1.Given the function f(x) = -2c + cx - x^2? and f^-1(5) = -1, find c
Answers
Here we have a quadratic function and we want to find the value of a constant with a given restriction.
We will find that c = 8.
So we have the function:
[tex]f(x) = -2c + cx - x^2[/tex]
We know that:
[tex]f(5)^{-1} = -1 = \frac{1}{-2c + c\cdot 5 - (5)^2}[/tex]
Notice that the above equation means that:
[tex]-2c + c\cdot5 - (5)^2 = -1[/tex]
Then we just need to solve the above equation for c:
[tex]-2c + 5c - (5)^2 = -1\\\\(-2 + 5)\cdot c - 25 = -1\\\\3\cdot c = -1 + 25\\\\3\cdot c = 24\\\\c = 24/3 = 8[/tex]
So we found that the value of c is 8.
This means that the function is:
[tex]f(x) = -16 + 8\cdot x - x^2[/tex]
You can see the graph below:
If you want to learn more, you can read:
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Related Questions
Plz answer will give brainliest
Answers
These triangles are congruent by SAS, therefore HI and IJ will be the same length.
3v = v + 60
2v = 60
v = 30
Hope this helps!
A ball is thrown vertically with a velocity of18 m/s. It’s height, h, in meters above the ground after t seconds is given by the equation: h= -5t2+10t+35. Algebraically, determine the following.
Find The maximum height of the ball and the time it takes to reach that height
The time it takes the ball to hit the ground.
PLEASE HELP!
Answers
Answer:
Step-by-step explanation:
First of all, something is wrong with either the wording in the problem or the equation that you wrote; if the upward velocity is 18, we should see 18t in the equation, not 10t. I solved using 10t.
To find the max height of the ball and the time it took to get there, we need to complete the square on this quadratic and solve for the vertex. That will give us both of those answers in one!
To complete the square, set the quadratic equal to 0 and then move over the constant, like this:
[tex]-5t^2+10t=-35[/tex] The rule is that we have to have a 1 as the leading coefficient, and right now it's a -5, so we factor that out, leaving us with:
[tex]-5(t^2-2t)=-35[/tex] and now we are ready to begin the process to complete the square.
The rule is: take half the linear term, square it, and add it to both sides. Our linear term is a -2 (from the -2t); half of -2 is -1, and -1 squared is 1. We add in a one to both sides. BUT when we put the 1 into the set of parenthesis on the left, we didn't just add in a 1, we have that -5 out front that is a multiplier. That means that we actually added in a -5 after it's all said and done.
[tex]-5(t^2-2t+1)=-35-5[/tex] and we'll clean that up a bit. The right side is easy, that's a -40. The left side...not so much.
The reason we complete the square is to put this quadratic into vertex form. Completing the square creates a perfect square binomial on the left, which for us is, along with the simplification on the right:
[tex]-5(t-1)^2=-40[/tex]
Lastly, we move the -40 back over by adding and setting the quadratic back to equal y:
[tex]-5(t-1)^2+40=y[/tex] and we see that the vertex is (1, 40). That translates to a height of 40 meters at 1 second after launch. That's the vertex which, by definition, is the max or min of the parabola. Because our parabola is negative, the vertex for us is a max.
To find out how long it takes the ball to hit the ground, set the quadratic equal to 0 and factor however it is you are currently doing this in class. You can continue to factor from the vertex form we have the equation in if you'd like. Let's do that, since we are already most of the way there. Begin here:
[tex]-5(t-1)^2=-40[/tex] and divide both sides by -5 to get
[tex](t-1)^2=8[/tex] and take the square root of both sides to "undo" that squaring on the left:
t - 1 = ±√8. Now add 1 to both sides to isolate the t:
t = 1 ± √8. In decimal form:
t = 1 + √8 is 3.828 seconds and
t = 1 - √8 is -1.828 seconds.
Since we all know that time will NEVER be a negative value, the time it takes the ball to hit the ground is 3.828 seconds.
What should be subtracted from thrice the rational number -8/3 to get
5/2?
Answers
Answer: -21/2 or -10.5
Step-by-step explanation:
Let x be the number that is going to be subtracted from the rational number
3 × (-8/3) - x = 5/2 ⇒ Write the equation
-8 - x = 5/2 ⇒ Do multiplication
-8 - x + x = 5/2 +x ⇒ Add x on both sides
-8 = 5/2 + x ⇒ Simplify
-8 - 5/2 = 5/2 + x - 5/2 ⇒ Subtract 5/2 on both sides
x = -21/2 = -10.5 ⇒ Simplify
Hope this helps!! :)
Please let me know if you have any questions
Someone please help me!! I don’t know the answer!!
Answers
Answer:
Step-by-step explanation:
Remark
The measurement of the arc is 3Pi
that represents 108 / 360 of the circle.
Equation
108/350 2 * pi * R = 3* pi
Solution
Pi is on both sides of the equation. They both cancel.
108/360 = 0.3
0.3 * 2 * R = 3
0.6 * R = 3
R = 3/0.6
R = 5
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Samuel played a video game. He gained some points, lost 87 points, and
finished with less than 320 points, Which of the following inequality
represents the given situation?
A.) n-87 < 320
B.) N + 87 < 320
C.) N-87 = 320
D.) n +87= 320
Answers
Answer:
A
Step-by-step explanation:
The correct inequality that represents the given situation is: A.) n - 87 < 320.
How to explain the equationThe situation states that Samuel played a video game and gained some points. Let's represent the points he gained as 'n'.
Next, it is mentioned that he lost 87 points. To represent this in the inequality, we subtract 87 from the initial points gained, which gives us 'n - 87'.
Finally, the situation specifies that Samuel finished with less than 320 points. This means that the final score, represented by 'n - 87', is less than 320.
This inequality represents that the initial points gained by Samuel (n) minus 87 points is less than 320 points, indicating that his final score is less than 320 points after losing 87 points.
Learn more about equations
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If you roll a standard number cube 42 times, how many times do you expect the cube to show a five?
Round your answer to the nearest whole number if needed.
Answers
Answer:
5
Step-by-step explanation:
this is probability
probability of 5 occuring once is = 5/42=0.119
therefore, probability of 5 occuring in 42 times is;
42 x 0.119=4.998
approximately 5
how to solve (n^(3)+3n^(2)+3n+28)-:(n+4) in long polynomial division?
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Answer:
Open the image. (Hope you don't mind about bad writing)
Second time posting this. Please help!! :)
Answers
Answer:
Step-by-step explanation:
[tex]\frac{480+24(x-40)}{x}[/tex]
The numerator of the rational expression the money he earned for 'x' hours
The rate at which William is paid for each hour in excess of 40 hours 24.
x = 50 hours = (40 + 10 ) hours
The amount paid for excess 10 hours = 24 *10 = 240
Total amount earned for the week = 480 + 240 = 720
To make a disinfecting solution, Alana mixes 2 cups of bleach with 5 cups of
water. What is the ratio of water to the total amount of disinfecting solution?
Answers
Answer:
Step-by-step explanation:
Ok
Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).
Answers
Answer:
Ax + By = C is standard form.
y + 1 = (2/3)(x - 8)
distribute the (2/3)
y + 1 = (2/3)x - (16/3)
Multiply each term by 3 to clear the fractions.
3y + 3 = 2x - 16
Subtract 2x from both sides.
-2x + 3y + 3 = - 16
Subtract 3 from both sides.
-2x + 3y = - 19
Correct form typically has the leading coefficient as a positive number so multiply each term by - 1.
2x - 3y = 19
Step-by-step explanation:
Answer:
The answer is 2x + -3y = 19
Step-by-step explanation:
got it right on edge
There are 5 brown horses and 4 tan horses in a barn. Sonia will randomly select two horses to ride with her friend. What is the probability that
the first horse selected is tan and the second horse selected is brown?
20/81
5/18
2/9
1/20
Answers
Answer:
5/18
Step-by-step explanation:
The total number of horses present is 9
The probability that the first selected horse is tan is 4/9
So , now for the second choice , we are left with 8 total horses of which 5 is brown
The probability is 5/8
So the joint probability is the product of this two
That will be;
5/8 * 4/9 = 5/18
Identify the range of the function shown in the graph.
Answers
Answer: The answer is all real numbers
Step-by-step explanation:
This is the answer because the line goes on infinitely and will pass through all of the numbers (negative, positive). Its not y [tex]\geq \\[/tex] 0 because it passes through 0 when the line goes through x (side to side) axis.
F={(-1, 2), (3, 2), (4,2), (0, 2)} Is Fa function and why/why not?
Answers
Answer:
yes it is a function A
Step-by-step explanation:
1 by 8 of the passenger of a train where children is there where 40 children traveling in the train on a Saturday how many Abbott were there in that that day?
Answers
Answer:
200 adults
Step-by-step explanation:
1/8 of the passengers (children) is 40
Total passengers in the train is 8/8
Therefore to get the total number of passengers is given by
(8/8) × 40 × (8/1)
= 240 passengers
Adults in the train = Passengers - Children
= 240 - 40
= 200 adults
How many index laws are there?
Answers
Answer:
There are three laws of indices.
A diver begins at 140 feet below sea level. She descends at a steady rate of 7 feet per minute for 4.5 minutes. Then, she ascends 112.2 feet. What is her current depth?
Negative 549.3 feet
Negative 59.3 feet
59.3 feet
549.3 feet
Answers
Answer:
Step-by-step explanation:
starting point: 140 feet below sea level.=-140
she then decends= 7(4.5)=31.5
-140-31.5=-171.5
finally she ascends 112.2 feet
-171.5+112.2=-59.3 feet or 59.3 feet below sea level
Answer:
It's B
Step-by-step explanation:
Find AC, given that line AD is the perpendicular bisector of BC
Answers
Answer:
wouldn’t it just be 21? because both are the same but mirrored
Grade improvement and study motivation
Answers
Answer:
yes you are write because when our results come with good marks and grade the we are motivate .
Step-by-step explanation:
thanks mark me brainlist
If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initially. When will the amount left be 2 grams? Round to the nearest tenth of a day.
Answers
Answer: [tex]26.4\ \text{days}[/tex]
Step-by-step explanation:
Given
Half life of radioactive substance is [tex]T_{\frac{1}{2}}=20\ \text{days}[/tex]
Initial amount [tex]A_o=2\ \text{days}[/tex]
Amount left at any time is given by
[tex]\Rightarrow A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}\\\\\Rightarrow 2=52^{\dfrac{-t}{20}}\\\\\Rightarrow 0.4=2^{\dfrac{-t}{20}}\\\\\Rightarrow 2^{\dfrac{t}{20}}=2.5\\\\\Rightarrow \dfrac{t}{20}\ln 2=\ln (2.5)\\\\\Rightarrow t=\dfrac{20\ln (2.5)}{\ln 2}\\\\\Rightarrow t=26.4\ \text{days}[/tex]
It takes 26.4 days to reach 2 gm.
2cm + 5cm + 6.4cm cuboid
Answers
Answer:
64 volume of the cuboid
formula used is lbh multiplies together.
Mark me as brainliest
Hope it helps:)
Step-by-step explanation:
Lucia gave Brenda half of the cash she had in the store counter at the end of the day. Brenda put the money in her purse and added one half of the amount she had from her own savings. Brenda had saved half of what Lucia earned in the store that day. Brenda took her purse and went to the dog shelter and brought food and treat packet for 5 dogs. Each packet cost her $15. How much money did Lucia earn at the store that day?
Answers
Answer:
$100
Step-by-step explanation:
The amount Lucia gave Brenda = Half the amount in the store counter
The amount Brenda added to the money Lucia gave her = Half the amount in her (Brenda) savings
The amount Brenda had saved = Half of the amount Lucia earned in the store that day
The number of food and treat packets Brenda bought = 5
The cost of each packet = $15
Let x represent the amount Lucia earned and let y represent the amount Brenda saved
We have;
x/2 = y
x/2 + y/2 = 15 × 5 = 75
Therefore, we get;
y + y/2 = 75
(3/2)·y = 75
y = 75 × 2/3 = 50
y = 50
From x/2 = y, we have;
x/2 = 50
x = 2 × 50 = 100
The amount Lucia earned in her store that day, x = $100
What is the quotient of the synthetic division problem below, written in polynomial form?
-1| 1 7 15 9 7
Answers
Answer:
Step-by-step explanation:
If we have 5 terms to the right of the -1 outside the box thing, that means that our original polynomial is a 4th degree (the degree is one lower than the number of terms in order to allow for the constant which has no variable). Set up the synthetic division as shown in the problem. The rule is to bring down the first term, the 1 to the right of the box, multiply it by the number outside, -1, and put that product up under the next number in line inside the box. Like this:
-1 | 1 7 15 9 7
-1
1
Now add straight down, multiply the sum by -1 and put that product up under the next term in line, the 15:
-1 | 1 7 15 9 7
-1 -6
1 6
Then add straight down again, multiply the sum by -1 and put that product up under the next term in line, the 9:
-1 | 1 7 15 9 7
-1 -6 -9
1 6 9
Then do the same thing. Add straight down, multiply the sum by -1 and put the product up under the next term in line, the 7:
-1 | 1 7 15 9 7
-1 -6 -9 0
1 6 9 0 7
This is the final result. The last number, the 7 is the remainder, but the rest of it makes up what we call the depressed polynomial and is a polynomial that is one degree less than the degree we started with. So this depressed polynomial is a 3rd degree. The numbers are the coefficients on the x terms:
[tex]1x^3+6x^2+9x+0R7[/tex] or more simply stated:
[tex]x^3+6x^2+9xR7[/tex]
b) 5(2x - 4)
Expand the following
Answers
Answer:
10x-20
Step-by-step explanation:
(5×2x)-(5×4)
10x-20
PLS HELP!
What effect will replacing x with (x + 7)have on the graph of the equation
y = x^2
Answers
Answer:
The answer would be C.
Compared to the original graph (red), the new graph (blue) is shifted 7 units to the left.
Step-by-step explanation:
Answer:
shift 7 units to the LEFT
Step-by-step explanation:
Three events A, B and C are defined over a sample space, S. Events A and B are independent. Events A and C are mutually exclusive. Given that P(A)= 0.04, P(B)=0.25, P(C)=0.20 and P(B/C)=0.15. Find for P(C/B)
Answers
Answer:
[(b/c)=0.15)]
Step-by-step explanation:
===================================================
Work Shown:
P(B/C) = P(B and C)/P(C) ... conditional probability formula
P(B and C) = P(C)*P(B/C)
P(B and C) = 0.20*0.15
P(B and C) = 0.03
------------
P(C/B) = P(C and B)/P(B) .... note the swap of B and C
P(C/B) = P(B and C)/P(B)
P(C/B) = (0.03)/(0.25)
P(C/B) = 0.12
------------
Extra notes:
The fact that events A and B are independent is not relevant.The fact A and C are mutually exclusive isn't used here either.This problem can be solved through Bayes' Theorem.Another alternative you can do is to set up a 3 by 3 contingency table to help solve this problem.Analyzing Graphs of Functions
Which graph shows a function where f(2) = 4?
Answers
Answer:
the first one
Step-by-step explanation:
check which graph passes through the point (2,4)
Answer:
First graph
Step-by-step explanation:
Edge
S is the centroid of the triangle. Find IT if ST= 9
Answers
Answer:
IT = 13.5
Step-by-step explanation:
Recall: According to the Centroid theorem the Centroid of is ⅔ of the distance of the vertex of the triangle to the midpoint of the opposite side.
This means that:
ST = ⅔(IT)
ST = 9 (given)
Substitute
9 = ⅔(IT)
Multiply both sides by 3
3*9 = 2(IT)
27 = 2(IT)
Divide both sides by 2
27/2 = IT
IT = 13.5
what is x(2)+y(6) if x=4 and y=(-4)
Also, can anyone just talk?
Answers
Answer:
-16
Step-by-step explanation:
Follow . PEMDAS
plug the numbers in
4*2 =8 and -4*6=24
add both...
-16.
Step-by-step explanation:
4(2)+(-4)(6)
8-24
-16
hope it helps..
hellppp meeeeeee pleaseeee
Answers
Answer:
Step-by-step explanation:
abscissa = x coordinate
ordinate = y coordinate
table:
A( 2,-3) / (2, -3) / 2/ -3
B(-1,-7) / (-1, -7) / -1/ -7
C(2,0) / (2,0) / 2 / 0
D(-9, 6) / (-9,6) / -9 / 6
E(2,4) . / (2,4) . / 2 / 4
F(0,-5) / (0,-5) / 0 / -5
A ball is thrown into the air with an upward velocity of 36 ft/s. It’s height h in feet after t seconds is given by the function h = -16t^2 + 36t + 9. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the balls maximum height ?
Answers
Answer:
Time taken for the ball to hit the ground back = 3.08 s
Step-by-step explanation:
h(t)= -16t² + 48t + 4
when will rhe object come back to hit rhe ground?
When the ball is at the level.of the ground, h(t) = 0.
0 = -16t² + 48t + 4
-16t² + 48t + 4 = 0
Solving the quadratic equation
t = 3.08 s or t = -0.08 s
Since the time cannot be negative,
Time taken for the ball to hit the ground back = 3.08 s
Hope this Helps!!!
Step-by-step explanation:
