Determine an equation for the pictured graph. Write your answer in factored form.
Remember to start with f(x) = a (x – ri)(x - 52)...
8
7
2
y =
Answers
An equation for the pictured graph and the equation for the pictured graph in factored form is: y = rs - r - s + 1.
Let's assume the equation for the graph in factored form is: y = a(x - r)(x - s), where 'a' is a constant and 'r' and 's' are the roots of the equation (x-intercepts of the graph). Since we are given that the graph passes through the points (0, -2) and (1, 0), we can use this information to find the values of 'r' and 's.'
Using the point (0, -2):
When x = 0, y = -2.
We can substitute these values into the equation:
-2 = a(0 - r)(0 - s)
Simplifying, we get: -2 = a(-r)(-s) or -2 = ars.
Using the point (1, 0):
When x = 1, y = 0.
Substituting these values into the equation:
0 = a(1 - r)(1 - s)
Simplifying, we get: 0 = a(1 - r)(1 - s).
Now, we have two equations:
-2 = ars (Equation 1)
0 = a(1 - r)(1 - s) (Equation 2)
From Equation 1, we can solve for 'a' in terms of r and s:
a = -2 / rs.
Now, substitute this value of 'a' into Equation 2:
0 = (-2 / rs)(1 - r)(1 - s).
To make further progress, we can divide both sides by -2:
0 = (1 / rs)(1 - r)(1 - s).
Next, to eliminate the fractions, multiply both sides by rs:
0 = (1 - r)(1 - s).
Finally, expand the right side of the equation:
0 = 1 - s - r + rs.
The equation for the pictured graph in factored form is:
y = rs - r - s + 1.
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Related Questions
There are a total of 82 students in a drama club and a yearbook club. The drama club has 18 more students than the yearbook club. How many students are in the drama club? the yearbook club?
Answers
Answer:
Drama club 82 students
yearbook club 100 students
The solution to which system of equations has an x-value of 3?
(A) x + 2y =-1; y=3x + 3
(B) 3x – Y= 2; x + 2y=-1
(C) y= 3x + 3; 230 + 3y=0
(D) 2x + 3y=0; x + 2y=-1
Answers
Answer:
D)
Step-by-step explanation:
find the value of given expression
[tex] \sqrt{56 - 7} [/tex]
Answers
Answer:
± 7
Step-by-step explanation:
Given
[tex]\sqrt{56-7}[/tex]
= [tex]\sqrt{49}[/tex]
= + 7 or - 7 , that is ± 7
Answer:
±7
Step-by-step explanation:
56 - 57
______
gives you 49
which then turns into ±7
⇒⇒⇒Hope this helps!
20 POINTS I could really use some help
Answers
Answer:
its 10 points...
Step-by-step explanation:
but b
Find the area of the composite shape shown below:
5 in
4 in
2 in
3 in
12 in2
20 in2
22 in2
16 in 2
Answers
Answer:
16 inches squared
Step-by-step explanation:
We can split the figure into two rectangles. Rectangle 1 will have an area of 2*3=6. Rectangle 2 will have an area of 2*5=10
10+6=16
HOPE THIS HELPS!!!!!!!!4=2/9x A) 6 B) 9 C) 15 D) 18
Answers
Answer:
D. 18
Step-by-step explanation:
multiply both sides by 9/2, the reciprocal of 2/9.4×(9/2)=x
express 4×(9/2) as a single fraction.4×9/2=x
multiply 4 and 9 to get 36.36/2=x
divide 36 by 2 to get 18.18=x
swap sides so that all variable terms are on the left hand side.x=18
Answer:
D 18
Step-by-step explanation:
you devide 4 by 2/9 and get your answer
A bird flies south. Its distance from its nest, as a function of time, is modeled by y = 20x + 1. Which statement best describes the function? A. Not enough information is given to decide. B. The function is linear at some points and nonlinear at other points. C. The function is linear. D. The function is nonlinear. SUBMIT
Answers
Answer:
Thee function is linear.
Step-by-step explanation:
Answer:
So it becomes a linear equation.
Step-by-step explanation:
Which is an equation of the line through (-8,-4) and (4, 5)?
Answers
Answer:
the right answer is A :)
3
=
10
q
start fraction, 3, divided by, 5, end fraction, equals, start fraction, q, divided by, 10, end fraction
q =q=q, equals
Answers
Pls help me find triangle MNP
Answers
3x=39
x=13
To find TP plug in x
3(13)-17=22
TP=TN so TN is also 22
Please Help. Due Soon!
Answers
Answer:
yes
Step-by-step explanation:
They are correct because the reciprocal ( flipped or opposite) of -2/5 is 5/-2
Tyler’s brother earns $15 per hour. The store offers him a raise—a 5% increase per hour. After the raise, how much will Tyler’s brother make per hour? i really need help
Answers
Answer:
$75per hour
Step-by-step explanation:
15×5=75 jshshhsbw
find the value of given expression
[tex] \sqrt{1221 \times 1221} [/tex]
Answers
Answer:
[tex]1221\sqrt{x}[/tex]
Step-by-step explanation:
1221 x 1221 = 1490841
square root of 1490841 is 1221
Answer:
[tex]1221[/tex]
Step-by-step explanation:
[tex] \sqrt{1221 \times 1221} \\ = 1221[/tex]
Please help! 19/20. Will give brainliest! Spam answers will not be tolerated! Giving quadruple points!
Factor. x²(x + 2) ‐ x(x + 2) ‐ 12(x + 2)
Answers
Answer:
(x + 2)(x - 4)(x + 3)Step-by-step explanation:
x²(x + 2) ‐ x(x + 2) ‐ 12(x + 2) =(x + 2)(x² - x - 12) = (x + 2)(x² - 4x + 3x - 12) = (x + 2)(x - 4)(x + 3)[tex]{ \sf{ factorise \: \: { \underline{ \green { \tt{ {x}^{2} (x + 2) - x(x + 2) - 12(x + 2)}}}}}}[/tex]
[tex]{ \sf{ \blue{ \:taking \: (x + 2) \: common}}} \\ \\{ \dashrightarrow { \sf{ \green{(x + 2)( {x}^{2} - x - 12)}}}}[/tex]
[tex]{ \dashrightarrow{ \sf{ \green{(x + 2)( {x}^{2} - (4x - 3x) - 12)}}}} \\ \\ { \dashrightarrow{ \sf{ \green{(x + 2)( {x}^{2} - 4x + 3x - 12)}}}}[/tex]
[tex]{ \dashrightarrow{ \green{ \sf{(x + 2)(x(x - 4) + 3(x - 4))}}}} \\ \\ { \dashrightarrow{ \underline{ \boxed{ \green{ \sf{(x + 2)(x + 3)(x - 4)}}}}}}[/tex]
A car museum wants to increase its collection by 20%. Currently the museum has 120 cars in its collection. How many cars would the museum need to add over the next year to meet its goal?
Answers
Answer:
24
Step-by-step explanation:
please help me simplify this
Answers
Step-by-step explanation:
Given
sin(α+β) cos(α-β) +cos(α+β) sin(α -β)
We can see it is in the formula of
sin(A + B) = sinA cosB + cosA sinB
So now
Sin ( α + β + α - β)
= sin 2α
Or we can write sin2α as
= 2 sin α * cos α
Hope it will help :)❤
True or false: Every sequence is either arithmetic or geometric. If this is true, explain. If false, give a counterexample to illustrate.
Answers
Answer:
No false
Step-by-step explanation:
Theres the fibonacci sequance 1,1,2,3,5,8...
I'm honestly sorry that I'm asking so many questions.
Solve for X in the Diagram.
Answers
Answer:
[tex]\Huge\boxed{x=8}[/tex]
Step-by-step explanation:
Hello There!
Remember the sum of all of the angles in a triangle is 180
so we can use this equation to solve for x
180 = 50 + 60 + 8x + 6
now we solve for x
step 1 combine like terms
50 + 60 + 6 = 116
now we have
180=8x+116
step 2 subtract 116 from each side
116 - 116 cancels out
180 - 116 = 64
now we have
8x = 64
step 3 divide each side by 8
8x/8=x
64/8=8
we're left with x = 8
Justify each step and explain your reasoning.
3(4x+6)=x-4
Answers
Answer:
x = −2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3(4x+6)=x−4
(3)(4x)+(3)(6)=x+−4(Distribute)
12x+18=x+−4
12x+18=x−4
Step 2: Subtract x from both sides.
12x+18−x=x−4−x
11x+18=−4
Step 3: Subtract 18 from both sides.
11x+18−18=−4−18
11x=−22
Step 4: Divide both sides by 11.
[tex]\frac{11x}{11}[/tex] = [tex]\frac{-22}{11}[/tex]
x = −2
(50pts) The distance covered and the time taken by a car are plotted in a graph.
a. Find the slope of the line in the graph.
b. Calculate the distance traveled by the car at the 20th second.
c. Calculate the speed of the car.
Answers
Answer:
a=2
b=40m
c=2m/s
Step-by-step explanation:
slope is rise over run so 10/5 simplified is 2/1 or 2
for b just look at the graph at the 20th second
for c you do distance over time so basically the same thing as a 10/5 which is 2m/s
Plz help me Find the indicated information
Answers
The figure is not drawn to scale. PQ and MN are straight lines.
Find ZZ
helpppp
Answers
45+z+87=180
132+z=180
z=48
A 15 ft tall tree with shadow of 25 ft, What is the length from end of shadow to top of tree?
Answers
Answer: A 29.2
Step-by-step explanation:
Answer:
The answer is 29.155, rounded to 29.2! Good luck!
a rectangle is 16 feet long and 8 feet wide find its area
Answers
The area of the rectangle is 128 square feet.
To find the area of a rectangle, you multiply the length by the width. In this case, the rectangle is 16 feet long and 8 feet wide.
Area = Length * Width
Substituting the given values:
Area = 16 feet * 8 feet
To perform the calculation, multiply the numbers:
Area = 128 square feet
Therefore, the area of the rectangle is 128 square feet.
The area of a rectangle represents the total amount of space enclosed within its boundaries. In this case, the rectangle measures 16 feet in length and 8 feet in width, so the area is calculated as 16 feet multiplied by 8 feet, resulting in 128 square feet.
The concept of area is fundamental in geometry and is used to measure the size of two-dimensional shapes. In the case of a rectangle, the area represents the product of its length and width, as every point within the rectangle contributes to its overall size.
Knowing the area of a rectangle can be useful in various situations. For example, if you want to determine how much flooring material is required to cover a rectangular room, you would need to know the area of the floor.
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What are ALL the 100 digits of pi?
Answers
Answer:
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679
Hope this helps; have a great day!
what strategy can be used to transform a quadratic function in vertex form to standard form
Answers
Hello, I Am BrotherEye
Answer:
This Transparent inquisition can be solved Below
Use transformations to graph a quadratic function in vertex form. A quadratic function in standard form, f(x) = ax² + bx + c, can be changed into vertex form by completing the square. The vertex form of a quadratic function is f(x) = a(x – 5)2 + k, where the vertex of the function is (h, k).
Step-by-step explanation:
Vertex form to standard form converter
Write the parabola equation in the vertex form: y = a*(x-h)² + k ;
Expand the expression in the bracket: y = a*(x² - 2*h*x + h²) + k ;
Multiply the terms in the parenthesis by a : y = a*x² - 2*a*h*x + a*h² + k ;
Best Of Luck
~
BrotherEye
4x – 5 = 2(2x + 1) Please help plss
Answers
Answer:
0=7
Step-by-step explanation:
Distribute
4−5=2(2+1)
4−5=4+2
Add 5 to both sides of the equation
4 − 5 = 4 + 2
4 − 5 + 5 = 4 + 2 + 5
Simplify Add the numbers
Add the numbers
4 = 4 + 7
Result
0=7
A school has 1200 students 1/3 are in the upper school. 2/5 in the middle school and the remainder in lower school. How many students are in lower school?
Answers
Answer:
257 students in the lower school
Step-by-step explanation:
you want to make the fractions have an equal denominator so make 1/3 5/15s and 2/5 to 6/15's, 5+6= 11/15s that leaves 4/15's for the lower part of the school
4 divided by 15 is 4.6 repeating so divide 1200 by 4.66 and boom
need help here pleaseeee
Answers
Sam picked 48 oranges in 5 minutes. How many oranges could she pick in 2 minutes?
Answers
Step-by-step explanation:
48 oranges in 5 minutes means she picked 48 oranges in 300 seconds.
Divide 48 by 300 to get what she would pick in one second.
This equals 0.16
Multiply 0.16 by 120 seconds [how many seconds are in two minutes].
This equals 19.2 oranges in two minutes. As she cannot pick 0.2 of an orange, she could pick 19.