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3 years ago

Simplify (1/3x+3)=5-x The answers 3/4 I just don’t know how to solve it.

Mathematics

1 answer:

omeli [17]3 years ago

4 0

(1/3x+3)=5-x

multiply both sides by three

1x+9=15-3x

add 3x to both sides

4x+9=15

subtract 9 from both sides

4x=3

divide both sides by 4 to isolate x

x=3/4

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If f(x)=x^3-12x^2+35x-24f(x)=x 3 −12x 2 +35x−24 and f(8)=0f(8)=0, then find all of the zeros of f(x)f(x) algebraically.

Neporo4naja [7]

Answer:

The zeros of f(x) are: (x - 1), (x - 3) and (x - 8)

Step-by-step explanation:

Given

$f(x)=x^3-12x^2+35x-24$

$f(8) = 0$

Required

Find all zeros of the f(x)

If $f(8) = 0$ then:

$x = 8$

And $x - 8$ is a factor

Divide f(x) by x - 8

$\frac{f(x)}{x - 8} = \frac{x^3-12x^2+35x-24}{x - 8}$

Expand the numerator

$\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 -8x^2 + 3x + 32x - 24}{x - 8}$

Rewrite as:

$\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 + 3x - 8x^2 +32x - 24}{x - 8}$

Factorize

$\frac{f(x)}{x - 8} = \frac{(x^2 - 4x + 3)(x - 8)}{x - 8}$

Expand

$\frac{f(x)}{x - 8} = \frac{(x^2 -x - 3x + 3)(x - 8)}{x - 8}$

Factorize

$\frac{f(x)}{x - 8} = \frac{(x - 1)(x - 3)(x - 8)}{x - 8}$

$\frac{f(x)}{x - 8} = (x - 1)(x - 3)$

Multiply both sides by x - 8

$f(x) = (x - 1)(x - 3)(x - 8)$

<em>Hence, the zeros of f(x) are: (x - 1), (x - 3) and (x - 8)</em>

7 0

2 years ago

Find the coordinates of a point that divides the directed line segment PQ in the ratio 5:3. A) (2, 2) B) (4, 1) C) (–6, 6) D) (4

Yuri [45]

Answer:

The answer is explained below

Step-by-step explanation:

The question is not complete we need point P and point Q.

let us assume P is at (3,1) and Q is at (-2,4)

To find the coordinate of the point that divides a line segment PQ with point P at $(x_1,y_1)$ and point Q at $(x_2,y_2)$ in the proportion a:b, we use the formula:

$x-coordinate:\\\frac{a}{a+b}(x_2-x_1)+x_1 \\\\While \ for\ y-coordinate:\\\frac{a}{a+b}(y_2-y_1)+y_1$

line segment PQ is divided in the ratio 5:3 let us assume P is at (3,1) and Q is at (-2,4). Therefore:

$x-coordinate:\\\frac{5}{5+3}(-2-3)+3 \\\\While \ for\ y-coordinate:\\\frac{5}{5+3}(4-1)+1$

4 0

3 years ago

Nine children on the swim team dont like ice cream if this represents 18% of children on the swim team how many children are on

bearhunter [10]

Answer:

Um.. Im not sure about this one.. you're in college?

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

in fred's catering order 5/12 of the lunches are sandwiches 2/12 are salads and 4/12 are pastas. Which equation can be used to f

GarryVolchara [31]

We can express an equation to find the fraction of the catering order that is sandwiches or salads by summing up the fractions of the sandwiches and the salads, in this case, the fraction of the sandwiches is 5/12 and the fraction of the salads is 2/12, then the equation looks like this:

c = 5/12 + 2/12, option B is the correct answer

7 0

1 year ago

Please help me it needs to be turned in tonight

Katarina [22]

Answer:

Step-by-step explanation:

1) x=14 y=40

2)a=10 b=37

3)u=62 v=59

4)s=9 t=14

5)u=66 v=38

hope this helps

6 0

2 years ago