Answer:
[tex]\frac{-11}{25}+\frac{-27}{25}i[/tex] given you are asked to simplify
[tex]\frac{-3+5i}{-3-4i}[/tex]
Step-by-step explanation:
You have to multiply the numerator and denominator by the denominator's conjugate.
The conjugate of a+bi is a-bi.
When you multiply conjugates, you just have to multiply first and last.
(a+bi)(a-bi)
a^2-abi+abi-b^2i^2
a^2+0 -b^2(-1)
a^2+-b^2(-1)
a^2+b^2
See no need to use the whole foil method; the middle terms cancel.
So we are multiplying top and bottom of your fraction by (-3+4i):
[tex]\frac{-3+5i}{-3-4i} \cdot \frac{-3+4i}{-3+4i}=\frac{(-3+5i)(-3-4i)}{(-3-4i)(-3+4i)}[/tex]
So you will have to use the complete foil method for the numerator. Let's do that:
(-3+5i)(-3+4i)
First: (-3)(-3)=9
Outer:: (-3)(4i)=-12i
Inner: (5i)(-3)=-15i
Last: (5i)(4i)=20i^2=20(-1)=-20
--------------------------------------------Combine like terms:
9-20-12i-15i
Simplify:
-11-27i
Now the bottom (-3-4i)(-3+4i):
F(OI)L (we are skipping OI)
First:-3(-3)=9
Last: -4i(4i)=-16i^2=-16(-1)=16
---------------------------------------------Combine like terms:
9+16=25
So our answer is [tex]\frac{-11-27i}{25}{/tex] unless you want to seprate the fraction too:
[tex]\frac{-11}{25}+\frac{-27}{25}i[/tex]
which of the following is a polynomial with roots 3,5i, and -5i
f(x)=x^3-3x^2+25x-75
f(x)=x^3-3x^2+15x-25
f(x)=x^3-15x^2+25x-75
f(x)=x^3-3x^2+15x-75
Answer:
f(x)=x^3-3x^2+25x-75
Step-by-step explanation:
Solve for x:
x^3 - 3 x^2 + 25 x - 75 = 0
The left hand side factors into a product with two terms:
(x - 3) (x^2 + 25) = 0
Split into two equations:
x - 3 = 0 or x^2 + 25 = 0
Add 3 to both sides:
x = 3 or x^2 + 25 = 0
Subtract 25 from both sides:
x = 3 or x^2 = -25
Take the square root of both sides:
Answer: x = 3 or x = 5 i or x = -5 i
How do you solve and graph this equation
Answer:
The graph is in the attachmentStep-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded region below a line or to the left if is a vertical line
>, ≥ - shaded region above a line or to the right if is a vertical line
----------------------------------------------------------
We have x ≥ 4:
solid vertical line x = 4
shaded region to the right
Algebra 2 help? please ill give brainliest
WILL PICK BRAINLIEST!!!!!!
Mrs. Hanger is painting the following picture of an H to hang in the entryway of her home. She has made the following scale drawing as her model. The scale used on the drawing is 1:6.
As you can see, the "H" is going to be painted brick red in the center of a rectangular beige background. This means the distance from the "H" to the top of the picture will be the same as the distance from the "H" to the bottom of the picture. Similarly, the distance from the "H" to the left side of the picture will be the same as the distance from the "H" to the right side of the picture. Finally, each segment of the "H" will have the same width.
1. What is the actual width of the painting? ________ inches
2. What is the actual height of the painting? ________inches
3. On the scale drawing, the top edge of the "H" is 5/6 inches from the top edge of the drawing. What is the actual height of the "H"? _________ inches
4. What is the actual width of the "H" (through the center)? ________inche
5. What is the actual distance from the left edge of the painting to the left edge of the "H"? _________inches
Answer:
1. 24
2. 30
3. 20
4. 12
5. 6
Please help I don’t know this!!!
Answer:
F
Step-by-step explanation:
∠C is opposite ( or across from ) side AB
In the same way
∠A is opposite side BC and
∠B is opposite side AC
Question 1 of 25
2 Points
Suppose the linear regression line y = 2.1x + 130 predicts sales based on the
money spent on advertising. If x represents the dollars spent in advertising,
and y represents the company sales in dollars, about how much can the
company expect in sales if it spends $50 in advertising?
O A. $650
O B. $235
O C. $105
O D. $323
SUBMIT
Find the values of X and Y
Answer:
see explanation
Step-by-step explanation:
Using the exact values of the trigonometric ratios
sin30° = [tex]\frac{1}{2}[/tex], cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]
Then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{17}{y}[/tex] = [tex]\frac{1}{2}[/tex]
Cross- multiply
y = 2 × 17 = 34
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{y}[/tex] = [tex]\frac{x}{34}[/tex] and
[tex]\frac{x}{34}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 34[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 17[tex]\sqrt{3}[/tex]
Hence
x = 17[tex]\sqrt{3}[/tex] and y = 34
(02.01 LC)
Is the following relation a function?
x y
1 4
−1 −2
3 10
5 16
Yes
No
Yes or no?
Yes. You should add commas next time to make it easier to read.
Answer:
Yes this is a function..
Step-by-step explanation:
We have to see the inputs and outputs for the function.
Here x represents input and y represents output.
For a relation to be a function there should be no repition in domain or input of the function i.e. every element in domain should be unique.
The domain for given relation is:
{1,-1,3,5}
All the inputs are only once mapped to the output so this relation is a function ..
What equation results from completing the square and then factoring?
x2 - 8x = 39
O A. (x-8)2 = 55
O B. (X-8)2 = 23
O C. (x-4)2 = 23
O D. (x-4)2 = 55
Answer:
[tex]\large\boxed{D.\ (x-4)^2=55}[/tex]
Step-by-step explanation:
[tex](a-b)^2=a^2-2ab+b^2\qquad(*)\\\\\\x^2-8x=39\\\\x^2-2(x)(4)=39\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\\underbrace{x^2-2(x)(4)+4^2}_{(*)}=39+16\\\\(x-4)^2=55[/tex]
Answer: the answer is D
Step-by-step explanation:
Please help ASAP it is due in 5 mins
Answer:
z = 5
Step-by-step explanation:
Given
- 0.25z = - 1.25 ( divide both sides by - 0.25
z = [tex]\frac{-1.25}{-0.25}[/tex] = 5
z = 5
Answer:
z = 5.
Step-by-step explanation:
-0.25 z = -1.25
z = -1.25 / -0.25
z = 5.
What is the value of x x=2.25
X=11.25
Answer:
2.25
Step-by-step explanation:
Answer:
x = 2.25
Step-by-step explanation
using process of elimination the only viable answer is 2.25
Which answer is the explicit rule for the sequence 2,9,16,23,30...
Answer:
see explanation
Step-by-step explanation:
These are the terms of an arithmetic sequence
The n th term ( explicit rule ) for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
d = 9 - 2 = 16 - 9 = 23 - 16 = 30 - 23 = 7 and a₁ = 2, hence
[tex]a_{n}[/tex] = 2 + 7(n - 1) = 2 + 7n - 7 = 7n - 5
The explicit rule for the sequence 2,9,16,23,30... is 7n - 5
How to write explicit rule for a sequence2,9,16,23,30
First term, a = 2Common difference, d = 9 - 2= 7
The explicit rule is defined by
nth term = a + (n - 1) d
= 2 + (n - 1)7
= 2 + 7n - 7
= 7n - 5
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solve 7r+ 2 = 5(r – 4)
Multiply the bracket by 5
I used PEMDAS
P= parenthesis
E= exponents
M=multiplication
D= division
A= addition
S= subtraction
7r+2= 5(r-4)
7r+2= 5r-20
Move 5r to the left hand side . Positive 5r changes to negative 5r
7r-5r+2= 5r-5r-20
2r+2=- 20
2r+2-2= -20-2
Move positive 2 to the right hand side. Changes to negative -2
2r+2-2= -20-2
2r= -22
Divide by 2 for 2r and -22
2r/2= -22/2
r= -11
Answer is r= -11
Answer:
r = (-11)
Step-by-step explanation:
7r + 2 = 5(r – 4)
7r + 2 = 5r – 4 * 5
7r + 2 = 5r – 20
7r - 5r = -20 - 2
2r = -22
r = -22/2 = (-11)
A decorator wants to line the bottom of 3 drawers with paper. If the bottom of each drawer measures 36 inches by 20 inches,
how many square inches of paper are needed?
A 1,040
B
1,080
C 2,040
D
2,160
Answer:
2160
Step-by-step explanation:
36*20=720 720*3=2160
To find the number of square inches of paper needed, multiply the length and width of each drawer to get the area, and then multiply that area by 3.
Explanation:To find the number of square inches of paper needed, we need to find the area of the bottom of each drawer and then add them together. The area of a rectangle is found by multiplying its length by its width. So, for each drawer, we multiply 36 inches by 20 inches to get an area of 720 square inches.
Since there are 3 drawers, we need to multiply the area of one drawer by 3. So, the total number of square inches of paper needed is 720 square inches times 3, which equals 2160 square inches.
Therefore, the correct answer is D) 2160.
24^2= 20^2+34^2-2(20)(34)cos(Q)
576=400+1156-(1360)cos(Q)
576=1556-(1360)cos(Q)
-980= -(1360)cos(Q)
To the nearest whole degree, the measure of angle Q is ____ degrees.
Answer: 50 degrees.
Step-by-step explanation:
To find the measure of the angle Q, you need to follow these steps:
- Knowing that:
[tex]-980= -(1,360)cos(Q)[/tex]
You can divide both sides of the equation by -1,360:
[tex]\frac{-980}{-1,360}=\frac{-1,360cos(Q)}{-1,360}\\\\\frac{49}{68}=cos(Q)[/tex]
- Finally, using the inverse function of the cosine, Arccosine, we get:
[tex]Q=Arcos(\frac{49}{68})\\\\Q=49.89\°[/tex]
To the nearest whole degree, this is:
[tex]Q=50\°[/tex]
Please help ASAP this is all due today
Answer:
x = 7.5
Step-by-step explanation:
Given
- 15 = [tex]\frac{x}{-0.5}[/tex]
Multiply both sides by - 0.5
- 0.5 × - 15 = x, hence
x = 7.5
Answer:
7.5.
Step-by-step explanation:
-15 = x / -0.5
Cross multiplying:
x = -15 * -0.5
= 7.5.
A study determined that there is a strong correlation between getting less than 8 hours of sleep a day and lower test scores. Can it be determined that the low test scores are caused by sleep deprivation? Explain.
A) Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance.
B)Causation cannot be proven because all students get less than 8 hours of sleep.
C)Causation can be proven because it is well known that less sleep lowers test scores.
D)Causation can be proven because an experiment was used to prove this hypothesis.
Answer:
Option A (Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance).
Step-by-step explanation:
Correlation is a concept which explains a linear relationship between two variables. The correlation constant lies between -1 and 1. 0 lies in the center of the interval. A negative correlation means an inverse relationship, and a positive correlation means a direct relationship. 0 technically means no linear relation between the variables. Further the correlation constant lies from 0, more the strength of the relationship. It is important to note that correlation shows a relationship between the two variables but it cannot determine the causation i.e. it cannot be concluded that one variable caused the other variable to occur. Even though having a strong correlation does not mean causal relationship. Therefore, correlation does not prove causation. This is because there are several other lurking and unobserved variables which affect the observed variables. The former class of variables are not accounted for in the correlation. Therefore, the exact magnitude of the causal relationship cannot be determined. Therefore, Option A is the correct choice!!!
Answer:
OPTION A: Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance.
Step-by-step explanation: I got it right on the test.
The probability that the fraction will be greater than 5/6
Answer:
11/16
Step-by-step explanation:
You could list all the possible fractions you will get:
Here are the's with 4 as the numerator:
4/4
4/5
4/6
4/7
Here are the one's with 5 as the numerator:
5/4
5/5
5/6
5/7
Here are the one's with 6 as the numerator:
6/4
6/5
6/6
6/7
Here are the one's with 7 as the numerator:
7/4
7/5
7/6
7/7
There are 4(4) different numerator-denominator combinations we can get.
Let's see which of these are bigger than 5/6.
If you think it is easier to look at the decimals of all these you can.
5/6=0.8333333333
----
4/4 =1
4/5 =0.8
4/6 =0.6666666666
4/7 =0.5714 (approximately)
There is only 1 bigger than 5/6 in this section.
5/4 =1.25
5/5 =1
5/6 =0.83333333333
5/7 =0.714 (approximately)
There is 2 bigger than 5/6 in this section.
6/4 =1.5
6/5 =1.2
6/6 =1
6/7 =0.857 (approximately)
There is 4 bigger than 5/6 in this section.
7/4
7/5
7/6
7/7
All of these are 1 or bigger because the numerator is bigger than or equal to the denominator so all 4 of these are bigger than 5/6 in this section.
P(fraction being greater than 5/6)=[\tex]\frac{\text{ the numbers I listed bigger than } \frac{5}{6}}{\text{ all the fractions I listed }}[/tex]
P(fraction being greater than 5/6)=[\tex]\frac{4+4+2+1}{4(4)}=\frac{11}{16}{/tex]
11/16
Answer:
1/6 or 11/16
Step-by-step explanation:
If you spin a spinner with the first spin giving the numerator and the second spin giving the denominator of a fraction, the probability of the fraction will be greater is 1/6 or 11/16.
6 - 5/6 = 1/6
However, there are 4 possible spots you could land on so, it would change to 11/16.
the graph of y=sin(x-3π/2) is the graph of the y=sin(x) shifted in which direction
Answer:
[tex]\frac{3\pi}{2}[/tex] units to the right
Step-by-step explanation:
If we have a parent function y = Sin(x), the function
y = Sin(x-b) would be the parent shifted b units righty = Sin (x+b) would be the parent shifted b units leftThe function given is [tex]y=Sin(x-\frac{3\pi}{2})[/tex]
So from the rules, we can clearly say that it is parent function shifted RIGHT by [tex]\frac{3\pi}{2}[/tex] units.
2nd answer choice is correct.
what is the value of 4r^2-8 when r=3?
Answer:
28
Step-by-step explanation:
So this means to replace the r you see in 4r^2-8 with 3.
Let's do that:
4(3)^2-8
Now to simplify this just use pemdas or a calculator:
4(9)-8 since 3^2 means 3*3=9
36-8
28
Answer:
28.
Step-by-step explanation:
Put r =- 3 and work it out:
That would be 4(3)^2 - 8
= 4 * 9 - 8
= 36 - 8
= 28.
Use the graph to determine the input values that correspond with f(x)=1.
Answer:
x = -7 and x = 2
Step-by-step explanation:
Look for the points on the graph where if you draw a horizontal line at y=1, you will intersect the curve.
By observation, we can see that this happens at x = -7 and x = 2
x = -7 and x = 2
How to elaborate the problem ?Here in the diagram, we can see that, a curve is present & 6 co-ordinates on that curve are given.
We have to find the values of x correspond with f(x) = 1
What are the input values ?f(x) = 1 means y = 1
So, if we draw a horizontal line at y = 1, which is parallel to x-axis.
Then, we can able to observe the points which are on the line y = 1.
So, the points on line y = 1 are (-7, 1) & (2, 1).
Hence, we can say that, input values that correspond with f(x) = 1 are x= -7 & x = 2.
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help pleaseee !!!! which description matches the function represented by this graph
Answer:
D. Linear decay.
Step-by-step explanation:
The data decays and lowers.
Answer with explanation:
If you will look at the graph of function, it is not a straight line.
Horizontal Asymptote is, y=0.
There is no vertical Asymptote.
Either it can be growth function or decay function.
But , if you will look at the graph of growth function, it begins from negative infinity and then starts increasing.
In this case graph is decreasing function.
So, The function represents
Option C:→ Exponential Decay
Is the line that passes through the points A(0,1) and B(2,5) parallel to the line that passes through the
points C(0,7) and D(4,15)?
Find the slope of AB
The slope of AB
Answer:
Yes the lines are indeed parallel. The slope of AB is 2
Step-by-step explanation:
Point C and point D are plotted on the graph. Plot points A and B to form rectangle ABDC with an area of 36 square units. Plot point E at (2, 4).
Step-by-step explanation:
pt C is (-4,-4)
pt D is (2,-4)
length of CD is 6 units
to form a rectangle AB must be parallel to CD, AC must be parallel to BD and AC and BD must be 6 units
Therefore...A =(-4, 2) and B = (2, 2)
Could you guys help me with number 4
Answer:
c
Step-by-step explanation:
Does 3 to the 2 power plus 3 to the 3 power equal 3 to the 5 power?
Please Explain!
3 to the 2nd power plus 3 to the 3rd power does not equal 3 to the 5th power. In actuality, 3^2 + 3^3 = 36, while 3^5 = 243.
Explanation:No, 3 to the 2nd power plus 3 to the 3rd power does not equal 3 to the 5th power. This is a common misconception when dealing with exponents. To clear this up, let's look at what these expressions actually mean:
3 to the 2nd power (3^2) = 3*3 = 9
3 to the 3rd power (3^3) = 3*3*3 = 27
So, 3^2 + 3^3 = 9 + 27 = 36
However, 3 to the 5th power (3^5) = 3*3*3*3*3 = 243
So, as you can see, 36 does not equal 243.
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What is the factorization of 81a6 -100
Answer:
see explanation
Step-by-step explanation:
81[tex]a^{6}[/tex] - 100 ← is a difference of squares which factors in general as
a² - b² = (a - b)(a + b)
81[tex]a^{6}[/tex] = (9a³ )² ⇒ a = 9a³ and 100 = 10² ⇒ b = 10
Hence
81[tex]a^{6}[/tex] - 100
= (9a³)² - 10²
= (9a³ - 10)(9a³ + 10)
Answer:
C
Step-by-step explanation:
Unit Test Is a pain I know
What was the range of snowfall in Denver?
Answer:
7.6 inches
Step-by-step explanation:
First of all we have to define range.
Range gives us the difference of two values between which the data is spread.
the formula for range is:
Range = Highest value - lowest value
By observing the diagram, we can see that
The highest value is = 8.5 inches
The lowest value is: 0.9 inches
So,
Range = 8.5 - 0.9
= 7.6 inches
So, the range is 7.6 inches ..
girardo is using the model below to solve the equation 3x+1=4x+(-4)
Answer:
x = 5Step-by-step explanation:
[tex]3x+1=4x+(-4)\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\3x-4x+1=4x-4x-4\\\\-x+1=-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=-4-1\\\\-x=-5\qquad\text{change the signs}\\\\x=5[/tex]
Answer:
The answer is B. In step one he should have added 3 negative x-tiles to both sides.
Step-by-step explanation:
is (0,0) a solution to this system y2x-1
(0,0) satisfies y > 2x - 1 but does not satisfy y ≤ x^2 - 4. C
(0,0) satisfies both inequalities.