We are given with a function y =2/(2x) . So , if we cancel the 2 from both numerator and denominator we are left with y = 1/x . Now , here we need to find the domain , bur let's Recall that Domain is the set of all values for which the given function is defined .Now , here , if we put x = 0 , then y will be not defined , but as for domain we need only the set of values for which the function is defined , so domain willn't include 0 , and for all real numbers except 0 , the given function is defined . So Our domain is [tex]{\boxed{\bf{(-\infty,0)\cup (0,\infty)}}}[/tex] and as this interval contains all real numbers except 0 , so domain can be further written as [tex]{\boxed{\mathbb{R}-\bf \{0\}}}[/tex] . Now , Range is the set of all output values of the function when we put the values of domain as input . So , now here when we put values of domain as input like let's put x = -1 , -2 , -3 , -4 , 1 , 2 , 3 ,..... we will get y = -1 , -1/2 , -1/3 , -1/4 , 1 , 1/2 , 1/3 and so on , now , the input will give output as 0 , iff input is Infinite , but as input can never be infinite, so output will never comes to 0 as the intervals of real numbers is [tex]{\bf{(-\infty,\infty)}}[/tex] it's an open interval so Infinity and -ve infinity is not concluded in the above interval because whenever we think a number as large as much we can think , their exists infinitely large numbers greater than it , assume you're thinking 10¹⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰ as the largest number you can think , but if we add 1 in that i.e 10¹⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰ + 1 comes to be greater than it , Hence , we don't include Infinity and -ve Infinity in the interval which represents the set of all real numbers. So now the range is same as the Domain i.e [tex]{\boxed{\bf{(-\infty,0)\cup (0,\infty)}}}[/tex] or [tex]{\boxed{\mathbb{R}-\bf \{0\}}}[/tex]
Hence , we concluded that :
[tex]{\bf Domain=\mathbb{R}-\bf \{0\}}[/tex][tex]{\bf Range=\mathbb{R}-\bf \{0\}}[/tex] Range = Domainplsssss
Variables y and x have a proportional relationship, where y = 9 when x = 3. What is the value of x when y = 36? Enter your answer in the box. x =
» Variables y and x have a proportional relationship, where y = 9 when x = 3. What is the value of x when y = 36? Enter your answer in the box.
Answer:[tex] \underline{ \boxed{ \orange{\bold{ 12}}}}[/tex]— — — — — — — — — —
Steps-by-step explanation:Since variables y and x have a proportional relationship, then the equation is in the form y=kx.
Given: y = 9 when x = 3.First, we need to find the constant of variation (k) by substituting the given to the equation of variation.
[tex] \tt y = kx \\ \tt \: \: \: \: 9 = k(3) \\ \tt k= \frac{9}{3} \\ \tt k= \blue{3}[/tex]The constant of variation (k) is 3. So, find the value of x when y = 36.
[tex] \: \: \: \: \tt y = 3x \\ \tt \: 36 = 3x\\ \tt \: \: \: \: \: x = \frac{36}{3} \\ \tt \: \: \: \: \: \: \: x= \underline{ \boxed{ \purple{ \tt{12}}}}[/tex]Hence the unknown value (x) is 12.
Tomas needs exactly 6 potatoes to make 12 potato pancakes.
Which of the following statements are true?
The answers are A, B, and D.
The given information is that Tomas needs 6 potatoes to make 12 potato pancakes. Thus, we can assume it takes 1 potato to make 2 potato pancakes.
An answer choice must have two times more pancakes than potatoes. Only A, B, and D satisfy this. The others can be confusing if the multiplication is not executed properly.
(The picture didn't come up but I think this is the answer)
What is the GCF of 15 and 48?
Hello.
First, let's clarify what the G.C.F. means.
It means "Greatest Common Factor"
So, let's find the Greatest Common Factor of 15 and 48.
First, let's list all the factors of 15:
1, 3, 5, 15
Here are the factors of 48:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Therefore, the GCF of 15 and 48 is 3.
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
A car travels 80 miles on 4 gallons of gas. At this rate, how many gallons will it need to travel 460 miles?
3 cups of water are needed to fillup the bottle completely. 10 cups of water are needed to fill up the bucket completely. Each cup has a capacity of 305 ml. What is the capacity of the bucket? Write your answer in litres and mililitres
Answer:
The bucket has a capacity of 3.05 Liters
Step-by-step explanation:
305ml × 10 = 3,050ml
3,050ml = 3.05L
Past due, need some help.
Answer:
1. pt. A) 96:38
pt. B) Because they are the same values, just flipped
2. pt. A) 38:46
pt. B) 19:23
Step-by-step explanation:
hope this helped
Orlando, Florida is approximately 61 square
miles less than the size of Tampa, Florida. If
Orlando is 114
square miles, find the size of
Tampa.
Answer:
sanaol alam ang sagot
Step-by-step explanation:
salamat sa points
solve for m
2= m/2 -7
thanks in advance
Plot six lines. Each line should pass through the origin and one of the six points. One is done for you.
Note that:
Given points: (0, -2) and (1, -4)Slope formula: Rise/RunPoint slope form formula: y - y₁ = m(x - x₁)To create the equation of the line, find the slope. Then, use point slope form to find the equation of the line.
Use the slope formula to find the slope.
Rise/Run = Slope=> Rise = -2; Run = 1=> Rise/Run = -2/1 = -2Use the point slope form formula.
y - y₁ = m(x - x₁) = Equation of line.=> y - (-4) = -2(x - 1) = Equation of line.=> y + 4 = -2x + 2=> y = -2x + 2 - 4=> y = -2x - 2Solution (Line 3): (Refer to graph 2)Note that:
Given points: (0, -2) and (-4, 3)Slope formula: Rise/RunPoint slope form formula: y - y₁ = m(x - x₁)To create the equation of the line, find the slope. Then, use point slope form to find the equation of the line.
Use the slope formula to find the slope.
Rise/Run = Slope=> Rise = -5; Run = 4=> Rise/Run = -5/4Use the point slope form formula.
y - y₁ = m(x - x₁) = Equation of line.=> y - 3 = -5/4{x - (-4)} = Equation of line.=> y - 3 = -5/4{x + 4}=> y - 3 = -5x/4 - 5=> y = -5x/4 - 2Solution (Line 4): (Refer to graph 3)Note that:
Given points: (0, -2) and (-3, -5)Slope formula: Rise/RunPoint slope form formula: y - y₁ = m(x - x₁)To create the equation of the line, find the slope. Then, use point slope form to find the equation of the line.
Use the slope formula to find the slope.
Rise/Run = Slope=> Rise = 3; Run = 3=> Rise/Run = 3/3 = 1Use the point slope form formula.
y - y₁ = m(x - x₁) = Equation of line.=> y - (-5) = 1{x - (-3)} = Equation of line.=> y - (-5) = 1{x + 3} => y + 5 = x + 3=> y = x - 2Hoped this helped!
What is the equation of the line that passes through the point (6,-7) and has a slope of -2
Answer:
y = -2x + 5
Step-by-step explanation:
to figure this out you may plug this equation into y = mx + b with b being the unknown
this goes to
-7 = -2(6) + b
then multiply 6 to -2
-7 = -12 + b
then add 12 to both sides
5 = b
b is 5 so that means the equation is
y = -2x + 5
A room has an area of 437 square feet. One dimension is 4 feet more than the other. Find the dimensions of the room
Answer:
1,748Step-by-step explanation:
Measure all three aspects--the length, width and height--of an object to get a three-dimensional measurement.
D = 437FT × 4 FEET
multiply the values in order to get the dimension
=> 1,748Factorise fully 5a² - 125b²
Answer:
5(a+5b)*(a-5b)
Step-by-step explanation:
Answer:
5 (a+5b)( a−5b)
Step-by-step explanation:
im stuck on this problem. can someone please help me.
The graph looks like an absolute function.
If we were to compare the function [tex]y= |x|[/tex] to this graph (see image attached), we see that the function in the graph has only shifted two to the right.
To write in function form, when shifting the graph horizontally
add within the function --> move the graph to the leftsubtract from within function --> move the graph to the rightIn this case, since we want to shift over two spots horizontally, we get the function is
y = |x -2|
Now we want to find the function that is increasing and decreasing over the same interval.
The only function that looks the most similar is y = 4|x-2|.
The reason for that is because the y = 4|x-2| is just a stretched version of y= |x-2| meaning the point where it is increasing or decreasing should stay the same. Look at the second image I attached.
Hope it helps!
The mean can be found when you add all the numbers in a set, and then divide that sum by the amount of numbers given. Find the average tree growth of four Douglas Fir trees: 2.2 in., 1 1/5 in., and 1 1/2 in.
Answer:
49/30
Step-by-step explanation:
To find the mean, add up 2.2 + 1 1/5 + 1 1/2 to get 49/10
Then divide that by 3 (it says four Douglas trees but you only put 3 types)
49/10 divided by 3 is 49/10 times 1/3, which is 49/30
Help me with number 2 please
Answer:
One solution
(2,0) is the point
Step-by-step explanation:
If the graphs of the equations intersect, then there is one solution that is true for both equations.
When the lines intersect, the point of intersection is the only point that the two graphs have in common, so the coordinates of that point are the solution for the two variables used in the equations.
The point of intersection is (2,0), because that is the point that both lines intersect at.
A shark can swim 30 mph how far can he travel per minute
Answer:
1/2 mile
Step-by-step explanation:
30miles / 60 minutes = (30/60) miles / 1 minute = (1/2) mile / 1 minute
five times a number, n, subtracted from 100
Answer:
100 - 5n
Step-by-step explanation:
100 - 5n
Hope this helps!
A rectangular prism has
the surface area of
460 m2. The length is 5
cm and the height is 12
cm. What is the width of
the rectangular prism?
Based on the calculations, the width of the rectangular prism is equal to 1,352.91 meters.
Given the following data:
Surface area of rectangular prism = 460 [tex]m^2[/tex]Length of rectangular prism = 5 cm to m = 0.05 m.Height of rectangular prism = 12cm to m = 0.12 m.The surface area of a rectangular prism.Mathematically, the surface area of a rectangular prism is given by this formula:
[tex]A =2(wl+hl+hw)[/tex]
Where:
A is the surface area.
l is the length.w is the width.h is the height.Substituting the given parameters into the formula, we have;
[tex]460 =2(w0.05+0.12(0.05)+0.12w)\\\\460=2(0.17w+0.006)\\\\460=0.34w+0.012\\\\0.34w=460-0.012\\\\0.34w=459.988\\\\w=\frac{459.988}{0.34}[/tex]
w = 1,352.91 meters.
Read more on rectangular prism here: brainly.com/question/3867601
Which One Doesn't Belong? Identify the equation that does
not belong with the other three. Explain your reasoning.
x + 4 = -2
x+5= -1
x+2=8
3- x=9
Answer:
x + 2 = 8
Step-by-step explanation:
When you solve the other problems you get x=-6 for all of them except c. You need to take the number and subtract ( or if its negative add) it to the other side to get your answer for each one. Once this is done the solution to x is found
find the value of x
Answer:
30°
Step-by-step explanation:
AB || DC (Given)
-> AB || DF
-> x = 30° (alternate angles)
27) Jim and his uncle went to the circus. Together they spent $30, 4/15 of that for a bus ride, 2/5 for food, 7/30 for tickets, and the rest on souvenirs. What part of their money did they spend on souvenirs?
Answer:
3 dollars
Step-by-step explanation:
4/15 of 30 = $8
2/5 of 30 = $12
7/30 of 30 = $7
8 + 7 + 12 = $27
30 - 27 = $3
They only had 3 dollars left after spending everything else they had.
Answer:
3/30
Step-by-step explanation:
4/15 so times 15 by 2 and 4 by 2 to get 8/30
leave 7/30 alone
2/5 five times 6 is 30, since you multiplied 5 by 6 you have to do 2 x 6 which is 12, 12/30
now you can add bc a common denominator 12 + 7 + 8 = 27
30 - 27 = 3, so 3/30ths was spent on souvenirs.
Solve for x and y.
Will give Brainliest
Answer: x=sqrt21, y=sqrt70
Step-by-step explanation:
Use the figure shown.
1. Name a pair of adjacent angles.
2. Name a pair of complementary angles.
3.Name a pair of supplementary angles.
4. Name a pair of vertical angles.
Answer:
Step-by-step explanation:
Ruchi measured the area of her kitchen as 2. 81 times 10 Superscript 4 square units. When she recorded the area, she wrote 2. 81 times 10 Superscript 4 square feet. Which statement about her labeling of the units is true? She is correct because dimensions of rooms must always be measured in feet and area would be square feet. She is correct because 2. 81 times 10 Superscript 4 ftSquared is equivalent to 2, 810 ftSquared, which is an average size for a kitchen since area is always so much more than length. She is incorrect because 2. 81 times 10 Superscript 4 is around 30,000 so the units must be smaller than feet. She most likely measured in inches. She is incorrect because 2. 81 is a small number. She probably measured in yards to arrive at such a small value.
Ruchi is incorrect because 2.81×10⁴ is around 30,000. so the units must be smaller than feet.
What is Units conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
As it is given that the measurement that Ruchi wrote is 2.81×10⁴ ft². And, the area of 2.81×10⁴ ft² is 28,100 ft² which is nearly 30,000 ft², while the size of an average house is 2,300 ft². Therefore, the area that is written by Ruchi is too big compared to an average kitchen.
Hence, Ruchi is incorrect because 2.81×10⁴ is around 30,000 so the units must be smaller than feet.
Learn more about Units conversion:
https://brainly.com/question/4736731
Find the value of x to the nearest tenth.
Answer:
x = 57.8°
explanation:
opposite length : 11hypotenuse length : 13[tex]\sf sin(x)= \dfrac{opposite}{hypotensue}[/tex]
[tex]\hookrightarrow \sf sin(x) = \dfrac{11}{13}[/tex]
[tex]\hookrightarrow \sf x = sin^{-1}(\dfrac{11}{13} )[/tex]
[tex]\hookrightarrow \sf x = 57.8[/tex]
Answer:
57.8° (nearest tenth)
Step-by-step explanation:
Use the sine trig ratio:
[tex]\mathsf{\sin(\theta)=\dfrac{O}{H}}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuseGiven:
[tex]\mathsf{\theta=x}[/tex]O = 11H = 13[tex]\implies \mathsf{\sin(x)=\dfrac{11}{13}}[/tex]
[tex]\implies \mathsf{x=\arcsin\dfrac{11}{13}}[/tex]
[tex]\implies \mathsf{x=57.8 \textdegree \ (nearest \ tenth)}[/tex]
Is X=4 a solution to the equation 7 + X = 15
YES OR NO
Answer:
[tex]7 + x = 15 \\ x = 15 - 7 \\ x = 8[/tex]
So; No
The times it took for 35 loggerhead sea turtle eggs to hatch in a simple random sample are normally distributed, with a mean of 50 days and a standard deviation of 2 days. assuming a 95% confidence level (95% confidence level = z-score of 1.96), what is the margin of error for the population mean? remember, the margin of error, me, can be determined using the formula m e = startfraction z times s over startroot n endroot endfraction. 0.06 0.11 0.34 0.66
The margin of error for the 95% confidence level is 0.66. Then the correct option is D.
What is the margin of error?The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.
The times it took for 35 loggerhead sea turtle eggs to hatch in a simple random sample are normally distributed, with a mean of 50 days and a standard deviation of 2 days. assuming a 95% confidence level (95% confidence level = z-score of 1.96)
The margin of error is given by
[tex]\rm Margin \ of \ error = z \times \dfrac{\sigma}{\sqrt{n}}\\\\Margin \ of \ error = 1.96 \times \dfrac{2}{\sqrt{35}}\\\\Margin \ of \ error = 0.6626 \approx 0.66[/tex]
The margin of error for the 95% confidence level is 0.66. Then the correct option is D.
More about the margin of error link is given below.
https://brainly.com/question/6979326
Answer:
D
Step-by-step explanation:
on edge
Find an equation for the parabola with focus (-4, 0) and directrix x=4.
HELP!
Answer:
[tex]y = - \frac{ {x}^{2} }{16} [/tex]
Step-by-step explanation:
First, notice the diretcrtirx is a negative horinzontal lie so this means we have a parabola facing downwards
Equation of a Parabola with center (h,k) >
[tex](x - h) {}^{2} = - 4p(y - k)[/tex]
Where p is the distance of the vertex to focus/ or distance to vertex to directrix
This emans that the vertex is halfway of (-4,0) and x=4.
Since this is a upwards parabola, the y value that lies on focal axis doesn't change so know this means that
The vertex is halfway between (-4,0) and (4,0).
So the vertex is (0,0).
Plugging that in we get,
[tex] {x}^{2} = - 4py[/tex]
The distance to the vertex or either the focus or directrix is 4 so p=4
[tex] {x}^{2} = - 4(4)y[/tex]
[tex] {x}^{2} = - 16y[/tex]
[tex]y = - \frac{ {x}^{2} }{16} [/tex]
Which expression is equivalent to 5y–3? startfraction 1 over 125 y cubed endfraction startfraction 1 over 5 y cubed endfraction startfraction 5 over y cubed endfraction startfraction 125 over y cubed endfraction
The expression that is equivalent to 5y⁻³ is start fraction 5 over y cubed end fraction.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
In order to find the expression that is equivalent to 5y⁻³, we need to use exponential properties,
[tex]5y^{-3}\\\\=\dfrac{5}{y^3}[/tex]
Hence, the expression that is equivalent to 5y⁻³ is start fraction 5 over y cubed end fraction.
Learn more about Expression:
https://brainly.com/question/13947055
Answer:
option C 5/y^3
Step-by-step explanation:
Carmen deposited $6,000 into a savings account that earns 2.8% interest compounded annually. How much will she have in her account (total) at the end of 3 years?
To help Carmen find the total after 3 years
We'll have to use the annual compound interest formula: A = P(1 + r)ⁿ
A = Final balance (?)
P = Principal balance (6000)
r = Rate (0.028)
n = years (3)
A = 6000(1 + 0.028)³
A = 6000(1.028)³
A = 6000(1.086373952)
A = 6518.243712
Round that to the nearest cent, and we get $6,518.24 as the answer.