Answer:
[tex]x=\frac{2(1\pm i\sqrt{2} )}{3}[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]√-1 is imaginary number iStep-by-step explanation:
Step 1: Define
3x² - 4x + 4 = 0
a = 3
b = -4
c = 4
Step 2: Find roots
Substitute: [tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4(3)(4)} }{2(3)}[/tex]Simplify: [tex]x=\frac{4\pm\sqrt{(-4)^2-4(3)(4)} }{2(3)}[/tex]Evaluate: [tex]x=\frac{4\pm\sqrt{16-4(3)(4)} }{2(3)}[/tex]Multiply: [tex]x=\frac{4\pm\sqrt{16-48} }{6}[/tex]Subtract: [tex]x=\frac{4\pm\sqrt{-32} }{6}[/tex]Factor: [tex]x=\frac{4\pm\sqrt{-1} \sqrt{32} }{6}[/tex]Simplify: [tex]x=\frac{4\pm4i\sqrt{2} }{6}[/tex]Factor: [tex]x=\frac{4(1\pm i\sqrt{2} )}{6}[/tex]Simplify: [tex]x=\frac{2(1\pm i\sqrt{2} )}{3}[/tex]Please explain as well how to do it. Thanks!
Answer:
The answer is B.
Step-by-step explanation:
Please refer to the attachment (ignore the horrible drawing, thank you).
Let the distance from P to T be red. The length of the red distance is x radians.
T’ is π-x. Thus, it is the red distance subtracted from the purple distance.
So, T’ is the reflection of T across the y-axis.
Therefore, we can simply multiply the x-coordinate of T to get T’.
T is (3/5, 4/5)
Then T’ must be (-3/5, 4/5).
Hence, our answer is B.
What is the Magnitude of 6.8
Santiago Chile (AP)
♥plz give me brain list it would help a lot! ♥
♥ お力になれて、嬉しいです ！♥What is the maximum for: P = 3x + 2y
Answer:
The maximum value of the function P= 3x + 2y
There is an accompanying graph in this problem. In the graph, there are 4 points to consider. I'll just assign letters on each point.
Point O is found in x = 0 ; y = 0 or (0,0)
Point A is found in x = 8 ; y = 0 or (8,0)
Point B is found in x = 6 ; y = 5 or (6,5)
Point C is found in x = 0 ; y = 8 or (0,8)
We will substitute x and y in the equation by its values per point.
Point A = 3(8) + 2(0) = 24 + 0 = 24
Point B = 3(6) + 2(5) = 18 + 10 = 28
Point C = 3(0) + 2(8) = 0 + 16 = 16
What sample size is needed to give a margin of error within +-6 in estimating a population mean with 95% confidence, assuming a previous sample had s=20.
Round your answer up to the nearest integer. sample size = _______.
Answer:
43
Step-by-step explanation:
The formula for Margin of Error =
Margin of Error = z × standard deviation/√n
Margin of Error= ± 6
z = z score of 95% Confidence Interval is 1.96
s = 20
n = sample size
±6 = 1.96 × 20/√n
Cross Multiply
±6 × √n = 1.96 × 20
±6 × √n = 39.2
Divide both sides by ±7
√n = 39.2/±6
√n = 6.5333333333
Square both sides
n = 6.5333333333²
n= 42.684444444
Rounding up to the nearest integer = 43
what is the answer for
3x÷2=6
Answer:
x = 4
Step-by-step explanation:
3x÷2=6
Multiply both sides by 2.
3x = 12
Divide by 3.
x = 4
Answer:
x=4
Step-by-step explanation:
To solve [tex]\frac{3x}{2}[/tex]=6 you need to isolate the variable. To do this you need to do the opposite operation of all of the constants.
First, multiply both sides by 2,
[tex]\frac{3x}{2}[/tex]*2=6*2
3x=12
Then divide both sides by 3,
3x/3=12/3
x=4
ABC is similar to XYZ. The lengths of two sides of each triangle are given in the figure. Find the length of side x.
Answer:
x=7/3
Step-by-step explanation:
AB/XY=BC/YZ
The length of {x} is equivalent to 7/3 units.
What is scale factor? How it is used in Dilating sides?Scale factor tells us by how much one quantity is greater than the other. It is denoted by K. Mathematically -
K = a/b.
Rewriting, we get -
a = Kb
If a side length [a] of any 2 - D figure is dilated by a scale factor of [k], then the length of new side will be [Ka].
Given is that ABC is similar to XYZ.
Since, the two triangles are similar, than their corresponding sides will be proportional to each other. This means that the ratio of corresponding sides will be equal. Mathematically -
BC/YZ = AB/XY = AC/YZ = K [scale factor]
We can write -
8/(2[tex]\frac{2}{3}[/tex]) = 7/x
8/(8/3) = 7/x
8 x 3/8 = 7/x
3 = 7/x
x = 7/3
Therefore, the length of {x} is equivalent to 7/3 units.
To solve more questions on dilation, visit the link below-
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True or false : dilations always have the same scale factor as the original shape
Answer:
Step-by-step explanation:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. ... After a dilation, the pre-image and image have the same shape but not the same size.
Answer:
I would say False
Step-by-step explanation:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. After a dilation, the preimage and image have the same shape but not the same size.
Hope this helps.
DJ has 16 movies, and Three-eighths of them are comedies. How many movies are comedies?
Answer:
16 * 3/8 = 6
6 movies are comedies
Answer: 6 movies are comedies.
Step-by-step explanation:
First expression three-eighths as a fraction then multiply it by the number of movies that DJ has in total.
three-eights = 3/8
3/8 * 16 = 48/8 = 6
3. What are all the real and complex solutions of x3 + 2x2 + 3x + 6 = 0? If necessary, round to the nearest tenth.
A. -1.5, 0.3 + 1.9i, 0.3 -1.9i
B. -2, √3, -√3, i√3
C. -2, i√3, -i√3
D. -1.5, 0.3 + i√1.9, 0.3 – √1.9
Answer:
it is C
Step-by-step explanation:
At a certain school,5/9 of the students are boys. Today, 2/3 of the boys brought their lunch. What fraction of the students are boys who brought their lunch
The fraction of the students are boys who brought their lunch is 5/6.
It is required to find the fraction of the students are boys who brought their lunch.
What is fraction?A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.
Given:
At a certain school, students are boys =5/9
students are boys brought their lunch=2/3
According to given question we have,
Divide 5/9 by 2/3
[tex]\frac{5/9}{2/3} \\\\\frac{5}{6}[/tex]
Therefore, the fraction of the students are boys who brought their lunch is 5/6.
Learn more details about fraction here:
https://brainly.com/question/10354322
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A pyramid has a square base with an area of 169 ft2. What is the perimeter of the base of the pyramid? A pyramid has a square base with an area of 169 ft2. What is the perimeter of the base of the pyramid?
Answer:
52 ft
Step-by-step explanation:
Given that:
We have an pyramid with square base.
Area of base of the square pyramid = 169 [tex]ft^2[/tex]
To find:
Perimeter of the base of pyramid = ?
Solution:
First of all, let us have a look at the formula of area of a square shape.
[tex]Area = Side \times Side[/tex]
Let the side be equal to [tex]a[/tex] ft.
Putting the given values in the formula:
[tex]169 = a^2\\\Rightarrow a =\sqrt{169}\\\Rightarrow \bold{a = 13\ ft}[/tex]
Now, let us have a look at the formula for perimeter of square.
Perimeter of a square shape = 4 [tex]\times[/tex] Side
Perimeter = [tex]4\times 13 = \bold{52\ ft}[/tex]
I said SAS but am not sure because the base could be two equal sides as well so could someone help me out?
Answer: C) SAS is correct
Check out the diagram below.
We're given BA = BC as shown in red.
The congruent angles are shown in blue. The larger angle is bisected into smaller equal halves.
The red segments are congruent by the reflexive property.
The angles mentioned are between the sides mentioned, so that's why we can use SAS.
Suppose babies born in a large hospital have a mean weight of 3685 grams, and a variance of 330,625. If 113 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by greater than 50 grams? Round your answer to four decimal places.
its not greater than 50 grams. and the answer rounder to the four decimal places is 32.6106
PLSSSSSSSSSSSSSS HELPPPP MEEEEEEE! ANSWER MY OTHER QUESTION!!!!
Answer:
Step-by-step explanation:
huh??
the length of a rectangle is increased by 15% while its perpendicular height is decreased by 15%. determine, if any, the percentage change in its area.
No change in area if sides of rectangle are equal.
Hope this helps.
Suppose a car that sells for $40,000 depreciates 10% per year. How many
years would it take for the car to have a value less than $25,000?
Answer:
It would take 5 years for the car to have a value of less than $25,000
Step-by-step explanation:
Exponential Decaying Model
The exponential function is often used to model natural decaying processes, where the change is proportional to the actual quantity.
We have the initial value of a car is $40,000. Each year it depreciates by 10%.
Thus the first year its value is 90% of the initial value:
V1 = 90 * $40,000 / 100 = $36,000
By the second year its value is 90% of $36,000:
V2 = 90 * $36,000 / 100 = $32,400
Note the value for a year n is the original value multiplied by 90% (or 0.9) to the power of n:
[tex]Vn = $40,000 \cdot 0.9^n[/tex]
To find the number of years needed to have a value of less than $25,000, we solve the equation:
[tex]40,000 \cdot 0.9^n = 25,000[/tex]
Dividing by 40,000:
[tex]0.9^n = 25,000/40,000 = 0.625[/tex]
Taking logarithms:
[tex]n\log 0.9=\log 0.625[/tex]
[tex]n=\log 0.625 / \log 0.9[/tex]
n =4.5
We'll round up to n = 5
It would take 5 years for the car to have a value of less than $25,000
Find the value of x that will make a and b parallel 5x+9 and 3x+11
Answer:
Step-by-step explanation:
5x + 9 = 3x + 11 ( Alternate angles )
5x - 3x = 11 - 9
2x = 2
x = 2/2
x = 1
Hope this helps
plz mark as brainliest!!!!!
A plane took off at a 15° angle to the ground and flew in Sydney’s direction. She is standing at a point 25 miles from the point where the plane took off. If the plane has traveled 20 miles in the air, about how far is Sydney from the airplane? Round your answer to the nearest whole number.
Answer:
8 mi
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
I just did it on edge and got it right.
The graph of a proportional relationship will always be a straight line that passes through the origin. Why?
Answer:
Being proportional between two entities, refers to the 'Constant of Proportionality' that would be fixed between them which establishes a relationship between them when multiplied or divided.
If we considered it on a graph, the 'Constant Of Proportionality' may take any real values between the coordinate pairs x and y [x,y]. As even 0 is a real number, it will surely be a constant of proportionality when multiplied since its product would result in itself (0). Hence, both x and y turns 0.
As the coordinates of the origin are always (0,0), the graph (Or the slope) would surely pass through the origin.
Example :
If we consider a graph such that x=y.
And if we multiply or divide any real number (a) between them.
ax=ay
As a is a variable, and can take the value of 0, the graph can pass through the origin as x and y nullify becoming the coordinates of the origin.
Explain to me in words how you would find the slope of this line
Answer:
Step-by-step explanation:
go from one point to the other. From the left point to the right point you are running across (to the right) three times. Then you are ¨rising¨ (going down) once. going to the right is positive. If you are going down its negative. Vise versa. The formula is Rise/Run. your answer would be -1/3. the one is negative because it went down.Then divide it and you have -0.333. I hope I helped!
Help please !!!!! Thanks
Answer:
7) y = -2
8) x = 4
Step-by-step explanation:
Any straight horizontal/vertical line you find will be x= or y=. The vertical lines are always x= because they only touch the x axis. It's the opposite for horizontal lines. For example, on number 7, the line touches -2 on the y axis. That's why it's "y=-2". Same goes for 8. the line only touches 4.
I hope this helped and wasn't confusing!
Please help me solve for all the numbers
Answer: 10,8,5 are all right angles (90 degrees) 7,6,9,2 are all acute angles and are 42 degrees
1 and 3 are obtuse angles and they are 117 degrees.
Step-by-step explanation:
6 x41=?????????????????
Answer:
the answer is 246
hope this helps
Plz i need an accurate answer help me plz. Choices -
-6 or 6
Answer:
6/2 or it can be 3 and that one will be with the one that says x=1 and 7 will be the answer for the one that says x=5 or it can be 14/2
Step-by-step explanation:
I hope this is what you mean
HELPPP ME PLEASSSEE :(
I am pretty sure the answer is d.
Answer:definitely a trinomial expression.
Step-by-step explanation:
Since it has 3, it’s a trinomial.
Please Note: IMAGE BELOW IS NOT DRAWN TO SCALE!
Given: Point E is the midpoint of AC and DF
Prove: ADEA AFEC
C
F
А
B
B
Answer:
more imformation?
Step-by-step explanation:
which is the right andwer?????????? please help me
Answer:
The first one
Solve 3 x 26 below by drawing place value models by typing the answer.
Answer:
Seven tens, eight ones.
Step-by-step explanation:
It's the answer. XD
Answer:
78
Step-by-step explanation:
1s place and tens place are in 78.
the charge for a 7 min call is Rs.42.
find the rate per min
42 dollars/7 minutes
÷ by 7 on both
6 dollars/1 minute
hope this helped
please make this brainliest
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = yj − zk,
S consists of the paraboloid
y = x2 + z2, 0 ≤ y ≤ 1,
and the disk
x2 + z2 ≤ 1, y = 1.
Since S is closed, you can use the divergence theorem, which says
[tex]\displaystyle\iint_S \vec F(x,y,z) \cdot \mathrm d\vec S=\iiint_R \mathrm{div}\vec F(x,y,z)\,\mathrm dV[/tex]
where R is the interior of the surface S.
We have
div F (x, y, z) = ∂/∂x (0) + ∂/∂y (y) + ∂/∂z (-z) = 1 - 1 = 0
so the flux would be 0.
In this exercise we have to calculate the flux by the divergent theorem:
The flux would be ZERO
Since S is closed, you can use the divergence theorem, which says:
[tex]\int\limits\int\limits_s {F(x,y,z} \, ds= \int\limits \int\limits\int\limits_R {divF(x, y, z)} \, dv[/tex]
where R is the interior of the surface S. We have:
[tex]\nabla F (x, y, z) = 1-1= 0[/tex]
so the flux would be ZERO.
See more about vectorial calculus at : brainly.com/question/6960786