The required transformed function is given by, g(x) = 5/(x-2) + 6
Given the parent function is, f(x) = 1/x
Now if we vertically stretched the function by a factor 5 units then the function becomes,
g(x) = 5/x
Again if we shifted to the right to 2 units then the function becomes,
g(x) = 5/(x-2)
Further if we shift up to 6 units then the function transformed to,
g(x) = 5/(x-2) + 6
Hence the ultimate transformed function is, g(x) = 5/(x-2) + 6.
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solve for x……………………..
Answer:
7.5/3
Step-by-step explanation:
7x-7.5 = 4x
-7.5 = -3x
x= 7.5/3
Which phrase best describes the transformation(s) of the following graph from the parent quadratic function? f(x)=(x-2)^2+3
The parent quadratic function is 2 unit right and 3 units up.
Given function is
f(x) = (x-2)² +3
= x² - 2² - 2×x×2 + 3
= x2 - 4 - 4X + 3
= X² - 4X -1
Parent function g(x) = x²
The parent function is shifted to 2 units in right and 3 units up.
Parent function transformations are shown in blue. This is a 1 unit shift down. Mirroring of the x-axis is done functionally by multiplying the superordinate function by the negative function.
A parent function is the simplest function that satisfies the definition of a particular function type. For example, consider linear functions that form a family of functions.
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Disclaimer:- your question is incomplete, Please see below for the complete question.
Which phrase best describes the transformation(s) of the following graph from the parent quadratic function? f(x)=(x-2)^2+3
Point D (8,2) is reflected across the y-axis to form point E.
What are the coordinates of point E?
Given MK is a median use the figure below to answer the questions below.
If JM = 23, then JL =
If LJ = 20, then ML =
Answer:
[tex]46, 10[/tex]
Step-by-step explanation:
A median is the segment drawn from the vertex of a triangle that bisects the opposite side.
A line passes through the point (-4, -8) and has a slope of 4.
Write an equation in slope-intercept form for this line.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-4)}) \implies y +8= 4 (x +4) \\\\\\ y+8=4x+16\implies {\Large \begin{array}{llll} y=4x+8 \end{array}}[/tex]
can you please help me
The height of the actual building, given the height of the model, can be found to be 1, 455 feet
How to find the height of the actual building?The model is such that every inch of the building on the model is 75 feet of the actual building.
This means that if the height of the building in the model is 19 ² / ₅ inches, then the height of the actual building would be:
= Height of building in model x Scale factor per inch
= 19 ² / ₅ x 75
= 97 / 5 x 75
= 1, 455 feet
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(8u^2+3u-4)+(8u^2+3u-1)-(3u^2-3u-8)
Simplify the expression
[tex]\mleft(8u^2+3u-4\mright)+\mleft(8u^2+3u-1\mright)-\mleft(3u^2-3u-8\mright)[/tex]Removing all the parentheses, taking special care to change the signs of the last three terms:
[tex]8u^2+3u-4+8u^2+3u-1-3u^2+3u+8[/tex]Now collect like terms:
[tex]8u^2+8u^2-3u^2+3u+3u+3u-4-1+8[/tex][tex]13u^2+9u+3[/tex]can you guys s show work for graph inequality for
-2<x<5
The graph of the inequality is a straight line on the x-axis
from -2 to 5 also, -2 & 5 are not included in the graph.
Given, an inequality
-2 < x < 5
we have to draw a graph for the given inequality,
as the value of 'x' is from -2 to 5.
So, the graph of the inequality is a straight line on the x-axis
from -2 to 5 also, -2 & 5 are not included in the graph.
Hence, the graph of the inequality is a straight line on the x-axis
from -2 to 5 also, -2 & 5 are not included in the graph.
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Solve. Round the answer to the nearest cent, if necessary.Last year the profit for a company was $483,000. This year's profit decreased by 2.1%. Find this year's profit.
year's
this year´s profit is $ 472857
Explanation
we can easily solve this by using a rule of three
so
Step 1
a)let x represents this year's profit
so
if it is decreases by 2.1 %
[tex]\begin{gathered} x=100-2.1\text{ = 97}.9 \\ x=97.9\text{\%} \end{gathered}[/tex]so, this year's profit is 97.9% of the last year profit
hence
[tex]\begin{gathered} \text{if} \\ 483000\rightarrow100\text{ \%} \\ x\rightarrow97.9\text{ \%} \end{gathered}[/tex]we can make a proportion
[tex]\frac{483000}{100}=\frac{x}{79}[/tex]finally, solve for x,
[tex]\begin{gathered} \frac{483000}{100}=\frac{x}{97.9} \\ \text{Multiply both sides by 9}7.9 \\ \frac{483000}{100}\cdot97.9=\frac{x}{97.7}\cdot97.9 \\ 472857=x \end{gathered}[/tex]therefore
this year´s profit is $ 472857
I hope this helps you
Write and equation for a line with a slope of 3 that passes through the point P(2,−5)
Answer:
y=3x-11
Step-by-step explanation:
In this question, we will use the point slope form:
Which has the equation:
[tex]y-y_1=m(x-x_1)\\subsitute:\\y+5 = 3(x-2) , (y--5=+5)\\y+5=3x-6\\y=3x-11[/tex]
Hope this helps!
The water bottle sale for a music festival started at 5:00 P.M. The table shows the linear relationship between the number of water bottles remaining and the number of hours since 5:00 P.M.
Which equation can be used to determine y, the number of water bottles remaining at the music festival x hours after 5:00 P.M.?
The equation used to determine y, the number of water bottles remaining at the music festival x hours after 5:00 P.M will be;
⇒ y = - 500x + 5500
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The table shows the linear relationship between the number of water bottles remaining and the number of hours since 5:00 P.M.
Now,
Find the linear equation for the given table as;
Take number of hours = x
And, Number of remaining bottles = y
So, Two points for the linear equation as;
⇒ (x, y) = (1, 5000) , (2, 4500)
Thus, The linear equation for the table is,
⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)
⇒ y - 5000 = (4500 - 5000) / (2 - 1) (x - 1)
⇒ y - 5000 = - 500 (x - 1)
⇒ y - 5000 = - 500x + 500
⇒ y = - 500x + 500 + 5000
⇒ y = - 500x + 5500
Thus, The equation used to determine y, the number of water bottles remaining at the music festival x hours after 5:00 P.M will be;
⇒ y = - 500x + 5500
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find the unit rate. round to the nearest hundredth, if necessary $200 for 15 ft
EXPLANATION
The unit rate is given by the following relationship:
Unit rate= $200/15ft = $13.3333.../ft
Then, rounding to the nearest hundreth:
Unit rate = $13.33/ft
If 180° ≤ ≤ 270 and S(A) = −4 then determine the exact values of cos(A) and tan(A)
Recall the definition of the sine of an angle on a right triangle:
[tex]\sin (A)=\frac{a}{c}[/tex]On the other hand, according to this diagram, the values for tan(A) and cos(A) are given by:
[tex]\begin{gathered} \cos (A)=\frac{b}{c} \\ \tan (A)=\frac{a}{b} \end{gathered}[/tex]Since 180≤A≤270, the right triangle that corresponds to the angle A on the coordinate plane looks as follows:
Where a and b are negative distances.
Since sin(A)=-4/7, we can assume that a=-4 and c=7. Use the Pythagorean Theorem to find the exact value of b:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \Rightarrow(-4)^2+b^2=7^2 \\ \Rightarrow16+b^2=49 \\ \Rightarrow b^2=49-16 \\ \Rightarrow b^2=33 \\ \Rightarrow|b|=\sqrt[]{33} \end{gathered}[/tex]We know that b should be negative. Then:
[tex]b=-\sqrt[]{33}[/tex]Substitute b=-sqrt(33) and c=7 to find the exact values for cos(A) and tan(A):
[tex]\begin{gathered} \cos (A)=-\frac{\sqrt[]{33}}{7} \\ \tan (A)=\frac{-4}{-\sqrt[]{33}}=\frac{4\cdot\sqrt[]{33}}{33} \end{gathered}[/tex]Therefore, the exact values for cos(A) and tan(A) are:
[tex]\begin{gathered} \cos (A)=-\frac{\sqrt[]{33}}{7} \\ \tan (A)=\frac{4\cdot\sqrt[]{33}}{33} \end{gathered}[/tex]12__-15 = -3
divide
multiply
add
subtract
Answer:
multiply 1 is the correct answer
12×1 - 15 = -3
Use distributive property and combining like terms to simplify.
5x-4y+2(y+x)
The simplified form is 7x - 2y.
Distributive property: What Is It?
This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
According to question,
5x-4y+2(y+x)
5x-4y+2y+2x
7x-2y
Hence, simplified form is 7x - 2y.
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Could you help me with these two questions? 20 points !
1 ) Create an equation in point-slope form that has a slop of 5 passing through the points (3,5)
2) Create an equation in point slop form that has a slop of 2 and passes through the points (-1, 6)
The equation of line are given as y = 5x - 10 and y = 2x + 8 respectively
Point-Slope FormulaThe point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point. The equation of a line is an equation that is satisfied by each and every point on the line. This means that a linear equation in two variables represents a line. The equation of a line can be found through various methods depending on the available information.
In this case, we have can proceed to write the equation of a straight line which is given as y = mx + c
m = slopec = y-interceptLet's find the y - intercept and write the equation.
y = mx + c
5 = 5(3) + c; c = 5 - 15 = -10
y = 5x - 10
2) We have the slope as 2 and the points are (-1, 6)
The equation of the line can be written in form of y = mx + c
6 = 2(-1) + c
6 = -2 + c; c = 8
The equation is given as y = 2x + 8
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Find the length of RS.A.73 unitsB.11 unitsC.About 8.5 unitsD About 3.3 units
Let,
[tex]\begin{gathered} R=(x_1,y_1)=(-4,1) \\ S=(x_2,y_2)=(-1,9) \end{gathered}[/tex]The expression to calculate the distance between two points is,
[tex]\begin{gathered} D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ D=\sqrt[]{(-1-(-4))^2+(9-1)^2} \\ D=\sqrt[]{(3)^2+(8)^2} \\ D=\sqrt[]{9+64} \\ D=\sqrt[]{73} \\ D=8.5\text{ units} \end{gathered}[/tex]Thus, the length of the line RS is 8.5 units, and the correct option is option C.
A bakery is selling breakfast platters. A platter of 12 bagels costs $10.80. Additionally, it costs $6.50 for a gallon of coffee.
What is the slope of this situation?
0.11
0.90
6.50
10.80
The slope of the given situation of selling breakfast platters is 0.90.
Given, the platter of 12 bagels costs $10.80.
The extra cost of $6.50 for a gallon of coffee.
To find the slope of the situation, we convert the situation into the equation of the line.
y=mx+c
here c is the extra cost that is 6.50.
12m=10.80
For 12 bagels , the cost is 10.80, then the slope will be the cost of each bagel.
m=10.80/12
m=0.90
m=$0.90
Therefore, option c 0.90 is the slope of the given situation of the bakery selling the breakfast platter of 12 bagels and a gallon of coffee.
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ions
aic
. Find the algebraic
expression:
3 more than the product of 2
and k
•
•
A) 3(2) + k
B) 3k + 2
C) 3 + 2k
D) 2k - 3
hi, I'm supposed to write a exponential equation for the graph but I'm not sure how to do it
d)
To determine the type of function, we would compare the y values. If the ratio of consecutive y values is the same, then the function is exponential. We have
2/1 = 4/2 = 8/4 = 2
Thus, it is an exponential function. The general formula for an exponential function is
y = ab^x
We would find a and b
Substituting x = 0 and y = 1 into the formula, we have
1 = ab^0
1 = a
Substituting x = 1 and y = 2 into the formula, we have
2 = ab^1
2 = ab
Substituting a = 1 into 2 = ab, then
2 = 1 * b = b
By substituting a = 1 and b = 2 into the original formula, the equation would be
y = 2^x
Given f(x) = 5x − 7 and g(x) = −4x + 2, what is (f − g)(x)? x − 9 x − 5 9x − 9 9x − 5
To get (f-g)(x), we're essentially just factoring out x from f(x) and g(x).
-> f(x) - g(x) = x(f-g), and by the properties , x(f-g) is the same as (f-g)(x).
Therefore, (f-g)(x) = 5x - 7 - (-4x + 2) = 5x - 7 + 4x - 2 = 9x - 9.
Answer:
[tex](f-g)(x)=9x - 9[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x) = 5x-7 \\ g(x) = -4x + 2\end{cases}[/tex]
To find (f - g)(x), subtract function g(x) from function f(x):
[tex]\begin{aligned}(f-g)(x)&=f(x)-g(x)\\&=(5x-7)-(-4x+2)\\&=5x-7+4x-2\\&=5x+4x-7-2\\&=9x-9\end{aligned}[/tex]
Therefore, the solution to the given composite function is:
[tex]9x-9[/tex]Write the equation of the line parallel to x+7y=21 that passes through the point (–14, 4).
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First, rearrange x + 7y = 21 into y = mx + c form.
x + 7y = 21
7y = - x + 21
y = -1/7x + 3
Parallel lines have the same gradient so gradient of line is -1/7.
Equation of line is now y = -1/7x + c.
Substitute (-14,4) into the equation to find c.
4 = -1/7(-14) + c
4 = 2 + c
c = 2
Hence, equation of line is y = -1/7x + 2.
Solve this equation for N. 3N + 5 = 38
ANSWER
N = 11
EXPLANATION
Given:
3N + 5 = 38
Desired Outcome:
Value of N
Solve for N
[tex]\begin{gathered} 3N+5=38 \\ subtract\text{ 5 from both sides} \\ 3N+5-5=38-5 \\ 3N=33 \\ divide\text{ both sides by 3} \\ \frac{3N}{3}=\frac{33}{3} \\ N=11 \end{gathered}[/tex]Hence, the value of N is 11.
Find the equation of the line shown. Enter your answer in point-slope form.AV15110SX15-10-51015-5-10151
From the graph given, we are asked to find the equation of line, with our answer in point slope form.
from the graph:
y = 9, x = 10
y1 = 5, x1 = 6
recall, the equation of a line is:
y = mx + b
slope m = y - y1/x - x1
m = 9 - 5/10 - 6
m = 4/4
m = 1
y = 1x + b
y = x + b
using the point slope form:
y - y1 = m(x - x1)
Where:
y = y coordinate of second point
y1 = y coordinate of point one
m = slope
x = x coordinate of second point
x2 = x coordinate of point one.
Therefore, the point slope equation is:
y - 5 = 1(x - 6)
y - 5 = x - 6
in a video store,a DVD that usually sells for $15 is marked 10% OFF that price. How much does the DVD cost now that it's on sale?
Answer
The cost of the DVD now that it's on sale will be $13.5
Explanation
DVD actual price = $15
10% off the price will be (10/100 x $15) = $1.5
The selling price of the DVD now will be $(15 - 1.5) = $13.5
∴ The cost of the DVD now that it's on sale will be $13.5
the side length of 11
A perfect square means that the given value is the result of the multiplication of an integer with itself, for example 2*2=4 →√
HELP PLEASE HELP PLEASE NEED IT NOW!!
You run m miles on Monday, the same amount on Tuesday, and 3 miles on Wednesday. Write an expression in the simplest form that represents the total amount in each situation.
(please show work)
The expression that represents the given situation is 2x + 3 = T.
What do we mean by expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, the expression to represent the given situation is:
Since the miles run on Monday and Tuesday are the same, then let the miles run be 'x'.
Miles run on Monday is x.Miles run on Tuesday is x.Miles' run on Wednesday is 3.Let, the total mile be T.
Now, the expression will be:
x + x + 3 = T2x + 3 = T
Therefore, the expression that represents the given situation is 2x + 3 = T.
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FreshmenSophomoreJuniors464Below, the two-way table is given for aclass of students.Seniors TotalMale2 2Female 36 3TotalIf a student is selected at random, find theprobability the student is a junior given that it'smale. Round to the nearest whole percent.[?]%
Solution
Step 1
Write out the expression for the probability of an event occurring
[tex]Pr(\text{ event occurring)}=\frac{Number\text{ of required events}}{\text{Total number of events}}[/tex]For this question,
The number of required events = The number of students that are male and Junior= 2
The total number of events = The total number of male students= 4+6+2+2 = 14
Step 2
Find the required probability after substitution
[tex]Pr(\text{student }is\text{ a junior given its male) =}\frac{2}{14}=\frac{1}{7}[/tex]Hence the probability the student is a junior given its a male = 1/7
In percentage, the probability will be
[tex]\begin{gathered} \frac{1}{\frac{1}{7}}=\frac{100}{x} \\ \text{x =}\frac{1}{7}\times100 \\ \text{x = 14.29\%} \end{gathered}[/tex]
Where x is the required percentage, to the nearest whole percent, the final answer is 14%
Julias frogs are 2/5 of the amount of Remus frogs. If Remus gives a half of his frogs to Julia, what will the ratio of Julia's frogs to Remus frogs be ?
Let:
Rf = Remus frogs
Jf = Julias frogs
[tex]Jf=\frac{2}{5}Rf[/tex]If Remus gives a half of his frogs to Julia, what will the ratio of Julia's frogs to Remus frogs be ? so:
[tex]\begin{gathered} Rf=\frac{5}{2}Jf \\ Jf=\frac{2}{5}Rf+\frac{1}{2}Rf=\frac{9}{10}Rf \end{gathered}[/tex]Therefore, the ratio will be:
[tex]\frac{\frac{9}{10}Rf}{Rf-\frac{1}{2}Rf}=\frac{9}{5}[/tex]please help me with this algebra question
Answer: D.
Hope it helps