In the following problem, what is the part? What number is 40% of 90?

What is the solution to this system of equations?

Basile [38]

Answer:

C. x = 3, y = -6

Step-by-step explanation:

You can divide the second equation by 2. Then you have ...

x +2y = -9

This gives you a couple of choices for solution. The x-coefficients match, so subtracting one equation from the other eliminates x:

(x +2y) -(x -2y) = (-9) -(15)

4y = -24 ⇒ y = -6

Adding the two equations eliminates y:

(x -2y) +(x +2y) = (15) +(-9)

2x = 6 ⇒ x = 3

The solution is (x, y) = (3, -6).

_____

Additional comment

I find it quick and easy to use a graphing calculator to find the solution. Many graphing calculators also make it simple to solve systems of equations in matrix form. Either way, you can obtain a solution in little more than the time it takes to enter the equations (or their coefficients).

5 0

3 years ago

Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?

Korvikt [17]

Remember that to factoring by grouping, we should split the expression into tow pairs that have something in common. The idea is that after factoring each pair, we get a binomial common factor. Is worth pointing out that you can pair factors in more than one way.

Let's check how to determine the factors of our expression by grouping:

Step 1. Look for common multiples between the terms.

Notice that 4 and 8 are multiples of 2, 8 is a multiple of 4, and all of them are multiples of 1, so we are going to try more than one pairing combination.

Step 2. Look for common factors between the variables.

Usually, we want to pair variables with higher exponents so when we factor each pair, we end up with another common factor in binomial form.

Step 3. Factor each pair; if you end with another binomial common factor, you nailed it. If not, try again.

Les't apply our steps to our expression $4x^3+x^2-8x-2$

Applying step 1, we are pairing $4x^3$ and $-8x$ . Remember to pair the remaining factors as well.

$(4x^3-8x)+(x^2-2)$

The common factor in the first pair is $4x$ , so lets factor that out

$4x(x^2-2)+(x^2-2)$

Look! we have the binomial common factor $(x^2-2)$ . Unfortunately, $4x(x^2-2)+(x^2-2)$ is not in our given choices, so let's try again:

This time we are going to group the higher variables (step 2) $4x^3$ and $x^2$

$4x^3+x^2-8x-2$

$(4x^3+x^2)+(-8x-2)$

The common factor in the first pair is $x^2$ , and the common factor in the second one is -2, so let's factor out both of them:

$(4x^3+x^2)+(-8x-2)$

$x^2(4x+1)-2(4x+1)$

This time, we got option A.

We can conclude that the correct answer is: A) x2(4x + 1) – 2(4x + 1)

3 0

3 years ago

4. A store had 86 DVDs and 52 CDs. When the equal number of DVDs and CDs were sold,

11Alexandr11 [23.1K]

Answer:

51 DVDs

Step-by-step explanation:

Let the number of DVDs and CDs sold be x each.

Initial

Number of DVDs= 86

Number of CDs= 52

After selling

Number of DVDs= 86 -x

Number of CDs= 52 -x

Given that there are 3 times as many DVDs than CDs left,

86 -x= 3(52 -x)

Expand:

86 -x= 156 -3x

Bring x terms to 1 side, constant to the other:

3x -x= 156 -86

Simplify:

2x= 70

Divide both sides by 2:

x= 35

Amount of DVDs left

= 86 -x

= 86 -35

= 51

3 0

3 years ago

$3,000 after 2 years at an interest rate of 10.0% is$ Round up to the nearest cent

Art [367]

I assume that the given interest (i) is compounded. To calculate for the future worth (F) of the given present investment (P) may be calculated by the equation,
F = P x (1 + i)^n
where n is the number of years. Substituting the given values,
F = ($3000) x (1 + 0.10)^2 = $3,630
Thus, the future worth of this investment is $3,630.0

6 0

4 years ago

Find any real solutions for the following equations. x3 - 1728 = 0

forsale [732]

12 * 12 * 12 is 1728

3 0

4 years ago

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