Answer:
[tex](- \infty, 2), (2, \infty)[/tex]
Step-by-step explanation:
Given the function:
[tex]f(x) = \dfrac{x+1}{x-2}[/tex]
To find:
Domain of the function.
Solution:
First of all, let us learn about definition of domain of a function.
Domain of a function is the valid input values that can be provided to the function for which output is defined.
OR
Domain of a function [tex]f(x)[/tex] are the values of [tex]x[/tex] for which the output [tex]f(x)[/tex] is a valid value.
i.e. The function does not tend to [tex]\infty[/tex] or does not have [tex]\frac{0}0[/tex] form.
So, we will check for the values of [tex]x[/tex] for which [tex]f(x)[/tex] is not defined.
For value to tend to [tex]\infty[/tex], denominator will be 0.
[tex]x-2\neq 0 \\\Rightarrow x \neq 2[/tex]
So, the domain can not have x = 2
Any other value of x does not have any undefined value for the function [tex]f(x)[/tex].
Hence, the answer is:
[tex]\bold{(- \infty, 2), (2, \infty)}[/tex] [2 is not included in the domain].
The table below shows the number of cars Jing sold each month last year.
What is the median of the data in the table.
13
16
19
20.5
23.5
Other:
Answer:
The median of the data in the table is 19.
Step-by-step explanation:
We are given the following data that shows the number of cars Jing sold each month last year below;
Number of cars Jing sold: 13, 16, 19, 20.5, 23.5
For calculating the median, firstly we have to observe that the number of observations (n) in our data is even or odd because;
If n is odd, then the formula for calculating median is given by;Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
If n is even, then the formula for calculating median is given by;Median = [tex]\frac{(\frac{n}{2} )^{th} \text{ obs.} + (\frac{n}{2}+1 )^{th} \text{ obs.} }{2}[/tex]
Here, the number of observations in our data is odd, i.e. n = 5.
So, Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{5+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{6}{2} )^{th} \text{ obs.}[/tex]
= 3rd obs. = 19
Hence, the median of the data in the table is 19.
(b) The train is 61 cm long and travels at a speed of 18 cm/s.
It takes 4 seconds for the whole of the train to cross a bridge.
Calculate the length of the bridge.
Answer:
The length of the bridge is 72 cm
Step-by-step explanation:
In order to find the length of bridge, we have to apply distance formula which is D = S × T where S represents speed and T is time :
[tex]d = s \times t[/tex]
[tex]let \: s = 18,t = 4[/tex]
[tex]d = 18 \times 4[/tex]
[tex]d = 72 \: cm[/tex]
The length of the bridge is 11 cm .
What is relationship between distance time and speed ?When an object moves in a straight line at a steady speed, we can calculate its speed if we know how far it travels and how long it takes. This equation shows the relationship between speed, distance traveled and time taken:
Speed is distance divided by the time taken.
For example, a car travels 30 kilometers in 2 hours.
Its speed is 30 ÷ 2 = 15km/hr.
Formula used :
Distance = Speed * Time
Time = Distance / Speed
Speed = Distance / Time
According to the question
Length of train = 61 cm
Speed of train = 18 cm/s
Time taken to cross the bridge = 4 seconds
In this length traveled by train = length of train + Length of bridge
( as time given is to completely cross platform )
Therefore,
length traveled by train = 61 + Length of bridge
formula used
Distance = Speed * Time
61 + Length of bridge = 18 * 4
61 + Length of bridge = 72
Length of bridge = 72 - 61
Length of bridge = 11 cm
Hence, the length of the bridge is 11 cm .
To know more about relationship between distance time and speed here :
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Find the slope of the line passing through the points -4,-3 and 8,-9
Answer:
-3/4
Step-by-step explanation:
Slope = Rise/Run
Between -4 and 8, the line runs 12 units. Between -3 and -9, the line rises -9 units.
-9/12 = -3/4
Answer:
-3/4
Step-by-step explanation:
how many 6-digit numbers can be created using8, 0, 1, 3, 7, and 5 if each number is used only once?
Answer:
600 numbers
Step-by-step explanation:
For six-digit numbers, we need to use all digits 8,0,1,3,7,5 each once.
However, 0 cannot be used as the first digit, because it would make a 5-digit number.
Therefore
there are 5 choices for the first digit (exclude 0)
there are 5 choices for the first digit (include 0)
there are 4 choices for the first digit
there are 3 choices for the first digit
there are 2 choices for the first digit
there are 1 choices for the first digit
for a total of 5*5*4*3*2*1 = 600 numbers
convert the equation f(x)=1/2x^2+3x-2 to vertex form
Answer:
Step-by-step explanation:
Hello, please consider the following.
The "vertex form" is as below.
[tex]y=a(x-h)^2+k\\\\\text{Where (h, k) is the vertex of the parabola.}\\[/tex]
Let's do it!
[tex]f(x)=\dfrac{1}{2}x^2+3x-2\\\\f(x)=\dfrac{1}{2}\left(x^2+3*2*x\right) -2\\\\f(x)=\dfrac{1}{2}\left( (x+3)^2-3^2\right)-2\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9}{2}-\dfrac{4}{2}\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9+4}{2}\\\\\large \boxed{\sf \bf \ \ f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{13}{2} \ \ }[/tex]
Thank you.
a pack of 4 choclates cost 1.80 pounds how much is the price per unit
Answer:
0.45p
Step-by-step explanation:
4 chocolates = £1.80
1 chocolate = x
x= 1.80× 1 = 1.80÷4 = 0.45p
1 = 0.45p
I HOPE THIS HELPED :)
The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70
[tex] d \propto v^2[/tex]
$\implies d=kv^2$
substitute the given values, $5=k(10)^2\implies k=\frac1{20}$
now, $d=\frac{1}{20}\times( 70)^2=\frac{70\times70}{20}=245$
A big blunder from my side, now fixed!
In the first quadrant you start at 5, 6 and move 4 units down. What point will you end up at? Thanks for your help! - Someone who's better at English than math
Answer:
(5, 2)
Step-by-step explanation:
(5, 6) go down 4 units means subtract 4 from the y
(5, 2)
The point to end up will be (5, 2).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
In the first quadrant you start at (5, 6 ) and move 4 units down.
Now,
Since, In the first quadrant you start at 5, 6 and move 4 units down.
Hence, The end up point = (5, 6 - 4)
= (5, 2)
Thus, The point to end up will be (5, 2).
Learn more about the coordinate visit:
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Which of these functions could have the graph shown below?
O A. f(x) = e^30x
O B. f(x) = 30^30x
O C. f(x) = 30^x
O D. f(x) = 30e^x
The functions could have the graph shown below will be y = 30eˣ. Then the correct option is D.
What is an exponent?Let a be the initial value and x be the power of the exponent function and e be the increasing factor.
The exponent is given as
y = a(e)ˣ
From the graph, the value of the exponent function at x = 0, will be 30.
Then the function will be
30 = a(e)⁰
30 = a
Then the exponent function is given as,
y = 30eˣ
Thus, the functions could have the graph shown below will be y = 30eˣ.
Then the correct option is D.
More about the exponent link is given below.
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PLEASE HELP ME !!!
given a function y = 5x² - 9x - 5
from the graph, determine the value of x when y = 0
Answer:
-0.4 or 2.3
Step-by-step explanation:
simple
each box is 0.1 unit
Answer:
Step-by-step explanation:
The answer is where the graph cuts the x-axis.
I can't see it very well but it looks like x = -0.4 and 2.3.
Which of these is NOT discrete data:
A. number of home-runs hit in a professional baseball game
B. air pressure in a car tire
C. cars per household in a town
D. number of pills in a container of vitamins
Answer:
B, air pressure in a car tire.
Step-by-step explanation:
Discrete data is data which come in intervals, and isn't continuous.
The number of home runs can only go 0 -> 1 -> 2 -> 3, you can't have 2.5 or 3.2 home-runs.
The number of pills in a container can also only go 0 -> 1 -> 2. Again, can't have 0.7 pills.
The number of cars per household is also discrete. The number of cars in a household goes 0 -> 1 -> 2, you can't have half a car!
However, the air pressure is continuous. If you're increasing the air pressure, it'll (in theory) go from 0 -> 0.000...001 -> 0.000..002 etc. It doesn't "jump" from 0 pressure -> 1 pressure like the others, it goes smoothly. It can be any value.
So the air pressure isn't discrete data.
[fill in the blank]
In this figure,AB and CD are parallel.
AB is perpendicular to line segment_____. If the length of EF is a units, then the length of GH is_____units.
Answer:
1. GH
2. a
Step-by-step explanation:
Perpendicular: When 2 lines meet at 90 degrees
1. It is line segment GH because AB and GH meet at a 90 degree angle (since there is a box at angle GHF indicating that it is 90 degrees)
2. It has to be a units because it is a rectangle where the top and bottom are congruent and the sides are too
This is a rectangle since AB and CD are parallel and GH can be a transversal line, according to same side interior angles theorem EGH is a also 90 degrees. That means FEG is 90 degrees too because then the quadrilateral will add up to 360 degrees
Solve the simultaneous equation
X+3y=13
X-y=5
Answer:
x = 7
y = 2
Step-by-step explanation:
In the above question, we are given 2 equations which are simultaneous. To solve this equation, we have to find the values of x and y
x + 3y = 13 ........ Equation 1
x - y = 5...........Equation 2
From Equation 2,
x = 5 + y
Substitute 5 + y for x in Equation 1
x + 3y = 13 ........ Equation 1
5 + y + 3y = 13
5 + 4y = 13
4y = 13 - 5
4y = 8
y = 8/4
y = 2
Since y = 2, substitute , 2 for y in Equation 2
x - y = 5...........Equation 2
x - 2 = 5
x = 5 + 2
x = 7
Therefore, x = 7 and y = 2
The base of a triangle is two times its height. If the area of the triangle is 36, then what is the height of the triangle?
We have:
h - height
b = 2h - base
A = 36 - area
so:
[tex]A=\frac{1}{2}\cdot b\cdot h\\\\A=\frac{1}{2}\cdot 2\cdot h \cdot h\\\\A=h^2\\\\36=h^2\quad|\sqrt{(\dots)}\\\\\boxed{h=6}[/tex]
Find the volume of the given shapes. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
5.
volume=l×w×h=8×6×7=336 mi³
6.
diameter=16 yd
radius=16/2=8 yd
[tex]volume=\frac{4}{3} \pi \times 8^3=\frac{2048}{3} \pi \approx 2144.67 \approx 2144.7 yd^3[/tex]
Find the he value of n if 4n=6 4
Answer: 16
Step-by-step explanation:
64/4=16
n=16
Answer:
16
Step-by-step explanation:
4n = 64
n = 16 --------> Divide by 4 on each side
Suppose y varies jointly as x & z. If y = -180 when z = 15and x = -3,then find y when x = 7 and z = -5. 1 point
Answer:
y = - 140
Step-by-step explanation:
The statement
y varies jointly as x & z is written as
y = kxzto find y when x = 7 and z = -5 we must first find the relationship between the variables
when y = - 180
z = 15
x = - 3
- 180 = k(15)(-3)
-180 = - 45k
Divide both sides by - 45
k = 4
The formula for the variation is
y = 4xzwhen
x = 7
z = -5
y = 4(7)(-5)
y = 4(-35)
y = - 140Hope this helps you
Whats the mean of the box plot 50 60 70 80 90 100
Answer:
75
Step-by-step explanation:
Mean = sum of all numbers / how many of numbers
=> 50 + 60 + 70 + 80 + 90 + 100 / 6
=> 450 / 6
=> 75
So, the mean of this data is 75.
A VERTICAL POLE OF CAST A SHADOW OF 4.5m LONG AT THE SAME TIME A TREE OF HEIGHT 24m LONG CAST A SHADOW OF 6m LONG. FIND THE HEIGHT OF THE POLE.
Answer:
18 metres
Step-by-step explanation:
4.5/6 = x/24
¾= x/24
x = 18 m
Each packet of the cooking oil weighs 2/5th of a kilogram and one kilogram of the cooking oil costs $6.5. Sara went to the grocery shop to buy some items to stock her kitchen. If she bought 8 packets of the cooking oil, how much money did she spend? A $19.60 B $18.20 C $20.80 D $23.40
Answer:
C) $20.80
Step-by-step explanation:
1 kg of cooking oil = $6.5
1 packet of cooking oil =2/5 kg
If 1 kg of cooking oil = $6.5
2/5kg of cooking oil = $X
Cross Multiply
1kg × $X = 2/5kg × $6.5
$X = 13/5
$X = 2.6
Hence 2/5kg of oil cost $2.6
Since 1 packet of oil = 2/5kg of oil , 1 packet of oil cost $2.6
The amount she spent if she bought if she bought 8 packets of the cooking oil is calculated as:
1 packet of oil = $2.6
8 packets of oil =
$2.5 × 8
= $20.80
Therefore,if Sara bought 8 packets of oil, the amount she would spend = $20.80
HELP i don’t know how to do this
Answer:
4a
Step-by-step explanation:
4a
the top and right are a-b, but you have to add the b’s back in, so really all sides are a
a+a+a+a=4a
Answer: 4a
Step-by-step explanation: perimeter is the length of all sides added together. Every length is given combine like variables and you will get 4a+2b-2b. 2b-2b is 0 which leaves you with 4a
If EH = 23, calculate AB.
Youngblood say you want me back in your life...
Answer:
2/4 = 23/AB
1/2 = 23/AB
AB= 46
Hope it helps ^_^
Given that p=x^2-y^2/x^2+xy
I. Express p in the simplest form
ii. Find the value of p if x=-4 and y=-6
Answer:
p = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
p = [tex]\frac{x^2-y^2}{x^2+xy}[/tex] ( factorise numerator and denominator )
x² - y² ← is a difference of squares and factors as (x - y)(x + y)
x² + xy ← factor out x from each term
= x(x + y) , thus
p = [tex]\frac{(x-y)(x+y)}{x(x+y)}[/tex] ← cancel (x + y) on numerator/ denominator
= [tex]\frac{x-y}{x}[/tex] ← substitute x = - 4, y = - 6
= [tex]\frac{-4-(-6)}{-4}[/tex]
= [tex]\frac{-4+6}{-4}[/tex]
= [tex]\frac{2}{-4}[/tex] = - [tex]\frac{1}{2}[/tex]
Which graph shows a linear function?
Answer:
the bottom
Step-by-step explanation:
Answer: the second one
Step-by-step explanation:
Convert to slope-intercept from: y-4=9(x-7)
Answer:
y = 9x - 59
Step-by-step explanation:
y - 4= 9(x-7)
y - 4 = 9x - 63
y - 4 + 4 = 9x - 63 + 4
y = 9x - 59
Answer:
Below
Step-by-step explanation:
● y-4 = 9(x-7)
Multiply 9 by (x-7)
● y-4 = 9x - 63
Add 4 to both sides
● y-4+4 = 9x-63 +4
● y = 9x - 59
what's 700.00divided by 120
Answer:
[tex]\Large \boxed{\frac{35}{6} }[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{700}{120}[/tex]
Reduce and simplify the fraction to lowest terms.
[tex]\displaystyle \frac{20(35)}{20(6)}[/tex]
[tex]\displaystyle \frac{35}{6}[/tex]
If a polygon has an area of 10 cm² and is dilated by a factor of 2, what will be the area of the dilated polygon?
Area depends on the product of sides,
so if the sides are shortened by a factor of 2, area will reduce by a factor of 4. (2×2)
new area = 10/4=2.5 cm²
find the lower quartile for the data {47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4}
Answer:
The lower quartile is 23.4
Step-by-step explanation:
The given data are;
47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4
Rearranging the data, we have;
5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4, 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2
The lower quartile, Q₁, is the (n + 1)/4 th term which is (16 +1)/4 = 4.25th term
However since we have an even set of numbers, we place a separator at the middle and we look for the median of the left half as follows
5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4║ 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2
We have two numbers (17.4 + 29.4) at the median of the left set of numbers, we find the average of the two numbers to get the lower quartile
The lower quartile is therefore = (17.4 + 29.4)/2 = 23.4.
i need help please asap 10 points!
Answer:
1) Real Number
2)Whole Number
3)Irrational Number
4)Rational Number
5)Integers
6)Natural Numbers
Write an equation for the line in the graph that passes through the points (0,4) and (12,16).
Answer:
We have,
y-y1=m(x-x1)
or,y-4=-1(x-0)
or,y-4=-x
or,x+y=4 is the required equation
Step-by-step explanation:
it it helps u ...plz mark it as brainliest
