Answer:
Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.
Step-by-step explanation:
We are asked to describe the transformation of function [tex]y=\frac{3}{4x-12}[/tex] as compared to the graph of [tex]y=\frac{1}{x}[/tex].
We can write our transformed function as:
[tex]y=\frac{3}{4(x-3)}[/tex]
[tex]y=\frac{3}{4}*\frac{1}{(x-3)}[/tex]
Now let us compare our transformed function with parent function.
Let us see rules of transformation.
[tex]f(x-a)\rightarrow\text{Graph shifted to the right by a units}[/tex],
[tex]f(x+a)\rightarrow\text{Graph shifted to the left by a units}[/tex],
Scaling of a function: [tex]a*f(x)[/tex]
If a>1 , so function is stretched vertically.
If 0<a<1 , so function is compressed vertically.
As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.
As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.
Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.
Final answer:
The equation y=3/4x-12 represents a linear function with a straight line graph, while y=1/x depicts a rectangular hyperbola with a curved graph showcasing an inverse relationship. These graphs exhibit fundamentally different behaviors, one being constant and the other varying.
Explanation:
The student's question involves comparing the graph of y=3/4x-12 to the graph of y=1/x. The first equation, y=3/4x-12, describes a linear function with a slope of 3/4 and a y-intercept of -12. This means it is a straight line that increases as x increases, crossing the y-axis at (0, -12).
On the other hand, the graph of y=1/x is a rectangular hyperbola. This curve approaches the x-axis and y-axis but never touches them, known as asymptotes. The hyperbola is divided into two parts, one in the first quadrant where both x and y are positive, and another in the third quadrant where both x and y are negative. This graph does not resemble a straight line at any part.
Comparatively, the key difference lies in the nature of their graphs - one is a straight line and the other a curved hyperbola, showcasing completely different behaviors. The linear equation reflects constant change, whereas the hyperbola’s rate of change varies with x, indicating an inverse relationship.
Garys unpaid credit card balance is $2543.32. His APR is 17.4% qnd he made ine new transaction for $320 whats his new balance
What is...a increased by 25%
Answer:
1..25a
Step-by-step explanation:
a + 25%·a = a(1 + 0.25) = 1.25a
_____
Comment on percentages
The symbol "%" is a shorthand way to write "/100", so 25% = 25/100 = 0.25.
Of course, 100/100 = 100% = 1.
Adding 25% of something to 100% of it gives 125% of it, the original amount multiplied by 125/100 = 1.25.
Answer:
1.25a
Step-by-step explanation:
a + 25%·a = a(1 + 0.25) = 1.25a
_____
Comment on percentages
The symbol "%" is a shorthand way to write "/100", so 25% = 25/100 = 0.25.
Of course, 100/100 = 100% = 1.
Adding 25% of something to 100% of it gives 125% of it, the original amount multiplied by 125/100 = 1.25.
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Manuel worked 5 days a week, and 6 hours each day. That week he earned $337.50. What was his hourly rate of pay?
Manuel's hourly rate of pay is calculated by dividing his total weekly earnings by the total hours he worked. He worked a total of 30 hours and earned $337.50, resulting in an hourly rate of $11.25.
The question asks us to calculate Manuel's hourly rate of pay based on the total amount he earned in a week and the number of hours he worked. To find the hourly rate, we need to divide the total earnings by the total number of hours worked.
Calculate the total number of hours worked in a week: 5 days a week times 6 hours each day equals 30 hours.
Divide Manuel's total earnings for the week by the total hours worked:
$337.50 divided by 30 hours equals an hourly rate of $11.25.
How many halves are in the following
12, 10, 13, 15,8 and 5
Several shapes are cut out of a piece of cardboard. Two squares of length x, five rectangles of length x and width y and two circles with radius z. The two squares and four of the rectangles are glued together to form a prism, and the two circles and the remaining rectangle are used to form a cylinder with height y. Which represents the combined volume of the two figures?
Marla says that every number in nineties is composite. Jackie says that one number in the nineties is prime. Who is correct?
Answer:
Jackie, 91, 97 is prime.
Step-by-step explanation:
Remember that a number greater than 2 is NOT prime if it is divided by any number different than 1, for example 6 is NOT prime because 3 divides 6. 7 is prime because the only divisors of 7 are 1 and 7.
So for the nineties 90 is divisible by 45.
91 is divisible by 7
92 is divisible by 2
93 is divisible by 3
94 is divisible by 2
95 is divisible by 5
96 is divisible by 2
97 IS PRIME, is just divisible by 1 and 97
98 is divisible by 2
99 is divisible by 3
Can someone help me? Please show your work.
write always, sometimes or never,a conjecture is _____ true
The circumference of a circle is divided into twelve equal arcs. The measure of each arc is degrees.
The measure of each of the arc in degrees is:
30 degree
Step-by-step explanation:We know that the circle is a whole of 360 degrees.
Now when we divide the circumference of a circle into 12 equal arcs, then the measure of each arc in degrees is calculated as the ratio of the 360 degrees to the number of arcs it has been divided.
Hence, the measure of each arc in degrees is:
[tex]\dfrac{360}{12}=30[/tex]
Hence, the measure in degrees is:
30 degree
How to subtract 546 from 735
a used truck for $4,500 he made an agreement with the dealer to put $1,500 and make payments of 350 for the next 10 months that extra costs paid by taking this bill bill is equivalent to what actual yearly rate of interest
Which values of P and Q result in an equation with exactly one solution? Qx-6=Px-103
Answer:
For any value of P & Q except when both are equal , we get One solution of equation.
Step-by-step explanation:
Given: Linear Equation, Qx - 6 = Px - 103
This equation has exactly 1 solution.
To find: Value of P and Q
First we solve the linear equation for value of x,
Qx - 6 = Px - 103
Transpose Px to LHS ( Left hand side ) we get,
Qx - Px - 6 = -103
Transpose 6 to RHS ( Right hand side ) we get,
Qx - Px = -103 + 6
Qx - Px = -97
taking x common in LHS, we get
( Q - P ) x = -97
Traspose ( Q - P ) to RHS, we get
[tex]x=\frac{-97}{Q-P}[/tex]
[tex]x=\frac{-97}{-(P-Q)}[/tex]
[tex]x=\frac{97}{P-Q}[/tex]
Thus, we are get only 1 value of x but it exist if P ≠ Q
otherwise no solution exist for the given linear Equation.
Therefore, For any value of P & Q except when both are equal , we get One solution of equation.
(4,7), (x,19); slope = 3 the pair points lies on the same line with the given slope. Find x
Calculate the noon sun angles for new orleans, usa and helsinki, finland on september 22. in the answer below, new orleans answer is listed first. refer to the notes on how to calculate noon sun angles. 36.5 degrees, 6.5 degrees 60 degrees, 30 degrees 83.5 degrees 53.5 degrees
Answer:
60 degrees, 30 degrees
Explanation:
Sun angle = 90° - Zenith angle
On September 22, the sun passes over celestial equator. Equinox occurs.
Zenith Angle = Latitude of the place
Latitude of New Orleans, US = 29.95° ≈ 30°
Latitude of Helsinki, Finland = 60.95° ≈ 60°
Thus, the Sun angle at noon at New Orleans would be 90° - 30° = 60°
and at Helsinki, Finland would be 90° - 60° = 30°
What is the shape of the following distribution?
{9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 19, 20}
negative skew
postive skew
symmetric
asymmetric with no skew
none of the above
The distribution is positively skewed, as indicated by the longer tail on the right side of the dataset representing higher values.
The shape of the distribution for the dataset {9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 19, 20} can be determined by looking at the tail of the distribution. Since the values gradually increase and then have a longer tail towards the higher numbers (with the largest values occurring less frequently), we can identify this as a positively skewed distribution. The distribution does not display symmetry, and the tail extends more significantly to the right, which is indicative of a positive skew. This is because the bulk of the data is located on the left side (lower values), while the right side (higher values) stretches out longer due to the presence of outliers or a gradual decrease in frequency.
SSA triangle problems may have zero, one, or two solutions, true of false?
Answer:
True.
Step-by-step explanation:
We use law of sine to solve the triangle when two sides and angle (SSA) is given.There are different cases possible .
1) If a < b sin A.
In this case No possible triangles or we can say there will be zero solutions.
2) If a > b sin A.
In this case there are Two triangles possible.In such cases at least one of the solutions will be an obtuse triangle.
3) If a = b sin A.
We have Unique solution or one solution.This is true for a right triangle.
Hence the given statement SSA triangle problems may have zero, one, or two solutions is True.
Answer: true
Step-by-step explanation:
Ap3x
Given: C is a point on the perpendicular bisector, l, of AB.
Prove: AC = BC
Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, BC. Using the definition of reflection, reflect BC over l. By the definition of reflection, C is the image of itself and A is the image of B. Since reflections preserve length, AC = BC.
Find the product
54.88 x 7.3
If a pizza is cut into 8 pieces and 3 children each eat one piece, what fraction of the pizza is gone
Find the area of A circle whose diameter is 8.3m round to the nearest tenth
Answer:
the answer is 54.1
Janice really likes potatoes. potatoes cost $0.50 per pound, and she has $5.00 that she could possibly spend on potatoes or other items. suppose she feels that the first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30. instructions: enter your answers as whole numbers.
a. how many pounds of potatoes will she purchase?
b. what if she only had $3.00 to spend?
Janice will purchase 4 pounds of potatoes if she has $5.00. If she only has $3.00 to spend, she will purchase 3 pounds of potatoes.
Explanation:To determine how many pounds of potatoes Janice will purchase, we need to subtract the cost of each pound of potatoes from her total budget until she no longer has enough money to purchase another pound. Let's go step by step:
Janice has $5.00 and the first pound of potatoes costs $1.50. After purchasing the first pound, she will have $5.00 - $1.50 = $3.50 left.
The second pound of potatoes costs $1.14, so she can buy the second pound and have $3.50 - $1.14 = $2.36 left.The third pound costs $1.05, so she can buy it and have $2.36 - $1.05 = $1.31 left.The fourth pound and any subsequent pounds cost $0.30 each. Since Janice has $1.31 left, she can afford $1.31 / $0.30 ≈ 4.37 pounds of potatoes.Therefore, Janice will purchase 4 pounds of potatoes.
If Janice only has $3.00 to spend, we can follow the same steps:
With $3.00, she can afford $3.00 / $0.30 = 10 pounds of potatoes. However, since the value of each pound decreases after the third pound, she can only purchase the first three pounds. The fourth pound would cost $0.30, but she doesn't have enough money left.Therefore, if Janice has $3.00 to spend, she will purchase 3 pounds of potatoes.
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Brook says there are 49 days until july 4 there are 7 days in a week in how many weeks will it be until july 4
7 weeks until July 4.
Calculating the Number of Weeks Until July 4
To determine in how many weeks it will be until July 4, given that there are 49 days left:
We know there are 7 days in a week.
We need to divide the total number of days by the number of days in a week.
The calculation is: 49 days ÷ 7 days/week.
Doing the division: 49 ÷ 7 = 7 weeks.
Suppose the first class in a frequency table of quantitative data is 0 dash 40-4 and the second class is 5 dash 95-9. what is the class midpoint of the first class?
Answer:
4 + 0 = 4/2 = 2 would be the answer.
Step-by-step explanation:
bryan rides the bus to and from work on the days he works at the library in one month he rode the bus 24 times solve the equation 2x=24 to find the number of days bryan worked at the library
What is the coefficient of the variable in the expression 4 − 3x − 7 + 6?
Answer:
the coefficient is -3
Step-by-step explanation:
what is 68% out of 25
In a right triangle, cosA=0.352 and sinA=0.936 What is the approximate value of tanA?
A- 0.329
B- 0.376
C-1.288
D-2.659
Answer:
tanA=2.6591
Step-by-step explanation:
[tex]tanA=\dfrac{sinA}{cosA} \\\\tanA=\dfrac{0.936}{0.352} \\\\tanA=2.6591[/tex]
If 210 people said football was their favorite sport to watch, how many people were surveyed?
Without additional data, such as the percentage of those surveyed who chose football, it's impossible to determine the total number of people surveyed from the information provided. The data given only specifies that 210 individuals selected football as their favored sport to watch.
Explanation:Based on the provided question, there's not enough information to determine the total number of people who were surveyed. The information given only states that 210 people picked football as their favorite sport to watch, but it does not provide the overall total number of people surveyed.
To calculate the total number of respondents, you need to know the ratio or percentage of people who chose football. For example, if you knew that football was chosen by 70% of those surveyed, you could use that information to calculate the total number of people. In this case, the equation would be 210 = 0.70 * x. Solving for x (the total number of people surveyed) would give you x = 210 / 0.70, which comes out to approximately 300 people.
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550 is 5% of what number?
27.5 if you divide 550by 5% you get 27.5
Which equations represent hyperbolas?
Answer:
The correct options are 2 and 5.
Step-by-step explanation:
The general form of conics is
[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]
This equation represents the hyperbola if
[tex]B^2-4AC>0[/tex]
compare the given equations with the general equation.
In option 1,
[tex]A=2,B=0,C=2,D=16,E=14,F=-9[/tex]
[tex]B^2-4AC=(0)^2-4(2)(2)=-16<0[/tex]
This equation does not represents a hyperbola.
In option 2,
[tex]A=2,B=0,C=-5,D=4,E=-10,F=57[/tex]
[tex]B^2-4AC=(0)^2-4(2)(-5)=40>0[/tex]
This equation represents a hyperbola.
In option 3,
[tex]A=-1,B=0,C=-7,D=5,E=2,F=-81[/tex]
[tex]B^2-4AC=(0)^2-4(-1)(-7)=-28<0[/tex]
This equation does not represents a hyperbola.
In option 4,
[tex]A=0,B=0,C=-2,D=1,E=4,F=15[/tex]
[tex]B^2-4AC=(0)^2-4(0)(-2)=0[/tex]
This equation does not represents a hyperbola.
In option 5,
[tex]A=-1,B=0,C=3,D=12,E=7,F=11[/tex]
[tex]B^2-4AC=(0)^2-4(-1)(3)=12>0[/tex]
This equation represents a hyperbola.
Therefore the correct options are 2 and 5.