The x- intercepts of a parabola are (0,-6) and (0,4). The parabola crosses the y- axis at -120. Lucas said that an equation for the parabola is y=5x^2+10x-120 and that the coordinates of the vertex are (-1, -125). Do you agree or disagree? List why?
Given:
The x- intercepts of a parabola are (0,-6) and (0,4).
The parabola crosses the y- axis at -120.
Lucas said that an equation for the parabola is [tex]y=5x^2+10x-120[/tex] and that the coordinates of the vertex are (-1, -125).
To find:
Whether Lucas is correct or not.
Solution:
The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.
[tex]y=a(x+6)(x-4)[/tex] ...(i)
The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).
[tex]-120=a(0+6)(0-4)[/tex]
[tex]-120=a(6)(-4)[/tex]
[tex]-120=-24a[/tex]
Divide both sides by -24.
[tex]\dfrac{-120}{-24}=a[/tex]
[tex]5=a[/tex]
Substituting [tex]a=5[/tex] in (i), we get
[tex]y=5(x+6)(x-4)[/tex]
[tex]y=5(x^2+6x-4x-24)[/tex]
[tex]y=5(x^2+2x-24)[/tex]
[tex]y=5x^2+10x-120[/tex]
So, the equation of the parabola is [tex]y=5x^2+10x-120[/tex].
The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is:
[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the equation of the parabola, [tex]a=5,b=10,c=-120[/tex].
[tex]-\dfrac{b}{2a}=-\dfrac{10}{2(5)}[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{10}{10}[/tex]
[tex]-\dfrac{b}{2a}=-1[/tex]
Putting [tex]x=-1[/tex] in the equation of the parabola, we get
[tex]y=5(-1)^2+10(-1)-120[/tex]
[tex]y=5-10-120[/tex]
[tex]y=-125[/tex]
So, the vertex of the parabola is at point (-1,-125).
Therefore, Lucas is correct.
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Passing through (-3, -6) and (2,9)
What is the equation of the line in point-slope form?
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
What is the equation of the line in slope-intercept form?
Answer:
slope-inercept form: y = 3x + 3 point-slope form: y - 9 = 3(x - 2)
Step-by-step explanation:
slope-intercept form:
y2 - y1 / x2 - x1
9 - (-6)/ 2 - (-3)
= 3
y = 3x + b
9 = 3(2) + b
9 = 6 + b
3 = b
y = 3x + 3
point-slope form:
y - 9 = 3(x - 2)
Find the measure of the indicated angle
Answer:
x=44°..
Step-by-step explanation:
base angle of isosceles triangle are equal68+68+x=180°{sum of angle of triangle}136°+x=180°x=180-136°x=44°hope it helpsstay safe healthy and happy. ..Answer:
the value of x is 44 i hope it will help you
For the given triangle find the exact value for sin(A). Assume angle C is a right angle.
Answer:
53.13 degrees
Step-by-step explanation:
In order to use sin we have to use the opposite side over the hypotenuse.
[tex]\frac{4}{5}[/tex] in this case
sin(A) = [tex]\frac{4}{5}[/tex]
[tex]A = sin^{-1} \frac{4}{5}[/tex]
Plugging this into the calculator you get about 53.13 degrees
Evaluate each of the following. help plz
Answer:
5!= 120
13!= 6227020800
12!/6!= 665280
10!/7! 3!= 120
5(4!)= 120
Step-by-step explanation:
Please help with this!!! 8 points!!!
Answer:
d
Step-by-step explanation:
A oil company has a large tank that holds the oil before it is distributed. If it costs $3.20 per cubic meter for oil, how much money would it cost to fill the entire tank?
A. $65,280
B. $68,000
C. $5,440
D. $67,200
Answer:
Option A, $65,280
Step-by-step explanation:
The volume of the tank is,
12×20×15+40×(50-15)×12
= 3600+16800
=20400 cubic meters
For each cubic meter, it costs $3.20, so for 20400 cubic meters it'll cost,
20400×$3.20
= $65,280
Answered by GAUTHMATH
Tìm x €N: a) 24:(2x-4)+14=26
on a coordinate gride what is the distance between (1,3) and (6,15)
Answer:
13
Step-by-step explanation:
Distance between points (1, 3) and (6, 15) is 13
The area of a wall in a house is 10.37 square metres. If a can of paint covers 3.1 square metres, how many cans of paint are needed to paint the wall?
Answer:
4 cans of paint
Step-by-step explanation:
Take the area of the wall and divide by the area that the can of pain will cover
10.37 / 3.1
3.34516129 cans
We need to round up to make sure we buy enough cans of paint
4 cans of paint
We can take area as,
Area = A
The required formula is,
→ A of wall ÷ A that paint's can will cover
Then find the no. of cans of paint that are needed to paint the wall.
Now use the formula,
→ A of wall ÷ A that paint's can will cover
→ 10.37 ÷ 3.1
→ 3.34516129032
→ 4 cans (by nearest value)
Hence, we need 4 cans to paint the wall.
how do you get sin theta
received good return from m center of rs 5000 (journal entry)
Answer:
Date Account Title Debit Credit
XX-XX-XXX Sales returns and Allowances Rs. 5,000
Accounts receivable - M Center Rs. 5,000
Inventory Rs. 5,000
Cost of Goods sold Rs. 5,000
Evaluate function from their graph
Answer:
f(-5) = 7
Step-by-step explanation:
f(-5) means find the y value when x = -5
y = 7 when x = -5
In which figure is DE BC
Answer:
Given: DB = 7.2 cm, AE = 1.8 cm and EC = 5.4 cm and DE || BC.
DB
AD
=
AC
AE
[by basic proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same.
7.2
AD
=
5.4
1.8
AD=
5.4
7.2×1.8
AD=
10
24
⟹AD=2.4cm
One circle has a circumference of 12π cm. Another circle has a circumference of 32π cm. What is the ratio of the radius of the smaller circle to the radius of the larger circle?
Options:
A: 3:8
B: 8:3
C: 1:3
D: 3:1
3:8
The ratio of small circle
12:32
If we divide both of them by 4 we get 3:8
Express each of the following negative angles as its equivalent positive angle between 0°and360°
+120°
Answer:
Dilated pupils
Long periods of wakefulness
Loss of appetite
Overconfidence
Over-excitement
Paranoia
Runny nose or frequent sniffles
White powder around nostrils
Legal issues
Missing or being late to work
Financial problems
Mood swings
Irritability
Depression
Which function is represented by the graph?
5
4
3
2
Of(x) = -x - 3] + 4
f(x) = -x + 3 + 4
f(x) = -x + 4 + 3
f(x) = -x + 4 + 3
-5 A-3 -2 -1 2 3 4 5
2+
-3
45
Step-by-step explanation:
The correct answer is f(x)=3^(x+3)
solve (algebra 1)− 0.32 + 0.18 = 0.25 − 1.95
Answer:
0.50=1.7. They do not equal each other
Step-by-step explanation:
Thats what I got from this question
the area of the rectangle is 48cm^2
show that x satisfies the equation x^2 + 7x -78 = 0
Answer:
No its doesn't satisfy the equation.
[tex]{ \bf{area = 2(l + w)}} \\ { \tt{48 = 2((x + 10) + (x - 3))}} \\ { \tt{24 = 2x + 7}} \\ 2x = 17 \\ x = 8.5 \\ \\ { \bf{in : \: {x}^{2} + 7x - 78 = 0 }} \\ x = 6 \: \: and \: \: - 13[/tex]
How many fives makes 6 tens
Answer:
12.
Step-by-step explanation:
6x10 = 60.
60 divided by 12 =5.
Answer:
12
Step-by-step explanation:
5x = 60
x = 12
divide x3-3x2+x-2 by 10x4-14x3-10x2+6x-10 the quotient is and the remainder is
Answer:
The quotient is 10x+16
The remainder is 28x²+10x+22
Step-by-step explanation:
Solution,
___________________________
x^3 - 3x^2 + x - 2 ] 10x^4 - 14x^3 - 10x^2 + 6x - 10 [ 10x + 16
10x^4 - 30x^3 + 10x^2 - 20x
16x^3 - 20x^2 + 26x - 10
16x^3 - 48x^2 + 16 x - 32
28x^2 + 10x + 22
Answer:
The quotient is 10x+16
The remainder is 28x²+10x+22
Step-by-step explanation:
Finish solving the system of equations.
x – 5y = 6
–x + 2y = –3
–3y = 3
What is the value of y?
Substitute the value of y back into one of the original equations to find the value of x. What is the value of x?
Answers: x = 1 and y = -1
Explanation:
Start where your teacher left off, which is -3y = 3.
We solve for y by dividing both sides by -3
That turns -3y = 3 into y = -1
Then we use this y value to find x
x - 5y = 6
x - 5(-1) = 6
x + 5 = 6
x = 6-5
x = 1
The solution is (x,y) = (1, -1)
Answer:
-1,1
Step-by-step explanation:
Decrease £19064.67 by 9.5%
Give your answer rounded to 2 DP. (decimal place)
Please Help !!!
Answer:
17253.52
Step-by-step explanation:
100-9.5=90.5
19064.67*0.905=17253.52
What is the scale of the y-axis in this coordinate graph?
A. 1 tick mark represents 1 unit
B. 1 tick mark represents 8 units
C. 1 tick mark represents 12 units
D. 1 tick mark represents 16 units
Answer:
Obviously B
Step-by-step explanation:
What is the soution of (Image below)
Answer:
A
Step-by-step explanation:
Starting with the original equation:
[tex]\sqrt{1-3x} =x+3[/tex]
Squaring both sides to remove the root, and expanding the right side:
[tex]1-3x=(x+3)(x+3)[/tex]
Multiplying the right side:
[tex]1-3x=x^{2} +6x+9[/tex]
Combine like terms:
[tex]x^{2} +9x+8[/tex]
Factor:
(x+8)(x+1)
If x+8=0, then x= -8
If x+1=0, then x=-1
Can someone help me with this math homework please!
Answer:
1 = Input G
2 = Input F
3 = Input H
Step-by-step explanation:
Factor completely x2 + 16
Answer:
not a factorable number i think
Step-by-step explanation:
There are 11900 films on Netflix. 13% of the films are action. How many films are action?
13% of 11900 films are action films =1547 films.
Answer:
[tex]{ \tt{ = \frac{13}{100} \times 11900 }} \\ = 1547 \: action \: films[/tex]
Last year, sales at a book store increased from $5,000 to $10,000. This year, sales decreased to $5,000 from $10,000. What percentage did sales
increase last year? What percentage did sales decrease this year?
Sales increased
last year, from $5,000 to $10,000. When sales dropped from $10.000 to $5,000 this year, sales decreased
Answer:
Last year sales increased by 200%. This year sales decreased by 50%.
Step-by-step explanation:
if x-y=9 and xy=2,find the value of (x square + y square)
Answer:
x² + y² = 85
Step-by-step explanation:
Using the expansion
(x - y)² = x² + y² - 2xy , then
x² + y² - 2xy = (x - y)² ( add 2xy to both sides )
x² + y² = (x - y)² + 2xy ← substitute given values
= 9² + 2(2)
= 81 + 4
= 85