Part (a)
She replaced x with -x to go from f(x) = 3(2)^x to g(x) = 3(2)^(-x). This will not reflect the graph of f(x) over the x axis. Instead, it will reflect over the y axis. This is because each input is negated from positive to negative, or vice versa. For instance the old input x = 2 becomes the new input -2. Applying this idea to every x input will mirror the curve over the vertical y axis.
==============================================
Part (b)
The correct equation should be g(x) = -3(2)^x
The negative out front is the same as -1.
We can think of it as g(x) = -1*f(x). The f(x) is the output value, or y value. If we multiply each y output by -1, this will flip every point over the horizontal x axis. A point like (0,3) moves to (0,-3) after doing this operation.
The table shows the amount of gasoline g (in gallons) left in your tank after you travel m miles.
Miles, m Gallons, g
0 20
20 19
40 18
60 17
A) Write a linear function that relates the amount of gasoline to the traveling distance.
B) How many gallons of gasoline are left after you drive 120 miles?
Answer:
A) [tex]y=-\frac{1}{20}x+20[/tex]
B) 14 gallons of gasoline
A linear function that relates the amount of gasoline to the traveling distance is : y = - (1/20)x + 20 and the gallons of gasoline left after you drive 120 miles will be 10 gallons.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.equation modelling : Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is a table shows the amount of gasoline [g] (in gallons) left in your tank after you travel [m] miles.
The given table is -
Miles [m] Gallons [g]
0 20
20 19
40 18
60 17
We can write the linear function as -
y = mx + c
We can write the slope as -
m = {(19 - 20)/(20 - 0)}
m = (- 1/20)
At [x] = 0, then [y] = 20. So, the equation will be -
y = (-1/20)x + 20
y = - (1/20)x + 20
At [x] = 120 miles -
y(120) = (-1/20 x 200) + 20
y(120) = - 10 + 20
y(120) = 10 gallons
Therefore, a linear function that relates the amount of gasoline to the traveling distance is - y = - (1/20)x + 20 and the gallons of gasoline left after you drive 120 miles will be 10 gallons.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
Write the mixed number as an improper fraction.
33/5
hi
answer correct and I will follow you
Answer:
you have the answer right
What is the y-intercept shown in the graph?
Answer:
0.5
Step-by-step explanation:
p=1/4q+8 make q the subject
Answer:
q = 4p - 32
Step-by-step explanation:
P = 1/4q + 8
Making q the subject
P - 8 = 1/4q
Divide both sides by 1/4
q = (p - 8) ÷ 1/4
= (P - 8) × 4/1
= 4p - 32
q = 4p - 32
Which of the following values is the solution to 11+3(3+4x)=32?
Select all of the answers that are elements of M = {x | x is a month of the year}
[x] x > 0 and x < 12}
{January, February, March, April, May, June, July, August, September, October,
November, December}
{April}
{September, October, November}
November
June
Answer:
{January, February, March, April, May, June, July, August, September, October, November}
Step-by-step explanation:
The set is formed by months of year with indexes larger than 0 and lesser than 12.
The year starts at month 1, which is January, and finishes at month 12, which is December.
Since we want lesser than 12, December is not part of the set. So the answer is given by:
{January, February, March, April, May, June, July, August, September, October, November}
I don't know how to do
Answer:
20
Step-by-step explanation:
14:x::22.401:12.80
can someone help me please
Answer:
15x + 9 (We combing like terms. Ex. 16x and -x)
Answer:
15x+9
Step-by-step explanation:
16x+7+2-x
16x-x+7+2
15x+9
Would a scale factor= 4/5 be enlarge, reduce, or preserve
Answer:
reduce, since 4/5 is smaller than 1
Step-by-step explanation:
I need to find the measure of 3.
The sum of three consecutive integers is 48. Find the integers.
Answer:
15,16 and 17.
Step-by-step explanation:
Let the three consecutive integers are x, x+1,x+2
ATQ,
x+x+1+x+2=48
3x+3=48
Subtract 3 from both sides,
3x+3-3=48-3
3x=45
x = 15
First integer = 15
Second integer = 15+1 = 16
Third interger = 15+2 = 17
Hence, three integers are 15,16 and 17.
Solve for g.
what is g equal to?
Answer:
[tex]\displaystyle g=\frac{4\pi^2l}{T^2}[/tex]
Step-by-step explanation:
Equation Solving
Given the equation
[tex]\displaystyle l=\frac{gT^2}{4\pi^2}[/tex]
It's required to solve it for g. Let's swap sides of the equation:
[tex]\displaystyle \frac{gT^2}{4\pi^2}=l[/tex]
Multiply by [tex]4\pi^2[/tex] to remove the denominator:
[tex]\displaystyle gT^2=4\pi^2l[/tex]
Divide by [tex]T^2[/tex]
[tex]\boxed{\displaystyle g=\frac{4\pi^2l}{T^2}}[/tex]
8-1 1/5
(Simplify your answer. Type a whole number, fraction, or a mixed number.)
orrect:
Answer:
34/5, 6 4/5
Step-by-step explanation:
1 1/5 = 6/5
8-6/5 = 40/5 - 6/5 = 34/5
Is it possible to build a triangle with sides lengths of 3,3 and 9
Answer:
it's not possible to build a triangle with side lengths of 3 3 and 9Step-by-step explanation:
I hope this helps!
Answer:
no its not possible
Step-by-step explanation:
Which inequality is equivalent to -6x>30
Answer:
x > -5
Step-by-step explanation:
[tex] - 6x > 30 \\[tex] 6x < - 30 \\ \frac{ 6x}{ 6} < \frac{- 30}{ 6} \\ x < - 5[/tex]
What is 81% of 134
Thanks
Answer:108.54
Step-by-step explanation:
Answer:
108.54
Step-by-step explanation: turn 81% into a decimal, .81, then multiply by 134.
What is the 10th term in this sequence: 4, 8, 10, 12,...
Answer:24? The numbers are increasing by 2 each time. Starting from 4, 8, 10, 12, 14, 16, 18, 20, 22, 24. Where 24 is the tenth number in the sequence.
Step-by-step explanation:
Figure ABCD is a kite.
10.
Ms. Abbott's 6th grade class has 18 students with brown eyes and 12 students with blue eyes. Ms. Downey's 6th grade class has 15 students with brown eyes and 10 students with blue eyes. What is the ratio of brown eyed students in Ms. Abbott's class compared to the brown eyed students in Mrs. Downey's classroom? Choose all of the correct answers.
a.
3:2
c.
6:5
b.
2:3
d.
18:15
Answer:
6:5
18:15
Step-by-step explanation:
Answer:
a and b
Step-by-step explanation:
7m + 2 - 3m + 6
Simplify this expression.
Answer:
4m+8
Step-by-step explanation:
7m+2-3m+6
combined the 7m and the 3m to get 4m
And combined the 2 and 6 to get 8
then add them to together and get 4m+8
Gianna surveyor students about their lunch time preference. Out of 50 students 20 prefer eating lunch at 11am. 15 prefer eating at 11:50 am, 10 prefer eating eating at 11:30am, 5 have no preference. Based on the information, what is the probability that a student chosen at random has no time preferences?.
Answer:
2.5 percent chance
Step-by-step explanation:
50 total students, only 5 students have no preference.
5% of 50 is 2.5
Find the measure of<1
Given that answer please
Answer:
<BCA = 44.4°
Step-by-step explanation:
Reference angle = <BCA = C
Opposite side length = x = 7 cm
Hypotenuse = y = 10 cm
Applying trigonometric ratio, we would have:
[tex] sin(C) = \frac{7}{10} [/tex]
[tex] C = sin^{-1}(\frac{7}{10}) [/tex]
[tex] C = 44.427004 [/tex]
<BCA = 44.4° (to 3 SF)
Jen makes knitted scarves to sell. At a craft fair, she sells 22 scarves. Each scarf sells for $35.
How much money does Jen make?
Answer:
770
Step-by-step explanation:
just do 22 x 35
X=-4+y and -2x-5y=15
Answer:
x=-5, y=-1
Step-by-step explanation:
Substitute x=-4+y into -2x-5y=15. So we have
-2(-4+y)-5y=15
8-2y-5y=15
-7y=7
y=-1
And x is -4+y so x= -4+(-1)= -5.
Can someone help? Thank you
Sarah rolls a fair dice 96 times.
How many times would Sarah expect to roll a number greater than 2?
Answer:
56
Step-by-step explanation:
Answer:
my 16 inch
Step-by-step explanation:
If a certain number of Grade IV students share 28 or 39 skill books in Mathematics,there are remainders of 4 and 3 books. What is the largest possible number of students?
Answer:
12 studentsStep-by-step explanation:
Below numbers are divisible by the number of students:
28 - 4 = 2439 - 3 = 36Lets find GCF of 24 and 36:
24 = 2*2*2*336 = 2*2*3*3GCF(24,36) = 2*2*3 = 12The largest possible number of students is 12
A store display shows two red shirts, four blue shirts, and
four shirts with red and white stripes. The display also
shows four pairs of blue jeans, two pairs of white pants, and
four pairs of red shorts. What is the probability of randomly
selecting an item with white or red on it?
0 2/5
03/5
0 3/10
1/5
Answer:
The probability is 3/5
Step-by-step explanation:
A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this question, we have that:
There are 2 + 4 + 4 + 4 + 2 + 4 = 20 itens.
Of those, 2 + 4 + 2 + 4 = 12 itens have white or red.
So
12/20 = 3/5
