Answers
[tex]\large{\boxed{\sf y = \dfrac{2}{3} | x -6|- 7}}[/tex]
Explanation:Absolute value of a graph formula:
y = a |x -h| + kIdentify the vertex : (h, k) = (6, -7)
Take two points: (6, -7), (9, -5)
[tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-5-(-7)}{9-6} \ = \ \ \dfrac{2}{3}[/tex]
Join them to build the equation: [tex]\bf{y = \dfrac{2}{3} |x - 6| - 7}[/tex]
Answer:
[tex]g(x)=\dfrac{2}{3}|x-6|-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 down}[/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]
[tex]f(0)=|0|=0 \implies \textsf{The vertex of the parent function is at (0, 0)}[/tex]
From inspection of the graph, the vertex of the transformed function is at (6, -7). Therefore, there has been a translation of:
6 units right7 units down[tex]\textsf{6 units right}\implies f(x-6) =|x-6|[/tex]
[tex]\textsf{and 7 units down}\implies f(x-6)-7=|x-6|-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-6)-7=a|x-6|-7[/tex]
The line goes through point (0, -3)
Substituting this point into the above equation to find [tex]a[/tex]:
[tex]\implies a|0-6|-7=-3[/tex]
[tex]\implies 6a=4[/tex]
[tex]\implies a=\dfrac{2}{3}[/tex]
Therefore,
[tex]\implies g(x)=\dfrac{2}{3}|x-6|-7[/tex]
Related Questions
URGENT PLEASE ANSWER. PHOTO OF PROBLEM ATTACHED. BRAINLIEST TO FIRST CORRECT ANSWER.
Answers
Answer:
27.23 inches
Step-by-step explanation:
question wants circumference over 2π/3 radians
2π/3 times 180/π = 120 degrees
120 is 1/3 of 360
so question wants 1/3 of the circumference
circumference is π times diameter
π times 26 = 81.6814089933
81.6814089933 divided by 3 =
27.2271363311 =
27.23
How 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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f(x) = 4x^2 - 3 find f(x + 2)
Answers
Answer:
f(x + 2) = 4x² + 16x + 13
Step-by-step explanation:
f(x) = 4x² - 3
Then
f(x + 2) = 4(x + 2)² - 3
= 4(x² + 4x + 2²) - 3
= 4(x² + 4x + 4) - 3
= 4x² + 16x + 16 - 3
= 4x² + 16x + 13
whats mean and median of 11, 18, 5, 20, 8, 124, 17?
Answers
Answer:
The mean would be 29 and the median would be 17
Step-by-step explanation:
Hope this helps! :)
Which of the following is equivalent to S = {spring, summer, autumn, winter}?
(you may select more than one)
{x | x = states in the United States}
{x|x is a season}
{x|x = planets in our solar system}
{x | x = former Presidents of the United States}
{x|x ≥ 1 and x < 5}
{x | x = sides of a standard dice}
Answers
Answer: {x | x is a season}
Step-by-step explanation:
Spring, summer, autumn, and winter are all seasons.
rewrite! Write an new and equivalent equation that is easier to solve
Answers
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given - an equation in it's general formTo do - convert the given equation into a form that is easy to solveGiven equation -
[tex]\bold{(x + 2) {}^{2} + 4(x + 2) - 5 = 0} \\ [/tex]
solve the parenthesis so as to obtain simpler terms
[tex]\bold{\implies \: ( x {}^{2} + 4x + 4 ) + 4x + 8 - 5 = 0}\\ [/tex]
solve the like terms and you'll obtain the required equation !
[tex]\bold{\implies \: x {}^{2} + 8x - 7 = 0}[/tex]
hope helpful ~
[tex]{\large{\red{\mapsto{\maltese{\underline{\green{\boxed{\blue{\underbrace{\overbrace{\pink{\pmb{\bf{Answer:}}}}}}}}}}}}}}[/tex]
x = -7, -1
Step-by-step explanation:
[tex] \sf {(x + 2)}^{2} + 4(x + 2) - 5 = 0[/tex]
let (x + 2) = y
So equation will be
[tex] \sf {y}^{2} + 4y - 5 = 0[/tex]
Further it becomes quadratic equation
we will solve it by breaking middle term method
[tex] \sf \implies {y}^{2} + 5y - y - 5 = 0 \\ \\ \sf \implies y(y + 5) - 1(y + 5) = 0 \\ \\ \sf \implies (y + 5)(y - 1) = 0[/tex]
Now put the value of y
[tex] \sf \implies (x + 2 + 5)(x + 2 - 1) = 0 \\ \\ \sf \implies (x + 7)(x + 1) = 0[/tex]
(x + 7) =0⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(x + 1) = 0
x = -7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ x = -1
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:
....
A bookstore had 120 copies of a magazine. Yesterday the bookstore sold
of these copies. How many copies were sold yesterday?
Write your answer in simplest form.
Answers
Answer:
120
Step-by-step explanation:
120 copies sold yesterday
if a (+)(+) makes a positive, (-)(-) make a positive (+)(-) make a negative why is -10+7=-3 but -8-3=-11 shouldn't this positive? can someone explain when these terms apply?
Answers
Step-by-step explanation:
-10+7=-3 because 10 i greater and (-)(+)=-
-8-3=-11 because the greatest number is in negative form that's why its not in positive form
Hey there!
Guide:
Negative & negative = positive
Positive & positive = positive
Negative & positive = negative
Positive & negative = negative
For -10 + 7 = -3 it doesn’t give you a POSITIVE because you’re working with a negative (-10) and a positive (7), which it results out to be a negative number (-3)
Whereas, -8 - 3 = -11, it doesn’t also give you a positive because you’re working with a negative (-8) and a somewhat positive (3 or -3 it depends how you look at the equation), it gave you a negative result (-11).
KEEP THAT GUIDE IN MIND WHEN YOURE WORKING WITH INTEGERS, IT MAY HELP ON THE LONG WRONG! :)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
2 times a number is 62 less than 284 , find the number
Answers
Answer:
The number is 111
Step-by-step explanation:
284-62= 222
2x111=284
Answer:
x = 111.
Step-by-step explanation:
Based on the given conditions, formulate: 2 * x = 284 - 62 Calculate the sum or difference:2 x = 222
Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1?
Answers
Using the normal distribution, it is found that 16.43% of adults in the US qualify for stage 1.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Researching the problem on the internet, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 122, \sigma = 22[/tex].
The proportion of adults in the US qualify for stage 1 is the p-value of Z when X = 160 subtracted by the p-value of Z when X = 140, hence:
X = 160:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 122}{22}[/tex]
Z = 1.73
Z = 1.73 has a p-value of 0.9582.
X = 140:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 122}{22}[/tex]
Z = 0.82
Z = 0.82 has a p-value of 0.7939.
0.9582 - 0.7939 = 0.1643.
0.1643 = 16.43% of adults in the US qualify for stage 1.
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The Math Campers are grouped into groups with 9 members each. Each group is asked to form a circle and they will be sitting on the ground. If the seating arrangement is circular, in how many possible ways can the 9 members be seated?
A. 40320
B. 362880
C. 5040
D. 720
Answers
Answer:
B. 362880
Step-by-step explanation:
! means permutation which means
arrangement of people or things in
sequence or
linear order
9! = 362880
9! = 9*8*7*6*5*4*3*2*1 = 362880
What is the length of the two equal sides?
What is the length of the third side?
Answers
Answer:
the length of the third side is 21
Step-by-step explanation:
let P be the perimeter of the triangle
a the length of the first and second sides
b the length of the 3rd side
…………………………………………………
Then
P = a + a + b
= 2a + b
Where b = a + 6
Therefore
P = 2a + (a + 6)
= 3a + 6
We substitute the numbers we have into the equation:
51 = 3a + 6
⇔ 45 = 3a
⇔ a = 15
Since b = a + 6 then b = 15 + 6 = 21
4. For v = -2i – 7j, find the unit vector in the direction of y, and write your answer as a linear combination of the standard unit vectors i and j
5. Find u•v if u = i + 2j and v = -i + 5j.
Answers
4. If v = -2i - 7j, then its magnitude is
||v|| = √((-2)² + (-7)²) = √53
and the unit vector in the direction of v is
[tex]\dfrac{v}{\|v\|} = \boxed{-\dfrac2{\sqrt{53}} \, \vec\imath - \dfrac7{\sqrt{53}} \, \vec\jmath}[/tex]
5. Given u = i + 2j and v = -i + 5j, we have
u • v = (i + 2j) • (-i + 5j) = -(i • i) - 2 (j • i) + 5 (i • j) + 10 (j • j)
Since i and j are orthogonal unit vectors, we have i • i = j • j = 1 and i • j = 0, so the product reduces to
u • v = -1 - 0 + 0 + 10 = 9
can someone please explain the process to me? this is from a final review i did so just ignore my wrong answer. Hoping to get a explanation so I can do my actual final in about an hour. thank you!
Answers
Answer:
The correct answer is supposed to be 3.36
Step-by-step explanation:
Add up all the numbers:
4 + 3.7 + 3.4 + 3 + 2.7 = 16.8
Divide by how many numbers there are:
16.8 ÷ 5 = 3.36
What is the distance between B to A
Please add the method.
The angle is 61 (a bit blurry)
Answers
Now
tan61=BH/OHtan61=BH/1980BH=1980tan61BH=3572(Rounded)AB
8+35723580Answer:
24.03 units (nearest hundredth)
Step-by-step explanation:
The distance between B and A is: AB = AH + HB
We have been given AH, so we just need to find the measure of HB.
First, find the angle AOH using tan trig ratio:
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = ∠AOHO = AH = 8A = OH = 19.80[tex]\implies \sf \tan(\angle AOH)=\dfrac{8}{19.8}[/tex]
[tex]\implies \sf \angle AOH = 22.00069835^{\circ}[/tex]
∠BOA = ∠BOH + ∠AOH
⇒ ∠BOH = ∠BOA - ∠AOH
⇒ ∠BOH = 61° - 22.00069835°
= 38.99930165°
Now we can find HB by again using the tan trig ratio:
Given:
[tex]\theta[/tex] = ∠BOH = 38.99930165°O = HBA = OH = 19.80Substituting given values:
[tex]\implies \sf \tan(38.99930165^{\circ})=\dfrac{HB}{19.80}[/tex]
[tex]\implies \sf HB=19.80 \tan(38.99930165^{\circ})[/tex]
[tex]\implies \sf HB=16.03332427[/tex]
Therefore:
AB = AH + BH
⇒ AB = 8 + 16.03332427
= 24.03 units (nearest hundredth)
what is the volume of a cylinder, in cubic feet, with a height of 8 feet and a base diameter of 18 feet? Round to the nearest tenths place
Answers
Answer:
188 feet
i know that the answer
nasa makatulong po
The volume of a cylinder, in cubic feet, is,
V = 2,034.7 feet³
We have to given that,
In a cylinder,
Height = 8 feet
And, Diameter = 18 feet
Hence, Radius of cylinder is,
r = 18/2
r = 9 feet
We know that,
Volume of cylinder is,
V = πr²h
Substitute all the values, we get;
V = 3.14 × 9² × 8
V = 2,034.7 feet³
Therefore, The volume of a cylinder, in cubic feet, is,
V = 2,034.7 feet³
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Which of the following is the most significant greenhouse gas due to its long lifespan in the environment?
A. Carbon dioxide
B. Argon dioxide
C. Oxygen
D. Nitrogen Oxide
Answers
I hope that helps.
Answer:
Carbon dioxide
Step-by-step explanation:
I think it’s carbon dioxide because, it is the most significant greenhouse gas. I also think it’s the carbon dioxide because the question is asking which one it is and I chose carbon dioxide.
Which number is a solution of the inequality x <-4? Use the number line to help answer the question. Number line starts like and ends like “ -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1. “
Answers
:
5 points
-5 IS the SolutIon to the inequallty x < -4 ana
the interval is the X E (-∞, -4) option first is
correct.
What is inequality?
It is defined as the expression in
mathematics in which both sides are not
equal they have mathematical signs either
less than or greater than, known as
inequality.
We have inequality:
x<-4
The solutions to the above inequality will
lie in the region (-0, -4)
X E (-00, -4)
From the number line, we can mark the
region for the above interval
please answer this question
Answers
The integration of the provided integration expression which is evaluated without using the beta function is equal to 1/1011.
What is integration?It is the reverse of differentiation. The differentiation is the rate of change of the function with respect to variables.
The integration is given below.
[tex]\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{(1 +x)^{2022}} \ dx[/tex]
Then the integration can be written as
[tex]\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{[(1 +x)^{1011}]^2} \ dx[/tex]
Let (1 + x)¹⁰¹¹ = t. Then 1011x¹⁰¹⁰ dx = dt.
Then we have
[tex]\rightarrow \int_{1}^{\infty } \dfrac{dt}{1011 \ t^2}[/tex]
Then integrate
[tex]\rightarrow \dfrac{1}{1011} \left [ \dfrac{-1}{t} \right ]_{1}^{\infty }\\\\\\\rightarrow \dfrac{1}{1011} \left [ \dfrac{1}{t} \right ]^{1}_{\infty }\\\\\\\rightarrow \dfrac{1}{1011} \left [ 1- 0 \right ]\\\\\\\rightarrow \dfrac{1}{1011}[/tex]
The integration of the provided integration expression which is evaluated without using the beta function is equal to 1/1011.
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Find X
A = 49
B = 27
C = 98
D = 76
Answers
Answer:
C=98°
Step-by-step explanation:
125°- 27°
=98°
NO LINKS!!!
Erica is playing Target One Fractions. She has these cards: 1,2,3,4,6.
a. Which three cards should she choose to make a whole number and a fraction that have a product close to 1?
b. Write an expression for the problem Erica will solve.
c. Solve the problem.
d. What is Erica's score for this round?
Answers
Answer:
a. 2, 3, 6
b. a/b × c = 1
c. a = 2, b = 6, c = 3 or a = 3, b = 6, c = 2
Step-by-step explanation:
Apparently, Erica wants to multiply a fraction by a whole number to get a result of 1. That means the fraction is the multiplicative inverse of the whole number.
__
a.There is only one set of three unique numbers among those given such that one of them is a composite number with the other two as factors. Erica must choose 2, 3, and 6.
__
b.If the three numbers are represented by a, b, c, Erica wants ...
a/b × c = 1
__
c.Multiplying the equation by b gives ...
ac = b
Among the numbers 1–6, only 2×3 = 6 will satisfy this equation. Erica can choose either of ...
a = 2, b = 6, c = 3 ⇒ (2/6)×3 = 1
a = 3, b = 6, c = 2 ⇒ (3/6)×2 = 1
__
d.No scoring information is provided.
Please solve (high points)
Answers
Answer:
a = 13.24 m
Step-by-step explanation:
Finding ∠A :
∠A + ∠B + ∠C = 180° (Angle Sum Property)∠A = 180° - 48° - 54°∠A = 180° - 102°∠A = 78°Applying the Law of Sines :
a / sin78° = 10 / sin48°a / 0.98 = 10 / 0.74a = 13.51 x 0.98a = 13.24 mAnswer:
13.2 m
Step-by-step explanation:
The Law of Sines can be used to solve a triangle when angles and one side are known.
__
setupThe angles of a triangle total 180°, so the missing angle A is ...
∠A = 180° -48° -54° = 78°
The Law of Sines tells us ...
a/sin(A) = b/sin(B)
a/sin(78°) = (10.0 m)/sin(48°)
__
solutionMultiplying by sin(78°), we find ...
a = sin(78°)/sin(48°)×(10.0 m) ≈ 0.978148/0.743145×(10.0 m)
a = 13.1623 m
The length of side 'a' is approximately 13.2 meters.
find the volume of a cone with a base radius of 6 cm and a height of 10 cm write in terms of pie
Answers
Answer:
Volume of the cone is 120 π cm³Step-by-step explanation:
Given that Base radius of cone is 6 cm and height is 10 cm and we need to find volume of the cone. Volume of cone is given by:
[tex] \\ \: \: \dashrightarrow \: \: \: \underline{\boxed{\pmb{\sf{Volume_{(cone)} = \dfrac{1}{3} \pi r^2 h }}}} \\ \\ [/tex]
On Substituting the required values, we get:
[tex] \\ \: \: \dashrightarrow \: \: \sf \: Volume_{(cone)} = \frac{1}{3} \times \pi \times {(6)}^{2} \times 10 \\ \\ \\ \: \: \dashrightarrow \: \: \sf \: Volume_{(cone)} = \frac{1} {\cancel{3}} \times \pi \times \cancel{36} \times 10 \\ \\ \\ \: \: \dashrightarrow \: \: \sf \: Volume_{(cone)} = \pi \times 12 \times 10 \\ \\ \\ \: \: \dashrightarrow \: \: \sf \: \: { \purple{Volume_{(cone)} =120 \pi \: cm^3 }}\\ \\ [/tex]
Volume of a cone is 120 π cm³the table shows the enrollment in a university class so far, broken down by student type.
adult education 7
graduate 2
undergraduate 9
Considering this data, how many of the next 12 students to enroll should you expect to be undergraduate students?
Answers
Answer:
6
Step-by-step explanation:
The number of students in the next 12 to enroll should you expect to be undergraduate students is 6.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
From the table,
Total number of students = 7 + 2 + 9 = 18
Number of undergraduates = 9
Probability of having a undergraduate student to enroll = 9/18 = 1/2
When the next 12 students are enrolled,
Number of undergraduates = 1/2 × 12 = 6
Hence 6 students are expected to be undergraduates in the next 12 students.
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What is the slope and y-intercept of this line?
y = -3x+9
A. slope: 3, y-intercept: -9
B. slope: -3, y-intercept: 9
C. slope: 1. y-intercept: -3
D. slope: 9, y-intercept: -3
Answers
And the Y-int:9
It costs $3.99 for 32 fl. oz. of soda. What is the unit rate?
Answers
Answer:= 0.124688 oz per fl
Step-by-step explanation:
This is a fraction equal to
3.99 oz ÷ 32 fl
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 32
3.99 oz ÷ 32
32 fl ÷ 32
=
0.124688 oz
1 fl
=
0.124688 oz
fl
= 0.124688 oz pe
The graph below describes the dependence of the time traveled from point A to point B, on the speed at which the traveling occurs. With the help of the graph answer the following questions: 2 4 t, h 6 8 10 12 14 16 200 400 600 800 v, km/h How much time is necessary for traveling between points A and B, when the speed is 800 km/hour; 250 km/hour; 120 km/hour?
Answers
The time needed to travel between points A and B when the speed is 800 km/hour; 250 km/hour; 120 km/hour are 2.25 hours, 7.2 hours and 15 hours, respectively
How to determine the time taken to travel?Given the distance and speed, the time taken to move between points is calculated using:
Time = Distance/Speed
The required graph is not given.
So, we assume that the distance between both points is:
Distance = 1800km
Using the assumed value above, we have:
When speed = 800km/hr
Time = 1800/800
Time = 2.25 hours
When speed = 250km/hr
Time = 1800/250
Time = 7.2 hours
When speed = 120km/hr
Time = 1800/120
Time = 15 hours
Hence, the time needed to travel between points A and B when the speed is 800 km/hour; 250 km/hour; 120 km/hour are 2.25 hours, 7.2 hours and 15 hours, respectively
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Which of the following pairs of triangles can be proven congruent through HL?
Answers
The pairs of triangles can be proven congruent through HL is option A.
Which of the following equations defines a line that passes through the points begin ordered pair negative 2 comma 7 end ordered pair and begin ordered pair 6 comma negative 9 end ordered pair?
Answers
The linear equation that passes through points (-2,7) and (6,-9) is given by:
y = -2x + 3
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line passes through points (-2,7) and (6,-9), hence the slope is given by:
m = (-9 - 7)/(6 - (-2)) = -2.
Hence, since when x = -2, y = 7, when x = 0, y = 7 - 2 x (0 - (-2)) = 3, which means that the y-intercept is of b = 3, and the equation is given by:
y = -2x + 3.
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