Which of the following is an equation in the form y = ax2 + bx + c of the parabola shown in the graph? Show your work.
A. y = −5x2 − 20x − 65
B. y = −5x2 − 20x − 20
C. y = −x2 − 27x − 90
D. y = −5x2 + 20x + 25
Answer:
Option D. y = – 5x² + 20x + 25
Step-by-step explanation:
We'll begin by obtaining the solutions to the equation from the graph. This can be obtained as follow:
The solutions are simply the values through which the graph cuts the x-axis.
The solutions are x = – 1 and 5.
Next, we shall obtain the equation for the graph as follow:
x = – 1 Or x = 5
x + 1 = 0 or x – 5= 0
(x + 1) (x – 5) = 0
Expand
x(x – 5) + 1(x – 5) = 0
x² – 5x + x – 5 = 0
x² – 4x – 5 = 0
Multiply through by 5
5x² – 20x – 25 = 0
Rearrange
0 = 0 – (5x² – 20x – 25)
= – 5x² + 20x + 25
Thus, the equation is:
y = – 5x² + 20x + 25
Tom has 40$ to spend. He spend $21.40 on a light saber. He needs to set aside $15 for a toda t-shirt. If skittles cost $0.58 per package, what is the maximum number of skittles packages he can buy? PLEASE HELP
Answer:
6
Step-by-step explanation:
40 - 21.40 = 18.6
18.6 - 15, for the amount he sets aside for shirt = 3.6 left to spend
3.6 divided by 0.58 = 6.20
so rounded, the answer should be 6 packages of skittles
Solve the equation 3(m + 5) = 3 + 3(2m + 2) for m.
Answer:
m=2
Step-by-step explanation:
Answer:
[tex]m=2[/tex]
Step-by-step explanation:
[tex]3\left(m+5\right)=3+3\left(2m+2\right)[/tex]
Expand:
[tex]3m+3\times5=3+3\times2m+3\times2[/tex]
[tex]3m+15=3+6m+6[/tex]
[tex]3m+15=6m+9[/tex]
Subtract 15 from both sides:
[tex]3m+15-15=6m+9-15[/tex]
[tex]3m=6m-6[/tex]
Subtract 6m from both sides:
[tex]3m-6m=6m-6-6m[/tex]
[tex]-3m=-6[/tex]
Divide both sides by -3:
[tex]\frac{-3m}{-3}=\frac{-6}{-3}[/tex]
[tex]m=2[/tex]
The graph shows the number of miles traveled by a train over a 5 hour trip.
180
160
140
120
100
Miles
Traveled
80
60
40
20
0
1
2
4
5
3
Hours
How fast is the train traveling?
A. 30 miles per hour
B. 32.5 miles per hour
C. 35 miles per hour
D. 40 miles per hour
Answer: 35
Step-by-step explanation:
Similar triangles vs con congruent explanation
Answer:
Similar triangle means that only the angles are the same, but the sides are not. Congruent means the angles and sides are the same.
how many line of symmetry has a kite
Answer:
1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
It takes 5 people 5 minutes to make 5 toys. How long would it take 100 people to make 100 toys?
Answer:
5 minutes
Step-by-step explanation:
5 people take 5 minutes to make 5 toys
1 person takes 25 minutes to make 5 toys
100 people take 0.25 minutes to make 5 toys
100 people take 0.05 minutes to make 1 toy
100 people take 5 minutes to make 100 toys
Find the coordinates of the midpoint of TU for T(3,1) and U(5,3)
==========================================================
The given points are T(3,1) and U(5,3)
The x coordinates of these given points are 3 and 5. Add them up to get 3+5 = 8. Then cut this in half getting 8/2 = 4. This is the x coordinate of the midpoint.
The y coordinates are 1 and 3. They add to 1+3 = 4. Then that cuts in half to get 4/2 = 2. This is the y coordinate of the midpoint.
The midpoint is (4,2)
Effectively, we just used the midpoint formula
[tex](x_m, y_m) = \left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right)[/tex]
In short: add the corresponding coordinates, then divide by 2.
Show Your Work. Find The Length of SU ~(Will Give Brainliest) :)
Answer: 14
Step-by-step explanation: 14 because QU is 24, RU is 19, so SU has to be 14. 24-5=19 19-5=14
Answer:
14
Step-by-step explanation:
QR = 5 RS = 5 and ST = 5
If all of these distances are equal to 5 then all you need to do is subtract the distance of RU, which is 19, from ST, which is 5, and that'll be your answer.
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify. The cube of the difference of 1 and a number.
Answer:
1-x=y cubed
Step-by-step explanation:
difference between 1 and a number is 1-x and the answer to this you cube.
how to solve V1 T2 = V2 T1
V1 = 600mL T1 = 77.0 V2 = ? T2 = 86.0
Answer:
V2 = 670.129
Step-by-step explanation:
V1T2 = V2T1
Let V2 = y
600 x 86.0 = y x 77.0
51600 = 77y
77y/77 = 51600/77
y = 670.129
since y= V2
V2 = 670.129
Find (f+g)(x).
f(x) = 2x2 – 2x+7
g(x) = 4x2 – 2x + 9
Answer:
6x^2 -4x +16
Step-by-step explanation:
(2x^2 -2x +7) + (4x^2 -2x +9)
6x^2 -4x +16
Find the exact value of sin(140°)cos(20°) – cos(140°)sin(20°)
Given :
An expression sin(140°)cos(20°) – cos(140°)sin(20°) .
To Find :
The value of given expression .
Solution :
We know ,
sin(A - B) = sin A cos B - cos A sin B
By comparing with above formula , we get :
A = 140° and B = 20° .
So , sin(140°)cos(20°) – cos(140°)sin(20°) = sin ( 140°- 20°) = sin 120° .
Now , [tex]sin 120^\circ{} = \dfrac{\sqrt{3}}{2}[/tex]
Therefore , the value of expression is [tex]\dfrac{\sqrt{3}}{2}[/tex] .
Hence , this is the required solution .
5 -x -x = -1 what is x ?
Answer:
x=3
Step-by-step explanation:
[tex]5 - x - x = - 1 \\ 5 - 2x = - 1 \\ - 2x = - 1 - 5 \\ - 2x = - 6 \\ x = \frac{ - 6}{ - 2} \\ x = \frac{6}{2} \\ x = 3[/tex]
hope it helped you:)
Answer:
3
Step-by-step explanation:
5-2x=-1
-5__-5
____-6
-2
3
Divide8/9 and 8. Express your answer in simplest form
Answer: The answer is 0.11 in decimal form.
Step-by-step explanation:
Solve for the following variable.
Answer:
answers in the explanation.
Step-by-step explanation:
1. x=12
2 x=7
3.x=8
4.x=5
Write The slope intercept Form of the equation of a line with a slope of -4 that passes through the point (4,4)
Answer: y = 4x - 12
Step-by-step explanation:
Plz helpp me!!?:) I don’t understand
-24 - (-13) = w
Simplify the left side
-24 + 13 = w
Add together like terms
-11 = w
202·87–100·87–2·87=
Step-by-step explanation:
202·87–100·87–2·87
=99.13
Answer:
8700
Step-by-step explanation:
If you want it evaluated, this is the answer. 202 ·87-100·87-2·87= 17574-100·87-2·87=17574-8700-2·87=17574-8700-174= 8700
4. So
3. Gecko Wireless has a 1000 minute monthly plan
that costs $29.95. Each bill also includes $2.95 for
federal communications tax and $0.05 per minute
over 1000. If m represent the minutes over 1000,
which equation represents the cost, p, of wireless
phone service? (MAFS.912.A-CED. 1.1)
defin
solut
a. P= 29.95 + 2.95
b. P=0.05 + m(29.95 +2.95)
P= 29.95 + 0.05m +2.95
d. P= (29.95 + 0.05)m +2.95. What equation should I use?
Answer:
[tex]P=29.95+0.05m+2.95[/tex]
Step-by-step explanation:
The monthly plan costs starts at $29.95, so we're not changing that.
For each monthly plan, we have to pay a tax of $2.95, so we're not changing that.
If we go over 1,000 minutes, we have to pay $0.05 for every minute we go over, and with the fact that [tex]m[/tex] represents each minute over 1,000, we're going to have to represent minutes over 1,000 as [tex]0.05m[/tex] in our equation.
Set up your equation:
[tex]P=29.95+0.05m+2.95[/tex]
Which inequality is true? Use the number line to help.
A number line going from negative 5 to positive 3 in increments of 1.
1.5 greater-than 2 and one-half
One-half greater-than 0.5
Negative 2.5 greater-than negative 1.5
Negative 3 and one-half greater-than negative 4.5
HELP ME
Answer:
c
Step-by-step explanation:
i did the assignment on E2020
Answer:
c
Step-by-step explanation:
Kiran is spending $12 on games and rides at another carnival, where a game costs $0.25 and a ride costs $1.
Answer:
10.75 is the answer I think
Given b(x) = [X+41, what is b(-10)?
4d - p = m
Solve for d
Answer:
d=(m+p)/4
Step-by-step explanation:
The given equation solved for d as d=(m+p)/4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 4d-p=m.
The given equation can be solved as
4d=m+p
Therefore, the given equation solved for d as d=(m+p)/4.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
What is the value 4 x (-6.3)
Answer:
-252
Step-by-step explanation:
4 * -6.3
-252
Anytime you multiply a positive number to a negative number, it will always be negative.
Best of Luck!
Answer:
-252 is the correct answer to this question
Solve: −6x+4≤−16−2x . Express your answer in interval notation. (Express your answer in interval notation. Use U to indicate a union of intervals, and "oo" to express ∞)
Answer:
[5, oo)
Step-by-step explanation:
Add 6x+16 to both sides:
20 ≤ 4x
5 ≤ x . . . . . . divide by 4
The solution interval is [5, oo).
Answer:
A is the answer
Step-by-step explanation:
Translate into Algebra.
Jim will be x years old in two years. At that time, his sister will be twice as old as he will be. How old is Jim's sister now?
Let s be Jim's Sister's age now
s = 2x
Solve using 2-step equations.
You got a job which only pays salary without commission.
You earn $40,000 per year. You're living with your parents,
so bills this month will only be $400, but you want to put
$2000 into your savings.
After paying bills and putting money aside in savings, how
much will you have left over?
I am a multiple of 70. I am between 500 and 1000. My tens digit is odd. What number could I be?
Plz help also can you show the explanation too!
Answer:
Step-by-step explanation:
490 = 70 * 7
560 = 70 * 8
630 = 70 *9
700 = 70 * 10
770
840
910
You can fill in the other 3
So the number can be 630 770 or 910
Answer:
630, 770, 910
Step-by-step explanation:
They are multiples of 70 and the tens place number is odd 630, 770, 910
4(2-4x)-3x=65 Whats the answer and how did you solve it?
Answer:
x= -3
Step-by-step explanation:
Distribute 4(2-4x) which leaves you with 8-16x-3x=65
combine the like terms which leaves you with 8-19x=65
subtract 8 from both sides 8-19x-8=65-8 which leaves you with -19x=57
lastly divide -19 from both sides which leaves you with x= -3