Step-by-step explanation:
i¹ = i
i² = i×i = -1
i³ = -1 × i = -i
i⁴ = -i×i = - -1 = 1
i⁵ = 1×i = i
...
so, when the exponent of i modulo 4 (the remainder when dividing by 4) = 0, then the result is 1.
= 1, then the result is i
= 2, then the result is -1
= 3, then the result is -i
233 modulo 4 = 1 (233/4 = 58, remainder 1).
so, the result is i (the third answer option).
Can someone please help me with this question thank you !!
Answer:
Area of cube = 6l²
= 6×2²
= 24 ft²
2 feet.
to find:how many square feet of wood he used to build the box.
solution:each side measures 2ft.
A=L²=(2 ft)²=4 ft²
A cube has 6 sides so the total quantity of wood is:
Wood=6×A
=6×4 ft²
=24 ft²
he used 24 ft² of wood to build the box.
Han and Priya want to know the mean height of the 30 students in their dance class. • The mean height for Han’s sample is 59 inches. • The mean height for Priya’s sample is 61 inches.
Answer:
60 inches
Step-by-step explanation:
Add 59+61 =120 which you divide by 2 for the mean of 60.
A stainless steel patio heater is a square pyramid. The length of one side of the base is 19.8 in. The slant height of the pyramid is 93.8 in. What is the height of the pyramid?
What is the domain of the function graphed below?
Answer:
The second option
Step-by-step explanation:
Hello!
The domain of a graph is the interval in which the graph is on the x values.
This graph has all the x values that are greater than or equal to -3, as the graph is to the right of it.
The answer would be the second option: [tex]D : x/x \geq -3[/tex]
The range is the y-values of the graph. The y value of this graph is above 0, so it would be y ≥ 0
I need this today
pls help
Answer:
5. radius= TD
inscribed angle =RQS
diameter =TA
6. radius=SY
secant=TU
Tangent=S
Is anyone good at math and can help me solve my math problems
Answer:
Hi! I'm not too bad at math so I hope I can help you. Except, I can't seem to find your question so please comment your question(s) to me so that I can help you. Have a great day:)
Xavier and Carlos have a bet to see who can get more “friends” on a social media side after 1 month. Carlos has 10 more friends than Xavier when they start the competition. After much work, Carlos doubles his amount of friends and Xavier triples his. In the end they have a total of 160 friends.
a. Write a system of equation that matches the verbal description given below if
c = number of Carlos’ friends and x = number of Xavier’s friends.
The system of equations that describes the situation is given by these two following equations:
c = 10 + x.2c + 3x = 160.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are c and x.
Carlos has 10 more friends than Xavier when they start the competition, hence:
c = 10 + x.
Carlos doubles his amount of friends and Xavier triples his. In the end they have a total of 160 friends, hence:
2c + 3x = 160.
More can be learned about a system of equations at https://brainly.com/question/24342899
The sum of two positive integers is 31. If the sum of the squares of these numbers is 625,find the smaller of the numbers.
Step-by-step explanation:
It is given that, the sum of two positive integers is 31 and the sum of the squares of these numbers is 625 and we are to find the smaller of the numbers.
So, let the two positive integers be x and y.
Therefore,
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x + y = 31 \: \: ........ \: (i) }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + y {}^{2} = 625 \: ...... \: (ii)}}} \\ \\[/tex]
Now, From the first equation we have,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x + y = 31 }}} \\ \\ [/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad y = 31 - x \: ...... \: (iii)}}} \\ \\ [/tex]
Now, substituting the value of y in equation (ii) we get :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x {}^{2} + (31 - x) {}^{2} = 625}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + (31 {}^{2} - 2.x.31 + x{}^{2} ) = 625}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + (961 - 62x + x{}^{2} ) = 625}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + 961 - 62x + x{}^{2} - 625 = 0}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 2 x {}^{2} + 336 - 62x = 0}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 2 x {}^{2} - 62x + 336 = 0}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 2( x {}^{2} - 31 + 168) = 0}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad \frac{2}{2} ( x {}^{2} - 31 + 168) = \frac{0}{2} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} - 31 + 168 = 0}}} \\ \\[/tex]
Now using the quadratic formula :
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }}} \\ \\[/tex]
Where,
a = 1b = -31c = 168[tex] \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ - (- 31) \pm \sqrt{ {31}^{2} - 4(1)(168)} }{2(1)} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 \pm \sqrt{ 961 -672} }{2(1)} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 \pm \sqrt{ 289} }{2(1)} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 \pm 17 }{2(1)} }}} \\ \\[/tex]
Now, we have two equations,
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 + 17 }{2} \: ... .....\: (iv)}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 - 17 }{2} ... .....\: (v)}}} \\ \\[/tex]
So, Equation (iv) :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 + 17 }{2} }}} \\ \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x = \frac{ 48 }{2} }}} \\ \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x = 24 }}} \\ \\ [/tex]
Now, Equation (v) :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 - 17 }{2}}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 14 }{2}}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \: 7}}}\\ \\ [/tex]
So, the value of x is 7 or 24Now, we are to find the value of y.
Substituting the value of x (24) in equation (iii) :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad y = 31 - x \:}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad y = 31 - 24 \:}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad y = 7 \:}}} \\ \\ [/tex]
Again, Substituting the value of x (7) in equation (iii) :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad y = 31 - x \:}}} \\ \\ [/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad y = 31 - 7 \:}}} \\ \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad y = 24 \:}}} \\ \\ [/tex]
Therefore,
The value of y is also 7 or 24.[tex] \\ [/tex]
So, The smaller of the numbers is 7 .
The sum of two positive integers is 31. If the sum of the squares of these numbers is 625, find the smaller of the numbers.
Given : -Sum of two positive numbers = 31Sum of squares of these numbers = 625To Find : - We have to find the smaller of the numbers .Concept : -This question belongs to quadratic equations so we have to find the answer by making equation and solving it .
To Assume : -Let the first no. be x Let the second no. be ySo let's get started with Solution :According to question , sum of two positive integers is 31 . So ,
x + y = 31 --------- ( Equation 1 )According to question , sum of square
of these numbers is 625 . So ,
x² + y² = 625 --------- ( Equation 2 )From equation 1 ( x + y = 31 ) , Value
of x :
x = 31 - yNow , putting value of x in eq. 2 :
x² + ( 31 - x )² = 625 x² + ( 31 )² - ( 2 × 31 × x ) + x² = 6252x² + 961 - 62x = 6252x² - 62x = 625 - 9612x² - 62x = -3362x² - 62x + 336 = 0 2(x² - 31x + 168 ) = 0x² - 31x + 168 = 0Solving it by using middle term
splitting :
x² -24x -7x + 168 = 0x ( x - 24 ) -7 ( x - 24 ) = 0( x - 7 ) ( x - 24 )So ,First number ,
x - 7 = 0x = 7 { Smaller Number }Second Number ,
x - 24 = 0x = 24Verification :According to question ,
Sum of numbers is equal to 31 :
x + y = 317 + 24 = 31L.H.S = R.H.SSum of squares of these numbers is equal to 625 :
x² + y² = 6257² + 24² = 62549 + 576 = 625625 = 625L.H.S = R.H.STherefore , our value for x and y are true. Thus our answer is valid.#[tex] \rm{Keep \: Learning}[/tex]Work out
21
% of
£
944.13
Give your answer rounded to 2 DP. I need right awnsers you can use calculators
Answer: £198.27
Step-by-step explanation:
944.13x0.21=198.2673Rounded to 2 decimal places that is 198.27Use the number line below to determine which of the following answer choices has statements that are all true.
Answer:
1st option, and 4th option
Step-by-step explanation:
Is it select one, or select all that are correct?
At a football game, 92% of people attending were supporting the home team, while 8% were supporting the visiting team. If 1564 people attending the game supported the home team, what was the total number of people attending the game?
The total number of people attending the game is 1700.
What is Percentage?Percentage in simple terms can be defined as a part per 100.
Percentage is a ratio or number which has to be defined as a fraction of 100.It is denoted by %.
If we are asked to calculate the percent of a number simply divide it by the whole part or number and then multiply with 100.
Percent of people supporting the home team = 92%
Number of people supporting the home team = 1564
Let x be the total number of people attending the game.
⇒ [tex]\frac{1564}{x}[/tex] × 100 = 92
⇒ [tex]\frac{1564}{x}[/tex] = 0.92
⇒ x = [tex]\frac{1564}{0.92}[/tex]
⇒ x = 1700
Hence, the total number of people attending the game will be 1700.
To learn more on Percentage, click:
https://brainly.com/question/28998211
#SPJ2
help me please- find the equation of line a
Check the picture below.
let's notice something, the equation of line B is in slope-intercept form, thus
[tex]y = 2x + \underset{\stackrel{\uparrow }{b}}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so using that grid scale, we can just get two points from the line A to get its equation, let's use those in the picture below
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-6)}}}\implies \cfrac{0+6}{6+6}\implies \cfrac{1}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{(-6)}) \\\\\\ y+6=\cfrac{1}{2}(x+6)\implies y+6=\cfrac{1}{2}x+3\implies y=\cfrac{1}{2}x-3[/tex]
Question 7 options:
5/7
7/5
2
9/7
Answer:
5/7.
Step-by-step explanation:
The rise = 5 and the corresponding run si 7.
Answer:
5/7
Step-by-step explanation:
so we start at the point (0,0). the slope is essentially
Rise/Run
so in this graph we see a point of (7,5)
the rise was 5 along the y axis and the run was 7 along the x axis.
so 5/7 is correct
PLSSS HELP ME
(5x5)/[10x22]-4\52
Answer: 21/572
[tex]\frac{5.5}{10 . 22} - \frac{4}{52}[/tex]
The dots stand for multiplication
Sarah bought 1250 grams of sugar. how many kilograms of sugar did she buy? A. 1.250 B. 12.50 C. 125.0 D 12500
Answer:
1.25 kg
Explanation:
1 kilograms is equal to 1000 grams============
1 g = (1/1000) kg======
So, 1250 gram = (1250/1000) kg
1250 gram = 1.25 kgWe know
1kg=1000gNow
Mass in kg:-
1250/10001.250kgOption A
Which fractions are equivalent to 1 2 ? Select all that apply. A. 2 4 B. 3 6 C. 3 4 D. 4 8
Answer:
A , B And D
2/4 divide both numbers by to and you get 1/2
3/6 divide both numbers by 3 and you get 1/2
4/8 divide both numbers by 4 and you get 1/2
evaluate: 3 /7 + ( −11 /4 ) + 16 /5 − ( −18 /7 )
Answer:
This is hard
Step-by-step explanation:
I'm so sorry I can't do it
Answer:
[tex]\frac{69}{20}[/tex]
Step-by-step explanation:
[tex]\frac{3}{7} -\frac{11}{4} +\frac{16}{5} +\frac{18}{7}[/tex]
= [tex]\frac{3}{7} +\frac{18}{7}-\frac{11}{4} +\frac{16}{5}[/tex]
= [tex]\frac{21}{7} -\frac{11}{4} +\frac{16}{5}[/tex] As both denominators have 7 you can add their numerators
=[tex]\frac{21}{7} -(-\frac{9}{20})[/tex] L.C.M
=[tex]\frac{21}{7} +\frac{9}{20}[/tex] L.C.M
=[tex]\frac{69}{20}[/tex]
Please help 50 points+Brainlest
Answer:
The correct polynomial is F. Calculation errors combining h terms and distributing -1.
Step-by-step explanation:
[tex]( - 4h + 3)( {h}^{2} + 9h - 1)[/tex]
[tex] - 4 {h}^{3} - 36 {h}^{2} + 4h + 3 {h}^{2} + 27h - 3[/tex]
[tex] - 4 {h}^{3} - 33 {h}^{2} + 31h - 3[/tex]
BRAINLIEST TO WHOEVER GETS IT RIGHT
Which of the following accurately shows the first step when solving the following system of equations by substitution?
f(x) = -4x^2 + 3x + 1
g(x) = -6x +5
a -4x^2+ 3x + 1 = -6x +5
b 4x^2 + 3x +1 - 6x + 5 = 0
c g(x)= -6(-4x^2 + 3x + 1) + 5
df() = -4(-6x + 5)^2 +3(-6x + 5) +1
Answer:
c and d
Step-by-step explanation:
because
- In f(x),evey time you find X you write(-6x+5) instead
4x²-----------4(-6x+5)²
3x+1------------3(-6x+5) +1
-In g(x),evey time you find X you write(-4x² +3x+1) instead
The results of a standardized test are normally distributed. The mean test score is 312. Of the scores, 16% are under 307. What is the standard deviation?
A: 10
B:5
Answer:
the answer is B five
Step-by-step explanation:
three hundred and seven minus three hundred and twelve
pls answer i give u anything
Answer:
the first one is 0.5 inches 1.27 centimeters
the second is 0.25 inches or 0.635 centimeters
Step-by-step explanation:
How were the policies of President Kennedy and President Johnson similar and different?
The ways that the policies of President Kennedy and President Johnson are similar and different is given below:
Both President were similar as they both were from heavily political and big families. Kennedy and Johnson were known to be similar in a lot of the ways especially in the way that they ran the country.After the assassination of Kennedy, Johnson was known to have followed the footsteps of his predecessor's and went ahead on implementing some of his programs. Johnson was known to have went ahead with the the anti-poverty program and the Civil Rights Bill.
What is a difference between John F. Kennedy and Lyndon Johnson?The differences between the both presidents were:
President Kennedy was known to be a better public speaker when compared to President Johnson.President Kennedy has his origin from the North, while that of Johnson was from the South.President Kennedy was used to be seen in affluent crowd, but Johnson was known to be a simple Texan Man.Conclusively, these two president were said to be very were similar, and yet they were different.
Learn more about President Kennedy from
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3.
Laura multiplied 27,890 by a fraction with a numerator of 12. The product
was less than 27,890. Which of the following statements is true about the
denominator of Laura's fraction?
Answer:
I don't see any optional answers, but the denominator must be greater than 12.
Step-by-step explanation:
27,890*(12/X) < 27,890
Therefore (12/X) < 1
and X > 12
i don’t understand this question
Step-by-step explanation:
to figure this out you would have to take all the numbers and do the rise over run technique
How long does it take for a $5000 investment to turn into a $7000 investment if it is compounded
semi-annually at 5.2%
Answer:
well over 3 years and almost over 4 months
Choose the angle which is vertical to angle BFC in the following figure.
answer A angle CFD
answer B angle DFE
answer C angle AFC
answer D angle EFA
Does anybody know this? I really need help.
Answer:
22 is th area
Step-by-step explanation:
please help me I need help please
Answer:
p = 4
Step-by-step explanation:
Given equation:
[tex]x^2+(p-3)y^2-4x+6y-16=0[/tex]
Standard equation of a circle:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
(where [tex](a,b)[/tex] is the centre of the circle, and [tex]r[/tex] is the radius)
If you expand this equation, you will see that the coefficient of [tex]y^2[/tex] is always one.
Therefore, [tex]p-3=1[/tex]
[tex]\implies p=1+3=4[/tex]
Additional information
To rewrite the given equation in the standard form:
[tex]\implies x^2+y^2-4x+6y-16=0[/tex]
[tex]\implies x^2-4x+y^2+6y=16[/tex]
[tex]\implies (x-2)^2-4+(y+3)^2-9=16[/tex]
[tex]\implies (x-2)^2+(y+3)^2=16+4+9[/tex]
[tex]\implies (x-2)^2+(y+3)^2=29[/tex]
So this is a circle with centre (2, -3) and radius √29
Find the value of x.
х
30°
24
Answer:
Step-by-step explanation:
x is the opposite side of angle 30°
34 is the adjacent side of 30°
So, find the value of x, we have use tan
[tex]\bf \boxed{ tan \ \theta = \dfrac{opposite \ side}{adjacent \ side}}}[/tex]
[tex]tan \ 30^\circ = \dfrac{x}{24} \\\\\\0.58 = \dfrac{x}{24}\\\\\\0.58*24=x[/tex]
x = 13.92
Please help me ASP! Could anyone tell me what 3 x what gets me to 90?
Answer:
3*30 = 90
Step-by-step explanation:
3*30 = 90
