Answer:
Step-by-step explanation:
(1 - i) / (sqrt(3 + 4i)
= (1 - i) / [tex]\sqrt{3 + 4i}[/tex]
=> multiply and divide by conjugate of denominator
= [tex](1 - i) / \sqrt{3 + 4i} * \sqrt{3 - 4i} / \sqrt{4 - 3i}[/tex]
= [tex](1 - i)*(\sqrt{3 - 4i} ) / (\sqrt{3 + 4i} *\sqrt{3 - 4i})[/tex]
= [tex](1 - i) * (\sqrt{3 - 4i} ) / \sqrt{(9 - 16i^{2} )[/tex]
= [tex](1 - i) * (\sqrt{3 - 4i} ) / \sqrt{(9 - (-16) )[/tex]
= [tex](1 - i) * \sqrt{3 - 4i} ) / \sqrt{25}[/tex]
= [tex](1 - i) * \sqrt{3 - 4i} / 5[/tex]
= [tex]\sqrt{(1 - i)^{2} } * \sqrt{3 - 4i} / 5[/tex]
= [tex]\sqrt{(1 + -1 -2i)*(3 - 4i)} / 5 \\\sqrt{-2i * (3 - 4i)} / 5\\\sqrt{-6i + 8*-1} /5 \\\sqrt{-6i - 8 } / 5[/tex]
Use the information in the table to solve Exercises 4-6.
Morgan's favorite spaghetti sauce is available in two sizes: pint
Each size and its price are shown in the table.
Size
Quantity (oz)
Price (5)
pint
16
3.98
quart
32
5.98
Answer:
Step-by-step explanation:
seventeen cus it is :)
A box's volume is equal to 600 cubic
inches. If the width of the box is 7
inches less than the length, and the
height is 10 inches less than the length,
find the dimensions of the box.
Answer:
Step-by-step explanation:
Length = x
width = x - 7
height = x - 10
volume = 600 in^3
Volume = L * w * h
600 = x * (x - 7)*(x - 10)
600 = x * (x^2 - 17x + 70)
600 = x^3 - 17x^2 + 70x
x^3 - 17x^2 + 70x - 600 = 0
There is a genius somewhere that could solve this using algebra. The rest of us have 2 choices. We can graph it (see below) or we could use a program that solves it for us. I'll do both for you.
a = 1
b = - 17
c = 70
d = - 600
There is only 1 real solution: x = 15
L = 15
w = 8
h = 5
That has to be one of the ugliest graphs made. It does into the hundreds of thousands and it still looks like a straight line. Trust me. It's not.
A rectangle has a length at least four more than five times the width. If the
perimeter is at least 44 units, find the least possible width.
Answer:
width of 3 units
Step-by-step explanation:
let 'w' = width
let '4+5w' = length
P = 2l + 2w
44 = 2(4+5w) + 2w
44 = 8 + 10w + 2w
36 = 12w
w = 36/12
w = 3
Solve the equation 4x^2 – 32x + 64 = 0.
Answer: x = 4
Step-by-step explanation: 4x^2−32x+64=0
4(x−4)(x−4)=0
x−4=0 x−4=0
x=4
someone please help and show work
Answer:
I already answered this for someone, but what you want to do is combine/cancel out like terms. So cancel out x on 2+7x/x to get 2+7/1. The first step in solving most rational equations is combining/canceling like terms, so follow through with that here.
help me pleassseeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
it is aas triangle
? Question
Emma also wonders how long it will take her balance of $300 to reach $450, assuming she doesn't make
any payments toward it. Write the equation to represent the situation, and solve it using the inverse
relationship between exponential and logarithmic expressions.
Type the correct response in the box. Use numerals instead of words. Round your answer to the nearest
tenth.
It will take about
years for Emma's balance to reach $450.
Part D
Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem:
Her initial balance is of $300, hence [tex]A(0) = 300[/tex].The growth rate is of 15%, hence [tex]r = 0.15[/tex]Then:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 300(1 + 0.15)^t[/tex]
[tex]A(t) = 300(1.15)^t[/tex]
It will reach $450 after t years, for which A(t) = 450, hence:
[tex]A(t) = 300(1.15)^t[/tex]
[tex]450 = 300(1.15)^t[/tex]
[tex]1.15^t = \frac{450}{300}[/tex]
[tex]1.15^t = 1.5[/tex]
[tex]\log{(1.15)^t} = \log{1.5}[/tex]
[tex]t\log{1.15} = \log{1.5}[/tex]
[tex]t = \frac{\log{1.5}}{\log{1.15}}[/tex]
[tex]t = 2.9[/tex]
It will take about 2.9 years for Emma's balance to reach $450.
A similar problem is given at https://brainly.com/question/14773454
Answer:
It will take about 2.9 years for Emma’s balance to reach $450.
(3/4(3/5) simplify i need the answer because i dont get it
Answer:
35 is already in the simplest form. It can be written as 0.6 in decimal form (rounded to 6 decimal places).
...
Reduce 3/5 to lowest terms
Find the GCD (or HCF) of numerator and denominator. GCD of 3 and 5 is 1.
3 ÷ 15 ÷ 1.
Reduced fraction: 35. Therefore, 3/5 simplified to lowest terms is 3/
Step-by-step explanation:
16. The quotient of 7 and a number
Answer:
7/n would be a algebraic express
Step-by-step explanation:
Help me please quickly
Answer:
x ≥ 1
Step-by-step explanation:
→ As it is a shaded circle you know it ≤ or ≥
x ≥ 1
Examine the following table, which represents some points on a line.
x 3 0 −3 −6 −9
y −3 −2 −1 0 1
What is the equation for the line in slope-intercept form?
y=−3x−2y is equal to negative 3 x minus 2, , ,
y=3x−2y is equal to 3 x minus 2, , ,
y=−13x−2y is equal to negative 1 third x minus 2, , ,
y=−13x−6y is equal to negative 1 third x minus 6, , ,
y=−3x−6
Answer:
(c) y = −1/3x −2
Step-by-step explanation:
We notice two things in the table.
y goes up by 1 when x goes down by 3.y = -2 when x = 0 (this is the y-intercept__
The slope of the line is ...
m = (change in y)/(change in x) = +1/-3 = -1/3
Then the slope-intercept equation is ...
y = mx +b . . . . . . slope m, y-intercept b
y = -1/3x -2
Answer is C
Step-by-step explanation:
math
a person whose height is 6 feet is walking away from the base of a streetlight
Can someone help me Expand 3(z+2)
Answer: 3z+6
Step-by-step explanation:
(3) (z+2)
(3) (z)+(3) (2)
3z+6
Clarke earns
2.5
%
interest a savings account each year. If Clarke deposits
$
2
,
000.00
into a savings account, how much interest will Clarke earn during the first year?
Answer:
$ 50.00
Step-by-step explanation:
Hope this helps!
Mark has $360 in his savings account and Trevor has $510 in his savings account. The interest rate is 3%. How
much will each person have in their savings account at the end of 5 years? Show your work.
Answer:
Mark: 54
Trevor: 765
Step-by-step explanation:
For each, you multiply the amount, time period, and the percentage.
(make sure to turn the percentage to a decimal)
I’m so sorry If my answer is wrong
what is the answer to 32÷(-8)=
Answer:
-4
Step-by-step explanation:
32÷(-8)=-32÷8
=-4
Describe the signs (positive/negative) of the coordinate in each of the regions shown below. Then give one point contained within each region.
Answer:
A = positive
B = positive, negative
C = negative
D = positive, negative
Answer:
A Positive coordinates (5,5) B Negative and Positive coordinates (-5,5) C Negative coordinates (-5,-5) D Negative and Positive coordinates (5,-5)
Step-by-step explanation:
Pls mark brianlist hope this helps .
Pharaoh, Diego, and Devonte all got jobs
at different clothing stores. At Pharaoh's
store it costs $48 to get 3 shirts. At Diego's
store it costs $96 to get 16 shirts. At
Devonte's store it costs $56 to get 14
shirts. Which one is the best deal.
Answer:
i think the answer is Devonte's store because you get 14 shirt for $56
Step-by-step explanation:
Pharaoh's good it's not too expensive but you only get 3 shirts , Diego's is too expensive even if you get 16 shirts it's for $96
Geri jogs every fourth day. Sarah jogs along the same path every fifth day. Both girls jog on the path on July 7. What is the next date they will both jog on the path?
Answer:
The next day they will both run on the path is July 27th.
We can find this by making columns writing every date and seeing when they intersect.
4 5
8 10
12 15
16 20
20
We can then add this to the current date to find the date they will next run together.
Step-by-step explanation:
hope this helps. . . <3
good luck! UwU
What is identity matrix.
Answer:
a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros. The effect of multiplying a given matrix by an identity matrix is to leave the given matrix unchanged.
which of the following numbers closest to 6? 34, 37, 38, 33.
John rented a jet ski for $199.95. The rental included a rental fee of $75 and an additional charge of $24.99 per hour. How many hours did John rent the jet ski?
Answer:
John rented the jet ski for 5 hours
Step-by-step explanation:
Step 1- Subtract $75 from $199.95 and you should end up with $124.95
Step 2- Divide $124.95 by $24.99 and you should end up with 5
Step 3- John rented the jet ski for 5 hours
Answer:
John rented the jet ski for 5 hours.
Step-by-step explanation:
Take the total cost: $199.95, and subtract $75 because that was included in the cost. You get 124.95. Next you divide $24.99 by 124.95, because $24.99 was the amount he paid per hour, and $124.95 is the amount that he paid in total for all the hours that he jet skied, and you get 5 hours.
50 POINTS What is the greatest common factor of 4k, 18k4, and 12?
A) 2
B) 4
C) 2k
D) 4k
Answer:
The greatest common factor of 4k, 18k4, and 12 is 2.
Answer A 2
Hope this helps
PLEASE HELP!!!
[tex]\sqrt\frac{7}{8}[/tex] In simplest radical form
Answer:
Step-by-step explanation:
[tex]\sqrt{\frac{7}{8} } = \sqrt{\frac{7}{8}*\frac{8}{8}[/tex]
= sqrt(56)/8
Answer:
(√14)/4
Step-by-step explanation:
You can "rationalize the denominator" after you take the root, or you can make the denominator a perfect square before you take the root.
[tex]\sqrt{\dfrac{7}{8}}=\dfrac{\sqrt{7}}{2\sqrt{2}}=\dfrac{\sqrt{7}}{2\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{14}}{4}\\\\\sqrt{\dfrac{7}{8}}=\sqrt{\dfrac{7}{8}\cdot\dfrac{2}{2}}=\sqrt{\dfrac{14}{16}}=\dfrac{\sqrt{14}}{4}[/tex]
write the sentence as an equation
46 less than m is 54.
Can someone please help me
Answer:
m - 46 = 54
Step-by-step explanation:
46 less than m is 54,
→ m - 46 = 54
Let's solve this equation,
→ m - 46 = 54
→ m = 54 + 46
→ [ m = 100 ]
So, the answer is 100.
Answer 15 and 16 and get 50 points
No link
Answer:
(1) x=5 (2) I think the answer to 16 is 3/5 but not 100% sure
Step-by-step explanation:
(1) 29=5x+4
Step 1: Flip the equation.
5x+4=29
Step 2: Subtract 4 from both sides.
5x+4−4=29−4
5x=25
Step 3: Divide both sides by 5.
5x /5 = 25 /5
x=5
what is 10 3/12 simplified??
Answer:
10 1/4
Step-by-step explanation:
A city has 3 new houses for every 7 old houses. If there are 21 new houses in the city, how many old houses are there
A. 49
B. 47
C. 52
D. 51
Answer:
A. 49
Step-by-step explanation:
ratio of houses is 3 new to 7 old
21 new is 7 times more than 3, so 7 will also be 7 times more
so, 21 to 49
I hope that made sense
Can anyone help me with this question please I really need help please I’ll mark as brainliest
Answer:
[tex]f(x)=-11\times(7^x^-^1)[/tex]
Step-by-step explanation:
Stare at the numbers. Especially the first two. First one is -11. Second is [tex]-11\times 7[/tex]. Let's guess you keep multiplying. [tex]-77\times 7=-539[/tex]. Smells correct, let's confirm with the last one: [tex]-539\times7 = -3773[/tex]. I think we found a pattern. Each element is 7 times the previous one. With some practice you can just write the function, else let's divide by -11 away and let's see what we get:
[tex]f(1) = 1=7^0; f(2)=7; f(3)=7^2; f(4)=7^3[/tex]. Basically, the exponent is 1 less than the value we're evaluating the function. That leads tho the following
[tex]f(x)=-11\times(7^x^-^1)[/tex]
You go out to dinner with 2 friends. The bill was $35.60, and you
add 20% tip. All 3 of you share the total cost equally. How much
money did each person pay?
Answer:
$14.24
Step-by-step explanation: