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3 years ago

10

What is 7 written as a percent? A. 7.2% B. 27% C. 72% D. 720%

2 answers:

Makovka662 [10]3 years ago

5 0

The answer is A 7.2%

Andre45 [30]3 years ago

4 0

It’s A.7.2% hope that helps!

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Find an equation of the plane with the given characteristics. The plane passes through the points (4, 3, 1) and (4, 1, -7) and i

Minchanka [31]

Answer:

$3x - 4y + z = 1$

Step-by-step explanation:

Given

$Point\ 1 = (4,3,1)$

$Point\ 2 = (4,1,-7)$

Perpendicular to $8x + 7y + 4z = 18$

Required

Determine the plane equation

The general equation of a plane is:

$a(x-x_1) + b(y - y_1) + c(z-z_1) = 0$

For $n =$

$(x_1,y_1,z_1) = (4,3,1)$

$(x_2,y_2,z_2) = (4,1,-7)$

First, we need to determine parallel vector $V_1$

$V_1 =$

$V_1 =$

$V_1 =$

$V_1$ is parallel to the required plane

From the question, the required plane is perpendicular to $8x + 7y + 4z = 18$

Next, we determine vector $V_2$

$V_2 =$

This implies that the required plane is parallel to $V_2$

Hence: $V_1$ and $V_2$ are parallel.

So, we can calculate the cross product $V_1 * V_2$

$V_1 =$

$V_2 =$

$n = V_1 * V_2$

$V_1 * V_2 =\left[\begin{array}{ccc}i&j&k\\0&2&8\\8&7&4\end{array}\right]$

The product is always of the form + - +

So:

$V_1 * V_2 = i\left[\begin{array}{cc}2&8\\7&4\end{array}\right]$ $-j\left[\begin{array}{cc}0&8\\8&4\end{array}\right]$ $+k\left[\begin{array}{cc}0&2\\8&7\end{array}\right]$

Calculate the product

$V_1 * V_2 = i(2*4- 8*7) - j(0*4- 8*8) + k(0*7 - 2 * 8)$

$V_1 * V_2 = i(8- 56) - j(0- 64) + k(0 - 16)$

$V_1 * V_2 = i(-48) - j(- 64) + k(- 16)$

$V_1 * V_2 = -48i +64j - 16k$

So, the resulting vector, n is:

$n =$

Recall that:

$n =$

By comparison:

$a = -48$ $b = 64$ $c = -16$

Substitute these values in $a(x-x_1) + b(y - y_1) + c(z-z_1) = 0$

$-48(x-x_1) + 64(y - y_1) -16(z-z_1) =0$

Recall that: $(x_1,y_1,z_1) = (4,3,1)$

So, we have:

$-48(x-4) + 64(y - 3) -16(z-1) =0$

$-48x + 192 + 64y -192 - 16z +16 = 0$

Collect Like Terms

$-48x + 64y - 16z = 0 - 192 + 192 - 16$

$-48x + 64y - 16z = -16$

Divide through by -16

$3x - 4y + z = 1$

<em>Hence, the equation of the plane is</em> $3x - 4y + z = 1$ <em></em>

4 0

3 years ago

Which expression is equal to (x+2)(−3x2+3x+1)?

padilas [110]

Multiply everything in the second parenthesis by x.

-3x^3 + 3x^2 + x

Multiply everything in the second parenthesis by 2.

-6x^2 + 6x + 2

Combine these two equations together.

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

Combine like terms.

-3x^3 - 3x^2 + 7x + 2

Hope this helps!
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7 0

4 years ago

Mrs. Fisher is remodeling her house and needs to buy wallpaper border for her living room. She used her tape measure and found t

Nesterboy [21]

Answer:23.7

Step-by-step explanation:

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4 years ago

Keith_Richards [23]

Answer:

Hey there!

For this question we want to find 32% of 1239500.

0.32(1239500)=396640.

Hope this helps :)

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3 years ago

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the graph of f(x), shown below, has the same shape as the graph of g(x)=x^2, but it is shifted up 3 units and to the right 1 uni

UkoKoshka [18]

A. Takes it 1 to the right and 3 up

8 0

4 years ago

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