Let f(x)=-4(2)^x. The graph of g(x)=f(x)+k is shown below. Identify the value of k.
Answers
Given:
The function is:
[tex]f(x)=-4(2)^x[/tex]
The graph of the function [tex]g(x)=f(x)+k[/tex] is given.
To find:
The value of k.
Solution:
We have,
[tex]f(x)=-4(2)^x[/tex]
[tex]g(x)=f(x)+k[/tex]
Using these two functions, we get
[tex]g(x)=-4(2)^x+k[/tex]
From the given graph it is clear that the graph of g(x) passes through the point (0,2). It means the point (0,2) satisfies the function g(x).
Substituting [tex]g(x)=2[/tex] and [tex]x=0[/tex] in the above function, we get
[tex]2=-4(2)^0+k[/tex]
[tex]2=-4(1)+k[/tex]
[tex]2=-4+k[/tex]
[tex]2+4=k[/tex]
[tex]6=k[/tex]
Therefore, the value of k is 6.
Related Questions
Suck please help thanks
Answers
Determine if these values form a right triangle. E
Answers
Answer:
They do not.
Step-by-step explanation:
a² + b² = c² c is the hypotenuse
9² + 12² = 17²
81 + 144 = 289
225 ≠ 289
What is the product?
2 3 4
5 9 -1 -7
11 5 -3
Answers
Answer:
-1247400
Step-by-step explanation:
See the Image below:) I believe this is what you are looking for.
Please help me Simplify 1-9÷7+3
Answers
Answer :
the answer is -4/5 or -0.8
step-by-step explanation:
1-9/7+3 = -8/10
now simplify that,
-8/2 = -4
10/2 = 5
so we have -4/5 0r -0.8
Answer:
[tex]1-9\div \:7+3\\9\div \:7\\=\frac{9}{7}\\=1-\frac{9}{7}+3\\=\frac{19}{7}\\\frac{19}{7}\\2\frac{5}{7}\\ans:=2\frac{5}{7}[/tex]
hope this helps you
what is the probability of seeing a sample mean for 21 observations less or equal to the sample mean that we observed
Answers
Answer:
[tex]P(x \le 21) = 0.69146[/tex]
Step-by-step explanation:
The missing parameters are:
[tex]n = 64[/tex] --- population
[tex]\mu = 20[/tex] --- population mean
[tex]\sigma = 16[/tex] -- population standard deviation
Required
[tex]P(x \le 21)[/tex]
First, calculate the sample standard deviation
[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_x = \frac{16}{\sqrt {64}}[/tex]
[tex]\sigma_x = \frac{16}{8}[/tex]
[tex]\sigma_x = 2[/tex]
Next, calculate the sample mean [tex]\bar_x[/tex]
[tex]\bar x = \mu[/tex]
So:
[tex]\bar x = 20[/tex]
So, we have:
[tex]\sigma_x = 2[/tex]
[tex]\bar x = 20[/tex]
[tex]x = 21[/tex]
Calculate the z score
[tex]x = \frac{x - \mu}{\sigma}[/tex]
[tex]x = \frac{21 - 20}{2}[/tex]
[tex]x = \frac{1}{2}[/tex]
[tex]x = 0.50[/tex]
So, we have:
[tex]P(x \le 21) = P(z \le 0.50)[/tex]
From the z table
[tex]P(z \le 0.50) = 0.69146[/tex]
So:
[tex]P(x \le 21) = 0.69146[/tex]
There is a population of millions of computer chips produced at a factory. The production process is so precious that it is known that the population standard deviation for their mass is 2 milligrams. We want to get a 95% confidence interval for the mass of a single microchip produced here. So we randomly sample 100 microchips. The sample average mass turns out to be 1972 milligrams. They found this by placing them all on a scale at once and finding a mass of 197.2 grams, and then dividing by 100. You don't think they would actually weigh each one individually, do you? That would be super annoying.
Required:
Find a 95% confidence interval for the mass of a microchip produced at this factory.
Answers
Answer:
The 95% confidence interval for the mass of a microchip produced at this factory is between 1971.608 milligrams and 1972.392 milligrams.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{2}{\sqrt{100}} = 0.392[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 1972 - 0.392 = 1971.608 milligrams
The upper end of the interval is the sample mean added to M. So it is 1972 + 0.392 = 1972.392 milligrams
The 95% confidence interval for the mass of a microchip produced at this factory is between 1971.608 milligrams and 1972.392 milligrams.
An exercise scientist wanted to test the effectiveness of a new program designed to increase the flexibility of senior citizens. They recruited participants and rated their flexibility according to a standard scale before starting the program. The participants all went through the program and had their flexibility rated again after a month. The scientist wants to test if the flexibility ratings are significantly higher after a month of the program. Assume that these participants can be considered a representative sample and that all other necessary conditions for inference were met. Which of these is the most appropriate test and alternative hypothesis?
a) Paired t test with H : Mafter before > 0
b) Paired t test with H.: Hafier-before +0
c) Two-sample t test with H: Mbefore > Hafter
d) Two sample t test with H.: wore Manter
e) Two sample t test with H: Meedore Aladder
Answers
Answer:
a) Paired t test with H : Mafter before > 0
Step-by-step explanation:
As we do not know anything about variances we will perform a paired t test.
We want to check the effectiveness of the new program designed to increase the flexibility of senior citizens.
So we will perform a test where the mean after the program is greater than the mean before the program.
The best option is a.
Option a defines both objectives paired t test and difference of mean after and mean before is greater than zero.
Other options are not correct as they miss out one of the both objectives.
Solve the area
I hate geometry
Answers
Answer:
Step-by-step explanation:
Area of a llgm = base * height
Base = 20 ft.
Height = 10 ft.
Area = 20*10 = 200 ft.
Hope it helps u
Please mark as brainliest
Thank You
Answer:
200ft
Step-by-step explanation:
Area of a parallelogram is b*h .
base, b=20ft
height, h= 10ft
Therefore, area= 20*10=200ft
The difference of two times a number and five is eight more than the number.
find the equation and solve for x
Answers
Answer:
x = 13
Step-by-step explanation:
The difference of two times a number and 5: [tex]2x-5[/tex]
Eight more than a number: [tex]x + 8[/tex]
You can create the following equality with this:
[tex]2x - 5 = x + 8[/tex]
Which is solved as follows:
[tex]2x-5=x+8\\2x-x=8+5\\x=13[/tex]
Answer:X= 13
Step-by-step explanation:
Step 1:
Let the unknown number be x
Such that the difference of two times a number and five is represented mathematically as 2x -5
And eight more than the number can be expressed as
8 +x
Joining the two expressions to get an equation becomes 2x-5= 8+x
Step 2: Solving for x
2x-5= 8+x
We first find like terms and solve
2x-x=8+5
We are now left with
x=13 as the answer.
See related question and answer here: https://brainly.com/question/17882257
What is the image of (-1, 1) when reflected across the line y = x?
Answers
Answer:
(1, -1)
Step-by-step explanation:
I can confirm that it is (1, -1)
A tree grows exactly one half meter in height per year. The tree is currently 8 meters tall. If someone hammers a nail into the tree at a height of exactly 2 meters, how high will the nail be after 12 years of growth
Answers
Answer:
2 meters
Step-by-step explanation:
Given
[tex]a= 8m[/tex] --- initial
[tex]r = \frac{1}{2}m/year[/tex] --- rate
[tex]t = 12\ yrs[/tex]
[tex]Nail = 2m[/tex]
Required
The height of the nail after 12 years
The top of the tree will continue growing at the given rate, however, the height of the nail will remain unchanged.
This is so because when trees grow, they grow from the top; i.e. the heights are increased at the top while the bottom remains unchanged.
Hence, the height of the nail after 12 years in 2m
The height of the average barn owl is 3 times the height of the average tree swallow. If x is the height of the tree swallow, which expression BEST represents the height of the average barn owl?
x+3
x−3
x×3
x÷3
Answers
Answer:
C; x*3
Step-by-step explanation:
WILL GIVE BRAINLIEST
A number n, when divided by 4, gives –10. What is the value of n?
Answers
-40/4 = -10
Hope this helps!
Help !!!!!!Select the values that make the inequality h < 2 true.
(Numbers written in order from least to greatest going across.)
Answers
2.001 > 2, so it is wrong. And from that value and onwards, the values are all greater than 2 so the ones I listed above are the answers.
The required value that makes the inequality h ≤ 2 true are -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.
Given that,
To Select the values that make the inequality h < 2 true.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The values that are less than and equal to 2 are, -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.
Thus, the required value that makes the inequality h ≤ 2 true are re, -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Find the equation of the linear relationship.
Answers
Answer:
y = -3x + 150
Step-by-step explanation:
2 points on the graph:
(30, 60) and (40, 30)
Slope:
m=(y2-y1)/(x2-x1)
m=(30 - 60)/(40 - 30)
m= (-30)/10
m= -3
Slope-intercept:
y - y1 = m(x - x1)
y - 60 = -3(x - 30)
y - 60 = -3x + 90
y = -3x + 150
If the surface area of the cone below is 628.32 m², find its volume.
I WILL MARK BRAINLEIST IF CORRECT AND 20 POINTS
Answers
Answer:
1586.91 m³
Step-by-step explanation:
From the diagram attached,
Applying,
A = πrl.................. Equation 1
Where A = surface area of the cone, l = slight heigth of the cone, π = pie.
make l the subject of the equation,
l = A/πr.............. Equation 2
From the question,
Given: A = 628.32 m², π = 3.14, r = 8 m
Substitite these values into equation 2
l = 628.32/(3.14×8)
l = 25 m
But,
l² = h²+r².................... Equation 3
Where h = height of the cone.
h = √(l²-r²)
h = √(25²-8²)
h = √(625-64)
h = √(561)
h = 23.69 m
Also Applying,
V = 1/3πr²h
Where V = volume of the cone.
Therefore,
V = (3.14×8²×23.69)/3
V = 1586.91 m³
Find the length of side b
B= _m
Answers
Answer:
b= 0.09475
Step-by-step explanation:
Huilan is 13 years younger than Thomas. The sum of their ages is 33. What is Thomas's age?
Answers
Answer:
Thomas is 20 years old
Step-by-step explanation:
33 - 13 = 20
Juan family hang their clothes outside to dry, if they use the dryer, there $400 monthly bill will increase by % wich means it will cost $700
Answers
Hope this helps :D
I can also explain if you need help
The radius of a cylindrical water tank is 4 ft and its height is 10 ft. What is the volume of the tank?
Answers
Answer:
160π cubic feet
Step-by-step explanation:
V= πr²h
V= π x 4²x 10
V = 160π cubic feet
A company's daily cost c, in hundreds of r dollars, to manufacture n items of a certain product can be modeled by the function c^-1(5)=80, Lording to the model, which of the following is the best interpretation of c ^1(5) = 80, where c^1 is the inverse function of c ?
a) The company's daily cost to manufacture 5 items of the product is $80.
b) The company's daily cost to manufacture 5 items of the product is $8,000.
c) The company's daily cost to manufacture 500 items of the product is $80.
d) The company's daily cost to manufacture 80 items of the product is $5.
e) The company's daily cost to manufacture 80 items of the product is $500.
Answers
Answer:
e) The company's daily cost to manufacture 80 items of the product is $500.
Step-by-step explanation:
We have that:
c is the cost in hundreds of dollars to manufacture n items. The input is the number of items, and the output is the cost, in hundreds of dollars.
Inverse function:
In the inverse function, the input and the output are exchanged from the original function, that is, in this situation, the input in the cost, in hundreds of dollars, and the output is the number of manufactured items.
c^-1(5)=80
Input of the inverse function is 5, which is the cost, in hundreds of dollars, that is, $500, to manufacture 800 itens. This means that the correct answer is given by option e.
In a place 100 soldiers had enough food for 60 days .how many soldiers leave the place so that food long last for 80 days
Answers
Answer:
48 soldiers leave the place.
Step-by-step explanation:
100/60=80/x100x=4800x=4800/100x=48hope it helps.
stay safe healthy and happy.Plz help me well mark brainliest if correct....??????????????...
Answers
Answer:
D). 100
Step-by-step explanation:
The range is the highest number-lowest number in data. 150 is the highest, 50 is the lowest. Therefore, 150-50=100
PLEASE HELP GUYS I’m being timed
Answers
The question is the base of the triangle, so we use the formula : b²=c²–a²
——————————————————————
[tex] {b}^{2} = \sqrt{c^{2} - {a}^{2} }[/tex]
[tex] {b}^{2} = \sqrt{ {16}^{2} - {8}^{2} } [/tex]
[tex] {b}^{2} = \sqrt{256 - 64} = \sqrt{192} [/tex]
[tex] \sqrt{192} =8 \sqrt{3} [/tex]
Find the Surface Area of this Prism
Answers
Answer:
[tex]54 m^2[/tex] is the correct answer I believe
Suppose that y varies inversely with x, and y= 3 when x = 10.
(a) Write an inverse variation equation that relates x and y.
Equation:
(b) Find y when x = 5
y =
Answers
Answer:
y=6
Step-by-step explanation:
the equation that relates x and y is y=30(1÷x)
HELP TIMED----AND NO BOTS WITH /BIT
A segment which goes through two points of a circle is a …
Arc
Chord
Diagonal
Radius
Secant
Answers
The map slake reads 2 inches =25 miles which distance does 6 inches represent
Answers
Answer:
75 miles
Step-by-step explanation:
Step 1: Set up a fraction given the data (Let "x" represent the distance in miles.)
[tex]\frac{25}{2} = \frac{x}{6}[/tex]
Step 2: Divide the given values (Given values are 25 over 2. We are doing this because we need to know the difference between those two figures.)
[tex]\frac{25}{2}\\\\25 \div 2\\\\= 12.5 \:or\: 12\frac{1}{2}[/tex]
Step 3: Multiply the result to the 6 (Since we've found the difference between them by division, we will have to do the opposite operation in order to find the answer.)
[tex]12\frac{1}{2}\times6\\\\= 75[/tex]
Therefore, 75 is the distance in miles.
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Find the Volume.
10 points
7 m
5 m
4 m
Answers
Answer:
140 m^3 = 7 x 4 x 5
Step-by-step explanation:
Volume = H * W * L
Which answers describe the shape below
Answers
Answer:
B. parallelogramStep-by-step explanation:
stay safe, stay healthy and blessed.
thank u
Answer:
a b c d e
Step-by-step explanation: