The parent function f(x) = x^2 is vertically stretched by a scale factor of 2, translated 14 units right, and 6 units up. Which equation below represents the new equation? 1. G(x) = 2(x-14)^2 + 6 2. G(x) = 1/2 (x-14)^2 = 6 3. G(x) = 2(x-14)^2 - 6 4. G(x) = 2(x+14)^2 + 6
Answer:
[tex](1)\; G(x)=2(x-14)^2+6[/tex]
Step-by-step explanation:
Assuming, right and up are positive directions.
The given parent function, [tex]f(x)=x^2[/tex]
Let [tex]f_1(x)[/tex] be the function when the parent function is stretched by a scale factor of 2.
So, [tex]f_1(x)=2f(x)[/tex]
[tex]\Rightarrow f_1(x)=2x^2[/tex]
Let [tex]f_2(x)[/tex] be the function when [tex]f_1(x)[/tex] is translated [tex]14[/tex] units right.
So, [tex]f_2(x)=f_1(x-14)[/tex]
[tex]\Rightarrow f_2(x)=2(x-14)^2[/tex]
Again, let [tex]f_3(x)[/tex] be the function when [tex]f_2(x)[/tex] is translated 4 units up.
So, [tex]f_3(x)=f_2(x)+6[/tex]
[tex]\Rightarrow f_3(x)=2(x-14)^2+6[/tex]
So, the resulting function, [tex]f_3(x)=G(x)=2(x-14)^2+6[/tex].
Hence, option (1) is correct.
Four movie tickets cost $40.00 dollars( look above for the rest of the question plss answer fast
Answer:
-7.5 US$
Step-by-step explanation:
that's how i got it =)
Answer: The answer is B
Step-by-step explanation:
help me with this please
It’s a test question.
Answer:
A # is odd
Step-by-step explanation:
Hypothesis-----> conclusion
How do I find angles c,g and k
Answer:
a. m<C = 50 deg
b. m<G = 125 deg
c. m<K = 75 deg
Step-by-step explanation:
a.
Look at the two lines marked parallel with 2 marks each.
Angle C and angle 50 deg are alternate interior angles of 2 parallel lines cut by a transversal That makes angle C congruent to the 50-deg angle.
Answer: m<C = 50 deg
b.
Angle G is vertical to thh 125-deg angle. Vertical angles are congruent, so m<G = 125 deg
Answer: m<G = 125 deg
c.
Look at the two lines marked parallel with one mark each.
Angles e and c are corresponding angles, so they are congruent.
m<E = m<C = 50 deg
The 125 deg angle and angle F are a linear pair, so their measures add up to 180.
f + 125 = 180
m<F = 55 deg
Angles E, F and K are the interior angles of a triangle, so their measures add up to 180 deg.
e + f + k = 180
50 + 55 + k = 180
k = 75
m<K = 75 deg
In ΔPQR, the measure of ∠R=90°, RP = 57 feet, and QR = 93 feet. Find the measure of ∠P to the nearest tenth of a degree.
Answer:
58.5
Step-by-step explanation:
hope it helps :)
Which rule best describes this transformation
Answer:
B
Step-by-step explanation:
(2/3) × (-6) × 5
please help me solve and show work
Answer:
-20
Step-by-step explanation:
Use PEMDAS
[tex]\frac 2 3 * -6 * 5\\\frac 2 3*-30\\\frac {-60}{3}\\-20[/tex]
Becky needs of $5,000 loan in order to buy a boat which loan option would allow her to pay the least amount of interest
Answer:
b 5.75%
Step-by-step explanation:
Someone please help me
Which expression has a value of 60?
360 ÷ 60
3,600 ÷ 6
3,600 ÷ 60
3,600 ÷ 600
Answer:
3,600/60
Step-by-step explanation:
The distribution of durations for which apartments remain empty after the resident moves out for one property management company over the past 10 1010 years was approximately normal with mean μ = 85 μ=85mu, equals, 85 days and standard deviation σ = 29 σ=29sigma, equals, 29 days. The property management company tags the files of the apartments that were empty for the shortest 5 % 5%5, percent of durations to have priority cleaning the next time their residents move out
A part of the question is missing which is;
What is the minimum duration for which an apartment remained empty for the company to update the kitchen appliances? Round to the nearest whole number.
Answer:
133 days
Step-by-step explanation:
We are given;
Population mean; μ = 85 days Population standard deviation; σ = 29 days
significance level; α = 5% = 0.05
Critical value of z at significance level of 0.05 = 1.645
Now, formula for z-score is;
z = (x - μ)/σ
Where x is the minimum duration for which an apartment remained empty for the company to update the kitchen appliances.
1.645 = (x - 85)/29
(1.645 × 29) = x - 85
47.705 = x - 85
x = 85 + 47.705
x = 132.705
x ≈ 133 days
Answer: 37 days
Step-by-step explanation:
9e^2x - 30e^x + 25 = 0
Please I need a step by step solution urgently
Answer:
Here you go
Step-by-step explanation:
The first term is, 9e2 its coefficient is 9 .
The middle term is, +30e its coefficient is 30 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 9 • 25 = 225
Step-2 : Find two factors of 225 whose sum equals the coefficient of the middle term, which is 30 .
15 + 15 = 30 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 15 and 15
9e2 + 15e + 15e + 25
Step-4 : Add up the first 2 terms, pulling out like factors :
3e • (3e+5)
Add up the last 2 terms, pulling out common factors :
5 • (3e+5)
Step-5 : Add up the four terms of step 4 :
(3e+5) • (3e+5)
Which is the desired factorization
9^4 x 9^5=9 to the power of what
Answer:
9⁹
Step-by-step explanation:
Hi there !
9⁴ ₓ 9⁵ = 9⁴⁺⁵ = 9⁹
Good luck !
A triangle has sides with lengths of 6 millimeters, 8 millimeters, and 11 millimeters. Is it a
right triangle?
Answer:
No
Step-by-step explanation:
Using the converse of Pythagoras' identity.
If the square on the longest side is equal to the sum of the squares on the other 2 sides, then the triangle is right.
longest side = 11
11² = 121
6² + 8² = 36 + 64 = 100 ≠ 121
Thus the triangle is not right.
Indiana’s population has increased by 9.5% since 2000, when it was about 6 million people. What is Indiana’s population now?
Answer:
The answer is 3,166.7
Step-by-step explanation:
2,000*9.5 = 19,000
19,000/6 = 3,166.6666
The measure of an angle is 9 more than twice its complement. Find the measure of each angle. Which equation below accurately translates the sentence and could be used to find the measure of each angle? 2x + 9 = 90 - x x + 9 = 2(x - 90) x = 9 + 2(90 - x) 2x = (x - 90) + 9
Answer:
1) Find the measure of each angle.
The measure of each angle = 63° and 27°
2) Which equation below accurately translates the sentence and could be used to find the measure of each angle?
a) 2x + 9 = 90 - x
Step-by-step explanation:
1) Find the measure of each angle.
Two Angles are Complementary when they add up to 90 degrees (a Right Angle)
Mathematically this is represented as:
x° + y° = 90°
From the above question, we are told that:
The measure of an angle is 9 more than twice its complement.
Let the complement of an angle be represented by x
And its measure of an angle be represented by y
Hence,
y = 2× x+ 9
y =(2x + 9)°
x° + y° = 90°
Substitute 2y + 9 for x
x + 2x + 9 = 90
Collect like terms
x + 2x = 90 - 9
3x = 81
Divide both sides by 3
3x/3 = 81/3
x = 27°
We find y(measure of the angle)
x + y = 90
27 + y = 90
y = 90 - 27
y = 63°
Therefore, the measure of each angle is given as:
Measure of an angle = 63°
Complement of an angle = 27°
2) Which equation below accurately translates the sentence and could be used to find the measure of each angle?
a)2x + 9 = 90 - x
b) x + 9 = 2(x - 90)
c) x = 9 + 2(90 - x)
d) 2x = (x - 90) + 9
Option a) is the correct option
6
TEL
X
-
4
2
44
is it a function or not a function
If Art weighs 200 pounds at sea level, how much will he weigh on Mt. Everest, which is 29,035 feet above sea level? _ pounds
(Round answer to three decimal places. Do not round the numbers in your work. Only round the final answer)
If an object weighs m pounds at sea level, then its weight W (in pounds) at a height of h miles above sea level is given by W(h) = m(4000/(4000 + h))2. (1 mile = 5280 feet)
(W of h equals m times the quantity of (4000 over the quantity (4000 plus h)) squared)
If Art weighs 200 pounds at sea level, how much will he weigh on Mt. Everest, which is 29,035 feet above sea level?
Answer:
its 1,456,000
Step-by-step explanation:
first you multiply 200 times 5280 and add 4000 if thats right uon
I dont understand can sombody solve this
Answer:
Option 1
Step-by-step explanation:
I found the exact moon graph on line . It says it is proportional because the line passes through the origin
find the labeled angles
Answer:
X = 25, Angles are 65 degrees
Step-by-step explanation:
3x-10 = x+40
2x=50
x=25
determine if the given equations are functions or not function
x = 3, y² = -5x -12, x² + y² =81. are all not functions. the others are functions.
Step-by-step explanation:
I just did it
A function assigns the values. The correct options are C and E.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
An equation is said to be a function if for each different value of x(input) it should give a different output. Therefore, for different inputs of x, the value of the output y should be different and unique. Also, the values if the equation produces the same output for two values of x it also said to be a function.
A.)
x = 3, since for every value of x the value is 3, which is not possible. Hence, this is not a function.
B.)
x² + y² = 81
For the given equation if the value of x is given as 0, the value of y will be,
x² + y² = 81
0² + y² = 81
y² = 81
y = ±√81
y = -9, 9
Hence, this can not be a function.
C.) y = -x + 11
For the given equation if the value of x is kept anything the value of y will be different. Thus, this is a function.
D.)
y² = -5x - 12
For the given equation if the value of x is given as less than -2.4, there will be two values of y. Thus, the given equation is not a function.
E.)
y = 2x² - 6x + 4
The given function will return will the same value of y for 2 different values of x. Hence, this is a function.
F.)
y = -7
Since the given equation can only have the value of y as 7. Therefore, it is not a function.
Hence, the equations that are a function are y = -x + 11 and y = 2x² - 6x + 4.
Learn more about Function:
https://brainly.com/question/5245372
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Jenny has $2.40 deducted from her monthly allowance every time she forgets to do a chore. If she forgets three times in one month, what will be the change in Jenny's total allowance?
Answer: The charge would be $7.20.
hope that helps.
Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 42% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 12%. There is only a 52% chance that she will find a tutor at such short notice.
Complete Question
Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 42% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 12%. There is only a 52% chance that she will find a tutor at such short notice
a What is the probability that Christine fails the course
b Christine ends up failing the course. What is the probability that she had found a tutor? (Round your answer to 4 decimal places.) Probability
Answer:
a
[tex]P(F) = 0.264[/tex]
b
[tex]P(T | F ) = 0.23636 [/tex]
Step-by-step explanation:
From the question we are told that
The probability that Christine will fail the course if she does not have a tutor is [tex]P(F| T') = 0.42[/tex]
The probability that Christine will fail the course if she has a tutor is [tex]P(F| T) = 0.12[/tex]
The probability that she will find a tutor is [tex]P(T) = 0.52[/tex]
Generally the probability that she will not find a tutor is
[tex]P(T') = 1 - 0.52[/tex]
=> [tex]P(T') = 0.48[/tex]
Generally the probability of failing the course is
[tex]P(F) = P(F \ n \ T) + P(F \ n \ T')[/tex]
=> [tex]P(F) = P(F| T) * P(T) + P(A | T') * P(T')[/tex]
=> [tex]P(F) = 0.12 * 0.52 + 0.42* 0.48[/tex]
=> [tex]P(F) = 0.264[/tex]
Generally if Christine ends up failing the course the probability that she had found a tutor? (Round your answer to 4 decimal places.) Probability is mathematically represented as
[tex]P(T | F ) = \frac{ P(F | T) * P(T)}{ P(F)}[/tex]
=> [tex]P(T | F ) = \frac{ 0.12 * 0.52}{ 0.264}[/tex]
=> [tex]P(T | F ) = 0.23636 [/tex]
Somebody please help!!
Answer:
-12
Step-by-step explanation:
Substitute x for 3
6(3-5)
Simplify in the parenthesis
6(-2)
multiply
-12
Yes I need help with x question and please check if my other answers are correct
b.
It snows 2 inches every hour so for x hours it will be x×2 inches
The equation: y = 2x
So for x hours we have 2x inches of snow
c.
x = 24, so y = 2×24 = 48
It will fall 48 inches of snow
6 bottles of shampoo cost $3.60. What is the unit price for
Answer:
$1.67
Step-by-step explanation:
6 divided by $3.60 = $1.67
It’s asking to write an equation of the line with a slope...please help!!
Answer:
y = -3/4x - 6
Step-by-step explanation:
Use y-intercept (0, -6) and slope -3/4 and put into y=mx+b form to solve for b
Remember that m is also known as slope!
-6=(-3/4 * 0) + b
b= -6
y= -3/4x - 6
Find the greater ratio - 6:7 and 7:8
Answer:
6:7
Step-by-step explanation:
Can someone please answer some of my questions?
*They are all math
Answer:
DA FA WERE ARE THE QUESTIONS?????????
Step-by-step explanation: