The parabola with equation $y=ax^2+bx+c$ is graphed below:
(attached)
The zeros of the quadratic $ax^2 + bx + c$ are at $x=m$ and $x=n$, where $m>n$. What is $m-n$?
Answers
Answer:
[tex]m-n=2[/tex]
Step-by-step explanation:
Instead of using the standard form, we can use the vertex form of a quadratic equation:
[tex]f(x)=a(x-h)^2+k[/tex]
Where a is the leading coefficient, and (h, k) is our vertex.
Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:
[tex]f(x)=a(x-2)^2-4[/tex]
Now, we need to determine a.
We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:
[tex]12=a((4)-2)^2-4[/tex]
Solve for a. Subtract within the parentheses:
[tex]12=a(2)^2-4[/tex]
Add 4 to both sides:
[tex]16=a(2)^2[/tex]
Square:
[tex]16=4a[/tex]
Solve:
[tex]a=4[/tex]
Thererfore, the value of a is 4.
So, our function is:
[tex]f(x)=4(x-2)^2-4[/tex]
Now, let’s find our roots. Set the equation to 0 and solve for x:
[tex]0=4(x-2)^2-4[/tex]
[tex]4=4(x-2)^2\\1=(x-2)^2\\x-2=\pm1 \\ x=2\pm1 \\ x=3\text{ or } 1[/tex]
So, our roots are 1 and 3.
The greater root is 3 and the lesser root is 1.
Therefore, m-n, where m>n, is 3-1 or 2.
Our final answer is 2.
Answer:
2
Step-by-step explanation:
Source: AOPS
Related Questions
Which equation is a line that passes through the points (4, 5) and (0, -3)?
Answers
Answer:
y = 2x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 5) and (x₂, y₂ ) = (0, - 3)
m = [tex]\frac{-3-5}{0-4}[/tex] = [tex]\frac{-8}{-4}[/tex] = 2
The line crosses the y- axis at (0, - 3) ⇒ c = - 3
y = 2x - 3 ← equation of line
Two students are taking a math test. After 5 minutes, one student is 13 done and the other is 28 done. How much ahead of the second student is the first
Answers
Given :
Two students are taking a maths test.
After 5 minutes, one student is 13 done and the other is 28 done.
To Find :
How much ahead of the second student is the first.
Solution :
Number of questions second student is ahead is :
[tex]n = 28 - 13\\\\n = 15[/tex]
Therefore, second student is ahead by first by 15 questions.
Hence, this is the required solution.
im having trouble figuring out what this question means |7| + -4=?
Answers
Answer:
3
Step-by-step explanation:
It means absolute value 7 plus -4
This means that if it were a -7, it would become positive because it is under absolute value bars...since it is positive nothing changes
7-4= 3
i am in doubt in this task
Answers
Answer:
zoomMeeting ID: 8570913589 Passcode: K58Ech
Explanation:
NO FACE SHOWING N^de ZOOM
Step-by-step explanation:
A mixture of green paint contains 9 pints of blue paint and 12 pints of yellow paint. To make the same shade of green paint using using 21 pints of blue paint, how much yellow would you need?
Answers
Answer:
28 pints of yellow paint needed
Step-by-step explanation:
Mixture of green paint = 9 pints of blue paints : 12 pints of yellow paint
Blue paint : yellow paint = 9 : 12
To make the same shade of green paint using using 21 pints of blue paint, how much yellow would you need?
Let
x = pints of yellow pint needed
Blue paint : yellow paint = 21 : x
Equate the ratios to find x
Blue paint : yellow paint
9 : 12 = 21 : x
9/12 = 21/x
Cross multiplication
9 * x = 12 * 21
9x = 252
Divide both sides by 9
x = 252 / 9
= 28
pints of yellow pint needed = x
= 28
2+8+9+4-3-4-6+9+5+3+8
Answers
[tex]2+8+9+4-3-4-6+9+5+3+8 \\ \\ = > 10 + 9+4-3-4-6+9+5+3+8 \\ \\ = > 19+4-3-4-6+9+5+3+8 \\ \\ = > 23-3-4-6+9+5+3+8 \\ \\ = > 20-4-6+9+5+3+8 \\ \\ = > 16-6+9+5+3+8 \\ \\ = > 10+9+5+3+8 \\ \\ = > 19+5+3+8 \\ \\ = > 24 + 3 + 8 \\ \\ = > 27 + 8 \\ \\ = > \green{\boxed{ 35}}[/tex]
Answer:
35
Step-by-step explanation:
2+8+9+4-3-4-6+9+5+3+8
10+13-3-4-6+9+16
23-13+25
10+25
35
Which statement correctly describes the relationship between the graph of f (x) and the graph of g(x) = f (x) – 4
Answers
Answer:
g(x) will be 4 units under f(x), and will be parallel.
Step-by-step explanation:
The only thing changing is the constant, or y-intercep. This is shown in -4, so 4 units lower. Slope will stay the same because it has not been modified in the expression for g(x).
Answer:
The graph of g(x) is the graph of f(x) translated 4 units down.
Step-by-step explanation:
The slope of the line whose equation is 6x = 4y - 7 is
A. 04
B. 2/3
C. 3/2
Answers
4y = 6x + 7
Divide by 4
y = 6/4x + 7
It would be C. 3/2
identify the slope of the line. then identify a point the line passes through:
1. y - 2 =1/4(x - 5)
2. y-7=-3(x+6)
Answers
Answer:
ummmm honey I'm confused already
Investors buy a studio apartment for $180,000. Of this amount, they have a down payment of $36,000. Their down payment is what percent of the purchase price? What percent of the purchase price would a $72,000 down payment be?
Their down payment is *blank*% of the purchase price.
Answers
Answer:
Answer: 36,000 would be 20 percent. 72,000 would be 40 percent. Step-by-step explanation: You just divide 36,000 by 180,000
X/12 - 9= 1 what is x?
Answers
Answer:
x = 120
Step-by-step explanation:
x/12 - 9 = 1
Inverse operations
x/12 - 9 = 1
+9 +9
x/12 = 10
*12 *12
x = 120
Answer:
x=120
Step-by-step explanation:
I would appreciate any help
Answers
-6. -6
————————-
x+2y= 4 x+y
-x -y - x -y
———————
y=4 (ANSWRR)
*PLUG IT IN*
x+4= 6
-4. -4
x=2 (ANSWER)
the last choice is correct
a
(10x – 23)
137°
b
What is the converse?
Answers
Answer:
x=16 alternate interior angles converse
Step-by-step explanation:
PLEASE HELP! ILL GIVE YOU BRAINLIEST
Answers
Answer:
In the first picture is B
In the second is C
Step-by-step explanation:
Answer:
the first one is A. 2n + 2 and the second is C. 3(y + 2)
Step-by-step explanation:
So for the first one, 5n + 2 - 3n, is basically combining the factors with the variable n, so you subtract 3n from 5n, giving you 2n + 2, or A.
The second one is kinda reverse. You have to find the one that makes the most sense via Distributive Property. So what you do is separate 3 from the others and put y + 6 in parentheses, like this:
3(y + 6)
But this isn't the answer, as if you do the distributive property with this answer, you would get 3y + 18, and that's not what we want to get. So what we have to do is divide 6 by 3, giving us 2, thus giving us our answer of C.
Hope I helped! ^w^
Isaiah and Cooper work at a dry cleaners ironing shirts. Isaiah can iron 25 shirts per hour, and Cooper can iron 30 shirts per hour. Cooper worked twice as many hours as Isaiah and they ironed 340 shirts between them. Write a system of equations that could be used to determine the number of hours Isaiah worked and the number of hours Cooper worked. Define the variables that you use to write the system.
Answers
Answer:
See Explanation
Step-by-step explanation:
[tex]25x + 30y = 340\\y = 2x\\[/tex]
x=number of hours Isaiah worked.
y=number of hours Cooper worked
Am I right vote you brainiest
Answers
Answer:
false
Step-by-step explanation:
just say bruh plz it would be funny enjoy the points
Answers
Answer:
bruh bruh bruh burh ty sm
Bru i finna dip chip & let it rip
sorry br*h is censored for some reason
Polygon ABCD slides 4 units left and 3 units up on the coordinate plane. If the original measure of angle A was 75 degrees, what is the measure of angle A'? 75 degrees 100 degrees 105 degrees 180 degrees
Answers
Answer:
A 75
Step-by-step explanation:
i did flvs
Answer:
75 degrees im doing the test now
Step-by-step explanation:
In the number 707B47.B is a prime number.If the number is rounder off to 3sf its value is 708000 what is the biggest value of B
Answers
The list of single digit primes is {2,3,5,7}. The largest prime is 7, so B = 7 is the largest possible value.
Also note how 707,747 rounds to 708,000 when rounding to 3 significant figures.
rewrite this expression
[tex] \sqrt[5]{x} [/tex]
Answers
hint there are 12 inches in a foot. your family recently had a family pressure taken your aunt asked you to take a picture of the portrait using your phone and send it to her if the original size of the portrait is 3 ft by 3 ft and the scale factor is 118 what would the size of the portrait be on ylour phone
Answers
Answer:
1,416
Step-by-step explanation:
multiply 12 by 116
I could really use your help:)
Answers
Answer:
Question 1: -3 and 6 in that order
Question 3: 3 and y=1/2x+3 in that order
Question 2: 2 and y=2x+4 in that order
Step-by-step explanation:
:)
Angela bought gifts for her friends, and each gift costs 10$. Let y represent the total cost and x represent the number of gifts. Write an equation to represent the proportional relationship between the total cost and the number of the gifts she bought.
Answers
Answer:
Step-by-step explanation:
If Angela bought gift for her friend and each gift costs 10$. This means that the more the number of her friends, the more the money she will pay and vice versa. This is known as a direct relationship.
Let y represent the total cost and
x represent the number of gifts
According to direct variation]
y ∝ x
y = kx
k is the constant of proportionality
If each gift item cost $10, x gift will cost 10x. The constant of proportionality in this case will be 10. Substituting, the equation will become;
y = 10x
Hence the required relationship is y = 10x
Giuliana has 22 quarters and dollar coins worth a total of $10.75.
Which equation can be used to find d, the number of dollar coins Giuliana has?
d – 22 + 0.25d = 10.75
0.25d + 22 – d = 10.75
0.25(22 – d) + d = 10.75
d + 0.25(d – 22) = 10.75
Answers
Answer:
0.25(22-d)+d=10.75
Step-by-step explanation:
None of the other equations make sense given the information
HELP!
(4x + 5y)(2x - 3y) + 3xy
Answers
(4x+5y)(2x-3y)+3xy
8x^2-12xy+10xy-15y^2+3xy
8x^2+xy-15y^2
I believe this should be the answer you need.
Evaluate the expression. 2. (3^6.3^-5)
Answers
Answer:
1.00000
Step-by-step explanation:
Well I'm not sure what that upside down V is
0
ef
gh
A. dº + fº = 180° B. gº + fº =
C. Cº + f 0 = 180° D. bº + 0 =
The circumference of a circle is 88c
Calculate the radius of the circle.
A. 14cm
B. 42cm
C. 56cm
D. 28cm
and 415.
Answers
About 28cm
circumference of a circle =radius×3.14
3.14÷circumference of the circle (88cm)=28.04.
About 28cm.
"Write the equation of the line that is perpendicular to the line x - 4y = 20 and passes through the point (2, -5)." Thank you in advance!
Answers
Answer:
y= -4x +3
Step-by-step explanation:
① Rewrite the equation in the form of y=mx+c, to find the gradient of the given line, m.
x -4y= 20
4y= x -20
y= ¼x -5 (÷4 on both sides)
∴ Gradient of line= ¼
② Find the gradient of the new line.
The product of the gradients of perpendicular lines is -1.
¼(gradient of line)= -1
gradient of line
= -1 ÷¼
= -1 ×4
= -4
③ Substitute the value of the gradient into the equation.
y= -4x +c
④ Find the value of c by substituting a pair of coordinates.
When x= 2, y= -5,
-5= -4(2) +c
-5= -8 +c
c= -5 +8 (+8 on both sides)
c= 3
Thus, the equation of the line is y= -4x +3.
I need help this is my last question (math class)
Answers
Answer:
Step-by-step explanation:
5.00 for 2 loaves is $2.50 a loaf.
She wants 5 loaves for $12.50
5*2.50= $12.50 so she is correct.
since four loaves would be ten dollars. add one more loaf and that would cost $2.50. so $10 + $2.50 is $12.50
The University of Washington Huskies tried throwing one of the longest Hail Mary's in history
- about 73 yards. For this pass, the ball's height over time was modeled by the function
h(t) = –16t2 + 64t + 6, where h(t) was the height in feet and t was the time in seconds.
Let's break down whether the Huskies ever had a chance.
1.
73 yards isn't just a long way to throw, it's a long way to run. To give his team the
best chance of running all the way down the field and catching the ball before it hits
the ground, the quarterback (passer) needs to keep the football in the air for a long
time. How long was the ball in the air?
Answers
9514 1404 393
Answer:
4.09 seconds
Step-by-step explanation:
The ball is in the air until h(t) = 0. Solving that equation for t, we have ...
0 = -16t^2 +64t +6
t^2 -4t = 3/8 . . . . . . rearrange, divide by 16
t^2 -4t +4 = 4 3/8 . . . add 4 to complete the square
(t -2)^2 = 4.375 . . . . write as a square
t = 2 +√4.375 . . . . . positive square root, add 2
t ≈ 4.09165
The ball was in the air about 4.09 seconds.