Write three numbers between 300 and 350 that are divisible by 2, 5, and 10

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

| 0 -1 -9 -26 -24

1 9 26 24 0

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

| 0 -2 -14 -24

1 7 12 0

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

| 0 -3 -12

1 4 0

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

John is going on a trip and the country he is traveling to uses the Celsius scale. He is curious about converting Celsius temper

Setler79 [48]

Answer:

$f(x)=\dfrac{9}{5}x+32$ converts Celsius to Fahrenheit.

$g(x)=\dfrac{5(x-32)}{9}$ converts Fahrenheit to Celsius.

Step-by-step explanation:

Write given data in the table

$\begin{array}{cc}x&f(x)\\^{\circ}\text{C}&^{\circ}\text{F}\\20&68\\30&86\end{array}$

Let the expression for the function be

$f(x)=ax+b$

Note, that this equation is linear equation and it is well-known fact that the Celsius to Fahrenheit dependence is linear.

Substitute corresponding values into this expression:

$68=20a+b\\ \\86=30a+b$

Subtract these two equations:

$86-68=30a-20a\\ \\10a=18\\ \\a=\dfrac{9}{5}$

Substitute it into the first equation:

$68=20\cdot \dfrac{9}{5}+b\Rightarrow b=68-36=32$

So,

$f(x)=\dfrac{9}{5}x+32$

This is the function which converts Celsius to Fahrenheit.

And function

$g(x)=\dfrac{5(x-32)}{9}$ converts Fahrenheit to Celsius.

4 0

3 years ago

Read 2 more answers

What are the domain and range of this function?

Arlecino [84]

Answer:

Correct answer: The third answer is correct

Step-by-step explanation:

The domain of each function is defined by observing the behavior of the function from left to right by following the growth of numbers on the x axis of real numbers.

In the same way, the range of each function is defined by observing the behavior of the function from the bottom y axis upwards by following the growth of numbers on the y axis of real numbers.

The given function extends from negative infinite to positive infinite on the x axis and that is the domain of this function.

The minimum of a given function is 4, which means that the function exists from 4 upwards and that is the range of the function.

Domain; all real numbers or x ∈ ( -∞ , + ∞)

Range: ( y ≥ 4 )

God is with you!!!

8 0

4 years ago

Y = x2 + 3x + 10 ....

Lerok [7]

It has complex roots so we can just say it is non factorable. The sum of the roots is -3 and the product is 10.

8 0

3 years ago

What is the answer ??

Andrews [41]

Answer:

M=1

Step-by-step explanation:

2m = 7/2 - 3/2

2m= 4/2

2m=2

M=2/2

M=1

5 0

3 years ago

Write three numbers between 300 and 350 that are divisible by 2, 5, and 10​

Write three numbers between 300 and 350 that are divisible by 2, 5, and 10