Where do the parabola defined by y=-22 + 4x + 1 and the line defined by y=-x+ 5 intersect? O (4,1) and (-1,6) O (-4,9) and (-1,6) (-4, 9) and (-1,-6) O (4,1) and (1, 4)
Answers
Answer:
(4,1);(1,4)
Step-by-step explanation:
The point on the parabolic equation y = -x² + 4x + 1 and line y = -x + 5 intersect is P ( 4 , 1 ) and Q ( 6 , -1)
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the parabolic equation be y = -x² + 4x + 1
Let the equation of line be y = -x + 5
Now , To find the points of intersection between the parabola y = -x² + 4x + 1 and the line y = -x + 5, we need to set the two equations equal to each other and solve for x and y simultaneously.
Setting y = -x² + 4x + 1 equal to y = -x + 5, we get:
-x² + 4x + 1 = -x + 5
Rearranging the equation, we get a quadratic equation in standard form:
-x² + 4x + x - 1 - 5 = 0
-x² + 5x - 6 = 0
Factoring the quadratic equation, we get:
-(x - 1)(x - 6) = 0
Setting each factor equal to zero and solving for x, we get two potential values for x:
x - 1 = 0 or x - 6 = 0
x = 1 or x = 6
Now, substituting the values of x back into the equation y = -x + 5 to find the corresponding y-values, we get:
For x = 1:
y = -1 + 5
y = 4
So, one point of intersection is (1, 4)
For x = 6:
y = -6 + 5
y = -1
So, the other point of intersection is (6, -1).
Hence , the point of intersection is P ( 4 , 1 ) and Q ( 6 , -1)
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Related Questions
A bag contains 4 red, 2 blue, 6 green and 8 white marbles. What is the probability of selecting a green marble, replacing it, then selecting a red marble
Answers
Answer:
14.7%
Step-by-step explanation:
Being that there is 4 red, 2 blue, 6 green, 8 white, that means there is 20 marbles, with 8 success, 8/20. Since the marble is not replaced, that drops it to 7/19 for the second pull. Multiply these together and you get 14.7%.
(8/20)*(7/19)=.147
.147*100=14.7
Hey saw this man Turns 250 per on per week Plus a 10% commission all sales over 5000 in one week hey cells Toto 14,000 what were his earning that week A.$1,050 B.$1,150 C.$400 D.$2,150
Answers
Answer:
B.$1,150
Step-by-step explanation:
Given data
Weekly earning= $250
commission= 10%
Sales= $14000
Hence the expression for his total earnings per week is
y= 0.1x-250
x= sales
y= total earning
y=0.1*14000- 250
y= 1400-250
y= $1150
Can someone help me with this please
Answers
Answer:
where is the diagram?
Step-by-step explanation:
The quotient of Alice’s income and 12 is 1,500
Answers
x/12 = 1500
Answer:
125
Step-by-step explanation:
x = 1500 / 12
= 125
Match the word with the definition.
Answers
Step-by-step explanation:
practical range = 8
vertical line test = 5
range = 3
domain = 2
relation = 1
function = 4
function Notation =6
practical domain=7
A set of twenty cards is labeled 1 through 20. Anna draws one card randomly. What is the probability that Anna will draw an even number greater than 10?
Answers
Answer:
50% chance
Step-by-step explanation:
What is the volume of the solld figure that has a helght of 11 feet and the following base?
volume___ft 3
Answers
Step-by-step explanation:
Area is 2D, and Volume is 3D
volume is L x W x H
area is L x W which has already been given to you so you just need to use the height given to you
38.28 x 11
How do I find the angles
Answers
Answer:
if there smaller than 90 degrees then it's acute if the angle is bigger then 90 degrees it's obtuse
Step-by-step explanation:
question in photo. i'll give brainliest to whoever gets it right/done quickest. thank you!
Answers
Answer:
Daniel's time: 3 minutes 45 seconds
Brandon's time: 3 minutes 27 seconds
Step-by-step explanation:
Well, 5 feet per every second so side A would be 327.6 / 3 = 109.2
then 489 / 5 = 97.8 add them two you get 207 seconds which is 3 minutes and 45 seconds for Daniel.
For Brandon you have to find the hypotenuse of the triangle which in short is 588.6 / 3 = 196.2
This was my first answer on this so though Its problebly not the best I hope I did something to help. ;-;
y is inversely proportional to x.
When =9, y = 8.
Find y when x= 6.
Answers
Answer:
y=12
Step-by-step explanation:
y is inversely proportional to x
y=k/x
k is a constant of proportionality
k=yx
y1x1=y2x2
8(9)=y2(6)
y2=8(9)/6
y2=12
Jack took out a 6-year loan for $25,000 to purchase a boat at a 4.5% interest rate. If the interest is compounded monthly, what will he have paid total over the course of the loan?
Answers
Answer: $32,732.58
Step-by-step explanation:
To calculate the total loan payment over the course of the loan period, use the future value formula:
= Loan amount * (1 + rate) ^ number of years
As this loan is compounded monthly, you need to convert certain terms to monthly figures:
Number of periods = 6 * 12 months = 72 months
Interest = 4.5 / 12 = 0.375%
Total payment:
= 25,000 * ( 1 + 0.375%)⁷²
= $32,732.58
He will have to pay $34,236.31 over the course of the loan.
Using the compound interest formula expressed as:
[tex]A =P(1+r/n)^{nt}[/tex]
P is the principal = $25000
r is the rate = 4.5% = 0.045
t is the time in years = 6 years
n is the compounding amount = (12)monthly
Substitute into the formula:
[tex]A =25000(1+0.045/12)^{12(7)}\\A=25000(1.36945)\\A = \$34,236.31[/tex]
Hence he will have to pay $34,236.31 over the course of the loan
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A square garden has an area of 400 square feet. Each side of the garden is (x-10) feet in length.
Write an equation that represents the AREA of the garden
Find the value of x using the square root method
What is the length of the side of the garden?
Answers
Answer:
400 = (x - 10)²
x² -20x -300 = 0
x = 30 and x = -10
Length side of the garden = 20 feet
Step-by-step explanation:
Given:
Area of square garden = 400 square feet
Length side of the garden = (x - 10) feet
Find:
Length side of the garden
Computation:
Area of square = side²
Area of square garden = Length side of the garden²
400 = (x - 10)²
400 = x² -20x + 100
x² -20x -300 = 0
x² -30x + 10x -300 = 0
x(x - 30) + 10(x - 30) = 0
(x - 30)(x + 10) = 0
So,
x = 30 and x = -10
Use x = 30 positive number
Length side of the garden = (x - 10) feet
Length side of the garden = (30 - 10) feet
Length side of the garden = 20 feet
At the start of 2014 Mike's car was worth £12000.
The value of the car decreased by 30% every year.
Work out the value of his car at the start of 2017.
Answers
The value of the car at the start of 2017 will be £ 4116
You are looking for a summer job at a sneaker shop. The most popular sneakers sold are shown below:
Answers
You buy 11 bagels with a $20 bill. How much change do you receive?
Answers
Answer:
You would receive $13.75
Step-by-step explanation: What i did was divided 7.50 by 6 so it would give me the price of 1 bagel(1.25).I subtracted 11 and 6 which would give me 5 so I know how much I need to calculate with the discount. Then I multiplyed 5 times 1.25 (6.25) so I could get the price for 5 bagels. After I added 7.50 and 6.25 which would give you your answer of $13.75.
I hope this helps and makes sense to you. Please mark brainlist!
Step-by-step explanation:
Answer:
You would receive $13.75
Step-by-step explanation:
What i did was divided 7.50 by 6 so it would give me the price of 1 bagel(1.25).I subtracted 11 and 6 which would give me 5 so I know how much I need to calculate with the discount. Then I multiplyed 5 times 1.25 (6.25) so I could get the price for 5 bagels. After I added 7.50 and 6.25 which would give you your answer of $13.75.
Hope u understand
Please mark brainliest
Thank You
Juan tiene que salir de su casa a estrenar futbol 20 minutos antes de las 4 PM. Escribe 4 formas diferentes de decir esa hora
Answers
Respuesta:
03:40 pm;
15: 40;
20 minutos antes de las 4 pm;
40 minutos después de las 3 pm
Explicación paso a paso:
20 minutos antes de las 4 de la tarde se pueden expresar de las siguientes formas:
Basado en un tiempo de 12 horas, podría escribirse tiene: 3: 40 pm
Usando el formato de reloj de 24 horas; donde 3 pm es equivalente a 15; por lo tanto, podría escribirse como: 15:40
Además, el tiempo se puede informar en palabras de la siguiente manera:
20 minutos antes de las 4 pm
También ;
40 minutos después de las 3 pm
5. A construction area has 6 cylindrical posts protecting the
equipment. They are filled with sand to reinforce them. If each
cylinder is 4 feet tall and has a diameter of 1 foot, how much sand
was needed to fill the cylinders?
Record your answer and fill in the bubbles on your answer. (If it’s wrong or random you will be reported)
document. Be sure to use the correct place value.
Answers
Answer: what’s the answer ?
Step-by-step explanation:
If each cylinder is 4 feet tall and has a diameter of 1 foot then the amount of sand needed to fill the cylinders is 19 cubic feet.
Given that there are 6 cylindrical posts protecting the equipment
To find tge amount of sand needed for cylinders,
We need to find the volume of each cylinder.
The cylinder is 4 feet tall and has a diameter of 1 foot,
Height is 4 feet
Diameter is 1 foot and radius is 1/2 feet.
Volume of cylinder = πr²h
=3.14×(1/4)(4)
=3.142 cubic feet.
As there are six cylinders.
Multiply 6 with 3.142
Amount of sand needed = 6×3.142
= 18.852 cubic feet.
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Tabitha was shooting free throws in gym class. She completed 7 of the shots, which was a third of 4 more than Joan completed. What is the number of free throws, n, that Joan completed?]
Answers
Answer:
17
Step-by-step explanation:
the following equation can be derived from the question
7 = 1/3(4 + n)
multiply both sides of the question by 3
21 = 4 + n
combine like terms
21 - 4 = n
n = 17
I NEED HELP PLSS ITS LIKE 200 POINTS
Answers
Answer:
y=-3/2x+3
Step-by-step explanation:
(0,3) and (2,0) tell us that the y intercept is 3 because at x = 0, y = 3.
This leaves the first and last choice only.
We can calculate the slope by 0-3 and 2-0, so -3/2 is the slope
Solve for x algebraically, x - 15 < 25
Answers
Answer:
x<40
Step-by-step explanation:
x-15<25
Add 15 since addition is opposite of subtraction, thus cancelling the 15 out on both sides.
x-15<25
+15 +15
x<40
---
hope it helps
What is the value of x?
Enter your answer in the box.
Answers
Step-by-step explanation:
which class are you
just to confirm
hey! please help i’ll give brainliest
Answers
Answer:
Heyo! the answer is A since their implying it's important :)
Kinyua spent 1/4 of his net salary on school fees. He spent 1/4 of the remainder on electricity and water bills. He spent 1/9 of what remained on transport. If he finally has she. 8400 calculate his total salary
Answers
Answer:
Let his net salary = x.
He spent 1/4th of x on School fees
Remainder = 1-1/4 = 3x/4
He spent 1/4th THE REMAINDER on Electricity and Water Bils
1/4 of remainder (3x/4) = 1/4 x 3x/4 = 3x/16
He spent 3x/16 of this salary on Electricity and Water Bills... We should subtract this to know our current value or cash at hand
New Remainder = 3x/4 - 3x/16
= 9x/16.
He spent 1/9th OF WHAT REMAINED ON TRANSPORT.
1/9 x 9x/16
=x/16
New Remainder
= 9x/16 - x/16
=x/2.
If he finally had 8,400
Then
x/2=8,400
x=2x8,400
x= 16,800.
This answer is Correct. You can check it by using our x as 16,800 and solve from the start... You'll arrive at 8400 as your remainder. Have a great day!!!
What equation is equivalent to 2 - 3 (5x+2) = 6?
A) -15x - 4 = 6
B) -15x + 4 = 6
C) -5x - 2 = 6
D) -5x + 2 = 6
Answers
Remember that the negative sign in 3 is multiplied with the 2, resulting in -4 in the end. The answer is not B.
Find the sum of x^2+3x and
-2x^2+9x+5
Answers
Answer: The answer is -x^2 + 12x + 5
Help,no links and please don’t guess. Will give the brainliest . It is a 4 grade question
Answers
Answer:
.7 or 7/10
Step-by-step explanation:
buddy+teddy:2.9
socko+peanut:2.2
2.9-2.2=.7
What is the value of 3'5/3'3
Answers
Answer:
1.05128205Step-by-step explanation:
hope it helps
#carryonlearning
Miguel bikes 23 km per hour and starts at mile 10. Gabby bikes 28 km per hour and starts at hour 0. Which system of linear equations represents this situation
Answers
Answer:
Miguel: d = 23t + 10
Gabby: d = 28t
Step-by-step explanation:
We can write the equation for each case in slope-intercept form, d = mt + b
Where,
d = total distance
t = time
m (rate) = distance/hr
b = initial value
✔️ Miguel:
m = 23 km/hr
b = 10 mile
Equation: subtitle the values into d = mt + b
d = 23t + 10
✔️ Gabby:
m = 28 km/hr
b = 0 mile
Equation: subtitle the values into d = mt + b
d = 28t + 0
d = 28t
a sequence of transformation is applied to a polygon. Select all statements which indicate a sequence of transformations where the resulting a polygon has an area greater than the original polygon.
A. Translate even units left, rotate 90 degrees clockwise about the origin.
B. Reflect over the x-axis, dilate about the origin by a scale factor of 1/2 translate up 5 unit.
C. Rotate 90 degrees counterclockwise around the origin, dilate about the origin by a scale factor of 3/2
D. Dilate about the origin by a scale factor of 2/3. rotate 180 degrees clockwise around the origin, translate down 2 units.
E. Dilate about the origin by a scale factor of 2, reflect over the y-axis, dilate about the origin by a scale factor of 2/3
Answers
Answer:
than originally shared this meeting will
3 = [?]
60°
120° 60°
Answers
Explanation: a triangle needs to be 180 degrees and if there’s already 120 degrees and we have to find ty e other angle it’s going to be 60
Ps pls make me the brainliest