write the equation polynomial whose graph contains the points (1,0),(-5,0),(-2,0),(-4,30)

Answers

Answer 1

Answer:

y = 3(x - 1)(x + 5)(x + 2)

Step-by-step explanation:

Given points:   (1, 0)   (-5, 0)   (-2, 0)   (-4, 30)

x-intercepts are when y = 0

Therefore, the x-intercepts are x = 1, x = -5 and x = -2

So (x - 1), (x + 5) and (x + 2) are all factors of the polynomial.

Therefore, the equation of the polynomial is:

y = a(x - 1)(x + 5)(x + 2)  where a is a constant to be found

To find the constant a, input the point (-4, 30) into the equation and solve:

⇒ a(-4 - 1)(-4 + 5)(-4 + 2) = 30

⇒ a(-5)(1)(-2) = 30

⇒ 10a = 30

⇒ a = 3

Therefore, the equation of the polynomial is:

y = 3(x - 1)(x + 5)(x + 2)


Related Questions


PLEASE HELP THIS IS AP CALCULUS IM LOSING MY MIND

A cup has the shape of a right circular cone. The height of the cup is 16 cm, and the radius of the
cm opening is 4 cm. Water is being poured into the cup at a constant rate of 3 cm. At what rate, in
cm per second, is the water level rising when the depth of the water in the cup is 6 cm? (The volume of a cone of height h and radius r is given by V=1/3pir^2h.

1. 1/64pi
2. 3/pi
3. 4/3pi
4. 9/4pi

Answers

Answer:

3.  [tex]\dfrac{4}{3 \pi}[/tex]

Step-by-step explanation:

Volume of a cone:

[tex]V=\dfrac13\pi r^2h[/tex]

(where r is the radius and h is the height)

Given:

h = 16 cmr = 4 cm

[tex]\implies r=\dfrac14h[/tex]

Therefore, substitute [tex]r=\frac14h[/tex] into the volume formula to find the volume of the cone in terms of h:

[tex]\implies V=\dfrac13\pi \left(\dfrac14h\right)^2h[/tex]

[tex]\implies V=\dfrac{1}{48}\pi h^3[/tex]

Differentiate with respect to h:

[tex]\implies \dfrac{dV}{dh}=3 \cdot \dfrac{1}{48} \pi h^2=\dfrac{\pi h^2}{16}[/tex]

Volume is increasing at a constant rate of 3cm/s:

[tex]\implies \dfrac{dV}{dt}=3[/tex]

Use the chain rule to find [tex]\dfrac{dh}{dt}[/tex]

[tex]\implies \dfrac{dh}{dt}=\dfrac{dV}{dt}\times\dfrac{dh}{dV}[/tex]

[tex]\implies \dfrac{dh}{dt}=3\times\dfrac{16}{\pi h^2}[/tex]

[tex]\implies \dfrac{dh}{dt}=\dfrac{48}{\pi h^2}[/tex]

When h = 6:

[tex]\implies \dfrac{dh}{dt}=\dfrac{48}{\pi \cdot 6^2}=\dfrac{4}{3 \pi}[/tex]

You are making a cover for the rectangular sofa cushion. How much fabric do you need to cover the entire cushion?
5 in.
48 in.
20 in.

Answers

Answer:

Measure the height of the cushion if you are covering a box cushion. Multiply the width of the cushion by two and the depth of the cushion by two, and add those numbers together to figure out how much fabric you will need to make the sides, front and back of the box cushion. Add 2 inches for seam allowances.

Step-by-step explanation:

Analyze the expression. 4(0.5x – 8) What expression is equivalent to the given expression? 2x – 32 2 x – 32 2x + 8 2 x + 8 8x – 8 8 x – 8 8x + 32

Answers

The given expression is equivalent to 2.0x-32.

We have given that

4(0.5x-8)

We have to determine the equivalent expression.

We have to use the distributive property here

What is the distributive property?

a(b+c)=ab+ac

Therefore, by using the distributive property we have,

4(0.5x-8)=2.0x-32

Therefore the given expression is equivalent to the first option

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WILL GIVE 5 STARS ON YOUR ANSWER AND A THANK YOU!!!

Answers

Answer:

I would say its B)13.50

Step-by-step explanation:

I say this because he has to buy a ticket for each person continuously so thats why I say this is the constant term added to/ subtracted from the variable term.

Hope this helped! :)

In the circle above, the radius (x) is 15 centimeters. Find the area of the shaded sector. Round to the nearest tenth.

Answers

Step-by-step explanation:

125°/360°×π×15²

=245.44cm²

please help me im confused

Answers

Step-by-step explanation:

x = 5

x = -7

x = 18

x = 14

these are the answers, comment if you still have doubts.

Two sides of a triangular field measure 11. 1 meters and 13 meters. The included angle measures 98° Find the measure of the third side to the nearest tenth of a meter

Answers

Answer: 18.2 I believe

PLEASE ANSWER ASAP GIVEING BRAINLIST


What statement is true about the frequency distribution below?


A.
It has an outlier.
B.
It has 3 modes.
C.
It has a median equal to the mean.
D.
It has a symmetric distribution.

Answers

I think it might be a
it has to be answerA

x² +12x+27 = 0

Find the roots of each equation by factoring

Answers

Answer:

x = -9, -3

Step-by-step explanation:

[tex] {x }^{2} + 12x + 27 = 0[/tex]

[tex](x + 3)(x + 9) = 0[/tex]

x = -3, -9

Answer:

-3 and -9

Step-by-step explanation:

Standard quaratic form: a² + bx + c = 0

x² + 12x + 27 = 0

find 2 numbers that multiply to 27 (the c-value), but add to 12(the b-value);

The numbers will be 9 and 3, since;

9 x 3 = 27

9 + 3 = 12

Now we can put these numbers in the standard factor form: (x + p) (x + q);

(x + 9) (x + 3) = 0

Now we can set each part equal to 0 and solve;

x + 9 = 0  => x = -9

x + 3 = 0  => x = -3

So the roots are;

-3 and -9

Hope this helps!

Find f(-2) for f(x) = 5•3^x
А. 1/45
B. -45
C.-30
D. 5/9

Answers

[tex]f(x) = 5 \cdot 3^x\\\\\\f(-2) = 5\cdot 3^{-2}\\\\~~~~~~~~~=5\cdot \dfrac 1{3^2}\\\\~~~~~~~~~=\dfrac 59\\\\\text{Hence the answer is D.}[/tex]

HELP I WILL GIVE 23 POINTS THIS IS REAL QUESTION

Answers

Answer:D)6

Step-by-step explanation:

6 students had four slices of pizza.

Which table represents a linear function?

Answers

the first one because your adding 3 to every number

what is the median of the distribution

Answers

Answer:

The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values.

Step-by-step explanation:

no

33-90 divided by 3 HELP ASAP PLS

Answers

Answer:
(33-90)/3 = (33/3)-(90/3)
= 11 - 30 = -19

Which of the following most accurately describes the polygon in the diagram?

Answers

Answer:

I do not understand either

PLEASE HELP WILL GIVE BRAINLIEST

Answers

Answer:

8in³

Step-by-step explanation:

Volume is given as the product of surface area and height.

V=Ah

Where h is height and A is surface area. Here, the surface area is given 1 square inches and the height is 8 inches then the volume will be given as

V=1*8=8 cubic inches

Therefore, the volume of the bird feeder is equal to 8 cubic inches

volume = area of base x height

The problem tells you this shape is the BASE of the bird feeder, which is 8 inches away from the other base. So we want to find the area of the shape and multiply it by it’s “height” of 8 inches.

To get area of the shape break it in two and find the area of the rectangle and the area of the triangle and add together.

area of a rectangle = length x width
a = 7 x 5
a = 35

area of a triangle = 1/2 base x height
a = 1/2 x 7 x 4
a = 14

area of shape
= area of rectangle + area of triangle
= 35 + 14
= 49

Volume of bird feeder
= area of base x height
= 49 x 8
= 392

The answer is: The volume of the bird feeder is 392 inches^3

I hope this helps and is the BRAINLIEST!

Great luck with your studies!!


Graph the number -3/4

Answers

Given : number -3/4 - and  number line​

To Find :  represent -3/4 - on number line​

Solution:

Numbers with a negative sign are less than zero

Right of zero represented by ‘+’ sign and to the left of zero represented by ‘–’ sign.

+ sign numbers can be denoted as simply numbers  

On a number line the number increases as we move to the right and decreases as we move to the left.  

1 : Draw a line and mark some points at equal distance on it

Mark a point as zero on it. Points to the right of zero are positive integers and are marked simply 1, 2, 3  and so on , while points to the left of zero are negative integers and are marked – 1, – 2, – 3 and so on

- 3/4

Divide number line between -1 & 0  in  4 Equal parts and go 3 part left of 0 to show - 3/4 on number line

Credit To: amitnrw for the answer https://brainly.in/question/9136802

Can you answer number 29 please?

Answers

Answer:

a. 90

b. 40

c. 55

d. 6

e. 72

Step-by-step explanation:

a: This is a rectangle so all the full corners are 90 degrees. ABC is a corner angle.

b: 1 and 3 are the congruent angles so 3 has the same measure as 1.

C: 1 is a part of the corner, which adds up to 90 degrees. That means angle 2 and angle 1 should add up to 90. They say m<1= 35, so 90-35=55.

d. In a rectangle, the interesecting lines have the same length. AC is 12, so then DB is 12. However, DE is halfway. Half of 12=6.

e. This one has a few steps. Angle 1 is 36, and angle 2 is the other part to the 90 degree corner. 90-36= 54. That gives us angle 2. We know all angles in a triangle add up to 180 degrees. The angle across from angle 2 in the same triangle is the same value, so that is also 54. To find angle 5, it must add up to 180 degrees. 54+54+x=180, in other words. 54+54=108. 180-108=72.

Find the volume of the triangular pyramid to the nearest whole number

Answers

Answer:

361

Step-by-step explanation:

it's 361 :)........

Explain how you would find the perimeter of this triangle.

Answers

Answer:

15.4

Step-by-step explanation:

[tex]\frac{u}{4}[/tex] = tan51.3° ⇒ u = 4tan51.3° ≈ 5

[tex]\frac{4}{v}[/tex] = cos51.3° ⇒ v = [tex]\frac{4}{cos51.3}[/tex] ≈ 6.4

P ≈ 4 + 5 + 6.4 = 15.4

The perimeter of the triangle is 18.56.

What is the perimeter of triangle?

The perimeter of the triangle is addition of all three sides.

Given:

The sides of angle is 4, u and v.

The angle of triangle is 51.3 degree.

For finding the value of u and v.

               [tex]tan\theta=\frac{opposite}{Adjacent}[/tex]

tan 51.3 = u/4

1.682 =u/4

u = 6.72

             [tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex]

cos 51.3 = 4/v

0.51 = 4/v

v = 7.84

Perimeter = u + v + 4

                 = 6.72 + 7.84 + 4

                 = 18.56.

Therefore, the perimeter of this triangle is 18.56.

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The small boxes in Figures A and B at the right are
congruent squares. The perimeter of Figure A is
48 inches. What is the perimeter of Figure B?
(The perimeter of a figure is the distance around it.)
E

Answers

Answer:

60 inches

Step-by-step explanation:

In diagram A, the perimeter (outer edge) is made of 16 sides of the boxes.

48/16=3, so each side is 3 inches.

In diagram B, the perimeter is made of 20 sides.

20x3=60

PLEASE HELP!! IM ON THE LAST QUESTIONNNN ( 30 points!)

Answers

[tex]~~~~~\pi r^2 = 513\\\\ \implies r = \sqrt{\dfrac{513}{\pi}}\\\\ \implies r= \sqrt{\dfrac{513}{3.14}}\\\\\implies r=12.78~ \text cm.}\\\\\text{Hence the radius is 12.78 cm.}[/tex]

Answer:

Step-by-step explanation:

Area of circle = πr²

[tex]\sf \boxed{r =\sqrt{ \dfrac{Area}{3.14}}}[/tex]

[tex]\sf r =\sqrt{\dfrac{513}{3.14}}\\\\r = \sqrt{163.38}\\\\r = 12.78 \ cm[/tex]

Line segment xy is dilated to create line segment x'y' using point t as the center of dilation. point t is the center of dilation. line segment x y is dilated to create shorter line segment x prime y prime. the length of t x prime is 6 and the length of t y prime is 9. the length of x x prime is 2. what is yt? 3 units 6 units 12 units 15 units

Answers

The length of segment YT will be equal to 12 units as the line segment XY is dilated to create line segment X'Y' using point t as the center of dilation.

What is dilation?

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

Triangles XYT and X'Y'T are similar to the AA Similarity Theorem

[tex]\dfrac{XT}{YT}=\dfrac{X'T}{Y'T}[/tex]

substitute the given values

[tex]\dfrac{8}{YT}=\dfrac{6}{9}[/tex]

[tex]YT=\dfrac{9\times 8}{6}[/tex]

[tex]YT=12\ units[/tex]

Hence the length of segment YT will be equal to 12 units as the line segment XY is dilated to create line segment X'Y' using point t as the center of dilation.

To know more about dilation follow

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Answer:

b

Step-by-step explanation:

took the test

Marcos walled his dog around the outside of the dog park.
The park is a rectangle 88,5 meters long and 56.2
meters wide. What is the perimeter of the park?

Answers

Well 88.5 +88.5+56.2+56.2= 289.4 meters in perimeter

MATH
can somebody help me with these questions?

Answers

I’m learning this in class as well
Ok so basically you just need to find 2 random points so like (30,100) and (20,30)
And my question for you is do you know the equation format?

Write an equation of the line in Slope-int form y= 1 /2x+1

Answers

hope this helps you

Your bill at a restaurant is $42.70. If you were to tip 20%, how much will you tip? What is the total with tip?

Answers

i believe the answer is 8.54, if you take 42.70 and multiply it by 20% you get 8.54!

Translate each verbal phrase into an algebraic expression:
1. 6 inches by the number n

Answers

6” x number so you need to multiple

Need help with this geometry question asap!

Answers

Answer:

Height = 18 units

Step-by-step explanation:

Given :

Volume= 162pi, radius= 3 units

We know,

Volume of Cylinder= Pi * (radius)^2*h

now you can substitute, (P.S: dont put the value of pi as it will get cancelled)

162 pi = pi* (3)^2* h

162= 9h

∴h= 162/9= 18

height is 18 units.

Hope it helps. But I am not sure if the answer is correct or not.

Answer:

[tex]v = \pi \: {r}^{2} h \\ where \: v = 162\pi \: \\ r = 3 \\ h = \frac{v}{ {r}^{2} } \\ h = \frac{162}{9} \\ h = 18 units[/tex]

A survey asked students whether they preferred to read on paper (P) or using electronic devices (E). Based on the survey, if a junior or senior is selected at random, what is the probability that the student prefers to read using an electronic device?

Answers

In the survey on students, the probability that the student prefers to read using an electronic device is 0.46 or 46%.

What is probability?

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A survey asked students whether they preferred to read on paper (P) or using electronic devices (E).

Based on the survey, if a junior or senior is selected at random. Here,

Total number of students is 240.Total number of student prefers to read using an electronic device is 110.

Thus, the probability that the student prefers to read using an electronic device is,

[tex]P=\dfrac{110}{240}\\P=0.46[/tex]

Thus, in the survey on students, the probability that the student prefers to read using an electronic device is 0.46 or 46%.

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