Given the function f(x) = (1/4)^x , how will g(x) = (1/4) ^x-3 + 5 be translated
Answers
See
x is decreased by 3 .
and y is increased by 5
So translation is
f(x)=(1/4)^xHence
f(x)=(1/4)^x-3+5So
x will go 3 units right
y will go 5units up
Graph attached
Answer:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]f(x)=\left(\dfrac{1}{4}\right)^x[/tex]
Translated 3 units to the right:
[tex]f(x-3)=\left(\dfrac{1}{4}\right)^{x-3}[/tex]
Translated 5 units up:
[tex]f(x-3)+5=\left(\dfrac{1}{4}\right)^{x-3}+5[/tex]
[tex]\implies g(x)=f(x-3)+5[/tex]
Therefore:
[tex]\textsf{g(x) is a translation of f(x) by }\left(\begin{array}{c}3\\5\\\end{array}\right)[/tex]
Related Questions
A ladder 20 m long rests against a vertical wall so that the foot of the ladder is 9 m from the wall. a Find, correct to the nearest degree, the angle that the ladder makes with the wall. b Find, correct to 1 d.p., the height above the ground at which the upper end of the ladder touches the wall.
Answers
Answer:
(a) 27°
(b) 17.9m
Step-by-step explanation:
According to the attachment
⠀
let AB be the ladder
BC be the distance between the ladder and wall
⠀
(a) We have to find ∠A by trigonometry formula
[tex] \sf \sin A = \frac{perpendicular}{hypotenuse} [/tex]
Here angle A is facing BC so it is perpendicular
and AB is the longest side so it is hypotenuse
[tex] \sf \implies \sin A = \frac{BC}{AB} \\ \\ \\ \sf \implies \sin A = \frac{9}{20} \\ \\ \\ \sf \implies \sin A = 0.45 \\ \\ \\ \sf \implies \sin A = \sin27{ \degree} \\ \\ \\ \sf \purple {A = 27{ \degree}}[/tex]
(b)
AC is the distance from the upper end of the ladder to ground
we will find it by Pythagoras theorem
[tex] \sf {hypotenuse}^{2} = {perpendicular}^{2} + {base}^{2} \\ \\ \\ \sf \implies {AB}^{2} = {BC}^{2} + {AC}^{2} \\ \\ \\ \sf \implies {20}^{2} = {9}^{2} + {AC}^{2} \\ \\ \\ \sf \implies 400 = 81 + {AC}^{2} \\ \\ \\ \sf \implies 400 - 81 = {AC}^{2} \\ \\ \\ \sf \implies 319 = {AC}^{2} \\ \\ \\ \sf \implies \sqrt{319} = AC \\ \\ \\ \sf \blue{\implies 17.86 = AC}[/tex]
Are the following ratios equivalent? 5 cookies: 8 glasses of milk and 7 cookies: 9 glasses of milk.
Answers
Answer:
no
Step-by-step explanation:
Maths question:
5% of 40
20% of 25
Answers
20% of 25 is 5
Enjoy
Answer:
1. 2
2. 5
Step-by-step explanation:
1. write 5% as
[tex] \frac{5}{100} [/tex]
Then,
[tex] \frac{5}{100} \: of \: \: 40 = \frac{5}{100} \times 40[/tex]
Therefore, the answer is 2
If you are using a calculator, simply enter 5 divided by 100 times 40 which will give you 2 as the answer.
2. Write 20% as 20/100
[tex] \frac{20}{100} \: of \: 25 = \frac{20}{100} \times 25[/tex]
Therefore, the answer is 5
If you are using a calculator, simply enter 20 divided by 100 times 25 which will give you 5 as the answer.
simplify. 5ab/15a+10a²
Answers
For a scavenger hunt, Jim's mom distributed a bag of 520 jelly beans evenly into 20 plastic containers and hid them around theyard. If, after the hunt, Jim has a total of 182 jelly beans, then how many of the plastic containers did he find?
A. 338
B. 140
C. 9
D. 7
Answers
Explanation:
First divide 520 and 20 to get the answer of 26.
Then, divide 182 and 26 to get 7.
I hope this helped!
find x.
An image of two parallel lines cut by a transversal. 8x-1 on top line and 3x-9 on bottom line . how do i get x
Answers
To solve this problem, we have to understand that the parallel lines cut will form two alternate angles which are equal to each other. The value of x is equal to -8/5
Alternate AnglesIn the given question, we have two alternate angles fixed at opposite end to each other.
Data;
8x - 13x - 9Since we've established that alternate angles are equal to each other, we can proceed to equate the two angles and solve for x
[tex]8x -1 = 3x - 9\\8x - 3x = - 9 + 1\\5x = - 8\\x =-\frac{-8}{5}[/tex]
The value of x is equal to -8/5
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What is the volume of this box? Cardboard box A. 15 cm3 B. 96 cm3 C. 120 cm3 D. 148 cm3
Answers
what is the anwer pls
Answers
Answer:
180 square yards
Step-by-step explanation:
there are 3 shapes that create the total area :
a large right-angled triangle to the right. its baseline is 16 yd. the left side is a bit complicated, we get to it.
a small middle rectangle with length 6 yd. it's width is 3 yd.
is area is 6×3 = 18 yd²
a large rectangle at the bottom left with length 11 yd and width 6yd.
its area is 11×6 = 66 yd²
now, how long is the left side of the triangle ? we need it as the height of the triangle to get the area
baseline × height / 2
we see that a part of the left side is 8 yd.
then the width of the middle rectangle is also a part of that left side : 3 yd.
and then we notice that the triangle goes a little bit below the top length side of the large rectangle. how much ? well the actual width of the large rectangle is 6 yd, but the side under the triangle says only 5 yd. so, the missing piece is 6-5 = 1 yd.
so, the full left side is
8 + 3 + 1 = 12 yd
and the area of the triangle is
16×12 / 2 = 16×6 = 96 yd²
so, the total area of the figure is
18 + 66 + 96 = 180 yd²
please help will mark Brainliest!!
Answers
Answer:
number 2
Step-by-step explanation:
im not that sure but i think it's that one
A local couple is deciding to invest their lifetime savings of $68,000.00 into a Fijian business. They are considering two businesses. Business A, in the food and beverage (FNB) industry, provides an annual cash income of about $8,000 for 10 years. Business B, in the clothing and textiles industry, provides an annual cash income of $7,500 for 11 years commensurate with their level of investment. If the couple on the other hand decide to leave their lifetime savings into a fixed deposit at their current bank, which is a large international bank, they would get about 1.5 percent per annum. The economy is currently in the expansionary phase of the business cycle. However, it is forecasted that a severe global downturn is expected in 1 years’ time and the resulting recession will last about 1 year thereafter. During the recession, it is expected that cash flows in the FNB industry will fall by 40 percent per annum. In the clothing and textiles industry, it is expected that cash flows will fall by about 35 percent per annum. The general elections are expected to be held in 4 years’ time. Policy changes around taxation could be expected but at present are uncertain.
Required:
i. Calculate the present value of the cash inflows of both alternatives and compare it against the investment required. Clearly show which investment is preferred
ii. Identify and discuss the key risks faced by the couple in each scenario
iii. Against the type of risks involved, please discuss which investment would you choose
Answers
The best investment option for this couple is the Food and Beverage industry because it is the one that gives them the highest profits within 11 years compared to the other alternatives.
How to calculate the profit of the couple in each investment alternative?To calculate the pair's gain in each alternative we must perform the following mathematical operations:
Food and beverage (FNB) industry
$8,000 × 10 years = $80,000$8,000 ÷ 100 = $80$80 × 40% = $3,200$80,000 - $3,200 = $76,800$76,800 + $8,000 = $84,800Clothing and textiles industry
$7,500 × 11 years = $82,500$7,500 ÷ 100 = $75$75 × 35% = $2,625$82,500 - $2,625 = $79,875Current Bank
$68,000 ÷ 100 = $680$680 × 1.5% = $1,020$1,020 × 11 = $11,200$68,000 + $11,200 = $79,220Based on the foregoing, it can be inferred that the best investment option for the couple is the Food and Beverage (FNB) industry because it is the one that leaves the highest profits despite the decrease in profits during the second year.
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what is the answer??
Answers
Answer:
76 unit^2
Step-by-step explanation:
Total area: (0.5 * base * height) +( length * breadth ) + (0.5 * base * height)
= (0.5 * 8 * 2) + ( 7*8) +( 0.5 * 8 * 3) = 8 + 56 + 12 = 76
A cylinder has a radius of 11 cm. The height
is 9 cm. What is the volume of the cylinder?
Answers
Answer:
621.72
Step-by-step explanation:
The explanation is that the formula is V=2HπR
Multiply all of that and you get your answer of 621.72
A plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labor. If the total bill was $190, how many hours did the plumber spend fixing the sink?
Answers
The plumber spend 3 hours to fixing the sink if the plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labour.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the plumber spend x hours to fixing the sink.
Then we can frame a linear equation in one variable:
55 + 45x = 190
45x = 135
x = 3 hours
Thus, the plumber spend 3 hours to fixing the sink if the plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labour.
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A bag contains 8 red marbles, 4 white marbles, and 5 blue marbles. You draw one marble at random. Find Pared and blue) (1 point) 40 o 17 00 o SIAMO 0
Answers
Answer:
5/(8+4+5) = 5/17
Step-by-step explanation:
total has (8 red +4 white+5 blue）= 17
we looking for blue , so is 5.
5/17
Audrey is running for student council president. she estmates her chances of winning to be 1/5 chance. Which likelihood describes aubrey's estimated chances of winning?
A. Impossible
B. Unlikely
C. likely
D. Certain
Answers
Answer:
B. Unlikely
Step-by-step explanation:
Generally speaking, a probability of 0.11 to 0.40 is unlikely. 1/5 is 0.2, which falls in this range.
Which equation says that the area of the picture
itself is 700 in ²?
Answers
Answer:
See below
Step-by-step explanation:
(36 - 2x) * (17-2x) = 700 I think, given the info
4x^2 - 106x + 612 = 700 expanded....
Translate to an equation and solve the following. The quotient of k and 22 is -66. What is k
Answers
Answer:
Below.
Step-by-step explanation:
k / 22 = -66
k = 22*-66
= -1452.
covert this rational number to its decimal form and round to the nearest thousandth. 7/9
Answers
Answer:
0.778 to the nearest thousandth.
Step-by-step explanation:
Dividing 7 by 9:
9) 7.000000
0.7777777 .... <-- quotient
So it is 0.778 to the nearest thousandth.
What are the coordinates of the focus of the parabola?
y=−0.25x2+6
Answers
simply an surds
√75+ √48 -2√675
Answers
The simplification of √75+ √48 -2√675 is -21√3.
What is a surd?Surds are irrational numbers.
To simplify the surd in the question above, we use the addition and subtraction of surds.
Addition and subtraction of surdsTwo or more surds can be added or subtracted if they are in the same basic form.
E.g
a√b+c√b = (a+c)√ba√b-c√b = (a-c)√bUsing the above example,
Given:
√75+√48-2√675Express the surds to the same basic form
5√3+4√3-(2×15)√35√3+4√3-30√39√3-30√3 = -21√3Hence, the simplification of √75+ √48 -2√675 is -21√3.
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A quarterback is standing on the football field preparing to throw a pass. His receiver is standing 20 yards down the field and 15 yards to the quarterback’s left. The quarterback throws the ball at a velocity of 60 mph towards the receiver at an upward angle of 30° (see the following figure). Write the initial velocity vector of the ball ⃑ , in component form.
Answers
Answer:
I did the work and uploaded the answer as a picture for you
I hope it was helpful!!
Step-by-step explanation:
Q) Rewrite these newspaper headline in PERCENTAGE?
1.There was a one in two chance that the goldfish would swin to left.
Answers
Answer:
There was a 50% chance that the goldfish would swim to the left
Step-by-step explanation:
Percentage means "amount in one hundred".
[tex]\textsf{one in two}=\sf \dfrac{1}{2}=\sf \dfrac{1\times 50}{2 \times 50}=\dfrac{50}{100}=50\%[/tex]
Newspaper headline:
There was a 50% chance that the goldfish would swim to the left.
What is the length of a side of an equilateral triangle inscribed in a circle with a radius of 10 cm?
Answers
Answer:
a = √3 * r
a = √3 * 10
a = 10√3 cm
Step-by-step explanation:
Linda asked the students of her class their hockey scores and recorded the scores in the table shown below:
Hockey Scores
Score Number of Students
0 2
1 1
2 3
3 6
4 2
5 3
6 2
Based on the table, what is the mean hockey score?
2.7
2.9
3.2
5.2
Answers
Answer:
C) 3.2
Step-by-step explanation:
[tex]\text{Mean}=\frac{2(0)+1(1)+3(2)+6(3)+2(4)+3(5)+2(6)}{19}\approx3.2[/tex]
Answer:
2.7
Step-by-step explanation:
the hockey score is 2.7
write two equations that when graphed look like this *see image*. please help its due soon and i will give ya 75 points for answering CORRECTLY thanks, 5 stars, and brainlist. thank
Answers
The graph is showing the equation of circle x²+y²=4
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.
The equation will be as follows:-
x²+y²=4
Hence the graph is showing the equation of circle x²+y²=4
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Which is in slope intercept form? Any fractions must be in simplest form.
A. 4y = -6x + 8
B. y = -6/4x+8/4
C. y = -3/2x+2
D. 6x + 4y = 8
Answers
Answer:
B and C are both in slope-intercept-form.
Step-by-step explanation:
Slope Intercept Form is --> y = mx + b, where m is the slope, and b is the y-intercept.
Both B and C have a slope (-6/4 for B, -3/2 for C) and both have a y-intercept (8/4 or 2).
I hope this helps. Please mark me brainliest!
PLEASE HELP?! IM SO CONFUSED!!
Answers
Answer:
C.
Step-by-step explanation:
-3 7/8 rounds down to -4
4.63 rounds up to 5
-4 x 6 + 5
-24 + 5
-19
her answer (-19.14) also rounds to -19
So yes, it is reasonable and the correct response is C.
x²+8x-16 by factorising method
what is the ans pls I need it fast ASAP
Answers
Answer:
this cannot be factored since nothing shares factorable groups/values
Step-by-step explanation:
hope this helps:)
please help asap giving brainiest and lots of points! this is an easy math/ engineering question if you dont know theres online calculators just pls help!
The initial velocity of a projectile is 57 m/sec, and the firing angle is 22°. Calculate the horizontal distance.
a 230 meters
b 330 meters
c 430 meters
d 130 meters
Answers
Answer:
a 230 metera 230 metersa 230 metersa 230 metersa 230 metersa 230 meters
Can anyone solve number 20?
Answers
Answer:
X=80
Step-by-step explanation:
Angle OAB=50(Properties of isosceles traingle)
X+50+50=180(sum of the interior angles of the traingle)
X=180-100
X=80