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beks73 [17]
3 years ago
7

Label From least to greatest 1/2, 1/3, 1/,6, 4/9

Mathematics
1 answer:
Sholpan [36]3 years ago
3 0

Answer:

1/6 4/9 1/3 1/2

Step-by-step explanation:

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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
Look at the graph shown:
lidiya [134]

Answer:

y = 3x - 1

Step-by-step explanation:

Although the coordinate plane is not given, we don't need it to find the solution. We have given all the conditions enough for the solution.

The y-intercept is (-1) and the function passes through the point ( 1, 2 ).

Only the function y = 3x -1 matches these conditions.

We can observe the points in the attached graph.

5 0
3 years ago
Read 2 more answers
Find the area of the figure.
mel-nik [20]

Answer:

192+128+112+36=468 not really sure if this is the answer

4 0
3 years ago
Read 2 more answers
If c(x) = 4x – 2 and d(x) = x^2+ 5x, what is (c circle d) (x)?
Xelga [282]

Answer:

4x² + 20x - 2

Step-by-step explanation:

To evaluate (c ○ d)(x), substitute x = d(x) into c(x)

c(x² + 5x)

= 4(x² + 5x) - 2

= 4x² + 20x - 2

7 0
3 years ago
How many real solutions are there for f(x) = (x + 3)^2 – 8?
Molodets [167]
There are 2 solutions. the highest degree of a polynomial is 2
5 0
3 years ago
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