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
A parallelogram has vertex at (-5 , -1) (-2, -1), (-3,-4), and (-6,-4). What is the approximate perimeter of the parallelogram round your answer to the nearest hundredth
Answers
Answer:
12.4 units
Step-by-step explanation:
We have to find the length of the sides of the parallelogram which is calculated using the formula for Distance
= √(x2 - x1)² + (y2 - y1)² where we are given the vertices (x1, y1) and (x2, y2)
For side A
(-5 , -1) (-2, -1)
= √(-2 -(-5))² + (-1 - (-1))²
= √(-2 + 5)² + (-1 + 1)²
= √3² + 0
= √9
= 3 units
For side B
(-2, -1), (-3,-4)
= √(-3 -(-2))² + (-4 -(-1))²
= √(-3 + 2)²+ (-4 + 1)²
= √-1² + -3²
= √1 + 9
= √10 units
= 3.1622776602 units
Approximately = 3.2 units
For side C
(-3,-4), (-6,-4).
= √(-6 -(-3))² + (-4 - (-4))²
= √(-6 + 3)² + (-4 + 4)²
= √-3² + 0²
= √9
= 3 units
For side D
(-5 , -1), (-6,-4)
= √(-6 - (-5))² + (-4 - (-1))²
= √(-6 + 5)² + (-4 + 1)²
= √-1² + -3²
= √1 + 9
= √10 units
= 3.1622776602 units
Approximately = 3.2 units
From the above calculation , we can see that,
side A = side C
side B = side D
The formula for the Perimeter of a Parallelogram is = 2(Side a + Side b)
= 2(3 + 3.2) units
= 2(6.2) units
= 12.4 units
a glass top of an office table is in the form of rectangle. The diagonal of the table have length 5x-11 and 2x+25
1.what is the value of x?
2.what us the length of the diagonal?
Answers
Answer:
1) The value of [tex]x[/tex] is 12.
2) The length of the diagonal is 49.
Step-by-step explanation:
1) If the glass is a rectangle, then both diagonal must have the same length, that is, the following equation must be solved:
[tex]5\cdot x - 11 = 2\cdot x + 25[/tex] (1)
We need some algebraic handling to determine the value of [tex]x[/tex]:
[tex]5\cdot x - 11 = 2\cdot x + 25[/tex]
[tex]5\cdot x - 2\cdot x = 25 +11[/tex]
[tex][5+(-2)] \cdot x = 36[/tex]
[tex]3\cdot x = 36[/tex]
[tex]x = 12[/tex]
The value of [tex]x[/tex] is 12.
2) If we know that [tex]x = 12[/tex], then the length of the diagonal ([tex]d[/tex]) is:
[tex]d = 2\cdot x + 25[/tex]
[tex]d = 49[/tex]
The length of the diagonal is 49.
Randy ran 13/4 miles on Monday and 2 2/4 miles on Tuesday. How far did
Randy run on both days?
Answers
Answer:
The answer is 5 3/4
Step-by-step explanation:
13/4 = 3 1/4
3 1/4 + 2 2/4 = 5 3/4
Hope this helped you!
* This is the correct answer, I have taken the test and am posting the answers in hopes of helping other people :] *
Based on the diagram, what is tanA?
Enter your answer in the boxes.
tanA=
Answers
Aw that's really nice of you thanks
thank you <3 appreciate it loads
I put the picture attached
Answers
Answer:
120 square inches
Step-by-step explanation:
True or false? A correct answer is worth (2 pts). Explain how you know for the additional (2 pts). Using complete sentence for (1 pts)
(5,2) is a solution to the equation 2x + 3y = 10.
Answers
answer (in words)
FALSE. the coordinate pair (5, 2) is not a solution to the equation [tex]2x+3y=10[/tex]. in order to figure out whether or not the statement is true or false, plug the [tex]x[/tex] and [tex]y[/tex] values from the coordinate pair (5, 2) into the given equation, [tex]2x+3y=10[/tex]. if both sides of the equation end up equal, the coordinate pair is a solution to the equation. if not, the coordinate pair is not a solution to that equation.
(i hope i explained that well enough, i'm better at explaining it algebraically as opposed to putting it into words lol)
answer (algebraic/steps for solving)
first, plug in 5 for [tex]x[/tex] in the equation [tex]2x+3y=10[/tex].
[tex]2x+3y=10[/tex] ⇒ [tex]2(5)+3y=10[/tex]then plug in 2 for [tex]y[/tex].
[tex]2(5)+3y=10[/tex] ⇒ [tex]2(5)+3(2)=10[/tex]now your equation is [tex]2(5)+3(2)=10[/tex]. all that's left to do is to simplify. you can do this in whatever order you'd like, but i'll start with multiplying 2 · 5.
[tex]2(5)+3(2)=10[/tex] ⇒ [tex]10 + 3(2) = 10[/tex]multiply 3 · 2.
[tex]10 + 3(2) = 10[/tex] ⇒ [tex]10 + 6 = 10[/tex]add 10 + 6.
[tex]10 + 6 = 10[/tex] ⇒ [tex]16=10[/tex]16 and 10 are not equal, therefore (5, 2) is not a solution to the equation [tex]2x+3y=10[/tex]. in order for a coordinate pair to be the solution to an equation, both sides of the equation need to end up equal after solving and simplifying.
i hope this helps! have a great rest of your day <3
if i made 70 dollars a week how much would i make in a month
Answers
Answer:
there are 4.3 weeks in a month
so then,
4.3 × 70 = 301
the awnser is:
301 dollors per month
i need help on this.
Answers
Answer:
answer is A hope this helps
Step-by-step explanation:
Can someone please help me with math.
Answers
Answer:
The answer would be B
Step-by-step explanation:
From 1 second to 3 seconds Denise had stopped
We can tell that this is true because looking at the graph we can see that from 1 to 3 seconds the distance stayed the same which indicates that Denise was not walking
Answer:
I think it is B between 1 and 3 bc a flat line shows no progress and the only area where is show a flat line is between 1 and 3 so he stopped walking at that point
Step-by-step explanation:
what is
2x(8+12)-5
tell if you know what it is
Answers
Answer:
40x-5
Step-by-step explanation:
What is the value of x?
Enter your answer in the box.
mm
Answers
Answer:
1938
Step-by-step explanation:
Kevin is making a picture frame. He has a piece of trim that is 3 feet long.
How many 14−inch-long pieces can Kevin cut from the trim?
How much of a foot will he have left over?
Kevin can cut______ 14−inch-long pieces with______ of a foot left over.
Answers
U 6x2 + 7x3 + 8x5 + 9 What is the degree of the polynomial?
Answers
Answer:it is 73x+9 degree of the polynomial
Step-by-step explanation:U 6x2 + 7x3 + 8x5 + 9 What is the degree of the polynomial
Marissa went on a trip and drove her car throughout the day. The graph below shows Marissa's distance from the starting point of her trip for different segments of time
What’s the answer to this please?
Answers
PLEASE HELP !! DUE SOON ! :(
Answers
Answer:
-3
Step-by-step explanation:
W = -3
X = 3
Z = -9
Y = 6
-3 + 3 = 0
-9 + 6 = -3
-3 + 0 = -3
Talia bas 26 $1 coins, 20-cent coins, 50-cent coins. The number of $1 coins is 6 more than the number of 20-cent coins. The total value of the coins is $17.20. How many 50-cent coins are there?
Answers
Answer:
8 fifty cents coin.
Step-by-step explanation:
Let's assign variable for the unknown number of coins.
Let there are 'x' number of $1 coins
'y' number of 20 cent coins
'z' number of 50 cent coints.
Totally there are 26 coins.
So, x+y+z=26
Now, there are 6 more $1 coins than 20-cent coins.
We can set up equation for this as
x= y+6
Now, total value of these coins is $17.20
We can setup equation as
100 x+20 y+50 z=1720
Now, substitute x as y+6
100(y+6) +20 y+50 z =1720
Distribute the 100 to get rid ( )
100 y+600 +20 y+50 z=1720
Combine like terms
120 y+50 z= 1120
Keep this equation as it is.
Plug in x as y+6 into x+y+z=26
y+6+y+z=26
2y+z=20
Now, take the two equations
2y+z=20
120y+50z=1120
Multiply first equation by -60 to eliminate the y terms when we add them.
-120y-60z=-1200
120y+50z= 1120
-------------------------
-10z =-80
Divide both sides by -10
z=8
Now, plug in z as 8 into 2y+z=20
2y+8 =20
Subtract both sides 8
2y=12
Divide both sides by 2
y=6
Now, plug in y, z values into the first equation.
x+6+8=26
x+14=26
Subtract both sides 14
x=12
So, there are eight 50-cent coins.
round to nearest thousandth
0.227
Answers
Answer:
is there another number after the 7 if so if it is 5 or bigger it rounds up but 1-4 rounds down
Step-by-step explanation:
Answer:
0.23!! =D
hundredths (1/100)
There are 3 fourths as many cows as pigs on an animal farm. If there are 35 pigs and cows on the farm, how many of them are pigs?
Answers
2/5 kilogram of soil fill 1/3 of a container. Can 1 kilogram of soil fit in the container?
Answers
Answer:
Yes
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
2/5 kilogram od soil = 1/3 of the container
So 2/5 + 2/5+ 1/5 = 1 kilo gram of soil
so 1 kilo will fit into the container
Jenny started with $5 in her piggy bank and earns an
allowance of $2 every 3 days.
Mika had saved $16 in his piggy bank from babysitting
but he spends $3 a day to buy a soda on his way home
from school.
Let x represent the number of days that have passed and
y represent the amount of money they have.
When will Jenny and Mika have the same amount of
money?
Answers
Answer:
x = 3 days y = $7
Step-by-step explanation:
Andrea has 5 bags with 2 marbles in each bag. Kori has 3
bags with 2 marbles in each bag.
How many more marbles does Andrea have?
Answers
Answer:
4 more marbles
Step-by-step explanation:
Andrea in total, has 10 marbles since 5*2 is 10
Kori in total, has 6 marbles since 3*2 is 6
Subtract 10 by 6 is 4
10-6=4
4 marbles
(GIVING BRAINLIEST!!!!)
Just answer number 3 and/or 4
Answers
Answer:
3) [tex]1 \frac{2}{4}[/tex] in
4) 3 days
Answer:
3. 2in. the 3 one on the list. 4. it snowed 3 1/4 3x
Step-by-step explanation:
Which expression(s) have the same value of the question on the picture?
Answers
Answer:
Options A, Option C and Option D
Step-by-step explanation:
[tex](\frac{2}{5})^2=(\frac{2}{5})^{1+1}[/tex]
= [tex](\frac{2}{5})(\frac{2}{5})[/tex]
= [tex]\frac{2\times 2}{5\times 5}[/tex]
= [tex]\frac{2^2}{5^2}[/tex]
= [tex]\frac{4}{5^2}[/tex]
= [tex]\frac{4}{25}[/tex]
Therefore, Options A, Option C and Option D are the correct options.
In ΔPQR, the measure of ∠R=90°, PQ = 5.7 feet, and RP = 3.8 feet. Find the measure of ∠P to the nearest tenth of a degree.
Answers
Answer:48.1897 = 48.2
Step-by-step explanation: cos P= 3.8/5.7
P= cos-1 (3.8/5.7)
P=48.1897 = 48.2
Rebecca's window store made a mosaic for the community center. The mosaic had a 7 × 7 array of different color square tiles. If each tile is 3 1/2 ft long, what is the area of the whole mosaic?
Answers
Answer:
600 1/4 ft²
Step-by-step explanation:
Window is a 7 * 7 square array
Length per tile = 3 1/2 ft long
Dimension of entire array :
3 1/2 * 7 by 3 1/2 * 7
7/2 * 7 by 7/2 * 7
49/2 by 49/2
Recall : Area of a square = a² ; where a = side length
Area of entire array :
49/2 * 49/2 = 2401 / 4 = 600 1/4 ft²
Find the value of x to the nearest degree.
Answers
Answer:
A. 66
Step-by-step explanation:
180 - 90 = 90
90 - 24 = 66
Answer will be 66
Hope this helps!
Which of these factored expressions are equivalent to 15x+45? Select all that apply
A-3(5x+15)
B-5(3x+9)
C-15(x+3)
D-15(x+45)
Answers
Answer:
A, B, C
Step-by-step explanation:
15x+45
3 (5x + 15)
5(3x +9)
15(x + 3)
Sue has $74,210 in a savings account. The interest rate is 15% per year and is not compounded. How much will she have in 2 years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), is the interest rate expressed as a decimal, and t is the time in years.
Answers
Answer:
$22,263
Step-by-step explanation:
15% of $74,210 is $11,131.50 so $11,131.50 X 2= $22,263
so after 2 years the total amount of money along with interest will be a total of = $96,473
help please!!!!!!!!!!
Answers
Answer:
3125
Step-by-step explanation:
cubed root of 125 = 5
5^5 = 3125
Hope this helps!!
La ultima alternativa es la correcta: 3 125
determine the total surface area.
Answers
Answer:
15 x 8 x 11 x 17 = 22440