Answer:
9-2i
Step-by-step explanation:
(1 + 2i) * (1 - 4i)
(1*1)-(1*4i)+(2i*1)-(2i)*(4i)
(1)-(4i)+(2i)-(8i^2)
i^2 = -1
1-4i+2i+8
1-2i+8
9-2i
The multiplication and simplification of the complex numbers (1 + 2i) x (1 - 4i) results in 9 - 2i.
Explanation:To multiply and simplify the complex numbers (1 + 2i) and (1 - 4i), we must use the distributive property, just like in normal algebra. We get (1*1) + (1*-4i) + (2i*1) + (2i*-4i), which is 1 - 4i + 2i - 8i². But remember, in complex numbers, i² equals -1, so it simplifies further to 1 - 2i -8(-1), or 1 - 2i + 8, and finally, 9 - 2i which is our final, simplified result.
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Solve the equation for all real values of x. 3tan^2x=3tanx
The equation 3tan²x = 3tanx solved for all real values of x is [tex]x = n\pi[/tex] or [tex]x = \dfrac{\pi + 4n\pi}{4}[/tex], where n is an integer
Solving the equation for all real values of x.
From the question, we have the following parameters that can be used in our computation:
3tan²x = 3tanx
This can be expressed as
3tan²x - 3tanx = 0
Factor out 3tanx
3tanx(tanx - 1) = 0
Expand
3tanx = 0 or tanx - 1 = 0
So, we have
tanx = 0 or tanx = 1
Take the arctan of both sides
x = tan⁻¹(0) or x = tan⁻¹(1)
Evaluate the arctan for all real values of x.
[tex]x = n\pi[/tex] or [tex]x = \dfrac{\pi + 4n\pi}{4}[/tex], where n is an integer
work out the next term of this quadratic sequence
6 9 15 24
Answer:
36
Step-by-step explanation:
6 9 15 24 ...
The sequence goes like this:
+3, +6, +9, +12, +15 (Adding 3 each time)
For example:
6 + 3 = 9 (First +3)
9 + 6 = 15 (Then +6)
15 + 9 = 24 (Then +9)
24 + 12 = 36
The next term of this quadratic sequence will be 36.
What is Quadratic equation?
An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The quadratic sequence is,
⇒ 6, 9, 15, 24
Now,
The first term = 6
The second term = 6 + 3 = 9
The third term = 9 + 6 = 15
The fourth term = 15 + 9 = 24
Thus, The pattern of adding are;
3 , 6 , 9, ..
So, For next term we add 12 in fourth term, we get;
The next term = 24 + 12
= 36
Thus, The next term of this quadratic sequence will be 36.
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An animal pen is in the shape of a triangle. One of the interior angles of the triangle is 40 degrees. The measure of the other interior angles are in the ratio 3 : 5. What are the measures of the other interior angles?
Final answer:
In a triangle, the sum of all interior angles is always 180 degrees. Given the ratio of the other interior angles, we can find their measures.
Explanation:
In a triangle, the sum of all interior angles is always 180 degrees. Given that one of the interior angles is 40 degrees, let's denote the measures of the other two angles as 3x and 5x. The sum of all three angles is 40 + 3x + 5x = 180. Simplifying this equation, we get 8x + 40 = 180. Subtracting 40 from both sides gives us 8x = 140. Dividing both sides by 8, we find x = 17.5.
Now, we can substitute the value of x back into the expressions for the other two angles. So, the first angle is 3x = 3(17.5) = 52.5 degrees, and the second angle is 5x = 5(17.5) = 87.5 degrees.
The results for a survey of 120 students who were selected randomly are as follows 60 students have a cell phone plan with company x. 36 students have a cell phone plan with company y. 24 students do not have a cell phone the total population of students was 380.Based on the data what is the best approximation for the total number of students who have a cell phone plan with company y?
Answer:
114
Step-by-step explanation:
find the solution below
Is (x +1) a factor of f(x) = x^3 + x^2 −4x − 4?
Select the appropriate response:
Yes
or
No
Answer:
Yes
Step-by-step explanation:
( x^3 + x^2) (-4x - 4)
x^2 ( x+1) -4 (x+1)
(x^2 - 4) (x+1)
(x-2) (x+2) (x+1)
X= 2 x=-2 x=-1
Answer:
Yes
Step-by-step explanation:
f(x) = x^3 + x^2 −4x − 4
Factor by grouping taking x^2 out of the first group and -4 out of the second
0 = x^3 + x^2 −4x − 4
x^2(x+1) -4(x+1)
Factor out (x+1)
0=(x+1)(x^2-4)
Now we have the difference of squares
0=(x+1) (x-2)(x+2)
x+1 is a factor
whats the area of a circle if the diameter is 24.26 mm
Answer:
approximately 462.24
Step-by-step explanation:
As the amount of time on homework increased, their grade in class ____________.
Answer:
Increases
Step by Step Explanation:
More time on your homework means more time to cheat/figure the answer out.
Answer:
Improved
Step-by-step explanation:
The more you study or do homework, the more you learn, and the better your grade
Simplify each equation. Tell whether the equation has one, no, or infinite
solutions.
5x + 6 = 2 + 3x
no solutions
one
infinite solutions
10pts will mark brainliest if right
Answer:
one solution
Step-by-step explanation:
5x + 6 = 2 + 3x
Subtract 3x from each side
5x-3x + 6 = 2 + 3x-3x
2x +6 = 2
Subtract 6 from each side
2x+6-6 = 2-6
2x = -4
Divide each side by 2
2x/2 = -4/2
x = -2
There is one solution
Answer:
One solution
Step-by-step explanation:
To solve, we need to isolate the variable, x
5x+6=2+3x
Subtract 2 from both sides
5x+4=3x
Subtract 5x from both sides
4= -2x
Divide both sides by -2
x= -2
There is one solution to this equation, -2
At the beginning of a snowstorm, Tristan had 3 inches of snow on his lawn. The snow then began to fall at a constant rate of 1.5 inches per hour. Assuming no snow was melting, how much snow would Tristan have on his lawn 4 hours after the snow began to fall? How much snow would Tristan have on his lawn after
tt
t hours of snow falling?
Answer:
Step-by-step explanation:
3+1.5*4
3+6
9 inches in total 4 hours from now
Answer:
3 + 1.5(4) = 9
then the second one will be: 3 + 1.5t
Step-by-step explanation:
1.5t is increasing do therefore that is the answer.
Brandon works at a nearby electronics store. He makes a commission of 14% on everything he sells. If he sells a camera for $588.00, how much money does Brandon make in commission?
Answer: cc
Step-by-step explanation:
Answer:
670.32
Step-by-step explanation
Mary bought 3 cartons of milk for $1.06 each. If she paid for the milk with a five-dollar bill, how much money should she get back
Answer:
shed get $1.82 back
Step-by-step explanation:
Answer:
She would get $1.82 back
Step-by-step explanation:
If she bought 3 cartons costing $1.06 each, you would have to multiply $1.06 by 3
$1.06 x 3 = $3.18
Then if she paid with a five dollar bill you have to subtract $3.18 from 5
5 - 3.18 = 1.82
$1.82 is the answer
9=8n what does n=
Please help
Solve the inequality.
8+8(x + 4) >32
The solution is
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form: x > - 1
Step-by-step explanation:
Answer:
x > -1
Step-by-step explanation:
To solve, we must isolate the variable, x
8+8(x + 4) >32
Distribute the 8
8+ 8*x +8*4
8+8x+ 32 >32
Combine like terms
8+32 +8x >32
40 + 8x >32
Subtract 40 from both sides
8x > -8
Divide both sides by 8
x > -1
What is 7 more than five times the number 9 divided by 15?
Answer:
10
Step-by-step explanation:
2) There are 45 dogs and 30 cats at the animal recovery center. Of these animals, there are 16 colored dogs and 8 solid cats. What percentage of the animals are solid colored?
Answer:
32%
Step-by-step explanation:
Total animals: 45 + 30 = 75
Coloured: 16 + 8 = 24
24/75 × 100
32%
Graph f(x) and its inverse, f^-1(x) , in the same coordinate grid.
Answer:
Included in screenshot
1. Lake Turkana is in the Great Rift Valley in northwest Kenya. As part of a study of water quality, the water temperature in the lake was measured at different depths. The data are shown in this scatter plot.
Answer:
a. 26° C
b. 40m
c. Yes
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
a. What was the approximate temperature at a depth of 70 m? At the surface?
26° C
b. At what depth was the temperature a little more than 27°C?
40 m
c. Do the points in the scatter plot show a relationship? Explain your thinking.
Yes, the scatter plot show a relationship between the depth and the temperature of Lake Turkana. It shows a negative correlation between the two variables. The deeper the lake is, the cooler the temperature .
Hope it will find you well.
Emilce pide 5 platos por semana para almorzar en la oficina. El menú ofrece 5 opciones diferentes. De cuantas maneras puede realizar el pedido de la semana si quiere repartir los platos?
Answer:
120 different ways
Step-by-step explanation:
For the first lunch, Emilce has 5 options to choose,
In the second lunch, now she has only 4 options, as one was already chosen.
Then, in the third lunch, she has 3 options.
In the fourth lunch, she has 2 options.
In the last lunch, she has just 1 option.
So, the number of different ways she can order her lunches in the week is:
5 * 4 * 3 * 2 * 1 = 120
She can order in 120 different ways.
Judy spent 1 hour and 15 minutes less than Sandy exercising last week Sandy Sprint 50 minutes less than Mary who's been 3 hours at the gym how long did Judy spend exercising
Answer:
Judy spent 55 min at the gym.
Step-by-step explanation:
From the three people that are listed in the problem Mary is the only one we know the actual time she was at the gym which is 3 h. Sandy on the other hand spent 50 minutes less sprinting than Mary, so we have:
Sandy = Mary - 50 minutes
Sandy = 3h - 50 minutes
Sandy = 3*60 - 50
Sandy = 180 - 50 = 130 minutes
Judy spent 1h and 15 min less than Sandy exercising so we have:
Judy = Sandy - 1h 15min
Judy = 130 min - (60 min + 15 min)
Judy = 130 min - 75 min = 55 min
Judy spent 55 min at the gym.
Vanessa draws one side of equilateral
△ABC on the coordinate plane at
points A(-2, 1) and B(4,1). What are
the two possible coordinates of vertex
C? Round to the nearest tenth.
Answer:
According to my calculation, the two possible coordinates of vertex C, is [tex](1,\sqrt{27}) and (1,-\sqrt{27})[/tex].
Answer:
According to my calculation, the two possible coordinates of vertex C, is .
Step-by-step explanation:
Luisa Díaz drove her vehicle about 7,200 miles last year. Her fixed costs totaled $1,058.40 and her variable costs were $1965.60 how much did it cost per mile
Answer:
$0.42
Step-by-step explanation:
Given:
Luisa Díaz drove her vehicle about 7,200 miles last year.
Total fixed cost = $1,058.40
Total variable cost = $1965.60
Question asked:
How much did it cost per mile ?
Solution:
Total cost of driving 7200 miles = Total fixed cost + Total variable cost
= $1,058.40 + $1965.60
= $3024
By unitary method:
Cost of driving 7200 miles = $3024
Cost of driving 1 mile = $3024 [tex]\div[/tex] 7200
= $0.42
Thus, cost of driving per mile is $0.42
What is the factored form of this expression? x2 + 9x + 16
Answer:
this problem is not factorable.
Step-by-step explanation:
Final answer:
The factored form of the quadratic expression x^2 + 9x + 16 is (x + 7)(x + 2), found by identifying two numbers that multiply to 16 and add up to 9.
Explanation:
To find the factored form of the expression x2 + 9x + 16, we are looking for two binomials that when multiplied together will yield the original quadratic expression. Since the coefficient of x2 is 1, we only need to find two numbers that add up to the coefficient of x (which is 9) and multiply together to get the constant term (which is 16).
To factor the quadratic expression, we look for two numbers that multiply to 16 and add to 9. These numbers are 7 and 2. Therefore, the factored form of the expression is (x + 7)(x + 2).
In this diagram, like segment AD is tangent and line segment AC is secant. If AB = 6 and BC = 18, what is the length of line segment AD?
9514 1404 393
Answer:
12
Step-by-step explanation:
The applicable relationship here is ...
AD² = AB·AC
AD = √(AB·(AB +BC)) = √(6·(6+18)) = √144
AD = 12
Find the area of the shaded segment. Round your answer to the nearest hundredth.
Answer:
2.57
Step-by-step explanation:
1/4×22/7×3×3=7.07
1/2×9=4.5
7.07-4.5=2.57
What type of angles are< 1 and <5?
vertical
supplementary
corresponding
complementary
Answer:
The type of angles of <1 and <5 are corresponding angles
Step-by-step explanation:
The daily high temperatures in Philadelphia for the first 15 days in February is normally distributed with a standard deviation of 2.5°. If it was 37° on Valentine's Day with a z-score of 2.4, the mean temperature is _________°.Immersive Reader
Answer:
The mean temperature is 31.
Step-by-step explanation:
The formula for the z-sore is
x - mean
z = ----------------------
(std dev)
In this case let's multiply both sides by (std dev), obtaining:
x - mean = z*(std dev).
Solving for (mean), we get
mean = x - z*(std dev)
Substituing 37 for x, 2.4 for z and 2.5 for (std dev), we get:
mean = 37 - (2.4)(2.5) = 31
The mean temperature is 31.
Final answer:
To find the mean temperature with the given z-score and standard deviation, the z-score formula is used. After calculation, the mean temperature in Philadelphia for the first 15 days of February is determined to be 31°.
Explanation:
The question is asking us to find the mean temperature in Philadelphia for the first 15 days in February, given that the daily high temperatures are normally distributed with a standard deviation of 2.5° and that on Valentine's Day (February 14th), the temperature was 37° with a z-score of 2.4. To solve for the mean temperature, we can use the z-score formula:
Z = (X - μ) / σ
Where:
Z is the z-score,
X is the value in the dataset,
μ is the mean, and
σ is the standard deviation.
We know Z = 2.4, X = 37°, and σ = 2.5°. Plugging these values into the z-score formula, we can solve for the mean (μ).
2.4 = (37 - μ) / 2.5
Multiplying both sides by 2.5, we get:
2.4 x 2.5 = 37 - μ
6 = 37 - μ
μ = 37 - 6
μ = 31°
Therefore, the mean temperature in Philadelphia for the first 15 days in February is 31°.
Given the following diagram, find the length of CB.
Find a value for m and n to make a true statement.
a) mx^2 - 36 = (3x + 6)(3x - 6)
b) (mx + ny)^2 = 4x^2 + 12xy + 9y^2
Answer:
Correct answer: a) m = 9 ; b) m = 2 and n = 3
Step-by-step explanation:
Given:
a) m x² - 36 = (3 x + 6) (3 x - 6) ⇒ m = ?
b) (m x + n y)² = 4 x² + 12 x y + 9 y² ⇒ m, n = ?
a) m x² - 36 (3 x + 6) (3 x - 6)
The right side of the equation is the difference of the square, so we will present the left side in the same way:
(√m x)² - 6² = (3 x + 6) (3 x - 6)
(√m x + 6) (√m x - 6) = (3 x + 6) (3 x - 6)
√m = 3 /² when we square both sides of the equation we get:
m = 9
b)
(m x + n y)² = 4 x² + 12 x y + 9 y²
The left side of the equation is the complete square of the binomial, so we will present the right side in the same way:
(m x + n y)² = (2 x)² + 2 · 2 x · 3 y + (3 y)² = (2 x + 3 y)²
(m x + n y)² = (2 x + 3 y)² ⇒
m = 2 and n = 3
God is with you!!!
For part (a), m must be 9 to make the equation true. For part (b), m can be 2 or -2, and n can be 3 or -3 to satisfy the equation.
Explanation:To find values for m and n to make the statements true, we must compare coefficients or recognize patterns in the given equations.
Part (a)
We have the equation mx^2 - 36 = (3x + 6)(3x - 6). We can expand the right side to get 9x^2 - 36. To make this equation true, we need the coefficient of x^2 on the left to be equal to the coefficient on the right, which is 9. Therefore, m must be 9 for the equation to be true.
Part (b)
We have (mx + ny)^2 = 4x^2 + 12xy + 9y^2. Expanding the left side, we get m^2x^2 + 2mnxy + n^2y^2. To equate it to the right side, we need m^2 = 4 and n^2 = 9. This gives us two possibilities each for m and n: m can be 2 or -2 and n can be 3 or -3.
plz can any1 help me out on this plz
15 points
Answer:
7/22
Step-by-step explanation:
Drama or Sports:
85 + 200 - 60
225
330 - 225 = 105
Probability: 105/330
7/22
The points (2,10) and (minus2,minus10) are plotted on the coordinate plane using the equation yequalsatimesx. How can you use the coordinates to find the value of a? Select the correct answer below, and fill in the answer box to complete your choice. (Type a whole number.) A. The value of a is the number that the y-values are multiplied by to get to the corresponding x-values. So, aequals nothing. B. The value of a is the absolute value of the difference of the y-values. So, aequals nothing. C. The value of a is the number that the x-values are multiplied by to get to the corresponding y-values. So, aequals nothing. D. The value of a is the absolute value of the difference of the x-values. So, aequals nothing.
Answer: The value of a is the number that the x-values are multiplied by to get to the corresponding y-values. So, a equals 5
We have
y=ax
so a is clearly the number we multiply by the x values.
Substituting either points (2,10) and (-2,-10),
10 = a(2)
a = 10/2 = 5