Answer:
a)zw = 44.295 cos(1.924) +isin(1.924))
b) z/w= 4.921 cos(-0.936) + isin(-0.936)
Step-by-step explanation:
Given:
z=13+7i
w=3(cos(1.43)+isin(1.43)
a. convert zw using De Moivre's theorem
First coverting z into polar form:
13^2 + 7^2 = 14.765
[tex]\sqrt{14.765}[/tex] =r
θ= arctan (7/13)
= 0.49394 (28.301 in degrees)
z= 14.765(cos(0.49394)+isin(0.49394) )
Now finding zw
zw= 14.765(cos(.494)+isin(.494))×3(cos(1.43)+isin(1.43))
Using De Moivre's theorem, the modulus will be multiplied
14.765 x 3=44.295
whereas the angles will be added
.494+1.43=1.924
Thus:
zw = 44.295 cos(1.924) +isin(1.924))
b)
finding z/w
z/w= 14.765(cos(.494)+isin(.494)) / 3(cos(1.43)+isin(1.43))
Using De Moivre's theorem, the modulus will be divided
14.765 / 3 = 4.921
whereas the angles will be subtracted:
.494-1.43=-0.936
Thus:
z/w= 4.921 cos(-0.936) + isin(-0.936) !
Look at the figure. Classify the pair of angles: <4 and <5.
Answer:
Option B
same-side interior angles
Step-by-step explanation:
Given in the question, two non parallel lines a and b.
The area between lines a and b is called the interior of the two lines.
Angles 4 and 5 are same-side interior angles.
Other options are wrong because:
A)The area which not between lines a and b is called the exterior
C)Corresponding angles are on same side of the traversal line.
Example
Angles 1 and 5
D)Alternate interior angles are in interior region but in opposite side of traversal line.
Example
Angles 3 and 5
help me im timed i cant figure it out
For this case we have to find the inverse of a function, follow the steps below:
Replace f (x) with y.We exchange the variables.We solve for "y".Finally we change y by [tex]f ^ {- 1} (x)[/tex]Then, it is observed that of option 3:
[tex]f (x) = 4x[/tex]
Replace [tex]f (x)[/tex]with y:
[tex]y = 4x[/tex]
We exchange the variables:
[tex]x = 4y[/tex]
We solve for "y":
[tex]4y = x\\y = \frac {x} {4}[/tex]
Finally we change y by [tex]f ^ {- 1} (x):[/tex]
[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]
Answer:
The correct option is C
Answer:
It's the third choice.
Step-by-step explanation:
f(x) = y = 4x
x = 1/4 y
Change the y to x:
so the inverse g(x) = 1/4 x.
1. If tan θ= -8/15 and if the terminal point determined by θ is in quadrant II, find cscθ sinθ+ tan θ.
Since
[tex]\csc(x)=\dfrac{1}{\sin(x)}[/tex]
we have
[tex]\csc(x)\sin(x)+\tan(x) = \dfrac{1}{\sin(x)}\cdot \sin(x)+\tan(x)=1+\tan(x)[/tex]
And since
[tex]\tan(x)=\dfrac{8}{15}[/tex]
we have
[tex]1+\tan(x) = 1-\dfrac{8}{15}=\dfrac{15}{15}-\dfrac{8}{15}=\dfrac{7}{15}[/tex]
The value of cscθ sinθ + tan θ is 7/15.
What is the relationship between cscθ and sinθ?cscθ is the reciprocal of sinθ.
We can find the value of the given expression below:The expression is given by cscθ sinθ + tan θ.
We can simplify this expression before solving it.
Let the expression be y = cscθ sinθ + tan θ.
cscθ = 1/sinθ
y = sinθ * 1/sinθ + tan θ
y = 1 + tan θ
The value of tan θ is given as -8/15.
We can substitute this above:
y = 1 + tan θ
= 1 - 8/15
= (15-8)/15
= 7/15
The value of the expression cscθ sinθ+ tan θ is found to be 7/15.
Therefore, the value of cscθ sinθ + tan θ is 7/15.
Learn more about trigonometric ratios here: https://brainly.com/question/24349828
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PLZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
How can you find the missing side length of a cube if you know the cube’s volume?
Answer:
See below
Step-by-step explanation:
In order to solve for the length of a cube, you must already know its width, depth, and volume. Then, arrange the problem as an equation:
Length x width x depth = volume
Next, solve the equation for the length. For example, If I have a cube with a width of 5ft, a depth of 5ft, and a volume of 50ft^3, I will solve for the length by arranging the values to fit the formula shown above:
L x 5 x 5 = 50
Then I'll multiply the values on the left:
25L = 50
And, finally, I will divide either side by 25, which leaves the answer:
L = 2ft
Hope this helps! Feel free to ask questions!
A survey was taken of 49 people to see if they watch basketball and/or soccer games on television. The results are shown in the Venn diagram.
Enter your answers in the boxes to complete the two-way table based on the given data.
Can someone help me please
Answer:
[tex]\begin{array}{cccc}&\text{Watch basketball}&\text{Don't watch basketball}&\text{Total}\\\text{Watch soccer}&7&12&19\\\text{Don't watch soccer}&17&13&30\\\text{Total}&24&25&49\end{array}[/tex]
Step-by-step explanation:
From the diagram you can see that
17 people watch only basketball;7 people watch both basketball and soccer;12 people watch only soccer;in total, 17+7+12=36 people watch some sports;so, 49-36=13 people do not watch sports.So, you can fill the table in following way
[tex]\begin{array}{cccc}&\text{Watch basketball}&\text{Don't watch basketball}&\text{Total}\\\text{Watch soccer}&7&12&19\\\text{Don't watch soccer}&17&13&30\\\text{Total}&24&25&49\end{array}[/tex]
Answer:
dude was right but heres photo proof
Step-by-step explanation:
who do I write the fraction 2/5 as an equivalent fraction with denominator 15x
Answer:
Step-by-step explanation:
multiply the top and bottom of the fraction by 15x
2*15x
=======
5*15x
30x
====
75x
Find the value of x. Round to the nearest tenth
Answer:
16.2
Step-by-step explanation:
A trick to remember for right triangles is SOH-CAH-TOA:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
Here, we have the side adjacent to the angle and the hypotenuse. So we should use cosine.
cos 22° = 15 / x
x = 15 / cos 22°
x ≈ 16.2
What is the value of a in the equation 3a+b=54 , when b=9 ?
Use substitution method
3a+9=54
3a+9-9=54-9
3a= 45
divide by 3
3a/3= 45/3
a= 15
Answer is a= 15
Answer:
a = 15
Step-by-step explanation:
3a + b = 54
3a + 9 = 54
3a + 9 - 9 = 54 - 9
3a = 45
3a divided by 3 = 45 divided by 3
a = 15
3 x 15 + 9 = 54
45 + 9 = 54
54 = 54
Which of the diagrams shows a reflection of the figure above?
Help ASAP
The coordinates after the reflection of the given graph are A'(1,-4), B'(2,-1), and C'(3,-3). The correct graph that shows the reflection is D).
Given :
The graph given has points -- (1,4), (2,1), and (3,3).
The following steps can be used in order to determine the correct figure that shows the reflection of the given graph:
Step 1 - According to the given graph. the points are A(1,4), B(2,1), and C(3,3).
Step 2 - According to the given data, take the reflection of the given graph.
Step 3 - So, after reflection about the x-axis, the points become A'(1,-4), B'(2,-1), and C'(3,-3).
Therefore, the correct option is D).
For more information, refer to the link given below:
https://brainly.com/question/1878272
Write parametric equations of the line y=4x-5
Answer:
A set of parametric equations for the line y = 4x - 5 is;
x = t
y = 4t - 5
Step-by-step explanation:
To find a set of parametric equations for the line y = 4x - 5;
We can assign either variable x or y equal to the parameter t, in this case we can easily let x = t
We then substitute x = t in the original equation;
y = 4t - 5
Therefore, a set of parametric equations for the line y = 4x - 5 is;
x = t
y = 4t - 5
6. I need help with question in the attached picture!
ANSWER
[tex]log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) =\log 7[/tex]
EXPLANATION
The given logarithmic expression is:
[tex] log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) [/tex]
We apply the product rule to the first two terms to get:
[tex]log( \frac{14}{3} \times \frac{11}{5} ) - log( \frac{22}{15} ) [/tex]
We the apply the quotient rule:
[tex]log( \frac{14}{3} \times \frac{11}{5} \div \frac{22}{15} ) [/tex]
[tex]log( \frac{14}{3} \times \frac{11}{5} \times \frac{15}{22} ) [/tex]
We cancel out the common factors and simplify to obtain:
[tex]log( 7 ) [/tex]
Required Knowledge.
log(ab) =log(a) + log(b)
log(a/b) = log(a) -log(b)
SOLUTION
log(14/3) +log(11/5) -log(22/15)
=log((14/3)×(11/5)) -log(22/15)
=log(154/15) -log(22/15
=log( (154/15) ÷ (22/15) )
=log( (154/15) × (15/22) )
=log(154/22)
=log(77/11)
=log(7)
Hence 7 is your answer...
Hope it helps...
Regards;
Leukonov/Olegion.
11. The slope of a linear function h(x) is 2. Suppose the function is translated 8 units up to get d(x). How can h(x) be
translated to the left or right to represent the same function d(x)? Explain your answer.
Answer:
See below.
Step-by-step explanation:
If we translate h(x) to the left it will override line d(x) because the slope of both lines is the same. H(x) will need to move 4 units to the left to do this (because the slope = 2 = 8/4).
To represent the same function as d(x), the linear function h(x) with a slope of 2 should be translated 4 units to the left, resulting in the function h(x+4). This horizontal shift increases the value of y by 8 units, which equates to the vertical shift applied to create d(x).
To translate the linear function h(x) to result in the same function as d(x), which is h(x) translated 8 units up, we need to consider the properties of linear functions and translations. Since h(x) has a slope of 2, we can denote it as h(x) = 2x + b, where b is the y-intercept. When h(x) is translated 8 units up to become d(x), the new function is d(x) = h(x) + 8 = 2x + b + 8. To counteract this vertical shift with a horizontal translation and maintain the same function as d(x), we must shift h(x) in such a way that every x value for h(x) yields the same y-value for d(x) after the translation.
To achieve this, we would have to shift h(x) to the left by 4 units, resulting in the function h(x+4). This is because for every 1 unit increase in x, the value of h(x) increases by 2 units (the slope), so a shift of 4 units left would increase y by 8 units, which is the same effect as the vertical translation applied to obtain d(x). Thus, h(x+4) = 2(x+4) + b = 2x + 8 + b, which aligns with d(x). This explanation confirms that the properties of linear functions and translation mechanics allow us to equate d(x) with a horizontally translated version of h(x).
7. The coordinates of the vertices of a rectangle are go
I by
R(-3,-4), E(3, 4), C(4,4), and T(4-4). Plot these points
on the coordinate plane at the right and connect them to
draw the rectangle. Then connect points E and T to form
diagonal ET.
a. Use the Pythagorean Theorem to find the exact
length of ET.
b. How can you use the Distance Formula to find the
length of ET? Show that the Distance Formula gives
the same answer
Answer:
a. By Pythagorean Theorem: [tex]ET=\sqrt{113}[/tex]
b. By Distance Formula: [tex]ET=\sqrt{113}[/tex]
Step-by-step explanation:
The given rectangle has vertices R(-3,-4), E(-3, 4), C(4,4), and T(4-4).
The points have been plotted on the coordinate plane as shown in the attachment.
a. Using the Pythagoras Theorem;
[tex]ET^2=EC^2+CT^2[/tex]
We substitute the side lengths to obtain:
[tex]ET^2=7^2+8^2[/tex]
[tex]ET^2=49+64[/tex]
[tex]ET^2=113[/tex]
Take positive square root to obtain:
[tex]ET=\sqrt{113}[/tex]
b. The distance formula is given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The endpoints of ET are at E(-3,4) and T(4,-4).
Using the distance formula;
[tex]ET=\sqrt{(4--3)^2+(-4-4)^2}[/tex]
[tex]ET=\sqrt{(7)^2+(-8)^2}[/tex]
[tex]ET=\sqrt{49+64}[/tex]
[tex]ET=\sqrt{113}[/tex]
x and y intercepts if y=3(x-1)^2-12
The x-intercepts are: (-1,0) and (3,0).
The y-intercept is: (0,-9).
Hope this helps!
3. Let's assume you purchase 100 shares of XYZ Company for $1 per share. After three months, the share price increases to $5. This means the value of the investment has increased from $100 to $500, for a capital gain of $____
Answer:
400
Step-by-step explanation:
The initial value of the investment is 100 *1 = $100
The final value of the investment after three months is 100 * 5 = $500
This means the value of the investment has increased from $100 to $500. The capital gain is the increase in the value of an investment;
500 - 100 = $400
how many yards can fit in 5 miles
Answer:
8800 yards
Step-by-step explanation:
1760 feet * 5 = 8800 yards
Answer:
8800
Step-by-step explanation:
I googled it
During the past seven weeks Diego spent between $11 and $17 for lunch each week
Answer:
c
Step-by-step explanation:
11+17 x 7=130
x=130
130 is bigger than 120 but smaller than 180
Three families are sharing the cost of renting a canoe for 7 days. The cost for each family is $14 per day. What is the total cost of renting the canoe for 7 days from the rental shop?
Answer:
294
Step-by-step explanation:
so three family's and 14$ a day so
14*3=42
then take 42 and times it by how many days so 7
so 42*7=294
Javier has been saving for a digital camera. He finds one on sale for $67.50. It usually costs $90.00. What is the percent of the discount?
A: 20%
B: 25%
C: 30%
D: 35%
Answer:
B: 25%
Step-by-step explanation:
$90.00 - $67.50 = $22.5
$22.5 / $90 = 0.25 = 25%
Answer:
B: 25%
Answer:
25%
Step-by-step explanation:
I will mark brainliest
Please help ASAP!!!!
Answer:
A. [tex]x=6[/tex] or [tex]x=1[/tex]
Step-by-step explanation:
The given function is:
[tex]y=x^2-7x+6[/tex]
When y=0; we have:
[tex]x^2-7x+6=0[/tex]
[tex]x^2-6x-x+6=0[/tex]
Factor by grouping:
[tex]x(x-6)-1(x-6)=0[/tex]
[tex](x-6)(x-1)=0[/tex]
Either [tex](x-6)=0[/tex] or [tex](x-1)=0[/tex]
Either [tex]x=6[/tex] or [tex]x=1[/tex]
It will take Adam four hours to drive to Disney Park, and 2.5 times less time if driving 45 mph faster. What is the distance Adam should cover to get to the park?
Answer:
120 miles
Step-by-step explanation:
we know that
The speed is equal to the distance divided by the time
Let
s------> the speed in mph
d-----> the distance in miles
t -----> the time in hours
s=d/t
solve for the distance
d=s*t
It will take Adam four hours to drive to Disney Park
s=x mph
t=4 h
substitute
d=4x -----> equation A
It will take Adam 2.5 times less time if driving 45 mph faster
so
s=(x+45) mph
t=4/2.5=1.6 h
substitute
d=1.6(x+45) -----> equation B
equate equation A and equation B
4x=1.6(x+45)
Solve for x
4x=1.6x+72
4x-1.6x=72
2.4x=72
x=30 mph
Find the distance d
d=4x -----> d=4(30)=120 miles
Answer:
120 miles
Step-by-step explanation:
Find the value of x in the figure. Please Explain
A)34.9
B)55.1
C)90
D)124.9
Answer:
90 because it’s a right angle and a right angle it 90 degrees
The two angles make up a right angle.
This means the two angles are complementary and need to equal 90 degrees.
X = 90 - 55.1 = 34.9
Which of the following is equal to the rational expression when x doesn’t equal 1 or -1? 5(x-1)/(x+1)(x-1) please help
Answer:
Final answer is [tex]\frac{5}{(x+1)}[/tex].
Step-by-step explanation:
Given expression is [tex]\frac{5\left(x-1\right)}{(x+1)(x-1)}[/tex] where x doesn’t equal 1 or -1. Now we need to find about which of the given choices is equal to the given rational expression. Choices are missing but we can still solve this problem.
[tex]\frac{5\left(x-1\right)}{(x+1)(x-1)}[/tex]
cancel out common factors from top and bottom.
[tex]=\frac{5}{(x+1)}[/tex]
Hence final answer is [tex]\frac{5}{(x+1)}[/tex].
Answer:
5/x+1
Step-by-step explanation:
A van travels 320 miles on 16 gallons of gas. Find how many gallons the van needs to travel 420 miles
The van needs 21 gallons of gas. Take 16/(320/420)
The van will need 21 gallons of gas to travel 420 miles, based on its fuel efficiency of 20 miles per gallon.
The student is asking how many gallons of gas a van needs to travel 420 miles, given that it travels 320 miles on 16 gallons of gas.
First, we calculate the van's fuel efficiency which is found by diving the miles traveled by the gallons of gas used. For the van in the question:
Fuel efficiency: 320 miles / 16 gallons = 20 miles per gallon (MPG)
Next, we can use this fuel efficiency to find out how many gallons will be needed for 420 miles. We divide the total miles by the MPG:
Gallons needed: 420 miles / 20 MPG = 21 gallons
Therefore, the van will need 21 gallons of gas to travel 420 miles.
Share £35 in ratio 2:3
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the equation.

The value of x in terms of p is .
The value of x when p is −5 is .
Answer:
15/p and -3
Step-by-step explanation:
4(px+1)=64
Distribute 4: 4px + 4=64
Subtract 4 from both sides : 4px+4-4=64-4
Divide by 4p: 4px/4p=60/4p
x=15/p
Write a function rule for the table.
f(x) = x + 1
f(x) = x
f(x) = –1 – x
f(x) = x –1
I assume one of the four options is the correct answer...
Remember that in order to determine if a function rule is correct, you should be able to plug an x value into the equation and get the corresponding y value as the answer.
The first option, f(x) = x + 1, is correct!
Answer: The correct option is (A) f(x) = x + 1.
Step-by-step explanation: We are given to write a function rule for the following table :
x -1 0 1 2
f(x) 0 1 2 3
From the given table, we see that
[tex]f(-1)=0=-1+1,\\\\f(0)=1=0+1,\\\\f(1)=2=1+1,\\\\f(2)=3=2+1.[/tex]
Therefore, the required function rule is given by
[tex]f(x)=x+1.[/tex]
Thus, option (A) is CORRECT.
What is the slope and y-intercept of this line?
y = –3x + 9
slope: 9, y-intercept: –3
slope: 3, y-intercept: –9
slope: –3, y-intercept: 9
slope: 1, y-intercept: –3
Answer:
C
Step-by-step explanation:
y=mx+b
b= y-intercept
m=slope
m=-3
b=9
[tex]\huge\boxed{Slope=-3,\;Y\;intercept=9.}[/tex]
___________________________________________________________
[tex]\boxed{Explanation}[/tex]
y=mx+b.
m is always where the slope is located.
b is always where the y intercept is located.
Therefore, since -3 is located at m that is the slope and 9 is located at b so that is the y intercept.
Find the length of AC if AB is 8, BC is 13, and B is between A and C?
Answer:
21
Step-by-step explanation:
Since B is between A and C, we can simply add 8 and 13 to get the length of AC becauswe B is on line AC. This gives us 8+13 or 21 as the distance between A and C.
A and C is 6 because 2 sides have to be bigger than the other