Given:
The parent function is:
[tex]f(x)=2^x[/tex]
The other function is:
[tex]g(x)=2f(x)[/tex]
To find:
The statement that describes a key feature of function g.
Solution:
We have,
[tex]f(x)=2^x[/tex]
[tex]g(x)=2f(x)[/tex]
Using these two functions, we get
[tex]g(x)=2(2)^x[/tex]
Putting [tex]x=0[/tex], we get
[tex]g(x)=2(2)^{(0)}[/tex]
[tex]g(x)=2(1)[/tex]
[tex]g(x)=2[/tex]
The y-intercept of the function g at (0,2). So, option A is correct and option B is incorrect.
We know that [tex]g(x)\to 0[/tex] as [tex]x\to -\infty[/tex] and it will never intersect the line [tex]y=0[/tex]. It means the horizontal asymptote of the function g is
Therefore, the correct option is A.
Answer:
A
Step-by-step explanation:
what is 2/3 of 4 hours and 30 minutes?
Find the missing side of the triangle. Round your answers to the nearest tenth if necessary.
12.4 in
3.1 in
16.7 in
11.2 in
Answer:
3.1 in
Step-by-step explanation:
a² + b² =c²
12=c
11.6=b
c²- b² = a²
12²-11.6²= 9.44
√9.44 = 3.07 Rounded = 3.1 in
Round 31.24 to 1 decimal place
Round 5.275 to 2 decimal place
Round 0.56489 to 3 decimal place
Answer:
1. 31.2
2. 5.28
3. 0.565
Step-by-step explanation:
Remember if the number is 1-4 round down and if the number is 5-9 round up.
Hope this is helpful
#happylearning
Alex bought 2 printer cartridges for $28 each and a printer for $85. He gave the cashier $150. How much change should Alex have received from the cashier?
Answer:
$9 in change
Step-by-step explanation:
Find the total cost of his purchases:
28 + 28 + 85
= 141
Find how much change he received by subtracting this from 150:
150 - 141
= 9
So, he should have received $9 in change
Where would the last point need to be in order to finish graphing a square using the points (1, 3), (5, 3), and (5, 7)?
A. (1, 5)
B.(5, 1)
C.(3, 7)
D.(1, 7)
what is the value of 642/3?
Step-by-step explanation:
[tex] \frac{642}{3} \\ [/tex]
= 214Answer:
[tex]214[/tex]
Step-by-step explanation:
[tex] \frac{642}{3} [/tex][tex] = 642 \div 3 \\ = 214[/tex]
Hope it is helpful...For the equation y=2x + 6, find the value of y when
(a) x= 0 (b) x= 1
(c) x=2 (d) x=3
WITH CALCULATION AND EXPLANATION PLEASE.FULL CALCULATION
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge \mathrm{ \underbrace{Answer}}[/tex]
The given equation is :
[tex] \huge \boxed{ y = 2x + 6 }[/tex]
Now, let's solve for each value of "x"
[tex]\mathrm {\hookrightarrow \:1. \: \: when \: \: x = 0}[/tex]
[tex]y = 2x + 6[/tex][tex]y = (2 \times 0) + 6[/tex][tex]y = 6[/tex][tex]\mathrm{\hookrightarrow 2.\: \: when \: \: x = 1}[/tex]
[tex]y = 2x + 6[/tex][tex]y = (2 \times 1) + 6[/tex][tex]y = 2 + 6[/tex][tex]y = 8[/tex][tex]\mathrm {\hookrightarrow \: 3. \: \: when \: \: x = 2}[/tex]
[tex]y = 2x + 6[/tex][tex]y = (2 \times 2) + 6[/tex][tex]y = 4 + 6[/tex][tex]y = 10[/tex][tex]\mathrm{\hookrightarrow \: 4. \: \: when \: \: x = 3}[/tex]
[tex]y = 2x + 6[/tex][tex]y = (2 \times 3) + 6[/tex][tex]y = 6 + 6[/tex][tex]y = 12[/tex][tex] \mathrm{✌TeeNForeveR✌}[/tex]
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
Equation = [tex]\large\bold{y = 2x + 6}[/tex]
a) [tex]x = 0[/tex]
Substitute the value of x as 0 in the equation.
[tex]y = 2x + 6 \\ y = 2(0) + 6 \\ y = 0 + 6 \\ y = 6[/tex]
✐ Answer of a) is [tex]\large\bold{y = 6}[/tex]
____________________
b) [tex]x = 1[/tex]
Substitute the value of x as 1 in the equation.
[tex]y = 2x + 6 \\ y = 2(1) + 6 \\ y = 2 + 6 \\ y = 8[/tex]
✐ Answer of b) is [tex]\large\bold{y = 8}[/tex]
____________________
c) [tex]x = 2[/tex]
Substitute the value of x as 2 in the equation.
[tex]y = 2x + 6 \\ y = 2(2) + 6 \\ y = 4 + 6 \\ y = 10[/tex]
✐ Answer of b) is [tex]\large\bold{y = 10}[/tex]
____________________
d) [tex]x = 3[/tex]
Substitute the value of x as 3 in the equation.
[tex]y = 2x + 6 \\ y = 2(3) + 6 \\ y = 6 + 6 \\ y = 12[/tex]
✐ Answer of d) is [tex]\large\bold{y = 12}[/tex]
____________________
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
what equation do I use to find the apothem?
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Find the range and the interquartile range of the given data set.
2, 4, 7, 8, 16, 19, 21
Select elther relation (If the set is a relation but not a function), function (If the set is both a relation and a function), or
neither (If the set is not a relation).
F=[(x, y) |x+y=10)
A. neither
B. Function
C. Relation
Answer:
B
Step-by-step explanation:
The given set F=[(x, y) |x+y=10) is a function.
What is a function?A relation is a function if it has only One y-value for each x-value.
The set F represents a relation since it contains ordered pairs of elements. Specifically, it contains all pairs (x, y) such that x+y=10.
For example, (2, 8) and (5, 5) are elements of F since 2+8=10 and 5+5=10.
However, it is not necessarily a function since it is possible for two different x values to have the same y value, which would violate the vertical line test for functions.
For example, both (2, 8) and (8, 2) are in F since 2+8=10 and 8+2=10.
Hence, the given set F=[(x, y) |x+y=10) is a function.
To learn more on Functions click:
https://brainly.com/question/21145944
#SPJ7
a rectangular lawn of dimensions 6x metres by x metres. In the centre is a rectangular flower bed of length (x + 4) m and width (x - 1) m. If the area of the shaded region is 40 m’, calculate the area of the flower bed.
Answer:
The area of flower bed is 8.96 m^2.
Step-by-step explanation:
Length of lawn = 6 x
width of lawn = x
length of flower bed = x + 4
width of flower bed = x - 1
Area of shaded region = 40 m^2
Area of the shaded region
6 x (x) - (x +4)(x -1) = 40
[tex]5 x^2 - 3 x - 36 = 0 \\\\x = \frac{-3\pm\sqrt{9 + 720}}{10}\\\\x = \frac{-3\pm 27}{10}=2.4 m, - 3 m[/tex]
As length cannot have negative value, so x = 2.4 m.
Area of flower bed = (x + 4)(x - 1) = (2.4 + 4)(2.4 - 1) = 8.96 m^2
Two amounts of money are in the ratio 8:3 if the second amount is 4.05,what is the value if the first amount?
Answer: 10.75 currency units
Step-by-step explanation:
The amounts of money are in the ration 8:3 which means that for every 3 units of the second amount, there are 8 units of the first.
Use direct proportion to solve:
8 : 3
x ; 4.03
Cross multiply to get:
3x = 32.24
x = 32.24 / 3
x = 10.75 currency units
Select the correct answer.
You're given side AB with a length of 6 centimeters and side BC with a length of 5 centimeters. The measure of angle A is 30°. How many
triangles can you construct using these measurements?
A. 0
B. 1
C. 2
D. Infinitely many
Answer:The answer is B
Step-by-step explanation:
you can use the expression 5n to determine the amount of money you have in cents, when you have n nickels. Find the amount of money you have, in cents, when you have 18 nickels
Answer:
90 cents
Step-by-step explanation:
Find how much money you have by plugging in 18 as n into the expression:
5n
5(18)
Multiply:
= 90
So, when you have 18 nickels, you have 90 cents
A city has 18 radio stations, including 4 college radio stations.
What is the probability that a randomly chosen radio station in this city is a college radio
station?
Write your answer as a fraction or whole number.
Answer:
2/9
Step-by-step explanation:
P=4/18=2/9
Compute the volume of the following composite solid
=======================================================
There are a few ways to do this.
One way is to slice horizontally to break up the L shape into two separate rectangular blocks. Refer to the diagram below to see what I mean.
The block on top has length 80-60 = 20 mm (horizontal), width 10 mm, and height 40 mm.
The volume of this block on top is L*W*H = 20*10*40 = 8000 mm^3, where mm^3 means "cubic millimeters"
The block down below has a length of 80 mm, width of 10 mm, and height of 60-40 = 20 mm (vertical). Its volume is L*W*H = 80*10*20 = 16000 mm^3
Add up the two volumes to get the overall volume: 8000+16000 = 24000 mm^3
---------------------
Another approach you could take is to do a vertical slice to form two separate blocks. You would follow similar steps mentioned in the section above to find the two volumes, and add up the smaller pieces.
Yet another way to find the answer is to find the area of the L shape, and then multiply that by the depth of 10 mm.
What is the constant of proportionality in the equation StartFraction x over y EndFraction StartFraction 2 over 9 EndFraction?
StartFraction 2 over 9 EndFraction
2
StartFraction 9 over 2 EndFraction
9
Given:
The equation is:
[tex]\dfrac{x}{y}=\dfrac{2}{9}[/tex]
To find:
The constant of proportionality.
Solution:
If y is directly proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is the constant of proportionality.
We have,
[tex]\dfrac{x}{y}=\dfrac{2}{9}[/tex]
On cross multiplication, we get
[tex]9x=2y[/tex]
Divide both sides by 2.
[tex]\dfrac{9}{2}x=y[/tex]
Interchange the sides.
[tex]y=\dfrac{9}{2}x[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]k=\dfrac{9}{2}[/tex]
The constant of proportionality is [tex]\dfrac{9}{2}[/tex]. Therefore, the correct option is B.
Help is needed please
Answer:
A
Step-by-step explanation:
Hope this helps!
Help me I don't know any
Answer:
25%
Step-by-step explanation:
(a)
We need to express in percent 8 as a percent of 32.
We have,
Numerator = 8
Denominator = 32
Percent,
[tex]P=\dfrac{8}{32}\times 100\\\\=25\%[/tex]
Hence, the required percentage is 25%.
Figure 2 was constructed using figure 1. For the transformation to be defined as a rotation, which statements must be true? Selext three options.
Answer:
The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).
The transformation is rigid.
Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.
If figure 1 is located 360° about point C, it will be mapped onto itself.
Step-by-step explanation:
Help me this is due soon
Answer:
It's (-1.5,-5.5)
Step-by-step explanation:
Answer:
-1.5 , -5.5
Step-by-step explanation:
It takes Amir 30 minutes to walk to work. If he drives, it takes him 1/3 of that time. What is the latest time that Amir can leave to drive to work and arrive by 9:00 am
the sum of 43.9 and 4 groups of a number
Answer:
10.975+10.975+10.975+10.975
Step-by-step explanation:
1 + 4.25n + 3/2p – 3 + (–2p) + 5/4n simplify
A. 5.5n – 1/2p – 2
B. 9.5n + 1.5p – 2
C. 9/4n − 1.5p − 4
D. 3.75n – p + 1
[tex]\longrightarrow{\green{A.\:5.5 \: n - \frac{1}{2} \: p - 2}}[/tex] ✔
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]1 + 4.25 \: n + \frac{3}{2} \: p - 3 + ( - 2 \: p) + \frac{5}{4} \: n [/tex]
Combining like terms, we have
[tex] = 4.25 \: n + \frac{5}{4} \: n + \frac{3}{2} \: p - 2 \: p + 1 - 3 \\ \\= 4.25 \: n + 1.25 \: n + 1.5 \: p - 2 \: p - 2 \\\\ = 5.5 \: n - 0.5 \: p - 2 \\ \\ = 5.5 \: n - \frac{1}{2} \: p - 2[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
At a football game, the ratio of men to women is 4:1 There are 9,000 people in total, and each ticket costs £10 Calculate the amount of money made from tickets sold to men. Remember to include units ( £ ) in your answer.
Answer:
£72000
Step-by-step explanation:
According to the Question,
Given, At a football game, the ratio of men to women is 4:1 & There are 9,000 people in totalThus, 5 ⇒ 9000 People
So, 4 ⇒ 7200 People(Men)
1 ⇒ 1800 People(Women)
And, each ticket costs £10Thus, The amount of money made from tickets sold to men is 7200 total Men x £10 Per Ticket Cost ⇒ £72000.
if f(x) = 2X -5 and g(x)=x^2-8 find (f+g)(x)
Answer:
im not dure
Step-by-step explanation:
In a certain arithmetic sequence, if -4 is the first term and 10 is the third term, which term is 157?
Answer:
a₁₅₇ = 1,088
Step-by-step explanation:
aₙ = a₁ + d(n-1); where 'd' if common difference
a₁₅₇ = -4 + 7(156)
= -4 + 1092
= 1,088
Answer:
157 is the 24th term
Step-by-step explanation:
The formula for arithmetic sequences is an=a1+(n-1)d,
where an is the nth term, a1 is the first term, n is the term position, and d is the common difference
First, we need to find the common difference using the 10.
Since it's the third term, we have 10=-4+(3-1)d
Solving for d gives us d=7
Next, we need to find the term number of 157
Thus, we have 157=-4+(n-1)*7
Solving for n gives us n=24
We can check it like this: Following order of operations (i.e. PEMDAS) gives us 24-1=23*7=161-4=157
!!!!!!!!!PLEASE HELP!!!!!!!!
What is the solution to the system of linear equations?
Step-by-step explanation:
is connected to graph before u learn this u must know your graph
Anca rolls two number cubes labelled 3 to 8. She adds the numbers that show on the cubes. List the possible outcomes. b) What is the probability of getting '13'? c) What is the probability of getting '21'? d) What result should occur the most?
Answer:
Find the theoretical probability that you will choose each color. P(green) = ___/___ ... 98% or 100%. 3. Bailey uses the results from an experiment to calculate the probability of each color of block being chosen from a bucket. He ... If the sum of the two number cubes in even, Player 1 (or) 2 scores a point.
Step-by-step explanation: