9514 1404 393
Answer:
d. 76(cos(3π/16) +i·sin(3π/16))
Step-by-step explanation:
To form the product of 38cis(π/8) and 2cis(π/16), multiply the magnitudes and add the angles:
38cis(π/8) × 2cis(π/16) = (38×2)cis(π/8 +π/16) = 76cis(3π/16)
___
In this context, a·cis(b) ≡ a(cos(b) +i·sin(b))
A triangle with side lengths of 8, 15, and 17.5 form a right triangle.
I would appreciate the help
9514 1404 393
Answer:
false
Step-by-step explanation:
You can check to see if the sum of squares of the smaller two numbers is equal to the square of the larger.
8² +15² vs 17.5²
64 +225 vs 306.25
At this point, you need go no further. The sum of two integers will not have a fractional part, so cannot be equal to 306.25.
289 vs 306.25 . . . . the long side is too long for a right triangle.
__
If you were familiar with some of the Pythagorean triples, you would know that the closest triple is {8, 15, 17}, so (8, 15, 17.5) does not represent a right triangle.
A few common Pythagorean triples are ...
{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}
Given P(A)=0.78P(A)=0.78, P(B)=0.65P(B)=0.65 and P(A\cup B)=0.873P(A∪B)=0.873, find the value of P(A\cap B)P(A∩B), rounding to the nearest thousandth, if necessary
Answer:
[tex]P(A\ n\ B) = 0.557[/tex]
Step-by-step explanation:
Given
[tex]P(A) = 0.78[/tex]
[tex]P(B) = 0.65[/tex]
[tex]P(A\ u\ B) = 0.873[/tex]
Required
Determine [tex]P(A\ n\ B)[/tex]
From laws of probability, we have:
[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]
Substitute in values
[tex]P(A\ n\ B) = 0.78 + 0.65 - 0.873[/tex]
[tex]P(A\ n\ B) = 0.557[/tex]
Hence, [tex]P(A\ n\ B)[/tex] is calculated to be 0.557
A circular garden has a diameter of 8 feet, and a rectangular garden has side lengths of 5 feet by 9 feet.
which garden is larger
Answer:
rectangular garden
Step-by-step explanation:
A flagpole 12 meters tall casts a 24-meter shadow. Nearby, luke stands and is 4 meters tall. Determine the length of luka's shadow. Include all labels.
Answer:
8 meters
Step-by-step explanation:
This is a question that deals with Proportion
Height of flagpole/Shadow of flagpole = Height of Luke/Shadow of Luke
Length of the shadow of Luke = x
= 12/24 = 4/x
We cross Multiply
12 × x = 24 × 4
x = 24 × 4/12
x = 8 meters
Hence, the length of the shadow of Luke = 8 meters
1.
Marsha’s cat weighs 15.41 pounds. Her bunny only weighs 4.79 pounds. About how much more does her cat weigh?
10 pounds
10.62 pounds
20 pounds
11 pounds
Answer:
it's about 10, but without rounding it's 10.62
Step-by-step explanation:
1) Nyla had 10 songs in a playlist on her phone. The playlist had two of her favorite artists, Beyonce
and Jennifer Lopez. How many of the songs from each artist could she have?
a) Create an equation to represent this situation. Explain what each of the variables represent.
Equation:
b) List at least five solutions to the equation above. How do you know that these are the
solutions to the equation you created?
Answer:
a) 10 = X + Y
b) X = 1, Y = 9
X = 2, Y = 8
X = 3, Y = 7
X = 4, Y = 6
X = 5, Y = 5
i) The inputted values of X and Y are the solutions of the equation because they sum up to the 10 songs on Nyla's playlist.
Step-by-step explanation:
The given parameters are;
The number of songs in the playlist on her phone = 10
The number of authors of the songs on her playlist = 2
The equation that represent the situation is given as follows;
X + Y = 10
Where X represent the number of Beyonce's song on her playlist and Y represent the number of Jennifer Lopez's song on her playlist
b) 5 possible solutions are;
X = 1, Y = 9
X + Y = 1 + 9 = 10
Which gives 1 Beyonce's and 9 Jennifer Lopez's songs
X = 2, Y = 8
X + Y = 2 + 8 = 10
Which gives 2 Beyonce's and 8 Jennifer Lopez's songs
X = 3, Y = 7
X + Y = 3 + 7 = 10
Which gives 3 Beyonce's and 7 Jennifer Lopez's songs
X = 4, Y = 6
X + Y = 4 + 6 = 10
Which gives 4 Beyonce's and 6 Jennifer Lopez's songs
X = 5, Y = 5
X + Y = 5 + 5 = 10
Which gives 5 Beyonce's and 5 Jennifer Lopez's songs
i) The inputted values of X and Y are the solutions of the equation because they sum up to the 10 songs on Nyla's playlist.
Completely factor f(x)=2x^4+11x^3+2x^2-15x given that f(-3/2)=0
Due today please help
Answer:
There isn't a picture
Step-by-step explanation:
Guys I really need help pls!!
Answer:
No, yes, yes, no
Step-by-step explanation:
23.6/4.02=5.87
2.36/40.2=0.0587
2360/402=5.87
2.36/0.402=5.87
236/4020=0.0587
Can someone please answer letter F ? It applies to the question 4 and the graph on the right , it’s not long .
Find the unknown length given that the triangles are similar.
Answer:
20 is the answer.Step-by-step explanation:
1. Make a proportion.
Set the numbers equal to each other.
I chose the numbers 9, 12, 15, and of course x.
Make the fractions in a way that the x is in the numerator if you want to make your life easier.
15/9 = x/12
2. Simplify
Cross multiply the numbers.
This will give you the equation of
9*x and 15*12
3. Make an equation
Simplify the numbers by mulitplying them
9x = 180
4. Divide both sides by 9
9x = 180
/9 /9
x = 20Hope this helped,
Kavitha Banarjee
Calculate the circumference and area of circle T
Answer:
785
Step-by-step explanation:
2500÷10=250
250×3.14=785
Solve for x. cosx =√3/2
Answer:
cos x=√3/2
cos x=60°. (cos60°=√3/2)
{x=60°}
Polka Dot Boutique is having a sale of 15% off previously marked down items. Gwen finds a pair of jeans originally priced at $45.00 and marked down 25%. She must pay a 6% sales tax on the final prices of the jeans. How much does Gwen spend at Polka Dot Boutique? Group of answer choices
Answer:
$30.41
Step-by-step explanation:
Given that:
Discount off = 15%
Original price = $45
Mark down on item = 25%
Sales tax on final price = 6%
Cost of Jean will be ;
Mark down price :
Original price - (Original price * markdown %)
$45 - ($45 * 0.25) = $33.75
Discounted price :
Markdown price - (markdown price * discount %(
$33.75 - (33.75 * 0.15)
= $28.6875
Final price :
Discounted price + (sales tax * discounted price)
28.6875 + (0.06 * 28.6875)
= $30.40875
= $30.41
How many solutions does this equation have? –7z − 7 = –4z + 8
The stopping distance, d ( in feet) for a van moving at a velocity (speed) v miles per hour is modeled by the equation:
d = 0.04v + 1.1v
What is the stopping distance for a velocity of 10 miles per hour?
a. 10 ft
b. 7 ft
c. 15 ft
d. 13 ft
Note: The must be [tex]0.04v^2[/tex] instead of [tex]0.04v[/tex].
Given:
The stopping distance, d ( in feet) for a van moving at a velocity (speed) v miles per hour is modeled by the equation:
[tex]d=0.04v^2+1.1v[/tex]
To find:
The stopping distance for a velocity of 10 miles per hour.
Solution:
We have,
[tex]d=0.04v^2+1.1v[/tex]
where, d is stopping distance and v is velocity.
Substitute v=10 in the given equation to find the stopping distance for a velocity of 10 miles per hour.
[tex]d=0.04(10)^2+1.1(10)[/tex]
[tex]d=0.04(100)+11[/tex]
[tex]d=4+11[/tex]
[tex]d=15[/tex]
So, the stopping distance for a velocity of 10 miles per hour is 15 ft.
Therefore, the correct option is c.
I NEED HELP ASAP FOR BRAINLIEST
Answer:
y=x+4
Step-by-step explanation:
slope intercept form: y=mx+b
m is the slope of the line and b is the y-intercept
slope: 1
y-intercept: 4
hopefully this helps :)
Answer:
y=x+4
Step-by-step explanation:
y=mx+b
m-is the slope and b-is the y-intercept
(x, y) = (0,4)
4=0+b so b =4
substitute in the equation
y=x+4
what is the cosine of angle D
Answer:
[tex] \frac{28}{45} [/tex]
Step-by-step explanation:
Please see the attached picture for the full solution.
If you study an extra 10 hours a week for a year (52 weeks) and you earn a four-year scholarship valued at $50,000, what is your hourly return on your investment in study time?
Answer:
$96.15Step-by-step explanation:
Step one:
given data
total number of weeks =52 weeks
study time per week is = 10 hours
total study time for the year = 52*10
=520 hours per year.
Step two:
given that the value of the scholarship for one year is $50,000.
we want to find the amount that an hour of study brings
so we have to divide the total scholarship by the amount of study time
50000/520
=$96.15
your hourly return on your investment in study time is $96.15
Show your work and solve 10w=6+24
Answer:
w=3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
10w=6+24
10w=(6+24)(Combine Like Terms)
10w=30
10w=30
Step 2: Divide both sides by 10.
10w /10= 30 /10
w=3
Will mark brainliest pls help
Answer:
18
Step-by-step explanation:
Add all the sides. But you are missing two sides. Soo since the top is 4, the bottom is two bc half is two. then the right side is 5 and the left, half is 2 so the other half is 3. 3+2=5! soooo the perimeter is 18.
Answer:
18
Step-by-step explanation:
We add up the side lengths,
[tex]5+4+3+2+2+2= 18[/tex]
by finding missing side lengths with subtraction and logic
and I'm pretty sure this is correct, but I like double-checking things.
This figure is made out of 2 rectangles,
2x5 and 3x2
The perimeter of each is 14 and 10
[tex]14+10-3-3=18[/tex]
the two 3's are the over lapping sides
We also get 18.
What is the slope of the line that passes through the points (9,5) and (21,1)? Write your answer in simplest form.
Answer:The slope of the line would be 1/3 because if you put those two coordinates in the table then you can see the the difference between 5 and 1 is 4 and the difference between 9 and 21 is 12 then do 4 divided by 12 and you get 1/3 for your slope.
Step-by-step explanation: I know math just trust me i am a sraight A student.
Bryan is buying notebooks and pens at an office supply store. Notebooks cost $3.59 and pens cost $1.49. He can spend up to $13 on these items. Let x represent the number of notebooks. Let y represent the number of pens. Enter an inequality that represents the situation.
Answer:if the notebooks cost 3.59 and pens cost 1.49, with x representing the notebooks and y representing the number of pens and an amount of $13, the inequality would be written as 3.59x+1.49y13
Step-by-step explanation:
Slope review
PROBLEM : What is the slope of the line whose equation has the following solutions? Give an exact number.
Solution: x = -2.5 y= 0.5
Solution: x=2 y = 2
The slope is:
To find slope, we must use the slope formula*.
[tex]m = \frac{2 - 0.5}{2 - (-2.5)} = \frac{1.5}{4.5}[/tex]
The slope is 1.5/4.5.
Systems of equations, solve by substitution please!
x + 7y = -37
4x - 3y = 7
Step-by-step explanation:
make the coefficients same
then if sign are same subtract the one you wanna cancel it then here it goes
lam gonna start making coefficient of x sam like this:
4.X+7y= -37
1.4X-3y=7
then i will subtract all x or cancel to each other then
4X+28y= -148
-
4X-3y=7
and then -×-=+
add all y
31y=141
y= 4.55 then we take one of the equation then substitute y to 4.55 so i chose first equation
X+7(4.55)=-37
X+31.85=-37
so take 31.85 to the side it will become -31.85
then X=-37-31.85
X=68.85
i hope that it will help you
what is 76.385 + 8.93
What is the slope ? M=
Answer:
-3/2
Step-by-step explanation:
The slope is found by
m = ( y2-y1)/(x2-x1)
Using the points (-4,11) and ( 0,5)
m = ( 11-5)/( -4-0)
= 6/-4
= -3/2
NEED HELP ASAP. WILL GIVE BRAINLIEST
Let w represent the sum of vectors u and v. Find the magnitude of w and the angle between w and u given the following information: u = 14 |v1 = 16 The angle between u and w is 120°.
The magnitude of w is approximately?
The angle between w and u is approximately?
Answer:
The magnitude of w is approximately 26.
The angle between w and u is approximately 32.2°.
Step-by-step explanation:
The magnitude of w is approximately 15.1, and the angle between w and u is approximately 62.67 degrees and this can be determined by using the given data.
Given :
Let w represent the sum of vectors u and v. |u| = 14 |v| = 16 The angle between u and w is 120°.a) The magnitude of 'w' is calculated using the below formula:
[tex]w = \sqrt{u^2+v^2+2uvcos\theta }[/tex]
Now, substitute the values of u, v, and [tex]\theta[/tex] in the above formula.
[tex]w = \sqrt{14^2+16^2+2\times14\times16\;cos120 }[/tex]
Simplify the above expression.
[tex]w =15.1[/tex]
b) The angle between w and u is calculated using the below formula:
[tex]tan\beta =\dfrac{vsin120}{u+vcos120}[/tex]
Now, substitute the above values of u and v in the above expression.
[tex]tan\beta =\dfrac{14\times sin120}{14+16\times cos120}[/tex]
Simplify the above expression in order to determine the value of [tex]\beta[/tex].
[tex]\beta = 62.67^\circ[/tex]
The magnitude of w is approximately 15.1, and the angle between w and u is approximately 62.67 degrees.
For more information, refer to the link given below:
https://brainly.com/question/13188123
please help with these few!!?
Answer:
Triangle 6: 74
Triangle 7: 29
Triangle 8: 61
Triangle 9: 33
Step-by-step explanation:
Every triangle has a total degree angle of 180 degrees. Add the two sides that are known and subtract the sum from 180 degrees to find out the last angle.
8 What value of x makes the equation 5(7x-3) - x=-4x – (-9- 2x)
true?
HELPPPPPPP PLEASE!!!!!
Answer:
i am so sorry that i dont know