The equation of g(x) is g(x) = 6x + 11
Step-by-step explanation:
Let us revise some transformation
A vertical stretching is the stretching of the graph away from the x-axis, If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by kIf the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k∵ f(x) = 2x + 5
∵ The graph of f(x) is stretched vertically by scale factor 3
- That means multiply f(x) by 3
∴ The equation of the new graph is 3(2x + 5)
∵ The new graph is translated 4 units down
- That means subtract 4 from 3(2x + 5)
∴ The equation of g(x) is g(x) = 3(2x + 5) - 4
- Simplify the equation of g(x)
∴ g(x) = 3(2x) + 3(5) - 4
∴ g(x) = 6x + 15 - 4
- Add the like terms in the right hand side
∴ g(x) = 6x + 11
The equation of g(x) is g(x) = 6x + 11
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Will mark brainliest and 12 points
Answer:
the third one
Step-by-step explanation:
hope it helps
Use unit multipliers to convert 50 square meters to square inches
50 square meters is equal to 77500 square inches
Solution:
Given that we have to convert 50 square meters to square inches
Use the following conversion factor
1 meter is equal to 39.3701 inch
That is,
[tex]1\ meter = 39.3701\ inch[/tex]
Now frame the conversion factor for square meters to square inches
[tex]1\ meter\ \times meter = 39.3701 \times 39.3701\ inch\ \times inch\\\\1\ m^2 = 1550\ in^2[/tex]
Now convert 50 square meters to square inches
Muliply both the sides by 50
[tex]1 \times 50\ m^2 = 1550 \times 50\ in^2\\\\50\ m^2 = 77500\ in^2[/tex]
Thus 50 square meters is equal to 77500 square inches
Which order pair is not a solution to the equation y = 2x² - 1.
(0, 6)
(3, 17)
(2, 7)
(-1, 1)
Answer:
(0, 6)
Step-by-step explanation:
plug each x in and find the y
Answer:
(0, 6)
Step-by-step explanation:
PLEASE HURRY! ;)
Which statements are true?
A;When triangle ABC is reflected over the y-axis to create triangle A'B'C' , the coordinates for B' are(1, -1) .
B;When triangle ABC is rotated 90 degrees clockwise about point A to create triangle A'B'C' , the coordinates for B' are (3,3]
C When triangle ABC is dilated from the origin by a scale factor of 1\4
to create triangle A'B'C', the coordinates for B'are (4,4)
D When triangle ABC is translated 2 units to the left and 1 unit down to create triangle A'B'C' , the coordinates for B' are (-1, 0)
E When triangle ABC is dilated from the origin by a scale factor of 5 to create triangle A'B'C', the coordinates for B' are (5,5)
The correct answer is: When triangle ABC is translated 2 units to the left and 1 unit down to create triangle A'B'C' , the coordinates for B' are (-1, 0). The true statement is D.
Let's analyze each statement:
A; When triangle ABC is reflected over the y-axis to create triangle A'B'C' , the coordinates for B' are (1, -1) .
To reflect over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. If the coordinates for B are (x, y), then after reflecting, the x-coordinate becomes -x. Since B has coordinates (1, 1), after reflection, B' will have coordinates (-1, 1). So, statement A is false.
B; When triangle ABC is rotated 90 degrees clockwise about point A to create triangle A'B'C' , the coordinates for B' are (3,3]
Rotation of 90 degrees clockwise about a point involves swapping x and y coordinates and negating the new x-coordinate. The point A is not given, but assuming it's (0, 0), if B has coordinates (x, y), then after rotation, B' will have coordinates (y, -x). If A is (0, 0) and B is (3, 1), after rotation, B' will have coordinates (1, -3), not (3, 3). So, statement B is false.
C; When triangle ABC is dilated from the origin by a scale factor of 1/4 to create triangle A'B'C', the coordinates for B' are (4,4)
Dilating by a scale factor of 1/4 means multiplying each coordinate by 1/4. If B has coordinates (x, y), then after dilation, B' will have coordinates (1/4 * x, 1/4 * y). Since B has coordinates (4, 4), after dilation, B' will have coordinates (1, 1). So, statement C is false.
D; When triangle ABC is translated 2 units to the left and 1 unit down to create triangle A'B'C' , the coordinates for B' are (-1, 0)
Translation involves adding/subtracting values to x and y coordinates. If B has coordinates (x, y), then after translation by (-2, -1), B' will have coordinates (x - 2, y - 1). Since B has coordinates (1, 1), after translation, B' will have coordinates (-1, 0). So, statement D is true.
E; When triangle ABC is dilated from the origin by a scale factor of 5 to create triangle A'B'C', the coordinates for B' are (5,5)
Dilating by a scale factor of 5 means multiplying each coordinate by 5. If B has coordinates (x, y), then after dilation, B' will have coordinates (5 * x, 5 * y). Since B has coordinates (4, 4), after dilation, B' will have coordinates (20, 20), not (5, 5). So, statement E is false.
So, the true statement is D.
-12.11-10.5=75.6-3.5x
Answer:
x = 28.06
Step-by-step explanation:
-12.11-10.5=75.6-3.5x
Put all the integers on one side and X on the other.
-12.11 - 10.5 - 75.5 = -3.5x
-98.21 = -3.5x
-98.21/-3.5 = x
x = 28.06
compare -6/11 -2/3 ^ = ^
Answer:
-40/33
Step-by-step explanation:
Answer:
-6/11 > -2/3
Step-by-step explanation:
6/11 = 18/33
2/3 = 22/33
Since 18/33 < 22/33 then 6/11 < 2/3 then -6/11 > -2/3
Find the equation of a line with the given points.
(0, -2) (-2, 10)
Oy=-2x + 10
Oy = 4x + 10
Oy=x-2
Oy=-6x - 2
Answer:
y=-6x-2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(10-(-2))/(-2-0)
m=(10+2)/(-2)
m=12/-2
m=-6
y-y1=m(x-x1)
y-(-2)=-6(x-0)
y+2=-6(x)
y+2=-6x
y=-6x-2
Evaluate 2(x-4) + 3x - x2 for x = 3.
O
A. -6
O
B. 2
a
O c. 6
OD. -2
Answer:
D. -2.
Step-by-step explanation:
2(x-4) + 3x - x2 for x = 3
= 2(3-4) + 3(3) - 3^2
= 2(-1) + 9 - 9
= -2 + 9 - 9
= -2.
a wave has a wavelength of 5m and a frequency of 68 hertz what is the speed
Answer:
Therefore the Speed of a wave is 340 m/s.
Step-by-step explanation:
Given:
Wave Length = 5 m
Frequency = 68 hertz
To Find:
Speed = ?
Solution:
Wave Speed:
Wave speed is the distance a wave travels in a given amount of time, such as the number of meters it travels per second.
Wave speed is related to wavelength and wave frequency.
The Formula is given by
[tex]Speed = Wavelength\times Frequency[/tex]
Substituting the values we get
[tex]Speed = 5\times 68=340\ m/s[/tex]
Therefore the Speed of a wave is 340 m/s.
A 50-foot tree casts a shadow 9 feet long. The sine of the angle between the ground and the line that connects the top of the shadow to the top of the tree is approximately
Final answer:
The sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree, given a 50-foot tree and a 9-foot shadow, is approximately 0.984, calculated using the definition of sine in a right triangle and the Pythagorean theorem.
Explanation:
The question involves finding the sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree, given that a 50-foot tree casts a 9-foot long shadow. In this scenario, we can visualize a right triangle where the tree represents the opposite side (height), the shadow represents the adjacent side (base), and the hypotenuse is the line from the top of the tree to the end of the shadow on the ground.
To find the sine of the angle, we use the definition of sine in a right triangle, which is sine(angle) = opposite / hypotenuse. However, before we can do that, we need to determine the length of the hypotenuse using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).
Let's calculate:
a (opposite) = 50 feet (Height of the tree)
b (adjacent) = 9 feet (Length of the shadow)
c (hypotenuse) = √(50² + 9²) = √(2500 + 81) = √2581 = 50.8 feet (approximately)
Now, we can calculate the sine of the angle:
sine(angle) = opposite / hypotenuse = 50 / 50.8 ≈ 0.984
Therefore, the sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree is approximately 0.984.
the regular shipping fee (in dollars) for an online computer store is given by the expression 0.5w + 4.49 where w is the weight (in pounds) of the item. the fee (in dollars) for rush delivery is given by 0.99w + 6.49. You purchase a 26.5 pound computer. How much do you save by using regular shipping instead of rush delivery?
By calculating the shipping fees for regular and rush delivery for a 26.5 pound computer, we find that regular shipping saves approximately 14.90 dollars.
Explanation:We must first calculate the fee for each method and then subtract the regular "shipping fee" from the rush delivery fee to find the savings.
Using the given expression, the regular shipping fee for a 26.5 pound computer is: 0.5*26.5 + 4.49 = 17.74 dollars. Meanwhile, the rush delivery fee for the same computer, using the other given expression, would be: 0.99*26.5 + 6.49 = 32.635 dollars.
Subtracting the regular fee from the rush fee, we find: 32.635 - 17.74 = 14.895 dollars. Therefore, you save about 14.90 dollars by choosing regular shipping over rush delivery.
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which inequality represents the graph below ?
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
What is the vertical asymptote of the function f(x) = 3 log(x + 3)?
The vertical asymptote of the function f(x) = 3 log(x + 3) is x =
.
The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3
Step-by-step explanation:
A symptote is a line that a curve approaches but never touches
The vertical asymptote of a logarithmic function is at the zero of the argumentf(x) = log(argument) has vertical aymptotes at argument = 0∵ f(x) = 3 ㏒(x + 3)
∵ The argument is (x + 3)
- Equate the argument by zero
∵ x + 3 = 0
- Subtract 3 from both sides
∴ x = -3
- The vertical asymptote of a logarithmic function is at the zero
of the argument
∴ The vertical asympotote of f(x) is x = -3
The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3
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Answer:
-3
Step-by-step explanation:
plato
Pls help me!!! Will mark brainliest!!!
These 4 questions answered and work shown
For Reference): Topics: Trig functions exact values and reciprocal trig functions exact values
Answer:
25) If f(x) = sin ([1/3] x) , find f(π/2).
Substitute with x = π/2
f(π/2) = sin ([1/3] *[π/2]) = sin (π/6) = 1/2
======================================
26) If f(x) = cos (2x) , find f(3π/4).
Substitute with x = 3π/4
f(3π/4) = cos ( 2 * 3π/4) = cos ( 3π/2) = zero.
======================================
27) If f(x) = sin (2x) + cos (3x) , find f(π/4)
Substitute with x = π/4
f(π/4) = sin ( 2 * π/4) + cos ( 3 * π/4) =
= sin ( π/2) + cos ( 3π/4)
= 1 - 1/(√2)
= 0.293
======================================
28) f(x) = tan (5x) - sin (2x) , find f(π/6).
Substitute with x = π/6
So, f(π/6) = tan (5 * π/6) - sin ( 2 * π/6)
= tan (5π/6) - sin (π/3)
= -1/(√3) - (√3)/2
= -1.443
6x−4=2(3x−2)
x = ___
(type your answer as a number, "no solution" or "infinite solutions")
Answer:
0=0
Step-by-step explanation:
Simply,there is no solution.
Evaluate -3x + 5( x +2)
Answer:
Step-by-step explanation:
Answer:
2x+10
Step-by-step explanation:
-3x+5(x+2)
-3*x+5*x+5*2
-3*x+5*x+10
(-3+5)*x+10
(-2)*x+10
2x+10
What is (8-2x2) to the power of two equal using pemdas?
Answer
(8-2×2) to the power of 2 is 16
Work: 2×2=4
8-4=4
4 to the power of 2 =16
Answer:
144
Step-by-step explanation:
in pemdas always do parenthesis first so it will be 8-2x2= 144 because
8 - 2= 6 x 2=12²=144The information from the settings menu titled "About" for an Apple iPod is given.
About
Songs
3639
Videos
32
Photos
0
Capacity
62.5 GB
Available
35.0 GB
Version
1.1.1
S/N
4H534PG7TY1
Model
MA148LL
Format
Windows
What percent of the memory capacity is still available? Round to the nearest percent. (GB stands for gigabytes.)
Answer:
Step-by-step explanation:
total capacity = 62.5 GB
available capacity = 35.0 GB
35 is what percent of 62.5
35 = x% * 62.5
35 / 62.5 = x%
0.56 = x%
56% = x <=====
56% of the memory capacity is still available.
To calculate the percentage of memory capacity that is still available, we can use the available capacity and total capacity information provided.
Given:
Capacity: 62.5 GB
Available: 35.0 GB
To find the percentage, we divide the available capacity by the total capacity and multiply by 100:
Percentage = (Available / Capacity) x 100
Percentage = (35.0 GB / 62.5 GB) x 100
Percentage ≈ 56%
Therefore, 56% of the memory capacity is still available.
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Please help me guys with this than you
Answer:theres nothimh here to answer
Step-by-step explanation:
Complete the inequality statement
7/10 ___ 11/20
> < =
Answer:
The person up there is right just saying:)
Step-by-step explanation:
what did the harlem renaissance celebrate accomplished and lead to in the early 1900’s
Answer:
The migration of the African-Americans to Harlem in the USA empowered the African-Americans in the society in the early 1900s. This was one of the greatest accomplishments of the African-Americans in history.
Explanation:
The "Harlem Renaissance" was originally called the "New Negro Movement." During the "Reconstruction Era," many of the African Americans felt a newfound empowerment in the society. They started leaving the South, where most of them were enslaved and maltreated. Many of them moved to other places such as "Harlem" in New York City. It became an ideal destination for many "Negros" and their number increased over time. This then became an African-American neighborhood.
African-Americans started producing plays with actors of their descent. Several Negro poets emerged describing the life of the African-Americans. Negros became more literate and able when it comes to expressing themselves in the society. They even had their own newspaper known as "The New Negro Movement."
What is the solution to the equation
?
Answer: [tex]x=9[/tex]
Step-by-step explanation:
Alright, lets get started.
[tex]log_{6}4x^2-log_{6}x=2[/tex]
Using the property of logs : [tex]log (m) - log(n)=log\frac{m}{n}[/tex]
[tex]log_{6}\frac{4x^2}{x}=2[/tex]
[tex]log_{6}4x=2[/tex]
Using the property of logs : [tex]if \ log_{a}m=n, \ then \ a^n=m[/tex]
So,
[tex]6^2=4x[/tex]
[tex]4x=36[/tex]
Dividing 4 in both sides
[tex]x=9[/tex] ...................... Answer
Hope it will help :)
Answer:
x = 9
Step-by-step explanation:
Determine the defined range
[tex]log^6 (4x^2) - log^6 (x) = 2, x = (0, + ∞)[/tex]
Use log^a (x) - log^a (y) = log^a (x/y) to simplify the expression
[tex]log6 (\frac{4x^{2} }{x} )= 2[/tex]
Simplify the expression
log^6 (4x) = 2
Convert the logarithm into an exponential form using the fact that log^a (x) = b is equal to x = a^b
[tex]4x=6^{2}[/tex]
Evaluate the power
4x = 36
Divide both sides of the equation by 4
x = 9, x = (0, + ∞)
Check if the solution is the defined range
x = 9
Evaluate –x + (–7.5) for x = 6.3.
Answer:
Step-by-step explanation:
The answer is 1.2, you want to replace the x with the 6.3 and then the -7.5 ends up turning into a positive. You then add the two together -6.3 + 7.5 = 1.2
Ms.Griffith lives on one of the highest floors in her apartment building. The elevator goes up one floor every 10.2 seconds. Along the way, it stops for a total of 45.8 seconds for people to get out. If it takes her 158 seconds to travel from the lobby to her apartment, what floor does she live on?
Answer:
Ms. Griffiths lives on 3rd floor
Step-by-step explanation:
The elevator moves 10.2 seconds from one floor to another and stops for 45.8 seconds for people to exit. Thus, add: 10.2 seconds + 45.8 seconds = 56 seconds
If it takes her 158 seconds to travel from the lobby to her apartment, then 158 seconds/56 seconds = 2.8 = 3 (approximately).
Therefore, she lives on 3rd floor.
Mathematically, the values ought to be 168 seconds /56 seconds = 3.
5 6/7-1 1/2
difference?
Answer: 4 5/14
Step-by-step explanation:
Hep me ASAP!!!! A.-2 B.4 C.7-3sqrt3 D.7- sqrt3
Answer:
7 - 3[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given
3 + [tex]\sqrt{x+7}[/tex] - [tex]\sqrt{3x}[/tex] ← substitute x = 9
= 3 + [tex]\sqrt{16}[/tex] - [tex]\sqrt{27}[/tex]
= 3 + 4 - [tex]\sqrt{9(3)}[/tex]
= 7 - 3[tex]\sqrt{3}[/tex]
The circumference of a circle is 43.96 millimeters. What is the circle's radius?
3. At the beginning of the day, a water tank contained 526.8 gallons of water. During the day,
some of the water was used to water a garden. At the end of the day, the water tank contained
318.05 gallons of water.
What was the total amount of water used that day?
a. 202.75 gallons
b. 208.75 gallons
C. 208.85 gallons
d. 210.80 gallons
Answer:
208.85
Step-by-step explanation:
It is 208.85 because when you have .8 + .05 =.85
Answer:
Step-by-step explanation:
the total amount of water used that day = 526.80 - 318.05 = 208.75 gallons.
8. Mr. Gardner is contemplating which shullle service to take lo the airport. Fost
Shullle charges a $5 pick-up fee and $0.25 per mile. Steady Shullle cholges a $2
pick-up fee and $0.50 per mile.
Part A: When will the two plans cost the same amount
Part B: If the airport is 20 miles away, which company should Mr. Gardner choose?
Answer:
Frosts second mile and steadys 6th mike
Step-by-step explanation:
Part A: The two plans will cost the same amount when the distance to the airport is 12 miles.
Part B: For a 20-mile distance, Mr. Gardner should choose Fost Shuttle, costing $10 compared to $12 for Steady Shuttle.
Let's solve Part A first:
Part A:
Let's denote the distance to the airport as d miles.
For Fost Shuttle:
Cost = Pick-up fee + Cost per mile × Distance
Cost = $5 + $0.25 × d
For Steady Shuttle:
Cost = Pick-up fee + Cost per mile × Distance
Cost = $2 + $0.50 × d
Now, we'll set up an equation to find when the two plans cost the same amount:
[tex]\[5 + 0.25d = 2 + 0.50d\][/tex]
Solving for d:
[tex]\[0.25d - 0.50d = 2 - 5\]\[-0.25d = -3\]\[d = \frac{-3}{-0.25}\]\[d = 12\][/tex]
So, the two plans will cost the same amount when the distance is 12 miles.
For Part B:
Given the distance is 20 miles, let's calculate the cost for each company:
For Fost Shuttle:
Cost = $5 + $0.25 × 20 = $5 + $5 = $10
For Steady Shuttle:
Cost = $2 + $0.50 × 20 = $2 + $10 = $12
Comparing the costs, Mr. Gardner should choose Fost Shuttle as it costs $10 compared to $12 for Steady Shuttle.
64/9 improper fraction
improper fraction
Answer:
If you want the mixed number,it is 7 1/9
Step-by-step explanation:
Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.