The factored form of the expression 16x² + 9y² over the complex numbers is; (4x + 3iy)(4x − 3iy)
How to factorize expressions?We want to find the factored form of the expression 16x² + 9y² over the complex numbers.
We can rewrite the given expression 16x² + 9y² as perfect squares;
= (4x)² + (3y)²
Now, from using the difference of squares formula, we know that;
a² - b² = (a + b)(a - b)
Thus;
(4x)² + (3y)² = (4x)² - (√-9)²y²) can be expressed as;
(4x + 3iy)(4x − 3iy)
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Simplify each sum or difference. State any restrictions on the variables.
x / 3x + 9 - 8/x² + 3x
Simplification of the equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex] is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.
As given in the question,
Given equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex]
Simplify the given equation,
x/ 3(x+3) - 8/x(x+3)
= (x² - 24) / 3x(x+3)
Restriction on the variables for the above equation is,
x≠ 0 , x≠ -3
Therefore, simplification of the equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex] is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.
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3 2/5 + 9 1/10 ?????…?.?
Answer: 25/2
Step-by-step explanation:
coverting the mixed numbers into improper fractions we get
17/5+91/10
getting a common denominator and adding the numerators we get 125/10
then we can simplify, which gets 25/2
Find the value of a. The diagram is not to scale.
21°-
129
(2q+6)°
9°
Answer:
−2322q−6945
Step-by-step explanation:
Simplify 129(2q+6) * 9 to 1161(2q + 6)
Expand by Distributing terms
21 - (2322q + 6966)
Remove parentheses.
21 - 2322q - 6966
Collect like terms.
-2322q + (21−6966)
Simplify
-2322q - 6945
Done
Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (√3, 0)
The equation of the circle that passes through the point (√3 , 0) and has a center at the origin is x^2 + y^2 = 3.
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (√3 , 0).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(√3 - 0)^2 + (0 - 0)^2
radius= √3
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = √3
(x - 0)^2 + (y - 0)^2 = (√3)^2
x^2 + y^2 = 3
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Find the center and the radius of each circle. x²+(y-4)²=11
The equation of the circle x^2 + (y - 4)^2 = 11 has a radius of √11 and a center located at (0 , 4).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, x^2 + (y - 4)^2 = 11, is in standard form, then
h = 0
k = 4
r = √11
Hence, the equation of the circle x^2 + (y - 4)^2 = 11 has a radius of √11 and a center located at (0 , 4).
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Write an equation in point-slope form for each pair of points. (1,10) and (5,42)
The point slope form of (1,10) and (5,42) is (y - 10) = 8(x - 1).
How to find the point slope form?A straight line is represented using its slope and a point on the line using point slope form. In other words, the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1, y1).
given that
the coordinates points are (1, 10) and (5,42)
(x1,y1) = (1,10)
(x2, y2) = (5,42)
The formula of point-slope is
(y - y1) = m(x - x1)
Here,
x1 = 1 and y1 = 10 but we don't know the value of m.
now,find the value of m using the following formula
[tex]m = \frac{(y2 - y1)}{(x2 - x1)} [/tex]
now, substitute the values, we get
[tex]m = \frac{(42 - 10)}{(5 - 1)} [/tex]
[tex]m = \frac{30}{4} [/tex]
m = 8
so, the value of m is 8.
substitute these values into the point-slope formula
(y - 10) = 8(x - 1)
Hence, the point slope form of (1,10) and (5,42) is (y - 10) = 8(x - 1).
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Find the value of x.
-2x = 3x + 6
Answer:
x= -6/5
Step-by-step explanation:
-6=3x+2x
-6=5x
x=-6/5
Answer:
x = - [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
- 2x = 3x + 6 ( subtract 3x from both sides )
- 5x = 6 ( divide both sides by - 5 )
x = - [tex]\frac{6}{5}[/tex]
This line graph shows the United States population from 1800 to 2000. A graph titled U S population has year on the x-axis, and millions of people on the y-axis. A line increases from 0 in 1800 to 300 in 2000. What was the population in the year 2000? about 50 million about 100 million about 200 million about 300 million
In the line graph it represents us to infer that the U.S. population in 2000 was about 300 million.
What is graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
WE have been given graph that titled U S population has year on the x-axis, and millions of people on the y-axis. A line increases from 0 in 1800 to 300 in 2000.
The line graph showed that:
The U.S. population was under 50 million in 1800
It increased exponentially after 1880
It reached around 300 million in 2000
The U.S. has seen its population rise exponentially over the last century such that; over 300 million and it was around the year 2000 that this milestone was reached.
Therefore U.S. population in 2000 was around 300 million.
In the line graph it represents us to infer that the U.S. population in 2000 was about 300 million.
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Answer:
300 million is ur answer:)
Step-by-step explanation:
how would you limit the domain for it to be one to one f(x)= x^4
Limit the domain to x > 0 for it to be one to one
How to limit the domain for it to be one to one?The function is given as:
f(x)= x^4
The above function is an even function
This means that
f(x) = f(-x)
So, for the function to be one to one, we have to limit the function to only the positive x values
Hence, limit the domain to x > 0 for it to be one to one
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Find the arithmetic mean a n of the given terms. a n₋₁ = 4, a₊₁ = -3
The arithmetic mean a n of the given terms a n₋₁ = 4, a₊₁ = -3 is [tex]a_{n}[/tex] = 1/2.
What is arithmetic mean?an=a1+d(n−1) by using this formula the arithmetic mean a n of the given terms are
[tex]a_{n}[/tex] = (-3 + 4)/2
[tex]a_{n}[/tex] = 1/2
The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.
The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values. Add the numbers together, for instance: a + b + c + d and so on, if there is a set of "n" numbers.
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The cost of renting a pool at an aquatic center is either 30 per hour or 20 per hour with a 40 non-refundable deposit. For how many hours is the cost of renting a pool the same for both plans?
If the cost of renting a pool at an aquatic center is either 30 per hour or 20 per hour with a 40 non-refundable deposit, then the cost of renting the pool is the same for both plans for 4 hours.
The number of hours for which the cost of renting the pool will be the same for both plans can be calculated by using an algebraic expression.
An algebraic expression is a type of equation that consists of both numbers and letters.
An algebraic expression for this problem can be given as,
30(x) = 20(x) + 40
Where x is equal to the number of hours.
The value of x can be calculated by rearranging the equation,
30(x) - 20(x) = 40
10(x) = 40
x = 40 ÷ 10
x = 4
Thus, the number of hours for which the cost of renting the pool same for both plans is 4 hours.
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can someone help me with this
We have given the expression -13y + 7 -11 - 4y to write as sum which is
-13y + 7 +(-11) + (-4y).
What is an mathematical expression?A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. (Number/variable, Math Operator, Number/variable) is the order in which an expression is composed.
Arithmetic operators and numbers make up a mathematical numerical expression. No equality or inequality symbols, or unidentified variables, are present.
Indeterminate variables, integers, and arithmetic operators make up an algebraic expression. Neither equality nor inequality symbols can be found in it.
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Element X decays radioactively with a half life of 15 minutes. If there are 420 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 4 grams?
If there are 420 grams of Element X, then it would take 100.7 of a minute to take the element to decay to 4 grams.
Given that the element X decays radioactively with a half life of 15 minutes.
We are required to find the time that would take the 420 grams of element X would take the element to decay to 4 grams.
Radioactive decay is basically the emission of energy in the form of ionizing radiation.
4=420*[tex](1/2)^{x/15}[/tex]
x=15* [tex]log_{2}[/tex] (105)
x=15*log (105)/log (2)
x=15*2.0212/0.3010
x=30.318/0.3010
x=100.72
After rounding it will be 100.7 of a minute.
Hence if there are 420 grams of Element X, then it would take 100.7 of a minute to take the element to decay to 4 grams.
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7. What's the sum of 2 and 24?
A. 10/20
B.
C. %20
D. %10
Answer:26
Step-by-step explanation:it's 26
Answer:
26
Step-by-step explanation:
You add 24 + 2 = 26 ( SUM means to ADD )
Write each arithmetic series in summation notation. 100+90+80+ . . . . . . +10
The algebraic expression or sigma (summation) notation is given by:
∑ = 10(100 + 10)/2
And its value is ∑ = 550
What is sigma notation?The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.
The equation for this type of problem is:
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
100+90+80+ . . . . . . +10
a1 =100an = 10n = 10∑ = 10(100 + 10)/2
∑ = 10(110)/2 = 5(110)
∑ = 550
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A garden is in the shape of a square with a perimeter of
32
feet. The garden is surrounded by two fences. One fence is around the perimeter of the garden, whereas the second fence is
2
feet from the first fence on the outside. If the material used to build the two fences is
$
1.18
per foot, what was the total cost of the fences?
Answer:
Step-by-step explanation:
32 / 4 = 8 = length or width (because it is a square both are the same)
8 + 2 = 10
10 + 10 + 10 + 10 = 40 (perimeter of outer fence)
32(1.18) + 40(1.18) = $84.96
(6x³)² I need answer asap please and thank you
y varies directly with x . Explain your answer.If x is doubled, what happens to y ?
If x is doubled then the value of y is also doubled.
What is direct variation?A sort of proportionality known as "direct variation" occurs when one quantity immediately changes in response to a change in another variable. This suggests that if one number increases, the other quantity will also rise proportionately. Similar to the last example, if one quantity declines, the other amount likewise declines. The link between direct variation and the graph will be linear, resulting in a straight line.
As y varies directly with x,
Using direct variation,
which implies y = kx
if x is doubled,
y = 2kx,
This implies that if x is doubled then the value of y is also doubled.
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what is 5u+10u for math 8?
Answer:
(5+10)u
= 15u
is the solution
Farmer ed has meters of fencing, and wants to enclose a rectangular plot that borders on a river. If farmer ed does not fence the side along the river, what is the largest area that can be enclosed?.
The largest area that can be enclosed will be 2812.5 square meters.
The perimeter of a rectangle is given as:
2L + 2W ∴ L = length and W = width
As the farmer does not want to fence the side along the river, then the formula will be:
P = L + 2w
Now
150 = L + 2w
L = 150 - 2w
Here the area is LW
Area = (150 - 2W)(W)
After solving we get
150 - 2W = 0 or W = 0
150 - 2W = 0
2W = 150
W = 75
Now, there are two solutions whether 0 or 75
Let's find their average 0+75 / 2 = 37.5
Now L = 150 - 2(37.5)
L = 150 - 75
L = 75
As the dimensions are L = 75 and W = 37.5
Area = L x W = 75 x 37.5 = 2812.5 square meters
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The complete question is:
Farmer Ed has 150 meters of fencing and wants to enclose a rectangular play that borders a river. If farmer Ed does not fence in the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
Ross joined a 30 week weight loss challenge. he lost 10.4 pounds int eh first 4 weeks if he maintains this rate of weight loss how many pounds will eh lose at the end of the 30 week challenge
Answer: 78 pounds
Step-by-step explanation:
10.4/4 = 2.6
2.6 * 30 = 78
Tionna wants to replicate a painting in an art museum. The painting is 3 feet wide and 6 feet long. She decides on a dilation reduction factor of 0.25. What size paper should she use? F. 4 in.× 8in. H. 8 in. × 16 in. G. 6 in. × 12in. J. 10 in. ×20 in.
10in × 20in is size paper should she use. That is, option J . 10in × 20in is the correct answer.
What are examples of linear equations?
Ax + By = C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.The given size of the painting is 3 feet wide and 6 feet long.
The value of 1 foot in inches,
1 foot = 12inches.
The size of the painting is 36 inches wide and 72 inches long.
width is, ( 0.25 × 36 ) = 9 inches. So option F . 4in × 8 in is not the answer and
the length is, ( 0.25 × 72 ) = 18 inches. So option G 6in × 12in and H. 8inch × 16 in are not the possible choices.
So, the reduced dimensions of the dilated painting are 9 inches wide and 18 inches long.
That is, option J . 10in × 20in is the correct answer.
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Finding the average rate of change of a function given its...
Find the average rate of change of g (x) = -2x²-x from x = 1 to x = 6.
Simplify your answer as much as possible.
0
18 08
X
k
Answer:
Mind you that the average rate of change is the gradient. Commonly we get it by using the formula that requires us to have also the y coordinates.
we can find them by plugging in the x-values in the function g(x)
x=1
[tex]g(1)=-2(1^{2} )-1\\g(1)=-3\\\\g(6)=-2(6^{2})-1\\ g(6)=-73[/tex]
now we have the points (1,-3) and (6,-73)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
that is the formula we will use
[tex]=\frac{-73-(-3)}{6-1} \\=\frac{-70}{5} \\=-14[/tex]
Assume an initial starting ft of 290 units, a trend (tt) of eight units, an alpha of 0.40, and a delta of 0.50. if actual demand turned out to be 278, calculate the forecast for the next period.
The forecast for the next period when the actual demand turned out to be 278 will be 294 units.
What is the forecast?The method of forecasting entails creating assumptions based on historical and current data. These might then be contrasted with what transpires.
Ft = 290, Tt = 8, α = 0.40, δ = 0.50, At = 278. Then the forecast for the next period will be
FITt = Ft + Tt
= 290 + 8
= 298 units
Ft + 1 = FITt + α(At − FITt)
= 298 + 0.40(278 − 298)
= 298 − 8
= 290 units
Tt + 1 = Tt + δ(Ft + 1 − FITt)
= 8 + 0.50(290 − 298)
= 8 − 4
= 4 units
FITt + 1 = Ft + 1 + Tt + 1
= 290 + 4
= 294 units
The forecast for the next period will be 294 units.
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What is the graph solution of 1 + k ≥ 4 or 9 + k < 2? ( I don't understand in how to solve this, if possible please do a step by step or at least explain how you got your answer.
Using the concept of the or operation, the solution of the given inequality in the number line is given at the graph in the end of the answer.
What is the result of the or operation between sets?The or operation between sets has as a result all the elements that belong to at least one of the sets.
For this problem, we have two inequalities:
1 + k ≥ 49 + k < 2.Then we solve the inequality then apply the or operation between them.
The solutions to the inequalities are given as follows:
1 + k ≥ 4 -> k ≥ 3 (numbers to the right of k = 3, with a closed interval).9 + k < 2 -> k < 2- 9 -> k < -7(numbers to the left of k = -7, with an open interval).The or operation will involve both the numbers to the left of k = -7 and the numbers to the right of k = 3 being plotted on the number line, as shown in the graph at the end of the answer.
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Chris buys an item for $6.43. He gives the cashier a $50 bill. How much money should Chris get back
Answer:
43.57
Step-by-step explanation:
subtract 6.43 from 50
Answer: 43.57
Step-by-step explanation: 50 dollars minus 6 dollars and 43 cents and it gives you 43.57
Find the sum of each infinite geometric series. 6+5+ 25/6 + . . .
The sum of the infinite geometric series 6+5+ 25/6 + . . is S = 36
The given geometric series is:
6 + 5 + 25/6 + . . .
The common ratio (r) of a geometric series is given by:
r = a(n) / a(n - 1)
Notice that in the given series:
a(1) = 6
a(2) = 5
a(3) = 25/6
Hence, the common ratio is
r = a(2) / a(1) = 5/6
Since 0 < r < 1, the series is convergent and the sum exists.
Use the sum formula:
S = a(1) / (1 - r)
Substitute a(1) 6 and r = 5/6 into the formula:
S = 6 / (1 - 5/6)
= 6 / (1/6)
= 36
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The graph below shows how the number of donations to a charity affects the expected total value of those donations.
In October, the charity received 60 donations.
If the graph continues in the same way, what is the expected total value of the donations in October?
I can't answer it but i hope someone else does :)
Maybe the answer - But there are limits depending on whether you donate the funds to a “50% charity” or a “30% charity.” As the name implies, the total deduction for gifts to 50% charities cannot exceed 50% of a taxpayer's adjusted gross income (AGI). Accordingly, donations to 30% charities are limited to 30% of AGI.
"one-third of a number is 12 less than the number itself"
translate as an equation not solved
Answer:
1/3 n = n - 12 Cross multiply
n = 3(n - 12)
n = 3n -36
2n = 36
n = 36/2
n = 18
Check:
1/3 (18) = 18 - 12
6 = 6
Hope this helps
HELP ME WITH THIS QUESTION PLS PLS
Answer: 49
Step-by-step explanation:
A=πr^2
A=π(7)^2
A=49π in^2
Answer: 49
Answer:
154 Inches square.
r=7
area= πr^2
= 22/7* 49
= 154
