Right triangles ABC and DEF are drawn to measure the slope of the line.

Given:

A graph of a polynomial passes through the point (-1, 60) and has three x-intercepts: (-4,0), (1, 0), and (3, 0).

To find:

The equation of the polynomial.

Solution:

A polynomial is defined as:

[tex]P(x)=a(x-c_1)(x-c_2)...(x-c_n)[/tex]

Where, a is a constant and [tex]c_1,c_2,...,c_n[/tex] are the zeros of the polynomial.

The given polynomial has three x-intercepts (-4,0), (1, 0), and (3, 0). It means [tex]-4,1,3[/tex] are the zeroes of the given polynomial and [tex](x+4),(x-1),(x-3)[/tex] are the factors of the given polynomial.

So, the equation of the polynomial is:

[tex]P(x)=a(x+4)(x-1)(x-3)[/tex]           ...(i)

It passes through the point [tex](-1,60)[/tex].

[tex]60=a(-1+4)(-1-1)(-1-3)[/tex]

[tex]60=a(3)(-2)(-4)[/tex]

[tex]60=24a[/tex]

Divide both sides by 24.

[tex]\dfrac{60}{24}=a[/tex]

[tex]2.5=a[/tex]

Putting [tex]a=2.5[/tex] in (i), we get

[tex]P(x)=2.5(x+4)(x-1)(x-3)[/tex]  

Therefore, the equation of the given polynomial is [tex]P(x)=2.5(x+4)(x-1)(x-3)[/tex].

Answer:

12[tex]x^{2}[/tex] + 6y

Step-by-step explanation:

bac=57

Step-by-step explanation:

lmk=50

abc= 63 (if they are parallel)

The function rule is f(x) = x - 12 and the complete table is

Input(x) Output(y)

32 20

14 2

6 −6

-2 -14

-10 -22

From the question, we have the following parameters that can be used in our computation:

Input(x) Output(y)

32 20

14 2

? −6

-2 -14

-10 ?

The slope is calculated as

m = (2 - 20)/(14 - 32)

m = 1

So, the equation is

y = mx + c

Using the points, we have

1(32) + c = 20

Evaluate

c = -12

So, we have

f(x) = x - 12

Using the above function, we have the following function values

f(-10) = -10 - 12 = -22

x - 12 = -6

x = 6

So, the complete table is

Input(x) Output(y)

32 20

14 2

6 −6

-2 -14

-10 -22

Read more about linear relation at

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Answer:

270km

Step-by-step explanation:

3 hours is 180 minutes

40 minutes - 60km

180 minutes - x km

x = 180/40 * 60 = 270km (the speed is 90km/h)

Answer:

the last one .

Step-by-step explanation:

like my answer and brainliest please

Answer:

so sorry i needed the points to ask my question.

Step-by-step explanation:

30 Students I hope it helps.

Respuesta:

$ 750 000

Explicación paso a paso:

Precio original = $ 800,000

Si el precio original se incrementa en una cuarta parte;

(800.000 + 1/4 * 800.000) = 800.000 + 200.000 = $ 1.000.000

Nuevo precio = $ 1,000,000

Si el nuevo precio se reduce en un cuarto;

1.000.000 - 1/4 (1.000.000)

1.000.000 - 250.000

= $ 750 000

El precio final es de $ 750.000

Answer:

C, because it equals in both sides

Answer:

The answer is C

Step-by-step explanation:

Answer:

Domain: All real numbers; Range: y > –2

Step-by-step explanation:

Asymptote is y = -2 so all y-values have to be greater than -2. The asymptote is horizontal so x-values can be all real numbers.

Answer:

what is the question tho?

Answer:

Hi! The answer to your question is 36.953

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

Answer:

Top first one is y=-3x-3.

Step-by-step explanation:

I know you will be able to figure out the rest. I will explain. The problem if I just give you the answers are you won’t be actually able to solve it when you encounter it on like a test or something.

The explanation:

m=rise/run.

c=y intercept/ where it is on the y-axis.

if you go down on the y axis, it would negative. The opposite will be true if you go up.

I also think it is supposed to be y=Mx+b instead of y=Mx+c.

hopefully that made sense.

Answer:

casino see  v

Step-by-step explanation:

j:)

Answer:

multiplication

Step-by-step explanation:

Answer:

See the attached

Step-by-step explanation:

The solution and filled in Venn diagram is attached

Answer:

Red

Step-by-step explanation:

Let x = number of laps and Let y = time taken to complete laps

She is able to run one lap in 7 minutes

Given this information we want to create an equation

the equation would be

7x = y

Now that we have created an equation we want to find how many laps she can run in 56 minutes.

The time is represented by 7 so we plug in 56 into y

so now we have

7x = 56

Finally we solve for x

*divide each side by 7*

56/7 = 8

7x / 7 = x

we're left with x = 8 meaning that she can run 8 laps in 56 minutes

In conclusion the answer is the Red one

Answer:

m∠2 = 16°

Step-by-step explanation:

m∠1 + m∠2 = 90°

(Complementary angles)

74° + m∠2 = 90°

m∠2 = 90° - 74°

m∠2 = 16°

The measure of the angles 2 is 16 degrees

complementary angles sum up to 90 degrees.

Given one of the angles to be 74 degrees, hence;

m<1 + m<2 = 90 degrees

74 + m<2 = 90

m<2 = 90 - 74

m<2 = 16 degrees

Hence the measure of the angles 2 is 16 degrees

Learn more on complementary angles here: https://brainly.com/question/16281260

Answer:

dont get it

Step-by-step explanation:

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

ON=5.099  

Hope it helps

Answer: C

Step-by-step explanation:

X’s are going by +2 and y’s by +3

After identifying the pattern, its eighth ordered pair is: (14, 22), option C.

--------------------------

The ordered pairs given are: (0, 1), (2,4), (4,7), (6, 10)

A similar problem is given at https://brainly.com/question/16599038

slope is 5/4 and y intercept is -10 from the given equation.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given equation is y=5/4x - 10

In the given equation the slope is 5/4 and y intercept is -10.

to draw the graph let us find few values

x    0      1            2          3           4

y     -10   -35/4   -30/4    -25/4    -5

Hence, slope is 5/4 and y intercept is -10 from the given equation.

To learn more on slope of line click:

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Answer:

i think its 637

Step-by-step explanation:

10^2+16^2=100+256=356^2

The first box should be 2 and the second should be 356

Answer:

7

Step-by-step explanation:

divide 7 to both side

7x/7=49/7

x=7

Answer:

a to L is 12 inches and a to n is 32 in                                                                          Step-by-step explanation:

Answer:

Total number of bottles Bar A get = 126

Total number of bottles Bar B get = 251

Total number of bottles Bar C get = 502

Step-by-step explanation:

Given - A distributor must distribute 879 bottles of beer among 3 bars. If the order of bar A is half that of bar B and a quarter of bar C.

To find - How many bottles do each bar get?

Proof -

Let us assume that

Total number of bottles Bar A get = x

Total number of bottles Bar B get = y

Total number of bottles Bar C get = z

Now,

Given that

Total bottles distributed = 879

⇒x + y + z = 879                  ..............(1)

Now,

Given that, the order of bar A is half that of bar B and a quarter of bar C

⇒x = [tex]\frac{1}{2}y[/tex] , x = [tex]\frac{1}{4} z[/tex]

⇒y = 2x                          .............(2)

  z = 4x                          ..............(3)

Now,

Put the values of y and z in equation (1), we get

x + 2x + 4x = 879

⇒7x = 879

⇒x = [tex]\frac{879}{7}[/tex] = 125.57

⇒y = 2(125.57) = 251.14

⇒z = 4(125.57) = 502.28

∴ we get

Total number of bottles Bar A get = x = 125.57 ≈ 126

Total number of bottles Bar B get = y = 251.14 ≈ 251

Total number of bottles Bar C get = z = 502.28  ≈ 502