Simplify the following expression:
(3i+ 4) -i + 4(6 +2i)
A. 14+8i
B. 27 + 11i
C. 14+41i
D. 28 + 10i
Answers
9514 1404 393
Answer:
D. 28 +10i
Step-by-step explanation:
As with any "collect terms" problem, you first identify the like terms, then add their coefficients. You can start with either the real or the imaginary terms to obtain a result that will point you to the correct answer choice. Of course, the distributive property works in the usual way.
(3i+ 4) -i + 4(6 +2i) = 3i +4 -i +24 +8i . . . . eliminate parentheses
= (4 +24) +(3 -1 +8)i . . . . . . . group like terms
= 28 +10i
Related Questions
pls help!! correct answer will be marked brainliest
Answers
Answer:
67.7
Step-by-step explanation:
Because it is the exact same as 67.7 angle n is. So it is 67.7 I went over this recently so I understand your pain!
) As an ice cube melts its surface area is decreasing at a rate of 6cm2/sec. Find the rate at which the length of each side is decreasing at the moment when each side has length 2 cm. [Hint: a cube has 6 sides and each side has area x 2 where x is the side length]
Answers
Answer:
The rate of decreasing of the length is 0.25 cm/s.
Step-by-step explanation:
The surface area of the ice cube is:
[tex]A_{ice}=6x^{2}[/tex]
Where x is the side of the cube.
Let's take the derivative of A with respect to "t" to get the rate of change.
[tex]\frac{dA_{ice}}{dt}=12x\frac{dx}{dt}[/tex]
We know that dA/dt = 6 cm²/s and x is 2 cm, so we just need to solve it for dx/dt which is the rate change of the length.
[tex]6=12(2)\frac{dx}{dt}[/tex]
[tex]\frac{dx}{dt}=\frac{1}{4}\: cm/s[/tex]
Therefore, the rate of decreasing of the length is 0.25 cm/s.
I hope it helps you!
What is the miss angle in F?
Answers
Answer:
45
Step-by-step explanation:
The two angles add to 90 degrees since they are a right angle
F + 45 = 90
F = 90-45
F = 45
Determine whether the statement is always, sometimes, or never true. Lines AB, CD, and EF determine plan P. If GH intersects AB, then GH lies on plan P.
Answers
=======================================================
Explanation:
The plane P can be thought of a perfectly flat ground. Now imagine a flag pole which represents line GH. If AB is drawn in chalk on the pavement, and this line AB intersects the base of the flagpole, then we've made AB and GH intersect. However, this example shows that GH is not on the plane P.
Is it possible to have GH be in the the plane? Yes. We could easily draw another chalk line on the ground to have it intersect AB somewhere. But as the previous paragraph says, it's also possible that GH is not in the plane.
Therefore, the statement is sometimes true
Find the sum of the geometric series if n=6, r= 1/4, a = 2.
Answers
Sn = a(1-r^n)/(1-r)
Sn= 8(1-1/4096)/3= 2.67
a letter to PTA chairman about school problems
Answers
Answer:
Dear Chairman/or MR.?….
Re: Concerns regarding insanitary conditions/health of children
I would be grateful if you could let me have the latest Minutes of PTA Meetings particularly if they relate to the health of young people as it relates to the lack of proper cleaning and the general insanitary conditions in the toilets and areas where food is consumed by children
Whilst l am aware that schools are always short of cash for what may be regarded as non-essentials, l would like the opportunity to discuss with you my ideas on dealing with this very important aspect of basic hygiene, cleanliness and education if it is found to be that the insanitary conditions are such which young people themselves may be partly responsible. If funds are needed for the purchase of specific items l have suggestions as to the raising of funds for these.
I look forward to hearing from you as a matter of urgency.
Yours sincerely,
, if addressed by name/ faithfully, if not by name,
Step-by-step explanation:
Casey boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 5.6 radians per minute and has a radius of 50 feet. The center of the Ferris wheel is 55 feet above the ground. Let t represent the number of minutes since the Ferris wheel started rotating.
a. Write an expression (in terms of t) to represent the varying number of radians θ Ryan has swept out since the ride started.
b. Write an expression (in terms of t) to represent Ryan's height (in feet) above the ground.
Answers
Solution :
It is given that :
Casey boarded a Ferry wheel at position of 3 'o' clock.
The angular speed of the Ferry wheel = 5.6 radians per minute
The radius of the Ferry wheel = 50 feet
The height of the center wheel of the Ferry from the ground = 55 feet
Let the number of minutes be = t
a). The expression of the varying number of radians θ is given by :
After t minutes, θ = angle swept
θ = 5.6 t radians
b). Finding the height from the center of the wheel.
We know that : y = r sin θ
Given r = 50 feet
So, y = 50 sin (5.6 t) feet
Therefore, the height above the ground can be found by :
h = y + 55 (from ground)
h = 50 sin (5.6 t) + 55 feet
Evaluate 4x - y if x = 3 and y = 6
Answers
Answer:
The answer is 6
Step-by-step explanation:
4 (3) - 6
12 - 6
= 6.
Solve for x. 4/x + 3/x =14 answer choices is 2,-2,1/2,3/7,1/4
Answers
Answer:
=1/2
Step-by-step explanation:
i hope i'm right
[tex]2 {a}^{2} - 3ab + {b}^{2} from3 {a}^{2} + 2ab - {b}^{2} [/tex]
Answers
Answer:
a (a - b)
Step-by-step explanation:
[tex]2a^{2}-3ab+b^{2} from 3a^{2} + 2ab - b^{2}[/tex]
Now, as [tex]2a^{2}-3ab+b^{2}[/tex] is from [tex]3a^{2} + 2ab - b^{2}[/tex]
so it will be subtracted :
[tex]3a^{2} + 2ab - b^{2}[/tex] [tex]-2a^{2}-3ab+b^{2}[/tex]
= [tex]a^{2} - ab[/tex]
= a (a - b)
if f(x)= 9+3x, find f(-2)
Answers
Answer:
f(-2) =3
Step-by-step explanation:
f(x) = 9+3x
Let x=-2
f(-2) = 9+3(-2)
= 9-6
= 3
f ( -2 ) = 9 + 3( - 2 )
f ( -2 ) = 9 - 6
f ( -2 ) = 3
What is the volume of this cube?
Answers
Answer:
1 cubic ft
Step-by-step explanation:
Volume = Length × width × height
= 1 × 1 × 1
= 1
Answer:
1 cubic ft
Step-by-step explanation:
Volume = l × w × h
= 1 × 1 × 1
= 1 cubic ft
Rob has 6 quarts of apple cider for the fall fair. He pours the cider into glasses to set on picnic tables. He pours 6 ounces of cider into each glass. How many glasses of cider does Rob set on the tables? Show your work.
Answers
Answer:
6 x 32 = 192 divided by 6 = 34
Step-by-step explanation:
Solving a word problem involving rates and time conversion
A car travels at an average speed of 52 miles per hour. How long does it take to travel 247 miles?
Answers
Answer:
It takes 4.75 hours(4 hours and 45 minutes) to travel 247 miles.
Step-by-step explanation:
This question is solved by rates, using a rule of three.
52 miles in one hour. How many hours for 247 miles?
1 hour - 52 miles
x hours - 247 miles
Applying cross multiplication:
[tex]52x = 247[/tex]
[tex]x = \frac{247}{52}[/tex]
[tex]x = 4.75[/tex]
It takes 4.75 hours = 4 hours and 3/4*60 = 45 minutes to travel 247 miles.
Help will be appreciated I need help with math
Answers
4. (0,-14)
5. (14,0)
6. (0,0)
HELP!!!!
5^m x (5^-7)^m = 5^12
Answers
Answer:
not sure lol but, like it up
Step-by-step explanation:
A semi-circle is connected to an isosceles triangle. The radius of the semi-circle is 2 inches, and the height of the triangle is 6 inches. Find the area of the composite figure.
Answers
Answer:
18.28 sq inches
Step-by-step explanation:
the area of the composite fig. =
(½×3.14×2²)+(½×4×6)
= 6.28 + 12 = 18.28
Estimate the solution to the following system of equations by graphing. 3x + 5y = 14
6x - 4y = 9
Answers
Step-by-step explanation:
hope helps u
have a nice day
What is the slope of a line that runs through (-2,4) and (3,7)
Answers
Answer: m=0.6
Step-by-step explanation:
Use the m= y2-y1/x2-x1 formula to calculate slope.
7-4=3
Divided by
3-(-2)=5
3/5= 3/5 or 0.6
Answer:
slope = 3/5
Step-by-step explanation:
slope = rise/run
---------------------------
y rises from 4 to 7 = 3
x runs from -2 to 3 = 5
slope = 3/5
If you rolled two dice, what is the probability
that you would roll a sum of 4?
Give your answer as a simplified fraction. Enter
the number that belongs in the green box.
3
second
first
1 2
4 5 6
11,1 1,2 1,3 1,4 1,5 1,6
22,1 2,2 2,3 2,4 2,5 2,6
33,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
55,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
Enter
Answers
Answer:
1/12
Step-by-step explanation:
3/36=1/12
DO NOW
1)_Write an equation that represents the
line whose slope is 5 and has a (-2,4) on
the line.
Answers
Answer:
y=5x+14
Step-by-step explanation:
Plug this into the equation y-y1=m(x-x1) where m is the slope. y1 is equal to 4, x1 is equal to -2, and m is equal to 5. This will make the equation y-4=5(x--2). This is equal to y-4=5(x+2). Use the distributive property to get y-4=5(x)+5(2). Simplify to get y-4=5x+10. We want to isolate y so we have to add 4 to both sides. This will be equal to y=5x+10+4. Combine like terms to get y=5x+14. Therefore, the equation is y=5x+14.
If this helps please mark as brainliest
4. A room has 20 seats - some are stools and some are chairs. Each stool has 3 legs and each chair has 4 legs.
Altogether there are 68 legs.
How many
stools are there?
Answers
Answer:
There are 12 stools in the room
4 more than a number is 12
Answers
Answer:
555
Step-by-step explanation:
Answer:
4 + x = 12
x = 8
Step-by-step explanation:
4 more than a number is 12
I will represent the mystery number as "x"4 + x = 12
x = 8
i need help badly due today
Answers
Answer:
Solid A
Step-by-step explanation:
Which of the following statements are true about solids shown above
Check all that apply
A prism a has a lateral surface are of 60 cm 2
B prism b has a total surface are of 110 cm 2
C prism b has larger surface area
D prisms A and B have different values for lateral surface area
Answers
Ans its b and c
Step-by-step explanation:
Three bowls and four mugs can hold a total of 2.52 litres of water. Each bowl can hold
70 ml more than a mug. How much water can a mug hold? Give your answer in litres.
(with full working)
Answers
9514 1404 393
Answer:
0.33 litres
Step-by-step explanation:
If a mug can hold a volume of m litres, then a bowl can hold a volume of m+0.07 litres. The total volume held by the given containers is ...
3(m +0.07) +4m = 2.52
7m +0.21 = 2.52 . . . . . . . . simplify
7m = 2.31 . . . . . . . . . . . . . subtract 0.21
m = 0.33 . . . . . . . . . . . . . divide by 7
Each mug can hold 0.33 litres.
Can someone help me please?
Answers
Answer:
.08
Step-by-step explanation:
Answer:
Hi, there your answer is 0.08
Step-by-step explanation:
common
factors of 10 and 20
Answers
Answer:
Step-by-step explanation:
common factor of 10 and 20 is 2 and 10 because 2 and 10 are the numbers which didides both the number exactly.
Find the volume. If you have any problems please tell me thank you.
Answers
Answer:
Step-by-step explanation:
Formula = V = l x w x h
V = 4.25 x 2.75 x 5
V = 58.438 --> 58.44
Solve 2x^2
+ x - 4= 0.
x2 +
= 0
DONE
Answers
[tex]\\ \sf\longmapsto 2x^2+x-4=0[/tex]
[tex]\\ \sf\longmapsto 2x^2+x=4[/tex]
[tex]\\ \sf\longmapsto 8(2x^2+x=4)[/tex]
[tex]\\ \sf\longmapsto 16x^2+8x=32[/tex]
[tex]\\ \sf\longmapsto (4x)^2+2(4x)(1)=32[/tex]
[tex]\\ \sf\longmapsto 4x^2+2(4x)(1)+1^2=32+1^2[/tex]
[tex]\\ \sf\longmapsto (4x+1)^2=33[/tex]
[tex]\\ \sf\longmapsto 4x+1=\pm\sqrt{33}[/tex]
[tex]\\ \sf\longmapsto 4x=-1\pm\sqrt{33}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-1\pm\sqrt{33}}{4}[/tex]