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3 years ago

( x - 7 )/ ( x - 2 ) = 5/4 , Therefore x = -------------

Mathematics

1 answer:

skad [1K]3 years ago

4 0

Answer:

x = -18

Explanation:

To solve this problem easily, we can cross multiply. You would multiply the numerator of the first fraction by the denominator of the second, and multiply the numerator of the second fraction by the denominator of the first. In this case, (x-7) would be multiplied by 4 and 5 would be multiplied by (x-2). The answers from these two calculations would each be one side of the equation.

After doing this, you can solve and isolate x.

Work is shown in the attached picture.

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What is the product?

Kipish [7]

The denominator of the second fraction can be factored as (a-2)(2a-7), then it becomes doable. You cancel the (2a-7) factors, and are left with:

$\frac{3a^2}{a(a-2)} \implies \frac{3a}{a-2}$

Do note that you have erased the fact that a≠0 and a≠7/2, so you should always mention that.

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2 years ago

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Use function notation to write the equation of the line

blondinia [14]

$f(x)=mx+b\to y=mx+b$

We have two points:

$(-3,\ 0);\ (-4,\ 7)$

The point slope form of the line:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

Substitute

$m=\dfrac{7-0}{-4-(-3)}=\dfrac{7}{-1}=-7$

$y-0=-7(x-(-3))\\\\y=-7(x+3)\\\\y=-7x-21$

Answer:

$f(x)=-7x-21$

8 0

2 years ago

Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you d

Sunny_sXe [5.5K]

Answer:

It will take 88.2 months to accumulate the amount

Step-by-step explanation:

Given;

Future value of money, FV = $25,000

investment per compound period, P = $200

interest rate, i = 0.75% x 12 = 9%

The number of monthly installments required to amount to FV is given by;

$n = \frac{ln(FVi +cp)-ln(cp)}{ln(c+i)-ln(c)}\\\\ n = \frac{ln(25000*0.09 +200*12)-ln(200*12)}{ln(12+0.09)-ln(12)}\\\\n = \frac{8.4446 -7.7832}{2.4924-2.4849}\\\\n = 88.2 \ months$

Therefore, it will take 88.2 months to accumulate the amount.

7 0

3 years ago

Suppose that the function g is defined, for all real numbers, as follows.

svetoff [14.1K]

Answer:

a) g(-2) = 0

b) g(-1) =1

c) g(4) = 2

Step-by-step explanation:

Given data

$g(x) = \frac{-1}{4x+1} if x < -2$

$g(x) = - (x+1)^{2} +1 if -2\leq x\leq 2$

$g(x) = 2 if x >2$

Step( i ):-

$g(x) = - (x+1)^{2} +1 if -2\leq x\leq 2$

put x = -2

$g(-2) = -(-2+1)^{2} +1 = -(-1)^{2}+1 = -1+1 =0$

g(-2) = 0

Step(ii):-

$g(x) = - (x+1)^{2} +1 if -2\leq x\leq 2$

Put x = -1

$g(-1) = -(-1+1)^{2} +1 = -(0)^{2}+1 = -0+1 =1$

g(-1) =1

Step(iii):-

$g(x) = 2 if x >2$

g(4) = 2

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3 years ago

For each point identify the axis or quadrant where the point is located…

My name is Ann [436]

Answer:

quadrant ll

Step-by-step explanation:

A point on the y-axis will always have an x-coordinate of zero. Instructions: In the figure above, the point with coordinates (4,2) is located in quadrant I. The point with coordinates (-3,4) is located in quadrant II.

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3 years ago