Which of the following functions has a graph in which the vertex and axis of symmetry are to the left of the vertex and axis of symmetry ofof f(x) = (x-1)2 + 1? Select all that apply.A.g(x) =2(x - 1)2 - 1
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The given function is
f(x) = (x - 1)^2 + 1
For a function whose vertex and axis of symmetry are to the left of the given function, the function would show a horizontal translation of the given function to the left by a certain number of units.
Recall, if a function, f(x) is translated d units to the left, the new function is
f(x + d)
Looking at the options,
Option B shows a horizontal translation of 2 units to the left
Option E shows a horizontal translation of 3 units to the left
Option F shows a horizontal translation of 2 units to the left
Thus, the correct options are B, E, F
Related Questions
determine whether each point is a solution of the linear inequality.
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4x+2y >= 6
Substitute the point into the inequality and see if it is true
4(3) + 2(4) >= 6
12 +8 >= 6
20 > = 6
This is true so the point is a solution
simplify: 64a^3 b^5/16ab^8
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Using the following properties:
[tex]\begin{gathered} x^y\cdot x^z=x^{y+z} \\ a^{-n}=\frac{1}{a^n},n\ne0 \end{gathered}[/tex][tex]\frac{64a^3b^5}{16ab^8}=\frac{64}{16}\cdot a^3\cdot a^{-1}\cdot b^5\cdot b^{-8}=4a^2b^{-3}=\frac{4a^2}{b^3}[/tex]Seven more than twice John's age is55. How old is John?A.48B.24C.31D.62
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First, express the problem as an equation. 'Seven more' means +7, 'twice John's age' means 2J. Let's express it.
[tex]7+2J=55[/tex]Once we express the equation, solve for J.
First, subtract 7 from each side.
[tex]\begin{gathered} 7-7+2J=55-7 \\ 2J=48 \end{gathered}[/tex]Second, divide each side by 2.
[tex]\begin{gathered} \frac{2J}{2}=\frac{48}{2} \\ J=24 \end{gathered}[/tex]Therefore, John is 24 years old.B is the answer.Deborah purchases a Copy Machine for her business; using the Installment-Buying method, the price tag on the copier is55000 with add-on-interest of 7% for 3 years.Finda) SIMPLE INTEREST FUTURE VALUE$6125
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$168.06
Explanation:Price tag = $5000
Principal = 5000
rate = 7% = 0.07
time = 3 years
Using the simple interest formula:
[tex]\begin{gathered} I\text{ = PRT} \\ I\text{ =interest} \\ I\text{ = 5000 }\times\text{ 0.07 }\times\text{ 3} \\ I\text{ = \$}1050 \end{gathered}[/tex][tex]\begin{gathered} FV\text{ = I + P} \\ FV=\text{futue value} \\ FV\text{ = 5000 + 1050} \\ FV\text{ = \$6050} \end{gathered}[/tex]The monthly payment:
[tex]\begin{gathered} 12\text{ months = 1 year} \\ nu\text{mber of months in 3 years = }3(12)\text{ = 36 months} \\ \text{monthly payment = }\frac{future\text{ value}}{nu\text{mber of months}} \end{gathered}[/tex][tex]\begin{gathered} \text{monthly payment = }\frac{6050}{36} \\ monthly\text{ payment = 168.0556} \\ To\text{ the nearest hundredth, the monthly payment is \$168.06} \end{gathered}[/tex]Reggie recorded the number of pages he read each day for five days.!!ROUND YOUR ANSWER TO THE NEAREST TENTHS!!
Answers
Given:
Mean, x = 32
number of data, n = 5
From the plot, we have the following:
Number of pages Frequency
25 2
32 1
36 1
42 1
Sum up the distance between each data point and the mean using the absolute value and divide by the number of data(n).
To find the measn absolute devialtion, apply the formula:
[tex]\text{MAD}=\frac{\Sigma|x_i-x|}{n}[/tex]Thus, we have:
[tex]\text{MAD=}\frac{|25-32|+|25-32|+|32-32|+|36-32|+|42-32|}{5}[/tex]Solving further:
[tex]\begin{gathered} \text{MAD}=\frac{|-7|+|-7|+|0|+|4|+|10|}{5} \\ \\ \text{MAD}=\frac{7+7+0+4+10}{5} \\ \\ \text{MAD}=\frac{28}{5} \\ \\ \text{MAD}=5.6 \end{gathered}[/tex]Therefore, the mean absolute deviation of the data is 5.6
ANSWER:
5.6
Which input in this table is incorrect?Cost ofTax onItem Item1.00.082.00 .163.00 .246.00 .5610.00.80Noter all entries are in dollarsTotal Costof Item1.082.163.247.5610.80A. 6.00B. 3.00C. 2.00D. 10.00I
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From the table, we can observe that the formula for the total cost of item is
[tex]\text{Total cost of item = Cost of item + Tax on item}[/tex]From the data in the table, cost of item 6.00 has the input incorrect because the sum of the cost of its item and tax on the item is,
[tex]\text{Total cost of item=6.00+56=6.56}[/tex]but the total cost was incorrectly inputed as 7.56.
Hence, the correct option is Option A.
Which answer choice correctly represents 1.436363636…? _A) 1.4236 __B) 1.4236 ___D) 1.4236 ____C) 1.4236
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The bar over the numbers indicates the patern that is repeating, so to know where to put it we need to identify what is repeating in 1.436363636...
As we can see, "1" and "4" are not repeating, but, starting from "3", the pattern always repeats.
So, thsi number is the same as saying 1.4 followed by repating 36.
So, the correct representation is:
[tex]1.4\bar{3}\bar{6}[/tex]Which corresponds to alternative C
Dolbear’s law states the relationship between the rate at which snowy tree crickets chirp and the air temperature of their environment. Formula 50+ n-40 over 4 Where t is a temperature degrees Fahrenheit and N is a number of chirps per minute. If n=74 find the temperature in degrees Fahrenheit,T
Answers
Given data:
N=74
Equation:
[tex]T=50+\frac{N-40}{4}[/tex]To find the temperature T given N=74 substitute in the equation the N by 74 and evaluate to get the corresponding value of T:
[tex]\begin{gathered} T=50+\frac{74-40}{4} \\ \\ T=50+\frac{34}{4} \\ \\ T=50+8.5 \\ \\ T=58.5 \end{gathered}[/tex]Then, in N=74 the temperature in degress Fahrenheit is 58.5°FIf line BC is the diameter of the circle below, what is the area of the circle? A. 9 square unitsB. 16 square units C. 36 square units D. 64 square units
Answers
C) 36π u²
1) As we're given the diameter, we can find out the radius by dividing the diameter by 2. According to that, the Diameter measure is 6 units long (8 -2)
2) So now, we can plug that into the following formula:
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A\text{ =}\pi\cdot6^2 \\ A=36\pi \end{gathered}[/tex]3) Hence, the answer is 36π u²
Theconcentration ofiron in a watersample is 500parts per million.Write thisconcentration asa fraction in yourjournal.
Answers
500ppm = 0.05%
Now, express the percentage as a fraction:
0.05/100 = 1/2000
Therefore:
[tex]500\text{ppm}=\frac{1}{2000}[/tex]Find the slope of the line passing through the points (-3, 3) and (5, 9).
Answers
Answer:
3/4
Step-by-step explanation:
plot the points on the graph use those points do rise over run 3= rise 4= run
Answer:
Slope = 3/4 OR 0.75x
are the angels complementary supplementary , or neither?
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Two angles are complementary if the sum of their degrees is equal to 90,
in this case the angles are complementary because
44° + 46 ° = 90°
Pls help I have a final on this number 1
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ANSWER:
1a)
*A reflection across the x-axis
*A vertical compression
*A horizontal translation 3 units left
*A vertical translation up 5 units
1b)
*A reflection across the x-axis
*A vertical stretch
*A horizontal translation 2 units right
*A vertical translation down 11 units
EXPLANATION:
Given:
[tex]\begin{gathered} f(x)=-\frac{1}{2}(x+3)^2+5 \\ h(x)=-3(x-2)^2-11 \end{gathered}[/tex]To:
Describe the transformation effects from the parent graph g(x) = x^2
Recall that a quadratic function in vertex form;
[tex]f(x)=a(x-h)^2+k[/tex]where;
a > 1 represents a vertical stretch
0 < a < 1 represents a vertical compression
-h represents horizontal translation right h units
+h represents horizontal translation left h units
k represents vertical translation up k units
-k represents vertical translation down k units
-a represents a reflection across the x-axis
1(a) Comparing the below-given function with the vertex function, the transformations are as listed below;
[tex]f(x)=-\frac{1}{2}(x+3)^2+5[/tex]*A reflection across the x-axis
*A vertical compression
*A horizontal translation 3 units left
*A vertical translation up 5 units
1(b) Comparing the below-given function with the vertex function, the transformations are as listed below;
[tex]h(x)=-3(x-2)^{2}-11[/tex]*A reflection across the x-axis
*A vertical stretch
*A horizontal translation 2 units right
*A vertical translation down 11 units
2/2q+3=1/8solve for q
Answers
the division between two equal numbers is always 1 so we can simplify 2/2
[tex]\begin{gathered} q+3=\frac{1}{8} \\ \\ q=\frac{1}{8}-3 \\ \\ q=\frac{1}{8}-\frac{3}{1} \\ \\ q=\frac{1\times1-8\times3}{8\times1} \\ \\ q=\frac{1-24}{8} \\ \\ q=-\frac{23}{8} \end{gathered}[/tex]the value of q is -23/8
Tell whether the blue figure is a rotation of the red figure about the ongin 1 e 12 yes O no If so, give the angle and direction of rotation. o 90° counterclockwise o 180° clockwise or counterclockwise 270° counterclockwise O not a rotation
Answers
Due to rotation :
(-x,y) turns to (x,y)
Thus rotation is 270
A local water park found that if the price of admission was $19, the attendance was about 1250 customers per day.When the price of admission was dropped to $11, attendance increased to about 2150 per day. Write a linearequation for the attendance in terms of the price,p. (A = mp + b)
Answers
when price of admission = $19
attendance = 1250 customers per day
The point (price, attendance) = (19, 1250)
when prcie of admission = $11
attendance = 2150 customers per day
The point (price, attendance) = (11, 2150)
Linear equation: A = mp + b
where m = slope
we use the two points (19, 1250) and (11, 2150) to get the slope:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ x_1=19,y_1=1250,x_2=11,y_2\text{ = 2}150 \\ m\text{ = }\frac{2150\text{ - 1250}}{11\text{ - 19}} \\ m\text{ = }\frac{900}{-8} \\ m\text{ = slope = -112.50} \end{gathered}[/tex][tex]A\text{ = -112.5p + b}[/tex]To get b, we will use any of the point and the slope:
[tex]\begin{gathered} \text{using the point (11, 2150) = (p, A)} \\ A\text{ = -112.5p + b} \\ 2150\text{ = -112.5(11) + b} \\ 2150\text{ = -1237.5 + b} \\ 2150\text{ + 1237.5 = b} \\ b\text{ = 3387.5} \end{gathered}[/tex][tex]A\text{ = -112.5p + 3387.5}[/tex]what equation has the solution for x=8
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Any equation that have the variable x and at x=8 the equation statisfy ,thta equation has the solution for x=8.
2. By substitution 2y + 2x =-4y + x =-5
Answers
We have to solve the following system by substitution:
[tex]\mleft\{\begin{aligned}2y+2x=-4 \\ y+x=-5\end{aligned}\mright.[/tex]When we have to solve a system via substitution, we clear out one variable on one equation and we replace it onto the second equation. In this example, we will clear out the variable y on the second equation (but you can try it with x also), then:
[tex]\begin{gathered} y+x=-5 \\ y=-5-x \end{gathered}[/tex]This answer will be substituted onto the first equation:
[tex]2(-5-x)+2x=-4[/tex]And we clear the variable x. We use the distributive property and the rules of an equality, we sum to both sides of the equation a value as shown:
[tex]\begin{gathered} 2(-5-x)+2x=-4 \\ -10-2x+2x=-4 \\ -10+0=-4 \\ -10=-4 \end{gathered}[/tex]This last equality is false. And as such, it means that the system above doesn't have solutions, the lines they represent are parallel and doesn't meet.
Note: We can also note that if you clear out the variable y, and treated as linear functions, the slope of both equations will be the same, which justifies why those two equations are parallel.
if [tex]f(x) = 3x + 4 \: and \: g(x) = 2[/tex]solve the value of x for which [tex]f(x) = g(x)[/tex]is true
Answers
we have and in the two expressions, then we can match this
where is and in the first equation we must put 2
from the secon
1. Express each of the following complex numbers in the form of a + ib a) (2 + 5i) + (1-i)
Answers
Given:
(A)
[tex](2+5i)+(1-i)[/tex]Solve:
[tex]undefined[/tex]Quadrilateral ABCD with points A (2, -1) , B (4, -4), C (2, -7), D (0,-4) is shown below. Write the equations of line symmetry in quadrilateral ABCD. Explain your reasoning.
Answers
Given
A Quadrilateral ABCD with points A (2, -1) , B (4, -4), C (2, -7), D (0,-4).
To find the equations of line symmetry in quadrilateral ABCD.
Explanation:
It is given that,
From the figure, it is clear that the quadrilateral is a Rhombus.
Since the Rhombus has two lines of symmetry AC and BD.
Therefore,
The equation of the line AC is,
[tex]\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-(-1)}{-7-(-1)}=\frac{x-2}{2-2} \\ \frac{y+1}{-7+1}=\frac{x-2}{0} \\ \frac{y+1}{6}=\frac{x-2}{0} \\ x-2=0 \\ x=2 \end{gathered}[/tex]Therefore the equation of the line of symmetry AC is, x=2.
Similarly, the equation of the line of symmetry BD is, y= -4, because BD is a horizontal line.
Reasoning:
Since the lines of symmetry are horizontal line and vertical line.
Hence, x=2, y=-4 are the equations of the lines of symmetry.
In ∆PQR, the measure of
Answers
The trigonometric ratio sin(θ) which applies to right triangles, is given by
[tex]\sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}}[/tex]Graphically,
Therefore, the ratio that represents the sine of angle P is
[tex]\sin (P)=\frac{45}{53}[/tex]What is 12^6 over 12^2 can you help me get the answer
Answers
Problem:
What is 12^6 over 12^2
Solution:
Applying the laws of exponents we have:
[tex]\frac{12^6}{12^2}=12^{6-2}=12^4=20736^{}[/tex]then, the correct answer is:
[tex]\frac{12^6}{12^2}=20736^{}[/tex]
What value of x satisfies this equation?10 (1.5)3580Round your answer to the nearest hundredth.
Answers
1) Solving for x, we can write out the following:
[tex]\begin{gathered} 10(1.5)^{3x}=80 \\ \\ \frac{10\cdot \:1.5^{3x}}{10}=\frac{80}{10} \\ \\ 1.5^{3x}=8 \\ \\ \ln \left(1.5^{3x}\right)=\ln \left(8\right) \\ \\ 3x\ln \left(1.5\right)=\ln \left(8\right) \\ \\ \frac{3x\ln \left(1.5\right)}{3\ln \left(1.5\right)}=\frac{\ln \left(8\right)}{3\ln \left(1.5\right)} \\ \\ x=\frac{\ln \left(2\right)}{\ln \left(1.5\right)} \\ \\ x\approx1.71 \end{gathered}[/tex]That's the answer: 1.71 (Rounded to the nearest hundredth
Which function is the inverse of f(x) = -5x-4?1414O 8(x)3x -F () --3x+O F1(x) = -4x+5Of '(x) = 4x+4
Answers
The given function is:
f(x) = -5x-4
or y = f(x)
and
y = -5x -4
The inverse of a function can be calculated by switching the y-values with the x-values. Therefore,
y = -5x -4 becomes x = -5y -4
x + 4 = -5y
y = (x+4)/ -5
or
f-1(x) = - (x+4)/5
Zack, a soup chef at a new restaurant, kept track of the first week's soup sales. Split pea Chicken noodle Cup 6 5 Bowl 4 3 What is the probability that a randomly selected soup was ordered in a cup and was chicken noodle? Simplify any fractions.
Answers
hello
to solve this question, we simply need to add (split pea + chicken noodle) in a cup and then proceed from there.
probability of ordering chicken noodles in a cup is
[tex]\begin{gathered} \text{split pea +ch icken noodles = 6+5=11} \\ ch\text{ icken noodles=}\frac{5}{11} \end{gathered}[/tex]the probabi
There were 12 birds in a tree.5 flew aways, what fraction of the birds flew away? write the fraction in lowest terms, using slash (/) to separate the numerator and denominator
Answers
Explanation:
5 out of the 12 birds that were in the tree flew away, so the fraction is: 5/12. This is already in lowest terms, because it can't be simplified.
Answer:
5/12 birds flew away.
Use the Standard Normal Table or technology to find the Z-score that corresponds to the following cumulative area.0.94
Answers
Cumulative area: 0.94
Using a Z-table you can identify
On a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides areshown in the figure below. The actual distance from Los Angeles to Las Vegas is270 miles. Find the actual distance from San Francisco to Las Vegas.
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Solution:
Given:
From the image, Los Angeles to Las Vegas = 1.0"
The actual distance from Los Angeles to Las Vegas = 270 miles.
Hence, the scale that can be used to relate the image and actual distances is;
[tex]1.0^{\prime}^{\prime}=270miles[/tex]From the image, San Francisco to Las Vegas = 2.1"
Thus, using the scale, the actual distance from San Francisco to Las Vegas will be;
[tex]\begin{gathered} 1.0^{\prime}^{\prime}=270miles \\ 2.1^{\prime}^{\prime}=270\times2.1 \\ =567miles \end{gathered}[/tex]Therefore, the actual distance from San Francisco to Las Vegas is 567 miles.
$0.42 x 0.5 helppp...
Answers
First, multiplicate the numbers ignoring the decimals:
Rewrite the product with 3 decimal places. (since there are 3 decimal places in both numbers)
0.210 = 0.21