Let f(x) = 2x
. Suppose that a new function g(x) is created by taking the
graph of f(x) and performing the following transformations:
• Reflection in the x-axis
• Reflection in the y-axis
• Vertical stretch by a factor of 3
• Translation up 2 units
• Translation right 3 units. [3, 2 marks]
a) Find a possible equation for g(x).
Assume that a new function g(x) is created by taking the graph of f(x) and performing the following transformations: vertical stretch by a factor of 3
What is meant by Reflection?A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to reflect another figure when every point in one figure is equidistant from every point in another figure. The reflected image should be the same shape and size as the original, but it should face in the opposite direction. Translation can also occur as a result of changes in position. The original image is referred to as the pre-image, and its reflection is referred to as the image. The pre-image and image are represented by ABC and A'B'C', respectively. The coordinate system may be used in the reflection transformation (X and Y-axis).To learn more about Reflection, refer to:
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Three friends rented a kayak. It cost $4 per hour per person to rent the kayak, plus $2 for each life jacket, and $3 to park the car. It cost $57 in all. How many hours did they spend kayaking? Write an equation and solve.
Answer:
13 hours
Step-by-step explanation:
Let y = the total cost
let x = hours
y = 4x + 5 5 = the one time fee of the jacket and the parking
57 = 4x + 5 Subtract 5 from both sides
52 = 4x Divide both sides by 4
13 = x
Which of the equations or inequalities below are true?O A. 7-26O B. 7-224O C. 7-23 5O D. 7 - 2 = -5
Given,
The equation orr inequalities are,
[tex]\begin{gathered} A)7-2\ge6 \\ B)7-2\ne4 \\ C)7-2\leq5 \\ D)7-2=-5 \end{gathered}[/tex]A) In the expression,
7 - 2 = 5
Hence, 7-2 =6 is incorrect.
B) In the expression,
7 - 2 = 5,
Hence,
[tex]7-2\ne4[/tex]Option B is correct.
C) In the expression,
7 - 2 = 5
7 - 2 < 5 is incorrect
Hence, 7 - 2 =< 5 is incorrect.
D)In the expression,
7 - 2 = 5
Hence, 7 - 2 =< -5 is incorrect.
Hence, option B is correct.
(4, 2); slope = 3 writing linear equations given point and slope
The standard equation of a line in point-slope form is expressed as;
y-y0 = m(x-x0) where;
m is the slope
(x0, y0) is the point on the line
Given
(x0, y0) = (4, 2)
From the coordinate;
x0 = 4 and y0 =2
slope m = 3
Substitute the given parameters into the equation as shown;
y-2 = 3(x-4)
Hence the linear equations given the point and slope id expressed as y-2 = 3(x-4)
Identify the domain and range and tell whether the relation is a function
For a function, every element in the domain must have a unique image in the range.
On checking the domain and range provided in the question, we can see that there are two images for the range when the domain equals -2:
[tex](-2,3)\text{ and (}-2,7)[/tex]Therefore, the given domain and range violate the property of a function.
The relation is NOT a function.
In an office building, 54 office are currently being rented, this represent 30% of the total units. how many offices are in the building
given that,
54 offices are currently rented
and it represent 30% of the total unit
to get the total offices in the building
let the total offices be x
30% of x = 54
30/100 X x = 54
cross multiply
30x = 5400
dividing both sides by 30
30x/30 = 5400/30
x = 5400/30
x = 180
therefore the total offices in the building is 180
Kala the trainer had two solo workout plans that she offers her clients. PlanA and plan B. Each client does either one or the other (not both) on Friday there were 3 clients who did plan A and 5 who did plan B. On Saturday there were 9 clients who did plan A and 7 who did plan B. Kala trained her Friday clients for a total of 6 hours and her Saturday clients for a total of 12 hours. How long does each of the workout plans last?
Answer:
Each of the workouts plans lasts 45 minutes.
Explanation:
Let the duration for Plan A workout = x
Let the duration for Plan B workout = y
Friday
• Plan A --> 3 clients
,• Plan B --> 5 clients
,• Kala trained her Friday clients for a total of 6 hours
[tex]3x+5y=6[/tex]Saturday
• Plan A --> 9 clients
,• Plan B --> 7 clients
,• Kala trained her Saturday clients for a total of 12 hours
[tex]9x+7y=12[/tex]The system of equations is solved simultaneously.
[tex]\begin{gathered} 3x+5y=6\cdots(1) \\ 9x+7y=12\cdots(2) \end{gathered}[/tex]Multiply equation (1) by 3 in order to eliminate x.
[tex]\begin{gathered} 9x+15y=18\cdots(1a) \\ 9x+7y=12\cdots(2) \end{gathered}[/tex]Subtract.
[tex]\begin{gathered} 8y=6 \\ y=\frac{6}{8}=0.75\text{ hours} \\ 0.75\times60=45\text{ minutes} \end{gathered}[/tex]Substitute y=0.75 into equation (2) to solve for x.
[tex]\begin{gathered} 9x+7y=12 \\ 9x+7(0.75)=12 \\ 9x+5.25=12 \\ 9x=12-5.25=6.75 \\ x=\frac{6.75}{9} \\ x=0.75 \end{gathered}[/tex]x=y=0.75 hours = 45 minutes,
Each of the workouts plans lasts 45 minutes.
Identify the composition that is represented by:r (90, O). T (-2, 4)A translation left 2, up 4 and then a reflection of 90°O A rotation of 90° and then a translation left 2, up 4.A reflection of 90° and then a translation left 2, up 4.O A translation of left 2, up 4 and then a rotation of 90°.
ANSWER:
A rotation of 90° and then a translation left 2, up 4.
STEP-BY-STEP EXPLANATION:
Since r (90, 0) is the first and means a 90 ° rotation and that T (-2, 4) is a translation of 2 units to the left (because it is negative) and 4 units up (because it is positive) , the answer is the option "A rotation of 90° and then a translation left 2, up 4."
A student is trying to solve the set of two equations given below:Equation A: x + z = 6Equation B: 3x + 2z = 1Which of the following is a possible step used in eliminating the z-term
Answer:
multiply equation A by -2
When you multiply possible options in each scenario to get the total number of combinations, this is referred to as the fundamental _____ principle.
Fundamental counting principle.
It is also called the counting rule, applying this principle we can know the number of outcomes by multiplying the options of each event together.
Find an equation of the tangent line to the graph of y = B(x) at x = 25 if B(25) = −1 and B ′(25) = − 1 5 .
The most appropriate choice for tangent to a curve will be given by-
[tex]3x + 2y = 73[/tex] is the required equation of tangent.
What is tangent to a curve?
Tangent to a curve at a point is the straight line that just touches the curve at that point.
Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by
[tex]y - y_1 = \frac{dy}{dx}|_{(x_1,y_1)} (x - x_1)[/tex]
Here,
y = B(x), B(25) = -1, B'(25) = -1.5
Equation of tangent =
[tex](y - (-1)) = -1.5(x - 25)[/tex]
[tex]y + 1=-1.5x +37.5\\y + 1 = -\frac{3}{2}x + 37.5\\2y + 2 = -3x + 75\\3x+2y = 75-2\\3x+2y=73[/tex]
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a coral reef grows 0.15 m every week. how much does it grow in 13 weeks? in centimeters
Given:
A coral reef grows 0.15 m every week.
Coral reefs grow 13 times 0.15m for 13 weeks.
[tex]=13\times0.15m[/tex][tex]=1.95\text{ m}[/tex]We need to convert m into cm.
[tex]1m=100cm[/tex]Multiply 1.95m by 100, we get
[tex]1.95\times100=195cm[/tex]Hence a coral reef grows 195cm in 13 weeks.
a bottle of ketchup holds 0.95 liters how maney milliliters does it hold?
Explanation:
The relation between liters and milliliters is:
[tex]1\text{ liter}=1000\text{ milliliters}[/tex]we have to multiply the liters by 1000
Answer:
The answer is 950 milliliters
Jan plans to tell two people each day and will ask that person to tell two other people each day through the day of the opening, and so on. Assume that each new person who hears about the soft opening is also asked to tell two other people each day through the day of the opening and that each one starts the process of telling their friends on the day after he or she first hears. When should Jan begin telling others about the soft opening in order to have at least 700 people know about it by the day it occurs?
Explanation:
From the given question, we can sketch the pattern observed
The figure above helps show how the number of people increases
Initially, Jan tells 2 more people, then the two people tell two more people, then they also tell two more people
Thus
we can see that the model is given by
[tex]\begin{gathered} (2)^n \\ where\text{ n is the number of days} \end{gathered}[/tex]In order to have at least 700 (it also means a minimum of 700), we will have the equation
[tex]2^n\ge700[/tex]We then solve for n
Taking the log of both sides
[tex]n\text{ }log2\ge log700[/tex][tex]n\ge\frac{log700}{log2}[/tex]So that
[tex]\begin{gathered} n\ge\frac{2.845}{0.301} \\ \\ n\ge9.451 \end{gathered}[/tex]So, the number of days will be at least 10 days (Rounded to the nearest whole day )
Issac says that T' will be located at (4,20)Isabella says that T' will be located at (4,12(who is correct and why?
In the given triangle :
The coordinate of T is ( 2, 10 )
Triangle TUV will be dilated by a scale factor of 2
Thus, multiply the coordinates of TUV by 2
T' = 2 x T
T' = 2 x ( 2, 10 )
T' = ( 2x2, 2x10)
T' = ( 4, 20 )
So, T' will be located at ( 4, 20 )
Issac says that T' will be located at (4,20)
Answer : Issac says that T' will be located at (4,20)
Large Small
3
Blue 17
Red 8 12
Find: P(Red and Small)
Remember to reduce your answer.
Enter
Using mathematical operations, we know that P(Red and Small) is 4/3.
What exactly are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The order of operations refers to the rules that define the sequence in which we should perform the operations necessary to solve an expression.Parentheses, Exponents, Multiplication, Division, and Addition Subtraction are also known as PEMDAS (from left to right).So, simple form of P(Red and Small):
Red balls: 8 (large) + 12 (Small) = 20 red ballsSmall balls: 3 (Blue small balls) + 12 (Red small balls) = 15 small ballsThen, P(Red and Small):
20/154/3Therefore, using mathematical operations, we know that P(Red and Small) is 4/3.
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Equation of line passing thru point -6,-3 and perpindicular to JK -2,7 and 6,5
Equation of the line passing through the point (-6,-3) and perpendicular to the line passing through (-2,7) and (6,5) is y = 4x -19.
First we will find the slope of the line passing through (-2,7) and (6,5).
Slope of the line = (5-7)/(6-(-2)) = -2/8 = -1/4.
We know that,
Product of the slopes of two perpendicular lines = -1.
Let the equation of the line we have to find be y = mx + c.
Slope will be m.
Hence, we can write,
m*(-1/4) = -1
m = -1*(-4/1)
m = 4
Putting (6,5) and m = 4 in y = mx + c , we get
5 = 4*(6) + c
5 = 24 + c
c = 5 - 24 = -19
Hence, the equation of the line is:-
y = 4x -19
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A birthday cake has a diameter of 9 inches. A wedding cake has a diameter of 14 inches. What is thedifference in area between the top surfaces of the two cakes?
90.32 square inches
Explanation
Step 1
the area of the circle is given by:
[tex]\text{Area}=\frac{\pi}{4}\cdot diameter^2[/tex]Step 2
find the areas
birthday cake
[tex]\begin{gathered} \text{Area}_b=\frac{\pi}{4}\cdot9^2 \\ \text{Area}_b=\frac{81\pi}{4} \\ \text{Area}_b=\frac{254.46}{4} \\ \text{Area}_b=63.61\text{ square inches} \end{gathered}[/tex]Now, the wedding cake
[tex]\begin{gathered} \text{Area}_w=\frac{\pi}{4}\cdot14^2 \\ \text{Area}_w=\frac{\pi}{4}\cdot196\text{ square inches} \\ \text{Area}_w=49\cdot\pi\text{ square inches} \\ \text{Area}_w=153.93\text{ square inches} \end{gathered}[/tex]Step 3
finally, find the difference
[tex]\begin{gathered} \text{difference}=153.93\text{ square inches-63.61 inches} \\ \text{difference}=90.32 \end{gathered}[/tex]so, the answer is 90.32 square inches
help video S-(x – 6)² +7 for 2 2 +3 x = 3 for Find f(3)
Explanation:
This is a function defined by parts. When x is not 3, the function has the equation on top, but when x is 3, the function has one value: 2.
Answer:
f(3) = 2
find the circumference of the circle L. Write your answer as a decimal, rounded to the nearest hundredth. the circumference is blank feet
Let us call C the circumference of the circle.
We know that the ratio of angle to circumference must be
[tex]\frac{106}{360}=\frac{1.25}{C}[/tex]cross multipication gives
[tex]106(C)=360\cdot1.25[/tex]Dividing both sides by 106 gives
[tex]C=\frac{360\cdot1.25}{106}[/tex][tex]C=4.25[/tex]which is our answer!
A school is organising a fun runThe fun run involves a 4
1
2
mile run around the field, then a 3
2
5
mile run back to the school. Find the total distance of the fun run.Give your answer as a mixed number in its simplest form.
The total distance of the fun run is 7 9/10 miles and it can be written in the simplest fraction form.
Fraction:
The fraction is the part of the whole thing.
For example, a cake is divided into four equal pieces, then each piece is represented by ¼.
Given,
A school is organizing a fun run. The fun run involves a 4 1/2 mile run around the field, then a 3 2/5 mile run back to the school.
Now, we need to find the total distance of the fun run and we have to write it as simplest form.
First we have to convert the given fraction into simplest fraction then we get,
=> 4 1/2 = 9/2
=> 3 2/5 = 17/5
Now , we have to add these to fraction in order to get the total distance,
=> 9/2 + 17/5
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(9/2, 17/5) = 10
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
=> 45/10 + 34/10
=> 79/10
While we convert this into mixed number then we get,
=> 79/10 = 7 9/10
Therefore, the total distance is 7 9/10 miles.
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Hello. I think I have the right answer. These types of questions have been giving me problems
EXPLANATION
Using a composite figure to approximate the area of the figure will give us the needed surface,
The area of the composite is approximately the area of the squares:
Area of square:
A= base * height = 1.0*1.0 = 1 cm^2
Since we have approximately 22 squares inside the figure, the approximate area will be as follows:
[tex]Area_{composite\text{ figure}}=22*1cm^2=22cm^2[/tex]Therefore, the solution is approximately 22 square units.
Point B is located at -2. Points C and D are each 8 units away from point B. Where are C and D located?
They are located 8 units away, so one has to be away in the left direction and the other one in the right direction
[tex]\begin{gathered} \text{ - 2 - 8 = -10 } \\ \text{ - 2 + 8 = 6} \end{gathered}[/tex]So, C and D are located at -10 and 6
name a 2 digit odd number that is composite
We should know that:
All the odd integers which are not prime are odd composite numbers. Examples of composite odd numbers are 9, 15, 21, 25
A total of $5000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $540?
Answer
The amount invested at
Step-by-step explanation:
The total amount invested is $5000
Let x be the investment at 5%
Let y be the investment at 15%
Mathematically, this can be expressed as
x + y = 5000 -- equation 1
Since the first part of the investment is invested at 5% and the second part is at 15%
0.05x + 0.15y = 540 --------- equation 2
The systems of equations can be solved simultaneously using the substitution method
x + y =5000 ----- equation 1
0.05x + 0.15y = 540 ------ equation 2
Isolate x in equation 1
x = 5000 - y
Substitute the value of x into equation 2
0.05(5000 - y) + 0.15y = 540
Open the parenthesis
250 - 0.05y + 0.15y = 540
Collect the like terms
-0.05y + 0.15y = 540 - 250
0.1y = 290
Divide both sides by 0.1
0.1y/0.1 =290/0.1
y = $2900
Recall that equation 1 is
x + y = 5000
y = $2900
x = 5000 - y
x = 5000 - 2900
x = $ 2100
Hence, the investment at 5% is $2100 and the investment at 15% is $2900
Mrs. Smith has 12 times as many markers as colored pencils. The total number of markers and colored pencils is 78. How many markers does Mrs. Smith have?ok...answers given so far are not helpful in explaining process.
Let:
x = Colored markers
y =
Line segment AB is on square ABCD. Segment EF on equilateral triangle EFG is 12 units longer than AB. Square ABCD and triangle EFG have equal perimeters. What is the length of AB?
The length of segment AB as required in the task content is; 36.
What is the length of segment AB?It follows from the task content that the length of the line segment AB which is a side of the square ABCD is to be determined.
Since the perimeters of triangle EFG and square ABCD are equal as given;
Let the length of segment AB = x.
Therefore, EF = x + 12.
Therefore, the perimeter of the equilateral triangle = 3(x +12).
While the perimeter of square ABCD is; 4x.
Therefore, since the perimeters are equal;
3(x + 12) = 4x
3x + 36 = 4x
36 = x.
On this note, thee Length of line segment AB is; 36.
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Which expression uses the commutative property to make it easier to evaluate
Let's begin by listing out the given information:
The commutative property states that for addition, the order in which we add numbers does not change their sum & for multiplication, the order in which we multiply does not change their product.
Mathematically expressed as:
[tex]\begin{gathered} x+y+z=y+z+x \\ x\cdot y\cdot z=y\cdot z\cdot x \end{gathered}[/tex]Therefore, the commutative property of this is:
[tex]\begin{gathered} \frac{4}{3}\cdot\frac{1}{5}\cdot18=\frac{4}{3}\cdot18\cdot\frac{1}{5} \\ \Rightarrow\frac{4}{3}\cdot18\cdot\frac{1}{5} \\ \end{gathered}[/tex]Therefore, Option D is the correct answer
4y+3+6xWhat is the numerical coefficient of the first term?What is the constant term?
We are given the following expression:
[tex]4y+3+6x[/tex]The numerical coefficient is the number that multiplies a variable, in this case, the first variable is "y" and the numerical coefficient is 4.
The constant in an expression is the number that does not multiply any variable, in this case, the constant is 3.
I need help answering this if you can show your work to the be good
Let:
x = Number of sodas purchased
y = Number of hamburgers purchased
The food truck charges $3 for sodas, so the total cost for sodas will be:
3*x=3x
also, it charges $8 for each hamburger, hence, the total cost for hamburgers will be:
8*y = 8y
Since Jack wants to spend no more than $30, the total cost must be less or equal than $30:
[tex]\begin{gathered} \text{Total cost }\leq\text{ 30} \\ \text{Total cost = total cost for sodas+total cost for hamburgers} \\ 3x+8y\le30 \end{gathered}[/tex]