PLZ HELP, DUE TONIGHT!! Find the values of a and b such that f(x) is continuous at x=
Answers
Answers:
a = 2 and b = -4
============================================================
Explanation:
Let's define the three helper functions
f(x) = ax^2 - bh(x) = 6j(x) = 5ax+bwhich are drawn from the piecewise function. The g(x) function will change depending on what the input is.
If x < 1, then g(x) = f(x). If x = 1, then g(x) = h(x)If x > 1, then g(x) = j(x)Since we want g(x) to be continuous at x = 1, this must mean the three functions f(x), h(x), j(x) must have the same output value when the input is x = 1.
Because h(x) = 6 is a constant function, the output is always 6 regardless of the input. Therefore, we want f(x) and j(x) to have 6 as their output when x = 1. Or else, the pieces won't connect.
Plug x = 1 into the f(x) function to get
f(x) = ax^2 - b
f(1) = a(1)^2 - b
f(1) = a - b
Set this equal to the desired output of 6 and we end up with the equation a-b = 6. Solving for 'a' leads to a = b+6.
------------
We'll use the same idea for j(x)
j(x) = 5ax + b
j(1) = 5a(1) + b
j(1) = 5a + b
5a+b = 6
5(b+6) + b = 6 ... plug in a = b+6; solve for b
5b+30+b = 6
6b+30 = 6
6b = 6-30
6b = -24
b = -24/6
b = -4
Which then leads to,
a = b+6
a = -4+6
a = 2
------------
Since a = 2 and b = -4, we go from this
[tex]g(x) = \begin{cases}ax^2-b, \ \ x < 1\\6, \ \ x = 1\\5ax+b, \ \ x > 1\end{cases}[/tex]
to this
[tex]g(x) = \begin{cases}2x^2+4, \ \ x < 1\\6, \ \ x = 1\\10x-4, \ \ x > 1\end{cases}[/tex]
Meaning
f(x) = 2x^2+4 and j(x) = 10x-4
You should find that plugging x = 1 into each of those two functions leads to 6 as the output.
The graph is shown below. Note the red graph f(x) is only drawn when x < 1. Similarly, j(x) is only drawn when x > 1. The orange point represents h(x) which only happens when x = 1. So as the name implies, the piecewise function g(x) is composed of pieces of the three functions f(x), h(x), j(x).
Related Questions
Factorize completely 3ac+6ab-15a
Answers
Answer:
3a(c + 2b - 5)
Step-by-step explanation:
Step-by-step explanation: The greatest common factor for the 3 terms here is 3a so factor out a 3a and what we're left with inside the parentheses is each of the terms in the original polynomial divided by 3a.
So we have 3a(c + 2b - 5) which is our final answer.
Someone please help me ?!?!?
Answers
Answer:
2nd is correct
Step-by-step explanation:
ok now mark me brainlist
Find the value of x and y.
Answers
Answer:
x=34[tex]\sqrt{2}[/tex]
y=34[tex]\sqrt{3}[/tex]
Step-by-step explanation:
If the unit's and ten's digits of a two digits of a two digit number are y and x, then the number is
Answers
Answer:
10x+ y
Step-by-step explanation:
The unit's digit is y and the ten's digit is x.
The ten's digit has a zero placed beside it .
So multiply x by 10 giving 10 x and then add the unit's digit .
This wil give 10x+ y
The number is 10 x + y
This can be elaborated through the use of numbers . Suppose we have unit's digit as 6 and the ten's digit as 5.
Multiply 10 by 5 and add 6
5*10 +6= 50+6= 56
What is the diameter of a sphere with a volume of 334 cm", to the nearest tenth of a
centimeter?
Answers
Answer:
8.6cm
Step-by-step explanation:
V = 4/3 pi r^3 = 334, solve for r = 4.30
double for diameter = 8.61
Step-by-step explanation:
you can see there
just click the photo
HELP NOW PLEASE I HAVE 10 MINUTES! 20 POINTS
If f(x) = 4x^2 + 1 and g(x) =x^2 - 5, find (f-g)(x)
Me and my procrastination habits smh
Also let me know if you can help with other questions I have 2 more
Answers
Slope:
2
3
y-intercept: (0,−6)xy0−63−4
let me know if this doesn’t make sense and i can fix it :)
Evaluate 5v + w for v = 4 and w = 16. Show work.
Answers
Answer:
36
Step-by-step explanation:
5(4)+16=20+16=36
A measure that describes the typical value of a data set
a
measure of variation
b
mean absolute deviation
c
statistics
d
range
e
measure of center
f
statistical question
Answers
e
measure of center
as A measure that describes the typical value of a data set mean,median and mode.
The probability of saving a penalty kick from the opposing team is .617 for a soccer goalie. If 7 penalty kicks are shot at the goal, what is the probability
Answers
Answer:
0.2754
Step-by-step explanation:
Probability of saving a penalty kick = 0.617
p = 0.617 ; q = 1 - p = 1 - 0.617 = 0.383
number of trials, n = 7
Number of saves, x = 5
Using the binomial probability relation :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 5) = 7C5 * 0.617^5 * 0.383^2
P(x = 5) = 21 * 0.0894181 * 0.146689
P(x = 5) = 0.2754
A circle has a diameter that measures 14in. what is the area of the circle to the nearest tenth?
Answers
Answer:
153.9
Step-by-step explanation:
14/2=7 which is the radius which you square and it results to 49. multiply that times pi for 153.86 or 153.9 to the nearest tenth.
Answer:
153.9
Step-by-step explanation:
We know that the equation to find the area of a circle in [tex]\pi r^2\\[/tex]. So we divide the diameter by half and we plug in the radius.
There are 7 movies that Christine wants to see over winter break. She only has time to see 4 of the movies. How
many different groups of 4 movies are possible, if the order in which they are seen is not important?
Answers
Answer:
35
Step-by-step explanation:
sdfghjkolkgdsdfghjkl
The possible number of the group the movies will be 840.
What are permutations and combinations?Permutation and combination are counting principles that are used in a variety of situations. A permutation is a count of the various arrangements that can be made from a given set of items. Details matter in permutation because the order or sequence is important.
Given that there are 7 movies that Christine wants to see over winter break. She only has time to see 4 of the movies.
The combinations will be calculated as:-
Combination = ⁷C₄
Combination = ( 7 x 6 x 5 x 4 )
Combination = 840
To know more about permutation and combination follow
https://brainly.com/question/28065038
#SPJ2
i dont get these questions on math help i give brainliest
Answers
Answer:
here a link to your answer
Step-by-step explanation:
https://brainly.com/question/20419046
plus the answer is b
Which equation can be used to find A, the area of the parallelogram shown?
A parallelogram with a base six meters, height seven meters, and diagonal side length eleven meters
A = 6 × 7
A = 6 × 11
A = 12 × 6 × 7
A = 12 × 6 × 11
Answers
Answer:
A = 6 x 7
Step-by-step explanation:
To find the area of a parallelogram we use the equation of Area = base x height. In this case since the base is 6 and the height is 7, we plus in these numbers for the variables (b x h) to get the area.
Find the height of triangle
Answers
Answer:
60
Step-by-step explanation:
First, divide 120 by two and get 60. Now do 120-60 to get 60. Set up proportion
60/x = x/60.
Cross multiply
x^2 = 3600
and now find the square root of 3600
60
how do i find the surface area of the sphere??
Answers
Answer:
98 π R
Step-by-step explanation:
Surface area of sphere = 4 π R²
= 2 π R × 2 R
= 49 π × 2 R
= 98 π R
Juan is a teacher and takes home 68 papers to grade over the weekend. He can grade at a rate of 6 papers per hour. How many papers would Juan have remaining to grade after working for 7 hours?
Answers
Answer:
26 papers
Step-by-step explanation:
Well this is pretty straight forward
if he can grade 6 papers an hour
we just multiply 6 by 7 to get how many papers he graded in 7 hours
6*7= 42
now we subtract 42 from 68 to get how many papers are left to be graded
68-42=26
26 papers are left
hii! i’ll give brainliest pls help
Answers
Answer:
b is correct
Step-by-step explanation:
Help pleasee want asap
Answers
Answer:
I'm pretty sure it is D since all the other ones are maximum value parabolas (and the questions asks for a minimum) other than D.
The perimeter of the parallelogram below is 50 cm and the length of AB = 10 cm. What is the length of side BC?
Answers
Answer:
15
Step-by-step explanation:
The length of BC=20cm I think
A circle of radius 1 is inside a circle of radius 5. The smaller circle is rotated clockwise
on the larger circle without slipping until it arrives back at its starting point P. How
many revolutions (turns) will the small circle make? Be careful. The answer is not 5.
Answers
9514 1404 393
Answer:
4
Step-by-step explanation:
Consider the arcs PQ and P'Q. When turns are made without slipping, these have the same measure. The length of arc PQ is ...
PQ = CP·θ
The length of arc P'Q is ...
P'Q = O₂Q·(∠PO₂Q)
Segment O₂A is parallel to CP, so angle AO₂Q is θ. Then ∠PO₂Q = θ+α, where α is the angle by which P' has rotated counterclockwise from A.
We are given that ...
CP = 5, O₂Q = 1
Using the above relations, we can write ...
5θ = 1(θ+α)
α = 4θ
That is, for every full turn θ = 2π, the smaller circle makes turns totalling 4(2π) = 8π, or 4 full turns.
The small circle makes 4 revolutions to arrive at its starting point.
Find the circumference of the given circle given a diameter of 40 cm.
Use 3.14 as an approximation of Pi.
Answers
Answer:
c. 125.6
Step-by-step explanation:
Pi= 3.14
r= d/2 = 40/2 = 20
[tex]2\pi \: r[/tex]
= 2 × 3.14 × 20
=125.6
What is the length of the hypotenuse?
Answers
Answer:
65 cm
Step-by-step explanation:
16^2 x 63^2 = 65^2
HELPP(David saves 12 % of his monthly salary.
If he saves $17.75, what is his monthly
salary?)
Answers
Answer:
147.92
Step-by-step explanation:
Let the monthly salary be x
He saves 12 % and that is 17.75
x* 12% = 17.75
Change to decimal form
x *.12 = 17.17
Divide each side by .12
x*.12 /.12 = 17.75/.12
x =147.91666666
Rounding to the nearest cent
x = 147.92
Enter a decimal that equivalent to 6/100
Answers
Answer:
0.06
Step-by-step explanation:
The black graph is the graph of y=f(x). Choose the equation for the red graph
Answers
Answer:
a. y= f(x-1)
Step-by-step explanation:
___________
please show your work
Answers
Answer:
52
Step-by-step explanation:
If JK bisects the angle, the two angles are equal
6x+2 = 8x-6
Subtract 6x from each side
6x-6x+2 = 8x-6x-6
2 = 2x-6
Add 6 to each side
2+6 =2x-6+6
8 =2x
Divide by 2
8/2 =2x/2
4 =x
Now find angle LJM, which is the sum of the two angles
6x+2 + 8x-6
14x -4
14*4-4
56-4
52
Answer:
D) 52
Step-by-step explanation:
since htere is an angle bisector that means that (6x+2) and (8x-6) are equal to each other
so
(6x+2)=(8x-6)
-6x -6x
2=2x-6
+6 +6
8=2x
/2 /2
x=4
no you plug x back into one of the equations so
6(4)+2=26
now 26x2=52
There are 11 teachers and 132 students at a middle
school. What is the ratio of teachers to students?
Answers
Answer:
[tex]\frac{1}{12}[/tex] or 1:12
Step-by-step explanation:
There are 11 teachers : 132 students
Because ratios are just another way of writing fractions, by putting this into a fraction we get:
[tex]\frac{11}{132}[/tex]
Dividing both the numerator and denominator (top and bottom) by 11, we get:
[tex]\frac{1}{12}[/tex]
Thus, the ratio is [tex]\frac{1}{12}[/tex], or 1:12
please help it’s my final
Answers
Answer:
-1/2
Step-by-step explanation:
y2-y1/x2-x1 is the formula
-2-(-1)/-6-(-8) = -1/2
Hope this helps.
Jane is playing basketball. After a series of 20 shots, Jane had scored 55% of the time. Five shots later, her scoring rate had increased to 56%. On how many of the last five shots did she score
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Answers
Answer: C. 3
help me plzz plzzz plzzzz
Answers
Answer:
60 degree
Step-by-step explanation:
a hexagon has a total sum of angles equal to 720
720/6 = 120
180-120 = 60