Nicole drove
355 miles using 17 gallons of gas. At this rate, how many gallons of gas would she need to drive 284 miles?

Answer:

 scoops 1       1/2     5      12.8   1.5    1.05     20    12.25

 milk      10     5       50   128    15     10.5   200    122.5

Step-by-step explanation:

The problem states 1 scoop per 10 oz of milk

1 scoop        x scoops

------------ = ------------

10 oz             5 oz

Using cross products

1 *5 = x * 10

Divide by 10

5/10 =x

1/2 scoops

1 scoop        5 scoops

------------ = ------------

10 oz             x oz

Using cross products

1 *x = 5 * 10

x =50

50 oz

1 scoop        x scoops

------------ = ------------

10 oz             128 oz

Using cross products

1 *128 = x * 10

Divide by 10

x =128/10

12.8 oz

1 scoop        1.5 scoops

------------ = ------------

10 oz             x oz

Using cross products

1 *x = 1.5 * 10

x =15

15 oz

1 scoop        x scoops

------------ = ------------

10 oz             10.5 oz

Using cross products

1 *10.5 = x * 10

Divide by 10

x =10.5/10

1.05 oz

scoop        20 scoops

------------ = ------------

10 oz             x oz

Using cross products

1 *x = 20 * 10

x =200

200 oz

scoop        12.25 scoops

------------ = ------------

10 oz             x oz

Using cross products

1 *x = 12.25 * 10

x =122.5

122.5 oz

Answer:

[tex]\underline {\text{P}\ \ |\quad1\quad| \quad\frac{1}{2}\quad|\quad5\quad|\quad12.8\quad| \quad1.5\quad| \quad1.05\quad|\quad20 \quad|\quad12.25\quad|}\\{\text{M}\ |\quad10\ \ | \quad 5\quad|\quad50\ \ |\quad128.\quad|\quad15\quad| \quad10.5\quad|\quad200\ |\quad122.5\quad|}[/tex]

Step-by-step explanation:

Set up the proportion as [tex]\dfrac{1 \text{ powder}}{10 \text{ milk}}=\dfrac{P}{M}[/tex], then cross multiply and solve for the variable.

Column 1: [tex]\dfrac{1}{10} =\dfrac{1}{M}[/tex] → M = 10

Column 2: [tex]\dfrac{1}{10} =\dfrac{P}{5}[/tex] → 5 = 10P → [tex]\frac{1}{2} = P[/tex]

Column 3: [tex]\dfrac{1}{10} =\dfrac{5}{M}[/tex] → M = 50

Column 4: [tex]\dfrac{1}{10} =\dfrac{P}{128}[/tex] → 128 = 10P  → 12.8 = P

Column 5: [tex]\dfrac{1}{10} =\dfrac{1.5}{M}[/tex] → M = 15

Column 6: [tex]\dfrac{1}{10} =\dfrac{P}{10.5}[/tex] → 10.5 = 10P  → 1.05 = P

Column 7: [tex]\dfrac{1}{10} =\dfrac{20}{M}[/tex] → M = 200

Column 8: [tex]\dfrac{1}{10} =\dfrac{12.25}{M}[/tex] → M = 122.5

Answer:

1

Step-by-step explanation:

Answer:

1   (plus 1/6 cup of the original 2/3 cup left over)

Step-by-step explanation:

The LCD of 1/2 and 2/3 is 6.  Thus, 1/2 and 2/3 are equivalent to 3/6 and 4/6.  3/6 divides into 4/6 once, with a remainder of 1/6 (cup).

Answer:  just one 1/2 cup serving can be made from 2/3 cup of cole slaw, with 1/6 cup of the original 2/3 cup of slaw left over.

Answer:

The square root of 84 is 9.1651...etc, so in a shorter form, 9.

Answer: [tex]\sqrt[2]{21}[/tex]

Explanation: Work is provided in the image attached.

Answer: [tex]\bold{\pm1, \pm5, \pm\dfrac{1}{3},\pm \dfrac{5}{3}}[/tex]

Step-by-step explanation:

Q             P

3x² - 3x + 5

Possible rational roots are all of the factors of P divided by all of the factors of Q, including both positive and negative values.

  [tex]\pm \dfrac{\text{factors of P}}{\text{factors of Q}}[/tex]

[tex]=\pm \dfrac{\text{factors of 5}}{\text{factors of 3}}[/tex]

[tex]=\pm \dfrac{1, 5}{1, 3}[/tex]

[tex]=\pm\dfrac{1}{1}, \pm\dfrac{5}{1}, \pm\dfrac{1}{3},\pm \dfrac{5}{3}[/tex]

Answer: ($4.19 x 1) + ($6.95 x 4) = $31.99

Step-by-step explanation: 4.19 is the price of the loaf of bread, so the first part of the equation ($4.19x), in this case the x is 1 since she bought only one loaf.

6.95 is the price of the turkey per pound, so our second part to the equation, ($6.95y), in this case y is 4 since the turkey weighed 4 pounds.

The complete equation is the combined cost of the turkey and bread so ($4.19x) + ($6.95y) = $?

The we replace the letters, ($4.19 x 1) + ($6.95 x 4) = $?

And then we add and multiply, ($4.19 x 1) + ($6.95 x 4) = $31.99

Answer:

a

Step-by-step explanation:

Answer:

CD

Step-by-step explanation:

The fastest way to get from D to AB is to go down CD

The distance from the point D to line AB is represented by the distance CD.

To find out the distance from a point to a line we have to draw a perpendicular to the line from a given point, this distance will be considered as the distance between the point and line.

Hence the distance from point D to line AB is CD(option A).

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Answer:

7

Step-by-step explanation:

3*8=24 and so 3*7 would =21 and 21+24=45

Jesse walked 7 dogs on Monday.

To find this answer, you must first find out how much money he made for walking dogs on Tuesday. To do so, multiple 8 (number of dogs) by 3 (amount of money earned per dog. This will give you 24, which you subtract from the total (45). 45 - 24 = 21. Finally, divide 21 (amount he made on Monday) by 3 (amount of money earned per dog) to get 7 dogs on Monday.

I hope this helps!

Answer: the first question is no. It is not a proportional relationship. Can you tell me what the options for the second question is please?

Answer:

[tex]x^{4}[/tex] + x³ - 10x² + 20x

Step-by-step explanation:

expand (x - 2)² and (x + 2)(x + 3) using FOIL

= (x² - 4x + 4)(x² + 5x + 6)

multiply each term in the second factor by each term in the first factor

= [tex]x^{4}[/tex] + 5x³ + 6x² - 4x³ - 20x² - 24 + 4x² + 20x + 24 ← collect like terms

= [tex]x^{4}[/tex] + x³ - 10x² + 20x

8 = 2 · 2 · 2

22 = 2 · 11

GCF(8, 22) = 2

Answer:

275 km  

Step-by-step explanation:

It has 1 - 3/8 = 5/8 of a tank left.

3/8  of a gallon gives 165 km

So 1 gallon  gives  165 / 3/8  = 165 * 8/3 km

5/8 gallon gives 168 * 8/3 * 5/8 km

= 165 * 5/3

=  275 km  (answer)

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=16\pi \end{cases}\implies 16\pi =\pi r^2\implies \cfrac{16\pi }{\pi }=r^2\implies 16=r^2 \\\\\\ \sqrt{16}=r\implies 4=r~\hfill \stackrel{\textit{diameter is twice the radius}}{d=8}[/tex]

The ascending order of the provided numbers is 4.045, 4.054, 4.405, 4.4005, and 4.504. This was achieved by comparing each decimal place from left to right.

The numbers 4.054, 4.045, 4.405, 4.504 and 4.4005 can be arranged in increasing order (from less to greater) by comparing each place value from left to right. When we compare these numbers, the arrangement from less to greater would be 4.045, 4.054, 4.405, 4.4005, and 4.504.

To do this, we first compare the numbers at each decimal place (tenths, hundredths, thousandths etc.), and arrange accordingly. We continue this process until we have the complete list in ascending order.

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Answer:

f(x) = -60 is your answer

Step-by-step explanation:

Plug in 3 for x

f(x) = 5x² - 7(4x + 3)

f(x) = 5(3²) - 7(4(3) + 3)

Follow PEMDAS. First, solve the parenthesis

3² = 9

4(3) + 3 = 12 + 3 = 15

f(x) = 5(9) - 7(15)

Multiply

f(x) = 45 - 105

Simplify. Subtract

f(x) = 45 - 105

f(x) = -60

f(x) = -60 is your answer

~

The value of f(3) in the function f(x) = 5x² - 7(4x+3) is -60.

To find the value of f(3), we need to substitute x = 3 into the given function f(x) = 5x² - 7(4x+3). First, let's simplify the expression inside the parentheses: f(x) = 5x² - 28x - 21. Now substitute x = 3: f(3) = 5(3)² - 28(3) - 21. Simplifying further, we get: f(3) = 45 - 84 - 21 = -60.

To find the value of f(3) for the given function f(x) = 5x² - 7(4x+3), we need to substitute 3 in place of x:

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Answer:

242 dollars / month. See guidelines below

Step-by-step explanation:

That depends largely on where she lives. The rule of thumb is to allow about 1/3 for rent after the government takes it's cut (that's all governments).

Here is an actual breakdown of how budgeting should be done.

These numbers are meant for Canada and are meant as a guide. In reality, if you live in the United States you will have to be spending more on medical for example and less somewhere else.

Now to your question. She has 29000 dollars. Debt is listed at 10%

10% of 29000 = (10/100) * 29000 = 2900 dollars.

Like most numbers having to do with money, most people don't understand large numbers and have to have them broken down.  In monthly terms, she can spend 2900 / 12 = 241.67 dollars / month on debt. That does not mean that she can add 241.67 of new debt every month. It means that she must first pay off what she owes, and then she gets to spend the balance on debt, but that is a very dangerous way to think. What she should say is if she has left over money that money can be transferred over to another category.

I know of very few people that can consider themselves debt free. Fewer of our American friends can make the claim.

The sources of these %s come from Credit Counselling Society (of Canada)

Answer:

y=[(8in*x)+6in]/12in

Answer:

A.0

Step-by-step explanation:

We can make 1/9 to 2/18

0 is 0/18,

1/2 is 9,18,

1 is 10/18

It is closest to 0/18

Answer:A

Answer:

x= -2

Step-by-step explanation:

1-)  8x+3-3x+3=x-2

2-) 5x+6=x-2

3-) 4x=-8

4-)x= -2

Answer:

C. 320 Cm

Step-by-step explanation:

To convert any value in meters to centimeters, just multiply the value in meters by the conversion factor 100.

3.2 meters=3.2*100=320 centimeters

Answer:

5.26 X 10^-3

Step-by-step explanation:

When you reflect a point across an axis, either the x value or the y value flips signs.

When you reflect across the x axis, the sign of the y value changes(+ to -) or (- to +)

When you reflect across the y axis, the sign of the x value changes (+ to -) or (- to +)

The point reflected across the x-axis because the sign of the y value changed/flipped, while the sign of the x value stayed the same.

Final answer:

Brandon reflected the point (-4, -6) across the x-axis to get the point (-4, 6), which is recognized by the unchanged x-coordinate and the sign reversal of the y-coordinate.

Explanation:

Brandon reflected the point (-4, -6) to get the point (-4, 6). This reflection occurred across the x-axis. We know this because the x-coordinate of the point remained unchanged, indicating that the point was not moved left or right. However, the y-coordinate changed from -6 to 6, which signifies that the point was reflected over the x-axis and moved from below the axis to an equal distance above the axis.

In reflections across the x-axis, the x-coordinate remains the same while the sign of the y-coordinate is reversed. Conversely, a reflection across the y-axis would keep the y-coordinate the same and reverse the sign of the x-coordinate.

In a coordinate system, negative or positive values for x and y are determined by their position relative to the origin. Points to the right of the origin and above the origin are usually considered to have positive coordinate values, with directions indicated by arrows on the axes. In Brandon's case, the negative y-coordinate became positive, affirming the x-axis as the axis of reflection.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (5, 2) and (0, -13). Substitute:

[tex]m=\dfrac{-13-2}{0-5}=\dfrac{-15}{-5}=3[/tex]

Answer:

3

Step-by-step explanation:

We are to find the slope of a line which passes through the two given points: (5, 2) and (0, -13).

We know the formula of the slope (m):

[tex]Slope[/tex][tex](m)[/tex]=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

So putting in the values of the coordinates of the given points in the formula to get:

Slope = [tex]\frac{-13-2}{0-5} =\frac{-15}{-5}[/tex] = 3

Therefore, the slope slope of a line which passes through the two given points: (5, 2) and (0, -13) is 3.

After simplifying Mateo's equation, we find that it results in an impossibility (2=-2), which means that the equation has no solution.

In order to find the number of solutions to Mateo's equation, we first need to simplify it. The equation given is 8-2(3-x)=4x-2(x+1). Distributing the numbers on each side of the equation, it turns into 8-6+2x = 4x -2x -2. Simplify it further into 2x + 2 = 2x - 2. If we subtract 2x from both sides, we get 2 = -2.

This result, 2 = -2, is not possible or true. Therefore, the given equation has no solutions. The correct answer to the question is therefore option A: No solution.

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Answer:

1824

That would be your total

Answer:

1824

Step-by-step explanation:

12*8+(12^3)=

We need to work these in the order of PEMDAS.  First is the parentheses and exponents.

12*8 + 1728

Next is multiplication.

96+1728

Now add.

1824

Answer:

Step-by-step explanation:

If you lose cash and someone finds it, you've lost it without recourse. If you lose a credit card, usually the issuer of the card can cancel it after your last verified purchase and replace the card for you. That is the main advantage.

You also have a record of what you've spent with a credit card. Sometimes you get a receipt and some sometimes you don't when you use cash.

Cash forces you to carry around coins, especially if you make a lot of small purchases in different places. Getting change for 2.22 cents from a 20 can be a little awkward and soon the big bills turn into many more little ones. Credit cards don't have that disadvantage.

Answer:

There are online services that will help someone monitor their credit and make a note of any changes in their credit score. Credit card monitoring keeps track of all open accounts and monitors hard inquiries. That way, if someone did not make the purchase, they can immediately tell the lender that the card has been compromised.

Step-by-step explanation:

This is an altered version of the information from the website given. I got a 100% on edgenunity.

Answer:

9

Step-by-step explanation:

Answer:

1250

Step-by-step explanation:

since 2% of the school is 25 students that means every 2% there is 25 students.

100/2 = 50

50*25 = 1250 students

Answer:

1250 = total students

Step-by-step explanation:

Students in the play = total students * percent in play

We know that the students in the play =25

We know the percent in the play is .02

Substitute what we know into the equation

25 = total students * .02

Divide each side by .02

25/.02 = total students *.02/.02

1250 = total students

Answer:

The equation of  line is shown below.

Step-by-step explanation:

The equation of line is

[tex]y+1=\frac{-3}{5}(x-4)[/tex]

It is the point slope form of a line, therefore the slope of the line is [tex]\frac{-3}{5}[/tex] and the line passing through (4,-1).

Rewrite the above equation in slope intercept form.

[tex]y=\frac{-3}{5}x+\frac{12}{5}-1[/tex]

[tex]y=\frac{-3}{5}x+\frac{12-5}{5}[/tex]

[tex]y=\frac{-3}{5}x+\frac{7}{5}[/tex]

The point slope form of a line is

[tex]y=mx+b[/tex]

Where m is the slope and b is y-intercept.

Therefore the slope of the line is [tex]\frac{-3}{5}[/tex] and the y-intercept of the line is [tex]\frac{7}{5}[/tex].

Slope is defined as

[tex]m=\frac{Rise}{Run}[/tex]

Since the slope is negative, therefore the run of the line is considered on the left side. The line rise by 3 and run by 5, therefore we will add 7 in y and subtract 5 from x.

The y-intercept is [tex](0,\frac{7}{5})[/tex].

[tex](0-5,\frac{7}{5}+3)=(-5,\frac{22}{5})=(-5,4.4)[/tex]

Therefore we have three points (4,-1), (-5,4.4) and (0,1.4). Plot the point on the coordinate plane and connect them be a straight line.

The graph line for y+1 = -3/5(x-4)

Plot the y-intercept at (0, 7/5).

From that point, move 5 units to the right and 3 units down to find another point on the line. This gives you the point (5, 4/5).

You can continue this pattern, moving 5 units to the right and 3 units down from the previous point to find more points on the line.

To graph the line with the equation y + 1 = -3/5(x - 4), we can first rearrange it into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Starting with your equation:

y + 1 = -3/5(x - 4)

Let's isolate y:

y = -3/5(x - 4) - 1

Now, we can distribute the -3/5 to both terms inside the parentheses:

y = (-3/5)x + (12/5) - 1

y = (-3/5)x + 12/5 - 5/5

y = (-3/5)x + 7/5

Now that we have the equation in slope-intercept form (y = mx + b), we can see that the slope (m) is -3/5, and the y-intercept (b) is 7/5.

Now, we can plot this line on the coordinate plane. Start by plotting the y-intercept, which is the point (0, 7/5), and then use the slope to find additional points on the line. The slope of -3/5 means that for every 5 units to the right, you go 3 units down.

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