Answer:
B. g(x) is shifted 5 units right and 2 units up from f(x).
g(x) = [tex]\frac{1}{x-5}[/tex] + 2 is compared to the parent function, f(x) = [tex]\frac{1}{x}[/tex] by g(x) is shifted 5 units right and 2 units up from f(x).
What is Translation of Functions?Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
Given parent function is,
f(x) = [tex]\frac{1}{x}[/tex]
And the translated function is,
g(x) = [tex]\frac{1}{x-5}[/tex] + 2
When f(x) becomes g(x), the first change occurred is [tex]\frac{1}{x}[/tex] changes to [tex]\frac{1}{x-5}[/tex].
That is f(x) changes to f(x-5).
This translation occurs when the function undergoes horizontal translation towards right.
Then [tex]\frac{1}{x-5}[/tex] is translated to [tex]\frac{1}{x-5}[/tex] + 2.
That is, f(x-5) is changed to f(x-5) + 2.
This occurs for the vertical translation towards up.
Hence the translation occurred is g(x) is shifted 5 units right and 2 units up from f(x).
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Mr. Lopez fruit salad recipe requires 3/4 of a cup of fresh peaches for 1 serving. He uses 9 cups of fresh peaches to prepare the salad. How many servings of the fruit salad did he prepare?
Answer:
6.75 servings
Step-by-step explanation:
[tex] \frac{3}{4} \times 9 = \frac{27}{4} = 6 \frac{3}{4} = 6.75[/tex]
Answer:
9 servings
Step-by-step explanation:
feel free to ask where you don't understand.
Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
1f(x) = x(x-a)²(x - b)4
2f(x) = x(x - a)³(x- b)²
3f(x) = x²(x-a)(x- b)²
4f(x) = x²(x-a)5(x- b)
The polynomial function that could represent the graph is f(x) = x²(x - a)(x - b)² with four turning points
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The maximum number of turning points of a polynomial function is always one less than the degree of the function.
Hence the polynomial represented by the graph is of degree 5 since it has 4 turning points. The polynomial function that could represent the graph is f(x) = x²(x - a)(x - b)²
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How many solutions does the following equation have?
7(y+3)=5y+8
A. No Solution
B. Exactly One Solution
C. Infinitely many solutions
Answer:
B. Exactly One Solution
Step-by-step explanation:
Given:
[tex]7(y+3)=5y+8[/tex]
Expand the brackets:
[tex]\implies 7y + 21 = 5y + 8[/tex]
Subtract 21 from both sides:
[tex]\implies 7y + 21-21 = 5y + 8-21[/tex]
[tex]\implies 7y=5y-13[/tex]
Subtract 5y from both sides:
[tex]\implies 7y-5y=5y-13-5y[/tex]
[tex]\implies 2y=-13[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{2y}{2}=\dfrac{-13}{2}[/tex]
[tex]\implies y=-\dfrac{13}{2}[/tex]
Therefore, the equation has exactly one solution.
Write an expression for the area of the trapezium below.
Expand any brackets and fully simplify your answer.
Which of the lines below is a line of symmetry?
O A. Red
•
B. Yellow
C. Neither
• D. Both
Both the Red and Yellow lines are lines of symmetry, Option D is correct.
What is Coordinate system?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Lines of symmetry in a figure are lines that divide the figure into equal parts.
The given figure is a square as we observe the four sides are equal in the given shape.
In a square, there are four lines of symmetry, each of which divides it into two identical parts.
The symmetry lines of a square are both its diagonals and the lines joining the midpoints of its opposite sides (bisectors).
In the given Figure, the Red lines cuts the shape into 2 equal halves vertically and the Yellow line cuts the shape into 2 equal halves diagonally.
Hence, both the Red and Yellow lines are lines of symmetry, Option D is correct.
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100 points helpppp now
Solve the inequality hurrry show your work
33+6f<33
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:f < 0 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 33 + 6f < 33[/tex]
[ subtract 33 on both sides ]
[tex]\qquad \tt \rightarrow \: 33 - 33+ 6f < 33 - 33[/tex]
[tex]\qquad \tt \rightarrow \: 6f < 0[/tex]
[tex]\qquad \tt \rightarrow \: f < 0[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Explain how to find the constant of proportionality for the ratio of robins to cardinals.
The constant of proportionality will be 3.
The complete question ks given below:-
Explain how to find the constant of proportionality for the ratio of robins to cardinals. A 2-column table with 4 rows. Column1 is labelled Cardinals with entries 5, 6, 9, and 10. Column 2 is labelled Robins with entries 15, 18, 27, and 30.
What is the ratio?In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.
Given data will be arranged as follows:-
robins 15, 18, 27, 30.
cardinals 5, 6, 9, 10.
The constant of proportionality will be calculated by taking a ratio of the data:-
[tex]\dfrac{Cardinals}{Robins} =\dfrac{15}{5}=\dfrac{18}{6}=\dfrac{27}{9}=\dfrac{30}{10}=3[/tex]
Therefore the constant of proportionality will be 3.
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A ration of two numbers is equal to 3:8 if the smaller number is 14 find the greatest number
Answer:
34 and ⅔
Step-by-step explanation:
added in the picture
Is 50.2 a rational or an irrational number, why?
Answer:
Rational.
Step-by-step explanation:
[tex]\textbf{A rational number is a real number that can be expressed as}~ \dfrac{p}{q},\\\\\textbf{where}~ p~ \textbf{and}~ q~ \textbf{are integers.}\\\\ \boxed{50.2 = \dfrac{502}{10}}\\\\ \textbf{50.2 can be expressed as a ratio of two integers,}~ \textbf{so it is a rational number.}[/tex]
Several paint mixtures are made by mixing blue paint and white paint. Paint Colors Blue Paint White Paint Mixture A 5 cups 12 cups Mixture B 6 cups 6 cups Mixture C 4 cups 12 cups Mixture D 5 cups 6 cups Which mixture has the highest ratio of blue paint to white paint? mixture A mixture B mixture C mixture D
The correct answer is option B which is mixture B will have the highest ratio of blue paint.
What is a ratio?In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.
The given ratios are:-
Mixture A = [tex]\dfrac{5}{12} = 0.41[/tex]
Mixture B = [tex]\dfrac{6}{6}= 1[/tex]
Mixture C = [tex]\dfrac{4}{12}= 0.33[/tex]
Mixture B = [tex]\dfrac{5}{6}=0.83[/tex]
Here the ratio of mixture B is the highest among all the options available.
Therefore the correct answer is option B which is mixture B will have the highest ratio of blue paint.
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the distance time graph represents a journey made by jo at the speed was jo walking for the first 15 minutes
The speed that Jo walked for the first 15 minutes is; 6 km/hr
How to Interpret Distance Time Graphs?The distance - time graph is missing and so i have attached it.
Now, the formula for speed is;
Speed = Distance/time
The distance after 15 minutes from the graph is 1.5km.
Now, 15 minutes when converted to hours is 15/60 = ¹/₄ hr
Thus, the speed that Jo walked for the first 15 minutes is;
Speed = 1.5/(¹/₄)
Speed = 6 km/hr
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The diameter of a circle is 62cm
by first calculating the radius work out the area of the circle
give your answer in cm² to 1.d.p
What is the median of the following data set?
(3, 4, 2, 8, 5)
02
03
04
06
Answer:
4
Step-by-step explanation:
The median is the middle number when the list is sorted from least to greatest or greatest to least.
We make this list to get 2,3,4,5,8 or 8,5,4,3,2 and the middle number in both lists is 4.
Which statements are true about the linear inequality y > three-fourthsx – 2? select three options.
The statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).
What is linear inequality?Linear inequality is defined as the comparison of two values using greater than, less than, greater than or equal to, and less than or equal to.
Using the general formula for linear inequality,
y >mx+ b
y > 3/4x - 2
Where m = slope of the graph
b = interception at y axis
Therefore, the statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).
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A = 1/ 7 - 4√3
B = 1/ 7+ 4√3
Find....
A) a² + b²
B) a³ + b³
The value of a2+b2 = 0.05
The value of a3+b3 = 41.73
Concept: (a+b)2 = a2+b2+2ab
(a-b)2 = a2+b2-2ab
(a+b)3 = a3+b3+3a2b+3ab2
(a-b)3 = a3-b3-3a2b+3ab2
(I) a²+b²=(1/7-4✓3)²+(1/7+4✓3)²
⇒ ( 1/49 - 48) +(1/49 + 48)=(1-2352/49) + (1+2353/49)
⇒ -47.97 +48.02= 0.05
(ii) a³+b³=(1/7-4✓3)³+(1/7+4✓3)³
⇒(-6.78)³ +(7.07)³
⇒-311.66 +353.39= 41.73
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A 10 ft slide will be installed on a playground. The top of the slide will be 8 ft above the ground.
What angle does the slide make with the ground?
Enter your answer in the box. Round your final answer to the nearest degree.
Answer
12
Step-by-step explanation:
Which statement is true about the information in the double line graph?
A. The number of customers at 12:00 was less on Friday than Saturday.
B. There were more customers on Saturday than Friday.
C. The number of customers was less Saturday than Friday at 10:00 a.m. because many customers slept later.
D. The highest number of customers on both days was at 12:00 p.m.
Answer:
the answer is d as 38 31 which are highest
Step-by-step explanation:
a is false as 38>31 which is on Saturday
b is false as Saturday customers were less we can infer from the last three on Friday
c false as Saturday was 12 people and Friday 6 people
Study the table.
x
y
–2
8
–1
2
0
0
1
2
2
8
Which best describes the function represented by the data in the table?
linear with a common ratio of 4
linear with a common second difference of 4
quadratic with a common ratio of 4
quadratic with a common second difference of 4
Answer:
quadratic with a common second difference of 4
Step-by-step explanation:
quadratic equations: Quadratic equations are the polynomial equations of degree 2 example - a[tex]x^2\\[/tex]+ b[tex]x[/tex] + c = 0.
[tex]\begin{array}{cc}x&y\\-2&8\\-1&2\\0&0\\1&2\\2&8\end{array}\right][/tex]
from the table it is clear that,
function is y = 2[tex]x^2\\[/tex]
so the function is not linear as the equation specifies.
formula to find second difference of a quadratic equation:
f(x + 2) - 2f(x + 1) + f(x)
therefore;
[tex]2(x+2)^2[/tex] - [tex]4(x+1)^2[/tex] + [tex]2x^2[/tex]
[tex]2(x^2 + 4x + 4) - 4(x^2 + 2x+ 1 ) + 2x^2[/tex]
[tex]2x^2 + 8x + 8 - 4x^2 - 8x - 4 + 2x^2[/tex]
[tex]4x^2 - 4x^2 + 8x - 8x +8 - 4[/tex]
4
therefore, the answer is quadratic with a common second difference of 4
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Circle o has a circumference of 28.3 cm. What is the length of the radius r?
What is the vertex of the graph of the function below?
y=x² + 4x-6
A. (2,0)
B. (-2,6)
C. (-2,-10)
D. (2,6)
Consider a quadrilateral with vertices A(2,2) , B(2,5) , C(7,2), and D(7,5). What is the shape and area of quadrilateral ABCD
Answer:
Shape is rectangle
Area of rectangle = length * width
= 5 * 3
= 15 units²
Evaluate.
4^3 + 8^2 = ??
Answer: 128
Step-by-step explanation:
[tex]4^3 = 4*4*4 = 16*4 = 64[/tex]
[tex]8^2 = 8*8 = 64[/tex]
[tex]64+64 = 128[/tex]
QUESTION 10, 11, 12 and 13, 40 POINTS FOR CORRECT AWNSER AND WILL BE BRAINLIEST PLS BE FAST!! I WILL DO ANYTHING U WANT
10. The missing conversion is 20.32 inches
11. Total number of red cars is 34
12. Total number of blue cars is 36
13. Total number of silver cars is 70
What is Ratio?Ratio is the number of times a quantity is contained more or less than another in a whole.
Analysis:
10. If 1 inch = 2.54cm
Then 8 inches = 8 x 2.54cm = 20.32 cm
First car park: Total number of cars = 60
ratio of red:blue:silver = 1:2:3
Total ratio = 1+2+3 = 6
number of red cars = 1/6 x 60 = 10
number of blue cars = 2/6 x 60 = 20 cars
number of silver cars = 3/6 x 60 = 30
second car park: Total number of cars = 80
ratio of blue: red: silver = 2:3:5
total ratio = 2+3+5 = 10
number of red cars = 3/10 x 80 = 24
number of blue cars = 2/10 x 80 = 16
number of silver cars = 5/10 x 80 = 40
11. Total number of red cars = 10+24 = 34
12. Total number of blue cars = 20+16 = 36
13. Total number of silver cars = 30+40 = 70
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Equation of graph problem
The parent function y=1/x²
How horizontal shifting of the graph takes place?If a function f(x) is shifted horizontally by k units the parent function f(x) becomes f(x+ k) where k>0
Here, the parent function y=1/x²
Add 3 to x in the denominator as the graph is shifted to left 3.
and, Add 1 to the fraction, because the graph is shifted up 1 unit.
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What value represents the vertical translation from the graph of the parent function f(x)=x² to the graph of the function
g(x)=(x+5)²+3?
Answer: 3
Reason:
Going from x^2 to (x+5)^2 means we shift the graph 5 units to the left.
The +3 at the end shifts the parabola up 3 units. This is because we add 3 to each y value. For instance a point like (0,25) moves to (0,28)
PLEASE HELP ME WITH THIS ASAP
A fountain sprays water into a pool as part of the filtration system. The projected path of water is modeled by the function given in the table, where x represents the time in seconds since the water left the fountain and f(x) represents the height in feet above the pool’s water line.
How many seconds does the water travel through the air?
–6
1.5
3
5
The water travels in 3 seconds.
The correct option is (C).
what is function?
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given information-
x 0 1 2 3 4 5
f(x) 1.5 2 1. 5 0 -2.5 -6
The image of table attached below.
Here, x represents the time (sec) and f(x) represent the height in feet above the pool’s water line.
From the table,
The height of the water started with 1.5 ft above.After one second the water height reached to the 2 feet above.After two seconds the water height reached to the 1.5 feet above.In 3rd second the water height comes down at the pool's water line.Hence, the water travel through the air for the 3 seconds.
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When is the best time to round a number in a multi-step problem?
Answer:
At the end of the multi step problem
PLEASE HELP ANSWER MY QUESTION ASAP!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: a_{33} = 1\degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
In a matrix, [tex] \sf a_{ij} [/tex] represents an element in " i " th row and " j " th column.
Henceforth, element [tex] \sf a_{33} [/tex] represents element in 3rd row and 3rd column.
[tex]\qquad \tt \rightarrow \:a_{33} = 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
After covering 4/5 of the journey, James found that he has traveled 48 km. How much of the journey is still left?
Answer:
12 km
Step-by-step explanation:
Let the total distance to be traveled = x
[tex]\sf \dfrac{4}{5} \ of \ the \ journey = 48\\\\[/tex]
[tex]\sf \dfrac{4}{5}*x = 48\\\\[/tex]
[tex]x = 48*\dfrac{5}{4}[/tex]
= 12 * 5
x = 60 Km
Distance still to traveled = 60 - 48 = 12Km
