Given:
The functions are:
[tex]f(x)=\log_4x[/tex]
[tex]g(x)=f\left(\dfrac{1}{3}x\right)[/tex]
The function f(x) is dilated to become g(x).
To find:
The effect on f(x).
Solution:
Transformation is defined as:
[tex]g(x)=f(kx)[/tex] ...(i)
Where, k is the factor of horizontal stretch and compression.
If 0<k<1, then the graph of f(x) stretched horizontally by factor [tex]\dfrac{1}{k}[/tex].
If k>1, then the graph of f(x) compressed horizontally by factor [tex]\dfrac{1}{k}[/tex].
It is given that
[tex]g(x)=f\left(\dfrac{1}{3}x\right)[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]k=\dfrac{1}{3}[/tex]
Therefore, the graph of f(x) stretched horizontally by factor [tex]3[/tex].
which two consecutive integers does q lie
Answer:
it lies between P and R because I tootk the test
write 7 pi divided by 60 in degrees
Answer:
You have reached the concluding section of our information about (7/60)×π rad to deg.
7pi/60 rad = 21°.
The radian measure is the standard unit of measure in the areas of math involving a circle like the sine and cosine function, just to name two trigonometric functions.
Using our calculator, formula and information, you have everything for changing the angle measurement at your disposal.
If you have found our post searching for 7pi/60 radian to degrees or a similar term, then you have gotten your answer as well: 7pi/60 rad ⇔ 21°.
Answer:210
Step-by-step explanation: took the test
What is an approximate average rate of change of the graph from X =22 and x = 26
Answer:
it is (22+26)/2=24
Step-by-step explanation:
HELPPPP PLSSSS Which is true about the polynomial ? It is a binomial with a degree of 2. It is a binomial with a degree of 3. It is a trinomial with a degree of 2. It is a trinomial with a degree of 3.
i am not getting it what are you asking
Brian rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is prime
The sum of the faces is going to fall in the range {2, 3, 4, …, 12}, which contains five prime numbers {2, 3, 5, 7, 11}. You can only have one sum at a time, so these outcomes are mutually exclusive. Then
Pr[sum is prime] = Pr[sum = 2] + Pr[sum = 3] + … + Pr[sum = 11]
• sum = 2 can only happen in 1 way (1 + 1)
• sum = 3 can happen in 2 ways (1 + 2, 2 + 1)
• sum = 5 can happen in 4 ways (1 + 4, 2 + 3, 3 + 2, 4 + 1)
• sum = 7 can happen in 6 ways (1 + 6, 2 + 5, …, 6 + 1)
• sum = 11 can happen in 2 ways (5 + 6, 6 + 5)
There are a total of 6² = 36 possible sums that can be rolled, each with probability 1/36 of occurring, so the probability of getting a prime sum is
(1 + 2 + 4 + 6 + 2)/36 = 15/36 = 5/12
Finding angle measures given two intersecting lines
Answer:
66, 114, 114
Step-by-step explanation:
angle 3=angle 1=66
angle 2=angle 4=180- angle 3=114
Calculate the sum of the first 30 terms in the sequence that begins with 70,65,60
[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle \Large \boldsymbol{} a_1=70 \ ; \ d=-5 \\\\S_n=\frac{a_1+a_n}{2} \cdot n \ ; \ a_n=a_1+(n-1)d \Longrightarrow \\\\\\ S_{30}=\frac{70+70-29\cdot5}{2} \cdot 30 =-75 \\\\\\Answer: S_{30}=-75[/tex]
Question 4 of 10
Solve the triangle. Round your answers to the nearest tenth.
find the volume of each figure. Round to the nearest tenth if necessary.
Answer:
112
Step-by-step explanation:
The volume is given by l*b*h=4*4*7=112
state the y-intercept of the line y = 3x -7
Answer:
-7
Step-by-step explanation: kahn
Answer:
(0,-7)
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 3x-7
The slope is 3 and the y intercept is -7
(0,-7)
2) John saved $5 in the first week of a year and then increased her weekly
savings by $1.75. If the nth week, her weekly savings become $20.75, find n.
Answer:
n = 9
Step-by-step explanation:
20.75 = 1.75n + 5
20.75 - 5 = 1.75n
15.75 = 1.75n
------- -------
1.75 1.75
9 = n
fx) = x2 - 8x + 15
g(x) = x-3
h(x) = f(x)/g(x)
Answer: [tex]\Large\boxed{h(x)=x-5}[/tex]
Step-by-step explanation:
[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppp\displaystyle\ \Large \boldsymbol{} h(x)=\frac{f(x)}{g(x)} =? \\\\\\f(x)=x^2-8x+15\\\\\\x^2-8x+\underbrace{15+1-1}_{15}=0 \\\\\\\underbrace{x^2-8x+16}_{(x-4)^2}-1=0 \\\\\\(x-4)^2-1\Longrightarrow f(x)=(x-5)(x-3)[/tex] [tex]\displaystyle\ \Large \boldsymbol{} h(x)=\frac{(x-3)(x-5)}{(x-3)}=\boxed{x-5}[/tex]
when a pen is sold at a discount of 15%.There is a gain of rs 10.But if it is sold at 25% discount there is a loss of rs 2.Find the Mark price of the pen.
The mark price of the pen is 120 rs
The first step is to write out the parameters given the question
Discount= 15%
Gain= rs 10
Discount= 15%
loss= rs
When a pen is sold at a discount of 15% there is a gain of rs 10
When the pen is sold at 25% discount there is a loss of rs 2
The mark price of the pen can be calculated as follows
15% = c.p + 10 rs
25 % = c.p - 2 rs
25%-15% = 10 rs +2 rs
10% = 12 rs
10/100 = 12 rs
0.1= 12 rs
12/0.1
= 120 rs
Hence the mark price of the pen is 120 rs
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Mark Price: RS. 120
The Gain Function is the difference between Resulting Price, which is the Mark Price including Discount Rate, and the Reference Price, where positive result represents Net Gain, as negative result represents Net Loss. Gain Function is described below:
[tex]G = \left(1-\frac{r_{D}}{100} \right)\cdot P_{M}-P_{R}[/tex] (1)
Where:
[tex]G[/tex] - Gain function, in monetary units.
[tex]r_{D}[/tex] - Discount rate, in percentage.
[tex]P_{M}[/tex] - Mark price, in monetary units.
[tex]P_{R}[/tex] - Reference price, in monetary units.
The Mark Price of the pen is the price shown on the label of the product, whereas the Reference Price is the purchase cost of the product from provider.
Based on what it is written on statement we have the following system of linear equations:
1) When a pen is sold at a discount of 15 %. There is a gain of RS. 10: ([tex]G = 10[/tex], [tex]r_{D} = 15[/tex])
[tex]\left(1-\frac{15}{100} \right)\cdot P_{M} - P_{R} = 10[/tex] (2)
2) But if it is sold at 25 % discount there is a loss of RS. 2: ([tex]G = -2[/tex], [tex]r_{D} = 25[/tex])
[tex]\left(1-\frac{25}{100} \right)\cdot P_{M} - P_{R} = -2[/tex] (3)
The solution of the resulting system of linear equations is:
[tex]P_{M} = 120[/tex], [tex]P_{R} = 92[/tex]
The mark price of the pen is RP. 120.
What is the solution to the system of equations graphed below? A (2, 5) B(-5, -3) C(0, 4) D(1, 1)
it's def c because that's where the intersection is, which is the solution (there is only one solution)
What is the domain of the function y=2.VX-6?
-00
0
3
6
Answer:
7675
Step-by-step explanation:
f76r87fgvbhdty
The domain of the function y=2.√(x-6) is all real numbers greater than or equal to 6.
What is a domain?The domain of the function is defined as the set of all the possible values of the function.
The square root function can only take non-negative values, so the expression inside the square root must be greater than or equal to zero:
x - 6 ≥ 0
To calculate the domain of a function, you need to determine the set of all possible input values (also known as the independent variable) that the function can accept and produce a valid output value (also known as the dependent variable). Here are the general steps to find the domain of a function:
Solving for x, we get:
x ≥ 6
Therefore, the domain of the function y=2.√(x-6) is all real numbers greater than or equal to 6. In interval notation, we can write the domain as [6, ∞).
To know more about the domain of the function follow
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Determine the percent of change. Round to the
nearest whole percent if necessary. State whether the
percent of change is an INCREASE or DECREASE.
Original: 250
New 100
Pls help
Answer:
DECREASE
Step-by-step explanation:
Not sure
But Hope It Help
What is the equation of the line of best fit for the following data? Round the
slope and y-intercept of the line to three decimal places.
Answer:
Step-by-step explanation:
I am going to assume that you are doing this on your calculator using the stat button as opposed to having to find it by hand which is so extremely long and drawn out, you'd be dead by the time we found the equation...
The equation of the line of best fit is
y = 1.383x - 1.526
I would explain to you how to do that, but it's a very involved process on your calculator. Find out how to do it and it's the easiest thing in the world!!!
The required equation of the line is y = 0.667x + 2.334
From the table given equation of the line is determined.
x = 4 7 10 12 13
y = 5 7 12 14 18
A line is a curve showing the shortest distance between 2 points.
Standard equation of line, y =mx + c
The slope of equation m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] and c is y intercept.
m = 7-5/7-4
m = 2/3
Now put m in the standard equation
y = 2x/3 + c - - - - -(1)
to find the value of c we will put a point (7, 7) in the equation.
7 = 7*2/3 + c
c = 7 - 14/3
c = (21-14)/3
c = 7/3
Put c in equation 1
y = 2x/3 + 7/3
y = 0.667 x +2.334
Thus, The required equation of the line is y = 0.667 x +2.334
Learn more about lines here:
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Help Now Please Find the surface area sphere
Answer:
900pi
Step-by-step explanation:
formula for sphere's surface area :
4πr^2
radius = 15 (30/2)
4*pi*15^2 = 900pi
Answer:
The surface area is 2827.43
Step-by-step explanation:
This is the formula:
A= 4 π r^2= 4· π· 15^2 = 2827.43339
Hope this helps you!
HELP BRAINIST AND POINT
Answer:
90 degrees
Step-by-step explanation:
general Pythagoras
c² = a² + b² - 2ab×cos(ABC)
with c being the side opposite of the angle ABC.
c = AC
a = AB
b = BC
(0-15)² + (0-0)² = (0-9.6)² + (0-7.2)² + (9.6-15)² + (7.2-0)² - 2×sqrt((0-9.6)²+(0-7.2)²)×sqrt((9.6-15)²+(7.2-0)²)×cos(ABC)
225 = 92.16 + 51.84 + 29.16 + 51.84 - 2×12×9×cos(ABC)
225 = 144 + 81 - 216×cos(ABC)
225 = 225 - 216×cos(ABC)
0 = cos(ABC)
ABC = 90 degrees
Trey took 5/4
hours to clean the bedroom. He took1/2
hours to clean the den. How much longer did it take Trey to clean the bedroom?
Write your answer as a mixed number in simplest form.
Answer:
3/4 more hours
Step-by-step explanation:
Hours taken to clean bedroom = 5/4
Hours taken to clean den = 1/2
How much more = 5/4 - 1/2
5-2/4 (common denominator)
3/4 more hours (It's a propper fraction, so we can't write it as a mixed number)
Answer from Gauthmath
What is the circumference of a circle with a diameter of 6 feet? Use 3.14 for pie.
Answer:
18.84
Step-by-step explanation:
Answer:
18.84
Step-by-step explanation:
consider the lines and the transversal drawn in coordinate plane below.
Answer:
i dont know man
Step-by-step explanation:
i dont know
i need help i can't get the right answer
Answer:
x = 50
Step-by-step explanation:
I guess, this diagram tells us that the lines are parallel.
that means that they cut the third line at the exact same angles.
and that means
3x - 26 = 2x + 24
x - 26 = 24
x = 50
3x-26=2x+24
3x-2x=24+26
x=50
please mark this answer as brainlist
find the area to this question
Answer:
170.54m²
Step-by-step explanation:
there are three shapes
triangle: is 1/2*3*5=7.5
square is 6*5=30
circle=3.14*6²=133.04
7.5+30+133.04=170.54
answer is 170.54
Help please I don’t understand this
Answer:
x=-2
sorry i messed up coord val :/
Step-by-step explanation:
Answer:
x = -2
Step-by-step explanation:
a parabola is symmetric (has a mirror image)
a parabola has ONE vertex (a highest or lowest point).
thus a line that goes through the vertex is it's axis of symmetry.
x = 5 , x=99, x=102 are vertical lines that intersect the x axis no matter what the y value is....
your axis of symmetry is a line that looks like X= SOMETHING
the "something" is the X value of the vertex, which is (-2,3)
this the equation x = -2 is the answer ... see the image
5. Which question is a statistical question?
Select Yes or No.
A. How long is lunch period at your school?
O Yes
Ο O No
B. How old is the oldest student in your
class? be
O Yes Ο Νο
C. How many classrooms are there in the
buildings of your school?
O Yes
D. What are the ages of all the people in
Ο O No
your class?
O Yes
Ο O No
How will the solution of the system y > 2x + 2/3 and y <
2x + 1/3 change if the inequality sign on both inequalities
is reversed to y < 2x + 2/3 and
y> 2x + 1/3?
Answer:
The solution will go from NO common solutions to infinite solutions between the 2 parallel lines.
Step-by-step explanation:
In the original case all solutions for equation 1 are above line 1 (y >) and all solutions for equation 2 are below line 2 (y <), so there is no overlap and therefore no common solutions. When reversed, all solutions for line 1 are below line 1 and all solutions for line 2 are above line 2. So the overlap is everything between the two lines.
Answer:
The shaded area would reverse on both inequalities.
The graphs do not overlap until the signs are reversed.
There are an infinite number of solutions in the system once the signs are reversed.
There are no solutions before they are reversed.
Step-by-step explanation:
edge 2021
Can someone explain how you got the answer!!
9514 1404 393
Answer:
20 square units
Step-by-step explanation:
The area is given by the formula ...
A = bh
where b is the base of the parallelogram, and h is the perpendicular distance between the parallel bases. Using the numbers from the figure, we have ...
A = 5·4 = 20 . . . . square units
_____
Additional comment
You will notice this is the same formula as is used for a rectangle. You can consider the parallelogram to have the same area as a rectangle of these dimensions if you look at what happens when you cut the right triangle from the right end and add it to the left end. The result is a rectangle 5 units wide and 4 units high.
The same formula applies even if the skew is so great that the bases do not overlap. (That much skew would not result in a triangle of the kind shown in this diagram.)
helpppppppppppppppppppppppppppppp
Answer:
D
Step-by-step explanation:
because the new number is changing to a new and all old is ready.
The product of¾ xy and 3/4is ____________.
Answer:
9/16xy
Step-by-step explanation:
Multiply through by 3/4
(3/4xy) × (3/4)
numerator =(3×3) = 9
denominator = (4×4) = 16
Simplifying = 9/16xy
