Answer:
Step-by-step explanation:
2.38 km x 10^4 = 23,800 decimeters
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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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°
PLEASE HELPPPPP I WILL MARK YOU BRAINLIEST Akai was eating a pizza over the course of the weekend. On Saturday night, he ate 3/4 of the pizza. On Sunday morning he ate 1/6 of the pizza, and on Sunday night he ate the rest of the pizza. What portion of the pizza did he eat on Sunday night?*
Answer:
50%
Step-by-step explanation:
34+16=50% he or she ate half of the pizza
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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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
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).
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
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:
8
Answer:
8
Step-by-step explanation:
8 is the digit after 7 and previous to 9
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:
Simplify the given expression below: (4+2i)-(1–7i)
Answer:
3 + 9i
Step-by-step explanation:
(4 + 2i) - (1 - 7i)
distribute the (-)
(4 + 2i) - 1 + 7i
combine like terms
3 + 9i
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.
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:
5000000 divided by what equals 400
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!
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!
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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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.)
The sum of two numbers is 24. One is 6 less than twice the other. Find the two numbers.
(apply polya's problem solving method)
Answer:
[tex]\huge\boxed{\sf x = 14 , y = 10}[/tex]
Step-by-step explanation:
Let the two numbers be x and y
Condition # 1:
x + y = 24 ---------------------(1)Condition # 2:
x = 2y - 6 ----------------------(2)[tex]\rule[225]{225}{2}[/tex]
Putting Equation # 2 in Equation # 1
2y - 6 + y = 24
3y - 6 = 24
Adding 6 to both sides
3y = 24 + 6
3y = 30
Dividing both sides by 3
y = 10
[tex]\rule[225]{225}{2}[/tex]
Putting y = 10 in Equation # 2
x = 2y - 6
x = 2(10) - 6
x = 20 - 6
x = 14
[tex]\rule[225]{225}{2}[/tex]
The two numbers are 10 and 14.
The sum of 2 numbers is 24.
let the number be x and y . Therefore,
x + y = 24
One is 6 less than twice the other. therefore,
2x - y = 6
Combine the equations
x + y = 24
2x - y = 6
3x = 30
x = 30 / 3
x = 10
x + y = 24
10 + y = 24
y = 24 - 10
y = 14
The 2 numbers are 10 and 14 .
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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
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
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
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
Select the correct graph for the function ƒ(x) = –x – 7.
Step-by-step explanation:
The second graph is the right one
Answer:
see below
Step-by-step explanation:
f(x) = -x-7 is of the form
y = mx+b where m is the slope and b is the y intercept
The line has a y intercept of (0,-7) and a slope of -1
A slope of -1 means the line goes down from left to right ( down 1 and to the right 1)
240 students to 12 teachers as ratio
Answer:
1 : 20 20 students for every 1 teacher
Step-by-step explanation:
divide both sides by 12
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!
Is the value of the first 5 ten times as great as the value of the second 5 in 5,045
Answer:
No
Step-by-step explanation:
Its 1000
If 3x = y - 5 and x = -4, then y =*
Answer:
y = -7
Step-by-step explanation:
3(-4) = y - 5
-12 = y - 5
y = -12 + 5
y = -7
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
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.