Answers
Answer:
[tex]\large{\boxed{\sf g(x) = \dfrac{1}{2} |x - 4| +7}}[/tex]
Explanation:
Absolute value of a graph formula:
y = a |x -h| + kIdentify the vertex : (h, k) = (4, 7)
Take two points: (4, 7), (6, 8)
[tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \dfrac{8-7}{6-4} \ = \dfrac{1}{2}[/tex]
Putting them together : [tex]\bf g(x) = \dfrac{1}{2} |x - 4| +7[/tex]
Answer:
[tex]g(x)=\dfrac{1}{2}|x-4|+7[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]
-----------------------------------------------------------------------------------------
Parent function: [tex]f(x)=|x|[/tex]
(with vertex at the origin)
From inspection of the graph, the vertex of the transformed function is at (4, 7). Therefore, there has been a translation of:
4 units right7 units up[tex]\implies f(x-4)+7=|x-4|+7[/tex]
From inspection of the graph, we can see that it has been stretched parallel to the y-axis:
[tex]\implies a\:f(x-4)+7=a|x-4|+7[/tex]
The line goes through point (0, 9)
Substituting this point into the above equation to find [tex]a[/tex]:
[tex]\implies a|0-4|+7=9[/tex]
[tex]\implies 4a=2[/tex]
[tex]\implies a= \dfrac{1}{2}[/tex]
Therefore,
[tex]\implies g(x)=\dfrac{1}{2}|x-4|+7[/tex]
Related Questions
The first term in a sequence is 72. The pattern follows the rule add 31. What are the next four terms?
Answers
Answer: 103, 134, 165, 196
Step-by-step explanation:
Second term: 72+31 = 103
Third term: 103+31 = 134
Fourth term: 134+31 = 165
Fifth term: 165+31 = 196
A train travels at a speed of 140km per hour. How many kilometers does it travel in:
a)1 hours b)2 hours c)3 hours d)20 minutes
Answers
Answer:
140kilo in 1hr and 280kilo in 2hr and 420kilo in 3hr and 28kilo in 20 min.
find the area figure below
Answers
Answer:
Area = 1
Step-by-step explanation:
I;ve attached my work below
Hope it helps, Let me know if you have any questions/concerns !
Have a nice rest of your day :)
help with math problem.
Answers
Answer:
Number of logs:
1. 48
2. 14
3. 90
4. 48
5. 100
Total: 300
Step-by-step explanation:
Just multiply the height with the number of trees then divide by 6. This is in theory if the length of all the trees were conjoined, as there would most likely just be less, then 300. This is because the remainder would be that of the multiplied trees height instead of getting the remainder of wood from each tree. So in case you want to try doing that option, simply divide the height first in feet by 8, then multiply that by the number of trees to give you an accurate answer of logs.
Answer:
see attached
total: 300 logs
Step-by-step explanation:
When calculations are repetitive, it is convenient to let a spreadsheet do them.
Here, the number of logs per tree is found by dividing the tree height by 8 feet. The number of logs from trees that height will be found by multiplying the number of trees by the number of logs that height will give.
The total number of logs is the sum of the numbers from all the tree heights.
__
The total number of logs is 300. (The rightmost column of the attached spreadsheet matches the rightmost column of your table.)
Hi i need help with this math question
Answers
Answer: 40x
Step-by-step explanation: addion multiplcation and divion
Answer:
x = 6Step-by-step explanation:
We note that the graph crosses the x- axis at the point (6 , 0)
Thus , g(6) = 0.
Find the original price given the total amount and tip rate. Total price 307.32 tip rate 20%
Answers
Answer:
256.10
Step-by-step explanation:
You want the original price given the total amount is 307.32 and the tip rate is 20%.
Tip addedAdding a tip multiplies the original price by (1 +tip rate). We can divide the total amount by this factor to find the original price:
307.32/(1+0.20) = 256.10
The original price was 256.10.
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In a 30-60-90 triangle the long leg is half the hypotenuse.
Answers
What is x if the volume of
the box is 70 in^3 ?
Answers
Answer:
12.25.
Step-by-step explanation:
1) the formula of the volume given in the condition is:
V=2*2/7*10x.
2) If V=70, then
2*2/7*10x=70, where x=12.25.
Answer:
(10x)(7/4)(2)=70
=10x=70/7/4/2
=10x=20
x=2
Answer: 2
Step-by-step explanation:
I need help on this assignment
Answers
The function shows one transformation, which is right one.
Original (parent) function would be √ X with the coordinates: (0,0), (1,1), (4,2), and so on. Looking at (1,1), it’s noticed that it’s now (2,1), which shows that the x has been affected due to the transformation of shifting right one unit.
Find the surface area of the parallelogram-based prism. Note: the prism has two parallelogram bases and four rectangular sides.
Answers
Answer:
1548 unit^2
Step-by-step explanation:
The area each of the 2 bases
= width * height
= 17 * 12
= 204 unit^2
2 have area 408 unit^2
Area of the lateral rectangles = 2 * 13 * 19 = 494 unit^2
Area of the top and bottom rectangles = 2 * 17 * 19 = 646 unit^2
Total surface area = 408 + 494 + 646
= 1548 unit^2.
What is the solution to this system of linear equations?
X - 3y = -2
X + 3y = 16
A. (7, 3)
B. (3, 7)
C. (-2, -3)
D. (-3, -2)
Answers
Answer:
x=7 and y=3
Step-by-step explanation:
Step: Solve x−3y=−2 for x:
x−3y=−2
x−3y+3y=−2+3y(Add 3y to both sides)
x=3y−2
Step: Substitute3y−2for x in x+3y=16:
x+3y=16
3y−2+3y=16
6y−2=16(Simplify both sides of the equation)
6y−2+2=16+2(Add 2 to both sides)
6y=18
6y
6
=
18
6
(Divide both sides by 6)
y=3
Step: Substitute3foryinx=3y−2:
x=3y−2
x=(3)(3)−2
x=7(Simplify both sides of the equation)
Answer:
x=7 and y=3
Answer:
Step-by-step explanation:
2x = 14
x = 7
7 + 3y = 16
3y = 9
y = 3
(7, 3)
answer is A
Performance-enhancing drugs affect an individual by which of the following?
A. Decrease an athlete's muscle mass and endurance.
B. Are legal in some sports.
C. Decrease an athlete's performance and energy levels.
D. Give performers an unfair advantage.
Answers
Answer:
Give performance an unfair advantage
Which is the graph of the linear inequality 2x – 3y < 12?
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
Answers
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2) and to the left of the line is shaded.
What are the characteristics of the graph of the inequality?Inequality of a graph is represented with the greater then(<), less then(>) or with the other inequity signs. The inequality line on the graph is represented with the dotted lines.
Characteristics of the graph of the inequality-
Open circle-When the value of the variable is equal to the given number, then the graph of the inequality has an open circle.Closed circle-When the value of the variable is not equal to the given number, then the graph of the inequality has a closed circle.The ray will move to the right-When the, value of the variable is greater than the number, then the ray will move to the right.The ray will move to the left-When the value of the variable is less than the number, then the ray will move to the left.The linear inequality given in the problem is,
[tex]2x - 3y < 12[/tex]
The graph of this line is attached below. Here, for the greater than sign, every thing on the left of the graph is shaded, and the line will be dotted because of inequality as shown in the attached image.
Hence, on a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2) and to the left of the line is shaded.
Learn more about the characteristics of graph of the inequality here;
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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.5 years, and standard deviation of 1.9 years.
If you randomly purchase one item, what is the probability it will last longer than 12 years?
Answers
Answer:
39.74 %
Step-by-step explanation:
12 years - 11.5 = .5 years
.5 / 1.9 = .2631 S.D above the mean
From z-score table this corresponds to .6026
60.26 are BELOW this life span
39.74 % are above 12 years
Using ratios in right triangles
Answers
Answer:
Your answer should be A) 0.34.
Step-by-step explanation:
Look at the other 3 triangle above and compare it to the below triangle that only has 70°.
One of the triangles is similar to the triangle below that has 70°.
Using the Side Length value we get 3.4/10 = 0.34.
what is 12 is 15 % of what?
Answers
Answer:
15% of eighty is equal to twelve
Find the measures of all of the angles.
1. ∠ABC =
2. ∠BCA =
3. ∠CAB =
Answers
2 is 20
3 is 30
This are the measures of t he angles okay do this si said did use did si is the answer
There is a new candy on the scene! The Delicious Candy Company
wants you to create the packaging for the launch of this new candy.
On possible shape for the
container is a rectangular prism. This is a
standard shape for boxes. Place in the measurements that you think
would work best for the candy box.
Answers
The measurements that would work for the box is 10cm for the length, 15cm for the width and 5cm for the height.
What are the possible dimensions of the candy box?The candy box has the shape of a rectangular prism. A rectangular prism is a is a three-dimensional shape with six faces, twelve sides and six verticies.
Volume = length x width x height
To learn more about rectangular prisms, please check: https://brainly.com/question/8890358
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|x|=x^2+x-15 solve the absolute value equation
Answers
Answer:
[tex]x=\sqrt{15,} -5[/tex]
Step-by-step explanation:
Which of the following is a valid conclusion ?
Answers
Answer:
interferances of the blood preser
Step-by-step explanation:
Consider the equation One-fourth(x – 5) = (y – 2)2. What is the equation of the directrix?
Answers
Considering the parabolic equation, the equation for the directrix is given by x = 4.9375.
What is the equation of a parabola given it’s vertex?The equation of a horizontal quadratic function, of vertex (h,k), is given by:
(y - k)^2 = 4p(x - h)
The directrix is given by:
x = h - p.
In this problem, the equation is given by:
(y - 2)² = 0.25(x - 5).
Hence h = 5, p = 0.25/4 = 0.0625, hence the directrix is:
x = h - p = 5 - 0.0625 = 4.9375.
More can be learned about parabolic equations at https://brainly.com/question/24737967
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What is the least two common multiplication 2 and 5
Answers
The LCM of 2 and 5 is the smallest positive integer 10 that is divisible by both 2 and 5 without any remainder.
Please help me.. there is a image
Answers
Answer: 2 and 4
Step-by-step explanation: They both have 3 x's
Answer:
Okay the mode means the most repeating number.
So if you write this all out:
1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4
You can now see that 3 is the most repeating number.
So 3 is the mode.
Step-by-step explanation:
Hope this helps!
From your neighborhood softie :)
The displacement of a 500 g mass, undergoing simple harmonic motion, is defined by the function :
x=-3.5sin(π/2t+(5π)/4)
Find
a. maximum kinetic energy
b. maximum potential energy
c. maximum mechanical energy
Answers
To solve this problem, we have to write out the simple harmonic motion equation and then use the respective formula to solve. The maximum kinetic energy, maximum potential energy and the maximum mechanical energy is equal to 7.56J.
Simple Harmonic MotionThe given equation of the simple harmonic motion is
[tex]x = 3.5sin(\frac{\pi}{2t} + \frac{5\pi}{4})\\[/tex]
Data;
ω = π/2k = 1.254N/mSolving this
[tex]\frac{dx}{dt} = \theta = -3.5 * \frac{\pi}{2} cos (\frac{\pi }{2}t + \frac{5\pi}{4})\\[/tex]
Let's calculate the maximum velocity.
[tex]V_m = \frac{3.5\pi}{2}[/tex]
This is only possible when cos θ = -1
The maximum kinetic energy is
[tex]K_m = \frac{1}{2}mv_m^2 = \frac{1}{2}* \frac{500}{1000} * (\frac{7\pi}{4} )^2\\K_m = 7.56J[/tex]
The maximum kinetic energy is 7.56J
The maximum potential energy can be calculated as
[tex]\omega^2 = \frac{k}{m} \\k = \omega^2 m \\k = \frac{\pi^2}{4} * \frac{500}{1000}\\ k= 1.254 N/m[/tex]
Using the value of spring constant, we can find the maximum potential energy
[tex]P.E = \frac{1}{2}kx^2\\P.E = \frac{1}{2} * 1.234 * 3.5^2\\P.E = 7.56J[/tex]
The maximum potential energy is 7.56J
The maximum mechanical energy is equal to the sum of maximum potential energy and the maximum kinetic energy.
[tex]ME = P.E + K.E\\ME = 7.56J[/tex]
The reason ME is equal to 7.56J is because when x is at maximum, v = 0 and makes kinetic energy equal to zero.
ME = 7.56J
From the calculations above, the maximum kinetic energy, maximum potential energy and the maximum mechanical energy is equal to 7.56J.
Learn more on simple harmonic motion here;
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Which expression is equivalent to the given expression? Assume the denominator does not equal zero
Answers
Answer:
Step-by-step explanation:
This question is based on the of expression. Therefore, the correct option is (A) that is, .
Given:
Expression :
We have to determined the expression is equivalent to the given expression.
According to the question,
It is given, to be assume that denominator does not equal zero.
Now by given expression, i.e.
Now, divide denominator by numerator we get,
Therefore, the correct option is (A) that is,
Find the slope pls help giving brainlest
Answers
Answer:
(3,-9)
Step-by-step explanation:
Please give brainliest please and good luck :)
If you dont know the answer or get it wrong i will report
Answers
I can only solve no.2
Step-by-step explanation:
CAB=ABC(ISCOSCELES TRIANGLE)
SO REPRESENT THEM BY X BECAUSE YOU DON'T KNOW THEM
THEIR SUM =180
SO,CAB+ABC+ACB=180
SUBSTITUTE THEIR VALUES
X+X+120=180
2X+120=180
2X=180-120
2X=60
[tex] \frac{2x}{2x} = \frac{60}{2 } [/tex]
cancel
so x is 30 degrees
Trust me
A jar contains 100 marbles. There are 7 blue marbles, 4 green marbles,
46 red marbles, and 43 yellow
marbles. What is the probability of
randomly selecting a yellow marble?
Enter the correct answer.
Answers
Answer:
43%
Step-by-step explanation:
If there are 43 yellow marbles out of 100 total, the fraction that will be used is 43/100. The percentage is found by dividing the numerator (top) by the denominator (bottom). The percentage is the first two numbers in the decimal. For future reference, if a decimal were to have more than 2 or 3 digits, the number would be rounded to the 4th and the decimal point would be placed between the 2nd and 3rd digits.
How many times wood a wood chuck chuck if a wood chuck could chuck wood.
Answers
Answer: about 700 pounds
According to the Poetry Foundation, a woodchuck would chuck As much wood as a woodchuck could chuck, If a woodchuck could chuck wood Researchers at Cornell determined that a woodchuck could chuck about 700 pounds.
Below is a the data set for the amount of time spent on FaceTime. Calculate the mean, median, mode, and range. Be sure to show your work!
Sunday 65, Monday 250, Tuesday 75, Wednesday m 65, Thursday 45, Friday 77, Saturday 80.
Mean:
Median:
Mode:
Range:
Answers
Answer: Mean - 93.8571428571, round however you need to
Median - 75
Mode - 65
Range - 205
Step-by-step explanation: Order the numbers first. 45,65,65,75,77,80,250.
Find the mean. 45 + 65 + 65 + 75 + 77 + 80 + 250 is 657. Divide by 7 is 93.8571428571.
Median is middle. It is 75.
Mode is the most common. - 65
Range is the highest subtracted by the lowest. 250 - 45 is 205.
