4) + 4(2.5) = 34\\24+10=34\\34=34\\[/tex]

Putting in Equation 2:

[tex]5(4) - 2(2.5) = 15\\20-5 = 15\\15=15[/tex]

ill. (5,5)

[tex]6(5) + 4(5) = 34\\30+20=34\\50\neq 34[/tex]

Putting in Equation 2:

[tex]5(5) - 2(5) = 15\\25-10 = 15\\15=15[/tex]

iv. (3,2)

[tex]6(3) + 4(2) = 34\\18+8=34\\26\neq 34[/tex]

Putting in Equation 2:

[tex]5(3) - 2(2) = 15\\15-4 = 15\\11\neq 15[/tex]

Hence,

(3,4) is only the solution to Equation 1.

(4, 2.5) is the solution to both equations

(5,5) is the solution to Equation 2

(3,2) is not the solution to any equation.

b. Is it possible to have more than one (x, y) pair that is a solution to both

equations?

The simultaneous linear equations' solution is the point on which the lines intersect. Two lines can intersect only on one point. So a linear system cannot have more than one point as a solution

So,

a. (3,4) is only the solution to Equation 1.

(4, 2.5) is the solution to both equations

(5,5) is the solution to Equation 2

(3,2) is not the solution to any equation.

b. No, it is not possible to have more than one (x,y) pair that is solution to both equations

Keywords: Linear equations, Ordered pairs

Learn more about linear equations at:

#LearnwithBrainly

The pair (3, 4) is a solution to both equations. The pairs (4,2.5), (5,5), and (3,2) are not solutions for either equation. There can be multiple solutions to simultaneous equations if the equations represent identical lines.

The subject of these equations involves the concept of simultaneous equations. We substitute the (x, y) pairs into both equations to determine whether they are solutions or not.

In simultaneous equations, it's possible to have more than one solution if the equations represent identical lines, otherwise there is usually a unique solution.

https://brainly.com/question/30319215

#SPJ3

Answer:

The speed of faster bus is 108 kmph and The speed of slower bus is 98 kmph  .

Step-by-step explanation:

Given as :

The two buses apart 1442 km

The time taken for apart = 7 hours

Let The speed of faster bus = x kmph

The speed of slower bus = ( x - 10 ) kmph

Now Speed = [tex]\dfrac{\textrm distance}{\textrm time}[/tex]

∵ Both the buses traveling in opposite direction

So, The speed of faster bus + the speed of slower bus =  [tex]\dfrac{\textrm distance cover}{\textrm time}[/tex]

Or, x + x - 10 = [tex]\frac{1442}{7}[/tex]

or, 2 x = 206 + 10

or, 2 x = 216

∴  x = [tex]\frac{216}{2}[/tex]

I.e x = 108  kmph

So, The speed of faster bus = x = 108 kmph

And The speed of slower bus = ( x - 10 ) = 108 - 10 = 98 kmph

Hence The speed of faster bus is 108 kmph and The speed of slower bus is 98 kmph  . Answer

Answer:

The Total number of adults ticket's is 15

The Total number of Senior citizen ticket's is 5

Step-by-step explanation:

Given as :

The total number of movies tickets were bought = 20

The cost of adults tickets = $ 8.00

The cost of senior citizen tickets = $ 4.00

The total money spent on movie tickets = $ 140

Let The total number of adults tickets = A

And The total number of senior citizen tickets = S

Now, According to question

The total number of movies tickets were bought = 20

I.e The total number of adults tickets + The total number of senior citizen tickets = 20

Or, A + S = 20

And $ 8 A + $ 4 S = $ 140  .........1

I.e 8 × ( A + S ) = 8 × 20

Or, 8 A + 8 S = 160         .......2

Solving the equation 1 and 2

Or, (  8 A + 8 S ) - (  8 A + 4 S ) = 160 - 140

Or, (  8 A - 8 A ) + ( 8 S - 4 S ) = 20

or, 0 + 4 S = 20

∴ S = [tex]\frac{20}{4}[/tex]

I.e S = 5

So, The number of Senior citizen ticket's = 5

Put The value of S in eq 1

So,  8 A +  4 × 5 = 140

Or, 8 A = 140 - 20

Or, 8 A = 120

∴  A = [tex]\frac{120}{8}[/tex]

I.e A = 15

So, The number of adult's tickets = 15

Hence The Total number of adults ticket's is 15

And The Total number of Senior citizen ticket's is 5    Answer

Answer:

She scored 1200 in all ten games

Answer:

1,200 points

Step-by-step explanation:

  120 points each game

×   10 games                  

   1, 200 points

Answer:

(18 miles/inch)(14 inches) = 252 miles

The distance between Nashville and Memphis is 252 miles.

Using the map scale of 1 inch to 18 miles, the distance between Nashville and Memphis, given as 14 inches apart on the map, is calculated to be 252 miles.

The question involves calculating the actual distance between two cities using a map scale. In order to find the distance between Nashville and Memphis, we'll use the scale given on the map to convert inches into miles.

The map scale is 1 inch:18 miles. Since the cities are 14 inches apart on the map, we can set up a simple multiplication to find the distance:

Therefore, the actual distance between Nashville and Memphis is 252 miles.

Answer:

a=-1

Step-by-step explanation:

2a-3=-5

2a=-5+3

2a=-2

a=-2/2

a=-1

Answer: Any number between 25 and 35 excluding both endpoints

(ie the number cannot be 25, the number cannot be 35)

One possible answer is 27 but there are infinitely many other choices

=======================================

Explanation:

The notation p ^ q in a logic math class setting means "p and q". Basically its a way of saying "both p and q are the case of some event happening". More specifically, it means that we have some number that is greater than 25 AND it is also less than 35.

If x is that number then p translates to x > 25. Statement q translates to x < 35

Flip both sides of x > 25 to get 25 < x.

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

So we have 25 < x  and x < 35. Those two combine to 25 < x < 35

Therefore x is some number between 25 and 35, where we leave out both endpoints. You can pick any number from this interval.

Answer:

THE FISRT GRAPH FOR THE QUESTION IS THE CORRECT ANSWER

Answer:

answer A or the first option

Step-by-step explanation:

Well, the main rules for negative numbers are that a negative combined with a negative always makes a positive. This rule applies almost everywhere, except subtraction. So, the rule also applies in division. So no matter what, if you divide a negative number with a negative number, the answer should always be positive.

The expression "negative 0.3 divided by negative 0.05" or -0.3/-0.05 has a positive quotient.

What is Quotient ?

Quotient is defined as the value resulting from dividing two numbers. When dividing two signed numbers (positive or negative), divide their absolute values and follow these rules:

(+) divided by (+) equals (+)

(-) divided by (-) equals (+)

(+) divided by (-) equals (-)

(-) divided by (+) equals (-)

To have a positive quotient, both the numerator and the denominator should have the same signs, either both (+) or both (-).

negative 0.3 divided by negative 0.05 :

-0.3/-0.05 = -/- = +

Therefore, The expression "negative 0.3 divided by negative 0.05" or -0.3/-0.05 has a positive quotient.

Learn more about quotient of signed numbers here: brainly.com/question/23578376

#SPJ2

Answer:

y+2x=9 is the line passing through (6,-3) parallel to y=-2x-5

Step-by-step explanation:

In the question we are given with a point (6,-3) and a line [tex]y=-2x-5[/tex]. we have to find the line passing through given point and parallel to given line.\

formula used: equation of a line passing through a point(a,b) with slope m is given by [tex](y-b) = m(x-a)[/tex].

here we have (a,b)=(6,-3) and the slope of the line is slope of [tex]y=-2x-5[/tex]

i.e, -2( coefficient of x).

therefore,  substituting point and slope in formula we get [tex]y+3 = -2(x-6)[/tex]

which simplifies to [tex]y+3= -2x+12\\ y+2x=9[/tex] is asked line equation

Answer:

6xy+x

Step-by-step explanation:

4xy+2xy=6xy

you do NOT ad the x since it is not xy

so the answer is 6xy+x

Step-by-step explanation:

If x is the number of t-shirts, and y is the number of sweatshirts:

10x + 15y ≥ 500

x + y ≤ 50

y ≥ x/2

And since x and y can't be negative:

x ≥ 0

y ≥ 0

Graph:

desmos.com/calculator/mw6dsei6jm

The boundaries of the feasible region are:

(0, 50), (0, 33.3), (28.6, 14.3), and (33.3, 16.7)

Since x and y must be integers, any non-integer solutions are not viable.

The maximum profit will be when the most product is sold.  Since sweatshirts are more profitable, we want to sell as much of that as we can.  

So they should sell 0 t-shirts and 50 sweatshirts for a maximum profit of $750.

Answer:

12

Step-by-step explanation:

h(x) = f(g(x))

Using chain rule:

h'(x) = f'(g(x)) g'(x)

h'(1) = f'(g(1)) g'(1)

h'(1) = f'(2) g'(1)

h'(1) = -4 × -3

h'(1) = 12

Leon needs to use 1/3 cup of olive oil for the amount of 1 teaspoon of cinnamon to maintain the same proportion as the original recipe.

Leon originally had a recipe that called for 2 teaspoons of cinnamon and 2/3 cup of olive oil. He now wants to adjust the recipe because he only has 1 teaspoon of cinnamon. To keep the proportions the same, he needs to halve the amount of the other ingredients as well.

Therefore, if 2 teaspoons of cinnamon requires 2/3 cup of olive oil, then 1 teaspoon of cinnamon will require half of 2/3 cup of olive oil, which is 1/3 cup of olive oil.

Step-by-Step Calculation

Answer:

three fourth mile=[tex]\frac{3}{4} mile[/tex]

Step-by-step explanation:

Given

⇒

[tex]\text{Distance from house to store}=\frac{1}{3} \times \text{Distance from house to friends house}\\ \text{Distance from house to friends house}= 3\times \frac{1}{4}\\ \text{Distance from house to friends house}=\frac{3}{4}[/tex]

Distance from her house to friends house  [tex]\frac{3}{4}[/tex] miles

Answer:

see the explanation

Step-by-step explanation:

we have that

The scale factor is

[tex]1\frac{1}{2}=1.5[/tex]

we know that

To find the length of the segment CZ, multiply the segment CR by the scale factor

so

[tex]CZ=CR(1.5)[/tex]

substitute

[tex]CZ=4(1.5)=6\ units[/tex]

therefore

Roy's diagram is not correct, because on the graph, Roy draws the length of the CZ segment equal to 10 units instead of 6 units.

Roy is using a scale factor equal to 2.5 instead of 1.5.

Answer:

The total volume of the solid is 1.67 cubic units.

Step-by-step explanation:

Each pyramid with a height of 2 units and a rectangular base with dimensions of 5 units × 0.25 units.

Therefore, the volume of each pyramid will be [tex]\frac{1}{3} \times \textrm {(Area of base rectangle)} \times \textrm {Height}[/tex]

= [tex]\frac{1}{3} \times (5 \times 0.25) \times 2 = 0.833[/tex] cubic units.

So, the total volume of the solid is (2 × 0.833) = 1.67 cubic units. (Answer)

Final answer:

To calculate the volume of the composite figure made from two identical pyramids with rectangular bases, we first find the volume of one pyramid using the formula for the volume of a pyramid and then multiply by two, resulting in a total volume of 1.666 cubic units.

Explanation:

The question involves calculating the volume of a composite figure made of two identical pyramids attached at their bases, with each pyramid having a rectangular base. The dimensions provided are a height of 2 units for each pyramid, and the rectangle's sides are 5 and 0.25 units. To find the volume of one pyramid, we use the formula for the volume of a pyramid, V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. The area of the rectangular base, B, is calculated as length × width = 5 × 0.25 = 1.25 square units. Substituting the values into the volume formula gives us V = (1/3)×1.25×2 = (1/3)×2.5 = 0.833 cubic units for one pyramid. Since the composite figure is made up of two such pyramids, the total volume is 2 × 0.833 = 1.666 cubic units.

Answer: No

Step-by-step explanation:

I can’t think of one but if you have a pegboard there is a formula called Pick’s Formula

Answer:

I don't really know but I can maybe figure it out

Explanation:

Recall that the slope is equal to the rise/run.

Rise = change in y = change in distance

Run = change in x = change in time

If we have a horizontal line, then there is no change in y. The rise would be 0 here. The run can be anything you want. Let's just call it x

Slope = rise/run = 0/x = 0

Therefore, all horizontal lines have a slope of 0.

The slope of a distance time graph represents the velocity because

velocity = (change in distance)/(change in time) = rise/run = slope

for example, a velocity of 10 meters per second represents a change of 10 meters over 1 second. The rise here woud be 10 meters and the run would be 1 second.

Answer:

25 revolutions

Step-by-step explanation:

step 1

Find the circumference of the road roller

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=77\ cm[/tex]

Convert to meters

[tex]r=77\ cm=77/100=0.77\ m[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]C=2(3.14)(0.77)[/tex]

[tex]C=4.8356\ m[/tex]

step 2

Calculate the number of revolutions that the roller will take to cover an area of 96.8 meter square

Remember that

The circumference of complete circle subtends one revolution

The circumference multiplied by the wide of road roller is equal to the area cover for the roller in one revolution

[tex]wide=80\ cm[/tex] ----> [tex]wide=0.80\ m[/tex]

[tex]4.8356(0.80)=3.86848\ m^2[/tex]

so

using proportion

Find out the number of revolutions for an area of 96.8 meter square

[tex]\frac{3.86848}{1}\ \frac{m^2}{rev}=\frac{96.8}{x}\ \frac{m^2}{rev} \\\\x=96.8/3.86848\\\\x=25\ rev[/tex]

Answer:

Model a community, 77% of which is houses, by placing orange houses on 77 of the 100 squares in the grid.

Step-by-step explanation:

Answer:  x = -20

================================

Explanation:

The expression 18+x is the same as x+18. This is because we can add two numbers in any order to get the same result. Example: 2+3 = 3+2 = 5.

Whats happening to the x is we add on 18. To isolate x, we undo this operation to subtract 18 from both sides.

Keep in mind that subtracting a negative from a negative will have us add the positive versions of the number, and the final result is ultimately negative. So that's why -2-18 = -20. You can think of it as 2+18 = 20 and you make the 20 negative.

Here's how the steps look like

--------

18 + x = -2

x + 18 = -2

x + 18 - 18 = -2 - 18 ... subtracting 18 from both sides

x + 0 = -20

x = -20

i have no idea how many apples should she sell

Answer:

She should sell 30 apples and 20 oranges

Step-by-step explanation:

3+2=5 so everytime she does that she gets another 5 fruit sold just add a 0 to both and boom 50. I hope thats right, im pretty sure it is

Answer:

35/9

Step-by-step explanation:

5/3*7/3

=35/9

Answer:

y=2

Step-by-step explanation:

-1+8y=23-4y

-1+12y=23

12y=24

y=2

Answer:

26/45 or about 58% of the log is left

Step-by-step explanation:

could be wrong though

The expression after performing the indicated operation written as trinomial is:

[tex]x^2+5x-8[/tex]

Step-by-step explanation:

Given

(x + 4)(x - 2) + 3x

We have to multiply (x + 4)(x - 2) and then add 3x to it

So,

[tex](x + 4)(x - 2) + 3x\\=[x(x-2)+4(x-2)]+3x\\= (x^2-2x+4x-8)+3x\\=x^2+2x-8+3x[/tex]

Combining alike terms

[tex]=x^2+2x+3x-8\\=x^2+5x-8[/tex]

The expression after performing the indicated operation written as trinomial is:

[tex]x^2+5x-8[/tex]

Keywords: Polynomials, Expressions

Learn more about polynomials at:

#LearnwithBrainly

Final answer:

To express (x + 4)(x - 2) + 3x as a trinomial, expand the product, combine like terms, and then add the additional term which results in the trinomial x² + 5x - 8.

Explanation:

To perform the indicated operations and express as a trinomial, we need to expand the binomial product and combine like terms with the additional term.

First, we expand the product: (x + 4)(x - 2) = x² - 2x + 4x - 8

Next, we combine the terms within the product: x² + (4x - 2x) - 8 = x² + 2x - 8

Now, we add the additional term: (x² + 2x - 8) + 3x

Lastly, we combine like terms: x² + (2x + 3x) - 8 = x² + 5x - 8