show all work to multiply 3 plus the square root of negative 16 times 6 minus the square root of negative 64
Answers
Answer:
\(\Huge \boxed{3+16i}\)
\(\rule[225]{225}{2}\)
Step-by-step explanation:
\(3+\sqrt{-16} * 6-\sqrt{-64}\)
Using imaginary number rule : \(\sqrt{-n} =\sqrt{n} *i\)
Where \(n\) is a positive integer.
\(3+\sqrt{16} *i* 6-\sqrt{64}*i\)
\(3+4i* 6-8i\)
Multiplying.
\(3+24i-8i\)
Combining like terms.
\(3+16i\)
\(\rule[225]{225}{2}\)
Answer:
3 + 16i
Step-by-step explanation:
3 + √-16 * 6 - √-64
= √-16 * 6 = 24i; √-16 * 6; √-16 = 4i
= 4 * 6i multiply the numbers 4 * 6 = 24
= 24 i
√-64 = 8i; √64 apply a radical rule
= √-1 √64
= √64 i; √64 = 8
= 8i
= 3 + 24i - 8i
= 3 + 16i
Related Questions
A straight line L is perpendicular to line 3x-2y+4=0. The area of triangle formed by the line L and coordinate axes is 27 sq.unit find equation of line L
Answers
3x-2y+4=0
3x+4=2y
( divide by 2)
3/2x+2=y
Now let’s find the perpendicular line to y=3/2x+2
You just have to get the opposite of the slope 3/2 which is -2/3
If you multiply 3/2 by -2/3 you will get -1 this proofs it really is the perpendicular slope your are looking for
Hence
The equation of line L is
y=-2/3+2
Which equation represents a line which is parallel to the line y= -7/6x-3
PLEASE HELP!!!!!
Answers
Answer: -6/7
Step-by-step explanation:
Think About the Process A jar contains only pennies, nickels, dimes, and quarters. There are 15 pennies, 18 dimes, and 21 quarters. The rest of the coins are nickels. There are 83 coins in all. How many of the coins are not nickels? If n represents the number of nickels in the jar, what equation could you use to find n?
Answers
Answer:
Comencemos por encontrar el número total de monedas en el frasco. Sabemos que hay 15 centavos, 18 monedas de diez centavos y 21 cuartos, así que:
Número total de monedas = número de centavos + número de monedas de diez centavos + número de cuartos
Número total de monedas = 15 + 18 + 21
Número total de monedas =
También sabemos que hay 83 monedas en total, por lo que el número de monedas de cinco centavos se puede encontrar restando el número de centavos, monedas de diez centavos y cuartos del total:
Número de monedas = número total de monedas - número de centavos - número de monedas de diez centavos - número de cuartos
Número de níquel = 83 - 15 - 18 - 21
Número de níqueles = 29
Por lo tanto, hay 29 monedas de cinco centavos en el frasco.
Para encontrar el número de monedas que no son níqueles, podemos restar el número de monedas del total:
Número de monedas sin níquel = número total de monedas - número de monedas
Número de monedas sin níquel = 83 - 29
Número de monedas sin níquel = 54
Así que hay 54 monedas en el frasco que no son monedas de cinco centavos.
Podemos usar la ecuación "n = número total de monedas - número de centavos - número de monedas de diez centavos - número de cuartos" para encontrar el número de monedas de cinco centavos en el frasco, donde n representa el número de monedas de cinco centavos. Sustituyendo los valores dados, obtenemos:
n = 83 - 15 - 18 - 21
n = 29
Por lo tanto, la ecuación es n = 29.
Step-by-step explanation:
espero te ayude en algo
which of the following corresponds to the predictor variable in simple linear regression?
Answers
In simple linear regression, the predictor variable is the independent variable, which is used to predict the value of the dependent variable. It is also referred to as the explanatory variable, as it is used to explain the variability in the response variable.
For example, in a study that examines the relationship between the hours studied and exam scores, the predictor variable is the number of hours studied, and the dependent variable is the exam score.
The predictor variable is plotted on the x-axis, while the dependent variable is plotted on the y-axis in a scatter plot. The relationship between the predictor and the dependent variable is represented by a straight line, which is determined by the regression equation.
The slope of the line represents the change in the dependent variable for each unit change in the predictor variable.
In summary, the predictor variable is the variable that is used to predict or explain the changes in the dependent variable in simple linear regression.
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X^2 - x=2
Solve for x
Answers
Answer:
To solve for x, you can start by moving the constant 2 to the other side of the equation by adding x to both sides:
x^2 - x = 2
x^2 - x + (1/4) = 2 + (1/4)
(x - 1/2)^2 = 9/4
x - 1/2 = +- (3/2)
x = -1/2 or x = 2
So the solutions for x are -1/2 and 2.
How can you find the number of 2/3’s in 6?
Answers
4
Step-by-step explanation:
The number of 2/3's in 6 can be found by dividing 6 by 3 and then multiplying the result by 2. The answer is 4.
IL GIVE BRAINLY IF YOU CAN HELP ME ON THESE 2
Answers
Answer:
THE answers to both questions are A
Step-by-step explanation:
Answer:
a for both
Step-by-step explanation:
just move point c on the graph where it tells u to. a translation only affects location
Pls help find area of the figure
Answers
The area of the octagon with a radius of 10 yds is 482.84 square yards.
How to calculate area?To find the area of an octagon with a radius of 10 yards, use the formula for the area of a regular octagon:
Area = 2 × (1 + √2) × radius²
Given that the radius is 10 yards, substitute the value into the formula:
Area = 2 × (1 + √2) × 10²
Simplifying further:
Area = 2 × (1 + √2) × 100
Area = 200 × (1 + √2)
Using a calculator, approximate the value of (1 + √2) to be approximately 2.4142:
Area ≈ 200 × 2.4142
Area ≈ 482.84 square yards
Therefore, the approximate area of the octagon with a radius of 10 yards is 482.84 square yards.
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PLEASE HELP I keep trying to figure it out
Answers
Answer:
6
Step-by-step explanation:
Yyyyyyyy
Y varies inversely with x, if y = -12 when x = 8 what is x when y = -9
Answers
Answer:
either 5 or 11
Step-by-step explanation:
(8, -12)
(5, -9) or (11, -9)
If y varies consistently with x then it would copy what happens, in a manner of speaking.
In this case, y increases by three, x would either add 3 or subtract 3
I am not completely sure on this.
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answers
Answer:
It is too garlicky.
Step-by-step explanation:
lol, uhm, this is a little bit of a strange question ngl, but I guess it's testing you on measurements and units, right?
Well, 12 gloves of garlic for every 900 mL of sauce in comparison to 8 cloves of garlic for every 500 mL of sauce is quite a difference to be honest, might even be too much in her opinion. 8 cloves for every 500 mL is more than 12 cloves for every 900 mL, so I'd say she'll think it's too garlicy.
I apologize, in advance, if I am incorrect.
The first 300 natural numbers are written in an ascending order of sequence. Now all the numbers at the odd places of this sequence are removed and, thus a new sequence is formed. From this new sequence, all the numbers at odd places are removed once again. This process continues till only one number remains at the end. What is this number?
Answers
The final number remaining in this sequence is the number 2.
We start with the first 300 natural numbers written in ascending order. We remove the numbers at odd places, which means we remove all the numbers at positions 1, 3, 5, and so on.
After the first removal, we are left with the numbers at even positions: 2, 4, 6, and so on.
Now, we repeat the process and remove the numbers at odd positions again. We remove numbers at positions 1, 3, 5, and so on from the remaining sequence.
After the second removal, we are left with the numbers at even positions again: 4, 8, 12, and so on.
We can observe that in each removal, the sequence reduces to half its size, and we are left with the numbers at even positions.
Continuing this process, we will eventually reach a point where we have only one number left.
Since we start with 300 numbers, after the first removal, we have 150 numbers. After the second removal, we have 75 numbers. After the third removal, we have 38 numbers. After the fourth removal, we have 19 numbers. After the fifth removal, we have 10 numbers. After the sixth removal, we have 5 numbers. After the seventh removal, we have 3 numbers. After the eighth removal, we have 2 numbers. Finally, after the ninth and last removal, we are left with a single number.
Therefore, the final number remaining in this sequence is the number 2.
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formula for the geometric sequence 1/2, 1, 2, 4
Answers
Answer:
\(a_{n}\) = \(\frac{1}{2}\) \((2)^{n-1}\)
Step-by-step explanation:
the nth term of a geometric sequence is
\(a_{n}\) = a₁ \((r)^{n-1}\)
where a₁ is the first term and r the common ratio
here a₁ = \(\frac{1}{2}\) and r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{1}{\frac{1}{2} }\) = 2 , then
\(a_{n}\) = \(\frac{1}{2}\) \((2)^{n-1}\)
Answer:
an = 2n-2
Step-by-step explanation:
correct answer got it right on test
whats the value of x?
Answers
Answer:
x=8.8125
Step-by-step explanation:
Keanu bought a new laptop computer and paid a
discount price that was 20% less than the $1,000 list
price. He also paid tax on the laptop equal to 6% of the
discount price. What is the total amount Keanu paid
for the laptop computer?
Answers
Answer:
$848
20% of 1000 = 200
1000 - 200 = 800
6% of 800 = 48
800 + 48 = 848
You have 200 feet of fencing to build a rectangular dog pen. If you want the pen to have the maximum possible area. What should the dimensions of the pen be? Show your work.
Answers
Answer:
Each side would be 50 ft
Step-by-step explanation:
200/4=50
50*50=2,500
Techinally this is a square so if they really want it to be a "rectangle" it would be 51 and 49 and the areas would be 2,499...but the answer should be 50
An ellipse has foci located at (2,4) and (2,16) and vertices located at (2,0) and (2,20) this ellipse is vertical
Answers
Answer:
The equation of the ellipse is \(\frac{(x-2)^{2}}{8^{2}}+\frac{(y-10)^{2}}{10^{2}} = 1\).
Step-by-step explanation:
The statement is incomplete, the most probable outcome may be the equation of the ellipse based on information given.
The equation of an ellipse whose major axis is vertical and is centered at a point different from origin is defined by:
\(\frac{(x-h)^{2}}{b^{2}} + \frac{(y-h)^{2}}{a^{2}} = 1\) (1)
Where:
\((h,k)\) - Coordinates of the center of the ellipse.
\((x,y)\) - Coordinates of a point in the line of the ellipse.
\(a\) - Length of the major semiaxis.
\(b\) - Length of the minor semiaxis.
The coordinates of the center of the ellipse is midpoint of the segment between vertices, which are collinear with foci:
\((h,k) = \frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2}(x,y)\) (1)
Where \(V_{1} (x,y)\) and \(V_{2} (x,y)\) are the coordinates of the vertices.
If we know that \(V_{1} (x,y) = (2,0)\) and \(V_{2} (x,y) = (2, 20)\), then the coordinates of the center ellipse are:
\((h,k) = (2, 10)\)
The length of the semimajor axis can be determined by using the following vectorial expression, which is equivalent to the Pythagorean Theorem:
\(a = \sqrt{[(h,k)-V_{1}(x,y)]\,\bullet\,[(h,k)-V_{1}(x,y)]}\) (2)
If we know that \((h,k) = (2, 10)\) and \(V_{1} (x,y) = (2,0)\), then the length of the semimajor axis is:
\(a = \sqrt{(2-2)^{2}+(10-0)^{2}}\)
\(a = 10\)
And the length of the minor semiaxis is found by means of this Pythagorean identity:
\(b = \sqrt{a^{2}-c^{2}}\) (3)
Where \(c\) is the length between the center and any of the foci. This distance can be found by using this vectorial formula:
\(c = \sqrt{[(h,k)-F_{1}(x,y)]\,\bullet\,[(h,k)-F_{1}(x,y)]}\) (4)
If we know that \((h,k) = (2, 10)\) and \(F_{1} (x,y) = (2,4)\), then the length between the center and any of the foci is:
\(c = \sqrt{(2-2)^{2}+(10-4)^{2}}\)
\(c = 6\)
And the length of the minor semiaxis is:
\(b = \sqrt{10^{2}-6^{2}}\)
\(b = 8\)
FInally, the equation of the ellipse is \(\frac{(x-2)^{2}}{8^{2}}+\frac{(y-10)^{2}}{10^{2}} = 1\).
what value does stage theories of development have
Answers
Answer:
Even if human development is continuous, there is some value in stage theories of development. A stage theory of development allows experts to examine the developmental progress of individuals and establish a basis for developmental changes. This can help identify developmental issues earlier. Stage theories can also help researchers who are examining physical development examine discrete changes in the brain that allow certain developmental milestones to be reached. Finally, stage theories can give one a sense of where an individual is developmentally, and can prepare the person for changes that may occur during their lifetime.
!!!WILL MARK BRAINLIEST IF ALL ARE ANWSERED!!! please provide short explanations
Answers
Answer:
20= 20
21. 10
22. 1.8
23. 4.4
24. 32
25. 7/9
If a=6, b=12,and c=4, then what does 2ab-c^2 equal?
Answer: 2(6)(12)-4^2 = 128
What is the prime factorization of 100,000?
Answer: 2^5× 5^5
Solve for x. 5.8 = 4x+0.2
Answer: x= 1.4
Find the area of this shape.
Answer: Area = 1.21
What is the lateral surface area of this rectangular prism?
Answer: 208 in^2
5/9 + 1/3 × 1/3 = 0.66666666666 = 2/3
Step-by-step explanation:
The prime factorization of 100,000 is 2^5 × 5^5. Since it has a total of 10 prime factors, 100,000 is a composite number.
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5.8-0.2=4+0.2−0.2
5.6 = 4x
5.6/4 = 4x/4
x= 1.4
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Square sides are equal..
A=a^2=1.1^2≈1.21
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The lateral surface area of a rectangular prism can be calculated by finding the sum of all the lateral faces of the prism, i.e. the total area excluding the area of the bases. The formula to find the surface area of a rectangular prism is given as, Lateral surface area of a rectangular prism = 2(l + b) h square units.
When a prism has its bases facing up and down, the lateral area is the area of the vertical faces. (For a rectangular prism, any pair of opposite faces can be bases.) The lateral area of a right prism can be calculated by multiplying the perimeter of the base by the height of the prism.
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joe smith scored 37 of his teams 100 points in a game. What percentage of points did he score?
Answers
Answer:
37%
Step-by-step explanation:
37/100
Write the equation of the line in slope intercept form that passes through the point (4,7) and is parallel to y = -7x + 8.
Answers
Answer:
y= -7x + 35
Step-by-step explanation:
(y - 7) = -7(x - 4)
y-7 = -7x + 28
y = -7x + 35
What does 64 squared with an exponent of -3 equal?
Answers
Answer:
1.4551915e-11 (e usually means amount of zeros after the number)
Step-by-step explanation:
Help i dont understand this
Answers
Answer:
b
Step-by-step explanation:
Fritz can build a bookcase in 8 hours and Holly can build the same bookcase in 10 hours. After working together for 3 hours, Fritz leaves how long will it take holly to finish the bookcase by herself?
Answers
Holy will take 13/5 or 2.6 hours to finish the bookcase.
What is relation between time and work?The relation between time and work is
Work Done = Time Taken × Rate of Work ·
or, Rate of Work = 1 / Time Taken ·
or, Time Taken = 1 / Rate of Work ·
Now it is given that,
Time taken by Fritz to build a bookcase = 8 hours
So, Bookcase build by Fritz in 1 hour = 1/8
Similarly,
Time taken by Holly to build a bookcase = 10 hours
So, Bookcase build by Holly in 1 hour = 1/10
So, bookcase build in 3 hours
Fritz = 3/8
Holly = 3/10
Total bookcase build in 3 hours = 3/8 + 3/10 = 27/40
So. remaining work = 1 - 27/40 = 13/40
Thus, Time taken by Fritz to complete the bookcase = 8 * (13/40) hours
= 13/5 or 2.6 hours
Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.
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a recipe needs 1/4 tablespoon salt. this same recipe is made 5 time,es how much total is needed?
Answers
Answer:
1 and 1/4
Step-by-step explanation:
If you multiply 1/4 five times, you will get your answer
Solve for x be sure to show your work.
Answers
Answer:
−37x−28 I am not fully sure
Step-by-step explanation:
What is the percent increase when 7,200 increases by 1,800? help asap
Answers
Answer:
1,800/7,200 as a percentage is 1/4 which is 25%.
Answer: 25%.
Step-by-step explanation:
because 1,800/7,200 as a simplyfly fraction
will be 1/4 and if you make it in persant it will be 25%
Hope this helps :)
2/7x +2y=14 in slope intercept form
Answers
Answer:
Slope intercept form is -1/7x + 7
!Hope this helps!
Step-by-step explanation:
Solve Using Substitution
-9x + 6y = 18
y = -6
Answers
Answer:
the answer should be x = -6
Step-by-step explanation:
-9x + 6y = 18
-9x + 6(-6) = 18
-9x - 36 = 18
-9x - 36 + 36 = 18 + 36
-9x = 54
-9x ÷ -9 = 54 ÷ -9
x = -6
The length of a rectangle is 4 ft longer than its width.
If the perimeter of the rectangle is 40 ft, find its area.
Answers
Answer:
96
Step-by-step explanation:
40=4x+8
32=4x
x=8
other side x+4 is 12
area is 12×8
96