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deff fn [24]
3 years ago
8

Express the product in simplest form.

Mathematics
1 answer:
Romashka [77]3 years ago
4 0
\frac{8}{2x+8} *  \frac{ x^{2}-16 }{4}

1. Cross cancel
\frac{4}{2x+8}* \frac{ x^{2} -16}{1}

2. Multiply numerators
4*x²-16 = 4x²-64

3. Multiply denominators
2x+8*1 = 2x+8

\frac{4 x^{2} -64}{2x+8}

4. Divide
\frac{4 x^{2} -64}{2x+8} = 2x-8

5. Simplify
2(x-4)

Answer is 2(x - 4)
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It's gonna be an irrational number because the length of the hypotenuse is 6.40312....... cm

{4}^{2}  + {5}^{2}  =  {41}^{2}

\sqrt{41}  = 6.403124237

An irrational number cannot be written as a simple fraction and the decimals would keep on going without a pattern (if it was repeating, it would be rational).

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3 years ago
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Fernando has been saving money to buy an e-book reader. A store has just marked down the price of its readers by 40%. Each reade
notsponge [240]

Answer: 65

Step-by-step explanation:

First you have to multiply. 150 x 0.4 = 60

Then you have to subtract 60 from 150, you get 90. Then subtract 25. 90 - 25 = 65.

4 0
3 years ago
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Which of the following is not a possible number of solutions when solving a system of equations containing a quadratic and a lin
Kobotan [32]

Answer:

3

Step-by-step explanation:

We have a system with two equations, one equation is a quadratic function and the other equation is a linear function.

To solve this system we have to clear "y" in both equations, and then equal both equations, then we will have a quadratic function and equal it to zero:

ax^2+bx+c=0, a\neq 0

Then to resolve a quadratic equation we apply Bhaskara's formula:

x_{1}=\frac{-b+\sqrt{b^2-4ac} }{2a}

x_{2}=\frac{-b-\sqrt{b^2-4ac} }{2a}

It usually has two solutions.

But it could happen that \sqrt{b^2-4ac} then the equation doesn't have real solutions.

Or it could happen that there's only one solution, this happen when the linear equation touches the quadratic equation in one point.

And it's not possible to have more than 2 solutions. Then the answer ir 3.

For example:

In the three graphs the pink one is a quadratic function and the green one is a linear function.

In the first graph we can see that the linear function intersects the quadratic function in two points, then there are two solutions.

In the second graph we can see that the linear function intersects the quadratic function in only one point, then there is one solutions.

In the third graph we can see that the linear function doesn't intersect the quadratic function, then there aren't real solutions.

7 0
3 years ago
What would be the angle between the two perpendicular lines.​
Anna007 [38]

Answer:

<em>90 degrees</em>

<em>90 degreesPerpendicular lines are lines that intersect at a <u>right (90 degrees) angle.</u></em>

5 0
3 years ago
A student solving for the acceleration of an object has applied appropriate physics principles and obtained the expression a=a1+
egoroff_w [7]

Answer:

a=\frac{3\times 7}{7}+\frac{12}{7}  (First step for obtaining a common denominator for the two fraction)

a=\frac{33}{7}\text{ m/s}^2

Step-by-step explanation:

\text{Given Expression: }a=a_1+\frac{F}{m}

where,

a is acceleration of an object.(Need to calculate)

a_1=3.00\text{ m/s}^2

F=12.0\text{ Kg.m/s}^2

m=7.00\text{ kg}

\text{Substitute }a_1, \text{ F, and m into expression and we get}

a=3+\frac{12}{7}

Now we will simplify above expression for a

First we make common denominator.

Common denominator is 7. So, we make both denominator 7. We multiply by 7 at top and bottom with 3. We get

a=\frac{3\times 7}{7}+\frac{12}{7}  (First step for obtaining a common denominator for the two fraction)

Now we combine the numerator

a=\frac{21+12}{7}

a=\frac{33}{7}\text{ m/s}^2



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3 years ago
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