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MariettaO [177]
3 years ago
5

Simplify each expression

Mathematics
1 answer:
avanturin [10]3 years ago
4 0

-6x-4y+2+3x+12y-6=(-6x+3x)+(-4y+12y)+(2-6)\\\\=-3x+8y-4\\\\-15x-3y+16x+4y=(-15x+16x)+(-3y+4y)=x+y\\\\-6x-4y+2+3x-12y+6=(-6x+3x)+(-4y-12y)+(2+6)\\\\=-3x-16y+8\\\\2x+2y-6x-3+2y+6=(2x-6x)+(2y+2y)+(-3+6)\\\\=-4x+4y+3

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What percentage of 67.5 is 7.02?<br><br> 27 is 144% of what?
djverab [1.8K]
\begin{array}{ccc}67.5&-&100\%\\\\7.02&-&p\%\end{array}\ \ \ |cross\ multiply\\\\\\67.5p=7.02\cdot100\\\\67.5p=702\ \ \ \ \ |divide\ both\ sides\ by\ 67.5\\\\p=10.4\ (\%)

Answer: 7.02 is 10.4% of 67.5.
7 0
3 years ago
Show that the equation x^3+7x-4=0 has a solution between x=0 and x=1
Aleksandr [31]

Step-by-step explanation:

Using the Intermediate Value Theorem, the following is applied:

"If f(x) is a continuous on interval [a,b] and we have two points f(a) and f(b) then there must be some value c such that f(a)<f(c)<f(b).

So here there must be a c such that

f(0) < f(c) < f(1)

Note: F(c)=0, the questions that the function have a solution between 0 and 1, so that means we must have some value, c such that f(c)=0 that exists

Next, plug in the x values into the function

f(0)  =  - 4

f(1) =  {1}^{3}  + 7(1) - 4 = 4

Since cubic functions are continuous and -4<0<4, then there is a solution c that lies between f(0) and f(1)

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2 years ago
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3 years ago
Two angles are complimentary. One angle measures 69 degrees. The other measures ( 5n + 1). What is the value of n?
iren [92.7K]

Answer:

Step-by-step explanation:

complimentary angles, when added = 90 degrees

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6 0
4 years ago
Simplify completely x^2+4x-45 / x^2+10x+9
S_A_V [24]

Answer: x - 5/x + 1

Step-by-step explanation:

This algebraic fraction

The task to be performed here is factorisation and simplification. Now going by the question,

x² + 4x - 45/x² + 10x + 9, the factorisation of

x² + 4x - 45 = x² + 9x - 5x - 45

= x(x + 9 ) - 5(x + 9 )

= ( x + 9 )(x - 5 ), don't forget this is the algebraic fraction's Numerator

The second part

x² + 10x + 9 = x² + x + 9x + 9

= x(x + 1) + 9( x + 1 )

= ( x + 9 )( x + 1 ), this is the algebraic denominator.

Now place the second expression which is the denominator under the first expression which is the numerator.

( x + 9 )( x - 5 )/( x + 9 )( x + 1 ).

You can see that, ( x + 9 )/( x + 9 ) divide each other , therefore therr then cancelled and left with

x - 5/x + 1

4 0
4 years ago
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