Answer:
[tex] \large \boxed{ \boxed{ \red{ \ \rm 5 \sqrt{2} ( \cos( \dfrac{7\pi}{4} ) + i \sin( \dfrac{7\pi}{4} ) )}}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:imaginary numberPEMDAStips and formulas:[tex] \sf \: formula \: of \: trigonometric \: form : \\ \rm r( \cos( \theta) + i \sin( \theta) )[/tex][tex] \rm \: r = \sqrt{ {a}^{2} + {b}^{2} } [/tex][tex] \rm \theta = \arctan( \dfrac{b}{a} )[/tex]given:z=5-5ilet's solve:complex number:a+bi
therefore
our a is 5our b is -5[tex] \sf sustitute \: the \: value \: of \: a \: and \: b \: into \: the \: modulus : [/tex]
[tex] \rm \: r = \sqrt{ {5}^{2} + ( { - 5)}^{2} } [/tex]
[tex] \sf simplify \: squres : [/tex]
[tex] \rm \: r = \sqrt{25 + 25} [/tex]
[tex] \sf simplify \: addition : [/tex]
[tex] \rm \: r = \sqrt{50} [/tex]
[tex] \sf rewrite \: 50 \: as \: 2 \times 25[/tex]
[tex] \sf r = \sqrt{2 \times 25} [/tex]
[tex] \sf use \: \sqrt{ab} \iff \: \sqrt{a } \sqrt{b} : [/tex]
[tex] \rm r = \sqrt{25} \sqrt{2} [/tex]
[tex] \therefore \rm \: r = 5 \sqrt{2} [/tex]
[tex] \sf sustitute \: the \: value \: of \: a \: and \: b \: into \: the \: agrument : [/tex]
[tex] \rm \theta = \arctan(\dfrac{ - 5}{5} )[/tex]
[tex] \sf simplify \: divition : [/tex]
[tex] \rm \theta = \arctan( - 1)[/tex]
[tex] \theta = - \dfrac{\pi}{4} [/tex]
[tex] \sf add \: 2\pi \: to \: get \: a \: positive \: agrument[/tex]
[tex] \rm \theta = - \dfrac{\pi}{4} + 2\pi \\ \rm\therefore \: \theta = \frac{7\pi}{4} [/tex]
[tex] \sf \: sustitute \: the \: value \: of \: \rm \: r \: and \: \theta : \\ \rm 5 \sqrt{2} ( \cos( \frac{7\pi}{4} ) + i \sin( \frac{7\pi}{4} ) )[/tex]
[tex]\text{And we are done!}[/tex]
please help if you can <3
Answer:
1) x = 71
2) x = 117
5)
m<1: 35
m<2: 77
m<3: 52
m<4: 77
m<5: 65
m<6: 25
Step-by-step explanation:
1)
x + 41 + 68 = 180
x + 109 = 180
x = 71
2)
x + 47 + 16 = 180
x + 63 = 180
x = 117
3)
<2 + 103 = 180
<2 = 77
<1 + 68 + 77 = 180
<1 + 145 = 180
<1 = 35
<4 + 103 = 180
<4 = 77
<5 + 41 + 77 = 180
<5 + 115 = 180
<5 = 65
<6 + 65 = 90
<6 = 25
<3 + 103 + 25 = 180
<3 + 128 = 180
<3 = 52
Which of the following statement(s) describes the rate of change of f over the interval 1.5 SXS 3? Select all that apply.
A. The rate of change is 1/2
B. The rate of change is 2
C. The rate of change is constant
D. The rate of change is increasing
Segment MP is a diameter of circle O.
Circle O is shown. Line segment M P is a diameter. Line segment N O is a radius. Angle N O P is 150 degrees.
Which equation can be used to find mArc M N?
mArc M N – 150 = 360
Answer:
[tex]arc\ MN + 150 = 180[/tex]
Step-by-step explanation:
Given
[tex]\angle NOP = 150^\circ[/tex]
See attachment for circle O
Required
Find [tex]arc\ MN[/tex]
The sum of angles in a semi-circle is 180 degrees.
So:
[tex]arc\ MN + \angle NOP = 180[/tex]
This gives:
[tex]arc\ MN + 150 = 180[/tex]
Hence, the equation is: [tex]arc\ MN + 150 = 180[/tex]
Answer:
A
Step-by-step explanation:
just took exam and got 100%
How many moles is 1.50 X 10^23 molecules NaCl ?
Answer:
One mole NaCI
hope it help :)
This data represents the number of books checked out of the school library by five students: 10, 15, 5, 10, 20 Find the mean absolute deviation. FIRST PERSON TO ANSWER GET BRAINLIEST!
Answer:
the answer is 12
Step-by-step explanation:
you are welcome
Answer:
12......................
Rope packaged in 80-foot lengths
must be cut into 12-foot pieces to
do a certain job. If 28 such pieces
of rope are needed for the job, how
many packages of rope are needed?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 28
Answer:
it would be 5
Step-by-step explanation:
any of the answer could have really worked (not 4 since that gives you less then what is needed) but in the end it would have been 5 because 5 leaves you with only 5.33 feet of rope left
80* any one of the four numbers (ex: 5) = your answer that you got (ex: 400)
then you divide that number by 28 (ex: 33.33) and if you want to go the extra mile then do the number that you got by dividing 28 minis the number of rope pieces needed
the whole thing >
80* 5 = 400
400/28 = 33.33
33.33- 28 = 5.33
hope this helps! :)
Carlos and Bonita were just hired at a manufacturing plant. Carlos will earn $12.50 per hour. He will earn a hiring bonus of $300. Bonita will earn $14.50, but she will not get a hiring bonus. After how many hours of working will they earn the same?
Answer:
after 3 hours
Step-by-step explanation:
through: (0,3), parallel to y= -2x + 4
Ella ran 6 times around her school building. then she ran 4 miles home. Her phone told her she ran 7 miles total. Which equation represents this situation A. 6+4x=7 B. 6x+4=7 C. 6(x+4)=7
how do you work out standard form in maths
Answer:
ok
Step-by-step explanation:
is that you write down 1 and 10 then you write x10 to the power of a number
PLEASE HELP THANK U SO MUCH
Answer:
Add the area of the rectangle to the area of the triangle.
6 x 7 = 42
3 x 6 x 0.5 = 9
So the area is 42+9=51
Let me know if this helps!
You get to fill a bag with any type of candy for $1.35 per gram. You get to the counter ad have 5.23 grams of candy. How much do you have to pay?
Answer:
about $7.06
Step-by-step explanation:
Answer:
$7.06
Step-by-step explanation:
unit cost: $1.35/gram
5.23 grams * $1.35/gram = $7.0605
Answer: $7.06
convert $98.60 to pounds
Answer:
71.18 pounds
Step-by-step explanation: HOPE THIS HELPS
Can someone plz help me plzzzz I’m being timed
Answer:
1 = 19. 3 = 21. 7 = 25
Step-by-step explanation:
w = t + 18
19 = 1 + 18
21 = 3 + 18
25 = 7 + 18
2/17=X/9
what does x equal??
Answer: Multiply to remove the fraction, then set equal to
0
and solve.
Exact Form:
X = 18 /17
Decimal Form:
X = 1.05882352 …
Mixed Number Form:
X = 1 1 /17
2
17
=
X
9
what does
x
equal??
Multiply both sides of the equation by
9
.
2
17
⋅
9
=
X
9
⋅
9
Simplify.
Tap for more steps...
18 /17 = X
Rewrite the equation as
X = 18 /17 .
X = 18 /17
The result can be shown in multiple forms.
Exact Form:
X = 18 /17
Decimal Form:
X = 1.05882352 …
Mixed Number Form:
X = 1 1 /17
Step-by-step explanation:
2/17=X/9
what does x equal??
There are 8 shirts in your closet, 4 blue shirts and 4 green shirts. You randomly select one to wear on Monday and then a DIFFERENT one on Tuesday. What is the probability you will wear blue on both days?
Question 8 options:
A. 5/14
B. 1/4
C. 1/2
D. 3/14
Answer:
1/4
Step-by-step explanation:
PLS HELP: SEVENTH GRADE MATH
Answer:x=15
Step-by-step explanation:3x15=45
45+45=90
19. Mr. Green teaches band, choir, and math. This year, he has 57 students that take at least one of (3 points)
his classes. He teaches band to 25 students. There are 9 students who have Mr. Green for math
and nothing else. Use the Venn diagram below:
Math
7
3
11
17
Band
Choir
How many students take exactly 2 classes with Mr. Green?
Answer:
The answer is "17 students with Mr. Green take exactly two courses".
Step-by-step explanation:
Following are the calculation to this question:
Alone band 11
Alone chorus 17
Choir and band alone 4
7 Maths alone and the band
Choir and Math alone 6
Chorus and Math Band 3
mathematics alone 9 +11+4+10+6+17 + M = 57
so
2 classes = 4+7+6 = 17
So, there are 17 students with Mr. Green take exactly two courses.
6. Find the constant of variation k for the direct variation.
4x = -y
K = -1
K=-1/4
K=4
K=-4
Given:
The equation for the direct variation is
[tex]4x=-y[/tex]
To find:
The constant of variation k for the direct variation.
Solution:
If y is directly proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is constant of variation or constant of proportionality.
We have,
[tex]4x=-y[/tex]
It can be written as
[tex]-y=4x[/tex]
Multiply both sides by -1.
[tex]y=-4x[/tex] ...(ii)
On comparing (i) and (ii),we get
[tex]k=-4[/tex]
Therefore, the correct option is D.
Find the median for the following set of numbers.
4, 18, 3, 29, 23
0 29
3
18
04
Answer:
3 is the median
Step-by-step explanation:
the median is just the middle number, the number in the middle of a sequence
3 is perfectly in the middle
hope this helps chu <3
Anyone know this ???
Answer:
The answer is D
Step-by-step explanation:
Have a great day
9. Which
of the following is a proper fraction?
A 12/10
B. 5/4
C.7/10
D.10 1/9
Answer:
c
Step-by-step explanation:
because in a proper fraction the numerator is less than the denominator
The product of a binomial and a trinomial is x3+3x2-x+2x2+6x-2 Which expression is equivalent to this
product after it has been fully simplified?
A cylinder has a volume of 36 cubic inches. What is the volume of a cone if it has the same radius and height as the cylinder?
Answer:
12 cubic inches
Step-by-step explanation:
volume of a cylinder= pi*r2*height
but we are given 36 as cylinder volume.
Therefore , 36 = pi*r2* height
r2*height = 36/pi, let call this equation 1
volume of a cone = pi*r2*height/3;
but from equation 1, r2*height =36/pi, substituting this value in volume of cone.
volume of cone= pi*(36/pi)/3 = 12 cubic inches
There are 25 headsets, 8 of them are not working properly. Find the percentage of headsets that are in good quality.
Answer:
68%
Step-by-step explanation:
Given data
Number of Headset= 25
Number of bad Headset= 8
Percentage of bad Headset= 8/25*100
= 0.32*100
= 32%
Hence the percentage of good Headset is
=100-32
=68%
Pls help I’ll give brainliest
Answer:
B) 7 gallons
Step-by-step explanation:
car begins with 12 gallons and, at a rate of 29 mpg, would allow the car to travel for 348 miles
car only traveled 140 miles so 208 miles more can be driven
208÷29 is approx 7 gallons
A cable company uses the formula S = 20,000 (1 + 0.08)^y to estimate the number of subscribers, S, that use their service after y years. If there were 20,000 cable television subscribers when the cable company began, what is the meaning of the expression (1 + 0.008) ^y?
Answer:
the expression above is
y = Subscribers after time t = S
a = Initial Subscribers =20,000
r = Growth rate = 0.08 = 8%
t = time in years = y
Step-by-step explanation:
A cable company uses the formula S = 20,000 (1 + 0.08)^y to estimate the number of subscribers, S, that use their service after y years. If there were 20,000 cable television subscribers when the cable company began, what is the meaning of the expression (1 + 0.008) ^y?
The above question represents Exponential growth
Exponential growth formula =
y = a( 1 + r) ^t
Where:
y = Population after time t
a = Initial Population
r = Growth rate
t = time in years
S = 20,000 (1 + 0.08)^y
Hence, the expression above is
y = Subscribers after time t = S
a = Initial Subscribers =20,000
r = Growth rate = 0.08 = 8%
t = time in years = y
Can somone please help me and explain very much appreciated and this is 7th grade math btw
Answer:
4 8.95h + 10 < 115
Step-by-step explanation:
Answer: 4) 8.95h + 10 < 115
Step-by-step explanation:
We know the inequality will be equal to less than 115 since it states that the order was less than $115.
The equation would look like: some amount of shin guards times 8.95 each + $10 shipping = less than $115
8.95h + 10 < 115
(h in the given equation is the amount of shin guards)
Pls help ASAP fast ...
i donk know Step-by-step explanation:
Answer:
Here is your answer
Step-by-step explanation:
How many degrees is angle A?
Answer:
128 degrees
Step-by-step explanation:
Answer: 112 degrees
============================================================
Explanation:
If we assume ABCD is a parallelogram, then the adjacent angles are supplementary.
So,
A+D = 180
A+68 = 180
A = 180-68
A = 112