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maria [59]
3 years ago
12

-4r -2r +5 what does that equal

Mathematics
1 answer:
VashaNatasha [74]3 years ago
8 0

Answer:

-6r +5

Step-by-step explanation:

-4r -2r +5

Combine like terms

(-4r-2r) +5

-6r +5

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Solve this equation using an algebraic method: (x + 4)( x - 4) = 9
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What is the total area of the shape
solong [7]

Answer:

Area : 704 square units

Step-by-step explanation:

First you do 16 x 10 = 160

then you do 32 x 17 = 544

then you add 160 + 544 = 704 (D)

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3 years ago
What is the area of the parllelogtam shown below
Umnica [9.8K]
<h3>Answer: 16 square units</h3>

Let x be the height of the parallelogram. Right now it's unknown, but we can solve for it using the pythagorean theorem. Focus on the right triangle. It has legs a = 3 and b = x, with hypotenuse c = 5

a^2 + b^2 = c^2

3^2 + x^2 = 5^2

9 + x^2 = 25

x^2 = 25-9

x^2 = 16

x = sqrt(16)

x = 4

This is a 3-4-5 right triangle.

The height of the parallelogram is 4 units.

We have enough info to find the area of the parallelogram

Area of parallelogram = base*height

Area of parallelogram = 4*4

Area of parallelogram = 16 square units

Coincidentally, the base and height are the same, which isn't always going to be the case. The base is visually shown as the '4' in the diagram. The height is the dashed line, which also happens to be 4 units long.

6 0
3 years ago
For s=5 and t=8, 3st²-s²:<br> 3st²-s² =
melomori [17]

Step-by-step explanation:

Given,

s=5

t=8

solution,

= 3st² - s²

= 3*5*8² - 5²

= 3*5*64 - 25

= 960 - 25

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8 0
2 years ago
|1/2b-8|=|1/4b-1|<br> b=____ and ____
Deffense [45]

Answer:

  b = 12 and 28

Step-by-step explanation:

The absolute value equation |1/2b-8| = |1/4b-1| resolves to a piecewise linear function with three pieces. There are two solutions.

<h3>Domains</h3>

The absolute value function on the left has a turning point where its value is zero:

  1/2b -8 = 0

  b -16 = 0

  b = 16

The absolute value function on the right has a turning point where its value is zero:

  1/4b -1 = 0

  b -4 = 0

  b = 4

For b > 16, both absolute value functions are identity functions. In this domain, the equation is ...

  1/2b -8 = 1/4b -1

For 4 < b < 16, the function on the left negates its argument, so the equation in this domain is ...

  -(1/2b -8) = 1/4b -1

For b < 4, both functions negate their arguments, so the equation in this domain is ...

  -(1/2b -8) = -(1/4b -1)

For the purpose of finding the value of b, this is effectively identical to the equation for b > 16. (The value of b does not change if we multiply both sides of the equation by -1.)

<h3>Solutions</h3>

<u>Domain b < 4 ∪ 16 < b</u>

  1/2b -8 = 1/4b -1

  2b -32 = b -4 . . . . . . . . multiply by 4

  b = 28 . . . . . . . . . . . . add 32-b to both sides

This solution is in the domain of the equation, so is one of the solutions to the original equation.

<u>Domain 4 < b < 16</u>

  -(1/2b -8) = 1/4b -1 . . . . equation in this domain

  -2b +32 = b -4 . . . . . . multiply by 4

  36 = 3b . . . . . . . . . . . add 2b+4 to both sides

  12 = b . . . . . . . . . . . . divide by 3

This solution is in the domain of the equation, so is the other solution to the original equation.

<h3>Graph</h3>

For the purposes of the graph, we have define the function g(b) to be the difference of the two absolute value functions. The solutions are found where g(x) = 0, the x-intercepts. The graph shows those to be ...

  b = 12  and  b = 28

__

<em>Additional comment</em>

Defining g(b) = |1/2b-8| -|1/4b-1|, we can rewrite it as ...

  g(b)=\begin{cases}7-\dfrac{1}{4}b&\text{for }b < 4\\-\dfrac{3}{4}b+9&\text{for }4\le b < 16\\\dfrac{1}{4}b-7&\text{for }16\le b\end{cases}

Then the solutions are the values of b that make g(b) = 0.

4 0
2 years ago
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