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Related Questions
Determine the inverse of the function f(x) = 3(x - 4)^2 + 5.
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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
(3)a train travel 252 km in 42 hours. what amount of time will it take to complete a journey of 350km. (4) calculate the cost of 15 article at $1.95 each cost. (5) if 25 article cost 43.75 how much does each cost. (6) A car travel 240km on 20 liter of petrol. how many liters of petrol is needed to travel 600km
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Answer:
(3)
Distance the train can travel=252km
Distance the train can travel in 1 hour=252÷42=6km
The time needed to cover 350km= 350÷6=58.4 hours.
(4)
The cost of 1 articles=$1.95
The cost of 15 articles= 15(1.95)=$29.25
(5)
Cost of 25 articles= 43.75
Cost of 1 article= 43.75/25=1.75
(6)
Liters of petrol needed when a car travels 240km=20litre
liters of petrol needed when a car travels 600km= 20/240 x600
20/24x60
20/4x10
5x10=50liter
x + 3 ? 3 = x what factor do I use in between 3 and 3
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Answer:
1 or 3
Step-by-step explanation:
factors of 3 r 1 and 3
that's why 3 is a prime number
Use elimination to solve.
3y-6x=7
-4y-3x=9
Answers
Answer:
x = -5/3, y = -1 or [tex](-\frac{5}{3}, -1)[/tex]
Step-by-step explanation:
Solving systems of linear equations using process of elimination involves eliminating one of the variables (and its coefficient) in order to solve the other variable either through addition or subtraction. However, there may be other mathematical operations necessary before one of the variables can be eliminated.
Equation 1: 3y - 6x = 7
Equation 2: -4y - 3x = 9
Step 1: Multiply Equation 2 by -2:
(-2)(-4y - 3x) = 9 (-2)
8y + 6x = -18
Step 2: Add "8y + 6x = -18" to Equation 1:8y + 6x = -18
+ 3y - 6x = 7
11y = -11
Step 3: Divide both sides by 11 to solve for y:[tex]\frac{11y}{11} = \frac{-11}{11}[/tex]
y = -1
Step 4: Substitute y = -1 into Equation 2 to solve for x:-4(-1) - 3x = 9
4 - 3x = 9
Step 5: Subtract 4 from both sides:4 - 4 - 3x = 9 - 4
- 3x = 5
Step 6: Divide both sides by -3 to solve for x:[tex]\frac{-3x}{-3} = \frac{5}{-3}[/tex]
[tex]x = - \frac{5}{3}[/tex]
Verify whether the values for x and y are correct by substituting their values into both equations:
x = -5/3, y = -1
Equation 1: 3y - 6x = 7
[tex]3(-1) - 6(-\frac{5}{3}) = 7[/tex]
-3 + 10 = 7
7 = 7 (True statement).
Equation 2: -4y - 3x = 9
-4(-1) - 3 (-5/3) = 9
[tex]-4(-1) - 3(-\frac{5}{3}) = 9[/tex]
4 + 5 = 9
9 = 9 (True statement).
Therefore, x = -5/3 and y = -1 are the solutions to the given systems of linear equations.
if a shirt is 50$ and is on sale for 20% off how much wil you pay with 6% sales tax
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Answer:
42.4 is the correct answer to this question
613209x659832=?
If you answer this correct congrats you're a genius
(and yes its possible I solved myself)
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Answer:
4.046149209.iS it correct?
Answer:
[tex]4,046149209.10^{11}[/tex]
Step-by-step explanation:
using computer pocket :))
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?
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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
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 $175 for the final month. What is the total profit for the first ten months of Jaxon's business?
Answers
Answer: 275$
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
solve for x! please help giving BRAINLIEST.
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Answer:
its 45
Step-by-step explanation:
The table below represents which equation?
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Answer:
the third answer is correct
Step-by-step explanation:
the starting point is 2 and it goes up by 3
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
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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.
What is the equation of the line??
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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.
Find the perimeter of the rectangle
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= 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.
63% to fraction
[tex] \frac{63}{?100} [/tex]
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Follow the steps mentioned below to write 0.63 as a fraction.
Step 1: Determine the number of digits after the decimal point in the decimal number. Here, there are 2 digits after the decimal point.
Step 2: Remove the decimal point and write the number by the power of 10 which is equal to the number of digits after the decimal point. So, here we will divide 63 by 102
Step 3: Express the fraction in simplified form.
So, 0.63 as a fraction is,
0.63 = 63/100
1)cot a/2 -tan a/2 = 2 cot a
2) cot b/2 + tan b/2= 2 cosec b
prove
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LHS = cot(a/2) - tan(a/2)
= (1 - tan^2(a/2))/tan(a/2)
= (2-sec^2(a/2))/tan(a/2)
= 2cot(a/2) - cosec(a/2)sec(a/2)
= 2(1+cos(a))/sin(a) - 1/(cos(a/2)sin(a/2))
= 2 (1+cos(a))/sin(a) - 2/sin(a)) (product to sums)
= 2[(1+cos(a) -1)/sin(a)]
=2cot a
= RHS
2.
LHS = cot(b/2) + tan(b/2)
= [1 + tan^2(b/2)]/tan(b/2)
= sec^2(b/2)/tan(b/2)
= 1/sin(b/2)cos(b/2)
using product to sums
= 2/sin(b)
= 2cosec(b)
= RHS
PLEASE HELP ITS DUE NOW!!!!!!
WILL MARK BRAINLIEST!!!!!
Answers
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]
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
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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°.
need help, im confused
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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
Mr. Martin drove away from his house without his wallet. He did a 180. Where is he heading now?
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Martin is heading to his house
painter has a 24-foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. To the nearest tenth of a foot, how high can the ladder safely reach?
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Answer:
this is a pythagorean theorem problem. 24 is the whole ladder, and if you draw it out, is a hypotenuse. 8 is a leg. . so 8^2 + b^2 = 24^2
b^2 = 512, so b = sqrt(512) = 22.6
The Shah family uses up 1/2-gallon jug of milk every 3 days. At what rate do they drink milk?
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Answer:
1 Gallon per 6 days
Step-by-step explanation:
1/2 *2 = 1
3*2 =6
Answer:
1/6 Gallons of Milk per Day
Step-by-step explanation:
1/2 / 3 = 1/6
Brainiest for answer as always
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X can Be mirrored vertically and then is supplementary to x
Answer:
X=33
Step-by-step explanation:
Hope this helps!!!
A definition of a statistical question is given below.
Statistical question:
Any question whose answer could involve working with more than one data value.
In each situation below, determine whether the question is a statistical question.
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Answer:
I dont know
Step-by-step explanation:
The other questions are about one person asking one other person about something to get numerical data.
If you only ask 1 person, you will have 1 answer. 1 answer is one data value, but statistical questions must have more than one data value.
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.
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Answer:
ccccccccccccccccccccccccccc
1 out of 5 apple were rotten . If 284 were edible, how many apples were harvested?
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Answer:
200 apple yet to go byhfhhf
284/4 = 71
5x71 (out of the ratio 4:5) = 355
Therefore 284:355,
355 apples were harvested, 284 edible, 71 rotten
There are about 3 × 1020 gallons of salt water on the earth, while there are about 6 × 1018 gallons of fresh water. About how many times the amount of fresh water is the amount of salt water? 200 times the amount 500 times the amount 2 times the amount 50 times the amount
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Answer C
Step-by-step explanation:
Write the number for six million fifty thousand.
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Answer:
6,050,000
Step-by-step explanation:
Answer:
6,500,000
Step-by-step explanation:
i inserted a picture of the question could you please make it short.
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Answer
B) 6²
E) 36
Step-by-step explanation:
[tex]6^{7}[/tex] / [tex]6^5[/tex] = 6^(7-5) = 6²
6² = 36
Hi, someone else asked this question and I know that the answer is 6, but don’t know why. Could someone explain this for me, please? If you can make me understand I’ll give you brainliest…
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Answer:
6
Step-by-step explanation:
I'm not exactly sure, but since 6 is the only number missing from this pattern, wouldn't it make sense for the answer to be 6?
Which inequality is true when the value of d is 14?
−d−9>−1.5
−d−9<1.5
−d−9>1.5
d−9<−1.5
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Answer:
-d - 9 < 1.5
Step-by-step explanation:
In this problem, my reasoning is shown below for each individual inequality. We can test each one to see if it is true or not.
[tex]-(14)-9>1.5?\\-14-9>1.5?\\-23>1.5?\\[/tex]
-23 is not greater than 1.5, so it can't be the first one. Let's try the next one.
[tex]-(14)-9<1.5?\\-14-9<1.5?\\-23<1.5?[/tex]
Yes! -23 is smaller than 1.5. So we can say that the second option is correct. But just for good measure, we can try the other two.
[tex]-(14)-9>1.5?\\-14-9>1.5?\\-23>1.5?[/tex]
Nope! -23 is not greater than 1.5. Let's try the last one.
[tex]14-9<-1.5?\\5<-1.5?[/tex]
And again... nope. 5 is not smaller than -1.5. So our reigning option is -d - 9 < 1.5. Hopefully this was helpful! If you have any more questions, let me know.
−d−9<1.5 inequality is true when the value of d is 14.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
We have to check the inequality which is true for d when it is 14.
−d−9>−1.5
-14-9>-1.5
-23>-1.5
The first option is false.
−d−9<1.5
-23<-1.5
So the inequality −d−9<1.5 is true for d=14.
−d−9>1.5
-23>1.5
The inequality is false.
d−9<−1.5
14-9<-1.5
5<-1.5
The inequality is false.
Hence, −d−9<1.5 inequality is true when the value of d is 14.
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