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Nesterboy [21]
2 years ago
13

What does x equals to if 3( x + 7 ) =57

Mathematics
1 answer:
zepelin [54]2 years ago
7 0

3(x + 7) = 57 |÷3

x + 7 = 57/3

x + 7 = 19 |-7

x = 19 - 7

x = 12

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2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap
telo118 [61]

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if \frac{p}{q} is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1  10  35  50  24

  <u>| 0  -1  -9  -26   -24</u>

   <u> 1    9  26  24    0</u>

Hence quotient is x^{3} +9x^{2} +26x+24

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1   9  26   24

   <u>| 0  -2  -14   -24</u>

   <u>  1    7    12     0</u>

Hence quotient is x^{2} +7x+12

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

(-3)^{2}+7(-3)+12=-9-21+12=0

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1  7  12

   <u>| 0 -3  -12</u>

    <u> 1    4    0</u>

Hence quotient is x+4.

So, f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)

Please have a look at the graph attached.

4 0
3 years ago
WILL GIVE BRAINLIEST!
kvasek [131]
1.D, both.
not sure of the other though
6 0
3 years ago
Read 2 more answers
URGENT Enter the values for the highlighted variables that show how to subtract the rational expressions correctly: StartFractio
Marrrta [24]

The value of the highlighted variables ave been determined a =6, b= 2 ,c= 6 , d = 2  , e = 6 , f = 6, g =1

<h3>What is an Expression ?</h3>

An expression are mathematical statement consisting of variables , constants and mathematical operators .

The given expression is

\rm \dfrac{2}{x^2-36} - \dfrac{1}{x^2 +6x} = \dfrac{2}{(x+6)(x-6)}-\dfrac{1}{x(x+a)}\\\\= \dfrac{bx}{x(x+6)(x-6)}-\dfrac{x-c}{(x+6)(x+6)x}\\\\= \dfrac{dx-x+e}{x(x+6)(x-6)}\\\\= \dfrac{x+f}{x(x+6)(x-6)}\\\\= \dfrac{g}{x(x-6)}

a = 6

b= 2

c= 6

d = 2

e = 6

f = 6

g =1

Therefore the value of the highlighted variables ave been determined.

To know more about Expression

brainly.com/question/14083225

#SPJ1

3 0
2 years ago
A certain book had an original rating of 27 out of 30 points on a survey chart. Each month, the rating fell by 3 points. Express
Natali [406]

Answer:

D.) f(m)=27−3m

Step-by-step explanation:

Given that:

Original rating = 27

Total possible rating points = 30

Drop in rating point per month = 3

m = number of months since release :

Hence,

F(m) = original rating - drop in rating per month * number of months since release

F(m) = 27 - 3(m)

F(m) = 27 - 3m

7 0
3 years ago
Choose the set of equations that best represent the following information:
Mandarinka [93]

Answer:

b

Step-by-step explanation:

8 0
3 years ago
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