the function g(x) was obtained by transforming f(x)=1/x Use the description of the transformation to write the equation representing g(x).f(x) Is vertically stretched by a factor of 2, reflected about the X axis, then shifted 5 units.
Answers
Since f(x) is vertically strectched by a factor 2, we get
[tex]f(x)\longrightarrow\frac{2}{x}[/tex]next, it is reflectec about the x-axis, then we have
[tex]\frac{2}{x}\longrightarrow-\frac{2}{x}[/tex]Finally, its shifted 5 units on x axis, then we have
[tex]-\frac{2}{x}\text{ --> }-\frac{2}{x+5}[/tex]which corresponds to option 2
Related Questions
LEVEL 1
Roses are red, violets are blue. The order of colors, is your clue.
Directions: Solve each
equation. The green
and purple equations
are fractions. Once you
have the answer, find
the number that is on
the colored line, and
put it on the matching
line next to the code.
1.8-(-3.7) =
-7.2 +4.1=-
-1.5 x (-0.2) =
-2/7 ÷ (-1/4) =___/
Code:
——-
HELP ASAP PLEASE..
Answers
Answer:
1.8-(-3.7)= 5.5
-7.2+4.1= -3.1
-1.5*(-0.2)= 0.3
-2/7÷(-1/4)= 8/7
code: 5.5,(-3.1),0.3,8/7
Identify the points in figure 1 that correspond to the points Q and S . Label them B and D . What is the distance between b and d
Answers
what is the distance between P and R?
Step 1
the easiest way to find the distance is by using the grid, just count the division, one division in an unit, so
between P and R, there are six units, so the distance is 6
Let f(x) = -2x^2– 7 and g(x) = 4x – 7.(fog)(x) =(gof)(x) =(fog)(1) =
Answers
Part 1.
The compositon fog is given by
[tex](f\circ g)(x)=-2(4x-7)^2-7[/tex]which gives
[tex]\begin{gathered} (f\circ g)(x)=-2(16x^2-56x+49)^{}-7 \\ (f\circ g)(x)=-32x^2+112x-98^{}-7 \\ (f\circ g)(x)=-32x^2+112x-105 \end{gathered}[/tex]Then, the answer is:
[tex](f\circ g)(x)=-32x^2+112x-105[/tex]Part 2.
The composition gof is given by
[tex](g\circ f)(x)=4(-2x^2-7)-7[/tex]Then, the answer is:
[tex](g\circ f)(x)=-8x^2-35[/tex]Part 3.
In this case, we need to substitute x=1 into the answer of Part 1, that is,
[tex]\begin{gathered} (f\circ g)(1)=-32(1)^2+112(1)-105 \\ (f\circ g)(1)=-32^{}+112-105 \end{gathered}[/tex]Therefore, the answer is:
[tex](f\circ g)(1)=-25[/tex]solve the equations. 13x - 6y = 22x= y + 6x=y=
Answers
5. Find the perimeter for the figure. Show the set-up and allwork.
Answers
The perimeter of a polygon is given by the sum of the length of its sides. For the polygon in the picture we have the following side lengths:
[tex]7,9x,10,3x,12,4x,15,2x[/tex]Then their sum is:
[tex]7+9x+10+3x+12+4x+15+2x[/tex]We can group like terms. Like terms are terms multiplied by the same power of x. In this case we have two groups of like terms: constants and terms multiplied by x. Then we group them:
[tex](7+10+12+15)+(9x+3x+4x+2x)[/tex]We can use the distributive property in the terms with x. For example:
[tex]ax+bx+cx=(a+b+c)x[/tex]We use this and we also add the constants so we get:
[tex]\begin{gathered} (7+10+12+15)+(9x+3x+4x+2x)=44+(9+3+4+2)x \\ 44+(9+3+4+2)x=44+18x \end{gathered}[/tex]AnswerThen the answer is that the perimeter of the figure is 18x+44.
What is 64 feet in 8 inches
Answers
Given
[tex]The\text{ actual house is 64ft long.}[/tex]To draw 64ft long house using a 8 inch scale.
Explanation:
Since the unit of inch is smaller than the unit of feet.
Then, by using the 8inches long scale.
Consider, 1 inch is equal to 8ft.
That implies,
[tex]\begin{gathered} 1inch=8ft \\ 8inch=8\times8ft \\ =64ft \end{gathered}[/tex]Hence,
Mr. Bernard paid $4,794 in social security tax on earnings of $68,000 one year. What was the social security tax rate for that year to the nearest hundredth of a percent)?6.85%7.05%7.15%7.65%None of these choices are correct.
Answers
Answer:
7.05%
Explanation:
Mr Bernard taxable income = $68,000
Amount paid as social security tax on earnings = $4,794
Let the social security tax rate = x
This gives:
[tex]\frac{x}{100}\times68,000=4,794[/tex]Next, solve for x:
[tex]\begin{gathered} 680x=4794 \\ x=\frac{4794}{680} \\ x=7.05 \end{gathered}[/tex]The social security tax rate for that year (to the nearest hundredth of a percent) is 7.05%.
Just need one answer.Is it reflectional symmetry, Rotational symmetry, or is it both
Answers
This is a simple question to solve.
First, let's focus on the reflection symmetry, What is it?
Having a reflection symmetry means if we split the image in half the left side is identical to the right side. To illustrate better, we have the following picture:
As we can see above, the left side of our shape is identical to the right side, it is like a reflection, so: yes, the image has reflectional symmetry.
Now let's focus on rotational symmetry. A
Find the volume for the solid picture. ROUND TO THE NEAREST HUNDREDTH
Answers
The given picture is in the shape of the cuboid
The general expression for the voulme of cuboid is : Length x Breadth x Height
In the given picture of cuboid we have :
Length = 9.6 in
Breadth = 6.75 in
Height = 2 in
So, the volume of given picture is :
[tex]\begin{gathered} \text{ Volume of Cuboid = Length}\times Breadth\times Height \\ \text{ Volume of Cuboid = 9.6}\times6.75\times2 \\ \text{Volume of Cuboid = }129.6in^3 \end{gathered}[/tex]To round off to the nearest hunredth : 129.6 will become 129.60
So, the volume of given solid picture is 129.60 in³
Answer : The volume of given solid picture is 129.60 in³
What is the first step to solving the following equation?5x – 11 = 42
Answers
Answer:
add 11 on both sides
Step-by-step explanation:
to solve this, you want x alone on one side. To achieve this, you first add 11 on both sides, so you only have the 5x alone.
Second step then is something to get only one x on the left side ;-)
(divide both sides by 5)
Answer:
the first step is to get the x term by itself on one side
need help with hw I'm stuck
Answers
The quadratic formula is:
[tex]\begin{gathered} \frac{\text{ -}b\pm\sqrt[2]{b^2\text{ -4ac}}}{2a} \\ The\text{ }equation\text{ }is: \\ 2x^2+3x\text{ -}5=4 \\ 2x^2+3x\text{ -}5\text{ -4=0} \end{gathered}[/tex]We need to equal to zero before using the formula.
Noah's mistake was that he stated c=-5 when c= -9
[tex]\begin{gathered} \frac{\text{ -}b\pm\sqrt{b^2\text{ -4ac}}}{2a} \\ =\frac{-3\pm\sqrt{(\text{ -3\rparen}^2\text{ -4\lparen2\rparen\lparen-9\rparen}}}{2(2)} \\ =\frac{-3\pm\sqrt{9\text{ +72}}}{4} \\ =\frac{-3\pm\sqrt{81}}{4} \\ =\frac{-3\pm9}{4} \\ \\ x1=\frac{-3+9}{4} \\ =\frac{6}{4}=\frac{3}{2}=1.5 \\ \\ x2=\frac{-3-9}{4} \\ =\frac{-12}{4} \\ =\text{ -3} \end{gathered}[/tex]x = 1.5 or x = -3
I have a question regarding a math topic on my review
Answers
The set of real numbers strictly contains the set of integers.
Every integer is a real number.
But pi is a real number and is not an integer
Hence choice A is correct
Simplify the expression.
(x)2(2xy3)5
2x3y15
32x7y8
32x7y15
10x3y8
Answers
Answer:
[tex]32x^7y^{15}[/tex]
Step-by-step explanation:
[tex]x^2 (2xy^3)^5 \\ \\ =x^2(2^5)(x^5)(y^{(3)(5)}) \\ \\ =x^2(32)(x^5)(y^{15}) \\ \\ =32x^7y^{15}[/tex]
Find the quotient. 1 5 – 2. + 3 1 55+3= 2 (Type a whole number, fraction, or mixed number.)
Answers
we have
[tex]5\frac{1}{2}\colon3[/tex]Convert mixed number to an improper fraction
5 1/2=5+1/2=11/2
substitute
(11/2):3=11/(3*2)=11/6
convert to mixed number
11/6=6/6+5/6=1+5/6=1 5/6
answer is
11/6 or 1 5/6
Question 4 (5 points)
In Brock's class of 24 students, 10 students report that math is their favorite class, 25% of the students report that science is
their favorite, and 1/3 prefer reading.. Show your work and/or explain your answer: Which subject is favored by the greatest
number of students? (5 points)
Answers
Mathi is favored by the greatest i.e 10 students, using percentage
What is percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The % sign is used to denote it.
There are 24 students in Brock's class
10 students say math is their favorite class , 25% say that science is their favorite class and 1/3 prefer reading.
Now you have to find out if more students prefer math or science. Well since the information tells you that 10 students prefer math, you need to find out that 25% of students prefer science and 1/3 prefer reading.
For 1st case, math favorite have 10 students,
For 2nd case, 25% of 24 is 24*25/100
=24*1/4
=6
And for 3rd case, who prefer reading is 1/3rd of students which is 24*1/3
=8
So Most students like math.
Hence, Mathi is favored by the greatest i.e 10 students.
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26. Find the perimeter of the polygon.3 ina. 15 inb. 21 inc. 9 in
Answers
To find the perimeter of the regular polygon, that in this case is a pentagon, multiply 5 by the sidelength of the pentagon, it means 5 times 3.
[tex]\begin{gathered} P=5\cdot3 \\ P=15 \end{gathered}[/tex]The perimeter of the polygon is 15in
Find an equation for the perpendicular bisector of the line segment whose endpointsare (-3, 2) and (7,6).
Answers
First, we need to find the midpoint. We can find it using the following equations:
[tex]\begin{gathered} Mp=(xm,ym) \\ xm=\frac{x1+x2}{2} \\ ym=\frac{y1+y2}{2} \end{gathered}[/tex]Where:
[tex]\begin{gathered} (x1,y1)=(-3,2) \\ (x2,y2)=(7,6) \end{gathered}[/tex]So:
[tex]\begin{gathered} xm=\frac{-3+7}{2}=\frac{4}{2}=2 \\ ym=\frac{6+2}{2}=\frac{8}{2}=4 \end{gathered}[/tex]Now, we need to find the slope of the line segment:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{6-2}{7-(-3)}=\frac{4}{10}=\frac{2}{5}[/tex]Since it is the line of the perpendicular bisector:
[tex]\begin{gathered} m\cdot mb=-1 \\ \frac{2}{5}mb=-1 \\ mb=-\frac{5}{2} \end{gathered}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-ym=mb(x-xm_) \\ y-4=-\frac{5}{2}(x-2) \\ y-4=-\frac{5}{2}x+5 \\ y=-\frac{5}{2}x+9 \end{gathered}[/tex]Answer:
[tex]y=-\frac{5}{2}x+9[/tex]does the mapping diagram represent a function
Answers
It is possible to show the relationship between input and output values using a mapping diagram. If there is only one output value associated with each input value, a mapping diagram illustrates a function.
What is a mapping diagram?A mapping diagram can be used to illustrate the connection between input and output values. A mapping diagram shows a function when each input value has a single related output value.Use the following test to determine whether a relation is a function given a mapping diagram for the relation: The outputs are a function of the inputs if each input has only one line attached to it. Every element of the domain is associated with exactly one element of the range in a function, which is a unique kind of relation. A mapping demonstrates the pairings of the elements. It displays the input and output values of a function, much like a flowchart would. The two parallel columns of a mapping diagram.As it is given in the description itself, that mapping diagram shows a function when each input value has a single related output value.
Therefore, it is possible to show the relationship between input and output values using a mapping diagram. If there is only one output value associated with each input value, a mapping diagram illustrates a function.
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Hello, I am having difficulty with this problem, thanks. Find the smallest numberFind the largest rational numberFind the smallest irrational number
Answers
In order to determine which of them is the smallest number, let's convert each number into a decimal number.
[tex]\sqrt[3]{9}=2.080083823\approx2.08[/tex][tex]\sqrt{3}=1.732050808\approx1.73[/tex][tex]\sqrt{\frac{1}{4}}=\frac{1}{2}=0.5[/tex][tex](-5)^{-2}=\frac{1}{(-5)^2}=\frac{1}{25}=0.04[/tex]Upon converting, we can easily that the smallest number is the fourth number which is (-5)^-2.
On the other hand, between the 4 numbers, there are only two rational numbers and these are the 3rd and the 4th number. Between the two, the largest rational number is the 3rd number which is √(1/4) equivalent to 0.5.
Lastly, between the 4 numbers, there are only two irrational numbers and these are the first and the second number. Between the two, the smallest irrational number is √3 which is equivalent to 1.73.
Zoo AttendanceZoo D 234,679Zoo E 872,544Zoo F 350,952For each zoo in the table, round the attendance to the nearest hundred thousand.4 grade student
Answers
Explanation
We can round to the nearest hundreds of thousands below.
Answer:
Zoo D: 200,000
Zoo E: 900,000
Zoo F: 400,000
The perimeters of the square and equilateral triangle shown below are equal. Which of the following is NOT a true statement about the figures. Remember: perimeter of a square = 4(one side), and perimeter of an equilateral triangle = 3(one side)
Answers
ANSWER
The incorrect option is Each side length of the square is 6 units
EXPLANATION
We are given that the perimeter of the square and the equilateral triangle are equal.
The length of the side of the square is 2x.
The perimeter of a square is given as:
P = 4 * L
=> P = 4 * 2x
P(square) = 8x
The length of side of the triangle is given as 3x - 1.5.
The perimeter of an equilateral triangle is given as:
P = 3 * L
=> P = 3 * (3x - 1.5)
P(triangle) = 9x - 4.5
Therefore, since both perimeters are equal:
8x = 9x - 4.5
Collect like terms:
9x - 8x = 4.5
x = 4.5
Now, for the options:
- The value of x is 4.5
- The perimeter of the square is 8 * 4.5 i.e. 36 units.
- Each side length of the square is 2 * 4.5 = 9 units
- Each side length of the triangle is :
3 * 4.5 - 1.5 = 13.5 - 1.5 = 12 units
So, the incorrect option is Each side length of the square is 6 units
Suppose that f is a one-to-one function, and f^-1 is its inverse. Suppose also that h(x) = 4 and g(x) = x^2 +xsecx. Then which of the following do we NOT know to be true?
Answers
Given:
The functions are,
h(x) = 4,
g(x) = x²+xsecx
The objective is to find which of the following is not known to be true.
Let's consider option (A).
[tex]\begin{gathered} (f\circ f^{-1}\circ h)(x)=(f(f^{-1})\circ h)(x) \\ =h(x) \\ =4 \end{gathered}[/tex]Thus, option (A) is true.
Let's consider option (B).
[tex]\begin{gathered} (g\circ h\circ f^{-1})(x)=(g(h(x))f^{-1})(x) \\ =(g(4))f^{-1})(x) \\ =((4^2+4\sec 4)f^{-1})(x) \\ =((16+4\sec 4)f^{-1}(x)) \end{gathered}[/tex]Since, the obtiaed answe doesn't matches with the given options.
Hence, option (B) is not true.
2 5 Evan mixed 2 pounds of nuts with 1 pounds of 3 6 7 raisins and 1 pounds of chocolate chips. How many 8 pounds did this mixture weigh? 1 3 24 B. © 6 6 3 6
Answers
Give that the nuts weigh 2 whole and a 2/3 pounds, raisins weigh 1 whole and a 5/6 ponds, and the chocolate chips weigh 1 whole 7/8 pounds.
All these ingredients are mixed to obtain the mixture.
Note that this mixture contains the above 3 things in the quantity mentioned. And there is no other stuff in the mixture.
So the weight of the individual ingredients would add up to get the weight of the mixture, therefore the weight of the mixture is calculated as,
[tex]2\frac{2}{3}+1\frac{5}{6}+1\frac{7}{8}\Rightarrow\frac{8}{3}+\frac{11}{6}+\frac{15}{8}=\frac{51}{8}=6\frac{3}{8}[/tex]Thus, the mixture weigh 6 whole and a 3/8 pounds.
Therefore, option (c) is the correct choice.
The perimeter of a square is (4x - 44). What is the length of each side?
Answers
The perimeter of square is given as,
[tex](4x-44)[/tex]Let length of side is denoted as S.
The formula for the perimeter of square is,
[tex]P=4\times S[/tex]To calculate the side of square , substitute the value of perimeter in the above formula.
[tex](4x-44)=4\times S\text{.}[/tex]Solving the equation we get,
[tex]4(x-11)=4\times S\text{.}[/tex][tex](x-11)=S.[/tex]The length of the square obtained is ,
[tex]S=(x-11).[/tex]A circle has a diameter of 300m. What is his circumference using pi?
Answers
To find the circumference using π = 3.14, we can proceed as follows:
1. The formula to find the circumference of a circle is:
[tex]C=2\pi r\Rightarrow D=2r\Rightarrow C=D\pi[/tex]2. That is, given the diameter, we can use it directly into the answer, since twice the value of the radius is the diameter of the circle:
[tex]C=300m\cdot3.14=942m[/tex]If we find the radius as:
[tex]D=2r\Rightarrow r=\frac{D}{2}=\frac{300m}{2}=150m[/tex]And If we use the next formula:
[tex]C=2\pi r=2\cdot3.14\cdot150m=942m[/tex]As we can see, in both cases, we found that the value for the circumference is equal to 942 meters (if we use π = 3.14).
In summary, the circumference of a circle that has a diameter of 300 meters is equal to 942 meters (C = 942m) (using π = 3.14).
The length of a rectangular garden is 9 feet longer than its width. If the garden's perimeter is 202 feet, what is the area of the garden in square feet?
Answers
We have the following rectangular garden
The perimeter is 202 feet, we can do the following equality
[tex]2(x+9)+2x=202[/tex]Now we solve "x"
[tex]\begin{gathered} 2x+18+2x=202 \\ 4x=202-18 \\ x=\frac{184}{4} \\ x=46 \end{gathered}[/tex]Now, we know the longer (l = 55) and the width (w = 46)
To find the area we use the following equation
[tex]\begin{gathered} A_R=l\cdot w \\ A_R=55\cdot46 \\ A_R=2530 \end{gathered}[/tex]In conclusion, the area of the garden is 2530 square feet
Liza hired a cleaning service to clean her house. To find C, the total cost of cleaning her house, she used the following formulaC=7.5x +25What is the dependent variable of the formula
Answers
The dependent variable of the formula
[tex]C=7.5x+25[/tex]is x
I need to know the system of equation in the photo
Answers
Solution:
The graph has a solution (4,-1);
That is, the system of equation must satisfy x=4 as y=-1.
LINE 1 has its y-intercept;
[tex]\begin{gathered} (0,1) \\ \end{gathered}[/tex]LINE 2 has its y-intercept as;
[tex](0,-5)[/tex][tex]\begin{gathered} x+2y=2 \\ 2y=-x+2 \\ y=-\frac{1}{2}x+\frac{2}{2} \\ y=-\frac{1}{2}x+1 \\ \\ x-y=5 \\ y=x-5 \end{gathered}[/tex]Thus, the system of equation that satisfy the graph is;
[tex]\begin{gathered} x-y=5 \\ x+2y=2 \end{gathered}[/tex]8 / 1/3 and 2 / 1/9 what's the generalizations can make about the equations
Answers
The generalization about the terms is that one is the cube root of the other
∛(8/9) = 2/3
What is generalizations in mathematics?Generalization can be viewed as a statement that holds true for a broad category of objects or numbers, as the method by which we arrive at a general statement, or as a means of transferring information from one context to another in the mathematics.
The equation represented as 8 / 1/3 and 2 / 1/9
is made an equated to each other and rearranged as follows
8 / 1/3 ⇔ 2 / 1/9
cross multiplying
8 * 1/9 ⇔ 2 * 1/3
8/9 ⇔ 2/3
the equation only holds true when the cube root sign is there then we have
∛(8/9) = 2/3
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which of the following number is rationalA
Answers
A rational number is any number that can be expressed as a ratio of two integers, in the form p/q.
We can say that root(16) is a rational number:
[tex]\sqrt[]{16}=4=\frac{4}{1}[/tex]