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brilliants [131]
3 years ago
13

Does the point given below occur on the line shown. Can you show the work please

Mathematics
1 answer:
Aneli [31]3 years ago
5 0
No it doesn't. 2*0.5 + 5*0 = 1, not 19
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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
X-5y=2 and 4x+2y=8 using elimination
kobusy [5.1K]

Answer:

y=0  x=2

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Kate can mow lawns at a constant rate of 4/5 lawns per hour. How many lawns can Kate mow in 20 hours?
weqwewe [10]

Answer:

16 lawns

Step-by-step explanation:

set up a proportion:

(4/5 ÷ 1) = (x÷20)

cross-multiply:

5x = 80

x = 16

8 0
2 years ago
Which of these describes an angle?
stealth61 [152]
A part of a line that connects two endpoints I believe
7 0
2 years ago
7) Is -2 a zero (or root) of f(x) = 7x3 + x2 - 9x + 5?
Masja [62]

Answer:

Step-by-step explanation:

i do not know

6 0
3 years ago
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