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Simplify the expression by rewriting it as a complex number in the standard form a+bi
Given:
The expression is
[tex]\sqrt{64}+\sqrt{-144}[/tex]
Rewriting it as a complex number in the standard form a+bi.
To find:
The missing values in the given simplification.
Solution:
We have,
[tex]\sqrt{64}+\sqrt{-144}[/tex]
It can be written as
[tex]\sqrt{64}+\sqrt{-144}=\sqrt{8^2}+\sqrt{-1\cdot 12^2}[/tex]
[tex]\sqrt{64}+\sqrt{-144}=\sqrt{8^2}+\sqrt{-1}\cdot \sqrt{12^2}[/tex]
[tex]\sqrt{64}+\sqrt{-144}=\sqrt{8^2}+i\cdot \sqrt{12^2}[/tex] [tex][\because \sqrt{-1}=i][/tex]
[tex]\sqrt{64}+\sqrt{-144}=\sqrt{8^2}+i\cdot 12[/tex]
[tex]\sqrt{64}+\sqrt{-144}=8+12i[/tex]
Therefore, the missing values are [tex]-1,\ i,\ 12i[/tex] respectively.
Answer:
Sample Answer for Edmentum
Like and Rate!
Step-by-step explanation:
Help please I will Brainly
Answer:
we have the same computer
Step-by-step explanation:
Answer:
[tex]114\:\mathrm{yd^2}[/tex]
Step-by-step explanation:
The composite shape consist of two rectangles. We can find the area of these two rectangles and add them to get our answer:
[tex]10\cdot9+6\cdot 4= 90+24=\fbox{$114\:\mathrm{yd^2}$}[/tex].
PLEASE HELP AND ANSWER ALL 3
Answer: 10.) -6 and it's B
11.) A
12.) C
Step-by-step explanation:
Which rule describes the translation?
y
5
B
С
O(x, y) - (x -8, y - 3)
O(x, y) = (x - 3, y + 8)
(x, y) + (x + 8, Y-3)
O (x, y) = (x + 3y + 8)
B'
C'
A
-5
D
A'
D'
Answer:
(x,y) -> (x + 8, y - 3)
Step-by-step explanation:
Move any point to the right 8 units, and down 3 units. You are just translating the shape, not dilating, reflecting, or rotating it.
What is the value of 1/2 x^3+3.4y when x=2 and y=5?
A hose fills a hot tub at a rate of 4.68 gallons per minute. How many hours will it take to fill a 338 gallon hot tub?
Answer:
1 hour and 12 mins and 56 seconds
Step-by-step explanation:
Hope this helps and have a great day!!!
father's step is 65cm long while his daughter's step 4dm long. they start walking together. when the father has walk 8 step, his daughter has walked... step
Answer:
5 steps
Step-by-step explanation:
[tex]65cm \times 8 = 520cm[/tex]
[tex]4dm = 40cm \\ 65 - 40 = 25[/tex]
[tex]25 \times 8 = 200cm \: gap[/tex]
[tex]200 \div 40 = 5[/tex]
Answer:
His daughter has walked 13 steps
Step-by-step explanation:
Unit Conversion
Each step of the father is 65 cm long and each step of his daughter is 4 dm long.
Recalling that 1 dm = 10 cm, then each step of the daughter is 4*10 = 40 cm long.
Now we can compare both measures. When the father has walked 8 steps, this distance is 8*65 = 520 cm, and the daughter has walked 520/40 = 13 steps.
His daughter has walked 13 steps
Sort the following expressions by rewriting tham is the table.
Answer:
Helllllllllllllllllo pls say it back or ur stupied
Step-by-step explanation:
Geometry pls halp... I have been asking this single question for over half an hour
Answer:
first one is SAS
Step-by-step explanation:
Help me I'm too tired to think and this is easy.
Please tell me if this number is greater than, less than or equal to 5. The number is -(-5)
Answer:
equal to
Step-by-step explanation:
two negatives equals positive
Answer:
Equal
Step-by-step explanation:
Double negative equals a positive. Gn
Please help 30 points
Answer:
The total surface area is 973.89 ft
Step-by-step explanation:
The formula for the surface area of a cylinder is A=2πrh+2πr2.
The top cylinder has a radius of 5 ft, and height of 2 ft.
The bottom cylinder has a radius of 10 ft, and a height of 2 ft.
Plug in the numbers for each and you get:
Top Cylinder:
A=2π(5)(2)+2π(5^2)
A=2π(10)+2π(25)
A= 62.83185307 + 157.079327
A= 219.9111801
A≈ 219.91
Bottom Cylinder:
A= 2π(10)(2)+2π(10^2)
A= 2π(20)+2π(100)
A= 125.6637061 + 628.3185307
A= 753.9822368
A≈ 753.98
Combined:
753.98 + 219.91 = 973.89
You are driving up a mountain. At the base of the mountain you see a sign that states the elevation above sea level is 3,720 feet at this point. You then travel a horizontal distance of 5 miles to the top of the mountain, and see another sign that states the elevation is 4,215 feet above sea level. What was the average slope of the mountain you just climbed in feet/mile?
A) 843 ft/mi
B) 744 ft/mi
C) 99 ft/mi
D) 0.0188 ft/mi
Step-by-step explanation:
Slope of the mountain
= Rise in height / Run in distance
= (4215ft - 3720ft) / 5 mi
= 495ft / 5mi
= 99ft/mi. (C)
Many states assess the skills of their students in various grades. One of the tests provided by a national association assesses the reading skills of 12th-grade students. In a recent year, the national mean score was 286 and the standard deviation was 38. Assuming that these scores are approximately Normally distributed, N(286, 38), use the 68-95-99.7 rule to give a range of scores that includes 95% of these students.
Answer:
95% of these scores are between 210 and 362.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 286, Standard deviation = 38
Use the 68-95-99.7 rule to give a range of scores that includes 95% of these students.
This is within 2 standard deviations of the mean. So
286 - 2*38 = 286 - 76 = 210
286 + 2*38 = 286 + 76 = 362
95% of these scores are between 210 and 362.
Please help this is worth 30 points
At the same time of day, a tree and a flagpole cast shadows as shown below.
How tall is the tree?
Answer:
16 feet
Step-by-step explanation:
Height of tree = [tex]\frac{20}{15}[/tex] × 12ft
= 16ft
Evaluate the expression when a =
and b = 6.
16a? – 4b =
Answer:
Step-by-step explanation:
16(1/4)^2 - 4(6)
16(1/16) - 24
1 - 24 = -23
Solve for x
5x + 2 = 17
Answer:
r
Step-by-step explanation:
r
Answer:
Step-by-step explanation:
Here you go mate
Step 1
5x+2=17 Equation/Question
Step 2
5x+2=17 Simplify
5x+2=17
Step 3
5x+2=17 Subtract 2
5x=15
Step 4
5x=15 Divide
answer
x=3
Hope this helps
HELP MY MOM IS GOING TO KILL ME
Answer:
−a2+17b
Step-by-step explanation:
Sarah has 782 stickers in her sticker book. It took 8 stickers to fill one page. She filled each page before putting stickers on another page. How many full pages of stickers does Sarah have
Answer:
97
Step-by-step explanation:
if there are a total of 782 stickers and 8 stickers fill one page the number of full pages can be found by dividing 782 by 8. Doing this gives us 97.75, but since the question is asking us about full pages the answer if 97 full pages of stickers.
Someone answer this for me. I will give u branily whoever right.
Step-by-step explanation:
21x+72+105+78=360
21x=105
x=5
if AB=BA= I then write the relation between matrix A and matrix B
Answer:
If AB = BA = I, then B is inverse of A and vice-versa.
Step-by-step explanation:
Given: AB = BA = I
To find: The relation between matrix A and B.
If AB = BA = I, then B is called the inverse matrix of A and is denoted by [tex]A^{-1}[/tex].
In that case, A is said to be invertible.
Also, if B is the inverse of A, then A is also the inverse of B.
Hence, the relation between A and B is that both are inverse of each other.
Help me pleaseeeeeeeeeeee
Answer: 990 lb
Step-by-step explanation:
t = (4 x 180) + (3 x 90)
t = 720 + 270 = 990
PLS HELP ASAP
WILL MARK BRAINLIEST
Answer:
first blank is x, then -7, then 11, then -11.
Step-by-step explanation:
Hope it helps!
guys help i dont know this Find the value of the expression 2x – 3y + 4z, if x = 10, y = -12 and z = 11.
Answer:
100 answer is correct
Step-by-step explanation:
2×10-3×-12+4×11
20+36+44
100 answer is correct
Step-by-step explanation:
2x-3y+4z
x=10
y=12
z=11
2(10)-3(-12)+4(11)
20+36+44
and the answer is 100
(made a lot of mistakes so edited answer!)
good day :)
It's for middle SCHOOL PLZzzz HELPPP!!!
You have a coupon for an additional 25% off the price of any sale item at a store. The store has put a robotics kit on sale for 15% off the original price of $40. What is the price of the robotics kit after both discounts?
Answer:
$25.50
Step-by-step explanation:
Answer:
(40)(15/100)=6
(40)(25/100)=10
10+6=16
orginal price at 40
After discounts 16
40-16=24
so you can buy it in 24$
Hope it helped you
If AD = 18 then
AB=
BC=
BC=
Step-by-step explanation:
where is the diagram or shape my guy
A petri dish has 10, 000 bacteria in it. After 4 hours the bacteria’s population increased to 20,000. If the number of colonies grows exponentially, write a formula for the number of bacteria in the dish at any time t, where t is in hours
Answer:
[tex]P(t) = 10000e^{0.1733t}[/tex]
Step-by-step explanation:
The population of bacteria grows exponentially, which means that it can be represented by a function in the following format:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate.
A petri dish has 10, 000 bacteria in it.
This means that [tex]P(0) = 10000[/tex]. So
[tex]P(t) = 10000e^{rt}[/tex]
After 4 hours the bacteria’s population increased to 20,000.
This means that [tex]P(4) = 20000[/tex], and we use this to find the growth rate. So
[tex]P(t) = 10000e^{rt}[/tex]
[tex]20000 = 10000e^{4r}[/tex]
[tex]e^{4r} = \frac{20000}{10000}[/tex]
[tex]e^{4r} = 2[/tex]
[tex]\ln{e^{4r}} = \ln{2}[/tex]
[tex]4r = \ln{2}[/tex]
[tex]r = \frac{\ln{2}}{4}[/tex]
[tex]r = 0.1733[/tex]
So, the formula is given by:
[tex]P(t) = 10000e^{0.1733t}[/tex]
y = -1X + 9
Use the equation to predict the number of visits per week to a coffee shop that is 3 blocks away.
Answer:
Step-by-step explanation:
It is a pity that we can't see the name of the units on the y axis. I sound like a grumpy old man (which I am), but the answer might be easy enough. Follow the line upwards from x=3 to the best fitting line. Then go left until you hit the y axis.
All other things being equal, you should get 6. I'm not positive about this because the units are differently spaced along each axis. But I do think you have the right equation y = -x + 9
Let Ln denote the left-endpoint sum using n subintervals and let Rn denote the corresponding right-endpoint sum. In the following exercise, compute the indicated left and right sums for the given function on the indicated interval.
L4 for f(x)=1/x−1; [2,3]
Answer:
[tex]L_4=0.7595[/tex]
Step-by-step explanation:
We are given that
[tex]f(x)=\frac{1}{x-1},[/tex][2,3]
We have to find L4
It means n=4
[tex]\Delta x=\frac{b-a}{n}=\frac{3-2}{4}=\frac{1}{4}=0.25[/tex]
Now, intervals are
[2,2.25],[2.25,2.50],[2.5,2.75],[2.75,3]
Now,
[tex]L_4=f(x_0)\Delta x+f(x_1)\Delta x+f(x_2)\Delta x+f(x_3)\Delta x[/tex]
[tex]L_4=\frac{1}{2-1}(0.25)+\frac{1}{2.25-1}(0.25)+\frac{1}{2.5-1}(0.25)+\frac{1}{2.75-1}(0.25)[/tex]
[tex]L_4=0.7595[/tex]
Use the fractions 36in./1yd and 2.54 cm/1 in convert 3yd to cm