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3 years ago

2-(4p+3)=-3(p+2)-(2p+3)

2 answers:

8 0

Ultimately, you want the <em>variable</em> p on one side of the equals sign, and the <em>value</em> of p on the other.

First, get rid of the parenthesis by <em>distributing.

</em>There is an invisible -1 in front of the first and last set of parenthesis, and a one times any number is the number itself, so you are essentially distributing the negative sign.
<em>
</em>So you have: 2-4p-3 = -3p-6-2p-3
<em>
</em>Next, <em>Combine like terms.
</em>
Can you take it from there?<em>

</em>

solmaris [256]3 years ago

8 0

Simplifying
2 + -1(4p + 3) = -3(p + 2) + -1(2p + 3)

Reorder the terms:
2 + -1(3 + 4p) = -3(p + 2) + -1(2p + 3)
2 + (3 * -1 + 4p * -1) = -3(p + 2) + -1(2p + 3)
2 + (-3 + -4p) = -3(p + 2) + -1(2p + 3)

Combine like terms: 2 + -3 = -1
-1 + -4p = -3(p + 2) + -1(2p + 3)

Reorder the terms:
-1 + -4p = -3(2 + p) + -1(2p + 3)
-1 + -4p = (2 * -3 + p * -3) + -1(2p + 3)
-1 + -4p = (-6 + -3p) + -1(2p + 3)

Reorder the terms:
-1 + -4p = -6 + -3p + -1(3 + 2p)
-1 + -4p = -6 + -3p + (3 * -1 + 2p * -1)
-1 + -4p = -6 + -3p + (-3 + -2p)

Reorder the terms:
-1 + -4p = -6 + -3 + -3p + -2p

Combine like terms: -6 + -3 = -9
-1 + -4p = -9 + -3p + -2p

Combine like terms: -3p + -2p = -5p
-1 + -4p = -9 + -5p

Solving
-1 + -4p = -9 + -5p

Move all terms containing p to the left, all other terms to the right.

Add '5p' to each side of the equation.
-1 + -4p + 5p = -9 + -5p + 5p

Combine like terms: -4p + 5p = 1p
-1 + 1p = -9 + -5p + 5p

Combine like terms: -5p + 5p = 0
-1 + 1p = -9 + 0
-1 + 1p = -9

Add '1' to each side of the equation.
-1 + 1 + 1p = -9 + 1

Combine like terms: -1 + 1 = 0
0 + 1p = -9 + 1
1p = -9 + 1

Combine like terms: -9 + 1 = -8
1p = -8

Divide each side by '1'.
p = -8

Simplifying
p = -8

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3 years ago

Name the solid and find its volume. Use 3.14 as the approximate value of pi.

sineoko [7]

It is given in the question that the solid is a cone with height of 16 units and radius of 7 units .

The formula of volume of cone is

$V = \frac{1}{3} \pi r^2 h$

To find the volume, we substitute the given values of r and h and use 3.14 for pi. That is

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3 years ago

What is the perimeter of △ABC?

timofeeve [1]

<h3>Given</h3>

ΔABC
A(-3, -1), B(0, 3), C(1, 2)

the length of the perimeter of ΔABC to the nearest tenth

<h3>Solution</h3>

The perimeter of a triangle is the sum of the lengths of its sides. The length of each side can be found using the Pythagorean theorem. Effectively, each pair of points is treated as the end-points of the hypotenuse of a right triangle with legs parallel to the x- and y-axes. The leg lengths are the differences betweeen the x- and y- coordinates of the points.

The difference of the x-coordinates of segment AB are 0-(-3) = 3. The y-coordinate difference is 3-(-1) = 4. So, the leg lengths of the right triangle whose hypotenuse is segment AB are 3 and 4. The Pythagorean theorem tells us

... AB² = 3² +4² = 9 +16 = 25

... AB = √25 = 5

You may recognize this as the 3-4-5 triangle often introduced as one of the first ones you play with when you learn the Pythagorean theorem.

LIkewise, segment AC has coordinate differences of ...

... C - A = (1, 2) -(-3, -1) = (4, 3)

These are the same leg lengths (in the other order) as for segment AB, so its length is also 5.

Segment BC has coordinate differences ...

... C - B = (1, 2) -(0, 3) = (1, -1)

The length of the line segment is figured as the root of the sum of squares, even though one of the coordinate differences is negative. The leg lengths of the right triangle used for finding the length of BC are the absolute value of these differences, or 1 and 1. Then the length BC is

... BC = √(1² +1²) = √2 ≈ 1.4

So the perimeter of the triangle ABC is

... AB + BC + AC = 5 + 1.4 + 5 = 11.4 . . . . perimeter of ∆ABC in units

_____

Please be aware that the advice to "round each step" is <em>bad advice,</em> in general. For real-world math problems, you only round the final result. You always carry at least enough precision in the numbers to ensure that there will not be any error in the final rounding.

In this problem, the only number that is not an integer is √2, so it doesn't really matter.