Can someone help me out?

Rational root theorems are used to determine the potential roots of a polynomial function

The function is given as:

[tex]f(x) = 2x^2 + 2x - 24[/tex]

Expand

[tex]f(x) = 2x^2 + 8x - 6x - 24[/tex]

Expand

[tex]f(x) = 2x(x + 4) - 6(x + 4)[/tex]

Factor out x + 4

[tex]f(x) = (2x -6)(x + 4)[/tex]

Set to 0

[tex](2x -6)(x + 4) = 0[/tex]

Split

[tex](2x -6) = 0\ or\ (x + 4) = 0[/tex]

Make x the subject in both cases

[tex]2x = 6\ or\ x= -4[/tex]

Solve for x

[tex]x = 3\ or\ x= -4[/tex]

So, the actual roots are 3 and -4

Recall that, the function is:

[tex]f(x) = 2x^2 + 2x - 24[/tex]

For a function,

[tex]f(x) = px^n + ax^{n-1} +.......+q[/tex]

According to rational root theorem, the roots of f(x) are:

[tex]Roots = \pm \frac{Factors\ of\ q}{Factors\ of\ p}[/tex]

The roots of 24 are:

[tex]24 = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]

The roots of 2 are:

[tex]2 = \pm1, \pm2[/tex]

So, the possible roots are:

[tex]Roots = \frac{\pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24}{\pm 1, \pm 2}[/tex]

This gives:

[tex]Roots = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24,\pm0.5, \pm1, \pm 1.5, \pm 2, \pm 3, \pm 4, \pm6\pm 12[/tex]

Remove repetitions

[tex]Roots = \pm0.5, \pm1, \pm 1.5, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]

Read more about rational root theorem at:

https://brainly.com/question/11015301

3 and -4 dudes and dudettes

edg2022

Step-by-step explanation:

Since B is the midpoint of AC. So,

AB = BC

12x - 12 = 4x + 28

12x - 4x = 28 + 12

8x = 40

x = 40/8

x = 5

Now,

AB = BC = 4(5) + 28

= 20 + 28

= 48 cm

Now

AC = AB + BC

AC = 48 + 48

AC = 96 cm

Answer:

x = -3

Step-by-step explanation:

7 + 2x/3 = 5

3 . 7 + 2x

-------------- = 5

3

21 + 2x

----------- = 5

3

Answer:

30/6 is correct

Step-by-step explanation:

Answer: the first option.

Step-by-step explanation:

Answer:

[tex]f(x) = \sqrt{x } - 2 \ \\ f(x) = 5 \sqrt{x} [/tex]

Answer:

can you add the options that would help

Step-by-step explanation:

vvvv

In meters he would 2.51 meters.

Answer: 67 diplomas

Step-by-step explanation:

0.5 diplomas per second = 1 diploma per 2 seconds

60/2 = 30

30+37 = 67

Correct me if I am incorrect

An equation that shows how the total number of diplomas signed depends on the number of seconds the principal spends signing them is y = 37 + 0.5x.

What is an equation?

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, let x be number of seconds the principal spends signing them. The principal already signed 37 diplomas. Th equation to illustrate this is 37 + 0.5x.

Answer:

Y=2

Step-by-step explanation:

If x=3 we can see that every two lines is 1 number up then the last

same for y access. Y=-2

Answer:

-2

Step-by-step explanation:

Answer:

802,083

Step-by-step explanation:

Answer: The correct answer is y=15(100)−5

Step-by-step explanation:

The equation is written as y = 100 - 5x. Then the amount of money left after 5 months will be $25.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Beth acquires $100 from her grandma. She intends to pay her grandma $15 every month until the cash is taken care of.

Let 'x' be the number of months and 'y' be the remaining amount. Then we have

y = 100 - 15x

The amount of money left after 5 months is calculated as,

y = 100 - 15 (5)

y = 100 - 75

y = $25

The condition is composed of y = 100 - 5x. Then how much cash left following 5 months will be $25.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

Answer:

17 quarters and 4 dimes

Step-by-step explanation:

17 · 0.25 = 4.25

4 · 0.10 = 0.40

4.25 + 0.40 = 4.65

I hope this helps!

Step-by-step explanation:

=

38.64=9.2h/2

=

38.64=4.6h

=

h = 38.64/4.6

h = 8.4

thats it

Answer:

$200

Step-by-step explanation:

$50 consutation + $150 5 hour fee.

=$200

The graph shows the linear function. I hope this helps.

Answer:

angle 4 is 47 degrees....

Answer:

$2,382.03

Step-by-step explanation:

Interest = Principal x Rate x Time

Answer:

21

Step-by-step explanation:

CANT SEE THEM

The shortest distance between the line y = 2x+4 and the point at (0.0) is 1.8 units option (A) is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that:

The equation of the line is:

y = 2x + 4

Or

2x - y + 4 = 0

The point is (0, 0)

As we know, the formula for the shortest distance between the line and a point:

D = |ax + bx + c|/√(a²+b²)

Plug x = 0 and y = 0

a = 2, b = -1, and c = 4

D = |2(0) + -1(0) + 4|/√(2²+(-1)²)

D = 4/√5

D = 1,78 ≈ 1.8 units

Thus, the shortest distance between the line y = 2x+4 and the point at (0.0) is 1.8 units option (A) is correct.

Learn more about the straight line here:

brainly.com/question/3493733

#SPJ2

Is (x-2) is a factor of x³-3x²-x +7 –

We are given –

[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf P(x) = x³-3x²-x +7[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf Q(x) =x - 2 [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf If \:Q(x) = 0[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf x - 2 = 0[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf x = 2[/tex]

Now Put x = 2 into the polynomial –

[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf P(2) = 2³-3(2)²-2+7}[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf P(2) = 8 - 3 \times 4 +5[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf P(2) = 8 -12 +5[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf P(2) = 13-12[/tex]

[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf P(2) =1 }[/tex]

________________________________________

Answer: No, absolutely not,

Step-by-step explanation: 6x2 = 12, so you have to multiply by 2 on each side. 1x2=2, so the equivilent ratio is 12:2!

Answer: Nope

Step-by-step explanation: No, because you can see they multiply 1 x 3 to get to 3, but if you multiply 6 x 3, it equals 18, not 12. (6 x 2 = 12) but they have to have the same denominator and numerator to be equivalent. Therefore, no, they are not equivalent.

Answer:

x=5/3

Step-by-step explanation:

Answer:

-5/3 or -9/4 is the answer

Step-by-step explanation:

Just completed it

Answer:

A

Step-by-step explanation:

The solutions to the given quadratic equation are x=-8 and x=3. Therefore, option A is the correct answer.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The given quadratic equation is 2x²+10x-48=0.

Here, x²+5x-24=0

x²+8x-3x-24=0

x(x+8)-3(x+8)=0

(x+8)(x-3)=0

(x+8)=0 and (x-3)=0

x=-8 and x=3

Therefore, option A is the correct answer.

To learn more about the solution of quadratic equation visit:

https://brainly.com/question/18305483.

#SPJ7

Answer: x=14

hopes this helps

Answer: your anwser is 19

Step-by-step explanation:

Add 55 to both sides.

2x=33+5

2x=33+5

2 Simplify  33+533+5  to  3838.

2x=38

2x=38

3 Divide both sides by 22.

x=\frac{38}{2}

x=  

2

38

​ 4 Simplify  

2

38

​  to  1919.

x=19

x=19

please mark brainliest

Answer:

y = 3x

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The Constant (K) is equal to 8/2 aka 0.25 making the formula now y = 0.25 × x

We have y as 3 so

3 = 0.25 × x we take the 0.25 to the other side by dividing on both sides.. this makes it cancel out on the right.

x is now equal to 3/0.25 which is 12. X = 12

Answer:

Is the answer 9 for the last x

Step-by-step explanation:

hope this helps

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

( − 3 , − 8 )

Equation Form:

x =- 3 , y = − 8

Step-by-step explanation:

Answer:

i don't know

Step-by-step explanation: