The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3
Step-by-step explanation:
A symptote is a line that a curve approaches but never touches
The vertical asymptote of a logarithmic function is at the zero of the argumentf(x) = log(argument) has vertical aymptotes at argument = 0∵ f(x) = 3 ㏒(x + 3)
∵ The argument is (x + 3)
- Equate the argument by zero
∵ x + 3 = 0
- Subtract 3 from both sides
∴ x = -3
- The vertical asymptote of a logarithmic function is at the zero
of the argument
∴ The vertical asympotote of f(x) is x = -3
The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3
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Answer:
-3
Step-by-step explanation:
plato
Mario works at a snack bar near the beach for 2 hours each Saturday. one Saturday, he started with 30 bottles of juice and sold 3/15 of the juice in the first hour. when he finished work, he had 6/15 of the juice left. what fraction did he sell in the second hour.
Answer:
12 bottles were sold in the second hour.
Step-by-step explanation:
This problem can be solved by implementing an equation in one variable.
The equation will utilize the given values including total bottles of juice, the amount of juice sold in the first hour and amount of juice remaining at the end.
The equation will also consist of the value to be found out, the amount of juice sold in the second hour.
The value to be found out is substituted by a variable.
The equation is then solved by transfer of values and/or variable on the opposite side of the equal sign.
When a value/ variable is transferred on the opposite side of the equal sign, the sign of the value/ variable becomes the opposite.
The negative sign becomes positive and multiplication becomes division, and vice-versa.
1. In the first hour, \frac{3}{15} of all the juice was sold.
\frac{3}{15} of 30 is calculated as
\frac{3}{15} x 30 = 6
6 bottles are sold in the first hour.
2. At the beginning of the second hour, the amount of juice remaining is assumed to be a.
3. As per the question, at the end of second hour, the remaining juice is \frac{6}{15}.
\frac{6}{15} of 30 is calculated as
\frac{6}{15} x 30 = 12
12 bottles are remaining at the end of the second hour.
4. Alternatively, at the end of second hour, 30 - 6 - a of the juice is remaining.
We get, 24 - a bottles are remaining at the end of the second hour.
We equate the above expression with 12, we get the following equation.
24 - a = 12
Next, we transfer a from left side to the right side of the equation.
24 = 12 + a
Next, we transfer 12 from right side to the left side of the equation.
24 - 12 = a
=> 12 = a
OR
a = 12
Hence, 12 bottles were sold in the second hour.
Mario sold 2/5 of his juice in the second hour after having sold 3/15 in the first hour and ending with 6/15 of the juice left.
Mario started with 30 bottles of juice and sold 3/15 of them in the first hour. To find out how many bottles that is, we multiply the total number of bottles by the fraction sold: 30 bottles x 3/15 = 6 bottles. After the first hour, Mario had 30 bottles - 6 bottles = 24 bottles left.
By the end of his shift, Mario had 6/15 of his original juice left. Again, we multiply the total number of bottles by the fraction left: 30 bottles x 6/15 = 12 bottles. So, at the end of his shift, Mario had 12 bottles unsold.
To find out how many bottles were sold in the second hour, we subtract the number left at the end from the number left after the first hour: 24 bottles - 12 bottles = 12 bottles sold in the second hour. To express this amount as a fraction of the original 30 bottles, we divide 12 by 30 to get 12/30, which simplifies to 2/5. Thus, Mario sold 2/5 of his juice in the second hour.
The ratio of the angle measures in a triangle is 4:5:9. What is the measure of each angle
Answer:
40, 50, and 90
Step-by-step explanation:
You know that there are 180 degrees in a triangle, so you'd use the ratio to find each angle by setting up your equation like this: 4x+5x+9x=180
Then, simplify the equation and solve for x:
18x=180x=10Then, plug 10 into each x value to find each angle measure:
4(10)=40, 5(10)=50, 9(10)=90
Final answer:
The measures of the angles in a triangle with a ratio of 4:5:9 are 40 degrees, 50 degrees, and 90 degrees respectively, calculated by dividing 180 degrees by the sum of the ratios and then multiplying by each individual ratio.
Explanation:
The question is asking us to find the measure of each angle in a triangle when the ratio of the angle measures is given as 4:5:9. To solve this, we will use the fact that the sum of the angles in any triangle is 180 degrees.
First, let's add the ratios together (4+5+9=18) to find the total number of parts that divide the 180 degrees. Now, divide the total degrees (180) by the number of parts (18) to find the measure of one part, which is 10 degrees. Then, multiply the value of one part by the number of parts for each ratio: 4 parts, 5 parts, and 9 parts.
The measure of the first angle (4 parts) is 4 x 10 = 40 degrees, the second angle (5 parts) is 5 x 10 = 50 degrees, and the third angle (9 parts) is 9 x 10 = 90 degrees. Hence, the measures of the angles in the triangle are 40 degrees, 50 degrees, and 90 degrees respectively.
Respond to the following based on your reading.
m
1. What amount of work is done when a force of 50 N is used to drag an object a distance of 20
meters across a floor?
i
2. What's the kinetic energy of an object that has a mass of 12 kilograms and moves with a velocity
of 10 m/s?
3. A skateboarder is inside
of a half-pipe, shown here.
Explain her energy
transformations as she
jumps off at point A, slides
to point B, and finally
reaches point c
G
4. If the skateboarder
continues going back and
forth on the half-pipe she'll
1) The work done is 1000 J
2) The kinetic energy is 600 J
3) There is a continuous conversion between kinetic and potential energy
Step-by-step explanation:
1)
The work done by a force when pushing/pulling an object is given by
[tex]W=Fd cos \theta[/tex]
where
F is the magnitude of the force
d is the displacement
[tex]\theta[/tex] is the angle between the direction of the force and of the displacement
In this problem, we have:
F = 50 N is the force
d = 20 m is the displacement
[tex]\theta=0[/tex], assuming the object is parallel to the displacement
Substituitng,
[tex]W=(50)(20)(cos 0)=1000 J[/tex]
2)
The kinetic energy of an object is the energy due to the motion of the object. It is given by
[tex]K=\frac{1}{2}mv^2[/tex]
where
m is the mass of the object
v is its speed
For the object in this problem,
m = 12 kg is the mass
v = 10 m/s is the speed
Substituting, we find
[tex]K=\frac{1}{2}(12)(10)^2=600 J[/tex]
3)
Here the skateboarder is moving on the half-pipe. According to the law of conservation of energy, the total mechanical energy, sum of kinetic and potential energy, is conserved:
[tex]E=KE+PE=const.[/tex]
This means that:
When the skateboarder is at the highest point of its motion, its potential energy PE is maximum, while the kinetic energy KE is zeroWhen the skateboarder is at the lowest point of its motion, its potential energy PE is zero, while the kinetic energy KE is maximumTherefore, there is a continuous conversion between potential and kinetic energy.
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Answer:
1. W = Fs
W = 50 N 20 m
W = 1,000 J
2. Ek=mv22
Ek=12kg×(10m/s2)2
Ek=12×1002
Ek=1,2002
Ek = 600 J
3. At point A, the skateboarder’s energy is all potential since she is high up (PE = mgh), and gravity has the potential to pull her down. She isn't moving, so she doesn't have velocity. Therefore, she doesn't have kinetic energy. At point B, she is moving the fastest during her ride and is as close to the ground as the ramp allows. Thus, her potential energy has been turned into kinetic energy due to her velocity and lack of height. At point C, if she comes to a stop on the other side of the half-pipe, her kinetic energy has been turned back into potential energy since she is high up again.
4. Eventually, the friction between the wheels and the ground will cause the skateboard to stop. Each time she goes back and forth, she will lose some of her initial energy from her drop-in, as long as she doesn't push off the sides at all.
Step-by-step explanation:
Penn foster :)
4(7+v) help me please i am so confused
Answer:
28+4v
Step-by-step explanation:
multiply each term in parenthesis by 4.
multiply the numbers 4×7+4v
= the solution 28+4v
Answer:
V = -7 or 28 + 4V
Step-by-step explanation:
distribute the 4 to the 7 and V ---> 28 + 4v = 0
subtract 28 from both sides ---> 4V = -28
divide 4 by both sides --> V = -7
Please help I don’t know how to-
Answer:
y is going back by 3's x is going back one
Step-by-step explanation:
16+13p-9p write an equivalent expression by combining like terms
Lines b and c are parallel. Horizontal and parallel lines b and c are cut by transversal a. Where line b intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, (18 x + 4) degrees, (7 x + 1) degrees. Where line c intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7. What is the measure of Angle2? mAngle2 = 31° mAngle2 = 50° mAngle2 = 120° mAngle2 = 130°
Answer:
mAngle2 = 50°
Step-by-step explanation:
A relative schematic has been attached bellow describing the problem.
In this case, we will be working with Supplementary angles. The latter denote angles which when summed together equal to 180°.
From the schematic we can identify the following Supplementary pairs as:
∠1 and ∠2
∠2 and ∠(18x+4)
∠(18x+4) and ∠(7x+1)
∠(7x+1) and ∠1
So lets start by finding the value of [tex]x[/tex] as follow. Since we know the supplementary pairs we have that
[tex](18x+4)+(7x+1)=180\\18x+7x+4+1=180\\25x+5=180\\25x=180-5\\25x=175\\x=\frac{175}{25} \\x=7[/tex]
Now we similarly know that ∠2 and ∠(18x+4) are supplementary. So lets replace the value of [tex]x[/tex] in ∠[tex]18x+4[/tex], we have
[tex]18(x=7)+4=126+4=130[/tex]
So finally we have
[tex]<2 + 130=180\\<2=180-130\\<2=50[/tex]
Thus we can say that ∠2 = 50° (which matches the second options from the available ones).
Answer:
50
Step-by-step explanation:
The sum of three consecutive integers is 42
Answer:
The integers are 13, 14, and 15.
Step-by-step explanation:
Let the smallest one be x.
Then, the other two integers are x + 1 and x + 2.
x + x + 1 + x + 2 = 42
3x + 3 = 42
3x = 39
x = 13
x + 1 = 14
x + 2 = 15
The integers are 13, 14, and 15.
Solve the system of linear equations by substitution 2x=12 x-5y=-29
Answer:
Step-by-step explanation:
2x = 12
x = 12/2
x = 6
And
x - 5y = -29
6 = - 5y = - 29
-5y = -29 - 6
-5y = -35
y = -35/-5
y = 7
The solution to the system of equation is (6, 7)
Given the system of equation
2x = 12 and
x - 5y = -29
From equation 1;
2x = 12
x = 6
Substitute x = 6 into equation 2:
x - 5y = -29
6 - 5y = -29
-5y = -29 - 6
-5y = -35
y = 7
Hence the solution to the system of equation is (6, 7)
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8W - 7w + 9 - 2 combining like terms
Answer:
The answer is 1w+7
Step-by-step explanation:
you first combine 8w and -7w to get 1w then you combine 9 and -2 to get 7
The mathematical equation for 900 times 2.
Answer:
900 × 2 ?
Step-by-step explanation:
900 × 2 ? i dont know but i hope its correct?
5/8 of a gallon of paint covers 14/5 of a wall find the unit rate
Answer:25/112
Step-by-step explanation:multiply 5/8 times 5/14.
3) x2+ y2 - x + 3y - 42 = 0
X+y=4
The solution is [tex](-1,5)[/tex] and [tex](7,-3)[/tex]
Step-by-step explanation:
The expression is [tex]x^{2} +y^{2} -x+3y-42=0[/tex] and [tex]x+y=4[/tex]
Using substitution method we can solve the expression.
Let us substitute [tex]x=4-y[/tex] in [tex]x^{2} +y^{2} -x+3y-42=0[/tex]
[tex](4-y)^{2} +y^{2} -(4-y)+3y-42=0[/tex]
Expanding and simplifying the expression, we get,
[tex]\begin{array}{r}{16-8 y+y^{2}+y^{2}-4+y+3 y-42=0} \\{2 y^{2}-4 y-30=0}\end{array}[/tex]
Let us use the quadratic equation formula to solve this equation,
[tex]\begin{aligned}y &=\frac{4 \pm \sqrt{16-4(2)(-30)}}{2(2)} \\&=\frac{4 \pm \sqrt{16+240}}{4} \\&=\frac{4 \pm 16}{4} \\y &=1 \pm 4\end{aligned}[/tex]
Thus, [tex]y=5[/tex] and [tex]y=-3[/tex]
Substituting y-values in the equation [tex]x+y=4[/tex], we get the value of x.
For [tex]y=5[/tex] ⇒ [tex]x=4-5=-1[/tex]
For [tex]y=-3[/tex] ⇒ [tex]x=4+3=7[/tex]
Thus, the solution set is [tex](-1,5)[/tex] and [tex](7,-3)[/tex]
Use the grouping method to factor this polynomial completely 3x^3+12x^2+2x+8
Answer:
(x+4)(3x^2 + 2)
Step-by-step explanation:
3x^3+12x^2+2x+8
3x^2(x + 4) + 2(x + 4)
(x+4)(3x^2 + 2)
Solve log x=5 will mark brainliest
Answer:
100000
Explanation:
We have the natural base of the log; 10.
Now, since we are solving for the value that is being "logged"
we can say 10 to the power of 5 equals.... what?
10^5 is 100000, x 100000.
Hope this helps!
Bartering was an early way that people _____.
1.exchanged currency in the form of paper or metal
2.exchanged a good or service directly for a good or service
3.talked to each other
4.shared financial information over long distances
Answer:
#2
Step-by-step explanation:
N/A
Bartering was an early way that people exchanged a good or service directly for a good or service. (option 2)
Bartering, the act of exchanging goods or services directly for other goods or services, was an early way that people engaged in trade and commerce.
Before the advent of standardized currency in the form of paper or metal, societies relied on bartering as a means of acquiring what they needed.
In a barter system, individuals would negotiate the exchange of items they possessed, often based on their mutual needs and values.
Hence the correct option is (2).
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What is the slope of the given points (0,-1) and (-2,-4)
Answer:
y= -5/2x - -1
Step-by-step explanation:
1. Identify two points on the line
2. Select one to be (x1, y1) and the other to be (x2, y2).
3. Use the slope equation to calculate slope.
Final answer should be in the formula y=mx+b
The slope of the line passing through the points (0, -1) and (-2, -4) is calculated using the formula (Y2-Y1)/(X2-X1) and results in a slope of 1.5.
Explanation:To find the slope of the line passing through two points, you can use the slope formula:
m = (Y2-Y1)/(X2-X1)
Applying this formula to the given points (0, -1) and (-2, -4):
Calculate the difference in the y-coordinates (rise): -4 - (-1) = -4 + 1 = -3.
Calculate the difference in the x-coordinates (run): -2 - 0 = -2.
Divide the rise by the run to get the slope: -3 / -2 = 1.5.
Thus, the slope of the line passing through the points (0, -1) and (-2, -4) is 1.5.
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While in Brazil, Jacob exchanged some
American dollars for Brazilian currency,
Brazilian real. He was given 45 Brazilian
real for $55. What was the approximate
exchange rate for Brazilian real per
dollar?
Answer:
1:1.22 Look at explanation and picture.
Step-by-step explanation:
If Jacob was given 45 Brazilian currency items for $55 you would need to divide 55 by 45 to see how much American dollars it would take to recieve one Brazilian currency.
For one Brazilian currency you need about (fig A) american currency for 1 brazilian currency.
The exchange rate for Brazilian real per American dollar for Jacob's transaction is approximately 0.8182 real per dollar, calculated by dividing the total amount of reals received by the dollars exchanged.
Explanation:To calculate the exchange rate of Brazilian real per American dollar for Jacob's currency exchange, we divide the amount of Brazilian real he received by the amount of American dollars he exchanged. Jacob received 45 Brazilian real for $55 US dollars. The calculation to find the exchange rate is as follows:
Determine the total amount of Brazilian real received: 45 real.Determine the total amount of American dollars exchanged: $55.Divide the amount in real by the amount in dollars to find the exchange rate: 45 real / $55 = 0.8182.The exchange rate is approximately 0.8182 Brazilian real per American dollar.It is important to compare this rate with the market rates mentioned, such as 35 cents/real or the government-set rate of 30 cents/real. It can be observed that Jacob's exchange rate is different from these rates, which illustrates how actual exchange rates may vary due to different factors such as service charges or varying rates across different currency exchange venues.
Edward wants to spend less than $115 to buy a
new shirt and some jeans. If a shirt costs $25,
choose an inequality to find the amount that
Edward can spend on a pair of jeans if he buys 3
pairs of jeans.
Answer: x < 30
Step-by-step explanation:
Let the cost of a jean be x
cost of a shirt = $25
cost of 3 jeans = 3x
since he wants to spend less than $115 , this means that
3x + 25 < 115
3x < 115 - 25
3x < 90
x < 30
What is the solution
3x-2y=14
5x+y=32
Answer:
solution is (6,2)
Step-by-step explanation:
3x - 2y = 14
5x + y = 32....multiply by 2
------------
3x - 2y = 14
10x + 2y = 64 (result of multiplying by 2)
------------add
13x = 78
x 78/13
x = 6
5x + y = 32
5(6) + y = 32
30 + y = 32
y = 32 - 30
y = 2
The total number of burgers sold from a restaurant from Monday to Sunday can be modeled by the function f(d)=200d3+542d2+179d+1605and the number of visitors to the restaurant from Monday to Sunday can be modeled by g(d)=100d+321, where d is the number of days since Monday. What is the average number of burgers per person?
Answer:
[tex]2d^2-d+5[/tex]
Step-by-step explanation:
The total number of burgers sold from a restaurant from Monday to Sunday:
[tex]f(d)=200d^3+542d^2+179d+1605[/tex]
The number of visitors to the restaurant from Monday to Sunday:
[tex]g(d)=100d+321[/tex]
To find the average number of burgers per person, just divide [tex]f(d)[/tex] by [tex]g(d).[/tex]
First, multiply [tex]g(d)[/tex] by [tex]2d^2[/tex] and subtract the result from [tex]f(d)[/tex]:
[tex]200d^3+542d^2+179d+1605-2d^2(100d+321)\\ \\=200d^3+542d^2+179d+1605-200d^3-642d^2\\ \\=-100d^2+179d+1605[/tex]
Then, multiply [tex]g(d)[/tex] by [tex]-d[/tex] and subtract the result from [tex]-100d^2+179d+1605[/tex]:
[tex]-100d^2+179d+1605-(-d)(100d+321)\\ \\=-100d^2+179d+1605+100d^2+321d\\ \\=500d+1605[/tex]
Now, multiply [tex]g(d)[/tex] by [tex]5[/tex] and subtract the result from [tex]500d+1605[/tex]:
[tex]500d+1605-5(100d+321)\\ \\=500d+1605-500d-1605\\ \\=0[/tex]
Hence,
[tex]f(d)=g(d)(2d^2-d+5)[/tex]
and the function
[tex]b(d)=2d^2-d+5[/tex]
represents the average number of burgers per person.
There are 30 major league baseball teams and 32 national football league teams. The expanded roster for major league baseball teams is 40 players and it is 53 for national football league teams. How many more players are in the national football league than in major league badeball?
To find out how many more players are in the NFL than in the MLB, calculate the total number of players in each league and then subtract. This results in 496 more players in the NFL.
Explanation:To determine how many more players are in the National Football League (NFL) than in Major League Baseball (MLB), you need to apply basic multiplication and subtraction.
Calculate the total number of players in MLB: The expanded roster for each MLB team is 40 players. There are 30 MLB teams. So, multiply 40 by 30 to get 1200 players.Calculate the total number of players in NFL: The expanded roster for each NFL team is 53 players. There are 32 NFL teams, so multiply 53 by 32 to get 1696 players.Find the difference: Subtract the total number of MLB players from the total number of NFL players to find the difference. So, 1696 - 1200 = 496 players.Therefore, there are 496 more players in the NFL than in the MLB.
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There are 496 more players in the National Football League than in Major League Baseball.
To find out how many more players are in the National Football League (NFL) compared to Major League Baseball (MLB), we will first calculate the total number of players in each league.
Step 1: Calculate the total number of players in each league
NFL:
Number of teams: 32Players per team: 53Total players in NFL:MLB:
Number of teams: 30Players per team: 40Total players in MLB:Step 2: Calculate the difference in total players
To find out how many more players are in the NFL than in the MLB, we subtract the total number of MLB players from the total number of NFL players:Conclusion
Thus, there are 496 more players in the National Football League than in Major League Baseball.
The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 6 and 9. What is the length of the altitude? A. 2004-04-01-01-00 B. 2004-04-01-01-00 C. 2004-04-01-01-00 D. 2004-04-01-01-00
Answer:
I think the answer is the second choice so B. Also your pretty
Answer:
its d ac/gi=bc/hi
Step-by-step explanation:
Mr. McNeely has a wooden box in the shape of a right rectangular prism. The box measures 2
feet by 3 feet by 2.8 feet. What is the surface area of the box?
Answer:
40ft^2
Step-by-step explanation:
multiply :
2(2*3)
2(2*2.8)
2(3*2.8)
Each value in the parenthesis are the areas of 3 different sides. You then multiply by two because there is another side opposite to the side that is the same.
then add all of those up
you get 40
How many x-intercept does the graph of y=2^2+5x+9
Answer:
there is only one x-intercept. The x-intercept is 2.6.
Step-by-step explanation:
A survey asked 40 students If they play an instrument and if they are in band.
1.25 students play an instrument.
2. 20 students are in band.
3. 20 students are not in band.
Which table shows these data correctly entered in a two-way frequency table?
Answer:
The correct answer is,
The two-way frequency table is given as:
Band Not in Band Total
Play instrument 20 5 25
Do not play instrument 0 15 15
Total 20 20 40
Step-by-step explanation:
Given that;
We are given a survey of 40 students regarding whether they play an instrument or not.
We are given an information as:
1. 25 students play an instrument.
2. 20 students are in band.
3. 20 students are not in band
Hence, the table can be formed as:
Band Not in Band Total
Play instrument 20 5 25
Do not play instrument 0 15 15
Total 20 20 40
Since, those who don't play any instruments can't even play band hence the value of that in table is 0.
Thus, Option C is correct.
Segment CD has endpoints (-4, 3) and (8, -1). Find the coordinates of the point that divides the line segment directed from C to D in the ratio of 2:3.
A) (-6/5, 26/5)
B) (4/5, 7/5)
C) (1/5, 13/5)
D) (16/5, 3/5)
Answer:
B
Step-by-step explanation:
If point [tex]O(x_O,y_O)[/tex] divides the segment CD with endpoints at [tex]C(x_C,y_C)[/tex] and [tex]D(x_D,y_D)[/tex] in the ratio [tex]m:n,[/tex] then
[tex]x_O=\dfrac{nx_C+mx_D}{m+n}\\ \\y_O=\dfrac{ny_C+my_D}{m+n}[/tex]
In your case,
[tex]x_C=-4\\ \\y_C=3\\ \\x_D=8\\ \\y_D=-1\\ \\m:n=2:3,[/tex]
then
[tex]x_O=\dfrac{3\cdot (-4)+2\cdot 8}{2+3}=\dfrac{-12+16}{5}=\dfrac{4}{5}\\ \\y_O=\dfrac{3\cdot 3+2\cdot (-1)}{2+3}=\dfrac{9-2}{5}=\dfrac{7}{5}[/tex]
Solve V = ℓwh for w.
w = Vℓh
Answer:
w = V/(ℓh)
Step-by-step explanation:
Divide the given equation by the coefficient of w:
V/(ℓh) = ℓwh/(ℓh)
w = V/(ℓh)
What conclusion can you make about the result of adding a rational and an irrational number?
Answer:
It is irrational
Step-by-step explanation:
if you combine a rational and irrational number it cannot be rational.
Adding a rational and an irrational number always results in an irrational number. The rational number doesn't affect the irrationality of the irrational number.
Explanation:The result of adding a rational and an irrational number is always an irrational number. For example, if you add the rational number 2 (which can be expressed as a ratio of two integers) and the irrational number sqrt(2) (which cannot be expressed as a ratio of two integers).
The result is 2 + sqrt(2), which is an irrational number.
Because the rational number doesn't affect the irrationality of the irrational number, the sum remains irrational.
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How do I solve
2(x+y)^2+(x+y)-6 ????
Answer:
2x2+4xy+2y+x+y−6
Step-by-step explanation:
Hope this helps!
Please Mark Brainliest!