Graph g(x)=-8|x|+1 help
Answers
Answer:
Step-by-step explanation:
using the vertex formula, f(x)=a|x-h|+k (vertex is (h,k)) (a is slope)
we can say that the vertex of this absolute value equation is (0,1). (this is because there is no h so we substitute it as 0)
your slope would be -8 (or -8/1 if you prefer using the (rise)/(run) technique. (keep in mind that you would be going down 8 and right 1 in this case.)
That's basically it I guess.
lol
The graph of the function \(\(g(x) = -8|x| + 1\)\) forms a "V" shape intersecting at the point (0, 1), with one side having a slope of -8 for \(\(x \geq 0\)\) and the other side having a slope of 8 for \(\(x < 0\)\).
To graph \(\(g(x) = -8|x| + 1\)\), we'll start by considering two cases: \(\(x \geq 0\) and \(x < 0\)\) since the absolute value function changes its behavior at x = 0.
Case 1: \(\(x \geq 0\)\)
For \(\(x \geq 0\), \(|x| = x\)\). So, \(\(g(x) = -8x + 1\)\).
Case 2: x < 0
For x < 0, \(\(|x| = -x\)\). So, \(\(g(x) = -8(-x) + 1 = 8x + 1\)\).
Now, we have two expressions for g(x) depending on the sign of x:
For \(\(x \geq 0\): \(g(x) = -8x + 1\)\)
For \(\(x < 0\): \(g(x) = 8x + 1\)\)
To graph the function, we'll plot points for both expressions and join them to create the final graph.
The table with values for x with corresponding g(x) is given below.
Now, we'll plot these points and join them to form the graph of \(\(g(x) = -8|x| + 1\)\):
The graph resembles two lines with different slopes intersecting at the point (0, 1). One line has a slope of -8, and the other has a slope of 8. The negative slope portion represents \(\(g(x) = -8|x| + 1\)\) for \(\(x \geq 0\)\), and the positive slope portion represents \(\(g(x) = 8x + 1\) for \(x < 0\)\). The graph is continuous and forms a "V" shape, touching the point (0, 1).
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Related Questions
Kiet needs to observe a science experiment every 6 minutes for one hour. He makes his first observation at 1:00 p.m. At what time will he make another observation?
Answers
Kiet will make his another observation at every multiples of 6 until it reaches at 60 which is at 2 : 00 pm.
Given that,
Kiet needs to observe a science experiment every 6 minutes for one hour.
He makes his first observation at 1:00 p.m.
Now he needs to make the observation every 6 minutes.
This means that his second observation will be at 1:06 pm.
Third observation will be at 1:12 pm.
Fourth will be at 1:18 pm.
It goes on like this for every multiples of 6.
His last observation will be at 2:00 pm which is at the 60th minute after 1.
Hence Kiet will make his observations at every multiples of 6 until it reaches 60.
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I also need to know the value of T
Answers
Answer:
hello
Step-by-step explanation:
\(137 = - 151 + t \\ 137 + 151 = t \\ t = 288\)
hope this is correct.
Which relation represents a function ?
Answers
Answer:
The third choice
Step-by-step explanation:
a relation is a function if an input has at most one output for a given input
Choices 1, 2 and 4 are not functions as they have two different outputs for the same input. (See the red ovals)
Agrocery store sells 4 avocados for $6.00. What is the unit cost of each avocado?
A) $2.40
B) $0.10
C $1.50
D
$0.60
Answers
Just take 4 and try dividing by 6
A bank loaned out 20,500, part of it at the rate of 9% annual interest, and the rest at 11% annual interest the total interest earned for both loans was 2,225.00 how much was loaned at each rate
Answers
The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.
Let the amount of money loaned at 9% be x
the amount of money loaned at 11% be y
According to the question,
Total money loaned = 20,500
Thus the equation formed is,
x + y = 20,500 ------ (i)
Simple interest is calculated by
I = P * r * t
where I is the simple interest
r is the rate of interest
t is the time
Thus, the interest on x = 0.09x
the interest on y = 0.11y
Total interest gained = 2,225
Thus the equation formed is,
0.09x + 0.11y = 2225 -------(ii)
Multiply (i) by 0.09
0.09x + 0.09y = 1845
Subtract the above from (ii)
0.02y = 380
y = 19000
x = 1500
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С
What is the solution to the equation 3x ÷ (-6) = -12?
Answers
Answer:
x=24
Step-by-step explanation:
First: Multiply -6 to both sides
Next: You get 3x=72
Then: Divide 72 by 3
Last:....
ANSWER: x=24
hi !! the answer is x= -24 :))
Find the value of x.
Answers
Answer: 111
Step-by-step explanation: its half of the circle
x = 42
\(\bold{SOLUTION:}\)
I need to know the percentage of drivers who are at least 45. Using the table in the picture.
Answers
The percentage of drivers who are at least 45 is 62%
How to determine the percentage of drivers who are at least 45.From the question, we have the following parameters that can be used in our computation:
The table of values
From the table, we have
Age 45 = 62 percentile
When represented properly
So, we have
Age 45 = 62%
This means that the percentage of drivers who are at least 45 is 62%
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John Doe, a super-genius student (known also under his nick-name Wile E. Coyote, super-genius) has just graduated from SPEA and found a job that will allow him to purchase a car to finally catch Roadrunner. He can either buy a new car at a cost of $22,000, buy a used car for $12000 or lease a new car for one year at a cost of $8,500 (assume total cash purchase up front, no financing or monthly payments required). The new car has a 20% chance of a serious break down resulting in a permanent impairment to the trade-in value. The trade-in value for the new car without a serious break down after one year is $18,000 but only $10,000 if the break down occurs. On the other hand, the used car has a 40% chance of suffering a major break down with a $8,000 decrease in the resale value. However, if it does not break down, Wile can sell it to a friend one year from now for $9,000 cash (assume he can also sell it to the friend for $4,000 if the breakdown occurs). Finally, the leased car has a 10% chance of breaking down with a repair cost of only $2,000, and if it doesn’t, Wile will not gain or lose anything by returning the car at the end of a one year lease period. NOTE: For the new and used car purchases all related repair costs resulting from a breakdown have been netted against the trade-in / resale value.
a. Construct a decision tree for Wile
b. What is the expected value of the new car?
c. What is the expected value of the used car?
d. What is the expected value of leasing the car?
Answers
Answer: See explanation
Step-by-step explanation:
a. Construct a decision tree for Wile
The solution to the question has been attached.
b. What is the expected value of the new car?
= [(0.2 × $10,000) + (0.8 × $18,000)] - $22,000
= $2000 + $14400 - $22000
= $16400 - $22000
= -$5600
c. What is the expected value of the used car?
= [(0.4 × $4000) + (0.6 ×$9000] - $12000
= $1600 + 5400 - $12000
= $7000 - $12000
= -$5000
d. What is the expected value of leasing the car?
= [(0.1 × -$2000) + (0.9 ×0)] - $8500
= -$200 - $8500
= -$8700
The first term of a geometric sequence is 5 and the multiplier, or ratio, is –2. What is the sum of the first 5 terms of the sequence?
Answers
Step-by-step explanation:
s1 = 5
s2 = s1 × -2 = 5×-2 = -10
s3 = s2 × -2 = -10 × -2 = 20
...
now, we could do all that manually.
but there is also a formula for geometric sequence.
in fact, there are 2 - one for finite and one for infinite sequences.
and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.
since we need the sum of the first 5 terms, which of the 2 do you think we need ?
of course, finite, because 5 is a normal number we can "touch". it is not infinity.
so, the formulas for finite sums of geometric sequences are :
if |r| < 1, Sn = a(1 - r^n)/(1 - r)
if |r| > 1, Sn = a(r^n - 1)/(r - 1)
if r = 1, Sn = na
if r = -1, then Sn = a or 0 depending on if n is odd or even.
the sequence is in general
s1 = a
sn = sn-1 × r
in our case a = 5, r = -2.
so, what form of the formula do we need ?
|-2| = 2, and 2 > 1, so ...
S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =
= 5 × 11 = 55
quick check, as the 5 terms are
5
-10
20
-40
80
and their sum is : 55
correct !
Find the elements of range that correspond to the elements 0 and 3 of the domain,
\(f = {(x, y): 3y - 2x=6}\)
Answers
The elements in the range that correspond to the elements 0 and 3 are y = 2 and y = 4 and the equations are solved.
Given data ,
To find the elements in the range that correspond to the elements 0 and 3 of the domain, we need to solve the equation 3y - 2x = 6 for the corresponding values of y when x = 0 and x = 3.
When x = 0:
Substituting x = 0 into the equation 3y - 2x = 6, we get:
3y - 2(0) = 6
3y = 6
y = 2
So, when x = 0, the corresponding value of y is 2.
When x = 3:
Substituting x = 3 into the equation 3y - 2x = 6, we get:
3y - 2(3) = 6
3y - 6 = 6
3y = 12
y = 4
So, when x = 3, the corresponding value of y is 4.
Hence , the elements in the range that correspond to the elements 0 and 3 of the domain are y = 2 and y = 4, respectively.
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what is 30 x 45 x 34 x89
Answers
Answer:
Step-by-step explanation:
on : to show More... Then click on √x to enter your answers using the Math Equation editor. Question 5 A frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It is determined that the height of the frog as a function of time can by modeled by h (t) = − 16t² +64t + 3. What is the height of the stump? O 3 ft -3 ft O 16 ft O 64 ft ◄ Previous 1 pts M Next ▸
Answers
The height of the stump is 3 ft.
The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.
In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:
h(0) = -16(0)² + 64(0) + 3
Since any term multiplied by zero is zero, we can simplify further:
h(0) = 0 + 0 + 3
Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.
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Find the value of each variable in the parallelogram.
Answers
Answer:
x = 9 and y = 15
Step-by-step explanation:
this is the answer because each side is equivalent to the parallel line so y would be whatever is across from it
Answer:
y=15
x=9
Step-by-step explanation:
they are parallel and equal to the opposite sides
Find the Value of X.
Answers
The value of x is 33.2
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent or equal.
Also the ratio of corresponding sides of similar triangles are equal.
Therefore;
Triangle EHG and EFG are similar
39/36 = 36/x
36 × 36 = 39x
39x = 1296
divide both sides by 39
x = 1296/39
x = 33.2
Therefore the value of x is 33.2
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Which term can be added to the list so that the greatest common factor of the three terms is 12h3?
36h3, 12h6, __________
Answers
The term that can be added to the list so that the greatest common factor of the three terms 12h3 36h3, 12h6, is 48h5
How can the term be known?A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.
The term that can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12 without any fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.
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5.
Which value of x would satisfy this inequality?
V3
4
2
A А.
С
D
000
4
10
Answers
Answer:
C) 4/5
Step-by-step explanation:
pi/4 = 0.7853981634
\(\frac{\sqrt{3} }{2}\) = 0.8660254038
3/4 = 0.75. It's less than pi/4, so not correct
9/10 = 0.9. It's more than 0.866, so not correct
4/5 = 0.8. It's right for both condition
8/9 = 0.888. It's more than 0.866, so not correct.
2 is less than or equal to y
Answers
Solution
\(2\leq y\)Sketch the graph of the given function. Then state the function’s domain and range. y = 4(4)x
Answers
To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.
Let's choose some x-values and calculate the corresponding y-values:
For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4
For x = -1, y = 4(4)^(-1) = 4(1/4) = 1
For x = 0, y = 4(4)^0 = 4(1) = 4
For x = 1, y = 4(4)^1 = 4(4) = 16
For x = 2, y = 4(4)^2 = 4(16) = 64
Now we can plot these points on a coordinate plane and connect them to form the graph of the function.
The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.
The domain of the function is all real numbers since there are no restrictions on the values of x.
The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.
finding angle measures between intersecting lines.
Answers
Answer: x=45°
Step-by-step explanation:
Angles opposite from each other are equal. The angle 160 degrees in red on the bottom encompasses two angles: BEG and CEG. Angle BEG is on the opposite side as FEA which means it is equal to x.
Since angle FED on the other side is 115, you subtract 115 from 160 to get 45 degrees.
Answer: x=45°
The angle BEG, which is opposite to the angle FEA, is determined to be 45 degrees.
According to the information provided, in a figure with an angle of 160 degrees (red angle on the bottom), there are two angles labeled as BEG and CEG. It is stated that the angle BEG is opposite to the angle FEA, making them equal, so we can represent this angle as x.
Additionally, it is mentioned that the angle FED on the other side measures 115 degrees.
To find the value of x, we subtract 115 degrees from the angle of 160 degrees.
=160-115
= 45
Thus, the solution is x = 45°.
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The desks in a school are arranged in 6 rows with 12 desks in each row. If the desks are
rearranged in rows of 8 desks, how many rows will there be?
Answers
Answer:
there will be 9 rows
Step-by-step explanation:
Mr. Lewis fixes electronic equipment. He uses the function f(x) = 80x + 250 to determine his total charge, f(x), in dollars, where x is the number of hours he works. Which statement represents the rate of change of the function?
Answers
Given:
Total charge, f(x), in dollars, for x number of hours is
\(f(x)=80x+250\)
To find:
The correct statement for the rate of change of the function.
Solution:
Slope intercept form of a linear function is
\(y=mx+b\) ...(i)
where, m is slope and b is y-intercept.
We have,
\(f(x)=80x+250\) ...(ii)
On comparing (i) and (ii), we get
\(m=80, b=250\)
Therefore, the slope or rate of change of the function is 80 and it represents that per hour changes are 80.
what would be your first step in completely factoring 6a^2-15a+6
Answers
The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).
In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:
3(2a^2 - 5a + 2)
Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.
The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:
3(2a - 1)(a - 2)
Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
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The top of a light house is 110m above the level of the water. The angle of depression from the top of the light house to a fishing boat is 18 degrees. How far is the fishing boat from the base of the light house? Round your answer to the hundredth place.
Answers
Step-by-step explanation:
it starts at positive 110m it's 18 negative degrees away
you take away negative 18 from positive 110m the answer would be positive cause your negative is smaller than your positive so your formula is 110meters take away 18 ( negative) that would be your answer ( if you want to) link that could help : https://youtu.be/jVvvUiExjes .
formula :
\(110 - 18\)
Please answer this:
-1 (t+8) = -7.1
Answers
Answer:
Step-by-step explanation:
Answer:
i am pretty sure is t = -0.9
Step-by-step explanation:
-1(t+8) = -7.1
(t+8) = 7.1
t = -0.9
Select the correct answer. Joel and Kevin are each putting money in a savings account to buy a new bicycle. The amount, in dollars, in Joel's savings account, x weeks after the start of the year, is modeled by function j. The amount of money in Kevin's account, at the same time, is modeled by function k. j(x) = 25 + 3x k(x) = 15 + 2x Which function correctly represents how much more money, in dollars, is in Joel's account than in Kevin's account x weeks after the start of the year? O A. (j − k)(x) = 40 + 5x (j − k)(x) = 40 + x (j-k)(x) = 10 + 5x (j-k)(x) = 10 + x O B. C. O D. Reset dtry Next
Answers
The correct answer is (j - k)(x) = 10 + x.
To find the difference in the amount of money between Joel's and Kevin's accounts, we subtract the value of Kevin's account (k(x)) from Joel's account (j(x)).
(j - k)(x) = (25 + 3x) - (15 + 2x)
= 25 - 15 + 3x - 2x
= 10 + x
This expression represents how much more money is in Joel's account compared to Kevin's account after x weeks.
Therefore, the correct function is (j - k)(x) = 10 + x.
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Please help and thank you
Answers
Daniella: Were you thinking of perpendicular lines?
Ori: It seems like you've got the basic idea, but your definition could be more precise.
Kaori: Yes! Well done. Here, have a cookie. You've earned it.
Complete the square to rewrite y = x^2 - 6x + 16 in vertex form. Then state wether the vertex is a maxium or minimum and give its coordinates.
A. Maximum at (3,7)
B. Maximum at (-3,7)
C. Minimum at (3,7)
D. Minimum at (-3,7)
will give brainly!!’
Answers
Answer:
C) Minimum at (3,7)
Step-by-step explanation:
Recall that vertex form is \(y=a(x-h)^2+k\):
\(y=x^2-6x+16\)
\(y=(x^2-6x+9)+7\)
\(y=(x-3)^2+7\)
Therefore, the vertex is \((h,k)\) or \((3,7)\) in this case. Because the parabola is positive, then the vertex has to be the minimum of the parabola, making choice C correct.
the radius of a cylindrical water tank is 4ft, and it’s height is 10ft. What is the volume of the tank?
Answers
Answer:
\(volume = 502.4ft^3\)
Step-by-step explanation:
\(volume = \pi r^2 h = 3.14 \times 4^2 \times 10 = 502.4ft^3\)
ANSWER ASAP! NEED HELP
