Asked by GhostGirl

Simplify 2(x-4)-3(x+2)
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Which is the product of (-1 2/5) (-2 3/4)
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What are the coordinates of W (-3,1) after a dilation with a scale factor of 2 centered at the origin?
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The average age of three people running for election is 42. A fourth person joins the race and the average drops down to 40. What is the fourth person"s age?
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Simplify: x^-3/x^0
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What is the factored form of the expression 6x^2-x-2?
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Solve for x:
4(2x-1)=5(2x+7)
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If all the edge lengths of a rectangular prism are multiplied by a scale factor of 2, how does the volume change?
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kp(x+1)-kp
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Two sides of a triangle have measures of 7km and 9km. Which is possibly the measure of the third side?
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Simplify:
a^2 b^5 c/ a^4 bc^3
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Which expression is equal to (x+6/3) divided by (x/7)
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Separate theses numbers into rational numbers, integers, and whole numbers: -1, 0, 36/2, -528, -7 1/3, 2.845
Answered by GPT 3.5
To simplify the expression 2(x-4)-3(x+2), we can distribute the terms inside the parentheses.

2(x-4) becomes 2x - 8.

-3(x+2) becomes -3x - 6.

Now we can combine like terms.

2x - 8 - 3x - 6

Simplifying further, we have:

-1x - 14

or

-x - 14
Answered by GPT 3.5
To find the product of (-1 2/5) and (-2 3/4), we can convert each mixed number into an improper fraction and then multiply the fractions together.

(-1 2/5) can be written as -7/5 in improper fraction form.

(-2 3/4) can be written as -11/4 in improper fraction form.

Now, we can find the product by multiplying the numerators and denominators together:

(-7/5) * (-11/4) = (7 * 11) / (5 * 4) = 77/20

So, the product of (-1 2/5) and (-2 3/4) is 77/20 or 3 17/20.
Answered by GPT 3.5
A dilation with a scale factor of 2 centered at the origin will multiply the coordinates of a point by 2.

To find the new coordinates of W (-3, 1) after the dilation, we can multiply each coordinate by 2.

For the x-coordinate:

-3 * 2 = -6

For the y-coordinate:

1 * 2 = 2

So, the new coordinates of W (-3, 1) after the dilation with a scale factor of 2 centered at the origin are (-6, 2).
Answered by GPT 3.5
To solve this problem, let's denote the ages of the three original people as A, B, and C. The average age of the three original people is 42, so we can write the equation:

(A + B + C)/3 = 42

We know that the average age decreases to 40 after a fourth person joins, so we'll now consider the fourth person's age as D. The total sum of ages with the fourth person is (A + B + C + D), and now we have four people, so we can write the equation:

(A + B + C + D)/4 = 40

To find the fourth person's age, we can multiply both sides of the second equation by 4 to eliminate the denominator:

A + B + C + D = 40 * 4
A + B + C + D = 160

Now we need to isolate the fourth person's age, so let's subtract the sum of the ages of the original three people from both sides:

D = 160 - (A + B + C)

So, the fourth person's age is 160 minus the sum of the ages of the original three people (A, B, and C).
Answered by GPT 3.5
The expression x^-3/x^0 can be simplified using the properties of exponents.

First, let's calculate x^-3. When we have a negative exponent, we can rewrite it as the reciprocal of the positive exponent. In this case:

x^-3 = 1/x^3

Next, let's calculate x^0. Any nonzero number raised to the power of 0 is equal to 1. Therefore:

x^0 = 1

Now we can rewrite the expression x^-3/x^0 as:

(1/x^3) / 1

When dividing by a fraction, we can invert the fraction and multiply. So:

(1/x^3) / 1 = 1 / (x^3 * 1) = 1/x^3

Thus, the simplified form of x^-3/x^0 is 1/x^3.
Answered by GPT 3.5
To find the factored form of the expression 6x^2 - x - 2, we need to factorize it.

The expression can be rewritten as:

6x^2 - 4x + 3x - 2

Now, we'll group the terms and factor by grouping:

(6x^2 - 4x) + (3x - 2)

Factoring out the greatest common factor from the first group, we have:

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

Notice that we now have a common factor of (3x - 2) in both terms. We can factor it out:

(2x + 1)(3x - 2)

So, the factored form of 6x^2 - x - 2 is (2x + 1)(3x - 2).
Answered by GPT 3.5
To solve for x in the equation 4(2x-1) = 5(2x+7), we will distribute the terms on both sides of the equation.

On the left side:

4(2x-1) = 8x - 4

On the right side:

5(2x+7) = 10x + 35

Now we can rewrite the equation:

8x - 4 = 10x + 35

To isolate x on one side of the equation, we will subtract 8x from both sides:

8x - 8x - 4 = 10x - 8x + 35

Simplifying further:

-4 = 2x + 35

Next, we will subtract 35 from both sides:

-4 - 35 = 2x + 35 - 35

Simplifying further:

-39 = 2x

To solve for x, we will divide both sides by 2:

-39/2 = 2x/2

Simplifying further:

-19.5 = x

Therefore, the solution for x in the equation 4(2x-1) = 5(2x+7) is x = -19.5.
Answered by GPT 3.5
When all the edge lengths of a rectangular prism are multiplied by a scale factor of 2, the volume of the prism will change.

The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height.

If we multiply each edge length by a scale factor of 2, the new dimensions of the prism will be 2l, 2w, and 2h.

Using the formula for volume:

New Volume (V') = (2l) * (2w) * (2h)

Expanding this expression:

New Volume (V') = 8 * l * w * h

So, when all the edge lengths of a rectangular prism are multiplied by a scale factor of 2, the new volume will be 8 times the original volume.

In other words, the volume of the prism will increase by a factor of 8.
Answered by GPT 3.5
Factoring out the common term "kp" in the expression kp(x+1) - kp:

kp(x + 1) - kp

We can rewrite it as:

kp(x + 1 - 1)

Simplifying further:

kp(x)

The simplified expression is kp(x).
Answered by GPT 3.5
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Given that the two sides of the triangle have measures of 7 km and 9 km, in order for a triangle to be formed, the length of the third side must satisfy the inequality:

x < 7 + 9
x < 16

Therefore, any measure less than 16 km could possibly be the length of the third side of the triangle.
Answered by GPT 3.5
To simplify the expression (a^2 b^5 c) / (a^4 bc^3), we can apply the rules of exponents and cancel out common factors from the numerator and denominator.

In the numerator, we have a^2 b^5 c, and in the denominator, we have a^4 bc^3.

To simplify the expression, we can subtract the exponents of common factors in the denominator from their respective exponents in the numerator.

This gives us:

(a^2 - a^4) b^(5-1) c^(1-3)

Simplifying further:

(a^2 - a^4) b^4 c^(-2)

Finally, we can rewrite c^(-2) as 1/c^2:

(a^2 - a^4) b^4 / c^2

So, the simplified form of the expression (a^2 b^5 c) / (a^4 bc^3) is (a^2 - a^4) b^4 / c^2.
Answered by GPT 3.5
To simplify the expression (x+6/3) divided by (x/7), we need to invert the divisor and multiply.

Recall that dividing by a fraction is the same as multiplying by its reciprocal.

So, we have:

(x+6/3) / (x/7) = (x+6/3) * (7/x)

Next, let's simplify by canceling common factors.

The 3 in the numerator can be canceled with the 3 in the denominator, and the x in the denominator can be canceled with the x in the numerator.

(x+6/3) * (7/x) = (x+2) * 7

So, the simplified expression is (x+6/3) divided by (x/7) = 7(x+2).
Answered by GPT 3.5
Sure! Let's categorize these numbers into rational numbers, integers, and whole numbers:

-1:
Rational number
Integer
Whole number

0:
Rational number
Integer
Whole number

36/2:
Rational number
Integer
Whole number

-528:
Rational number
Integer
Whole number

-7 1/3:
Rational number

2.845:
Rational number