What are the solutions of the equation 2x2=2 use a graph of the related function
Answers
2x² = 2
x² = 1
x = √1
x = 1
The solution is both -1 and 1 and the graph is shown below
Answer:
[tex]x=-1\text{ or }x=1[/tex]
Step-by-step explanation:
We have been given an equation [tex]2x^2=2[/tex]. We are asked to find the solutions of our given equation.
First of all, let us divide both sides of our equation by 2.
[tex]\frac{2x^2}{2}=\frac{2}{2}[/tex]
[tex]x^2=1[/tex]
Upon taking square root of both sides of our equation we will get,
[tex]x=\sqrt{1}[/tex]
[tex]x=\pm 1[/tex]
[tex]x=-1\text{ or }x=1[/tex]
Therefore, [tex]x=-1\text{ or }x=1[/tex] are two solutions for our given function.
Related Questions
In the state of pennsylvania, each automobile license plate number consists of three letters followed by a four-digit num ber. how many distinct license plate numbers can be fonned
Answers
26 letters each place, 10 numbers each place
26 x 26 x 26 x 10 x 10 x 10 x 10 = 175,760,000 different plates can be made
what is the remainder when 599 / 9
Answers
see attached picture
answer is 66 with remainder of 5
Answer: The remainder is 5
Step-by-step explanation:
599 /9
59 / 9 = 6
6 ×9 = 54
that means remainder 5
Join the 5 beside the last 9, making it 59 again
repeat the first process again, i.e 59/9 = 6
6×9 = 54
Remaining 5
Therefore 9 can go into 599, 66times with a remainder of 5
the raptors have lost 5 out of their last 11 games.They have not had any ties or forfeits. What is The ratio of wins to losses for the raptors?
Answers
Answer: 6:5
Step-by-step explanation:
Given: The total number of games played by raptors = 11
The number of games lost by them = 5
Then, the number of wins = 11-5=6
We know that the ratio of A to B is given by :-
[tex]A:B[/tex]
Similarly, the ratio of wins to losses for the raptors is given by :-
[tex]\text{Number of wins: Number of losses}\\\\=6:5[/tex]
Hence, the ratio of wins to losses for the raptors = 6:5
Answer:
B
Step-by-step explanation:
How would you describe the difference between the graphs of f(x)=2/3 x^3 and g(x)=2/3(-x)^3
Answers
When graphed, g(x) is a copy of f(x) reflected over the y axis.
A plane left Atlanta at 11:30 a.m. and flew to an airport near Boston. The plane was due at Boston at 3:15 p.m. The plane arrived 25 minutes late. The time of the trip was?
Answers
Answer: 4 HOURS AND 10 MINUTES
Step-by-step explanation:
1 HOUR IS 60 MINUTES.
60X4=240 MINUTES
240 MINUTES+10 MINUTES=250 MINUTES
250 MINUTES=4 HOURS AND 10 MINUTES.
The time elapsed during the trip is 4 hours 10 minutes.
Given that,
The plane left Atlanta at 11:30 a.m. and flew to an airport near Boston.
The plane was due at Boston at 3:15 p.m.
In mathematics, it deals with numbers of operations according to the statements.
Since A plane takes off from Atlanta at 11:30 a.m. and landed at Boston airport at 25 minutes later than the actual time of arrival.
The time of arrival was 3:15 PM but because of the delay, at 3:40 the plane landed at Boston airport. For 3:40 pm we have 15:40 on a 24-hour clock. So,
The time elapsed = 15:40 - 11:30
= 4 : 10
Implies 4 hours 10 minutes
Thus, the time elapsed during the trip is 4 hours 10 minutes.
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Select all that apply. Which of the following represent the same ratio?
A. 2 to 3
B. 2:5
C.3 to 2
D.2/3
Answers
A and D.
A. 2 to 3 can be translated to 2/3, which is obviously the same as D. 2/3.
Write the equation of the line with a slope of 4 that contains the point (5, 8).
Select one:
a. y=4x−27
b. y=4x−12
c. y=4x+28
d. y=4x+8
Answers
slope(m) = 4
(5,8)...x = 5 and y = 8
sub and find b, ur y int
8 = 4(5) + b
8 = 20 + b
8 - 20 = b
-12 = b
equation is : y = 4x - 12
A business is using two painters to paint 3 offices, each with 1,200 square feet of wall space. one painter can paint 190 square feet per hour. the other painter can paint 130 square feet per hour. how long will it take the two painters working together to paint the 3 offices?
Answers
let A = total area of the wall space
t = total time they both need
Painter 1 = 190 square feet per hour
Painter 2 = 130 square feet per hour
total area = 1200 ft^2 (3) = 3600 ft^2
The function would be:
A = 190t + 130t
3600 = 190t + 130t
3600 = 320t
t = 11.25 hrs
Evaluate the expression and enter your answer in the box below. 8 + |10|
Answers
Answer: 18
Hope this helped :)
Please give brainliest
8 + 10 =
18
in 2006, the population of a certain country per square mile of land was 81. In 2014, the persons per square mile was 85.24. assume the relationship between years, x, and persons per square mile,y, is a linear relationship
Answers
The population density in the country increased at a rate of about 0.53 persons per square mile each year between 2006 and 2014, demonstrating a linear relationship.
Explanation:You are looking at a linear relationship between years and population density in a particular country. Years are represented by 'x' and persons per square mile are represented by 'y'. To find the relationship, we need to identify the slope of the line, which represents the rate of change in population density per year.
To find the slope, we subtract the y-values and divide by the change in x-values: (85.24 - 81) / (2014 - 2006) = 0.53 persons per square mile per year.
This tells us that, on average, the population density in this country increased by about 0.53 persons per square mile each year between 2006 and 2014.
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The population density of the country increased at a linear rate of around 0.53 persons per square mile each year between 2006 and 2014.
Explanation:In this problem, we are dealing with a linear relationship between years(x) and persons per square mile(y). Here, we need to find the slope of the line to understand the rate at which the population density is increasing per year. The slope of a line in a linear relationship is given by the formula slope = (y2 - y1) / (x2 - x1). Here, (x1, y1) refers to the year and population density in 2006 which are (2006, 81) respectively, and (x2, y2) refer to the year and population density in 2014 which are (2014, 85.24) respectively.
Substitute these values into the formula:
Slope = (85.24 - 81) / (2014 - 2006)= 0.53 (approx).
So, the population density increase was about 0.53 persons per square mile per year between 2006 and 2014.
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If 5 executives attend a meeting and all shake hands before and after the meeting, how many handshakes occur?
Answers
Mind helping a brother here! 20 points! Thanks!
Answers
(b) Im not sure about this one but if your chance of winning a gift card is less than 1% then I doubt that both brothers would win.
Which of the following is not equivalent to the formula d = rt?
[tex] \frac{d}{r}= t[/tex]
r = dt
[tex] \frac{d}{t} = r[/tex]
[tex]\frac{d}{rt} = 1[/tex]
Answers
Answer:
Option B, r=dt is not equivalent
Step-by-step explanation:
We have given that : The formula d=rt
To find which is not equivalent in the following
so,
1) [tex]\frac{d}{r}=t[/tex] is equivalent
2) [tex]r=dt[/tex] is not equivalent because, [tex]r=\frac{d}{t}[/tex]
3) [tex]\frac{d}{t}=r[/tex] is equivalent
4) [tex]\frac{d}{rt}=1[/tex] is equivalent
therefore option B is not equivalent.
A number is no more than five. How would you graph this inequality?
A. Draw an open circle on 5 and shade to the left.
B. Draw a closed circle on 5 and shade to the left.
C. Draw an open circle on 5 and shade to the right.
D. Draw a closed circle on 5 and shade to the right.
Answers
Answer:
the answer is B
Step-by-step explanation:
My teacher said it was
Aimee is flying a plane for the first time! The air traffic controller tells her to fly at 500 m above the ground or higher. Write an inequality that is true only for elevations (h) at which Aimee should fly.
Answers
To represent the elevations at which Aimee should fly her plane, the inequality h ≥ 500 is used, where h represents Aimee's elevation in meters. This indicates that Aimee must fly at an elevation of 500 meters or higher, as per the air traffic controller's instructions.
Explanation:The question asks for an inequality that represents elevations at which Aimee should fly her plane, according to the instructions given by the air traffic controller. Aimee is told to fly at 500 meters above the ground or higher. To write this inequality, we let h represent the elevation (in meters) at which Aimee should fly. Therefore, the inequality that only allows for elevations 500 meters or higher is: h ≥ 500.
This inequality means that Aimee's elevation, h, should be greater than or equal to 500 meters. This is a simple linear inequality in one variable, which is a fundamental concept in algebra. Understanding how to represent real-world scenarios with inequalities is crucial in solving problems related to constraints and conditions that have a range of possible values.
What number multiplies to -160 and adds to 27?
Answers
The numbers are 32 and -5.
Proof:
32-5=27
32*-5=-160
Petrolyn motor oil is a combination of natural oil and synthetic oil. it contains 5 liters of natural oil for every 6 liters of synthetic oil. if 498 liters of synthetic oil are used, how many liters of petrol oil will be made
Answers
5 L natural oil/ 6 L synthetic oil = x L natural oil/498 L synthetic oil
x = 415 L natural oil
So, if petrol oil contains 498 L synthetic oil, it has a corresponding amount of 415 natural oil. Adding these two would be the total volume of the petrol oil. That would be 415+498 = 913 L petrol oil.
the real number √13 belongs to which set of numbers
Answers
A hyperbola with center at (0, 0), with x-intercepts at (4, 0) and (-4, 0), with b = 1, and opening horizontally has the equation
Answers
Answer:
It´s x2/16-y2/1=1
Step-by-step explanation:
The equation of the hyperbola is x²/16 - y²/1 =1
What is a hyperbola?A symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone. A plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant : a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.
Given here: hyperbola with center at (0, 0), with x-intercepts at (4, 0) and (-4, 0), with b = 1 . Now we know The standard equation of the hyperbola is [(x²/a²) – (y²/b²)] = 1, where the X-axis is the transverse axis and the Y-axis is the conjugate axis.
Therefore the hyperbola opening horizontally has the equation with x-intercepts at (4, 0) and (-4, 0), with b = 1 is x²/16 - y²/1 =1
Hence, The equation of the hyperbola is x²/16 - y²/1 =1
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What type of triangle has side lengths 2, √11, and √15? please leave details as to how you got to your conclusion im confused
Answers
right if a² + b² = c²
аcute if a² + b² > c²
obtuse if a² + b² < c²
We have a=2, b=√11 and c=√15
2² + (√11)² = 4 + 11 = 15
and
(√15)² = 15
15 = 15 ⇒ right triangle.
Hope this helps.
Answer:
right triangle.
Step-by-step explanation:
The given length of the three sides of the triangle are
[tex]2,\sqrt{11},\sqrt{15}[/tex]
We will now check whether these three numbers are Pythagorean triple or not. If it is a Pythagorean triple then the triangle will be a right triangle.
Pythagorean triple:- If the sum of square of any two sides is equal to the square of the third side then the lengths are Pythagorean triple and the triangle is a right triangle.
Now, we do the below operation:
[tex]2^2+(\sqrt{11})^2\\\\=4+11\\\\=15[/tex]
Now, let us square the third side
[tex](\sqrt{15})^2\\\\=15[/tex]
Since, we got both values equal. Hence, the length of sides are Pythagorean triple.
And therefore, the triangle is right triangle.
Determine whether the formula describes y as a function of x. Explain your reasoning.
y = -x
Answers
Simplify square root of (1-cos)(1+cos)/cos^2
Answers
(1-cosx)(1+cosx)=1+cosx-cosx-cos²x=1-cos²x=sin²x
sin²x
____
cos²x
tg²x
A spinner and 4 cards are shown below: A spinner with 5 equal sectors is shown in the figure. The colors Green, Blue, Purple, Yellow, and Red are marked on it. The arrow points at the purple color. Four cards are shown on the right side. The colors Red, Yellow, Blue, and Pink are marked on them. Jane spins the spinner and selects a card without looking. What is the probability that the spinner stops at purple and a pink card is selected?
Answers
The probability of the spinner landing on purple and a pink card being selected is 1/20 or 5%.
Explanation:The subject of this question is probability, a branch of Mathematics. Let's determine the probability of the spinner landing on purple and choosing the pink card. There are 5 equal sectors in the spinner, which means every color has a 1/5 chance to be chosen on any spin. Therefore, the probability of it landing on purple is 1/5.
As for the cards, there are four of them, meaning each card also has a 1/4 chance of being selected. Therefore, the probability of selecting a pink card is 1/4.
Because these are independent events (one does not affect the outcome of the other) we can calculate the simultaneous probability by multiplying the individual probabilities. Thus, the total probability of the spinner landing on purple and a pink card being selected is (1/5) * (1/4), which equals 1/20 or 5%.
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Keiko is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Keiko has been adding money. Suppose that x and y are related by the equation =20x+550=y .
* Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
What was the starting amount of money in the account?
What is the change per week in the amount of money in the account?
Answers
the starting amount would be the 550, because it doesn't have a variable assigned to it.
change per week is 20 since it is being multiplied by the number of weeks
The starting amount of money in the account was $550
The change per week in the amount of money in the account per week is by $20.
We have a equation - 20x+550=y
where -
x represent the number of weeks Keiko has been adding money and y represent the total amount of money in the account (in dollars).
We have to determine -
1). What was the starting amount of money in the account.
2). What is the change per week in the amount of money in the account.
What is the general equation of a straight line ?The general equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to question, we have -
20x+550=y
Rearranging the equation, we get -
y = 20x + 550, which is a equation of straight line with slope = 20.
Now, in order to calculate the starting amount of money in the account, put x = 0 above, we get -
y = 20 x 0 + 550 = $550
Money in the account during week 1 = M(1) = 20 x 1 + 550 = $570
Money in the account during week 2 = M(2) = 20 x 2 + 550 = $590
Change per week in the amount of money in the account = M(2) - M(1) = $590 - $570 = $20
Hence,
The starting amount of money in the account was $550
The change per week in the amount of money in the account per week is by $20.
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Which of the following indicates that the roots of a quadratic are irrational
a) discriminant is zero
b) discriminant is negative
c) discriminant is rational
d) discriminant is prime
Answers
All prime discriminants will result in an irrational root, but not all irrational roots have prime discriminants
PLEASE HELP IMAGE ATTACHED!!! the area of this parallelogram is 120mm^2. Find the value of X
Answers
A=bh, in this case:
A=hx
x=A/h, we are told that A=120mm^2 and h=10mm so
x=120mm^2/10mm
x=12mm
A furniture factory makes 5 recliners for every 3 couches. If the factory makes a total of 56 recliners and couches in a day, how many recliners were made? Select the correct proportion to solve this problem.
Answers
In ratios, 'things go with the same things', so recliners have to be both in the numerator or denominator. The 8 is misleading. That's the total, and the problem is all about recliners and couches only
How many different arrangements of the letters in the word SCHOOL are there?
A) 1440
B) 720
C) 360
D) 120
Answers
If you don't consider the duplication of 2 O's, then the total cases are:
6! = 720
However, we should eliminate the duplication cases of 2 O's:
Since for each arrangement, you can always switch 2 O's to create a duplicated case, for example, SCHOOL, you can switch the 2 O's but they are duplicated
So the final answer will be 720 / 2 = 360
How many times bigger is a metric ton than a kilogram?
Answers
the water was pumped out of a backyard pond. what is the domain of this graph
Answers
Time t would be the domain, 0 to t.
The domain of a graph represents the set of all the possible x-values for a function. In the context of this question, the domain could represent all the possible time values it took for water to be pumped out of the pond. However, the exact domain can't be identified without specific graph or additional information.
Explanation:To determine the domain of the graph related to the water being pumped out of a backyard pond, you would need to consider the horizontal range of the graph. The domain of a graph in mathematics represents the set of all the possible x-values that the function can have. In the context of this problem, the domain could represent the time over which the water was being pumped out. The dependence of the quantity of water on the time creates a function whose domain (all possible time values during the pumping) we are looking for. However, without the specific graph or additional information, we cannot directly identify the domain.
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