Answer:
f(x) = - 4x² - 20x + 56Step-by-step explanation:
f(x) = a(x - x₁)(x - x₂) - factored form of the equation of the parabola with zeros x₁ and x₂
x-intercepts at (2,0) and (-7,0) means zeros: x₁=2 and x₂=-7
So:
f(x) = a(x - 2)(x + 7) - factored form of the equation of the parabola with x-intercepts at (2,0) and (-7,0)
The parabola passing through point (1, 32) means if x=1 then f(x)=32
Then:
32 = a(1 - 2)(1 + 7)
32 = a(-1)(8)
32 = - 8a
a = - 4
Therefore the equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32):
f(x) = -4(x - 2)(x + 7)
Expanding to standard form:
f(x) = -4(x - 2)(x + 7)
f(x) = -4(x² + 7x - 2x - 14)
f(x) = -4x² - 20x + 56
The equation of the parabola with x-intercepts at (2,0) and (-7,0) and passes through the point (1,32) is
f(x) = -4 ( x - 2 ) ( x + 7 )
Its standard form is
f(x) = -4x² - 20x + 56.
What is a parabola?It 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
We have,
To find the equation of a parabola we use the factored form of a quadratic equation.
f(x) = a ( x - m ) ( x - n)
Where a is the leading coefficient and m and n are the zeros of the quadratic.
The equation has x-intercepts at (2, 0) and (-7, 0) so we can say that,
m = 2
n = -7
Now the equation passes through (1, 32) = (1, 32) so we have,
32 = a ( 1 - 2 ) ( 1 - (-7) )
32 = a ( -1 ) ( 1 + 7 )
32 = a ( -1 )8
32 = -8a
a = -32 / 8
a = -4
We have,
m = 2
n = -7
a = -4
The equation of the parabola is:
f(x) = a ( x - m ) ( x - n)
f(x) = -4 ( x - 2 ) ( x + 7 )
We can expand to its standard form as:
f(x) = ( -4x + 8 ) ( x + 7 )
f(x) = -4x² - 28x + 8x + 56
f(x) = -4x² - 20x + 56
Thus the equation of the parabola with x-intercepts at (2,0) and (-7,0) and passes through the point (1,32) is f(x) = -4 ( x - 2 ) ( x + 7 ) and its standard form is f(x) = -4x² - 20x + 56.
Learn more about parabola here:
https://brainly.com/question/4074088
#SPJ2
What is the equation of in line slope intercept from that has a slope of 4 and goes through the point -8 -16
Answer:
Step-by-step explanation:
is your qustion like -8-16 because its -24
Answer:
y = 4x + 16
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 )
Here m = 4, thus
y = 4x + c ← is the partial equation
To find c substitute (- 8, - 16) into the partial equation
- 16 = - 32 + c ⇒ c = - 16 + 32 = 16
y = 4x + 16 ← equation of line
Please answer these questions for 8th Grade Algebra! First-person to answer will be marked as brainiest! Worth lots of points!
1. x<=20
2. k<0
3. d<-3
4. m<=11
5. a>=3
6. 6<-5
This should help
Solve the equation. If the equation is an identity or if it has no solution, write identity or no solution.
1) 7n + 5 − 9n = 8 − 2n − 3
2) 4(t + 2) = 10
3) 4y+2=−13(8−12y)
The factory makes boxes that each hold one candle. The boxes measure 1 inch × 1 inch × 9 inches. The factory owner makes a stack of 40 candle boxes. What is the volume of the stack?
Answer:
360 inch^3
Step-by-step explanation:
Volume of 1 box = 1 x 1 x 9 = 9 inch^3
Volume of 40 boxes = 40 x 9 = 360 inch^3
This is a topic on mensuration. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary). I'll be uploading notes on this topic soon. At the meantime, you can take a look at other topics or some tips as well!
Answer:
360 in
Step-by-step explanation:
L × W × H
1 × 1 ×9 = 9in
9 × 40 = 360 in
Can someone please answer 4 divided by 29.5 thank you!
Answer:
First when dividing you will need to remove the decimal point by multiplying by 10 IN THIS CASE. Once you found the answer, you need to bring back the decimal point.
40÷295
= .135593
PLZ ANSWER ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: C
Step-by-step explanation: it is stretched out more.
Answer:
C
Step-by-step explanation:
C Is An Oval Not A Circle, Therefore it is different
find the value of 3v - 10 given that -2v + 4 = 8
Answer:
-16
Step-by-step explanation:
v=-2
I found this because since it is given that -2v+4=8; If v=-2 then the equation is true, because -2(-2) + 4 = 8. So since v=-2, plug in -2 into v of 3v-10; which would be (3(-2))-10, which is equal to -16.
please hurry
making it 18 points !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The cost of catering a dinner is $11.95 per person plus $25 for delivery and setup. Which statement is true about the graph of the function that represents the average cost per person?
The horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.
The horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.
The vertical asymptote x = 0 represents that the cost per person approaches $0 as the number of people increases.
The vertical asymptote x = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.
B.) The horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.
Good luck with the test! :)
The horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.
What are asymptotes?"An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity."
"The curves visit these asymptotes but never overtake them. The method opted to find the horizontal asymptote changes involves comparing the degrees of the polynomials in the numerator and denominator of the function. If both the polynomials have the same degree, divide the coefficients of the largest degree terms."
From the equation, y = 11.95x + 25
And from the given graph it is clear that the horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.
Hence, A is the correct option.
To know more about asymptotes here
https://brainly.com/question/17767511
#SPJ2
Solve for x.
75°
11x-2
Answer:
x=7
Step-by-step explanation:
help pleaseeeeeeeeee
Answer:
C.
Step-by-step explanation:
hi can someone help me with this
Answer:
=−12y+11.7 I believe it's that but I am not completely sure
I believe it is
The price of a television was reduced $250 to $200. By the percentage was the price of the television reduced?
A. 20%
B. 25%
C. 80%
D. 50%
please help I'm not good at math!!
Answer:
B. 25%Step-by-step explanation:
The price decreased by 50, and that is 25% of 200.
Answer:
The answer is 20%
Step-by-step explanation:
I'm not amazing at percentages so this is what I did. Search up 20 percent of 250. Then it says 50. 250 minus 200 is 50, so the answer is 20%
I hope this helped and if it did I would appreciate it if you marked me brainliest.
thank you and have a nice day!
Find the amplitude:
y= 5 cos (1/4x)
Answer:
for 5cos(1/4x)
Amplitude=5
PLEASE ITS ALREADY LATE AND I NEED TO TURN IT TODAY
Example 1 Fatima works as an intern at a construction company earning $10 per hour. Her office is open 8
hours per day, 5 days a week. Analyze Fatima's potential earnings for the 12 weeks she interns at the
company this summer.
A. Write a function rule to model
the situation
B. Identify the independent
variable
C. Identify the dependent
variable
f(x) =
Answer:
4800
Step-by-step explanation:
I attached a picture of the work.
We need to made a function that will help us solve this
f(x)=dx; d = $ per hour, x = # of hours
step 1) identify d (in this case, the money made per hour) which = 10
f(x)=10x
step 2) identify x (# of hours total) which = 480
f(x)=10(480)
step 3) solve the equation
f(x)=4800
independent variable:
the number of hours
dependant variable:
the amount of money made after 12 weeks
FIRST TO ANSWER WITH IT CORRECT GETS 50 POINTS AND A BRAINLIST THING
Answer:
2. 36
3. 8
4. 64 - 32
5. 7
I hope that this helps you, I'm not sure if number 4 is correct, but I am 100% sure that the rest are correct. I did the math for all of the questions and they should all be correct. I hope you have a wonderful evening!
Nick can do a certain job in 3 hours less than it takes bonnie to do the same job. If they complete the job together in 9 hours, what equation could be used to determine how long it will take bonnie to do the job alone
Answer:
Step-by-step explanation:
Let the number of hours Nick does the job alone to be x - 3 hours
Hence, in 1 hour, Nick has done 1/x - 3
Together they complete the job in 9 hours
Hence, let's represent the job as 1
9/x + 9/x - 3 = 1
Multiply through by (x)(x-3)
9(x- 3) + 9(x) = 1
9x - 27 + 9x = (x)(x-3)
-27 = x² - 3x
x² - 3x +27 = 0
Find the slope of the line passing through the points (-9, 4) and (-9, -9)
Answer:
There is no slope, it is undefined and the line would continue to go up from the position x= -9
brainliest if correct please
ILL GIVE Brainliest
find the area of the polygon
Answer:
27.5 units^2
Step-by-step explanation:
Total area = Area of triangle ILH + Area of parallelogram JKLI
Area of triangle ILH
= 1/2 * b * h
= 1/2 * 5 * 5
= 12.5 units^2
Area of parallelogram JKLI
= bh
= 3 * 5
= 15 units^2
Total area
= Area of triangle ILH + Area of parallelogram JKLI
= 12.5 + 15
= 27.5 units^2
Pleas help meh!!I really need help!!!
Answer:
360ft^2
Step-by-step explanation:
We know that the height is always 8 ft. So lets find the area of two of the 4 walls.
We multiply by 2 because there are two of the same wall.
2(8ft x 10ft) = 160ft^2
Now lets find the area of the other wall.
2(8ft x 15ft) = 240ft^2
Now we add it up
160 + 240 = 400
400ft^2
But wait! We aren't done yet! We still have to subtract out the door and window which is 60ft^2.
400 - 60 = 360
360ft^2
Consider Brainliest! Hope I helped!
What’s the answer for 65°
15x + 10
Answer:
7
Step-by-step explanation:
65° + 15x + 10 = 180° (co-interior angles are equal)
15x + 75° = 180°
15x = 180° - 75°
15x = 105°
x = 105/15
x = 7
hiii, this geometry please help
HELP THIS IS DUE TONIGHT!!
What is the LCM (least common multiple) of the following
16ab^3 5a^2b^2 20ac
Also ^ means that it’s an exponent
subtract (7x^5-12x^2y+33y^2) from (5x^5-5x^2y+9y^2) simplify your results:
Answer:
- 2 [tex]x^{5}[/tex] + 7x²y - 24y²
Step-by-step explanation:
( 5 [tex]x^{5}[/tex] - 5x²y + 9y² ) - ( 7 [tex]x^{5}[/tex] - 12x²y + 33y² ) =
5 [tex]x^{5}[/tex] - 5x²y + 9y² - 7 [tex]x^{5}[/tex] + 12x²y - 33y² =
( 5 [tex]x^{5}[/tex] - 7 [tex]x^{5}[/tex] ) + ( - 5x²y + 12x²y ) + ( 9y² - 33y² ) =
- 2 [tex]x^{5}[/tex] + 7x²y - 24y²
Read and understand the situation below, and make a complete plan to solve Mang Jose’s problem.
Mang Jose wants to paint the exterior of his house. He needs to know how many gallons of paint he would need. So, he asks his friend Juan to help him, according to Juan one (1) gallon of paint can cover an area of 250 square feet. Help Mang Jose prepare a budget for his project if his house exterior is 2700 square feet. Do a research on the different prices of one (1) gallon of paint depending on its brand name and choice of colors. Make a proposal budget for three (3) different colors of paint with its corresponding brand name.
Explanation:
Let's assume these are the different prices of one (1) gallon of paint for three different brand name and choice of colors:
1. Delux brand: Red = $19 per gallon
2. Golden sun: White = $15 per gallon
3. Luxury: Green = $20 per gallon.
Based on the data above, Mang Jose's budget could be drafted:
1. if he chooses the Delux brand/color red, then he will need approximately 11 gallons of the paint (2700/250 square fit) = 10.8, which would cost = $209 (11*$19).
2. if he chooses the Golden sun brand/color white then he will need approximately 11 gallons of paint (2700/250 square fit) = 10.8, which would cost = $165 (11*$15).
3. if he chooses the Luxury brand/color green then he will need approximately 11 gallons of paint (2700/250 square fit) = 10.8, which would cost = $220 (11*$20).
Mushrooms are healthy food for wild songbirds. Adam buys a 3.5 oz container of mealworms for $8.75. Marco buys a 3.75- oz container of mealworms for $9.75. Which container is a better buy?
Answer:
Adam's container
Step-by-step explanation:
Given
Adam
[tex]Weight = 3.5\ oz[/tex]
[tex]Amount = \$8.75[/tex]
Macro
[tex]Weight = 3.75\ oz[/tex]
[tex]Amount = \$9.75[/tex]
Required
Determine the better buy
First, we need to determine the unit cost per oz of each
i.e.
[tex]Unit\ Cost = \frac{Amount}{Weight}[/tex]
For Adam:
[tex]Unit\ Cost = \frac{8.75}{3.5}[/tex]
[tex]Unit\ Cost = 2.5[/tex]
For Marco:
[tex]Unit\ Cost = \frac{9.75}{3.75}[/tex]
[tex]Unit\ Cost = 2.6[/tex]
The better buy of both is the one with the smaller unit cost.
Since 2.5 < 2.6, we can conclude that Adam's container is a better buy
find the measure of y
please
Answer:
y=140
Step-by-step explanation:
if it's an option
Which is the "The sum of 4 times a number and 7" as an algebraic expression?
A)4(x+7)
B)(4.7)+x
C)4-7+x
D)4x+7
WILL GIVE BRAINLY IST TO WHOEVER answers correctly and QUICK
Lucinda is writing a coordinate proof to show that a diagonal of a parallelogram partitions the parallelogram into two equal areas.
Enter your answers in the boxes to complete Lucinda's proof.
Since KLMN is a parallelogram and a parallelogram's opposite sides are parallel and congruent, the coordinates for M are (4x,__).
In △KMN, the length of the base is ___ and the height is ___. So an expression for the area of △KMN is ___.
In △KLM, the length of the base is 3x and the height is 2y. So an expression for the area of △KLM is ___.
Comparing the area of the two triangles that are formed by a diagonal of the parallelogram shows that a diagonal of a parallelogram partitions the parallelogram into two equal areas.
Answer: Do you have a picture or a diagram
Step-by-step explanation:
Not the answer but I need help .. it’s the same question but I’ve added the diagram if anyone can help?
A section of a railway has a slope of approximately 0.47. In this section, a vertical change of 1 unit corresponds to a horizontal change of what length? Round your answer to the nearest hundredth.
Step-by-step explanation:
A slope of 0.47 means that, for every 100 feet of horizontal change, the vertical rise = 47 feet
We can use a proportion here
0.47 / 1 = 1 / x
Cross-multiply
0.47x = 1*1
0.47x = 1
Divide both sides by 0.47
x = about 2.13 units
An architect is planning a triangular pool with a perimeter of 99 ft.Two of the sides measure 20 and 42, respectively, what is the length of the missing side(x)?Solve for x
Given:
Perimeter of the triangle = 99 ft
Length of two sides are 20 ft and 42 ft.
To find:
The length of missing side.
Solution:
Let the missing side be x.
Perimeter of a triangle is the sum of all sides of that triangle.
[tex]x+20+42=99[/tex]
[tex]x+62=99[/tex]
Subtract 62 from both sides.
[tex]x=99-62[/tex]
[tex]x=37[/tex]
Therefore, the missing side of the triangle is 37 ft.