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natita [175]
3 years ago
6

Find for x 1/5x + 1/3= 3(2/3x -2)

Mathematics
1 answer:
topjm [15]3 years ago
6 0

Answer:

The value of x  for the given expression is  (95/27)

Step-by-step explanation:

Here, the given expression is:

\frac{1}{5} x + \frac{1}{3}   = 3(\frac{2}{3}x -2)

Now here  solving for the value of x , we get

\frac{1}{5} x + \frac{1}{3}   = 3(\frac{2}{3}x) -6\\\implies\frac{1}{5} x + \frac{1}{3}   = 2x -6

Now, taking the variable terms on 1 side, we get

\frac{1}{5} x   - 2x   = -6 -  \frac{1}{3} \\\implies\frac{x  - 10x}{5}   = -(\frac{6(3)  +1}{3} )

or, \frac{-9x}{5}   = -\frac{19}{3}   \implies x  = \frac{19}{3}  \times\frac{5}{9}   = \frac{95}{27}

Hence,  the value of x = (95/27)

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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
Please help me i need to finish this i’m tired (please use grid if you can) asap!!!
jasenka [17]

The linear equation is y = 4x - 4

And the graph of the linear equation can be seen in the image below.

<h3>How to graph the last line?</h3>

It seems that you already are good at graphing, so I will try to explain how to find the equation more in detail.

Remember that a general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

In this case, we know that the y-intercept is -4, then b = -4, replacing that we get:

y = a*x - 4

Now we also can see that this line passes through the point (2, 4), this means that if we evaluate in x = 2, the outcome should be y = 4, replacing that we get:

4 = a*2  - 4

4 + 4 = a*2

8 = a*2

8/2 = a = 4

Then the slope is 4, and the linear equation is:

y = 4x - 4

The graph is below.

If you want to learn more about linear functions:

brainly.com/question/4025726

#SPJ1

8 0
1 year ago
Can anyone explain how to do A?
ElenaW [278]
Show me the picture of the octagon. But remember that if the diameter is shown than always do half of the diameter to get the radius. Hope this helps

4 0
3 years ago
Read 2 more answers
Helppppppppppppppppp
Maksim231197 [3]

\huge \tt༆ Answer ༄

The respective terms used for the lines are ~

  • a.) Line a = Tangent

  • b.) Line b = Radius

  • c.) Line c = Diameter

  • d.) Line d = Secant
3 0
3 years ago
Read 2 more answers
I need help please with step by step it would help me a lot
pav-90 [236]

Answer:

Domain: (-infinity, +infinity) since you can pick any x values.

Range: [0, +infinity) since it does not go below the x axis.

Step-by-step explanation:

The graph is a parabola given by y=x^2

lets pick a few x values:

x = 1 gives us y = 1^2, which = 1

x = -1 gives us y = (-1)^2, which = 1

The parabola's domain is any x value as it extends to infinity.

For its range, you can see that it does not go below the x axis at x = 0. Therefore, the range of the parabola is from [0, infinity]

4 0
3 years ago
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