Review the graphs of f(x) = –x5 + 2x4 + 1 and g(x), which is a translation of f(x).
On a coordinate plane, g (x) curves down through (negative 3, 3) to (negative 2, 1) and then curves up to (negative 0.5, 3.8). It then curves down through (0, 0) into quadrant 4. y = f (x) curves down through (negative 1, 3) to (0, 1) and then curves up to (1.5, 3.8). It then curves down through (2, 0).
How can g(x) be expressed in terms of f(x)?
g(x) = (–x5 + 2x4 + 1) + 2
g(x) = –(x + 2)5 + 2(x + 2)4 + 1
g(x) = (–x5 + 2x4 + 1) – 2
g(x) = –(x – 2)5 + 2(x – 2)4 + 1
Answer:
choice B
g(x) = –(x + 2)5 + 2(x + 2)4 + 1
The function g(x) can be represented in terms of f(x) like this:
g(x) = -(x - 2)⁵ +2(x - 2)⁴ + 1.
Hence, 4th option is the right choice.
What does it mean to translate a graph?The translation is the process of moving a graph horizontally or vertically. To put it another way, each point on the parent graph is translated to the left, right, up, or down, to get the translated graph.
How do we solve the given question?We know that g(x) is a transformation of f(x) = -x⁵ + 2x⁴ + 1.
Since, g(x) is the transformation of f(x) we try to find the relation between the points on f(x) and g(x).
Let the point on f(x) be (x₁, y₁) and that on g(x) be (x₂, y₂).
f(x) passes through the points (-1, 3), (0,1), (1.5, 3.8), and (2, 0).
Corresponding points on g(x) are (-3, 3), (-2, 1), (-0.5, 3.8), and (0, 0).
We can see that the y-coordinate is the same for corresponding points. So, y₂ = y₁.
For the x-coordinate, we see that for every corresponding point on g(x), it is 2 less than the point on f(x). So, x₂ = x₁ - 2.
Now, in the function f(x), we have x = x₁. So to find the function g(x), we substitute the value of x₂ = x₁ - 2 = x - 2 in f(x) to get the equation of g(x).
∴ g(x) = f(x-2)
or, g(x) = -(x - 2)⁵ +2(x - 2)⁴ + 1.
∴ The function g(x) can be represented in terms of f(x) like this:
g(x) = -(x - 2)⁵ +2(x - 2)⁴ + 1.
Hence, 4th option is the right choice.
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If A=[xy5−8] determine the values of x and y for which A2=A.
Answer:
x = 9, y = -72/5Step-by-step explanation:
Given the 2 by 2 matrix [tex]A = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right][/tex] , we are to find the value of x and y for the expression A² = A to be true.
First we need to find A² by multiplying the same matrix together
[tex]A^2 = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right] \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\\\ \ we \ normally \ multiply \ the \ rows \ of \ the \ first \ matrix \ with \ the \ column \ of \ the \ second \\\\A^2 = \left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right]\\\\Since \ A^2 = A,\ hence;\\\\\left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right] = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\[/tex]
Equating the first row and second column of both matrices together, we will have;
5x-40 = 5
add 40 to both sides of the equation
5x-40+40 = 5+40
5x = 45
x = 45/5
x = 9
Similarly, we will equate the second row and second column of both matrices to have;
5y+64 = -8
Subtract 64 from both sdies
5y+64-64 = -8-64
5y = -72
y = -72/5
Hence the value of x is 9 and y is -72/5
Matrices are used to represent data in rows and columns
The values of x and y are 9 and -14.4 respectively.
Matrix A is represented as:
[tex]\mathbf{A = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]
Calculate [tex]\mathbf{A^2}[/tex]
[tex]\mathbf{A^2 = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] \times \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]
Recall that [tex]\mathbf{A^2 = A}[/tex]
This means that:
[tex]\mathbf{\left[\begin{array}{ccc}x^2++5y&5x-40\\xy-8y&5y+64\end{array}\right] = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]
So, by comparison
[tex]\mathbf{5x - 40 = 5}[/tex]
[tex]\mathbf{5x = 40 + 5}[/tex]
[tex]\mathbf{5x = 45}[/tex]
[tex]\mathbf{x = 9}[/tex]
Similarly
[tex]\mathbf{5y + 64 = -8}[/tex]
[tex]\mathbf{5y =-64 -8}[/tex]
[tex]\mathbf{5y =-72}[/tex]
[tex]\mathbf{y =-14.4}[/tex]
Hence, the values of x and y are 9 and -14.4 respectively.
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Find the decimal equivalent to 4/15
To find a decimal that is equavalent to 4/15, all we need to do is divide.
4 / 15 = 0.26666...
Best of Luck!
Maria has an 8 sided die that is numbered 1 to 8. She rolls the die 96 times. About how many times can she expect to roll an 8?
Answer:
12 times.
Step-by-step explanation:
96÷8=12
round 2481.65 to the neartheast 10 tenth
2481.7
^ is the tenth place.
The 5 would either round it up or down by one-tenth. Since we like big numbers... we'll round it to 7 from 6.
Answer:
2481.7
Step-by-step explanation:
Find the number in the tenth place
6
and look one place to the right for the rounding digit
5
. Round up if this number is greater than or equal to
5
and round down if it is less than
5
A ternary digit is either 0, 1, or 2. How many sequences of 6 ternary digits containing a single 1 and a single 2 are there?
Answer:
30sequences
Step-by-step explanation:
Using nx (n-1)
And
n is the number of ternary digits in the number.
So For 6 digits n is 6 so the number of numbers that have exactly one 1 AND exactly one 2 is 30.
That is 6(6-1)= 30
The dimensions of a right rectangular prism are 1.5 cm, 0.5 cm and 2. 25 cm.
What is the volume of the prism?
A. 0.75 cm
B. 1.6875 cm
C. 3.375 cm
D. 4.25 cm
The volume of the right rectangular prism having dimensions 1.5 cm, 0.5 cm and 2. 25 cm. will be V=1.6875 [tex]cm^3[/tex]
What is Volume?Volume is defined as the space covered by any object in the three dimensions having coordinates in all three sides is called as volume.
We know that the volume of the Rectangular prism is given as:
[tex]\rm V=L\times W\times D\\\\\\V=1.5\times 0.5\times 2.25\\\\\\V=1.6875\ \ \ cm^3[/tex]
Hence the volume of the right rectangular prism having dimensions 1.5 cm, 0.5 cm and 2. 25 cm. will be V=1.6875 [tex]cm^3[/tex]
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Witch are examples of unit rates
Answer:
30 miles in 2 hours
Step-by-step explanation:
Answer:
A unit rate is a rate where the second quantity is one unit , such as $34 per pound, 25 miles per hour, 15 Indian Rupees per Brazilian Real, etc. Example 1: A motorcycle travels 230 miles on 4 gallons of gasoline. Find the average mileage per gallon.
Step-by-step explanation:
choose all expressions that are equal to 28.3. A. 27 + 0.91 + 0.39 B. 0.01 + 28.02 C. 9.9 + 9.8 + 9.6 D. 0.02 + 28 + 0.28 E. 27.3 + 1
Answer:
i think... a d and e?
Step-by-step explanation:
Madison's breakfast was a bagel and juice. She spent a total of $4.30.
Madeline spent $6.00 on 2 bagels. How much did Madison pay for her
juice? *
Answer:
$1.30 for juice
Step-by-step explanation:
If madeline bought 2 bagels for $6 then one bagel must be $3. Madison spent $4.30 so $3 was the bagel and $1.30 was the juice.
At 11:00 p.m. , the temperature in Alaska was -5 degrees. Four hours earlier, the temperature was 40 degrees warmer. What was the temperature at 7:00 p.m. ?
Answer:
35°
Step-by-step explanation:
-5° + 40° = 35°
So the ansWer is 35°
What does the mean and median mean of numbers
Answer:
Mean is all numbers added up divided by the amount of numbers in the set.
Median is the number that occurs the most in a set.
Step-by-step explanation:
Helene wrote a report. It took her 4 hours to write 24 pages.
What was her unit rate in pages per hour?
A.
1 득
page per hour
B.
page per hour
C. 6 pages per hour
D. 7 pages per hour
Answer:
C
Step-by-step explanation:
24÷6= 6 Hope this helps.
One number is eight less than a second number. Four times the first is 4 more than 5 times the second. Find the numbers
Question 958954: One number is five less than a second number. Five times the first is eight more than two times the second. Find the numbers.
hope this helps!
-35x+85x-4=26 what is x
Need an answer quickly. Left my book at my friends house.
Answer:
A. 3
B. 3/4
C. 1/4
Step-by-step explanation:
1/4 of 12 is 3
3 plus 6 is 9 and 9 is 3/4 of 12
12 minus nine is also three leaving the tank still a 1/4 tank empty
20 POINTS!!!!! A cartographer is making a city map. Line m represents Murphy Street. The cartographer translates points on line m along the vector angleleft1, −3angleright to draw Nolan Street. Draw the line for Nolan Street on the coordinate plane and complete its equation. What is the image of (0, 3) in this situation?
Answer:
[tex]y=2x-2[/tex] and image of (0,3) is (1,0).
Step-by-step explanation:
From the given graph it is clear that the line of Nolan Street passes through the points (0,-2) and (1,0).
So, the equation of Nolan Street is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-2)=\dfrac{0-(-2)}{1-0}(x-0)[/tex]
[tex]y+2=2x[/tex]
[tex]y=2x-2[/tex]
So, the equation of the Nolan Street is [tex]y=2x-2[/tex].
It is given that the cartographer translates points on line m along the vector <1, −3> to draw Nolan Street. So, the rule of translation is
[tex](x,y)\to (x+1,y-3)[/tex]
The image of (0, 3) in this situation.
[tex](0,3)\to (0+1,3-3)=(1,0)[/tex]
The image of (0,3) is (1,0).
which graph shows the function f(x)=x with an input of (f(x-3)
please help me asap!!
Answer:
Step-by-step explanation:
B
The correct graph of the function is shown in option (B).
What is graph?A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.
The given function is,
f(x) = y = x (1)
To find the graph of f(x -3),
Substitute x = x- 3 in equation (1),
y = x- 3
The slope of the graph is 1,
And the y intercept at x = 0,
y = -3
So the graph of the function y = x - 3 can be plotted as,
Hence option (B) is correct option.
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which is greater, a third of 36 or one-sixth of 138?
Answer:
one-sixth of 138
Step-by-step explanation:
36÷3=12. 138÷6=23
12<23
Therefore, one-sixth of 138 is greater than a third of 36.
Help me plz ASAP explain why
Answer:
a. -2
b. 3
c. 3
d. -3
e. x=-2
Step-by-step explanation:
When a question asks for f(x), it is basically just asking for what the y-value is at the given point of x. So for example, to solve the first one: f(-4), we see that the x-value is -4. This means it is asking for the y-value at x=-4. As we can see from the graph, where x = -4, the y-value is -2 (along the bottom flat line) therefore f(-4) = -2.
This is the same for the other three, f(0) = 3 because the line at x=0 is crossing at y=3. etc.
Finally e is difference because it is instead asking for the x-value when y=6. To solve this we just need to find a point on the graph where the line is at y=6. This, as we can see is at the top of the highest point and occurs where x=-2.
Hope this helped!
simplify the equation 3(u-6)-7u
Answer:
-4u-18
Step-by-step explanation:
1. Is -2.75 a whole number rational number or a integer ?
Answer:
its an integer
Step-by-step explanation:
Because it has a negative sign
evaluate 6 to the power of -3
Use exponent rule: x^-y = 1/x^y
6^-3
= 1/6^3
= 1/216
Best of Luck!
Explain how to find the y-intercept of a linear equation.
Answer: simply
Step-by-step explanation: Example: 15y= -5x+0 First move -5 to other side of equal sign. So 15y+5x=0 Then simply by dividing by 5. So 5y+x=0
If (42)p = 414, what is the value of p? 7 8 12 16
Answer:
the correct answer is not there
Step-by-step explanation:
I'm not sure if "7, 8, 12, and 16" were answer choices but none of those are correct
Step-by-step explanation:
to find the value of p you'd need to divide 441 by 42 and the answer is 9.9
A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 12.17. How much paper of each shade has been used in it?
Answer:
15.6 is the right answer
Step-by-step explanation:
Determine the simple interest. The rate is an annual rate. Assume 360 days in a year. p = $502.45,r=5.3%,t = 53days The simple interest is $ (Do not round until the final answer. Then round to the nearest cent as needed.)
Find the extraneous solution of the equation |2x−12|=−4x.
Answer:
X=2
Step-by-step explanation:
|2x -12| = -4x
2x-12 = -4x
2x - (-4x) = 12
2x +4x =6x
6x=12
x=12/6
x=2
Among all baskets purchased in the South or West neighborhoods, what is the Basket ID of the basket with the largest total revenue? Click here to reference the data needed to answer the question. a. 5531 b. 718 c. 5056 d. None of these choices are correct
Answer:
c. 5056
Step-by-step explanation:
The revenue is maximized when the units sold are increased if the selling price is constant. The basket ID 5056 has more units then the other two baskets and its invoice total is greater than the other baskets. The basket 5056 has largest total revenue to the company.
Which single transformation can be applied to the graph of y = 72 [tex]\sqrt{x}[/tex] to produce the graph of y = 9 [tex]\sqrt{x}[/tex]?
A.vertical translation
xxB.vertical compression
C.horizontal translation
D.horizontal compression
its b
Answer:
B. Vertical Compression
Step-by-step explanation:
You've answered the question; However, I'll assist with the explanation;
Given
Original: [tex]y = 72\sqrt x[/tex]
Translated: [tex]y = 9\sqrt x[/tex]
Required
Determine the type of transformation applied to the original function
Observing both functions, we notice that [tex]\sqrt x[/tex] is a common factor;
This implies that the function was compressed or stretched along the y axis (vertically)
To determine if its vertical compression or stretch;
We have to divide the translated function by the original function;
[tex]Ratio = \frac{9\sqrt x}{72\sqrt x}[/tex]
[tex]Ratio = \frac{9}{72}[/tex]
[tex]Ratio = 0.125[/tex]
Because 0.125 < 1, then the transformation is a vertical compression
Answer:
B
Step-by-step explanation: