The parent function, f(x) = 5^x, has been vertically compressed by a factor of one-half, shifted to the left three units and down two unlts.
Choose the correct function to represent the transformation.
Answers
Answer: Choice C
[tex]\displaystyle g(x) = \left(\frac{1}{2}\right)5^{x+3}-2[/tex]
=====================================================
Explanation:
The 1/2 out front handles the vertical compression by 1/2. For example, if two points are vertically spaced by 10 units, then their new vertical distance is now (1/2)*10 = 5 units.
The x+3 in the exponent means "shift 3 units to the left". Effectively what's going on is that the old input x is now x+3, ie 3 units larger than before. This shifts the xy axis itself 3 units to the right. If we held the curve fixed in place while the xy axis moved like this, then it gives the illusion the curve is moving 3 units to the left.
Then finally the -2 at the very end shifts the curve down 2 units. This is because whatever the y coordinate is, we subtract 2 from it to do this vertical shifting. For example, the point (0,62.5) shifts 2 units down to (0,60.5)
Related Questions
An experimental plane just after takeoff climbs with a speed of 500 km/h at an angle of 37 degrees with the horizontal. A) At what rate is the plane gaining altitude? (Hint, the vertical component of velocity is the rate that the plane is gaining altitude). B). What is the horizontal component of velocity for the plane?.
Answers
The rate is the plane gaining altitude (y) is 300 m/sec and The horizontal component (x) of velocity for the plane is 400 m/sec.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
An experimental plane just after takeoff climbs with a speed of 500 km/h at an angle of 37 degrees with the horizontal.
A. The rate is the plane gaining altitude (y) will be
[tex]\rm y = v * sin \theta\\\\y = 500 *sin 37\\\\y = 300 \ m/sec[/tex]
The rate is the plane gaining altitude (y) is 300 m/sec
B. The horizontal component (x) of velocity for the plane will be
[tex]\rm x = v * cos \theta\\\\x= 500 *cos 37\\\\x = 400 \ m/sec[/tex]
The horizontal component (x) of velocity for the plane is 400 m/sec.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
Which sequence is geometric and which is arithmetic?
Answers
The table on the left is arithmetic
This is because each term is increasing by the same amount (2) each time.
3+2 = 55+2 = 77+2 = 99+2 = 11--------------------------------------------
The table on the right is geometric
Why? Because this time we are multiplying each term by the same value (2) to get the next term.
3*2 = 66*2 = 1212*2 = 2424*2 = 48Both involve the number 2, but the first table uses addition while the second table uses multiplication.
1) Arithmetic
~3,5,7
common difference of 2
2)Geometric
~3,6,12
each term is found by multiplying the previous one by a fixed number
Hopefully this helped- have a good day)
What is the reciprocal of -3?
Answers
Hi!
I can help you with joy!
How to Find the Reciprocal of a Number?
[tex]\star\bigstar[/tex] Simply flop the number over.
Example: Suppose we need to find the reciprocal of 2.
We flop it over and get
[tex]\displaystyle\frac{1}{2}[/tex]
Thus, the reciprocal of -3 is
[tex]\displaystyle-\frac{1}{3}[/tex]
Hope it helps!
Enjoy your day! :)
[tex]\bf{-MistySparkles^**^*[/tex]
Solve for x and y!
Please show your work! To get brainliest!
Answers
As per questions:-
Image 1:-
[tex]x = 15 \sqrt{3} \\ y = 30[/tex]
Image 2:-
[tex]x = 16 \\ y = 8[/tex]
Image 3:-
[tex]x = 8 \\ y = 4[/tex]
(Also check the attached 3 images for explanation.
If using Brainly app, please swipe the images to the right to see the remaining images.)
A house was bought 20 years ago for $160,000. Due to inflation, its value has increased about 7% each year. Write a function that models the value of the home over time. What is the house worth today?
Answers
As a result of inflation, the worth of the house today is $619,149.51.
What is inflation?Inflation is the persistent rise in the general price levels. As a result of inflation, the value of the house would increase overtime.
What is the worth of the house?The formula for calculating future value:
FV = P (1 + r)^n
Where:
FV = Future value
P = Present value
R = interest rate
N = number of years
$160,000x (1.07)^20 = $619,149.51
To learn more about future value, please check: https://brainly.com/question/18760477
PLEASE HELP ASAP!! the slope of a line is -2. Two points on the line are (eight, a) and (2, 4). what is the value of a?
Answers
Answer:
a=4
Step-by-step explanation:
What equals 12 using 2 2 2 2
Answers
Answer:
The equation can't use any number that isn't 2 and the answer can only have 4 twos. They have to have a combination of addition, subtraction, multiplication, and division. Not all of them have to be used though.
Step-by-step explanation:
Name all the factors of 12
Answers
Answer:
1,2,3,4,6,12
Step-by-step explanation:
Answer:
1,2,3,4,6,12
Step-by-step explanation:
1x12=12
2x6=12
3x4=12
4x3=12
6x2=12
12x1=12
What is the y-intercept
in this equation?
y = mx + b
Answers
Answer/Step-by-step explanation:
In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line.
Brainliest?!
Answer:
b
Step-by-step explanation:
remember that m is the slope and b is the y intercept.
y is your output value and x is your input.
What DIY tools do you use in math-riddle-and no protractors is not the word.
Answers
Answer:
Step-by-step explanation:
how the heck are we supposed to know this?????
Answer:
You use multiplyers
I really need helpppp! Can someone please help me out with this??? ASAP (:
Answers
Answer:
(x,y) (-6,2)
Step-by-step explanation:
3x+11y =4
-2x-6y=0
3x+11y = 4
x= -3y ( add this for x)
3(-3y) +11y =4
-9 +11y =4
2y = 4
y = 2
slove for x now
x =3x2
x = -6
answer
(x,y)(-6,2)
The value of a machine depreciated each year by 10%of its value at the beginning of that year .If the value of a new machine is GHC 2500,find its value at the end of the third year.
Answers
Answer:
Heyy
Step-by-step explanation:
Lets Price of article is 100
Dep value after 1 year =100−
100
100×10
= 90
Dep. value after 2 year =90−
100
90×10
=81
Dep. value after 3 years =81−
100
81×15
=68.85
Total Dep. =100−68.85 = 31.15%
What mixed number has the sum of 3
Answers
Answer:
1 1/2
Step-by-step explanation:
1+1= 2.
1/2+1/2= 1.
So add those up and you get 3. Please mark me brainliest?
CAN SOMEONE PLEASE HELP ME!
Answers
Answer:
A) 20 represents the amount of money saved in one month or amount saved per month. This is the slope or rate of change of the function.
B) 50 represents the amount of money already present in the account when she starts saving. This is the y-intercept of the function.
C) It will take 5 weeks for her to save $150
Step-by-step explanation:
A) 20 represents the amount of money saved in one month or amount saved per month. This is the slope or rate of change of the function.
B) 50 represents the amount of money already present in the account when she starts saving. This is the y-intercept of the function.
C) The time to reach $150
150 = 20(w) + 50
20(w) = 150 - 50
20w = 100
w = 100/20
w = 5
It will take 5 weeks
Tom is making a cover for a box that is 4.5 feet long and 23 inches wide. what will be the area of a cover in square inches
Answers
Answer:
154in²
Step-by-step explanation:
4.5 ft = 54in
2(54 + 23) = 154in²
Find the value of 2x+5
x=4
y=3
Answers
You are ordering pizzas. The pizza cost $18. The sales tax is 6%, and you give a 15% tip. What is the total?
Answers
Answer:
$21.94
Step-by-step explanation:
I'm not sure how many pizzas were ordered, but let's say you just got one large pizza that was $18.
First, the sales tax - 6%
$18 + 6% = $19.08
Then you give a 15% tip.
$19.08 + 15% = $21.94
If ⅙ of a roll of wallpaper covers ¼ of the wall. How many rolls of paper are needed to cover 4 walls?
Answers
Answer:
if 1/6 of a roll of paper covers 1/4 of a wall, this means that we will need 4/6 of a roll to cover a whole wall, now the question is asking how many rolls will we need to cover 4 walls, we already know that it takes 4/6 to fill one wall so if we add 4/6+4/6+4/6+4/6 we will get 16/6 or 2 4/6
we will need 16/6 or 2 4/6 of rolls of paper to cover 4 walls
9x9x9x9x9 divided by 3
Answers
Answer:
19683
Step-by-step explanation:
9x9x9x9x9 ÷ 3
59049 ÷ 3
19683
Y'all help me pls Plsssssss
Answers
Answer:
A. 1.06
B. $6,784
Step-by-step explanation:
I = A - P = $384.00
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 6%/100 = 0.06 per year.
Solving our equation:
A = 6400(1 + (0.06 × 1)) = 6784
A = $6,784.00
The total amount accrued, principal plus interest, from simple interest on a principal of $6,400.00 at a rate of 6% per year for 1 year is $6,784.00.
Score for Question 1: of 3 points) • Marcos can seal 5 envelopes every minute. Jerry can seal 7 envelopes every minute. They both seal envelopes for 1 hour nonstop. How many more envelopes does Jerry seal than Marcos? Show your work.
Answers
Answer: 120
Step-by-step explanation: Jerry Would Seal 420 In 1 Hour, and Marco's would seal 300 in 1 hour, so Jerry sealed 120 more than Marco's.
Answer:
The answer is 120
Step-by-step explanation:
which of the following can be used to appropriately measure the weight of a car
Answers
Ton is the answer.
Hope it helps!
You spend 15 on a meal including tax and want to leave a tip that is 20% of the 15 what is the Total cost with the tip
Answers
Answer:
$18.00
Step-by-step explanation:
If the meal is $15.00, 20% of that meal's cost would be $3.00.
$15.00 * .20 = $3.00
Adding the tip to the meal's cost will give you a total cost of $18.00.
~~~~~~~~~~~~~~~~~~~~~~~
Let me know if you have any more questions! Spread the Love.
2
Select the correct answer from each drop-down menu.
Zahid started the construction of an equilateral triangle inscribed in a circle. Which segments need to be drawn to create the triangle?
o.
To finish his construction, Zahid needs to draw segments DF,V, and
Answers
The joining of each three, two penultimate points on the circumference
of the circle, without intersection gives an equilateral triangle.
Response:
The segments that Zahid needs to draw are; DF, BF, and BDHow can the equilateral triangle be constructed from the given construction on the circle?The assumption can be taken that, the steps used to construct the
equilateral triangle inscribed in the circle by marking along the
circumference of the circle at 6 points using the radial length.
Therefore;
The lengths of the chords formed by joining a marked points to another point such that one marked point is between the two are equal.
Which gives;
The length of the chord, DF = The length of the chord, BF = The length of the chord, BD
Given that the joining DF, BF and BD forms a triangle, and DF = BF = BD, we have;
ΔBDF is an equilateral triangle, therefore;
To finish his construction, Zahid needs to draw segments DF;
BF, and BDLearn more about geometric construction here:
https://brainly.com/question/13160630
Raul works at a movie theatre. The function f(x) represents the amount of money in dollars Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. F(x) = 3x2 16 g(x) = the square root of five times x cubed Find f(g(x)). F of g of x equals the square root of the quantity 15 times x to the fifth power plus 16 dollars over hour f of g of x equals the square root of the quantity 15 times x to the fifth power plus 16 dollars over hour f(g(x)) = 15x3 16 dollars over hour f(g(x)) = 15x3 16 tickets over hour.
Answers
Answer:
f(g(x)) = 15x3 + 16 dollars over hour
Step-by-step explanation:
I just took the exam and got it right for this problem
Raul works at a movie theatre. The function f(x) represents the amount of money in dollars Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works.
f(x) = 3x^2 + 16
g(x) = the square root of five times x cubed
Find f(g(x)).
A triangle has vertices at (−2, −2), (−2, −5), and (−4, −5). The triangle is translated 2 units to the right and rotated 90° clockwise about the origin. What are the coordinates of its image?
( , ), ( , ), ( , ) → ( , ), ( , ), ( , ),
Answers
Step-by-step explanation:
translated (shifted) 2 units to the right (positive x direction) creates the points
(-2 + 2, -2) = (0, -2)
(-2 + 2, -5) = (0, -5)
(-4 + 2, -5) = (-2, -5)
and now we rotate these points 90° clockwise around the origin.
that means a positive x turns into a negative y, a negative y into a negative x, a negative x into a positive y, and a positive y into a positive x.
and a 0 just trades places.
therefore,
(0, -2) becomes (-2, 0)
(0, -5) becomes (-5, 0)
(-2, -5) becomes (-5, 2)
so, overall
(-2, -2) becomes (-2, 0)
(-2, -5) becomes (-5, 0)
(-4, -5) becomes (-5, 2)
Which expression represents a negative number? pls awnser fast.
Answers
Answer:
YELLOW
Step-by-step explanation:
Just always keep this tip in mind:
A negative times a positive is a negative, and a negative times another negative cancels out to become a positive.
If there is an odd number of negatives multiplied together, the outcome will always be negative.
You select a card from a deck that contains 25 red cards, 12 blue cards, 8 yellow cards, and 5 red cards. What is the probability of drawing a red card?
Answers
Answer: 3/14!
Your welcome!
Step-by-step explanation: The probability P is actually formulated as "the successful outcomes S" over "the total number of possible outcomes T," that is P = S/T You are expecting to draw a blue card. Therefore the probability will beP (one blue card) = 6/28 = 3/14!
A triangle has angle measures that are related as follows:
• The largest angle is eight times the smallest angle.
• The middle angle is triple the smallest angle..
a) write an equation to model the relationship
b) solve the equation and then determine the measure of each angle. Sketch the triangle and label the angle measures.
Answers
Answer:
a) a +8a +3a = 180°
b) 15°, 45°, 120°
c) see attached
Step-by-step explanation:
a)Let 'a' represent the measure of the smallest angle. The largest angle is 8a, and the middle angle is 3a. The sum of angles, as always, is 180°.
a +8a +3a = 180° . . . . . . equation modeling the relationship
__
b)12a = 180° . . . . . . collect terms
a = 15° . . . . . . . divide by 12
3a = 3×15° = 45°
8a = 8×15° = 120°
The angle measures are 15°, 45°, and 120°.
__
c)see attached. We have arbitrarily let the shortest side be 10 units.
If three times a number is increased by 24, the result is 16 less than seven times the same number. Find the number.
Answers
Answer:
10
Step-by-step explanation:
let x = unknown number
three times x is increased by 24
so 3x + 24
this is equal to 16 less than 7 times x
so 3x + 24 = 7x - 16
we now solve for x
3x + 24 = 7x - 16
add 16 to both sides
3x + 24 + 16 = 7x - 16 + 16
3x + 40 = 7x
subtract 3x from both sides
3x - 3x + 40 = 7x - 3x
40 = 4x
divide both sides by 4
40/4 = 10
4x / 4 =x
x=10
the unknown number is 10