Transformations are used to change the position of a function from one point to another. When f(x) is reflected over the y-axis, the new function g is [tex]g(x) = x + 8[/tex]
Given that:
[tex]f(x) = -3+|x - 11|[/tex]
To reflect across the y-axis, we use the following transformation rule:
[tex](x,y) \to (-x,y)[/tex]
So, the new function is:
[tex]g(x) = f(-x)[/tex]
If [tex]f(x) = -3+|x - 11|[/tex], then:
[tex]f(-x) = -3+|-x - 11|[/tex]
Factor out -1
[tex]f(-x) = -3+|-1(x + 11)|[/tex]
Remove absolute sign
[tex]f(-x) = -3+1 \times (x + 11)[/tex]
[tex]f(-x) = -3+x + 11[/tex]
Collect like terms
[tex]f(-x) = x + 11-3[/tex]
[tex]f(-x) = x + 8[/tex]
Hence, the new function is:
[tex]g(x) = x + 8[/tex]
Read more about transformations at:
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Mr. Bearfield deposited $3,500 in a new investment account. -The investment pays 8% interest compounded annually on this account. -Mr. Bearfield did not make any additional deposits or withdrawals. What is the balance of the account at the end of three years?
Answer:
In 3 years, you will have $4,408.99
Step-by-step explanation:
The formula used in the compound interest calculator is A = P(1+r/n)^(nt)
A = the future value of the investment
P = the principal investment amount
r = the interest rate (decimal)
n = the number of times that interest is compounded per period
t = the number of periods the money is invested for
Find the total surface area of this cuboid,
5 cm
4 cm
6 cm
Answer:
148
Step-by-step explanation:
Sa=2(lw+lh+wh)
Sa=2(4*5+4*6+5*6)
148=2(4*5+4*6+5*6)
Answer:
100 cm sq
Step-by-step explanation:
The answer is 100 cm sq because the formula would be:
SA= Ph + 2B
Sa= 10 x 6 + 2 x 20 (5 x 4)
SA= 60 + 40
SA= 100 cm sq
Please make me brainliest!!!
please help .thanks
Answer:
2 and 1/5 is greater than 2.15
Step-by-step explanation:
This is true because 1/5 is equal to .20 which is greater than .15
Answer:
B, >
Step-by-step explanation:
2 1/5
2*5= 10+1= 11
11/5 vs 2.15
2.2 vs 2.15
2.2 > 2.15
Given point (8,0) and slope 2/3, fill in the blanks to put in point slope form. y-____=____(x-___) *
Answer:
3y = 2(x -8)
Step-by-step explanation:
this is the sol I could provide
The correct answer is y-0=2/3•(x-8).
Use the given slope and point to substitute into the point-slope formula y−y1=m(x−x1).
What does (f+g)x mean?
Answer:
(f + g)(x) means f(x) + g(x)
General Formulas and Concepts:
Alg I
Function NotationCombining like termsAlg II
Composite FunctionsStep-by-step explanation:
(f + g)(x) is the number form of "f plus g of x", meaning that we add the functions f and g together respect to x.
Another way to write (f + g)(x) is f(x) + g(x), which is the number form of "f of x plus g of x", still meaning that we are adding the 2 functions together.
what is the proportional realashionship
Answer: "Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality"."
Step-by-step explanation: I got this from a website. Hope it works!!!
Find the values of x and y.
(10x – 4)º
16yº
(18y – 18)°
6(x + 2)°
Answer:
The value of x is 4 and the value of y is 9
Step-by-step explanation:
In the attached pictures we can see that two lines are intersecting with each other and four angles are form. The angles opposite to each other are also called vertical angles.
The opposite pairs of angles are:
(10x-4)° and 6(x+2)°
(18y-18)° and 16y°
When two lines intersect each other, the vertical angles formed are congruent(Can also be called equal in measurement)
So,
[tex]10x-4=6(x+2)\\10x-4 = 6x+12[/tex]
Subtracting 6x from both sides
[tex]10x-4-6x = 6x+12-6x\\4x-4 = 12[/tex]
Adding 4 on both sides
[tex]4x-4+4 = 12+4\\4x = 16[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4} = \frac{16}{4}\\x = 4[/tex]
AND
[tex]18y-18=16y[/tex]
Adding 18 on both sides
[tex]18y-18+18 = 16y+18\\18y = 16y+18[/tex]
Subtracting 16y from both sides
[tex]18y-16y = 16y+18-16y\\2y = 18[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2} = \frac{18}{2}\\y = 9[/tex]
Hence,
The value of x is 4 and the value of y is 9
A regression line has a slope of 2.334. If the mean of the x-coordinates of the data points is 6.607, and the mean of the y-coordinates is 10.738, what is the y-value of the y-intercept of the line to three decimal places?
Answer:
- 4.683
Step-by-step explanation:
Given that:
Slope of regression line = 2.334
Mean of x coordinate = 6.607
Mean of y coordinate = 10.738
Y value of the y intercept of the line :
The value of the intercept can be obtained using the the relation :
Mean of y coordinate - slope(mean of x coordinate)
Ybar - slope(xbar)
10.738 - 2.334(6.607)
= −4.682738
= - 4.683 ( 3 decimal places)
Hence, intercept = - 4.683
Answer:
- 4.683
Step-by-step explanation:
What is the standard deviation of this data? Round your answer to the nearest hundredth of a number?
10, 12, 8, 2
Answer:
3.74
Step-by-step explanation:
Count, N: 4
Sum, Σx: 32
Mean, μ: 8
Variance, σ2: 14
Hope this helped!
Mary made a 48.5% on her math test. Which of the following shows a fraction and a decimal equivalent to 48.5%? 485 A and 0.485 10.000 485 B and 48.5 100 485 С and 4.85 100 485 D and 0.485 1.000
please show me the work I need it right know☹️
B.
you can eliminate A and D because grades are distributed by 100. and c only has 4.85 when the question says she made a 48.5
HELP! will give brainliest!!! The United States released 5.877 billion metric tons of carbon
dioxide into the environment through the burning of fossil fuels in a recent year. If
1 trillion pounds = 0.4536 billion metric tons, how many trillion pounds of carbon
dioxide did the United States release in that year?
Answer:
13.0 trillion pounds of carbon dioxide
Step-by-step explanation:
5.877 ÷ 0.4536 = 12.9563492063
rounded to 1 decimal place =
13.0 trillion pounds of carbon dioxide
The carbon dioxide released by United States is 12.9563 trillion pounds
What is conversion?In math, conversion is the process of changing the value of one form to another for example inches to millimeters, or liters to gallons.
Now it is given that,
Amount of carbon dioxide released by United States = 5.877 billion metric tons
It is also given that,
1 trillion pounds = 0.4536 billion metric tons
So, 1 billion metric tons = (1/0.4536) trillion pounds
Thus, 5.877 billion metric tons = (5.877/0.4536) trillion pounds
⇒ 5.877 billion metric tons = 12.9563 trillion pounds
Thus, the carbon dioxide released by United States is 12.9563 trillion pounds
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Answer to this please?
Answer:
D) 117
Step-by-step explanation:
All angles of a triangle will always add up to 180 degrees. Thus, 22 + 41 = 63, 180 - 63 = 117.
Shawn wanted to rent a mo-ped for the afternoon. The rental fee for a mo-ped was $10 plus $7 for each hour he used the bike. Write an expression that represents the cost for h hours. Then, decide how much Shawn spent if he rented the mo-ped for 3 hours.
Answer:
Total cost= $31
Step-by-step explanation:
Giving the following information:
The rental fee for a mo-ped was $10 plus $7 for each hour he used the bike.
First, we need to structure the total cost formula:
Total cost= 10 + 7h
h= number of hours
Now, for 3 hours:
Total cost= 10 + 7*3
Total cost= $31
At the candy store, Sophie filled a bag with 2\dfrac232 3 2 2, start fraction, 2, divided by, 3, end fraction kilograms of candy. \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction of the weight of the candy was from chocolate covered pretzels.
Answer:
[tex]Chocolate\ Weight = \frac{2}{3}kg[/tex]
Step-by-step explanation:
Given
[tex]Candies =2\frac{2}{3}\ kg[/tex]
[tex]Chocolate = \frac{1}{4}[/tex] of the candies
Required
Determine the weight of the chocolate pretzels ---- This completes your question
To determine the weight, we simply multiply the fraction of chocolates by the total weight of the candies.
i.e.
[tex]Chocolate\ Weight = \frac{1}{4} * 2\frac{2}{3}[/tex]
Convert Fraction
[tex]Chocolate\ Weight = \frac{1}{4} * \frac{8}{3}[/tex]
[tex]Chocolate\ Weight = \frac{1 * 8}{4 * 3}[/tex]
[tex]Chocolate\ Weight = \frac{8}{12}[/tex]
Simplify
[tex]Chocolate\ Weight = \frac{2}{3}kg[/tex]
F(-3,2)G(-3-1)H(-1,-1)I(0,1) rotation by 270 degrees about the origin
Answer:33
Step-by-step explanation:
What is the slope and y-intercept of the
graph shown below?
Answer:
m=1.5 b=4
Step-by-step explanation:
Find the Slope.
(2, 8) and (4, -3)
5)A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service.
Answer: your Answer is $75 dollars.
Step-by-step explanation:
$25 + $50 = $75
Answer:
[tex]C = 50x + 25[/tex]
Step-by-step explanation:
The $50 charge can be interpreted as the slope, as it varies based on the amount of time the service takes. The $25 can be interpreted as the y-intercept, as you'll get charged $25 no matter how long the service takes. Thus, we can plug these values into the slope-intercept form equation.
[tex]y = mx + b\\C = 50x + 25[/tex]
BRAINLY AND POINTS FOR STEP BY STEP
b-4z =a for b
____
5
Answer:
Dividing both sides of 5x = 4 by 5 yields x = 4 _. 5 . The value of x can now be ... tuting −1 for a into the equation b = –a + 3 gives b = −(−1) + 3, or b = 4. ... ___. 82 − (2i)2 . Since i2 = −1, this can be simplified to 24 − 6i − 40i − 10. __.
hope this helps also Brainliest please:)
Answer:
b=7a+4z
Step-by-Step Explanation
I just took the test, this is right, but I'll give you a step-by-step because I want a Brainiest :D
b-4z over 7=a
Multiply both sides by 7
b-4z=7a
Aded 4z to both sides
Your answer is b=7a+4z
Please give me Brainiest!!!!
if a football is thrown upward, its height above the
ground is given by the equation s=-16t^2+Vot+so, where
Vo and so are the initial velocity and intial height of the
Football, respectively, and t is the time in seconds.suppose
the football is thrown from the top of a building that is
192 feet tall, with an initiae speed of 96 feet per second.
a)write the polynomial that gives the height of the Football in terms
of the variable t (time)
b) what is the height of the Football after 2 seconds have
Clapsed? Will the football hit the ground after 2 seconds?
Answer:
a) s = -16[tex]t^{2}[/tex] + 192t + 96
b) Height of the football after 2 seconds is 448 feet.
ii. The football would not hit the ground after 2 seconds.
Step-by-step explanation:
Given:
s = -16[tex]t^{2}[/tex] + [tex]V_{o}[/tex]t + [tex]s_{o}[/tex]
where: s is the height of the football above the ground, t is the time, [tex]V_{o}[/tex] is the initial velocity and [tex]s_{o}[/tex] is the initial height.
The height of the building = [tex]V_{o}[/tex] = 192 feet and the initial speed of the ball = [tex]s_{o}[/tex] = 96 feet per second, then;
s = -16[tex]t^{2}[/tex] + 192t + 96
a) The polynomial is given as:
s = -16[tex]t^{2}[/tex] + 192t + 96
b) The height of the football when t = 2 seconds is;
s = -16(2) + 192(2) + 96
= -32 + 384 + 96
= -32 + 480
s = 448
The height of the football when t = 2 seconds is 448 feet.
ii. The football would not hit the ground after 2 seconds.
HELP!!!!!!!!!!!!!!!!!!!!!
Answer:
56 riders
Step-by-step explanation:
With the proportion given, cross multiply, then divide:
70 × 80 = 56005600 ÷ 100 = 56So, the answer is 56 ridersI hope this helps!
[tex] \:\:\:\:\:\frac{70}{100} = \frac{x}{80} \\ \\ = > \frac{7 \cancel0}{10 \cancel0} = \frac{x}{80} \\ \\ = > x = \frac{7 \times 80}{10} \\ \\ = > x = \frac{7 \times 8 \cancel0}{1 \cancel0} \\ \\ = > x = \green{\boxed{56 \: rides}}[/tex]
A firefighter is standing 33 feet away from a 45 foot tall building. The firefighter looks up and sees that a cat that is stuck on the top of the building and also notices a dog in a second flooor window that is 15 feet above ground. What is the angle of elevation of the cat?
Given :
Distance of firefighter from the building, D = 33 feet.
Height of building, h = 45 feet.
To Find :
The angle of elevation of the cat.
Solution :
Let, angle of elevation is Ф.
We know, tan Ф = h/D
tan Ф = 45/33
Ф = tan⁻¹( 45/33 )
Ф = 53.75°
Therefore, angle of elevation is 53.75° .
Hence, this is the required solution.
Using the periodic table, choose the more reactive nonmetal.
Si or S
Answer:
S
Step-by-step explanation:
S is closer to the top right of the table, which is a generally good rule for determining reactivity of NONMETALS. METAL reactivity increases to the bottom left.
Solve for x: 4 over 5 x + 4 over 3 = 2x x = Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar. (2 points)
Answer:
x = 10/9
Step-by-step explanation:
Solve for x:
(4 x)/5 + 4/3 = 2 x
Put each term in (4 x)/5 + 4/3 over the common denominator 15: (4 x)/5 + 4/3 = (12 x)/15 + 20/15:
(12 x)/15 + 20/15 = 2 x
(12 x)/15 + 20/15 = (12 x + 20)/15:
(12 x + 20)/15 = 2 x
Multiply both sides by 15:
(15 (12 x + 20))/15 = 15×2 x
(15 (12 x + 20))/15 = 15/15×(12 x + 20) = 12 x + 20:
12 x + 20 = 15×2 x
15×2 = 30:
12 x + 20 = 30 x
Subtract 30 x from both sides:
(12 x - 30 x) + 20 = 30 x - 30 x
12 x - 30 x = -18 x:
-18 x + 20 = 30 x - 30 x
30 x - 30 x = 0:
20 - 18 x = 0
Subtract 20 from both sides:
(20 - 20) - 18 x = -20
20 - 20 = 0:
-18 x = -20
Divide both sides of -18 x = -20 by -18:
(-18 x)/(-18) = (-20)/(-18)
(-18)/(-18) = 1:
x = (-20)/(-18)
The gcd of 20 and -18 is 2, so (-20)/(-18) = (-(2×10))/(2 (-9)) = 2/2×(-10)/(-9) = (-10)/(-9):
x = (-10)/(-9)
Multiply numerator and denominator of (-10)/(-9) by -1:
Answer: x = 10/9
4. Rudy is training for a race. On Monday he ran
2 km. On Tuesday he ran 15% farther than on
Monday. If he increases his running distance
by the same percentage each day, on which day
will he first run more than 4 km?
A. Wednesday
B. Thursday
C. Friday
D. Saturday
Answer:
C
Step-by-step explanation:
You add .3 km to the first day (tuesday)
then .6 then next day (wedneday)
next you add .9 on the next day (thursday)
finally you add 1.2 km on Friday
2.3+0.6+0.9+1.2=4 km
please help:) please help:)
Answer:
Your answer is A) =
Step-by-step explanation:
100 - 2(20)
100 - 40 = 60
3(20) = 60
2
y + 4
3
How do I write this in a word phrase
Answer:
To write an expression, we often have to interpret a written phrase. For example, the phrase “ 6 added to some number” can be written as the expression x + 6, where the variable x represents the unknown number.
Step-by-step explanation:
how to simplify this ......
A function is defined by f(x)= x/4. What is f(-8)?
- 2
- -1/2
- 1/2
- 2
Answer:
need this as quick as possible pls
Step-by-step explanation:
Answer:
[tex]f(-8)=-2[/tex]
Step-by-step explanation:
We have the function:
[tex]f(x)=\frac{x}{4}[/tex]
And we want to find f(-8).
So, simply substitute -8 for x. This yields:
[tex]f(-8)=\frac{-8}{2}[/tex]
Divide:
[tex]f(-8)=-2[/tex]
Hence, our answer is -2.
The number of people who attended a concert on Friday was 34 the number of people who attended the same concert on Saturday. A total of 840 people attended the concert on those two days. How many people attended the concert on Saturday?
Answer:
8
the answer is 806
Step-by-step explanation:
840-36=806