Using the Factor Theorem, the quadratic equation is given by:
[tex]f(x) = 6(x^2 + 10x + 24)[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem, we have a quadratic function, meaning that it has two roots, and it passes through (-6,0) and (-4,0), hence the roots are [tex]x_1 = -4, x_2 = -6[/tex], thus:
[tex]f(x) = a(x + 4)(x + 6)[/tex]
[tex]f(x) = a(x^2 + 10x + 24)[/tex]
Considering that it passes through (-3, -18), we can find a, hence:
[tex]18 = a[(-3)^2 + 10(-3) + 24][/tex]
[tex]3a = 18[/tex]
[tex]a = 6[/tex]
Hence the equation is:
[tex]f(x) = 6(x^2 + 10x + 24)[/tex]
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
Put the differential equation 9ty+ety′=yt2+81 into the form y′+p(t)y=g(t) and find p(t) and g(t). p(t)= help (formulas) g(t)= help (formulas) Is the differential equation 9ty+ety′=yt2+81 linear and homogeneous, linear and nonhomogeneous, or nonlinear?
Answer:
[tex]p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }[/tex]
g(t) = 0
And
The differential equation [tex]9ty + e^{t}y' = \frac{y}{t^{2} + 81 }[/tex] is linear and homogeneous
Step-by-step explanation:
Given that,
The differential equation is -
[tex]9ty + e^{t}y' = \frac{y}{t^{2} + 81 }[/tex]
[tex]e^{t}y' + (9t - \frac{1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t(t^{2} + 81 ) - 1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t^{3} + 729t - 1}{t^{2} + 81 } )y = 0\\y' + [\frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) } ]y = 0[/tex]
By comparing with y′+p(t)y=g(t), we get
[tex]p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }[/tex]
g(t) = 0
And
The differential equation [tex]9ty + e^{t}y' = \frac{y}{t^{2} + 81 }[/tex] is linear and homogeneous.
Which inequality is true when s = -4 and t = 2?
1. s > t
2. s < -t
3. -s < t
4. -s < -t
Find the probability of being below 514 if the mean of a normal distribution is 474 and the standard deviation is 32.
1,873
Step-by-step explanation:
what is 3 5/15+2 2/5
PLS HELP!!
Answer:
5.73
Step-by-step explanation:
I hope that's help u
Answer:
5 11/15
Step-by-step explanation:
Convert the 2/5 to a fraction over 15 by multiplying it by 3. You result with 6/15. You can now easily add 3 5/15 + 2 6/15. They result in 5 11/15.
HELP IM IN A MIDDLE OF A TEST!! A locker combination has four nonzero digits. If no digit can be repeated and the first three digits are 1-2-3, what is the probability that the fourth digit is 4?
A.) 1/6
B.) 1/7
C.) 1/8
D.) 1/9
NO LINKS PLEASE
Answer:A
Step-by-step explanation:
got right in quiz
so i have 136 sq units in surface area of a rectangle how do i get 136
plz helps as so you can
Answer:
well you answered the question in your question: you have Area = 136 square units. How you got it, you need to be more specific. Maybe it's because the side lengths are 2 * 68 for example. If anything provide more info. tried to help the best I can
Step-by-step explanation:
Austin correctly answered 92% of the questions on a geography quiz.
Liz answered 47 of the 50 questions correctly.
Use the drop-down menus to explain who earned the higher score.
Answer:
Liz scored more because she would score 94%, while Austin only scored 92%
HELPP!!! PLEASEEEEEEEEE
Answer:
No
Step-by-step explanation:
(0, 0) Is not a answer because ithe point does not fall within the shaded area
Jacob bought some supplies for his lemonade stand. He purchased lemons for $4.85, sugar for $3.16, containers for $18. Taxes were included in all the prices. How much money did Jacob spend on all his purchases?
Answer:
26.01
Step-by-step explanation:
What is the area of a parallelogram with a height of 6 feet and a base of 10.5 feet?
33 ft 2
60.5 ft 2
65 ft 2
63 ft 2
Answer:
[tex]area = base \times height \\ = 10.5 \times 6 \\ = 63 \: {ft}^{2} [/tex]
Find the shaded area of the circle below.
Answer:
area of the circle,
radius=10m
diameter=20m
πr²
3.14×100
314m²
area of the triangle=1/2×20×10
=100
area of the shaded area=314-100=214 m²
the answer is option H
If u know pls help me I have no clue
Answer:
7 ft3
Step-by-step explanation:
Kathy has a circular hot tub in her backyard with a radius of 5.5 feet. She wants to place a decorative border around the circumference of the hot tub. If the border costs $6.70 per foot, how much will the border for the hot tub cost?
After that incident, the Civil defense team decided to buy new trucks with ladders higher than 100 feet. They found 2 different trucks with same height of ladders. The first truck costs $145,000 and will cost $0.31 per mile traveled based on the current gas prices. The second truck will cost $160,000 but gets better gas mileage, costing $0.27 per mile. They need to decide which truck is the best deal.
Answer:
the first truck
Step-by-step explanation:
the cost difference between the first truck and the second truck = $160,000-$145,000 = $15,000
the difference of gas cost between the first truck and the second truck = $0.31 - $0.26= $0.05 per mile.
so,
I think, this is a very significant number of truck cost compared with gas cost
for the best deal, the first truck is the best choice.
HI could some please help me out , I will give BRAINLEST
Answer:
[tex]y=-1/3x+2[/tex]--------------------------
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]=\frac{2-1}{0-3}[/tex]
[tex]=1/-3[/tex]
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-1=-1/3(x-3)[/tex]
[tex]y-1=-1/3x+1[/tex]
[tex]y=-1/3x+2[/tex]
--------------------
hope it helps...
have a great day!!
It takes 0.750.75 cups of sugar to make a batch of lemon cookies. I have 5.55.5 cups of sugar. How many batches can I make?
Amy is analyzing a job offer. Amy's salary analysis, the annual salary is 48,500, the benefits are 401K matched up to 2,500/year in bonuses, the average monthly rent, 1,100 and average monthly Utility costs are 200. how much income with benefits can she expect? choose below, 43,500 48,500 56,000
Answer:
d
Step-by-step explanation:
d
I REALLY NEED HELP!
Solve the equation:
X=-1
no problem, lllllllllllollllllllll
A family on vacation records the time in hours) and the distance (in miles) that they travel. The data are shown in the scatter plot below.
Distance (miles)
YA
450
400
350
300
250
200
L
150
100
50
0
0 1 2 3 4 5 6 7 8 9
Time (hours)
Based on the scatter plot, the family travels miles in the first 3.5 hours.
If you answer with a link I will report you and get your account blocked
Answer:
In the first 3.5 hours, the family travelled 175 miles.
Step-by-step explanation:
We have the table:
time (hours) distance ( miles)
0 0
1 50
2 100
3 150
4 200
5 250
6 300
7 350
8 400
9 450
This seems like a linear relationship, let's write the general line:
y = a*x + b
That represents this situation, y is the distance in miles and x is the time in hours.
In the line equation, a represents the slope and b the y-intercept.
And if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of the line is:
a = (y₂ - y₁)/(x₂ - x₁)
In this case we have a lot of points for the line, we can use any pair we want (we actually should use a few different pairs to see that the slope is always the same)
So if we use the first two (0, 0) and (1, 50)
the slope is:
a = (50 - 0)/(1 - 0) = 50
Now, if we use the third and fifth points (4, 200) and (5, 250) now the slope is:
a = (250 - 200)/(5 - 4) = 50/1 = 50
So we can conclude that the slope of the equation is a = 50
Then the equation is something like:
y = 50*x + b
To find the value of b, we can use any of the points of the line, for example (0, 0)
This means that when x = 0, y also must be 0, then:
0 = 50*0 + b
0 = b
Then the equation is:
y = 50*x
Now, to answer how many miles the family travelled in the first 3.5 hours, we just need to replace x by 3.5 in the equation:
y = 50*3.5 = 175
In the first 3.5 hours, the family travelled 175 miles.
The rectangle is rotated 180 degrees about the orgin. What are the new coordinates of point D?
Answer:2,2
Step-by-step explanation:
Rotate and flip
Plz give me a branliest
ALGEBRA II HELP :/
Please show work the answer will be a 2 digit number
20 POINTS
BRAINLIEST
Use synthetic division and the Remainder Theorem to find P(a)
(like f(x) i think)
x^3+4x^2-8x-6
a= -2
Answer:
18
Step-by-step explanation:
f(x) = x³+4x²-8x-6
P(a) <=> P(x)
-2 | 1 4 -8 -6
|
| -2 -4 24
----------------------------
1 2 -12 18
PLEASE HELP SOLVE FOR PT. A AND B
Answer:
a=1; b=14
Step-by-step explanation:
you have to form a perfect square
(a+b)²=a²+b²+2ab
If you add a one you will get a perfect square
x²+2x+1 = (x+1)²
if you added a one in one side you have to added to the other side too
(x+1)² = 13+1
(x+1)² = 14
Answer:
a = 1, b = 14
Step-by-step explanation:
To complete the square
add ( half the coefficient of the x- term)² to both sides , that is
x² + 2(1)x + 1 = 13 + 1
(x + 1)² = 14
with a = 1 and b = 14
A) Angela has more than 8 cats in her studio apartment. (Too bad she's allergic.) Write an inequality that represents the number of cats in Angela's apartment.
Answer:
c > 8
where c = cats
Step-by-step explanation:
Note that
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
6. Find the sum of the geometric series.
a1=-9 a5=-729 r=-3
Answer:
Sn = -9(1-(-3)^n)/4
Step-by-step explanation:
Since r < 1, the sum of nth term of a geometric sequence is expressed as;
Sn = a(1-r^n)/1-r
a is the first term
n is the number f terms
r is the common ratio
An = -9(1-(-3)^n)/1-(-3)
Sn = -9(1-(-3)^n)/4
Hence the sum of the nth term of the series is Sn = -9(1-(-3)^n)/4
Goro just bought a new television for $610.00. He made a down payment of $64.00 and will pay monthly payments of $26.00 until it is paid off. How many months will Goro be paying?
Answer:
Step-by-step explanation:
Let the total Cost = y
Let the monthly payment number = x
Let the y intercept = 64
y = 26x + 64
610 = 26x + 64 Subtract 64 from each side
-64 - 64
546 = 26x
26x = 546 Divide by 26
x = 546/26
x = 21 months
Simplify : (3-3y+y)
ANSWER ?
PLS HELP THIS IS MY FINAL
Answer: C. 25.6
Step-by-step explanation:
Given CSC A= sqrt(85)/6 and that angle A is in Quadrant I, find the exact value of cot A
in simplest radical form using a rational denominator.
The exact value of cot A will be 0.857.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The co-secant of angle A is √85 / 6. And that angle A is in Quadrant I.
Then the value of angle A will be
csc A = √85 / 6
1 / cos A = √85 / 6
cos A = 6 / √85
A = 49.4°
Then the exact value of cot A will be
cot A = cot 49.4°
cot A = 0.857
The exact value of cot A will be 0.857.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ2
The Smith family was one of the first to come to the U.S. They had 8 children. Assuming that the probability of a child being a girl is .5, find the probability that the Smith family had: (do not round your answers)
Answer: Hello some part of your question is missing below is the missing part
Missing question: Find the probability that the Smith family had at least 6 girls?
answer : 0.1406
Step-by-step explanation:
Number of children = 8
probability of a child being a girl ( success ) = 0.5 (
P( boy ) ( q ) = 1 - 0.5 = 0.5
P( at least 6 girls ) = p(k = 6 ) + p(k = 7 )
= 0.109375 + 0.03125 ≈ 0.1406
( using Binomial probability Calculator )
Simplify:
2
(
5
+
3
x
)
+
(
x
+
10
)
2(5+3x)+(x+10)
Answer:
7x + 20
Step-by-step explanation:
I dont have a explanation, but this could be right. :)