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3 years ago

Expand (x-2) (x-1). Must be in polynomial form.

1 answer:

6 0

To expand two terms such as these, we can use the method called FOIL (stands for First, Outer, Inner, Last). Here is what I mean:

We have two terms: (x - 2)(x - 1)

We should first multiply the First two terms of each term in order to complete the F stage:

(x)*(x) = $x^{2}$

So then, we take the two outer terms and multiply them together to complete the O stage:

(x)*(-1) = -x

So far we have two things that we have calculated; at the end of the FOIL process we will have four.

To keep going with the FOIL, we now multiply the two inner terms to complete the I stage:

(-2)*(x) = -2x

Last but not least, we need to complete the L stage - so we multiply the two last terms of each term:

(-2)*(-1) = 2

Now that we have our four terms, let us add them together and combine like terms:

$x^{2} + (-x) + (-2x) + 2$

Since -x and -2x both have the x portion in common and they are added together, we can add them to create one single term:

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

So now that we have our terms completed, we can combine into one polynomial equation:

$x^{2} + (-3x) + 2$ or $x^{2} -3x+2$

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Mark wants to put a fence around his square yard.He knows that his yard is shaped like a square and the area of the yard is 110.

vichka [17]

Answer:

27.5 is the answer good luck

Step-by-step explanation:

good luck my G

3 0

3 years ago

A bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 5%per year. If the interest received

marin [14]

Answer: $31000 was loaned at 13%.

Step-by-step explanation:

Let x represent the amount loaned out at 13% interest rate.

Let y represent the amount loaned out at 5% interest rate.

The bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 5%per year. It means that

x + y = 68000

The interest received made from $x in one year is

13/100 × x = 0.13x

The interest received made from $y in one year is

5/100 × x = 0.05y

If the interest received was $5880, it means that

0.13x + 0.05y = 5880- - - - - - - - - 1

Substituting x = 68000 - y into equation 1, it becomes

0.13(68000 - y) + 0.05y = 5880

8840 - 0.13y + 0.05y = 5880

- 0.13y + 0.05y = 5880 - 8840

- 0.08y = - 2960

y = - 2960/- 0.08

y = 37000

x = 68000 - y = 68000 - 37000

x = $31000

5 0

3 years ago

Let f(x)=x^3-x-1

alexira [117]

$f(x) = x^3 - x - 1$

To find the gradient of the tangent, we must first differentiate the function.

$f'(x) = \frac{d}{dx}(x^3 - x - 1) = 3x^2 - 1$

The gradient at x = 0 is given by evaluating f'(0).

$f'(0) = 3(0)^2 - 1 = -1$

The derivative of the function at this point is negative, which tells us the function is decreasing at that point.

The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so

$y = -x + c$

Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).

$f(0) = (0)^3 - (0) - 1 = -1$

So the point (0, -1) lies on the tangent. Substituting into the tangent equation:

$y = -x + c \\\\ -1 = -(0) + c \\\\ -1 = c \\\\ \text{Equation of tangent is } \boxed{y = -x - 1}$

6 0

3 years ago

A playstation 5 is $900 and costs $50 per game. A xbox is $400 and costs $60 per game. How many games will it take for both cons

belka [17]

Answer:

It would take a PlayStation 5 and 2 games to equal an Xbox and 10 games.

Step-by-step explanation:

I made a list that increase in the increments of the game price.

Something like this:

900—400~consoles alone

950—460~1 game

1000–520~2 games

1050—580~3 games

1100—640~4 games

1150—700~5 games

1200—760~6 games

1250—820~7 games

1300—880~8 games

1350—940~9 games

1400—1000~10 games

Left side is PlayStation 5 and right side is Xbox. The first row is the price of the consoles alone and then each row after that is the price of the console with an additional game. As you can see, the third row down on the left, the PlayStation 5 with 2 games is $1,000. If you look at the eleventh row on the right, you can see that Xbox with 10 games is also $1,000

3 0

2 years ago

-3/4 + (-3/4) <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%203%7D%7B4%7D%20%20%2B%20%20%5Cfrac%7B%20-%203%7D%7B4%7D%20

nika2105 [10]

Firstly, since these two fractions have the same denominator, add the numerators up: $\frac{-6}{4}$

While it appears that the answer is -6/4, you can further simplify it by dividing the numerator and denominator by 2: $-\frac{6}{4}\div\frac{2}{2}=-\frac{3}{2}$

Your answer is $-\frac{3}{2}$ 

3 0

3 years ago