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4 years ago

If C = 2m2 + m and D = 2 – 6m + 2m², find an expression that equals 2C - 2D in standard form.

1 answer:

3 0

C = 2m^2 + m
D = 2 - 6m + 2m^2

2C = 2(2m^2 + m) = 4m^2+2m
2D = 2(2-6m+2m^2) = 4-12m+4m^2

2C - 2D =
4m^2+2m-(4-12m+4m^2) =
4m^2+2m-4+12m-4m^2 =
0m^2 + 14m -4 =
14m - 4

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Can anyone help me find the coordinates (?,?) given that the shape is a parallelogram? (15 points)

xxTIMURxx [149]

The missing coordinates of the parallelogram is (m + h, n).

Solution:

Diagonals of the parallelogram bisect each other.

Solve using mid-point formula:

$$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right )$

Here $x_1=m, y_1=n, x_2=h, y_2=0$

$$=\left( \frac{m+h}{2}, \frac{n+0}{2}\right )$

$$\text{Midpoint} =\left( \frac{m+h}{2}, \frac{n}{2}\right )$

<u>To find the missing coordinate:</u>

Let the missing coordinates by x and y.

Here $x_1=0, y_1=0, x_2=x, y_2=y$

$$\text{Midpoint}=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )$

$$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )$

$$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{x}{2}, \frac{y}{2}\right )$

Now equate the x-coordinate.

$$ \frac{m+h}{2}=\frac{x}{2}$

Multiply by 2 on both sides of the equation, we get

m + h = x

x = m + h

Now equate the y-coordinate.

$$\frac{n}{2} = \frac{y}{2}$

Multiply by 2 on both sides of the equation, we get

n = y

y = n

Hence the missing coordinates of the parallelogram is (m + h, n).

5 0

3 years ago

Write an algebraic expression for:<br><br> The product of 12 and the sum of a number and negative 3

lbvjy [14]

The product of 12 and the sum of a number and negative 3 is 12(x - 3)

<h3>How to represent algebraic expression?</h3>

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, multiplication etc.).

In other words, an algebraic expression is a mathematical statement that contains a combination of numbers, symbols, variables and mathematical operators.

Therefore, the product of 12 and the sum of a number and negative 3 is as follows:

let

the number = x

Hence,

12 × (x + (-3))

12 × (x - 3) = 12(x - 3)

learn more on algebraic expression here: brainly.com/question/13099621

#SPJ1

3 0

2 years ago

Use compatible numbers to estimate the quotient. 394.6÷9

lora16 [44]

Your answer is 43.8444444 and simplified you could also put it as 16.035

6 0

4 years ago

Which describes the combined variation in the formula h=V/pie r2

Mice21 [21]

Answer:

The correct option is (c).

Step-by-step explanation:

The combined formula is given by :

$h=\dfrac{V}{\pi r^2}$ ...(1)

h is height

V is volume

r is radius

It is clear from formula (1) that h varies directly with V and inverse;y with the square of r.

Hence, the correct option is (c).

6 0

3 years ago

Solve each equation for y by rewriting it in slope-intercept form (y = mx + b). Also state the slope and y-intercept of each.

Radda [10]

Answer:

Step-by-step explanation:

So we just want to get y by itself

2x - 4y = 8

4y = 2x - 8

y = (2/4)x - 2

y = (1/2)x - 2

In this form the y intercept and slope are easy to see. the slope is m and y intercept is b.

slope = 1/2

y intercept = -2

3 0

3 years ago