Answer:
The function that represents g(x) is the third choice: g(x) = (x − 4)^2 + 9
Step-by-step explanation:
The original function has been shifted 9 units up (a vertical transformation). To show a vertical transformation, all we have to do is either add or subtract at the end of the function.
To show a shift upwards, we add the value of change.
To show a shift downwards, we subtract the value of change.
In this case, the original function f(x) = [tex]x^{2}[/tex] was translated 9 units up. Since we shifted up, we simply add 9 to the end of the function: g(x) = [tex]x^{2}[/tex] + 9
The original function has also been shifted 4 units to the right. This is a horizontal transformation. To show a horizontal transformation, we need to either add or subtract within the function (within the parenthesis).
To show a shift to the left, we add the value of change.
To show a shift to the right, we subtract the value of change.
*Notice: Moving left does NOT mean to subtract while moving right does NOT mean to add. The rules above are counterintuitive so pay attention when doing horizontal transformations.
In this case, the original function f(x) = [tex]x^{2}[/tex] was translated 4 units to the right. Since we shifted right, we must subtract 4 units within the function/parenthesis: g(x) = [tex](x-4)^{2}[/tex]
When we combine both vertical and horizontal changes, the only equation that follows these rules is the third choice: g(x) = (x − 4)^2 + 9
Answer: C
Step-by-step explanation:
Find the indicated side of the
right triangle.
45°
y
6
45°
Answer:
6
Step-by-step explanation:
tan 45 = 6 / x
1 = 6 / x
x = 6
Note :
Tan 45 value = 1
Answer:
x=6
Step-by-step explanation:
Since this is an isosceles triangle, the sides must be equal next to the base angles that are equal
x=6
HELP ASAP PLEASE!!!!!
what is the factorization of the polynomial below -x^2-2x+48
I HOPE IT WILL HELP YOU. I DID HOW I KNOW .
A shopkeeper marks his goods 25% above the cost price and gives discount of 10% on the marked price white gain percent make
answer is 6.3
I've had this question before
Pls help me with this pls
SOMEONE PLEASE ANSWER THIS ASAP!!
The population of Arlington High School can be modeled using the equation P(t) = 3,500(1.027)^t , where t represents the number of years since 2010
Is the population of Arlington High increasing or decreasing? Explain how you can tell using the equation.
How do you interpret the statement that P(6)= 4,107
SOMEONE PLEASE ANSWER THIS
Step-by-step explanation:
Arlington is increasing because it has 1.027, if it was 0.27 it would be decreasing
If p(6)= 4107 that means after 6 years there would be a total population of 4107
What is an equation for this graph?
Answer:
sinx
Step-by-step explanation:
the shape of the graph shows a sine graph, which is usually denoted by asinbx+c
a is amplitude/2 = 2/2 = 1
b is the period, 360 = 360/b, b=1
since the graph starts at (0,0), c =0
hence, this graph is 1sin1x = sinx
The equation is y = sin(x)
Question 7 of 25
The graph of F(x) can be compressed vertically and shifted to the right to
produce the graph of G(X). If F(X) = x2, which of the following could be the
equation of G(x)?
A. G(x) = {(x - 6)
O B. G(x) = {(x+6)
O c. G(x) = 2(x+6)
O D. G(X) = 2(x-6)
Can someone explain
Answer:
You need to use sohcahtoa to find your answer.
first you gotta identify what sides of the triangle you have.
You're missing the hypotenuse, and you have the value of the adjacent.
since you have the adjacent and need the hypotenuse, you're going to use cosine to find x
cos(65) = 16/x
x = 37.859
Answer:
x = 37.85
this is a standard "trig" question
it requires two pieces of insight.
First that a triangle has 180° interior angles.
from that you can determine that the third angle is 25° because
90 + 65 + β = 180
the red symbol lets you know that it is 90°
the second think that will help is SOHCAHTOA
that is if you have a "right triangle" (one with a 90° angle)
in this problem (in your mind rotate the triangle so the 65° is at the bottom left and the two long sides are pointing up
in this case you have the 16 on the bottom (adjacent to the angle) and
the x is on the hypotenuse...
you have the A& H that is COS
thus you have cos(65) = [tex]\frac{16}{x}[/tex]
x = 37.85
Step-by-step explanation:
Jon and Kristen are both increasing the number of minutes they jog each day, as shown in the tables.
Jon
Day Minutes
0 15
1 17
2 19
3 21
Kristen
Day Minutes
0 22
1 23
2 24
3 25
Which system of linear equations could be used to determine which day they will jog for the same number of minutes, where d represents the day and m represents the number of minutes?
Answer:
A system of linear equations that could be used to determine which day they will jog the same number of minutes is presented as follows;
m = 2·d + 15
m = d + 22
Step-by-step explanation:
The table of values for the number of minutes Jon and Kristen jog each day is presented as follows;
Jon
[tex]\begin{array}{ccc}Day&&Minutes\\0&&15\\1&&17\\2&&19\\3&&21\end{array}[/tex]
Kristen
[tex]\begin{array}{ccc}Day&&Minutes\\0&&22\\1&&23\\2&&24\\3&&25\end{array}[/tex]
The slope of the data representing Jon's data, m = (21 - 15)/(3 - 0) = 2
Therefore, the equation representing Jon's data is given as follows;
m - 15 = 2·d
m = 2·d + 15
The slope of the data representing Kristen's data, m = (25 - 22)/(3 - 0) = 1
Therefore, the equation representing Kristen's data is given as follows;
m - 22 = d
∴ m = d + 22
The system of linear equations that could be used to determine which day they will jog the same number of minutes is therefore;
m = 2·d + 15
m = d + 22
The answer is in the picture below!
a random number generator is used to model the patters of animals in the wild. this type of study is called
Answer:
This type of study is called a simulation
Step-by-step explanation:
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.8 years, and standard deviation of 1.7 years. The 10% of items with the shortest lifespan will last less than how many years?
Answer:
3.6 years
Step-by-step explanation:
Using the standard normal probability distribution table, we obtain the Zscore which is 10% to left of the distribution.
The Zscore gives, - 1.282
To obtain the number of years, let this be x ;
Recall, the Zscore formula :
Zscore = (x - μ) / σ
x = number of years
μ = 5.8
σ = 1.7
Zscore = (x - μ) / σ
-1.282 = (x - 5.8) / 1.7
-1.282 * 1.7 = x - 5.8
-2.1794 = x - 5.8
-2.1794 + 5.8 = x
x = 3.6206
x = 3.6 years
Ashipment department on time ships 500 boxes per day. Approximately 97% of those shipments are shipped on time. The remaining 3% are shipped later. Approximately how many shipments are shipped later per day?
Answer:
15 boxes were shipped late
Step-by-step explanation:
late = 3% = 0.03
500 x 0.03 = 15 boxes
THIS IS SO HARD HELP PLEASE
Answer:
second one: EFG NML
THIRD: 82°
identify the area of a regular decagon with side length 2 m rounded to the nearest tenth
Answer:
Area = 14.8
Step-by-step explanation:
Area = 5/2 + a^2*sqrt(5 + 2 sqrt(5) )
This formula given the side length, calculates the area.
a = 2
Area = 2.5 + 2^2 * sqrt(5 + 2*sqrt(5) )
Area = 2.5 + 4 * sqrt(5 + 2*2.236)
Area = 2.5 + 4* sqrt(5+ 4.4721)
Area = 2.5 + 4*sqrt(9.4721)
Area = 2.5 + 4*3.0776
Area = 2.5 + 12.3107
Area = 14.8107
Answer:
A ≈ 30.8 m2
Step-by-step explanation:
Can someone help with these 2?
Answer:
a. 25 ft squared
b. 0.3
Step-by-step explanation:
a. if the perimeter is 20 that means that each side would be 5 because its a square and 5 x 5 is 25.
b. 0.3 to the third power is 0.027
Cual es la respuesta 5%9(12-32)
Answer:
i need more detail
Step-by-step explanation:
A line with slope 3 intersects a line with slope 5 at the point (10, 15). What is the distance between the x-intercepts of these two lines?
The distance between the intercepts of both lines is 2 units
The equation of a line in slope intercept form is:
[tex]y = mx + b[/tex]
Where:
[tex]m \to[/tex] slope
[tex]b \to[/tex] y intercept
For the first line, we have:
[tex]m_1 = 3[/tex] ---- the slope
So, the equation of the first line is:
[tex]y = 3x + b_1[/tex]
For the second line, we have:
[tex]m_2 = 5[/tex] --- the slope
So, the equation of the second line is:
[tex]y = 5x + b_2[/tex]
Both lines intersect at (10,15) means that (10,15) is a common solution to the equation of both lines
i.e.
[tex](x,y) = (10,15)[/tex]
Substitute these values in the first equation and solve for b
[tex]y = 3x + b_1[/tex]
[tex]15 = 3*10 + b_1[/tex]
[tex]15 = 30 + b_1[/tex]
[tex]b_1 = 15 - 30[/tex]
[tex]b_1 = -15[/tex]
So, the equation of the first line is
[tex]y = 3x - 15[/tex]
Repeat the same process for the second line
[tex]y = 5x + b_2[/tex]
[tex]15 = 5*10 + b_2[/tex]
[tex]15 = 50 + b_2[/tex]
[tex]b_2 = 15 - 50[/tex]
[tex]b_2 = -35[/tex]
So, the equation of the second line is
[tex]y =5x - 35[/tex]
The x intercept is when [tex]y =0[/tex]
So, we substitute 0 for y and solve for x in the equations of both lines
For line 1
[tex]y = 3x - 15[/tex]
[tex]0 = 3x - 15[/tex]
[tex]3x= 15[/tex] ---- Collect like terms
[tex]x = 5[/tex] --- Divide both sides by 3
The x intercept of line 1 is 5
For line 2
[tex]y =5x - 35[/tex]
[tex]0 = 5x - 35[/tex]
[tex]5x = 35[/tex] --- Collect like terms
[tex]x = 7[/tex] -- Divide both sides by 5
The x intercept of line 2 is 7
The distance (d) between both is the difference in the intercepts:
[tex]d = 7 - 5[/tex]
[tex]d = 2[/tex]
Read more about intercepts at:
https://brainly.com/question/12791065
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each verbal description to its equivalent function rule as applied to the given function below. The function f stretched vertically by a factor of 2 and translated down by 3 units. arrowBoth The function f reflected about the y-axis and translated 3 units left. arrowBoth The function f stretched vertically by a factor of 3 and translated up by 2 units. arrowBoth The function f translated 2 units down and 3 units right. arrowBoth
Answer:
The function f stretched vertically by a factor of 2 and translated down by 3 units. ---> [tex]g(x) = 14x +7[/tex]
The function f reflected about the y-axis and translated 3 units left. ---> [tex]g(x) = -7x-16[/tex]
The function f stretched vertically by a factor of 3 and translated up by 2 units. ---> [tex]g(x) = 21x +17[/tex]
The function f translated 2 units down and 3 units right. ----> [tex]g(x) = 7x -18[/tex]
Step-by-step explanation:
Explanation could not be submitted; So, I added it as an attachment
Answer: answer below :)
Step-by-step explanation:
Write an expression for the area and the perimeter of this rectangle. The rectangle has a length of 15 and a width of x-5
Answer:
Area: 2(15 + (x - 5))
Perimeter: 2(15)+2(x - 5)
Step-by-step explanation:
To find area you need to add the two sides together and multiply by two, this is as far as you can get with x.
Area: 2(15 + (x - 5))
To find perimeter, you need to find the singular lengths and multiply by two so this is as far as you can get.
Perimeter: 2(15)+2(x - 5)
Hope this helped.
find formula of s in terms of a, b, cos(x)
Answer:
[tex]\displaystyle s = \frac{2ab\cos x}{a+b}[/tex]
Step-by-step explanation:
We want to find a formula for s in terms of a, b, and cos(x).
Let the point where s intersects AB be D.
Notice that s bisects ∠C. Then by the Angle Bisector Theorem:
[tex]\displaystyle \frac{a}{BD} = \frac{b}{AD}[/tex]
We can find BD using the Law of Cosines:
[tex]\displaystyle BD^2 = a^2 + s^2 - 2as \cos x[/tex]
Likewise:
[tex]\displaystyle AD^2 = b^2+ s^2 - 2bs \cos x[/tex]
From the first equation, cross-multiply:
[tex]bBD = a AD[/tex]
And square both sides:
[tex]b^2 BD^2 =a^2 AD^2[/tex]
Substitute:
[tex]\displaystyle b^2 \left(a^2 + s^2 - 2as \cos x\right) = a^2 \left(b^2 + s^2 - 2bs \cos x\right)[/tex]
Distribute:
[tex]a^2b^2 + b^2s^2 - 2ab^2 s\cos x = a^2b^2 + a^2s^2 - 2a^2 bs\cos x[/tex]
Simplify:
[tex]b^2 s^2 - 2ab^2 s \cos x = a^2 s^2 - 2a^2 b s \cos x[/tex]
Divide both sides by s (s ≠ 0):
[tex]b^2 s -2ab^2 \cos x = a^2 s - 2a^2 b \cos x[/tex]
Isolate s:
[tex]b^2 s - a^2s = -2a^2 b \cos x + 2ab^2 \cos x[/tex]
Factor:
[tex]\displaystyle s (b^2 - a^2) = 2ab^2 \cos x - 2a^2 b \cos x[/tex]
Therefore:
[tex]\displaystyle s = \frac{2ab^2 \cos x - 2a^2 b \cos x}{b^2- a^2}[/tex]
Factor:
[tex]\displaystyle s = \frac{2ab\cos x(b - a)}{(b-a)(b+a)}[/tex]
Simplify. Therefore:
[tex]\displaystyle s = \frac{2ab\cos x}{a+b}[/tex]
1.
Graph the data in the table. Which kind of function best models the data? Write an equation to model the data.
A. exponential; y = –6 • 1.5x
B. quadratic; y = –x2
C. exponential; y = 6 • 2.5x
D. linear; y = –3x – 6
Answer:
D. linear; y = –3x – 6
B. quadratic; y = –x2
Step-by-step explanation:
Let
A (0,-2) B (1,-3) C (2,-4) D ( 3,-5) E (4,-6)
using a graph tool
see the attached figure N 1
case a) exponential
see the attached figure N 2
case b) quadratic
see the attached figure N 3
case c) linear
see the attached figure N 4
case d) linear
see the attached figure N 5
therefore
the answer is
the case c) linear
...............................................................................................................................................
Answer:
For the first part
What type of function best models the data in the graph?
✔ quadratic
y = 0.433x2 for the second part.
...............................................................................................................................................
Answer:
Option (2).
Step-by-step explanation:
From the figure attached,
Since there is a common difference in each successive term and previous term of y,
= -3
= -3
Therefore, this data represents a linear equation.
Now we choose two points from the table given.
Let the points are (0, -6) and (1, -9)
Slope of this line 'm' =
m = = -3
Y-intercept 'b' = -6
Equation of the line will be,
y = -3x - 6
Option (2) will be the answer.
Given 4 points A, B, C, D where no 3 points are collinear, any 2 points have a distance greater than 10. Prove that there exist two points out of 4 given points with greater distance 14.
Answer:
idea how to tell your loved one how you feel? How about a love song?
Find the value of x. Round to
the nearest tenth.
27
15
X
11
x = [?1°
Answer:
38.2°
Step-by-step explanation:
[tex]sin {}^{ - 1} ( \frac{15 \times sin(27)}{11} )[/tex]
[tex]= 38.2[/tex]
Answered by GAUTHMATH
The list below shows the number of books read by students in Aram’s class over the summer. What is the mode of the data
3,6,12,4,3,5,4,8,4,10,4,8,7,5,7
Answer:
the mode is 4 because it appears the most times in the detail set
Answer:
The mode is 3
Step-by-step explanation:
The mode of a set of numbers is whatever number appears the most. So here, you have four 4's, which is the most common number
5. Which of the following pairs of operations solve the equation 3x + 5 = 17?
a. subtract 5 then divide by 3
b. divide by 3 then subtract 5
c. add five then multiply by 3
d. multiply by 3 then add five
Answer:
a
Step-by-step explanation:
3x+5=17
3x=17-5
3x=12
x=4
Anna read 6 pages of a book then stopped. She later decided to continue the book and read 7 more pages every day.
Let d represent the number of days since Anna decided to continue the book and p represent the total number of pages of the book she had read.
Complete the table using the equation p=7d+6.
d p
7
8
9
10 76
Answer: 55, 62, 69, 76
Step-by-step explanation:
(to complete the table, plug d values into the equation to find p values)
p = 7d + 6, d = 7
p = 7(7) + 6 = 49 + 6 = 55
p = 7d + 6, d = 8
p = 7(8) + 6 = 56 + 6 =62
p = 7d + 6, d = 9
p = 7(9) + 6 = 63 + 6 =69
p = 7d + 6, d = 10
p = 7(10) + 6 = 70 + 6 =76
last one help me asap please and thank you
Answer:
y = -3/4x + 3.
often contains information about the author's experiences with the subject matter of
9. The author's introduction to a book, also called a/an
the book.
A. glossary
B. Index
C. table of contents
D. preface
Im quite sure it’s d wanna make sure
cho tam giác ABC. gọi M,N lần lượt là trung điểm AB,AC trên tia đối của tia NM lấy điểm D sao cho N là trung điểm MD, chứng minh
a, CD song song AM
b, CD = MB
d, tam giác BMC= tam giác DCM
e, MN= 1/2 DC
Mình gửi bạn
Bạn xem câu cuối có sai đề không
(c) 63 divided by 3 = 21 , Show how you use this to work out 0.63 divided by 0.3.
Answer:
0.63 ÷ 0.3 = 63 x 10^-2 ÷ 3 x 10^-1 = 63 / 3 x 10^(-2--1) = 21 x 10^-1 = 2.1
Answer:
2.1.
Step-by-step explanation:
63/3 = 21
0.63 = 63 / 100
and 0.3 = 3 / 10
so 0.63/0.3 = 63 /100 / 3/10 = 63/100 * 10/3
= 63/3 / 10
So the answer is 21 / 10 = 2.1.
