The range of a function is the set of all possible outputs (y-values) for a given input (x-value).
Given the function f(x) = [x+3]-5, we can see that the function first adds 3 to x and then subtracts 5. The square bracket notation around (x+3) indicates that the function is taking the greatest integer less than or equal to (x+3).
For any input x, the output of the function will always be the greatest integer less than or equal to (x+3) - 5. Therefore, the output of the function is always an integer less than or equal to -2.
So the range of the function is [-5, -2] U (-2, ∞)
Option A) [-5,∞) is incorrect as the range starts with -5 but the function output is always less than or equal to -2.
Option B) (-5,∞) is incorrect as the function output is always less than or equal to -2.
Option C) [3,∞) is incorrect as the function output is always less than or equal to -2.
Option D) (3,∞) is incorrect as the function output is always less than or equal to -2.
The correct answer is (-2, ∞)
Calculate the values of angles A and C of triangle ABC, where b =17.23cm,c=10.86cm and B=10 1 degree 15
Answer:
C = 38.18°; A = 40.57°
Step-by-step explanation:
B = 101' 15"
B = 101° + (15/60) = 101 + 0.25 = 101.25°
b =17.23cm,c=10.86cm
From Sine rule :
c/ sin C = b / Sin B
10.86 / sin C = 17.23 / sin 101.25
SinC = (sin 101.25 * 10.86) / 17.23
Sin C = 10.651328 / 17.23
Sin C = 0.6181850
C = Sin^-1(0.6181850)
C = 38.183716
C = 38.18°
Sum of angles in a triangle = 180°
A + B + C = 180°
A + 101.25° + 38.18° = 180°
A = (180 - (101.25 + 38.18))
A = 40.57°
The airplane travels 1,650 miles in 3 hours. What is
the unit rate?
Answer:
550 miles per hour
Step-by-step explanation:
A hot air balloon went from an elevation of 6,039 feet to an elevation of 3,288 feet in 42 minutes. What was its rate of descent?
Answer:
65.5 feet per second
Step-by-step explanation:
In order to calculate the rate of descent we first need to find the difference in heigh that the hot air balloon descended. We do this by subtracting the initial height from the end height like so...
6,039 - 3,288 = 2,751 ft
Now that we have the difference in height we need to divide this by 42 since that is the amount of time it took for this descent to occur.
2,751 ft / 42s = 65.5 ft/s
Finally we can see that the rate of descent was 65.5 feet per second
Please help! I need the equation of this line.
Answer: why?
Step-by-step explanation:
Please help quick will give brainliest!
Answer:
The statement that correctly uses limits to determine the end behavior of f(x) is;
[tex]\lim\limits_{x \to \pm \infty} \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}= \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }[/tex] so the end behavior of the function is that as x → ±∞, f(x) → 0
Step-by-step explanation:
The given function is presented here as follows;
[tex]f(x) = \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}[/tex]
The limit of the function is presented as follows;
[tex]\lim\limits_{x \to \pm \infty} \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}[/tex]
Dividing the terms by x², we have;
[tex]\lim\limits_{x \to \pm \infty} \dfrac{\dfrac{7 \cdot x^2}{x^2} + \dfrac{x}{x^2} + \dfrac{1}{x^2} }{\dfrac{x^4}{x^2} +\dfrac{1}{x^2} }= \lim\limits_{x \to \pm \infty} \dfrac{7 + \dfrac{1}{x} + \dfrac{1}{x^2} }{x^2 +\dfrac{1}{x^2} }[/tex]
As 'x' tends to ±∞, we have;
[tex]\lim\limits_{x \to \pm \infty} \dfrac{7 + \dfrac{1}{x} + \dfrac{1}{x^2} }{x^2 +\dfrac{1}{x^2} } = \lim\limits_{x \to \pm \infty} \dfrac{7 + 0 + 0 }{x^2 +0 } = \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }[/tex]
However, we have that the end behavior of 7/x² as 'x' tends to ±∞ is 7/x² tends to 0;
Therefore, we have;
[tex]f(x) \rightarrow 0 \ as \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }[/tex]
The statement that correctly uses limits to determine the end behavior of f(x) is therefor given as follows;
[tex]\lim\limits_{x \to \pm \infty} \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}= \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }[/tex] so the end behavior of the function is that as x → ±∞, f(x) → 0.
Complete the statement. Round to the nearest hundredth if necessary.
0.3 km ≈ ? mi
Answer:
0.186 mile rounded = 0.19
Step-by-step explanation:
the answer is 0.19
The figure is one-fourth of a circle.
What is the perimeter of the figure?
Use 3.14 for π.
One fourth of a circle with a radius of 11 cm.
GIVING BRAINLIEST IF YOU SOLVE IT (:
Answer:
around 39.27
Step-by-step explanation:
2*11*3.14=69.08/4=17.27+22=39.27
Due in a few minutes-please help me solve these geometry problems!!!
Answer:
You must be 65.3 ft. closer
Step-by-step explanation:
The first triangle has a length x along the ground and a height of 50 with a 90 degree angle between the ground and the tree. The angle of elevation is 25 degrees.
By the definition of tangent:
tan(25)=50/x
Solve for x
x=50/tan(25)=107.225
The second triangle has a length y along the ground and a height of 50 with a 90 degree angle between the ground and the tree. The angle of elevation is 50 degrees.
By the definition of tangent:
tan(50)=50/y
Solve for y
y=50/tan(50)=41.955
The difference between x and y is how much closer to the tree you must be.
x-y=65.27
Enter the value of n so the expression (7y + 6) + (3y – 2) is equivalent to (ny + 4),
Answer:
10
Step-by-step explanation:
A rectangle is 2 feet wide and 4 feet long. A second rectangle is created by increasing the length and width of the first by a scale factor of
2.5. What is the area, in square feet, of the second rectangle?
Answer:
B
Step-by-step explanation:
A farm covers land in the shape of a trapezium. The length of the northern boundary of the farm is 265 m and length of the southern boundary is 180 m. The perpendicular distance from the northern end to the southern end is 90 m.
a Draw a diagram of the farm and find its area to the nearest square metre.
b Write your answer to part a to the nearest hectare.
c The farmer decides to purchase his neighbour's farm, which is in the shape of a rectangle but has the same area as his farm. What are possible dimensions neighbour's farm? Give your answer in metres.
Answer:
Step-by-step explanation:
Part A
Givens
b1 = 265
b2 = 180
h = 90
Formula
Area = (b1 + b2)*h / 2
Solution
Area = (265 + 180) * 90 / 2
Area = 445 * 90 / 2
Area = 40050 / 2
Area = 20025 square meters
Part B
1 hectare = 10000 square meters
x hectare = 20025 square meters Cross multiply
x * 10000 = 20025 * 1 Divide by 10000
x = 20025 / 10000
x = 2.0025
Rounded to the nearest hectare that would be 2
Part C
The best shape is a square.
That would mean that the area is given by
s^2 = 20025
sqrt(s^2) = sqrt(20025)
s = 141.51
Each side of the rectangle (square) = 141.51
Solve by factoring: x2 – 9x + 20 = 0
A. x = - 4 and x = - 5
B. x = 4 and x = 5
C. x = 20 and x = - 9
D. x = - 4 and x = 5
Show your work
Answer:
Answer
Given equation is:
x
2
−9x+20=0
⇒x
2
−5x−4x+20=0
⇒(x−4)(x−5)=0
⇒x=4andx=5
Pls, answer fast with an explanation. At a carnival, it costs $138.00 for 92 tickets. Write an equation that can be used to find the total cost (c) for any number of tickets (t) you buy.
Which value is greater 4/5 or 70%
Answer:
4/5
Step-by-step explanation:
4/5 = .8
70% = .7
Answer:
4/5
Step-by-step explanation:
d. How much of each ingredient would you need to make an identical recipe that serves 18 people?
what is the centimeters per hour. PICTURE. I REALLY NEED HELP
Answer:
1 Centimeter per Hour: 1 Centimeter per hour is approximately equal to 2.777 778 x 10-6 meters per second (SI unit).
Step-by-step explanation:
1 Centimeter per Hour: 1 Centimeter per hour is approximately equal to 2.777 778 x 10-6 meters per second (SI unit).
4. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
IT'S NOT B
Write a rule for the linear function in the table.
A. f(x) = –3x – 4
B. f(x) = -1/3x - 4
C. f(x) = x – 7
D. f(x) = 3x + 4
Answer:
A. f(x) = -3x - 4
Step-by-step explanation:
What is 5/6 - 3/8
A. 1/3
B. 9/16
C. 1/12
D. 11/24
Answer:
The correct answer is D
Step-by-step explanation:
Omh pls help me 6thh grade math it's do in 10 mins
Answer:
1. 42
2. d cuz it has nothing-
3. A
all im saying cuz ik u can do this
Answer:
number 1 is 52% i am goin through them
Step-by-step explanation:
What is the value of X ?
Answer:
i think x = 4
Step-by-step explanation:
Acil cevap lütfen hemen atarsanız sevinirim (✿^‿^)♥️♥️♥️
Answer:
hai :D
Step-by-step explanation:
Also try D
A bag contains 4 Snickers bars and 1 Twix bar, and the outcome is drawing a Twix bar. Does the phrase that describes the probability of drawing a Twix bar change from Part A?
a: yes, because there are still only two possible outcomes.
b:No, because it is still less likely to have an outcome of drawing a Twix.
c: yes, because it is still less likely to have an outcome of drawing a Twix.
d:No, because there are still only two possible outcomes.
Answer:
C. Yes,because it is still less likely to have an outcome of drawing a Twix.
Step-by-step explanation:
Please answer this question CORRECTLY!!!!!
Is (9, 0) a solution to the equation y = 9? yes no
Answer:
I'm going to say no
Step-by-step explanation:
Because y in the pair y is zero not 9.
Does stencil two overlap exactly with the original image? Describe what you see. After the transformations are complete, what can you say about the points that make up stencil one and the points that make up the original image ? Explain
Answer:
No, stencil two does not overlap the original pattern exactly. Not all the points on stencil two coincide with the points on the original pattern. There is a subtle difference near the boundaries of the two shapes.
Step-by-step explanation:
flora has a summer job where she earns $9.50 per hour. At this company, employees get a 10% raise after working for 400 hours. If flora works 640 hours over the summer, how much money will she make?
Solve the system of equations.
−10y+9x=−9
10y+5x=−5
The Value of (441)2 – (440)2 is :
(i) 841 (ii) 1 (iii) 881 (iv) 0
Can someone plz help me!!
Answer:
145°
Step-by-step explanation:
upper left angle inside triangle is 180-137, or 43°
lower right angle inside triangle is 180-(43 + 102) or 35°
'?' measures 180 - 35 which is 145°
Help me solve this problem
2|m/2|-1>3
Answer:
is this even a equation
Step-by-step explanation: