We define transformations as operators that act on functions by modifying them in some given way. One type of transformation is a translation, which will move the whole graph of the function in some give direction.
For a general function f(x), we will find that the equation for the result of shifting the graph up by 4 units and left by 2 units is:
g(x) = f(x + 2) + 4
----------------------------------
Let's see how to solve this.
We need to start by defining the two most common translations (also known as shifts).
Horizontal translation:
For a given function f(x), an horizontal translation of N units is written as:
g(x) = f(x + N)
where if N is positive, the translation is to the left.
If N is negative, the translation is to the right.
Vertical translation:
For a given function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
Where if N is positive, the translation is upwards.
If N is negative, the translation is downwards.
Here for an unknown function f(x), we want to write the equation that gives a shift up of 4 units and left by 2 units.
The shift up of 4 units is written as:
g(x) = f(x) + 4
The shift of 2 units to the left is written as:
g(x) = f(x + 2)
These two together give:
g(x) = f(x + 2) + 4.
This is the equation we wanted to get.
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Round 47,754,099 to the nearest thousand.
A. 47,750,000
B. 47,754,000
C. 47,755,000
D. 48,000,000
Answer:
es 56,000.
Step-by-step explanation:
Determine the value of x.
A)
[tex]8 \sqrt{3} [/tex]
B) 4/
[tex] \sqrt{3} [/tex]
C) 4
D
[tex] 4\sqrt{3} [/tex]
A coin is flipped 80
times. It lands tails 47
times. What is the Probability
1/2 or 50% because each flip of a coin is independent from the last and a fair coin has an equal probably of landing on either side.
Please help me!!
The formula to find the kinetic energy of an object measured in joules,E, is E=1/2mv2, where m represents the mass of the object in kilograms and v represents the velocity (or speed) of the object in meters per second. What is the equation to find m in terms of E and v ?
Thank you very much!!
Answer:
E=1/2mv2, v/10./17
Step-by-step explanation:
i need brainlest <3Use the given property of equality to complete the statement. Reflexive Property of Equality b + 5 + 12 =
Answer:
b=-17
Step-by-step explanation:
1) add common terms aka 5 and 12, which is 17
b+17=0
2) move seventeen to the other side by doing the opposite opperation of addition which is subtraction
b=-17
what number is the opposite of - 5/12
Answer:
5/12
Step-by-step explanation:
opposite is on the other side of the number line. 5/12 is the answer
12−x2y if x=−7 and y=2
Answer:
the answer is 16 im pretty sure
A line that includes the points (k, 0) and (3,-2) has a slope of -2. What is the value of k?
k =
Submit
9514 1404 393
Answer:
k = 2
Step-by-step explanation:
The slope formula gives the slope between two points:
m = (y2 -y1)/(x2 -x1)
-2 = (-2 -0)/(3 -k)
Multiplying by (3 -k) gives ...
-2(3 -k) = -2
3 -k = 1
k = 3 -1 = 2
The value of k is 2.
The fastest a human has ever run is 27 miles per hour. How many miles per minute did the human run? Explain your answer.
Answer:
0.45 miles per minute
Step-by-step explanation:
Jonathan has 1 3/14 hours to practice guitar. If he spends 1/8 hours on each song, how many songs can he practice
Answer:
Step-by-step explanation:
1 3/14 divided by 1/8
17/14x8
17x4/7
68/7
9 5/7
Anybody? need help asap
Answer:
x = -1
Step-by-step explanation:
5x + 3 -2x = 2(x + 1) >>> Simplify by combining terms
3x + 3 = 2x + 2 >>> Subtract 2x and 3 from both sides
x = -1
7. The area of a square is shown below. Find
the side length of the square.
A = 25 in.2
Answer:
5 in
Step-by-step explanation:
5in*5in = 25in ^2
What is 1,432 rounded to the nearest 100?
Answer:
1400
Step-by-step explanation:
1432 is closer to 1400 than 1500 because it ends in 32 and is below 50 on the number line
Express the distance 4,300,000 meters using scientific notation in meters, and then in millimeters.
Answer: 4.3 × 10^6 meters, and 4.3 × 10^9 millimeters.
Explanation: In order to find the scientific notation of a large number, you want to move the decimal point to the left until you only have one digit to the left of the number, then you can count the spaces you have moved, and this will make the power of 10 that you'll add to the end. This seems a little confusing, but let's look at it through the example.
Step 1) Move the decimal point to the left until there's only one digit to the left of the decimal:
4,300,000 turns into 4.300000
Step 2) Count the number of digits you've moved.
Above, we moved 6 spaces to the left.
Step 3) Add the decimal to the front, and then 10^the number of spaces you moved
4.3 (from step one) × 10^6 (from step two)
= 4.3 × 10^6
It works the same way for the millimeter question, just convert meters into millimeters before you start the problem, and then solve it using the steps above! I hope this helped you :)
The scientific notation in meters and millimeters are
- 4.3 x [tex]10^{6}[/tex] meters
- 4.3 x [tex]10^{9}[/tex] millimeters
What is scientific notation?It is a way of writing very large or very small numbers where a number between 1 and 10 is multiplied by a power of 10.
Example:
310,000,000 can be written in scientific notation as 3.1 ✕ 10^8.
We have,
Distance = 4,300,000 meters
1 meter = 1000 millimeters
So,
4,300,000 meters = 4,300,000,000 millimeters
We can write 4,300,000 in scientific notation as:
= 4.3 x [tex]10^{6}[/tex] meters
We can write 4,300,000,000 millimeters in scientific notation as:
= 4.3 x [tex]10^{9}[/tex] millimeters
Thus the scientific notation in meters and millimeters are
- 4.3 x [tex]10^{6}[/tex] meters
- 4.3 x [tex]10^{9}[/tex] millimeters
Learn more about scientific notations here:
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The length of a rectangle is 2.5 times its width
The perimeter of the rectangle is 84
centimeters. Find the dimensions of the
rectangle.
Answer:
210
Step-by-step explanation:
2.5 times 84 = 210
need help with this please
Answer: plug 32 in for m
Step-by-step explanation:
What is 49.4x20.62 rounded to the hundredths
Answer:
1018.600 I think SORRY IF I'M WRONG!!!
Step-by-step explanation:
Answer:
1018.620 and u r correct my guy
Please help ! Anyone know the answer?
Answer: a
Step-by-step explanation:
can anyone help me with this quickly please :)
To find the y-value that matches with the x-value, we will need to plug in the x-value and simplify the expression.
f(-2) = sqrt(-2 + 2) - 6
f(-2) = sqrt(0) - 6
f(-2) = -6
f(-1) = sqrt( -1 + 2) - 6
f(-1) = sqrt(1) - 6
f(-1) = 1 - 6
f(-1) = -5
f(2) = sqrt(2 + 2) - 6
f(2) = sqrt(4) - 6
f(2) = 2 - 6
f(2) = -4
f(7) = sqrt(7 + 2) - 6
f(7) = sqrt(9) - 6
f(7) = 3 - 6
f(7) = -3
Hope this helps!! :)
Solve using elimination.
8x − 7y = –5
–x + 4y = –15
Answer:
Therefore, the values of "x" and "y" are -1000/312 and -115/39 respectively.
Step-by-step explanation:
★ Solution :-[tex] \sf \leadsto 8x - 7y = -5 - - - (i)[/tex]
[tex] \sf \leadsto -x + 4y = -15 - - - (ii)[/tex]
By first equation,
[tex] \sf \leadsto 8x - 7y = -5[/tex]
[tex] \sf \leadsto 8x = -5 + 7y[/tex]
[tex] \sf \leadsto x = \dfrac{-5 + 7y}{8} [/tex]
Now, we can find the original value of y.
[tex] \sf \leadsto -x + 4y = -15[/tex]
[tex] \sf \leadsto \bigg( \dfrac{-5 + 7y}{8} \bigg) + 4y = -15[/tex]
[tex] \sf \leadsto \dfrac{-5 + 7y}{8} + 4y = -15[/tex]
[tex] \sf \leadsto \dfrac{-5 + 7y + 32y}{8} = -15[/tex]
[tex] \sf \leadsto \dfrac{-5 + 39y}{8} = -15[/tex]
[tex] \sf \leadsto -5 + 39y = -15(8)[/tex]
[tex] \sf \leadsto -5 + 39y = -120[/tex]
[tex] \sf \leadsto 39y = -120 + 5[/tex]
[tex] \sf \leadsto 39y = - 115[/tex]
[tex] \sf \leadsto y = \dfrac{ - 115}{39} [/tex]
Now, we can find the original value of x.
[tex] \sf \leadsto 8x - 7y = -5[/tex]
[tex] \sf \leadsto 8x -7 \bigg( \dfrac{ - 115}{39} \bigg) = -5[/tex]
[tex] \sf \leadsto 8x + \dfrac{805}{39} = -5[/tex]
[tex] \sf \leadsto \dfrac{312x + 805}{39} = -5[/tex]
[tex] \sf \leadsto 312x + 805 = -5(39)[/tex]
[tex] \sf \leadsto 312x + 805 = -195[/tex]
[tex] \sf \leadsto 312x = -195 - 805[/tex]
[tex] \sf \leadsto 312x = -1000[/tex]
[tex] \sf \leadsto x = \dfrac{-1000}{312} [/tex]
[tex]\textsf {\underline{Answer-}}\\[/tex]
Therefore, the values of x and y are -1000/312 and -115/39 respectively.
if a+b=6 and ab=9 find the value of a3+b2
What is the maximum increase in sales that can be sustained assuming no new equity is issued
Answer:
Example 1 is 25%
Example 2 is 3.5%
Example 3 could be $10,464.41 See attached.
Step-by-step explanation:
Example 1
An increase of sales to $9,500 is an increase of:
Sales increase = ($9,500 - 7,600) / $7,600
Sales increase = .25, or 25%
Assuming costs and assets increase proportionally, the pro forma financial statements will look like this:
Pro forma income statement Pro forma balance sheet
Sales $ 9,500.00 Assets $ 23,875.00 Debt $ 7,000.00
Example 2.
Return on equity (ROE) is a measure of financial performance calculated by dividing net income by shareholders' equity. Because shareholders' equity is equal to a company’s assets minus its debt, ROE is considered the return on net assets. ROE is considered a gauge of a corporation's profitability and how efficient it is in generating profits.
Example below given on 2nd example is 60% payout ratio type question with constant debt equity ratio.
Return on equity 34008 / 90400 = 0.37619469
A / S = $ 34,008 / $ 90,400 = 37.6%
L / S = $ 9,040 / $ 90,400 = 10%
Change in Sales or ΔSales = $ a - $ 90.400 = $ b
EFN = (.376 x $ b) - (.10 x $ b ) - ((profit margin x $ a) x (1 - .dividend payout ratio))
Formula EFn = 0 = full subtraction of EFN
Example 3 - Calculation of the EFN:
Total Assets last year = $ 6.5 Million
Total Sales last year = $ 21.0 Million
Total Current Liabilities last year = $ 2.1 Million
Profit Margin = 4% of sales
Forecasted Sales = $ 24.5 Million
Dividend Payout Ratio or d = 60%
A / S = $ 6.5 / $ 21.0 = 31%
L / S = $ 2.1 / $ 21.0 = 10%
Change in Sales or ΔSales = $ 24.5 - $ 21.0 = $ 3.5
EFN = (.31 x $ 3.5) - (.10 x $ 3.5) - ((.04 x $ 24.5) x (1 - .60))
EFN = $ 1.085 - $ .35 - ($ .98 x .40)
EFN = $ .735 - $ .392
EFN = $ .343
9) What 2 numbers have a total of 28 and a difference of 6?
Answer:
Sum: 17 + 11 = 28
Difference: 17 - 11 = 6
Step-by-step explanation:
The sum of x and y is 28. In other words, x plus y equals 28 and can be written as equation A:
x + y = 28
The difference between x and y is 6. In other words, x minus y equals 6 and can be written as equation B:
x - y = 6
Now solve equation B for x to get the revised equation B:
x - y = 6
x = 6 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 28
6 + y + y = 28
6 + 2y = 28
2y = 22
y = 11
Now we know y is 11. Which means that we can substitute y for 11 in equation A and solve for x:
x + y = 28
x + 11 = 28
X = 17
Summary: The sum of two numbers is 28 and their difference is 6. What are the two numbers? Answer: 17 and 11 as proven here:
Sum: 17 + 11 = 28
Difference: 17 - 11 = 6
Answer:
17 +11 = 28
hope this helps
In a trial, an expert witness uses the conservation of momentum to demonstrate which initial velocities would give the final states that occurred in the accident. Can using the conservation of momentum be justified in this case? Yes, because momentum is conserved in all collisions. No, momentum is only conserved in elastic collisions which this is not. No, energy is always conserved, but momentum is only sometimes conserved. Yes, because momentum is conserved in inelastic collisions which all car accidents are.
Answer:
Yes, because momentum is conserved in all inelastic collisions which all car accidents are
Step-by-step explanation:
What is law of conservation of momentum?
It states that In a equilibrium the initial momentum is equal to to the final momentum of the body
Or
[tex]\\ \sf\longmapsto \Delta P=P[/tex]
Answer:
• Yes, because momentum is conserved in all collisions.
Step-by-step explanation:
→ Elastic collision, inelastic collision and perfectly inelastic collision, linear momentum is conserved assuming no external forces acting on the system.
In elastic collision
[tex] \dashrightarrow \: { \tt{m _{1}u _{1} + m _{2} u_{2} = m_{1}v_{1} + m_{2}v_{2}}} \\ [/tex]
In inelastic collision
[tex] \dashrightarrow \: { \tt{m_{1}u_{1} + m_{2}u_{2} = (m_{1} + m_{2})v}}[/tex]
PLEASE HELP WILL MARK BRAINLIEST!!TY!!
Answer:AB = 5/2 and CD = 2/-5, perpendicperpendicular
Step-by-step explanation:
0+5 = 5
2+2=4
1+2=3
8-5=3
Write the equation of a line that
goes through the points (3,7) and
(-3,5).
Answer:
[tex]y = mx + c \\ 7 = 3m + c \\ 5= - 3m + c \\ 2c = 12 \\ c = 6 \\ 7 = 3m + 6 \\ 3m = 1 \\ m = \frac{1}{3} \\ y = \frac{1}{3} x + 6[/tex]
determine the domain and range of the function F= {(2,1),(30,-7),(34,1),(54,0)
Answer:
Domain = 2,30,34,54
Range = 1,-7,1,0
Step-by-step explanation:
Domain = x input
Range = y output
Your function is f(x) = y.
Robert types 152 words per minute. How long will it take Robert to type 2,508
words?
Answer:
16.5 minutes
Step-by-step explanation:
2508/152 = 16.5
Check: 152 x 16.5 = 2508
Find the LCM for 5,9
Answer:
45 :)
Step-by-step explanation:
Evaluate the function for
f(x) = x + 3 and g(x) = x2 − 2.
(f − g)(8t)=
Answer:
f(0)=0
Step-by-step explanation: