Which congruence criteria is met in the following scenario?
ASA
SAS
SSS
HL
AAS

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]

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3 and -4 dudes and dudettes

edg2022

Answer:

y = 3x

Step-by-step explanation:

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.

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Length + width = 1/2 the perimeter:30/2 = 15

Area = length x width

List the factors of 50: 1, 2, 5, 10, 25, 50.

Find the two factors that when added together equal 15:

Dimensions are 5 cm by 10 cm.

See attachments for answer and math work.

Solving the trigonometric equation, it is found that it takes 40 seconds to complete one turn.

The height is modeled by:

[tex]h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]

The initial height is [tex]h(0) = 15[/tex], hence, one turn is completed when h(t) = 15.

[tex]h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]

[tex]15 = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]

[tex]\cos{\left(\frac{\pi}{20}t\right)} = \frac{15}{15}[/tex]

[tex]\cos{\left(\frac{\pi}{20}t\right)} = 1[/tex]

The length of one turn is of [tex]2\pi[/tex], and [tex]\cos{(2\pi)} = 1[/tex], hence, the solution is found according to:

[tex]\frac{\pi}{20}t = 2\pi[/tex]

[tex]t = \frac{40\pi}{\pi}[/tex]

[tex]t = 40[/tex]

It takes 40 seconds to complete one turn.

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Answer:

D. 40 seconds!! Props to guy above.

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:

- 154v + 10b - 6

Step-by-step explanation:

-54v + 10b - 100v - 6

-154v + 10b - 6

Answer: the first option.

Step-by-step explanation:

Answer:

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

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:

$200

Step-by-step explanation:

$50 consutation + $150 5 hour fee.

=$200

Answer:

angle 4 is 47 degrees....

Answer:

Graph: Refer to attached image

Solution: (-5,-3)

Step-by-step explanation:

First graph to two equations.

Refer to the image attached to see what the equations would look like when graphed.

Wherever they intersect is the solution.

They intersect at (-5,-3) therefore (-5,-3) is the solution to the system of equations

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.

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Answer:

x = -3

Step-by-step explanation:

7 + 2x/3 = 5

3 . 7 + 2x

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

3

21 + 2x

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

3

Answer:

a = 160 square units

Step-by-step explanation:

The areas of the image are 160, 22.5 and 10 square units

The area of the polygon is given as:

A =10 square unit

The area of the image of the polygon is calculated as:

[tex]A_k = A * k^2[/tex]

When k = 4, we have:

[tex]A_4 = 10 * 4^2[/tex]

[tex]A_4 = 160[/tex]

When k = 1.5, we have:

[tex]A_{1.5} = 10 * 1.5^2[/tex]

[tex]A_{1.5} = 22.5[/tex]

When k = 1, we have:

[tex]A_{1} = 10 * 1^2[/tex]

[tex]A_{1} =10[/tex]

Hence, the areas of the image are 160, 22.5 and 10 square units

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Answer:

10$

Step-by-step explanation:

dollars hope it helps

Answer:

its 10$

Step-by-step explanation:

Answer:

$2,382.03

Step-by-step explanation:

Interest = Principal x Rate x Time

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

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:

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:

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:

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:

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: 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:

i don't know

Step-by-step explanation:

Answer:

802,083

Step-by-step explanation:

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:

can you add the options that would help

Step-by-step explanation:

vvvv

Answer:

21

Step-by-step explanation:

CANT SEE THEM