Translate each graph as specified below.(a) The graph of =yfx is shown. Translate it to get the graph of =y+fx2.(b) The graph of =ygx is shown. Translate it to get the graph of =yg−x5.
Answers
See graphs below
Explanation:[tex]\begin{gathered} a)\text{ y = f(x)} \\ f(x)\text{ + 2 is a translation of 2 units upward} \\ To\text{ get }y\text{ = f(x )+ 2, we will assign values to x and add 2 to its y coordinates in order to get } \\ \text{the coordinates of the new one} \end{gathered}[/tex]let x = -2, -1, 0, 1, 2
on the original
when x = -2, y = -3
new y coordinate = -3 + 2 = -1
when x = -1, y = 0.5
new y -coordinate = 0.5 + 2 = 2.5
when x = 0, y = 1
new y coordinate = 1 + 2 = 3
when x = 1, y = 1.5
new y oordinate = 1.5 +2 = 3.5
when x = 2, y = 5
new y-coordinate = 5 + 2 = 7
plotting the new points against x:
b) y = g(x)
y = g(x - 5)
subtract 5 from the x coordinate of the previous line
We will assign values for x, in order to get values of y
let x = 0, 1, 3
when x = 0, y = 0
new x coordinate = 0 - 5 = -5
when x = 1, y = 4
new x coordinate = 1 - 5 = -4
when x = 3, y = 7
new x coordinate = 3 - 5 = -2
plotting the points on the graph:
Related Questions
A small town has two local high schools. High School A currently has 900 students and is projected to grow by 50 students each year. High School B currently has 500 students and is projected to grow by 100 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Graph each function and determine which high school is projected to have more students in 4 years.
Answers
ANSWER
Red line: function A(t)
Blue line: function B(t)
High school A is projected to have more students in 4 years.
EXPLANATION
We have,
• A: number of students in school A after t years
,• B: number of students in school B after t years
School A is projected to have 50 more students each year, while school B is projected to have 100 more students each year. Thus, both functions are linear.
High school A starts with 900 students and each year it will have 50 more,
[tex]A(t)=900+50t[/tex]On the other hand, high school B starts with 500 students and each year will have 100 more,
[tex]B(t)=500+100t[/tex]In 4 years each school will have,
[tex]A(4)=900+50\cdot4=900+200=1100[/tex][tex]B(4)=500+100\cdot4=500+400=900[/tex]The graphs of each function are lines. The graph of A is a line passing through points (0, 900) - which is the y-intercept, and (4, 1100).
The graph of B is a line passing through points (0, 500) and (4, 900).
From these calculations and from the graph, we can see that function A has a higher value than function B at t = 4. Hence High School A is projected to have more students in 4 years.
The population of a village increases by 25% every year. The District Assemblygrants the village GH¢ 150.00 per head at the beginning of every year. If thepopulation of the village was 5.000 in the year 2005, calculate the Assembly'stotal grant from 2005 to 2010.
Answers
Explanation
We are given the following information:
• The population of a village increases by 25% every year.
,• The District Assembly grants the village GH¢ 150.00 per head at the beginning of every year.
,• The population of the village at the beginning of the year 2005 is 5,000.
We are required to determine the total grant from 2005 to 2010.
This is achieved th
Jamie is cutting for a craft project.she has a ribbon that is 2 1/4 inches long. How many pieces of ribbon can she cut that are 3/8inches long
Answers
Total Lenght = 2 1/4
Lenght of each piece = 3/8
Divide the total lenght by the lenght of each piece:
Total lenght = 2 1/4 = (2*4+1)/4 = 9/4
Total lenght / lenght of each piece = (9/4 ) / (3/8)
To divide 2 fractions we can multiply by the inverse of the second fraction:
[tex]\frac{9}{4}\times\frac{8}{3}=\frac{72}{12}[/tex]Simplify by 12:
6
Answer: 6 pieces
What is the measure in degrees of an angle that is
54/ 360
of a turn through a circle?
Answers
The measure of the angle through a circle will be 54°.
We are given that:
The measure in degrees of an angle = 54 / 360 of a turn through a circle.
This means that:
An arc should be proportional to the angle.
The circle have the angle as 360 degrees.
So, the angle will become:
54 / 360 × 360° = 54°
Therefore, we get that, the measure of the angle through a circle will be 54°.
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The points U, V, W and X all lie on the same line segment, in that order, such that the ratio of UV : VW:W X is equal to 1:3 : 4. If U X = 8, find VX.
Answers
The points U, V, W and X all lie on the same line segment, in that order, such that the ratio of UV : VW:W X is equal to 1:3 : 4. If U X = 8, find VX.
In this problem we have that
UV+VW+WX=UX -----> by addition segment postulate
we have
UX=8 units
so
UV+VW+WX=8 -------> equation A
UV/VW=1/3 ------> equation B
UV/WX=1/4 -----> equation C
Solve the system of equations
In equation B isolate the variable VW
so
3UV=VW
VW=3UV -------> equation D
In equation C isolate the variable WX
4UV=WX
WX=4UV ------> equation E
Substitute equation D and equation E in equation A
UV+(3UV)+(4UV)=8
solve for UV
8UV=8
UV=1
Find VW
VW=3UV
VW=3(1)=3 units
FInd WX
WX=4UV
WX=4(1)=4 units
Find out the value of VX
we have that
VX=VW+WX
substitute
VX=3+4=7 units
therefore
VX=7
write the number 9,700,000 in scientific notation
Answers
Explanation
[tex]9700000[/tex]All numbers in scientific notation or standard form are written in the form
[tex]a\cdot10^b^{}[/tex]where a is a number between 1 and 10, and b is a integer positive or negative
Step 1
Move the decimal 6 times to left in the number so that the resulting number, a= 9.7, is greater than or equal to 1 but less than 10
so
Suzy was reading Aniya's math notebook. Aniya wrote forty-six thousand three hundredfifteen > 46, 350. Suzy replied, "I think there is an errorExplain why Suzy said this using numbers, words, or another method to representyour thinking
Answers
it is an error because the number is
[tex]46,315[/tex]b. expanded form
[tex]\begin{gathered} 40,000+ \\ 6,000 \\ 300 \\ 50 \\ 0 \\ ------ \\ 46,350 \end{gathered}[/tex]c. 46,350 to the nearest thousand
[tex]46,350\longrightarrow46,000[/tex]801/4 is 5% of what number
Answers
5% could be express as 0.05
a number coul be express as x
then
[tex]x*0.05=\frac{801}{4}[/tex]solving for a number (x)
[tex]x=\frac{801}{4*0.05}=4005[/tex]4005
Suppose 225 trout are seeded into a lake. Absent constraint, their population will grow by 25% a year. If the lake can sustain a maximum of 3500 trout, use a logistic growth model to estimate the number of trout after 5 years. trout
Answers
It is known that the population growth model is given by:
[tex]P=P_0e^{kt}[/tex]Initial population is 225 so P0=225 so it follows:
[tex]P=225e^{kt}[/tex]Each year the population will increase by 25% so it follows:
[tex]\begin{gathered} P_0+0.25P_0=225e^k \\ e^k=\frac{5}{4} \\ k\ln e=\ln (\frac{5}{4}) \\ k\approx0.2231 \end{gathered}[/tex]So the population function is:
[tex]P=225e^{0.2231t}[/tex]The population in 5 years is given by:
[tex]P=225e^{0.2231\times5}\approx686.4960025[/tex]Hence the population of trout will be 686.4960025 after 5 years which can be rounded to 687.
Interior angle sum of a polygon: Find all the variables
Answers
We can see that angle d is the supplement of 97°. So d = 180°-97°= 83°
We can see that angle c and 97° are corresponding. So c=97°
If we see the triangle we can deduce that it is isosceles. So, the angles of the triangle would be (26°, 77°, 77°)( Since the sum of all angles must be equal to 180° and two angles must be equal)
The angle a is the supplement of angle 77°, so a= 180°- 77° = 103°.
The angle b is the supplement of angle 77°, so b= 180°- 77° = 103°.
Finally, we can find the angle e formulating the following equation:
540° - a - b - c- d = e (Since the sum of the angles of a pentagon must be equal to 540°)
540° - 103° - 103° - 97° - 83° = e (Replacing)
154° = e (Subtracting)
-121+17:[(93:3+3):2]x50=? 1) 2) 3) 4) 5) 6)
Answers
Hope this helped
Thank you
Student Beyonce You decide to buy a Super Size Hamburger Combo at the Burger Princess for 5.95. much change would you receive from 10.00. division Subtraction multiplication addition
Answers
Answer: 4.05
Just subtract 10.00 by 5.95 to get 4.05
hope this helps :)
Please help me with a question Rewrite the polar equation r=3sin(0) as a Cartesian equation.
Answers
Given,
The expression is,
[tex]r=3sin\theta[/tex]Required
The cartesian form of the given expression.
The cartesian form of the expression is,
Cindy read a total of 8 books over 2 months. If Cindy has read 20 books so far, how many
months has she been with her book club? Solve using unit rates.
months
Submit
3
Answers
Write an expression to represent the perimeter of the figure below: p=
Answers
Answer:
[tex]P=6x-8[/tex]
Step-by-step explanation:
Using the formula for the perimeter of a rectangle,
[tex]P=2(x+4+2x-8) \\ \\ =2(3x-4) \\ \\ =6x-8[/tex]
A coordinate map of the local grocery store is shown below. ice cream is located at the point (-8,0) sprinkles. are located at the point (-8,6)
Answers
The points (-8,0) & (-8,6)
To find the distance between then
Apply the distance formulae for coordinates:
[tex]\text{ Distance=}\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]Substitute the coordinates:
[tex]\begin{gathered} \text{ Distance=}\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ \text{ Distance=}\sqrt[]{(6-0)^2+(-8-(-8))^2} \\ \text{ Distance=}\sqrt[]{6^2+0} \\ \text{Distance =6 units} \end{gathered}[/tex]So, Icecream is 6 units away from the sprinkles
Answer : 6 unit
Find the center and the radius of the circle whose equation is x^2+y^2+8x-10y-23=0
Answers
Finding the equation of the standard form:
[tex]\begin{gathered} x^2+y^2+8x-10y-23=0 \\ x^2+y^2+8x-10y=23 \\ x^2+8x+16+y^2-10y+25=23+16+25 \\ \\ \\ (x+4)^2+(y-5)^2=64 \end{gathered}[/tex]
Based on the image, h = -4, k = 5 and r = 8, then...
Answer:
Center: ( -4, 5)
Radius: 8
Answer:the center would be (-4 -5)
Hope this helps
Yurly and his brother Anduray are each mailing a birthday gift to a friend. Yuriy's package weighs one lesspound than three times the weight of Anduray's package. The combined weight of both packages is 7pounds.Part 3: Yuriy and Anduray each graph the system that represents this situation. Who is correct? Explain why.
Answers
Yuriy
Explanations:[tex]\begin{gathered} \text{Let the weight of Yuriy's package be w}_y \\ \text{Let the weight of Anduray's package be w}_a \end{gathered}[/tex]Yuriy's package weighs one less pound than three times the weight of Anduray's package.
[tex]w_y=3w_a-1[/tex]The combined weight of both packages is 7 pounds
[tex]w_y+\text{ }w_a=\text{ 7}[/tex]The graph representing the two equations is:
3a) Find length between A(-3,8) and B(5,-4) in simplest radical form:
Answers
Find length between A(-3,8) and B(5,-4) in simplest radical form:
we know that
The distance between two points is equal to
[tex]d=\sqrt[]{(y2-y1)^2\text{ +(x2-x1)\textasciicircum{}2}}[/tex]we have
(x1,y1)=A(-3,8)
(x2,y2)=B(5,-4)
substitute in the formula
2. Calculate the distance MI for the length of the zipline cable. 3. Calculate the angle at which our zipliners will be descending toward the island . Safety regulations state that the angle at which a zipline cable meets the launching point cannot be smaller than 68 degrees . Please determine if we are in compliance with these regulations
Answers
right
[tex]\begin{gathered} AI)\text{ 400 ft} \\ MI)412.31\text{ f} \\ \text{angle = 76} \end{gathered}[/tex]Explanation
Step 1
AI?
we have a rigth triangle
then
let
[tex]\begin{gathered} AB=side1 \\ AI=side\text{ 2} \\ IB=\text{ hypotenuse} \end{gathered}[/tex]we can use the pythagorean Thoerem to find the missing vale
so
[tex]\begin{gathered} (AB)^2+(AI)^2=(BI)^2 \\ \text{replace} \\ 300^2+(AI)^2=500^2 \\ so \\ (AI)^2=500^2-300^2 \\ AI=\sqrt[]{500^2-300^2}=\sqrt[]{160000}=400 \\ AI=400 \end{gathered}[/tex]Step 2
MI?
let
[tex]\begin{gathered} \text{angle}=x \\ \text{opposite side=100 m} \\ \text{adjacent side=400 m} \end{gathered}[/tex]so, we need a function that relates those 3 values
[tex]\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]replace
[tex]\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan x=\frac{400}{100} \\ \tan x=4 \\ \text{hence} \\ x=\tan ^{-1}(4) \\ x=75.96 \\ \text{rounded} \\ x=76\text{ \degree} \end{gathered}[/tex]As 76 is greater than 68, the zipline cable compliance with these regulations.
Also, the hypotenuse (zipline ) is
[tex]\begin{gathered} (MI)^2=(AI)^2+(AM)^2 \\ \text{replace} \\ (MI)^2=(400)^2+(100)^2 \\ (MI)^2=170000 \\ MI=\sqrt[]{17000} \\ MI=412.31\text{ ft} \end{gathered}[/tex]I hope this helps you
use the diagrams to answer the following questions Number 7
Answers
To solve this we going to need the Tangent-Secant Interior Angle Theorem
Works in the following way
Using that formula we get
[tex]\begin{gathered} \beta=\frac{x}{2} \\ \\ 2\beta=x \\ \\ x=2*35\degree \\ x=70\degree \end{gathered}[/tex]Answer: x=70°
Use the protractor to find the measure of ABC. Then classify the angle.
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We are asked to find the measure of angle ABC and classify the angle.
As you can see from the figure, vertex A is at 30° and vertex C is at 155°
So, the angle ABC is
[tex]\angle ABC=155\degree-30\degree=125\degree[/tex]So, the angle ABC is 125°
Now recall that an obtuse angle is greater than 90° and less than 180°
Since 125° is between 90° and 180°, therefore, the angle ABC is an obtuse angle.
[tex]m\angle ABC=125\degree,\quad obtuse[/tex]Help me question 20 please find the domain and range
Answers
-2v + 9 = 25 what is it?
Answers
-2v + 9 = 25
-2v=25-9
-2v=16
v=16/-2
v=-8
Please provide the slope and the work showing how you got the slope for each equation please!
Answers
Slope for (16, -10) and (16, 15) is undefined, slope for (-19, -6) and (15, 16) is 11/17, slope for (19, -2) and (-11, 10) is -2/5, and slope for (12, -18) and (-15, 18) is -4/3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
For (16, -10) and (16, 15)
m=15-(-10)/16-16=15+10/0=25/0=undefined
For (-19, -6) and (15, 16)
m=16-(-6)/15-(-19)
=22/34=11/17
For (19, -2) and (-11, 10)
m=10-(-2)/-11-19
=10+2/-30
=-12/30=-2/5
For (12, -18) and (-15, 18)
m=18-(-18)/-15-12
=36/-27
=-12/9
=-4/3
Hence slope for (16, -10) and (16, 15) is undefined, slope for (-19, -6) and (15, 16) is 11/17, slope for (19, -2) and (-11, 10) is -2/5, and slope for (12, -18) and (-15, 18) is -4/3.
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Write the equation to solve and then find the measure of each acute angle(3x + 8° (2x + 12)°
Answers
We have here a right triangle, and that is why we have two acute angles (that is, the measure of each of them is less than 90 degrees).
We also know that the sum of the inner angles of a triangle is 180 degrees.
Having this information at hand, we can proceed as follows:
[tex](3x+8)+(2x+12)+90=180[/tex]This is the equation. Now, we need to solve this equation to find x, and then we need to use the algebraical equations to find each of the acute angles.
Solving the equation
1. Sum the like terms (like terms have the same variable or they are constants.)
[tex]3x+2x+8+12+90=180[/tex]Then, we have:
[tex]5x+110=180\Rightarrow5x=180-110\Rightarrow5x=70[/tex]2. We need to divide each side of the equation by 5 to isolate x:
[tex]\frac{5x}{5}=\frac{70}{5}\Rightarrow x=14[/tex]Now, we have x = 14. Therefore, the values for each of the acute angles are (we need to substitute the value of x in each equation):
a. 3x + 8 ---> 3 * (14) +8 = 42 + 8 =50. Hence, one acute angle measures 50 degrees.
b. 2x + 12 ---> 2 * (14) + 12 = 28 + 12 = 40 degrees. Therefore, the other acute angle measures 40 degrees.
In summary, the equation to solve is:
[tex](3x+8)+(2x+12)+90=180[/tex]And the values for each of the acute angles are 50 and 40 degrees.
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced. Assume that you take out a $3000 loan for 30 months at 9% APR. How much of the first month's payment is interest? (Round your answer to the nearest cent.)
Answers
Given parameters:
[tex]\begin{gathered} P=Loan\text{ amount=\$3000} \\ r=rate\text{ intersest per period=9\%=}\frac{9}{100\times12}=\frac{0.09}{12}=0.0075 \\ n=n\nu mber\text{ of payments=30 months} \\ \end{gathered}[/tex]We can now apply the formula below to calculate the payment amount per period
[tex]A=P\frac{r(1+r)^n}{(1+r)^n-1}[/tex][tex]\begin{gathered} A=3000\times\frac{0.0075(1+0.0075)^{30}}{(1+0.0075)^{30}-1} \\ \\ A=3000\times\frac{0.0075(1.25127)}{(1.25127)-1}=\frac{28.1536}{0.25127}=112.05 \end{gathered}[/tex]Thus his monthly payment will be $112.05
But since we have to get the interest on the first month's pay,
The interest is
[tex]r\times P=0.0075\times3000=\text{ \$22.5}[/tex]Thus, $22.50 is the interest on the first month's payment
Write a rule for the nth term of the geometric sequence given a_7=58, a_11=94
Answers
We are told the sequence is arithmetic. This means that the difference between one therm and the next is a constant.
We are also given two terms of the sequence. Let's see what their difference is
[tex]a_{11}-a_7=94-58=36[/tex]This means that, in general
[tex]a_{k+4}-a_k=36[/tex]With this, we can deduce that the difference between any two cnsecutive terms will be 9, for example
[tex]a_7=58,a_6=49,a_5=40,a_4=31,a_3=22[/tex]Indeed,
[tex]a_7-a_3=58-22=36[/tex]Now we should find the first term of the sequence, a₀, in order to find the rule for the nth term.
[tex]a_2=13,a_1=4,a_0=-5[/tex]In general, the rule for the nth term of an arithmetic sequence is given by
[tex]a_n=a_0+d(n)[/tex]where d is the difference between two consecutive term. In this case we have
[tex]a_n=-5+9\cdot n[/tex]with n=0,1,2,....
A line has a slope of 2/3 and contains point A(-6,-4) and point B (a, 2) what is the value of a?
Answers
From the point-slope formula, we have:
[tex]y-y_0=m(x-x_0)[/tex]where m is the slope, (x_0,y_0) are known points.
In this case, we have the slope and two points, we can substitute in the formula to get:
[tex]\begin{gathered} \text{if:} \\ (x,y)=(-6,-4) \\ \text{and} \\ (x_0,y_0)=(a,2) \\ \Rightarrow-4-2=\frac{2}{3}(-6-a) \\ \Rightarrow-6=-\frac{2\cdot6}{3}-\frac{2}{3}a \\ \Rightarrow-6=-4-\frac{2}{3}a \\ \Rightarrow-6+4=-\frac{2}{3}a \\ \Rightarrow-2=-\frac{2}{3}a\Rightarrow a=-\frac{2}{-\frac{2}{3}}=\frac{3\cdot2}{2}=\frac{6}{2}=3 \\ a=3 \end{gathered}[/tex]therefore, a=3
Note: you can also find a if you use the slope formula.
Solve for r and s. 2r + 6s =6 and 6r +2s =2 what kid of line are they
Answers
r = 0, s = 1
The lines are neither parallel nor perpendicular
Explanation:The given equations are:
2r + 6s = 6........(1)
6r + 2s = 2........(2)
Multiply equation (1) by 3
6r + 18s = 18........(3)
Subtract equation (2) from equation (3)
16s = 16
s = 16/16
s = 1
Substitute s = 1 into equation (2)
6r + 2(1) = 2
6r + 2 = 2
6r = 2 - 2
6r = 0
r = 0/6
r = 0
Make r the subject of the formula in equation (1)
2r = -6s + 6
r = -3s + 6
The slope of the line represented by equation (1) = -3
Make r the subject of the formula in equation (2)
6r = -2s + 2
r = (-2/6)s + (2/6)
r = (-1/3)s + 1/3
The slope of the line represented by equation (2) = -1/3
As seen above, the slope are not equal and are not negative inverses of each other. therefore, the lines are neither parallel nor perpendicular