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:
https://brainly.com/question/12865301
find the value of x that makes m|n
Answer:
x = 60°
Step-by-step explanation:
Two parallel lines will have the same angle if another line intersects them. That means 2x+15° = 135°.
2x = 120°
x = 60°
Answer:
opposite number of -18
Chandler wants to raise 200$ to buy a new gaming system. He already has 80$ and plans to save 40$ a week. How many weeks will it take chandler to raise enough money to buy his gaming system?
Answer:
3 weeksStep-by-step explanation:
Step one:
given data
expected amount =$200
cash already at hand=$80
savings per week=$40
let the number of weeks be x
Step two:
the linear function for the situation is the same as the equation of a straight line
y=mx+c------1
200=4x+80
solve for x
200-80=40x
120=40x
divide both sides by 4
x=120/40
x= 3 weeks
Chandler will save for 3 weeks
Pls help it's due tonight
Answer:
6.25 colonies of bacteria per +pH change from 7 to 9
Step-by-step explanation:
It seems to go from 57.5 to 70 or maybe 57 or 58
Either way I will go with my guess of 57.5
Rate of Change= (70-57.5)/(9-7)=(12.5)/(2)=6.25 rate of change for colonies of bacteria per positive pH change from 7 to 9
Betty bought 3 packages of chocolate cupcakes and 7 packages of vanilla cupcakes. Each package contains 24 cupcakes. Which equation is NOT a way to find c, the number of cupcakes Betty bought in all?
Answer:
The equation to find the number did cupcakes bought in all =
= 3c + 7c
= c(3 + 7)
The total number Betty bought in all = 240 cupcakes.
Step-by-step explanation:
Let the amount of cupcakes in a package be represented by c
Betty bought 3 packages of chocolate cupcakes and 7 packages of vanilla cupcakes.
The equation to find the number did cupcakes bought in all =
3 × c + 7 × c
= 3c + 7c
= c(3 + 7)
Each package contains 24 cupcakes
The total number = 3(24) + 7(24)
= 240 cupcakes.
Solve the equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.
x = -3 and 1
x = -2
No real roots.
x = 3 and -1
Answer:
No real roots.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Algebra II
Imaginary Roots: √-1 = iStep-by-step explanation:
Step 1: Define
-3x² + 2x = 1
Step 2: Rewrite in Standard Form
Subtract 1 on both sides: -3x² + 2x - 1 = 0Step 3: Define
a = -3
b = 2
c = -1
Step 4: Find roots
Substitute in variables: [tex]x=\frac{-2\pm\sqrt{2^2-4(-3)(-1)} }{2(-3)}[/tex]Exponents: [tex]x=\frac{-2\pm\sqrt{4-4(-3)(-1)} }{2(-3)}[/tex]Multiply: [tex]x=\frac{-2\pm\sqrt{4-12} }{-6}[/tex]Subtract: [tex]x=\frac{-2\pm\sqrt{-8} }{-6}[/tex]Here we see that we cannot take the square root of a negative number. We will get no real roots and only imaginary ones.
Find the surface area of the prism
Answer:
the answer is 29
Step-by-step explanation:
A newspaper is rolled into a cylindrical shape of approximate diameter 4cm It is wrapped for posting with a strip of paper which goes about 2 1/2 times round the newspaper Use the value 3 for π to find the approximate length of the wrapping paper. And 2. Calculate the total surface area of a solid cone of slant hight 10cm and base diameter 10 cm.Use the value 3.14 for π
Answer:
30 cm
[tex]863.5\ \text{cm}^2[/tex]
Step-by-step explanation:
d = Diameter of cylinder = 4 cm
n = Number of times the strip of paper is turned = [tex]2\dfrac{1}{2}=2.5[/tex]
Diameter of the cylinder will be approximately equal to the diameter of the paper wound. Length of one turn will be circumference of the paper
Circumference of the paper
[tex]c=\pi d\\\Rightarrow c=3\times 4\\\Rightarrow c=12\ \text{cm}[/tex]
Total length of the paper will be the number of turns multiplied by the length of one turn
[tex]l=nc\\\Rightarrow l=2.5\times 12\\\Rightarrow l=30\ \text{cm}[/tex]
Length of the strip of paper is 30 cm.
2.
l = Slant height = 10 cm
d = Base diameter = 10 cm
r = Radius of base = [tex]r=\dfrac{d}{2}=\dfrac{10}{2}=5\ \text{cm}[/tex]
Total surface area of cone is given by
[tex]S=\pi r^2+\pi rl\\\Rightarrow S=\pi r(r+rl)\\\Rightarrow S=3.14\times 5(5+5\times10)\\\Rightarrow S=863.5\ \text{cm}^2[/tex]
The total surface area of cone is [tex]863.5\ \text{cm}^2[/tex].
Create a 5th degree trinomial that has a constant term of 3.
Answer:
[tex]2x^5+3x^2+3[/tex] is a trinomial having with:
three terms degree 5 and The constant term '3'Step-by-step explanation:
Considering the trinomial
[tex]2x^5+3x^2+3[/tex]
Any polynomial with 3 terms is a trinomial, so it is a trinomial.It is clear that '5' is the highest power of the 'x' variable. so, the polynomial has a degree of 5.
'3' is the constant term. The reason is that any term with no variable is called a 'constant' term. So, '3' is the constant term.
Therefore, [tex]2x^5+3x^2+3[/tex] is a trinomial having with:
three terms degree 5 and The constant term '3'2. Which system of inequalities are represented by the graph below:
a) y 2x + 4
y<-x + 4
b) y> 2x + 4
y <-X + 4
c) Y S-2x + 4
y>X-2
d) y 2x + 4
YS-X+4
tem of equations have?
Answer:
12
Step-by-step explanation:
Use the slope-intercept form y=mx+b to find the slope m and y-intercept b
.
Slope: 12
y-intercept: (0,−2)
question in the picture!!
looking for the answer of 1) , 2) and 3)
show your work using numbers!!
Answer:
1. 24%
2. 30%
3. 30%
Step-by-step explanation:
1. 100%/25= 4% 4%*6=24%
2. 100%/50= 2% 2%*15=30%
3. 100%/40=2.5% 2.5%*12= 30%
3x-2(x+5)=14 then x
Answer:
x = 24
Step-by-step explanation:
3x-2(x-5)=14
remove the parentheses using distributive property
3x-2x-10=14
collect like terms
x-10=14
move constant to the right side and change the sign
x=14+10
calculate ( add the numbers together)
x = 24
Jade's car used 2 gallons to travel 46 miles. How many gallons of gas would she need to travel 207 miles?
Answer:
9 gallons
Step-by-step explanation:
2/46 = 0.04347826086 gallon per mile
0.04347826086 x 207 miles =
9 gallons
likewise 133 degree is equal to 87 degree in the second at what temperature will both thermometer read the same
Here's your answer..........
Can someone please explain how to find the answer? My old teacher didn’t do it this way and I’m lost :/
Answer:
the triangle means "change in". so triangle x means the change in the x values and triangle y means change in y values so yeah mental calculate the difference
Can h help with this?
OMGGG CAN YALL ANSWER THIS !
In a newspaper, it was reported that the number of yearly robberies in Springfield in 2012 was 90, and then went down by 50% in 2013. How many robberies were there in Springfield in 2013?
Answer:
m
Step-by-step explanation:
m
Answer:
There were 140 robberies in Springfield in 2012.
Step-by-step explanation:
Let's marked (named) robberies in 2012 with x, which is worth 100%
196 robberies in 2013 worth 100% + 40% = 140%
Now we will make proportion
x : 196 = 100 : 140
When we multiply external and internal members we get
140 x = 196 · 100 => 140 x = 19600 => x = 19600/140 = 140
x = 140 robberies in 2012
What is the minimum value for the function shown in the graph?
(pls help asap thank you :^)
A circle has a diameter of 26 mm. What Is Its circumference?
Use 3.14 for 1, and do not round your answer. Be sure to Include the correct unit in your answer
A rectangle has a perimeter of 100 inches, and
one side has length x. Express the area of the
rectangle as a function of x.
Use the function in part a to find the dimensions of the rectangle with permitter 100 inches and the largest possible area
Answer:
a. A = 50x - x² b. length = 25 inches and width = 25 inches and the maximum area is 625 in²
Step-by-step explanation:
a. The perimeter of a rectangle P = 2(L + W) where L = length and W = width. Now, given that P = 100 inches and W = x, substituting these into the equation, we have
P = 2(L + W)
100 = 2(L + x)
dividing both sides by 2, we have
100/2 = L + x
50 = L + x
making L subject of the formula, we have
L = 50 - x
Now, the are of a rectangle A = LW. Substituting the values of L and W, we have
A = LW
A = (50 - x)x
A = 50x - x²
b. To find the largest possible area of rectangle with perimeter 100 inches, we differentiate A and equate it to zero to find the value of x that maximizes A.
So, dA/dx = d(50x - x²)/dx
dA/dx = d50x/dx - dx²/dx
dA/dx = 50 - 2x
dA/dx = 0 ⇒ 50 - 2x = 0
50 = 2x
dividing both sides by 2, we have
x = 50/2
x = 25
To find it this gives maximum value for A, we differentiate A twice.
d²A/dx² = d(50 - 2x)/dx
d²A/dx² = d50/dx - d2x/dx
d²A/dx² = -2
Since d²A/dx² = -2 < 0, so x = 25 gives maximum value for the area, A.
Since W = x = 25 in and L = 50 - x. So, L = 50 - 25 = 25 in
So, the maximum area A = LW = Lx = 25 in × 25 in = 625 in²
The dimension with perimeter 100 inches that give maximum area are length = 25 inches and width = 25 inches and the maximum area is 625 in²
molly bought a lunch special that was originally $14 today it is on sale for 20% off what is the sale price of the lunch special
Reflections of the coordinate plane homework 3
Answer:
can we have more info please?
Step-by-step explanation:
Please help me!!!! I will mark as brainlist!!
Answer:
117 i think
Step-by-step explanation:
because you need to find the distance from a to b which is 13 units
then you need to find the distance from b to c which is 9 units
and then 9 x 13 is 117
Help!!! Thanks :))))))
Answer:
80
Step-by-step explanation:
180-60=120
120-40=80
PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
Answer:
1.75=5n or 5n=1.75
Step-by-step explanation:
There are 5 n's on the bottoms so you are doing 5 times n (5n) and then 1.75 is on the top so the equation has to equal 1.75
Answer:
5n=1.75
Step-by-step explanation:
the image, the area of the tape diagram indicating 1.75 is equal to the sum of the areas of all five parts in the diagram such that each part indicates n.
here, we have assumed that 1.75 represents an area of the first rectangle , and n represents the area of each of the small rectangle
CORRECT ANSWER GETS BRAINLIEST !
Vana lives 6 miles from the library and 18 miles from the museum . To the nearest mile . What is the shortest distance from the museum to the library ?
A.16mi
B.17mi
C.19mi
D.20mi
Answer:
C
Step-by-step explanation:
I just took the quiz :D
May I have Brainiest???
Which number is rational?
1. –2.1010010001...
2. –0.8974512...
3. 1.2547569...
4. 5.3333333...
PLEASE HELP ITS A UNIT TEST AND TIMED
Answer:
4.) 5.3333333....
Step-by-step explanation:
Rational numbers are either repeating decimals:
[tex]\frac{1}{3}= 0.333333333....[/tex]
Include terminating decimals:
[tex]\frac{1}{8}= 0.125[/tex]
Are all numbers that can be written as a quotient of integers:
[tex]\frac{a}{b},b\neq 0[/tex]
Options (1), (2), and (3) are neither repeating, terminating, and can't be written as a quotient of integers.
Option (4) has repeating decimals, so this is rational.
:Done
300% of 82 is what number?
Answer:246
Step-by-step explanation:
What survival rate in the 10th year would make the average rate of loss over the 10-year period equal to 38.0%?
Answer: 63%
Step-by-step explanation:
First find the rate of loss that would cause the average rate of loss over the 10-year period equal to 38.0%.
Assume that rate is x.
38 = (36.2 + 29.0 + 46.2 + 37.5 + 40.9 + 40.0 + 32.6 + 40.5 + 40.1 + x) / 10
38 = (343 + x ) / 10
380 = 343 + x
x = 380 - 343
x = 37%
The survival rate is the opposite of the rate of loss which means that the survival rate is;
= 1 - rate of loss
= 1 - 37%
= 63%
A ski club rents cross-country skis. The table below shows the cost of rentals for two and four days. Number 1 2 3 of Days Rented Rental Cost ($) 12 17 22 27 Which explicit formula models the cost of renting skis from the club? o an . = 12 + 5n O an . 10n An = 5 + 5n O an an = 7+5n
Answer:
an = 7 + 5n
Step-by-step explanation:
First we know that for each number of days rented the cost increase by 5 so we get an - (?) + 5n.
We also know the first number is 12 for 1 day, so for 0 days, or the starter cost, is 7. We get this by subtracting 5 from 12.
Hence the answer an = 7 + 5n
Answer:
Step-by-step explanation:
find x (11x-1) (20x-3) 151
Answer:
x=5 I think
Step-by-step explanation:
just search it up online