Answers
[tex]\large{\boxed{ \ g(x) = -\dfrac{7}{4} | x -5| +0 \ }}[/tex]
Explanation:Absolute value of a graph formula:
y = a |x -h| + kIdentify the vertex : (h, k) = (5, 0)
Take two points : (5, 0), (9, -7)
[tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \dfrac{-7-0}{9-5} \ = \ -\dfrac{7}{4}[/tex]
Join the variables together: [tex]\bf g(x) = - \dfrac{7}{4} | x -5| +0[/tex]
Answer:
[tex]f(x) = -\dfrac{7}{4}|x-5|+0 [/tex]
Step-by-step explanation:
The function in the coordinate Plane is an absolute value function . Consider the parent function
[tex]f(x) = |x| [/tex]
Recall the properties of transformation
f(x+a), If a<0 ⇒ It moves to righta.f(x),If a<0 ⇒ It flips upsidedownf(x)+a,If a>0 ⇒ It moves up & a<0 It moves downFrom the inspection of the graph,It has moved to right by 5 units, Thus
[tex]f(x - 5) = |x - 5| [/tex]
Apparently, It has neither shifted up or down, hence
[tex]f(x - 5) +0= |x - 5|+0 [/tex]
Looking at the graph, we can see that it has been reflected vertically. It tells us we have to multiply it by a negative constant
[tex] -a f(x - 5) +0= -a |x - 5| +0[/tex]
take (9,7) to figure out a.
set x to 9 and the LHS expression to 7[tex] -a | 9- 5| =7[/tex]
Solving the equation yields:
[tex] \boxed{a = - \frac{7}{4} }[/tex]
hence, our function is [tex]\boxed{f(x) = -\dfrac{7}{4}|x-5|+0} [/tex]
Related Questions
caculate the area of this triangle
Answers
Answer: 99 cm²
Step-by-step explanation:
The area of a triangle can be found with [tex]a=\frac{b*h}{2}[/tex] so we will plug in the given values and solve.
[tex]\displaystyle a=\frac{b*h}{2}[/tex]
[tex]\displaystyle a=\frac{(18 cm)(11cm)}{2}[/tex]
[tex]\displaystyle a=\frac{198\;cm^2}{2}[/tex]
[tex]\displaystyle a= 99\;cm^2[/tex]
B x h= 198
Area= 99 squared cm
Right triangles and trigonometry
Answers
Answer:
x = 13.83
Step-by-step explanation:
[tex]sin(70^{o}) =\frac{13}{x}[/tex]
[tex]x=\frac{13}{sin(70^{o} )} =13.83[/tex]
Hope this helps
find the equation of the circle with centre (2,3) and which touches the x-axis
Answers
Answer:
(y-3)^2=4p(x-2)
Step-by-step explanation:
C(h,k)
The equation is (y-k)^2=4p(x-h)
Answer:
(x-2)² + (y-3)² = 9
Explanation:
Circle Formula: (x - h)² + (y - k)² = r²
As touches x axis, coordinates: (2, 0)
radius: √(2-2)² + (3 -0)² = 3
Now find equation:
= (x-2)² + (y-3)² = 3²
= (x-2)² + (y-3)² = 9
Determine the consumers’ surplus of the market price is set at the equilibrium price (remember that x is measured in thousands)
Answers
Answer:here the answer
Step-by-step explanation:
....
4/8 plus 2/4 find the common denomnator
Answers
Answer:
The common denominator is 4.
Step-by-step explanation:
4/8 simplified is 2/4.
Therefore, we can now add them together.
2/4 + 2/4 = 1.
Hope this helps:) Goodluck!
The first aircraft has 59 more seats than the second aircraft. The third aircraft has 42 fewer seats than the second aircraft. If their total number of seats is 407, find the number of seats for each air craft.
Answers
Answer:
first aircraft=189
second aircraft=130
third aircraft=88
Step-by-step explanation:
1st = x+59
2nd = x
3rd= x-42
x + 59 + x + x - 42 = 407
3x + 59- 42 = 407
3x + 17 = 407
3x = 407 - 17
x=390÷3
=130
1st=130+59=189
2nd=130
3rd=130-42=88
Simplify the following expression:
4 + √-4 + √-9 + 7
A. 11 + 5i
B. 5 - 11i
C. 11 + √13i
D. 15 + 0i
Answers
Write 7.03 x 10-3 as an ordinary number
Answers
Answer: 0.00703
Step-by-step explanation: The ordinary number, or standard form, of this expression would be 0.00703 because here, we are multiplying 7.03 in scientific notation by a power of ten that is negative. If any exponential power of 10 is being multiplied and is negative, the digits move that same number of places to the right of the decimal point to render a smaller number than it was in the expression. Hope this helps!
At what nominal rate, compounded semi-annual, would $6,000.00 have to be invested to amount to
$9,066.41 in 6 years?
The rate would be
%. (If needed, round to 1 decimal place.)
Answers
PLEASE HELP AND FAST
This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
48 mm²
64 mm²
112 mm²
384 mm²
Answers
Answer:
The answer is D
Step-by-step explanation:
The solution is in the file
230 is 12% of what number? Use proportion to find the answer.
Answers
Answer:
hello!!!
the answer is 1916.6
please read the explanation it always helps... trust me!
Step-by-step explanation:
alrighty so....
we what to find the number that when we take 12% of we get 230...
okay we have to switch things up in the percent formula since we dont have the total number just the percentage and the percent number itself (i hope that isnt confusing.. the math is easier tho)
230 x 100= 23000 --> 23000/12= 1,916.6
Answer:
1,916.67
Step-by-step explanation:
1230/12 = x/100.
12x= (230)(100).
12x=23000.
x= 23000/100
x = 1,916.67
Which of the following is equivalent to the expression below?
√16x^3
8x 2/3
4x 3/2
8x 3/2
4x 2/3
Answers
So that is equal to
8*3/2=12
Help me answer this question :((((
Answers
Answer:
97.5
Step-by-step explanation:
75,85,90,105,120,150
90 and 105 are the middle, and median means the middle, but you can only have one answer.
90+105=195
195÷2=97.5
97.5 is the middle of all these numbers
Part A: The length of two sides of a triangle are:
Side 1:
Side 2:
The perimeter of the triangle is
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (7 points)
Part B: What is the length of the third side of the triangle? Show your work. (7 points)
Answers
Part A: The total length of the two sides, 1 and 2, of the triangle is 10x² + 14x - 8
Part B: The length of the third side of the triangle is 10x³ -2x² - 16x + 2
Calculating the sides of a triangleFrom the given information,
The length of side 1 is
6x² - 4x - 2
and the length of side 2 is
18x + 4x² - 6
Part A
The total length of the two sides, 1 and 2, of the triangle will be
Length of side 1 + Length of side 2
That is,
6x² - 4x - 2 + 18x + 4x² - 6
This becomes,
6x² + 4x² + 18x - 4x - 2 - 6
10x² + 14x - 8
Therefore, the total length of the two sides, 1 and 2, of the triangle is 10x² + 14x - 8
Part B
The length of the third side will be
Perimeter of the triangle - the total length of sides 1 and 2
From the given information,
The perimeter of the triangle is 10x³ + 8x² - 2x - 6
Then,
Length of third side = 10x³ + 8x² - 2x - 6 - (10x² + 14x - 8)
Length of third side = 10x³ + 8x² - 2x - 6 - 10x² - 14x + 8
Length of third side = 10x³ + 8x² - 10x² - 2x - 14x - 6 + 8
Length of third side = 10x³ -2x² - 16x + 2
Hence, the length of the third side of the triangle is 10x³ -2x² - 16x + 2
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sixty students were surveyed at random about their favorite music genre. Out of population 1,000 students, how many how many will prefer pop music?
Answers
So we want to know how many out of 1000 people did not listen to any type of the three music types that were surveyed If 30% of people listened to pop, 26% of people listened to rock and 20% of people listened country music. So first lets see how many people liked the three types of music: 30%+26%+20%=76%. So 24% of people did not like the three types of music that were surveyed. Finally we need to see how many people in 1000 is 24%. 24% out of 1000 people is 0.24*1000=240 people. So 240 people didn't like the 3 types of music.
Please help me do this :)))))))
Answers
Answer:
x=6
Step-by-step explanation:
BC=7
x+1=7
x=7-1=6
x=6
about 1 2 of the population has red hair if 800 people were ramdomly sampled about how many of them would you expect to be read heads
Answers
Answer:
10-12
Step-by-step explanation:
1.5% of 800 is 12
in a certain triangle angle c is 40 degrees more than the sum of the measure of angle a and angle b. the measure of angle a is 20 degrees less than the measure of angle b. find the measure of each angle
Answers
Step-by-step explanation:
the sum of all angles in a triangle is always 180°.
angle c = angle a + angle b + 40
angle a = angle b - 20
angle a + angle b + angle c = 180
using the second equation in the first :
angle c = (angle b - 20) + angle b + 40 = 2×angle b + 20
using this and the second equation in the third equation :
(angle b - 20) + angle b + (2×angle b + 20) = 180
4×angle b = 180
angle b = 45°
angle a = angle b - 20 = 45 - 20 = 25°
angle c = angle a + angle b + 40 = 25 + 45 + 40 = 110°
V
Write 8.4% as a fraction in simplest form.
Answers
Answer:
21/250
Step-by-step explanation:
Converting percentage to fraction :
Divide by 100%8.4%/100%8.4/100Multiply both sides by 10 to remove the decimal8.4 x 10 / 100 x 1084/1000Divide both sides by 4(84/4)/(1000/4)21/250How much water should be added to 22 ml of 12% alcohol solution to reduce the concentration to 11%
Answers
The amount of water that is needed to be added to the 12% concentration solution to make it 11% concentrated is 2 ml.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given that the alcohol solution of 22 ml has a 12% of concentration. Therefore, the amount of alcohol in the solution is,
12% of 22ml = 2.64ml
Since the amount of alcohol should be the same while the concentration should be diluted, therefore, the amount of alcohol in the final solution can be written as,
[tex]11\%\ of\ x = 2.64{\rm\ ml}\\\\\dfrac{11}{100} \times x = 2.64\\\\x = 24\rm\ ml[/tex]
As the total solution with 12% concentration was 22 ml, while the total solution with 11% concentration was 24 ml.
Hence, the amount of water that is needed to be added to the 12% concentration solution to make it 11% concentrated is 2 ml.
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Tom, Lily, and Shelby, competed as a team in a scavenger hunt. They were given a list of items to find around their neighborhood. Together the three of them found every item on the list. Tom found 1/3 of the items, and Lily found 4/9 of the items. Which area model represents the fraction of the item on the list that Shelby found?
Answers
The f(x) represents the fraction of the items on the list that Shelby found if Tom found 1/3 of the items, and Lily found 4/9 of the items.
What is a fraction?A fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
Let's suppose the Total items in the list is x and Shelby found f(x) item.
Tom found 1/3 of the items, and
Lily found 4/9 of the items.
Then,
[tex]\rm f(x) = x - (\dfrac{1}{3}+ \dfrac{4}{9})\\\\\rm f(x) = x - (\dfrac{3+4}{9})\\\\\rm f(x) = x - \dfrac{7}{9}\\\\\\\rm f(x) = \dfrac{9x-7}{9}\\\\[/tex]
Thus, the f(x) represents the fraction of the items on the list that Shelby found if Tom found 1/3 of the items, and Lily found 4/9 of the items.
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a number 1-72 is chosen at random find each probability
P( multiple of 9)
Answers
The selection of a random number from 1 - 72 is an illustration of probability, and the probability of selecting a multiple of 9 is 1/8
How to determine the probability?The sample size is given as:
n = 72
There are 8 multiples of 9 from 1 to 72.
So, the probability that a multiple of 9 is selected is:
P(Multiple of 9) = 8/72
Simplify
P(Multiple of 9) = 1/9
Hence, the probability of selecting a multiple of 9 is 1/8
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Question 3 (2 points)
Suppose that the mean cost of a haircut for a man is $28 and the mean cost of a
haircut for a woman is $44.
Which statement is true about the cost of haircuts?
Answers
The statement that is true about the cost of haircuts is "On Average, the cost of a man's haircut is $16 less than the cost of a women's haircut".
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
Given that the mean cost of a haircut for a man is $28 and the mean cost of a haircut for a woman is $44. Therefore, the statement that is true about the cost of haircuts is "On Average, the cost of a man's haircut is $16 less than the cost of a women's haircut".
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Simplify.
2
5x² - 7x + 3
-
10
+ 8x² + 9x
I need help
Answers
Answer:
621 i guess
Step-by-step explanation:
18x² + 2x² - 7
Tap on a clip to paste it in the text box.
I need help in 17 & 18 & 19 :(
Answers
Answer:
The perimeter of the rectangle is 28 units
PLEASE HELP IM SO CONFUSED
Answers
Answer:
Lake Carters, Lake Amistad, Lake Alamo
Step-by-step explanation:
Starting with lake Alamo:
current level: 1,080
Full pool: -48.5
This indicates that the level is currently 48.5 feet below a full pool
Therefore, the level of it as a full pool is 1,080 + 48.5, or 1,128.5 feet
Lake Amistad:
Current Level: 1,038
Full pool: -7.1%
This indicates that the level is currently 7.1% below a full pool
subtract 7.1% from 100%
100-7.1=92.9
Percent formula:
P% * X = Y
P = 92.9
Y = 1038
X = 1038 / 92.9%
X = 1117.33
Full pool = 1117.33
Lake Carters
Current level: 1078
Full pool: + 60/13
This indicates that the level is currently 60/13 above a full pool
60/13 = 4.62
1078 - 4.62 = 1073.38
full pool = 1073.38
So, the order is Lake Carters, Lake Amistad, Lake Alamo
8. There are 12 people that have entered a gaming tournament with prizes for 1st place, 2nd place, and 3rd place. How many combinations of winners can there be?
220
1320
1728
360
Answers
Answer:
1728
Step-by-step explanation:
When there is 3 places you have to sqaure 12 by 3
12^2= 144
144*12= 1728
Hope this helps.
A pool is leaking at a rate of a quarter of a gallon per minute. What is this rate in gallons per hour?
Answers
Answer:
15 gallons per hour
Step-by-step explanation:
So, what is given in the equation is that 1/4 of a gallon is leaking per minute. We have to change this to gallons per hour. Set it up like this:
[tex]\frac{\frac{1}{4}gallon }{1 minute} *\frac{60 min}{1 hour}[/tex]
Use a calculator and multiply 1/4 by 60.
After doing this, you should get:
[tex]\frac{15 gallons}{1 hour}[/tex]
Thus, the answer is the pool will leak 15 gallons per hour.
Hope this helps!! Ask questions in comments if needed!
Please tell me what the value of x is
Answers
:
40 degrees
Gustavo is in a contest where he will win one of four possible prizes. He creates a four-part spinner to represent the four prizes that he has an equal chance of winning: a video game system, a bicycle, a watch, and a gift card. He spins the spinner several times to demonstrate the likelihood of winning a certain prize.
What is true about Gustavo’s method of data collection and his data on the possible prizes?
Gustavo used an experiment where the data is qualitative.
Gustavo used an experiment where the data is quantitative.
Gustavo used a simulation where the data is qualitative.
Gustavo used a simulation where the data is quantitative.
Answers
The correct option about Gustavo’s method of data collection and his data is Gustavo used a simulation where the data is qualitative.
What is qualitative data?Qualitative data is data that describes the properties that a certain object or event possesses. The numerical value assigned to qualitative data do not have an significance. A simulation is a form of test run for an actual event.
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Answer:
ITS C
Step-by-step explanation: