1. Solve: |x| = 5
{-5}

{-5, 5}

{5}

{-1, 5}

2. Solve: | m + 8| = 16
{-24, 8}

{8, 16}

{8}

{-24}

3. Solve: |2n - 3| = 5
{1, -4}

{-1, 1}

{-1, 4}

{1, 4}

4. Solve: |x/3 + 1| = 6
{-21, 15}

{-7, 15}

{-15, 21}

{7, 15}

5. Solve |2 - 3x| = 7.
{-3, 5/3}

{-3, 15}

{-5/3, 3}

{-15, 3}

6. Solve |2y - 2| = y.
{2/3, 2}

{1/3, 2}

{2, 5}

{2, 3}

The solution to the system of equations 2x + 3y = 4 and x - y = -3 is (x, y) = (-1, 2).

To solve this system, we can use the method of substitution or elimination. For example, here's how we can use the elimination method:

The solution to the system of equations is (x, y) = (-1, 2).

Jax's sister has 3 times as many marbles as Jax. By using multiplication, we calculate that if Jax has 6 marbles, his sister, therefore, would have 18 marbles.

In this problem, Jax's sister has 3 times as many marbles as Jax. If Jax has 6 marbles, we get the number of marbles that his sister has by multiplying 6 with 3. That's because we're given that she has 3 times the amount of marbles that Jax has.

So, the calculation would be 6 * 3 = 18. Therefore, Jax's sister has 18 marbles. The principle used here is multiplication in basic arithmetic. It's a method of scaling quantities based on given ratios or proportions. In this case, the ratio given was '3 times as many'.

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Answer:

The cost per gallon of gasoline, rounded to the nearest hundredth is $2.73.

Step-by-step explanation:

The cost of 16.1 gallons of gasoline = $43.95

So, the cost of 1 gallon of gasoline is given by = [tex]\frac{43.95}{16.1}[/tex]

= $2.7298 rounded $2.73.

Therefore, the cost per gallon of gasoline, rounded to the nearest hundredth is $2.73.

Answer:

Carter should measure two times the flour in the cup to obtain the quarter of cup he needs to the recipe.

Step-by-step explanation:

To solve this problem you should use a simple equation. As Carter has a cup that holds an eighth of the cup and he need to add a quarter cup to the recipe he needs to find a factor that multiplied by [tex]\frac{1}{8}[/tex] gives as result the [tex]\frac{1}{4}[/tex] he needs, that is:

1. Let´s name x the factor and we have the following equation:

[tex]\frac{1}{8}*x=\frac{1}{4}[/tex]

2. Solving for x:

[tex]\frac{x}{8}=\frac{1}{4}[/tex]

[tex]x=\frac{8}{4}[/tex]

[tex]x=2[/tex]

The result x=2 means that Carter should measure two times the flour in the cup to obtain the quarter of cup he needs to the recipe.

Answer:

1/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Givens:

If Martha needs 1 piece of paper and ribbon, then she need to use 4 packs of paper and 3 packs of ribbons, because when she uses one pack of paper, she use it all, but from the pack of ribbons, it remains some.

From the first pack Marta has 3 papers and 4 ribbons. So, she uses all 3 papers, and 3 ribbons, and there remains 1 ribbons without use.

From the second pack, Marta uses 3 papers but only 2 ribbons, because she also uses the one ribbon that left from the first pack. So, from the second pack, she only uses 2 ribbons, and there are 2 ribbons left.

From the third pack, she again uses all three papers, but only 1 ribbon, so there is three ribbons left.

From the fourth pack she uses three papers agains, but she doesn't need a new pack of ribbons, because she has three from the third pack.

Now, specifically, the least common number refers to the least common multiple of 3 and 4, which is 12, because if we write down the multiples for both numbers, we have:

3, 6, 9, 12, 15, ...

4, 8, 12, 16, 20,...

As you can see, the least common number is 12.

Therefore, the least number of kites Marta can make without any supplies left over is 12.

Hence, the fraction of their garden will be unplanted is [tex]\frac{5}{16}[/tex].

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

If the Browns plant [tex]\frac{3}{16}[/tex] tomatoes, [tex]\frac{1}{4}[/tex] cabbage, and [tex]\frac{2}{8}[/tex]  pepper.

So,

The unplanted plants are [tex]\frac{5}{16}[/tex].

[tex]\frac{3}{16}+\frac{1}{4}+\frac{2}{8}\\\\=\frac{3+4+4}{16}\\\\=\frac{11}{16}\\\\[/tex]

Then, the fraction of their garden will be unplanted

[tex]\frac{16}{16}-\frac{11}{16}=\frac{5}{16}[/tex]

Hence, the fraction of their garden will be unplanted is [tex]\frac{5}{16}[/tex].

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Nicole needs 750 meters of ribbon to make 1,000 bows, with each bow requiring 0.75 meters of ribbon. This is calculated by multiplying 1,000 by 0.75.

To determine how many meters of ribbon Nicole needs to make 1,000 bows where each bow requires 0.75 meters of ribbon, we need to perform a simple multiplication. Given:

1. Number of bows = 1,000

2. Length of ribbon per bow = 0.75 meters

We multiply these two values:

1,000 bows × 0.75 meters per bow = 750 meters

Thus, Nicole needs 750 meters of ribbon to make all the bows.

Let’s break down the process step-by-step:

The fraction of the cars in the lot are either white or blue is 7/12.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, in the car lot, 4/12 of the cars are white and 3/12 of the cars are blue.

Either white car or blue car means sum of white and blue car

Now, 4/12 + 3/12

= (4+3)/12

= 7/12

Therefore, the fraction of the cars in the lot are either white or blue is 7/12.

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The original price of the cape, before a 30% discount that resulted in a sale price of $126, was $180. Since 70% of the original price equals the sale price, dividing $126 by 0.7 yields the original price.

To find the original price of an item that has been discounted by 30%, we first recognize that the sale price represents 70% of the original price because 100% - 30% = 70%. If $126 is the sale price, it is 70% of the original price.

To find 100% of the original price, you can set up a proportion or simply divide the sale price by 0.7.

Using division:

Original Price = Sale Price / 0.7
Original Price = $126 / 0.7
Original Price = $180

Therefore, the original price of the cape was $180.

When we include sales tax in the calculation, assuming we know the tax rate, we would add that to the original price to get the total cost that will be paid at the register.

However, this question doesn't provide a tax rate, so we only calculate the original price.

The x-intercept will be at (16,0) and the y-intercept at (0, 6).

We have to solve for y by substituting 0 as the value of x. This will be:

24x + 64y = 384

24(0) + 64y = 384

64y = 384

y = 384/64

y = 6

We have to solve for x by substituting 0 as the value of y. This will be:

24x + 64y = 384

24x + 64(0) = 384

24x = 384

x = 384/24

x = 16

In conclusion, the x-intercept will be at (16,0) and the y-intercept at (0, 6).

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Answer:

Sample Answer: The x-intercept, at the point (16, 0) indicates the choice to produce fruit for 16 minutes. In 16 minutes, producing 24 cans of fruit a minute, all 384 cans for the order will be completed. The zero for the y-value represents that no time is spent producing cans of vegetables.

Step-by-step explanation:

80%, 85%, 90%.

=      =        =  

4/5, 17/20, 9/10     is least to greatest.

4/5 equals to 80 out of 100. 17/20 is equal to 85 out of 100. 9/10 is equal to 90 out of 100.