The function which is representative of the transformation of the parent function f(x) = log4x by reflecting it over the x-axis, stretching it vertically by a factor of two, and shifting it up five units is g(x) = -2log4(x) + 5. Option C is correct.
The reflection over the x-axis is given by the transformation:
f₁(x) = - f(x)
Therefore, the first step we get is:
f₁(x) = - log(4x)
Stretching by a factor n along the y-axis is given by the transformation:
f₂(x) = n · f₁(x)
Therefore, we will get:
f₂(x) = -2 · log(4x)
Shifting a function up of a quantity n is given by:
f₃(x) = f₂(x) + n
Therefore, we will get:
f₃(x) = -2 · log(4x) + 5
So,
g(x) = -2 log4(x) + 5
Thus, the function which is representative of the transformation of the parent function f(x) = log4x by reflecting it over the x-axis, stretching it vertically by a factor of two, and shifting it up five units is g(x) = -2log4(x) + 5. Option C is correct.
To learn more about transformation of a function visit:
https://brainly.com/question/2675216
#SPJ1
If 5x to the power of 7 times s = 20x to the power of 4, which expression is equivalent to z
The expression that is equivalent to x is ∛4/s
How to determine the equivalent of x?In this question, the mathematical statement of the equation is given as
5x to the power of 7 times s = 20x to the power of 4
When the mathematical statement is represented as an equation, we have the following representation
5x⁷ * s = 20x⁴
Divide both sides by x⁴
So, we have the following representation
5x⁷/x⁴ * s = 20x⁴/x⁴
Evaluate the quotients
This gives
5x³ * s = 20
Divide both sides by 5
x³ * s = 4
So, we have
x³ = 4/s
Take the cube root of both sides
x = ∛4/s
Hence, the solution is x = ∛4/s
Read more about equivalent expressions at
https://brainly.com/question/15775046
#SPJ1
My decimal is 300ths less than 3/10
Answer:
0.001? or -299.7
Step-by-step explanation:
so i don't have idea what do you meaning so
0,3:300=0.001 or 0,3-300=-299.7
so i think i help
There are 240 kids in primary school 2/5 of pupils come to school by car and 15% walk. The remainder came by bus. How many came by bus?
Answer:
132
Step-by-step explanation:
240/5=48
48*2=96
240-15%=204
240-204=36
96+36=132
The number of pupils who came by bus is 108.
Total number of kids in school = 240
Fraction of pupils who came to school by car = 2/5
Number of pupils who came to school by car = [tex]\frac{2}{5}[/tex] × 240
= 96
Percentage of pupils who came to school by walk = 15 %
Number of pupils who came to school by walk = [tex]\frac{15}{100}[/tex] × 240
= 36
Number of people who came by bus
=Total number of kids in school - number of pupils who came by car - number of pupils who came by walk
= 240 - 96 - 36
= 108
Therefore, the number of pupils who came to school by bus = 108.
To know more about word problems:
https://brainly.com/question/13818690
A new car is purchased for 27,100 dollars. The value of the car depreciates at a rate of 7% per year. Which equation represents the value of the car after 6 years?
In exponential relations, we can represents given values like this:
[tex]f(x)=a*c^x[/tex]
c = growth/decay factora = starting point/y-interceptSolving the QuestionWe're given:
27,100 dollars = starting pointDecay factor = 7% per year⇒ Plug this information into [tex]f(x)=a*c^x[/tex]:
[tex]f(x)=27,100*(0.93)^x[/tex]
Why input 0.93 and not 0.07? Let's think of it this way: To calculate the new price of the car after one year, we find 93% of 27,100.
The dependent variable is the price (y) and the independent variable is the time in years (x).
f(x) = pricex = timeTherefore, to find the value of the car after 6 years, we plug in 6 as x:
[tex]f(x)=27,100*(0.93)^6[/tex]
Answer[tex]V=27,100*(0.93)^6[/tex]
a sample is the set of all the people or objects whose properties are to be described and analyzed by the data collector.
The statement that "the sample is set of all people or objects whose properties , are to be described and analyzed by the data collector " is False .
In the question ,
it is given that ,
The sample is the set of all the people or objects whose properties are to be described and analyzed by the data collector .
But we know that the Population is defined as "set of all people or objects whose properties are to be described and analyzed by the data collector"
and the Sample is the Subset or subgroup of the population .
Therefore , the given statement is False .
The given question is incomplete , the complete is
State whether the statement is True or false "a sample is the set of all the people or objects whose properties are to be described and analyzed by the data collector " .
Learn more about Population here
https://brainly.com/question/28791285
#SPJ4
Solve this equation using the "Distributive Property".
[tex] \sf 3(x - 2) = 21[/tex]
Answer:
x = 9
Step-by-step explanation:
Start by dividing both sides by the singular number, 3. We divide by 3 and not 21 because 21 is the result of the equation, not the coefficient.
[tex]\frac{3\left(x-2\right)}{3}=\frac{21}{3}[/tex]
We got 21 over 3 because you cannot divide 3 times an unknown number subtracted by 2 by 3. This is because we do not know the number. So that's where 21 comes in.
Next, simplify this equation by dividing whole numbers.
[tex]\frac{3}{3} = 1[/tex]
[tex]1\left(x-2\right) = \left(x-2\right)[/tex]
[tex]\frac{21}{3} = 7\\= x-2 = 7[/tex]
Lastly, add 2.
[tex]x - 2 + 2 = 7 + 2\\2 + 2 = 4\\7 + 2 = 9\\= x - 4 = 9\\x = 9[/tex]
Why x - 4 is 0: We assume x is always equal to 1, since 4 does not go into 1, the result would be 0. x - 0 = 0. Therefore, the problem became x = 9.
Hope this helps!
The perimeter of a rectangle i 202020 centimeter. The length i 666 centimeter. What i the area of the rectangle?
quare centimeter
The area of the rectangle is, 24 square centimeter.
What is area?
Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Let, the perimeter of the rectangle is 20 centimeter.
The length is 6 centimeter.
Suppose the width of the rectangle is y.
So,
Perimeter = 2(6) + 2(y)
20 = 12 + 2y
8 = 2y
y = 4
Hence, the width of the rectangle is 4 centimeter.
Since,
Area of rectangle = length x width
A = 6 x 4
A = 24
Therefore, the area of the rectangle is, 24 square centimeter.
To know more about the area, click on the link
https://brainly.com/question/25292087
#SPJ4
Write an equation for the trend line shown on the scatter plot.
An equation for the trend line shown on the scatter plot is y = 5x + 15.
How to find an equation for the trend line?In order to determine a linear equation for the trend line (line of best fit) that models the data points described in the scatter plot above, we would have to calculate the slope of this line.
By critically observing the scatter plot, we can reasonably and logically deduce the following points through which the trend line passes through:
Points (x, y) = (2, 25)
Points (x, y) = (6, 45)
Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (45 - 25)/(6 - 2)
Slope, m = 20/4
Slope, m = 5.
At point (2, 25), a linear equation for the trend line can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x represents the length of trip (in days).y represents the weight (lbs).Substituting the given parameters into the formula, we have;
y - y₁ = m(x - x₁)
y - 25 = 5(x - 2)
y - 25 = 5x - 10
y = 5x - 10 + 25
y = 5x + 15.
Read more on slope here: brainly.com/question/25239789
#SPJ1
Malik wrote a total of 4 pages over 2 hours. How many hours will Malik have to spend this week in order to have written a total of 16 pages? Solve using unit rates.
Answer:
8 hours
Step-by-step explanation:
if it takes 2hrs to do 4 pages it takes an hour to do 2 pages
2*8=16
1*8=8
8 hours
hope it helps
The area of a rectangle i 223. 2 m2. If the length i 16 m, what i the perimeter of the rectangle?
The perimeter of the rectangle is 59.9 m.
The area of the rectangle is = 223.2 m²
the length(L) of the rectangle is = 16 m
we know that the area of the rectangle is given by
Area = Length x Breadth
A = LB
therefore ,
LB= 223.2
16 x B = 223.2
B = 223.2/ 16
B = 13.95 m
∴ breadth or the rectangle is 13.95 meter.
Now , we know that the perimeter of the rectangle is given by ,
(P) perimeter = 2( Length + Breadth )
P = 2(L + B)
P = 2( 16 + 13.95)
P = 2( 29.95)
P = 59.9 m
So the perimeter of the rectangle is 59.9 meter.
Learn more about area and perimeter here :
https://brainly.com/question/11957651
#SPJ4
here is a line that includes the point (9,1) and has a slope of 1/9. what is its equation in slope intercept form?
[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{9}}(x-\stackrel{x_1}{9}) \\\\\\ y-1=\cfrac{1}{9}x-1\implies {\Large \begin{array}{llll} y=\cfrac{1}{9}x \end{array}}[/tex]
11. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the triangles
Complete the following statement. Write your answer as a decimal or whole number.
% of $58 = $58
Answer: 1.72
Step-by-step explanation:
Write an absolute value equation representing all numbers x whose distance from 1 is 11 units.
The absolute value equation representingnumbers all x whose distance from is 11 units is
|1 - x| = 11 What is absolute value?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
A number can never have a negative absolute value.
How to write the absolute value equationThe equation is written in the form below
|1 - x| = 11
removing the absolute value sign
1 - x = ± 11
solving for x for positive value
1 - x = 11
1 - 11 = x
x = -10
solving for x for negative value
1 - x = -11
1 + 11 = x
12 = x
The absolute value equation as required is |1 - x| = 11 the values of is 12 or -10
Learn more absolute values here:
https://brainly.com/question/24368848
#SPJ1
Grace and her dad are planning to attend the state fair. An adult ticket is $15. The price of an adult ticket is one half the price of a student ticket plus $8. Write an equation to determine how much grace will pay for a student ticket.
1/2 x + 8 = 15 Grace will pay for a student ticket
the question requests the cost of a "student ticket." Because we don't know, let's assume the student ticket price is "x" dollars.
Because we know from the question that "the price of an adult ticket is half the price of a student ticket plus $8.00," we can represent the adult ticket price as follows:
1/2 x + 8
If we also get "An adult ticket costs $15.00" from the question, we can write the equation as:
1/2 x + 8 = 15
Grace will pay for a student ticket
To learn more about Cost:
https://brainly.com/question/15135554
#SPJ4
Actual Unemployment Rate = 8%
Natural Unemployment Rate = 5%
What is the Cyclical Unemployment rate?
The Cyclical Unemployment rate is 3%.
What is unemployment?Unemployment simply means a scenario where those who are willing and able to work can't find suitable jobs.
Actual Unemployment Rate = 8%
Natural Unemployment Rate = 5%
The Actual Unemployment rate will be:
= Cyclical Unemployment Rate + Natural Unemployment Rate
8% = 5% + C
C = 8% - 5%
C = 3%
C = Cyclical Unemployment rate
The unemployment is 3%.
Learn more about unemployment on:
brainly.com/question/305041
#SPJ1
Pressure =
72 N
A
Calculate the force when the pressure is 18 N/m² and the area is 4 m².
Select your answer.
Force
Area
9.5 N
B
14 N
C
22 N
D
Pressure = Force/Area
According to question, we have
18 = Force/4
force = 72 N
Given (x – 1)^2 = 50, select the values of x.
x = –49
x = 51
x = 1+5√2
x = 1-5√2
Answer:
[tex]x=1+5\sqrt{2}, 1-5\sqrt{2}[/tex]
Step-by-step explanation:
[tex](x-1)^2=50 \\ \\ x-1=\pm 5\sqrt{2} \\ \\ x=1 \pm 5\sqrt{2}[/tex]
kelsey has a bag full of jellybeans that weighs 3 1/2 pound. She gave her friend 1/3 of the bag. if she paid $2.58 per pound of jellybeans, how much money did she spend on the amount of jellybeans she gave away?
(PLUS 25 POINTS)
Answer: $3.01
Step-by-step explanation:
1. You first have to find out how much she spent for ALL the jellybeans, you find this by multiplying the pounds by the cost per pound.
(7/2)*(2.58)
Kelsey spent $9.03 for the 3 1/2 pound bag of jellybeans
2. You now have to find out how much she spent for 1/3 if the bag. You do this by multiplying the total cost by 1/3.
(1/3)(9.03)
3.01
ANSWER: Kelsey spent $3.01 on the amount of jellybeans she gave away.
change this root into a power
Answer:
I think it would be 12^1/4
Step-by-step explanation:
I hope this is what you were asking for :)
PLSS HELP find x, y and z
The values of x, y and z in the angles are as follows
x = 30 degreesy = 15z = 150 degreesHow to find the angles on parallel line cut by a transversal?When parallel lines are cut by a transversal line, angle relationship are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.
The parallel lines forms angles relationships.
Therefore,
x = 2y (alternate angles)
z = 2x + 90 (alternate angles)
Using substitution,
z = 2(2y) + 90
z = 4y + 90
x + 2x + 90 = 180 (sum of angles on a straight line)
3x = 180 - 90
3x = 90
x = 90 / 3
x = 30°
Hence,
30 = 2(y)
y = 30 / 2
y = 15
z = 4(15)+ 90
z = 60 + 90
z = 150°
learn more on angles here; https://brainly.com/question/11553350
#SPJ1
helppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:1/6.4, and there are 5.4 times as many pigs as cows.
Step-by-step explanation: In this scenario there are 64 animals, 54 pigs and ten cows. So the ration is 10/64, which can be simplified if you like to 1/6.4
There are 54 pigs for every 10 cows, which is the same as 5.4/1.
For every cow there is 5.4 pigs, so however many cows there are you can take that number and multiply it by 5.4 to get the number of pigs.
Answer:
5/32
5.4
Step-by-step explanation:
54:10 is the ratio of pigs to cows.
It could be assumed that there are 54 pigs and 10 cows.
Problem is asking for the ratio of cows to all animals. So,
Add up the pigs and cows to get 64 total animals.
Input the numbers to the ratio cows:all animals
10:64
Change to a fraction
5/32
How many times the number of cows is the number of pigs. This can be found by dividing the number of pigs by the number of cows.
54 / 10 = 5.4
The number of pigs is 5.4 times more than the number of cows.
Find the quotient 2 divided by 3/7
[tex]2\div \cfrac{3}{7}\implies \cfrac{2}{1}\div \cfrac{3}{7}\implies \cfrac{2}{1}\cdot \cfrac{7}{3}\implies \cfrac{14}{3}\implies 4\frac{2}{3}[/tex]
The quotient for the expression is 4.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
2 ÷ [tex]\frac{3}{7}[/tex]
= 2 / (3/7)
= (2 x 7) / 3
= 14/3
Now,
3 ) 14 ( 4
12
2
Remainder = 2
Quotient = 4
Thus,
The quotient is 4.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
What type of polygon is this figure
Answer:
Step-by-step explanation:
what are the two related linear equations for |x – 2| = 5.
The two related linear equations for |x – 2| = 5 are x - 2 = 5 and x - 2 = -5
How to determine the related equations?From the question, we have the equation to be
|x - 2| = 5
This equation is an absolute value function
The general rule of an absolute value function is that:
An equation represented as y = |x| can be expressed as y = x or y = -x
Using the above guideline as a guide, we have the following representation of |x – 2| = 5
x - 2 = 5 and x - 2 = -5
Hence, the equations are x - 2 = 5 and x - 2 = -5
Read more about absolute value at
https://brainly.com/question/24368848
#SPJ1
I need help please!!
Answer:
9/14 (9 over 14)
Step-by-step explanation:
Use the figure below for the following problems (not drawn to scale).
Given: m/1 = 70.
What is m25?
O a
.Ob
Oc
Od
125⁰
40°
70°
55°
2
76
The value of m∠5 is 125°. option A is the correct answer
From the question, we have
m∠1=70°
As the sides are equal.
∠2=∠3=(180°-70°)/2
= 55°
∠5 = 180°-55° (Linear pair)
= 125°
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
To learn more about subtraction visit: https://brainly.com/question/2346316
#SPJ1
Someone please help me out on this ( this is due tonight )
Answer the 2 question in the photo!
Answer:
1. 190 degrees
2.
For the red triangle
-2,4, -4,2 -2,1
For the blue triangle
-2,-5 -5,-5 -7,-4
I don't know if this is correct but I hope this helps :)
PLEASE HURRY !! A cone has a radius of 10 inches and a height of 6 inches.
What is the volume of the cone to the nearest tenth in ³.
Use 3.14 to approximate pi
628 in^3
157 in^3
125.6 in^3
634in^3
Volume of the cone is 628 In^3
What is cone?
A cone can be seen as a set of non-congruent circular disks that are stacked on one another such that the ratio of the radius of adjacent disks remains constant.
Cones typically have pyramidal shapes with circular cross sections. A right cone is a cone with the vertex located above the base's middle. Right circular cone is another name for it. If you know the height and radius of a cone and plug those values into a formula, you can quickly determine the volume of a cone.
The volume of a cone defines the space or the capacity of the cone. A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called apex or vertex. A cone is formed by a set of line segments, half-lines or lines connecting a common point, the apex, to all the points on a base that is in a plane that does not contain the apex.
According to the question
The volume of a cone = (1/3) πr2h cubic units
r=10 inch
h=6 inch
π=3.14
Volume=0.33(3.14)(10)(10)(6)
volume=628 [tex]inch^3[/tex]
Learn more about volume of cone from the link below
https://brainly.com/question/22252398
#SPJ1
I need Help pleaseeeeeeeeeeeeeeee
Answer:
D
Step-by-step explanation:
500 user in a day that mean in 2 days you get 1000 user cause the double of 500 is 1000