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erastovalidia [21]
3 years ago
11

What is the difference? StartFraction x Over x squared minus 16 EndFraction minus StartFraction 3 Over x minus 4 EndFraction Sta

rtFraction 2 (x + 6) Over (x + 4) (x minus 4) EndFraction StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction StartFraction x minus 3 Over (x + 5) (x minus 4) EndFraction StartFraction negative 2 (x minus 6) Over (x + 4) (x minus 4) EndFraction
Mathematics
2 answers:
blagie [28]3 years ago
8 0

Answer:

Cara multiplied only 4 and 7 together and did not multiply 4 and 13.

Step-by-step explanation:

katovenus [111]3 years ago
5 0

Answer:

The option "StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction" is correct

That is \frac{-2(x+6)}{(x+4)(x-4)}

Therefore \frac{x}{x^2-16}-\frac{3}{x-4}=\frac{-2(x+6)}{(x+4)(x-4)}

Step-by-step explanation:

Given problem is StartFraction x Over x squared minus 16 EndFraction minus StartFraction 3 Over x minus 4 EndFraction

It can be written as below :

\frac{x}{x^2-16}-\frac{3}{x-4}

To solve the given expression

\frac{x}{x^2-16}-\frac{3}{x-4}

=\frac{x}{x^2-4^2}-\frac{3}{x-4}

=\frac{x}{(x+4)(x-4)}-\frac{3}{x-4}  ( using the property a^2-b^2=(a+b)(a-b) )

=\frac{x-3(x+4)}{(x+4)(x-4)}

=\frac{x-3x-12}{(x+4)(x-4)} ( by using distributive property )

=\frac{-2x-12}{(x+4)(x-4)}

=\frac{-2(x+6)}{(x+4)(x-4)}

\frac{x}{x^2-16}-\frac{3}{x-4}=\frac{-2(x+6)}{(x+4)(x-4)}

Therefore \frac{x}{x^2-16}-\frac{3}{x-4}=\frac{-2(x+6)}{(x+4)(x-4)}

Therefore the option "StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction" is correct

That is \frac{-2(x+6)}{(x+4)(x-4)}

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Find a unit vector in the same direction as the given vector: v = −14.5i + 2.5 j.
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ANSWER

-  \frac{29}{866}  \sqrt{866} i + \frac{5}{866}  \sqrt{866} j

EXPLANATION

The given vector is v = −14.5i + 2.5 j.

The magnitude of this vector is

|v|  =  \sqrt{ {( - 14.5)}^{2}  +  {2.5}^{2} }

v|  =  \sqrt{ {( - 14.5)}^{2}  +  {2.5}^{2} }

v|  =  \sqrt{ 216.5}  =  \frac{ \sqrt{866} }{2}

The unit vector in the direction of this vector is

=  \frac{v}{ |v| }

= -   \frac{14.5}{ \frac{ \sqrt{866} }{2} } i +    \frac{2.5}{ \frac{ \sqrt{866} }{2} } j

=  -  \frac{29}{866}  \sqrt{866} i + \frac{5}{866}  \sqrt{866} j

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Step-by-step explanation:

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Step-by-step explanation:

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MANUFACTURING A shoe manufacturer spends $2.50 to make sandals and $4 to make running shoes. During a typical month, they spend
jonny [76]

Answer:

200 pairs of sandals

Step-by-step explanation:

Represent the sandals with x and the running shoes with y.

In a typical month:

Total = 2500

In April

Total = 3000

Required

The number of sandals in a typical month

<u>In a typical month:</u>

If 1 sandal costs 2.50, then x costs 2.50x

If 1 running shoe costs 4, then y costs 4y

The total is:

2.50x + 4y = 2500

<u>In April:</u>

If 1 sandal costs 2.50, then 2x costs 5x ---- <em>we used 2x because the pairs is doubled </em>

If 1 running shoe costs 4, then y costs 4y

The total is:

5x + 4y = 3000

The equations are:

5x + 4y = 3000

2.50x + 4y = 2500

Subtract

5x - 2.50x + 4y - 4y = 3000 - 2500

2.50x = 500

x = \frac{500}{2.50}

x = 200

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2 years ago
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