Write a polynomial equation for a graph that passes through the point (-1, 60) and has three x-intercepts: (-4,0),
(1, 0), and (3, 0)
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].
which two ratios represent quantities that are proportional?
Answer:
C, because it equals in both sides
Answer:
The answer is C
Step-by-step explanation:
I WILL NOT ACCEPT LINKS! AND WILL REPORT!!! Please help with this geometry question. An explanation would be nice!
ON=5.099
Hope it helps
how to do this question plz answer me step by step plzz plz please
Answer:
See the attached
Step-by-step explanation:
The solution and filled in Venn diagram is attached
ahhh help please find the perimeter
Answer:
12[tex]x^{2}[/tex] + 6y
Step-by-step explanation:
If ∠1 and ∠2 are complementary angles, and m∠1 = 74°; find m∠2
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
How to find complementary anglescomplementary 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
What does the y-intercept represent in the graph below?
Graph the equation y=5/4x - 10 using the y intercept point and slope
slope is 5/4 and y intercept is -10 from the given equation.
What is Slope of Line?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:
https://brainly.com/question/14511992
#SPJ2
Paul and his family are discussing how to pay for his college education. The cost of tuition at the college that Paul wants to attend is $9,000 per year. Paul’s parents will pay 85% of the tuition cost every year, and he will pay the rest. Paul has one year to save enough money to attend her first year of college. What is the minimum amount of money he should save every month in order to reach her goal?
Answer:
i think its 637
Step-by-step explanation:
solve for X
7x=49 (brainliest)
Answer:
7
Step-by-step explanation:
divide 7 to both side
7x/7=49/7
x=7
Help this is due in 2 minutes
In a survey of 292 students, about 9.9% have attended more than one play. Which is closest to the number of students in the survey who have attended more than one play?
Answer:
so sorry i needed the points to ask my question.
Step-by-step explanation:
30 Students I hope it helps.
Un distribuidor debe repartir 879 botellas de cerveza entre 3 bares. Si el pedido del bar A es la mitad que el del bar B y la cuarta parte del bar C. ¿Cuántas botellas le tocan a cada bar?
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
Which of the following pairs of equations has (5, 3) as a solution?
Answer:
the last one .
Step-by-step explanation:
like my answer and brainliest please
Question is in picture
Answer:
casino see v
Step-by-step explanation:
j:)
I'LL GIVE YOU 5 STARES HELP. Find the area of the figures shown below and drop the correct result Into the appropriate blank. DRAG & DROP THE ANSWER 14 cm 55 cm 8 cm 11 36 m² 5 cm 38 cm 8 cm 58 cm 39 m2 8 m 40 m² 11 4 m 70 cm 10 m
Solve -4x + 6(x + 2) = 20.
Answer:
4
Step-by-step explanation:
-4x +6x +12 = 20
2x + 12 = 20
2x = 8
x = 4
Answer:
X=4
Step-by-step explanation:
-4x+6x+12=29
2x=8
x=4
Good luck .
work out the equation for each graph in the form
y=mx+c
please help !
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.
HELP PLEASE.
Area=
If there is no value under the square root enter a 1.
10^2+16^2=100+256=356^2
The first box should be 2 and the second should be 356
-4(-2)+(-12)÷(+3)+-20+(+4)+(-6)
Answer:
-18
Step-by-step explanation:
[tex]-4(-2)+\frac{(-12)}{+3}-20+(+4)+(-6)=8-\frac{12}{3}-20+4-6=8-4-20+4-6=-18[/tex]
Answer:
-18Step-by-step explanation:
-4(-2)+(-12)÷(+3)+-20+(+4)+(-6). [B.E.D.M.A.S rule] (First bracket)
= 8 - 12 ÷ 3 - 20 + 4 - 6. (Then division)
= 8 - 4 - 20 + 4 - 6. (Then after addition)
= 8 + 4 - 4 - 20 - 6
= 12 - 30. (At last subtraction)
= -18 (Ans)
Si el precio de un artículo que es $800.000 se aumenta en su cuarta parte, y el nuevo precio se disminuye en su cuarta parte. ¿Cuál es su precio final? Explica el procedimiento
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
29 + _ = 1000
vabbshs jsjsjsjs
Answer:
dont get it
Step-by-step explanation:
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
A car travels at a steady speed. It covers 60km in 40 minutes. How far will it travel in 3 hours, assuming it continues at the same rate?
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)
What's the domain and range of the exponential growth function? (please help asappp no spam please or links or anything like that!!! will give brainliest)
Domain: All real numbers; Range: All real numbers
Domain: x > –2; Range: y > –2
Domain: x < –2; Range: All real numbers
Domain: All real numbers; Range: y > –2
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.
need help asap i have 25minutes left
bac=57
Step-by-step explanation:
lmk=50
abc= 63 (if they are parallel)
What is the inverse you would use to solve this problem: c/2=16
Answer:
multiplication
Step-by-step explanation:
Plz help i don't wnat links i want you to show the answer on here i trust you will.
A=__in^2 i will give the brainlist 20 points btw
Answer:
a to L is 12 inches and a to n is 32 in Step-by-step explanation:
A pattern of ordered pairs is shown.
(0, 1), (2,4), (4,7), (6, 10)
The pattern continues. What is the eighth ordered pair in the pattern?
A. (8,13) B. (14, 18). C. (14, 22) D. (16, 19)
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)
From them, we can see that for each new ordered pair, x increases by 2, and y increases by 3.Thus, the next ordered pairs are: (8, 13), (10, 16), (12, 19), (14, 22).The eighth ordered pair is given by (14,22), option C.A similar problem is given at https://brainly.com/question/16599038
ANSWER CORRECTLY AND ILL MARK YOU AS BRAINIEST
Six containers have the following ounces in them: 6.2, 8.07, 9.4. 2.11, 5, 6.173 (Do not round your answer
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
hi, how can i graph the equation,
10i + 16p = t
?? thanks