Answer:
96-26=70 books she bought at the yard sale
Determine the inverse of the function f(x) = 3(x - 4)^2 + 5.
f(x) as given has no inverse. We see that, for instance, f(1) = f(7) = 32; that is, two different values of x give the same value of f(x), so f is not one-to-one.
We can however restrict the domain over which f is defined to extract an invertible function. One such choice would be to restrict to the interval x ≥ 4, which I'll demonstrate below.
Recall the definition of function inverse:
f(f^(-1)(x)) = x
Then for this function, we have
3 (f^(-1)(x) - 4)² + 5 = x
3 (f^(-1)(x) - 4)² = x - 5
(f^(-1)(x) - 4)² = (x - 5)/3
√((f^(-1)(x) - 4)²)= √((x - 5)/3)
For all x, √(x²) = |x|. Then √((f^(-1)(x) - 4)²) = |f^(-1)(x) - 4|, but by restricting x ≥ 4, or x - 4 ≥ 0, we have the condition that f^(-1)(x) - 4 ≥ 0, and so by definition (of the absolute value function) the absolute value reduces to the positive case. In short, we end up with
f^(-1)(x) - 4 = √((x - 5)/3)
and hence the inverse
f^(-1)(x) = √((x - 5)/3) + 4
A soccer player runs a total of 12 miles during a 4 hour game.
What is the unit rate?
Answer:
3
Step-by-step explanation:
12 divited by 4 =3
Write an expression that represents the perimeter of the triangle.
Answer:
(3m - 2) + (2m + 7) + (5m - 3)
Step-by-step explanation:
Perimeter is found by combining all side measurements together to find the total measurement. In this case, combine the sides:
(3m - 2) + (2m + 7) + (5m - 3) is your answer.
If you need a simplified expression, simply combine all the like terms together. Like terms are terms with the same as well as same amount of variables:
(3m + 2m + 5m) + (7 - 2 - 3)
(10m) + (2)
10m + 2 is your answer.
~
A movie theater sends out a coupon for 75% off the price of a ticket.
Answer:
X times .7 = y.
Step-by-step explanation:
I know what question you are reffering to, don’t worry. <33
Write the number for six million fifty thousand.
Answer:
6,050,000
Step-by-step explanation:
Answer:
6,500,000
Step-by-step explanation:
Mr. Martin drove away from his house without his wallet. He did a 180. Where is he heading now?
Martin is heading to his house
Simon is driving his car on a highway at a constant speed. The below table shows the relationship between the amount of
gasoline left in his car and the distance traveled on the highway.
Answer:
ccccccccccccccccccccccccccc
In a survey of 1400 people who owned a certain type of car, 700 said that would buy that type of car again. What percent do the people surveyed were satisfied with the car? Please help me with this and explain step by step on how I am able to get the answer so I could keep that in mind!
Answer:
50% since 700 is half of 1400
A seed sprouted and grew 2/3 of a foot in 3 months. What was its rate of growth in feet per month?
Answer:
2.6 inches repeating per month
Answer:
2/9
Step-by-step explanation:
Write an equation that could be used to convert X miles into Y inches.
Answer:
y = 63360x
Step-by-step explanation:
we know 1 mile = 63360 inches
So: y = 63360x
x mile
& y inch
Jaxon's start-up business makes a profit of $500 during the first month. However, the company records a profit of -$50 per month for the next eight months and a profit of $175 for the final month. What is the total profit for the first ten months of Jaxon's business?
Answer: 275$
Step-by-step explanation:
500
-50 x 8 = -400
500 - (-400) = 100
100 + 175 = 275$
================================================================
Explanation:
The first month has a profit of +500 or simply 500.
The next 8 months have a profit of -50 per month, so we have -50*8 = -400 in profit here. A negative profit indicates debt. So far, the profit is 500 + (-400) = 500 - 400 = 100 dollars. This result is positive, so the company is in good shape so far.
It gets in better shape when adding on the final 175 profit from the tenth month. The final profit is 100+175 = 275 dollars
x + 3 ? 3 = x what factor do I use in between 3 and 3
Answer:
1 or 3
Step-by-step explanation:
factors of 3 r 1 and 3
that's why 3 is a prime number
Sum of the Angles of a Triangle
If the three angles of a triangle
are equal, what is the
measurement of each angle?
B
C
[?] degrees
9514 1404 393
Answer:
60°
Step-by-step explanation:
If the measure of the angle is represented by A, then the sum of the three angles in the triangle is ...
A +A +A = 180°
3A = 180° . . . . . . . simplify
A = 180°/3 = 60° . . . . . divide by the coefficient of A
The three angles in an equi-angular triangle are all 60°.
__
Additional comment
If the angles are equal, so are the opposite sides. The three sides in an equi-angular triangle are also equal. Generally, such a triangle is called an equilateral triangle. It is useful to remember the angles in an equilateral triangle are all 60°.
One interesting consequence of this is that the smallest angle in any triangle can never be larger than 60°.
Two students are working on the same homework assignment. Antonia has completed 18 out of 45 questions. Oliver has completed 20% of the questions. Which student has completed the most questions, and why?
Answer: Your anwser who has the most completed it would be the person with 18 questions anwsered out of 45
Step-by-step explanation:
The reason of this is becuase 20 percent of 45 if 9 and thats 9 questions out of 45 so 18 questions out of 45 is more
please mark brainliest thank you
PLEASE HELP IT IS DUE RIGHT NOW!!!
WILL MARK BRAINLIEST!!!!!
Answer:
(-2,-5)
Step-by-step explanation:
How many groups of 1/4 are in 7.
There is 28.
7 ÷ 1/4 = 28
1)cot a/2 -tan a/2 = 2 cot a
2) cot b/2 + tan b/2= 2 cosec b
prove
Find the perimeter of the rectangle
= 2(2 + 3) units
= 2 × 5 units
= 10 units.
Answer:The perimeter of the rectangle is 10 units.
Hope it helps.
Do comment if you have any query.
613209x659832=?
If you answer this correct congrats you're a genius
(and yes its possible I solved myself)
Answer:
4.046149209.iS it correct?
Answer:
[tex]4,046149209.10^{11}[/tex]
Step-by-step explanation:
using computer pocket :))
need help, im confused
Answer:
Part A: correct
Part B: $20
Step-by-step explanation:
Part B:The amount Vanessa pays for her printer and 2 cartridges is ...
$90 +2(25) = $140
The amount Tia pays for her printer and 2 cartridges (c=2) is ...
t = 80 +20(2) = 120 . . . . dollars
Then the difference in the amounts they pay is ...
$140 -120 = $20
if each of the following quadrilaterals are trapezoids find the missing measures. show your work.
Question 2 (Essay Worth 10 points)
(07.02 MC)
An equation is shown below:
3(2x - 7) = 3
Part A: How many solutions does this equation have? (4 points)
Part B: What are the solutions to this equation? Show your work. (6 points)
Answer:
Part A: 1 solution
Part B:
3(2x-7)=3
6x-21=3
+21 +21
6x=24
/6 /6
x=4
Step-by-step explanation:
First you distribute 3(2x-7)=3 to 6x-21=3. Next you do inverse operations by adding 21 to both sides of the equation to get 6x=24. Finally you divide both sides by 6 to get x=4
if a shirt is 50$ and is on sale for 20% off how much wil you pay with 6% sales tax
Answer:
42.4 is the correct answer to this question
I can use structure to decide where to place the first digit in a quotient. A strongly agree B. agree C. disagree qD. strongly disagree
Answer: For this question, it's just like a self-survey. If you understand this concept strongly or not really, you go with that answer like strongly agree, agree, etc.
solve for x! please help giving BRAINLIEST.
Answer:
its 45
Step-by-step explanation:
Correct = brainiest
Answer:
∠AOC = 98°
∠BOC = 82°
∠DOE = 39°
Step-by-step explanation:
∠DOE = 180 - (43 + 98)
= 39°
∠BOC = 180 - ∠DOB
= 180 - 98
= 82°
∠AOC = ∠DOB (they are vertical angles which are equal)
Abigail has been saving her earnings from her lemonade stand. Abigail has 30 dollars to spend. If she buys a new hat for 15 dollars, how many ribbons can she buy with the remaining money if they cost 4 dollars each?
PLEASE HELP ITS DUE NOW!!!!!!
WILL MARK BRAINLIEST!!!!!
Answer:
(- 4, - 10 )
Step-by-step explanation:
y = 5x + 10 → (1)
y = 4x + 6 → (2)
Substitute y = 5x + 10 into (2)
5x + 10 = 4x + 6 ( subtract 4x from both sides )
x + 10 = 6 ( subtract 10 from both sides )
x = - 4
Substitute x = - 4 into either of the 2 equations and evaluate for y
Substituting into (1)
y = 5(- 5) + 10 = - 20 + 10 = - 10
solution is (- 4, - 10 )
__________
[tex] \: [/tex]
[tex] \sf{y = 5x + 10...(1)}[/tex]
[tex] \sf{y = 4x + 6...(2)}[/tex]
Subtitute (1) to (2)[tex] \sf{y = 4x + 6}[/tex]
[tex] \sf{5x + 10 = 4x + 6}[/tex]
[tex] \sf5x - 4x = 6 - 10[/tex]
[tex] \sf{x = - 4}[/tex]
.
Subtitute x = -4 to (1)[tex] \sf{y = 5x + 10}[/tex]
[tex] \sf{y = 5( - 4) + 10}[/tex]
[tex] \sf{y = - 20 + 10}[/tex]
[tex] \sf{y = - 10}[/tex]
.
[tex] \longmapsto \sf{( - 4 , - 10)}[/tex]
is -3/2 parallel to 2/3
Answer: The parallel slope of 2/3 is 2/3 . m=2/3
Step-by-step explanation: Parallel slopes have the same slopes.
If a slope is 2/3, the parallel slope will be the same. So, the parallel slope will also be 2/3.
Therefore, the answer is m=2/3
Answer:
No.
Step-by-step explanation:
Parallel lines have the same slope. Perpendicular lines have opposite reciprocal slopes. In this instance, -3/2 is perpendicular to 2/3, not parallel.
What is the equation of the line??
Answers:
m = -2/3
b = 1
equation: y = (-2/3)x + 1
This is the same as writing [tex]y = -\frac{2}{3}x+1[/tex]
===========================================================
Explanation:
There are a few approaches, but I like to start at the y intercept whenever it is an integer. The y intercept is where the diagonal line crosses the vertical y axis. In this case, that location is (0,1) telling us that b = 1 is the y intercept.
From that starting anchor point, we need to find a way to get to another point on this line. There are a few ways to do this, but we can move down 2 and to the right 3 units to go from (0,1) to (3,-1). This "down 2 right 3" motion directly leads to the slope of rise/run = -2/3
---------------
Alternatively, you can start at something like (-3,3) and move down 4 and move right 6 to arrive at (3,-1). Note how rise/run = -4/6 = -2/3. No matter where you start, moving along this line will involve a "down 2 right 3" movement pattern. Be sure to reduce any fractions as much as possible.
Yet another alternative is to apply the slope formula using any two points on the line. Preferably they have integer coordinates.
----------------
However you determine the slope, it's m = -2/3 after fully reducing. It along with b = 1 is plugged into y = mx+b to get y = (-2/3)x+1 as the equation of this line. It's in slope intercept form.
