18x^2-2 factor completely

The boy is 9

9x2=18

18+9=27

In this explanation, we'll determine the age of the boy using algebraic equations based on the given information. Let's represent the boy's age as X and his sister's age as 2X.

Let's set up the equations based on the information provided:

1. The boy's age: X years

2. His sister's age: 2X years (twice as old as the boy)

3. The sum of their ages: 27 years

Using these three pieces of information, we can create an equation to find the value of X (the boy's age).

1. The first equation represents the sum of their ages:

X + 2X = 27

2. Simplify the equation by combining like terms:

3X = 27

3. Now, isolate X by dividing both sides of the equation by 3:

X = 27 / 3

4. Calculate X:

X = 9

So, the boy is 9 years old.

Let's represent the boy's age as X and his sister's age as 2X. The sum of their ages is given as 27 years.

1. We can express the sum of their ages in an equation:

X + 2X = 27

2. Combine the like terms on the left side of the equation:

3X = 27

3. To find the value of X, isolate X on one side of the equation. We do this by dividing both sides of the equation by 3:

X = 27 / 3

4. Simplify the expression:

X = 9

Thus, the boy is 9 years old, and his sister is twice as old, which makes her 18 years old (2 * 9 = 18).

The sum of their ages, 9 + 18, indeed equals 27.

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since you know Lainey has 20 markers and the total cost is $6, all you have to do is solve 20/6 to find the cost of each marker. So, the answer would be about $2.33 dollars, since 20/6 would equal $2.333333333... and I just rounded it up. Hope I helped you! Good luck (:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.

so 13

13.  A prime number is a number which cannot be factored anymore.  4 can be factored as 2 x 2, 26 can be factored as 13 x 2, and 15 can be factored as 3 x 5.

Answer:The answer is 25

Step-by-step explanation:Hope this helps:)It’s 100% correct

Answer:

c

Step-by-step explanation:

Final answer:

The expression 16 x (-3/8) + 16 x 1/4 is evaluated using the distributive property to get -6 + 4, which equals -2.

Explanation:

To evaluate the expression 16 x ( -3/8) + 16 x 1/4 using the distributive property, we will distribute the 16 into the terms inside the parentheses.

Here is the step-by-step process:

Multiply 16 by (-3/8): 16 × (-3/8) = -6.

Multiply 16 by 1/4: 16 × 1/4 = 4.

Add these two results together: -6 + 4 = -2.

Therefore, the evaluation of the expression 16 x ( -3/8) + 16 x 1/4 is -2.

Step 1. Split the second term in 2x^2 - x - 21 into two terms

2x^2 + 6x - 7x - 21

Step 2. Factor out the common terms in the first two terms, then in the last two terms.

2x(x + 3) -7(x + 3)

Step 3. Factor out the common term x + 3

(x + 3)(2x - 7)

495/220 can be simplified to 9/4 by dividing the numerator and denominator by 55

the answer to what is 495/220 in simplest form is 9/4

y^5 is your answer hope it helps!

A manufacturing company has the following fixed monthly costs and unit variable costs:

Rent = $2,200

Utilities = $375

Variable costs for materials and assembly = $13.25/unit

Monthly labor = $750

Given is the product is sold at $24.99 per unit

Let the number of units sold be x

Adding total cost = [tex]2200+375+750=3325[/tex]

Equation becomes:

[tex]3325+13.25x=24.99x[/tex]

[tex]11.74x=3325[/tex]

x= 283.21

So, rounding it to nearest whole number we get, 283 units.

The equivalent ratios are calculated as;

1) 16/20

2) 8/12

3) 8/9

4) 9/21

5) 4/5

6) 6/9

Equivalent ratio is a ratio that is equal to another ratio when broken down or when numerator and denominator are multiplied by same number.

1) The ratio is given as 4/5.

If the denominator is 20, then it means the equivalent numerator will be;

(20/5) * 4 = 16.

Equivalent ratio = 16/20

2) The ratio is given as 2/3.

If the denominator is 12, then it means the equivalent numerator will be;

(12/3) * 2 = 8.

Equivalent ratio = 8/12

3) The ratio is given as 24/27

If the denominator is 9, then it means the equivalent numerator will be;

(9/27) * 24 = 8

Equivalent ratio = 8/9

4) The ratio is given as 3/7.

If the numerator is 9, then it means the equivalent denominator will be;

(9/3) * 7 = 21.

Equivalent ratio = 9/21

5) The ratio is given as 8/10.

If the denominator is 5, then it means the equivalent numerator will be;

(5/10) * 8 = 4.

Equivalent ratio = 4/5

6) The ratio is given as 30/45.

If the numerator is 6, then it means the equivalent denominator will be;

(6/30) * 45 = 9.

Equivalent ratio = 6/9

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There is 1 serving of lemon juice to 3 cups water. Hence why it's 1:3 ratio.

Since it's 1:3, then 2 servings to 6 cups of water, so on and so forth.

Multiply your lemon juice servings by 3 to find out how many cups of water for the table.

To find how much lemon juice for 36 cups of water, just divide 36 by 3 to get 12. 12 servings of lemon juice is just right for your 36 cups of water.

Answer: There is 12 servings of lemon juice needed for 36 cups of water.

Step-by-step explanation:

Since we have given that

Number of cups of water to make lemonade = 36

Ratio of lemon juice to water = 1 : 3

So, number of lemon juice cups be x

number of cups of water be 3x.

According to question, it becomes,

[tex]3x=36\\\\x=\dfrac{36}{3}\\\\x=12[/tex]

Hence, there is 12 servings of lemon juice needed for 36 cups of water.

For this case, we have:

The generic definition of the distributive property is:

[tex]a (b + c) = ab + ac\\[/tex]

Therefore, the option that fits the definition is given by:

[tex]9 (t + 5) = 9t + 45[/tex]

where the property is verified.

Thus, the correct option is A.

Answer:

Option A

In probability, the outcomes of rolling a die are considered. The probability of getting a number less than 7 is 1 or 100% and the probability of rolling a number greater than or equal to 3 is 2/3 or approximately 66.67%

This question falls under the topic of probability in Mathematics. In the case of a single die, there are 6 possible outcomes because a die has 6 faces.

For the probability of getting a number less than 7, all outcomes (1,2,3,4,5,6) are less than 7. Thus, the probability is 6 out of 6 or 1.

For the probability of getting a number that's greater than or equal to 3, the favorable outcomes are 3,4,5,6. So, there are 4 such outcomes. The probability, in this case, is 4 out of 6, which simplifies to 2/3.

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The equation of a parallel line through point (h, k) can be found by altering the given line's equation this way:

To change this equation to point-slope form, solve for y (without expanding the x-term). If there is any constant added to the x-term, add its opposite (so it appears with y).

Here, that looks like ...

... 2(x+9) -5(y-9) = 0

... -5(y-9) = -2(x+9) . . . . add the opposite of the x-term

... y - 9 = 2/5(x +9) . . . . this is the point-slope form you want

_____

To put the equation in general form, multiply by the common denominator of any fractions, and subtract the stuff on the right side of the equal sign. Factor out any common factors of the integer coefficients and constant, and multiply by -1 if the leading coefficient is negative.*

Here, we multiply by 5 (and eliminate parentheses) to get

... 5y -45 = 2x +18

... -2x +5y -63 = 0 . . . . right side subtracted

... 2x -5y +63 = 0 . . . . . leading coefficient made positive. This is your general form.

___

* Actually, I can find no requirement that General Form have a positive leading coefficient. Nor is there a requirement that the coefficients be mutually prime. However, these are requirements for the very similar Standard Form, which has the constant on the right side of the equal sign, instead of the left. Since leading minus signs tend to get lost, IMO, it is a good idea to make the leading coefficient positive, even if it is not a requirement.

Answer:

a)Domain is all positive integers.

b)C(2000)=$7600

c) For C(x)<10000,  less than 3846 items should be manufactured.

Step-by-step explanation:

Given that cost function is C(x)=5000+1.3x, where x is the number of manufactured items.

a) The domain of C(x) means the range of values x can take. Since x is the number of manufactured items, it cannot be negative and fraction.

Hence domain is all positive integers.

b)To find the cost of 2000 items, we should plugin x=2000 in C(x).

That is cost of 2000 items, C(2000)=5000+1.3(2000)=5000+2600=$7600

c) We are asked to find the number of items such that cost is kept below 10,000 that is C(x)<10000

            5000+1.3x<10000

Subtract 5000 from both sides

                     1.3x<5000

Divide with 1.3 on both sides

                    [tex]x<\frac{5000}{1.3}[/tex]

                     x<3846.2

Hence number of items must be less than 3846 for C(x)<10000

Final answer:

The reasonable domain of the cost function is x >= 0. The cost of 2,000 items that must be kept below $10,000 is $7,600. The greatest number of items that can be manufactured with a cost below $10,000 is 3,846 (rounded down).

Explanation:

The reasonable domain of the cost function is x >= 0 since the number of items manufactured cannot be negative. In other words, the function is valid for all non-negative values of x.

To find the cost of 2,000 items that must be kept below $10,000, we substitute x = 2,000 into the cost function:
C(2,000) = 5,000 + 1.3 × 2,000

Simplifying this equation, we get:
C(2,000) = 5,000 + 2,600 = $7,600

To determine the greatest number of items that can be manufactured with a cost below $10,000, we need to solve the inequality:
5,000 + 1.3x < 10,000

Simplifying this inequality, we have:
1.3x < 5,000

Dividing both sides of the inequality by 1.3, we obtain:
x < 3,846.15

The greatest number of items that can be manufactured with a cost below $10,000 is 3,846 (rounded down).

Correct me if I am wrong.

10 Steaks

2 Steaks for Table 6

4 Steaks for Table 7

4 Steaks for Table 11

2 + 4 + 4 = 10

ya i say 10 as well.

First, let's convert the radical terms to exponents. Remember the following:

[tex]\sqrt[n]{x^m} = x^\frac{m}{n}[/tex]

[tex]\sqrt{x^5} = x^{\frac{5}{2}}[/tex]

[tex]\sqrt[4]{x^9} = x^{\frac{9}{4}}[/tex]

[tex]\sqrt[6]{x^5} = x^{\frac{5}{6}}[/tex]

After substituting in the values we just found, our expression looks like:

[tex]\dfrac{(x^{\frac{5}{2}})(x^{\frac{9}{4}})}{x^{\frac{5}{6}}}[/tex]

Now, remember that we can add the exponents of terms that have the same base and are being multiplied by each other. Also, remember that we can subtract the exponents of terms with the same base that are being divided by each other. This is represented as:

[tex]x^a \cdot x^b = x^{(a + b)}[/tex]

[tex]\dfrac{x^c}{x^d} = x^{(c - d)}[/tex]

Thus, we can simplify our expression even more:

[tex]\dfrac{(x^{\frac{5}{2}})(x^{\frac{9}{4}})}{x^{\frac{5}{6}}}[/tex]

[tex]\dfrac{x^{\frac{19}{4}}}{x^{\frac{5}{6}}}[/tex]

[tex]x^{\frac{47}{12}}[/tex]

Our answer is [tex]\boxed{m = \dfrac{47}{12}}[/tex].

Answer:

75,575 - ten-thousands place; this 7 is worth 70,000

75,575 - thousands place; this 5 is worth 5,000

75,575 - hundreds place; this 5 is worth 500

75,575 - tens place; this 7 is worth 70

75,575 - ones place; this 5 is worth 5

2w + 2l = 25

2 * 2 + 2l = 25

Simplfiy.

4 + 2l = 25

Subtract 4 from both sides.

2l = 21

Divide both sides by 2.

l = 10.5

Now that we have the value of l, we can find the area.

A = lw

A = 10.5 * 2

A = 21.

The length is 10.5cm.

The area of the rectangle is 21cm^2

Area is a squared number.  We know that from the label we use when we solve problems involving area.  Perimeter is a single unit label.  This single unit label can also be used to find scale factor, since single unit labels are one-to-one.  If the area of polygon F is 36, that means that the single unit measure was a number that was squared to get to the area.  Same goes for polygon G.  That means that in order to find the single unit measure of each of those we have to take the square root of the area.  The square root of 36 is 6, and the square root of 4 is 2.  6:2 is the scale factor, but that can be reduced to 3:1, larger to smaller.

Answer:

1/3

Step-by-step explanation:

khan academy answer

Final answer:

Each student will receive 2 slices of pizza, as there are a total of 32 slices from 4 pizzas divided among 16 students.

Explanation:

To determine the number of pizza slices each student receives, we need to calculate the total number of slices available and then divide this by the number of students. Given that there are 4 pizzas and each pizza is cut into 8 slices, we have:

Multiply the number of pizzas by the number of slices per pizza: 4 pizzas × 8 slices/pizza = 32 slices.

Divide the total number of slices by the number of students: 32 slices ÷ 16 students = 2 slices/student.

Therefore, the function that represents the number of pizza slices each student receives is 2 slices per student.

Answer:

3n - 8 > 22

Step-by-step explanation:

Let the number be n.  Then "eight less than three times the number" is represented by 3n - 8 > 22.

Answer:

i need help too yall

Step-by-step explanation:

I started off by changing 4 1/5 into 21/5 to make the division easier.

To divide the mixed number 4 1/5 by the fraction 2/3, first convert the mixed number to an improper fraction. The operation becomes (21/5) ÷ (2/3). By multiplying 21/5 by the reciprocal of 2/3, which is 3/2, we find that the result is 63/10. When converted back to a mixed number, 63/10 is expressed as 6 3/10.

The task is to do the operation 4 1/5 divided by 2/3 and expressing the answer as a mixed number in simplest form. To divide fractions, we usually multiply by the reciprocal. First, convert 4 1/5 to an improper fraction which gives us 21/5.

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