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].
Solve for x help please
Answer:
A. 5
Step-by-step explanation:
Based on the secant and tangent theorem, (4 + x)*4 = 6²
We can solve for x using the equation which describes the relationship between secant and tangents.
Thus,
[tex] (4 + x)*4 = 6^2 [/tex]
[tex] 4*4 + x*4 = 36 [/tex]
[tex] 16 + 4x = 36 [/tex]
Subtract 16 from both sides
[tex] 4x = 36 - 16 [/tex]
[tex] 4x = 20 [/tex]
Divide both sides by 4
[tex] \frac{4x}{4} = \frac{20}{4} [/tex]
[tex] x = 5 [/tex]
16. Acme car rental agency charges a fee of $29 per day plus $0.15 per
mile. Travel Ease car rental agency charges $20 per day plus $0.25 per
mile. For a one-day trip, what mileage would make the two rates equal?
Answer:
90 miles
Step-by-step explanation:
0.15x + 29 = y ---- acme car agency
0.25 x + 20 = y ---- travel ease agency
0.15x + 29 = 0.25x + 20
9 = 0.1x
x = 90
Alex has a block of wood that is in the shape of a prism with the dimensions shown. He cuts a 10-cm square hole through the center of the prism. What is the volume of the remaining solid?
Answer:
1,120
Step-by-step explanation:
Find the volume of the larger figure. This can be represented using the formula for volume.
V = lwh
V = 5*18*18
V = 1620
Now, find the volume of the cut out piece of the wood. We will subtract this from the larger block.
V = lwh
V = 5*10*10
V = 500
Subtract, and you will have your answer.
1620 - 500 = 1,120
assume the initial velocity is 60 feet/second. what is the maximum horizontal distance possible and at what angle does this occur
Answer:
h = 112.5 feets
Step-by-step explanation:
The equation for horizontal distance "h" in feet of a projectile with initial velocity v₀ and initial angle theta is given by :
[tex]h=\dfrac{v_o^2}{16}\sin\theta\cos\theta[/tex]
We know that, [tex]2\sin\theta\cos\theta=\sin2\theta[/tex]
So,
[tex]h=\dfrac{v_o^2}{32}\sin2\theta[/tex]
Now we need to find the maximum horizontal distance possible and at what angle does this occur.
For maximum distance angle should be 45 degrees. Som,
[tex]h=\dfrac{60^2}{32}\sin2(45)\\\\h=112.5\ \text{feet}[/tex]
So, 112.5 feets is the maximum possible distance.
HELP ME!!!!And I mark as BRAINLIEST✨✨make sure show proper working
Answer:
54 km/h
Step-by-step explanation:
From H to G:
Let the distance be x km.
Average speed = distance/time
60 = x/ 3
60*3 = x
x = 180 km
From G to F:
Let the distance be y km.
Average speed = distance/time
45 = y/2
45*2 = y
y = 90 km
From H to F:
Total distance = x + y = 180 + 90 = 270 km
Total time = 3 + 2 = 5 hours
Average speed from H to F
= Total distance/ total time
= 270/ 5
= 54 km/h
PLZ HELP I KINDA NEED THIS PLZ
Select the correct answer. The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2?
A. W
B. X
C. Y
D. Z
Answer:
It's is C. Y
Step-by-step explanation:
There is the graph and you can see it by yourself :)
m-m-1/2=1-m-2/3 ( will mark brainiest)
Answer:
Step-by-step explanation:
m= 1/2
this is answer ..........
hope it helps
pls mark my answer as the brainliest
Answer:
M = 5/6
Step-by-step explanation:
m-m-1/2=1-m-2/3
You combine like terms, in this case, the m-m and 1-2/3.
-1/2 = -m + 1/3
Now you need to isolate the m so you subtract 1/3 from both sides.
-1/3 - 1/2 = -m
Combine like terms again.
-5/6 = -m
But m needs to be positive so you divide both sides by -1.
m = 5/6
This should be the answer!
how to solve 2x(x+3)=2x^2+15
Answer: x = 5/2 = 2.5
Step-by-step explanation:
Given expression
2x (x + 3) = 2x² + 15
Expand parentheses and apply the distributive property
2x · x + 2x · 3 = 2x² + 15
2x² + 6x = 2x² + 15
Subtract 2x² on both sides
2x² + 6x - 2x² = 2x² + 15 - 2x²
6x = 15
Divide 6 on both sides
6x / 6 = 15 / 6
x = 15/6
[tex]\boxed{x=\frac{5}{2} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Step-by-step explanation:
2x^2 + 6x = 2x^2 + 15
2x^2-2x^2+6x=15
6x = 15
x= 5/2 when simplified
Last question.... please help
Answer:
B {-10 , -6 , 10}
Step-by-step explanation:
D= {-1 , 0 , 4}
When x = -1 ;
y = 4x - 6
y = 4*(-1) -6
= -4 - 6
y = -10
When x = 0,
y = 4 *0 -6
y = -6
When x = 4,
y = 4*4 - 6
= 16 - 6
y = 10
Range = { -10, -6 , 10}
A group of 13 friends all want to ride a roller coaster. The coaster seats 15 in a single file row from front to back. How many ways can they arrange themselves?
Answer:
Step-by-step explanation:
Geometry, please answer question ASAP
Answer:
B.
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
1 : sqrt(3) : 2
From the 1 and 2, we see that the hypotenuse must be twice the length of the short leg.
From the 1 and sqrt(3) we see that the long leg is sqrt(3) times the length of the short leg.
Now we check for these two ratios in each choice.
A.
1 is twice 1/2. Check
sqrt(3)/2 is sqrt(3) times 2. Check
B.
10 is twice 5, not twice 5/2. This does not check.
C.
2sqrt(2) is twice sqrt(2). Check
sqrt(6) is 2sqrt(2) time sqrt(3). Check
D.
6 is twice 3. Check
3sqrt(3) is sqrt(3) times 3. Check
Answer: B.
Answer:
B
Step-by-step explanation:
Angle ratio = 30 : 60 : 90
Side ratio = x : x√3 : 2x
[tex]A) x = \frac{1}{2}\\\\ \ x\sqrt{3 } = \frac{1}{2}*\sqrt{3}=\frac{\sqrt{3}}{2} \\\\2x = 2*\frac{1}{2}=1[/tex]
True
[tex]C) x = \sqrt{2} \\\\x\sqrt{3}=\sqrt{2} *\sqrt{3} =\sqrt{2*3}=\sqrt{6}\\\\2x=2\sqrt{2} \\[/tex]
True
[tex]D) \ x = 3\\\\x\sqrt{3}=3\sqrt{3}\\\\2x = 2*3 = 6[/tex]
True
The supply station donated 115 notebooks to mrs.Michale to give to her class there are 28 students in her class mrs.Michale gives each student the same number of notebooks how many notebooks does she give each student
Answer:
4.107
Step-by-step explanation:
115/28=4.107
In the triangle shown below, find the value of a given that b
53V2
Answer:
a=53
Step-by-step explanation:
[tex] \sin(45) = \frac{a}{53 \sqrt{2} } \\ \frac{ \sqrt{2} }{2} = \frac{a}{53 \sqrt{2} } \\ a = 53[/tex]
I hope I helped you^_^
Answer:
a = 53
Step-by-step explanation:
This is a 45- 45- 90 triangle with sides in the ratio x : x : x[tex]\sqrt{2}[/tex]
x are the legs and x[tex]\sqrt{2}[/tex] the hypotenuse
Here x[tex]\sqrt{2}[/tex] = 53[tex]\sqrt{2}[/tex] , then x = 53
That is the leg a = 53
La madre de rosita se ha comprado una mascarilla por un valor de 1 25 dolares al mismo tiempo se ha comprado un paquete de jabones de 2 00 dolares y luego compra un gel de alcohol en 3 00 dolares después de pagar le queda 7 65 dolares que debemos saber que tengo que hacer para obtener el resultaron
Answer:
La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos es de $13.90
Step-by-step explanation:
La información dada son;
El valor de la máscara = $ 1.25
El valor del paquete de jabones = $ 2.00
El valor del gel de alcohol = $ 3.00
La cantidad que le quedaba después de pagar = $ 7.65
Por lo tanto, tenemos;
La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = La cantidad que le quedaba después de pagar + El valor del gel de alcohol + El valor del paquete de jabones + El valor de la mascarilla
Por lo tanto;
La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = $ 7.65 + $ 3.00 + $ 2.00 + $ 1.25 = $ 13.90.
Josh has an aquarium 30 inches deep it takes him 5 minutes to fill the bucket with 3 inches of water he estimates that it will take him under an hour to fill the entire bucket with water if you correct explain why or why not
I assume your question should be rephrased as "Josh has a bucket 30 inches deep..."
Josh is correct in estimating that it will take him under an hour to fill the entire bucket with water.
Given:
The bucket is 30 inches deepIt takes Josh 5 minutes to fill the bucket with 3 inches of waterTo find: If Josh is correct in estimating that it will take him under an hour to fill the entire bucket with water
It is given that, to fill the bucket with 3 inches of water, it takes Josh 5 minutes.
Using Unitary method, we can say that, to fill the bucket with 1 inch of water, it takes Josh [tex]\frac{5}{3}[/tex] minutes.
Then, to fill the bucket with 30 inches of water, it takes Josh [tex]\frac{5}{3} \times 30[/tex] minutes.
Solving, we can say that it takes Josh 50 minutes to fill the bucket with 30 inches of water.
Since the bucket is 30 inches deep, we can say that it takes Josh, 50 minutes to fill the entire bucket, which is just under an hour.
So, Josh is correct in assuming that it will take him under an hour to fill the entire bucket with water.
Learn more about Unitary method here:
https://brainly.com/question/12470900
The image below shows two dilated figures with lines IJ and JK drawn. If the smaller figure was dilated by a scale factor of 2, what relationship do lines IJ and KL have?
Answer:
IJ = 2*KL
Step-by-step explanation:
Given that the smaller figure was dilated to create the bigger figure with a scale factor of 2, it therefore means, the dimensions of the smaller figure was increased by times 2 of its dimensions to create the bigger figure.
Thus, the relationship that would exist between line IJ and KL, is that IJ is twice the size of KL.
The relationship is: IJ = 2*KL
X=3816371/(27×63) solve for x
Answer:
X = 14,700
Step-by-step explanation:
you can use a calculator to get the x.
X=3816371/(27×63)
Roselyn is driving to visit her family, which live 150 150150 kilometers away. Her average speed is 60 6060 kilometers per hour. The car's tank has 20 2020 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 66 kilometers per liter. Fuel costs 0.60 0.600, point, 60 dollars per liter. How long can Roselyn drive before she runs out of fuel?
Answer:
She can go 120 km before she runs out of fuel
It will take 2 hours.
Step-by-step explanation:
150 km is the distance
60 km/ h is the speed
The gas tank is 20 liters
We can go 6 km per liter
Fuel costs .60 dollars per liter
We need to determine how far she can go on a tank of gas
20 liters * 6 km / liter = 120 km
She can go 120 km before she runs out of fuel
120 km = 60 km/ h * x hours
Divide each side by 60
120/60 = x
2 hours
Answer:
Hopes this helps!
Step-by-step explanation:
simplfy the given equation using the distributive property 5x + 2(x - 3) = -2(x - 1)
Answer:
x = [tex]\frac{8}{9}[/tex]
Step-by-step explanation:
5x + 2 (x - 3) = -2 (x - 1)
5x + 2x - 6 = -2x +2
5x + 2x + 2x = 2 + 6
9x = 8
x = [tex]\frac{8}{9}[/tex]
Answer:
The value of x in the given equation is 0.89
Step-by-step explanation:
5x + 2(x - 3) = -2(x - 1)
Distribute 2 to (x - 3)
5x + 2x - 6 = -2(x - 1)
Distribute 2 to (x - 1)
5x + 2x - 6 = -2x + 2
Combine 5x and 2x on the left side of the equation.
7x - 6 = -2x + 2
Add 6 on both side of the equation.
7x = -2x + 8
Add 2x on both sides of the equation.
9x = 8
Now divide 9 from 8. Make sure you round the decimal because the quotient of these numbers is a repeating decimal.
x = 0.89
So, the value of x is 0.89
Graph y = tanx for -pi/4 ≤ x ≤ pi/4. What is the range?
Answer:
( -1, 1 )
Step-by-step explanation:
For f ( x ) = tan x ; Range = R (real no.)
Range in interval = ( -1, 1 )
Answer:
Step-by-step explanation:
The graph is below(picture)
● tan Pi/4 = 1
● tan -Pi/4 = -1
So the range is [-1;1]
9. a) A computer can finish to download an application file in 4 minutes of 600 MB per minute, 6.1 P
(1) Find the size of the application file. 1. L
(ii) How long does it take to download the file when the download rate increase
to 800 MB per minutes?
Answer:
1) 2400MB
2) 3 minutes
Step-by-step explanation:
1) 600 MB/Min * 4 Min = 2400MB
2) at 800 MB/Min a 2400MB file will require 2400MB/800MB/Min
2400/800 = 3Min
A ball is thrown vertically upward from the ground with an initial velocity of 111 ft/sec. Use the quadratic function h(t) = −16t2 + 111t + 0 to find how long it will take for the ball to reach its maximum height (in seconds), and then find the maximum height (in feet). (Round your answers to the nearest tenth.)
Answer:
t=3.5 seconds
Step-by-step explanation:
Given
h(t) = −16t^2 + 111t + 0
h'(t)= -32t + 111
Maximum height occurs when h(t) = 0 and the ball begins to fall
h(t)= -32t + 111=0
-32t + 111=0
-32t=-111
Divide both sides by -32
t=3.46872
Approximately, t=3.5 seconds
Recall,
Maximum height occurs when h(t) = 0
h(t)= -32t + 111=0
= -32(3.46872)+111
= -110.99904+111
= 0.00096 ft
MATH QUESTION: When 8668/25 + 4141/9 - 5533/25 is computed and written as a mixed number in simplest form, what is the fractional part of that mixed number?
Answer:
23/45
Step-by-step explanation:
8668/25 + 4141/9 - 5533/25
= 26348/45
= 585(23/45)
=23/45
PLEASE HELP! I'M TIMED
Which phrase represents this expression?
(62−42)×3
3 times the difference of 62 and 42
3 times the difference of 42 and 62
the difference of 62 and the product of 3 times 42
the difference of the product of 3 times 42 and 62
Solving expression
[tex]\\ \rm\Rrightarrow (62-42)3[/tex]
[tex]\\ \rm\Rrightarrow 3(20)[/tex]
[tex]\\ \rm\Rrightarrow 60[/tex]
Answer:
3 times the difference of 62 and 42
Step-by-step explanation:
(62−42)×3
The difference of 62 and 42 times 3
plz help me Identify the domain and range of relation ({3,-2),(8,1),(-9,2),(1,8)}
Answer:
domain { -9,1,3,8)
range{ -2,1,2,8}
Step-by-step explanation:
The domain is the inputs
Domain = 3,8,-9,1
We write them in the order from smallest to largest
domain { -9,1,3,8)
The range is the outputs
Range = -2,1,2,8
We write them in the order from smallest to largest
range{ -2,1,2,8}
Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
When and , the value of the expression is
Answer:
-2, 6
Step-by-step explanation:
(x - 6)(x + 2) = 0
x - 6 = 0 x+ 2 = 0
x = 6 x = -2
The values of x that would result in the given expression being equal to 0, in order from least to greatest, are -2 and 6.
Which of the following points lie in the solution set to the following system of inequalities? y < −3x + 3 y < x + 2 (1, −5) (1, 5) (5, 1) (−1, 5)
Answer: (1, −5)
Step-by-step explanation:
Plot the given inequalities on coordinate plane.
For y < −3x + 3, plot y =−3x + 3
At x=0, y= 3
At y =0, 0=-3x+3
⇒ x= 1
so, plot points (0,3) and (1,0) and join to get y =−3x + 3, since inequality has '<' sign, so shade( in red) below line area and line should be dotted.
For y < x + 2, plot y = x + 2
At x=0, y= 2
At y =0, x=-2
so, plot points (0,2) and (-2,0) and join to get y = x + 2, since inequality has '<' sign, so shade( in orange) below line area and line should be dotted.
Now, plot all given points (1, −5) (1, 5) (5, 1) (−1, 5), we can clearly observe that (1, −5) lies in the solution set. (in common shaded region)
Answer:
The correct answer is 1, -5
Step-by-step explanation:
4x+5 ≤ 2x-3 is equivalent to
Answer:
x ≥ -4
Step-by-step explanation:
4x+5 ≤ 2x-3
Collect like terms
4x-2x ≤ -3-5
Simplify
2x ≤ -8
Divide both sides by 2
2x / 2 ≤ -8 / 2
x ≥ -4
Which of the following numbers is between 0.08 and 0.4?
(A) 0.019
(B) 0.009
(C) 0.109
(D) 0.91
(E) 0.409
Answer:
C
Step-by-step explanation:
the numbers between 0.08 and 0.4 are:
0.09, 0.10, 0.11, 0.12, 0.13, 0.14, 0.15, .16, 0.17, 0.18, 0.19, 0.20, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39
I bolded the number closest to your answer choices, hope this helps!
Zula has a conical bird feeder with a volume of 64.3 cubic centimeters and a height of 7 centimeters. Which equation can be used to find the area of the circular lid needed to cover the bird feeder?
Answer: [tex]64.3=\frac{1}{3}(B)(7)[/tex]
Step-by-step explanation:
[tex]V=\frac{1}{3} Bh[/tex]
B is the area of the base
h is the height of the cone
[tex]V=64.3 cm^3[/tex]
[tex]h=7cm[/tex]
[tex]64.3=\frac{1}{3}(B)(7)[/tex]
[tex]192.9=(B)(7)[/tex]
[tex]B=192.9/(7)[/tex]
[tex]=27.56cm^2[/tex]