HELP ASAP
Write 8,350,000,000 in scientific notation.
8.35 × 10−9
8.35 × 109
835 × 10−7
835 × 107
[tex]8.35 \times {10}^{9} [/tex]
or
[tex]835 \times {10}^{7} [/tex]
please answer this question
let x be the real part of z
let y be the imaginary part of z
[tex]arg(x +i y - 1) = arg(x + iy + 3i) \\ arg(x - 1 + iy) = arg(x + (y + 3)i) \\ arctan( \frac{y}{x - 1} ) = arctan( \frac{y + 3}{x} ) \\ arctan( \frac{ (\frac{y}{x - 1} ) - ( \frac{y + 3}{x}) }{1 +( \frac{y}{x - 1} )( \frac{y + 3}{x} )} ) = 0 \\ arctan( \frac{ \frac{xy - (x - 1)(y + 3)}{x(x - 1)} }{ \frac{x(x - 1) + y(y + 3)}{x(x - 1)} } ) = 0[/tex]
[tex]arctan( \frac{xy - xy - 3x + y + 3}{x {}^{2} - x + y {}^{2} + 3y } ) = 0 \\ \frac{ - 3x + y + 3}{x {}^{2} - x + y {}^{2} + 3y} = tan(0) = 0 \\ - 3x + y + 3 = 0 \\ y = 3x - 3[/tex]
[tex] \frac{x - 1}{y} = \frac{x - 1}{3x - 3} = \frac{x - 1}{3(x - 1)} = \frac{1}{3} \\ [/tex]
Answer:
[tex]\dfrac{x-1}{y}=\dfrac{1}{3}[/tex]
Step-by-step explanation:
Sums of real and imaginary numbers are known as complex numbers:
[tex]\large\boxed{z = x + iy}[/tex]
(where x is the real number and iy is the imaginary number).
Complex numbers can be represented on an Argand diagram.
The x-axis is the real axis.The y-axis is the imaginary axis.z = x + iy is represented on the diagram by the point P(x, y).
[tex]\textsf{Argument of a complex number $= \boxed{\arg z}$}[/tex]
It is the angle between the positive real axis and the line joining that number to the origin on an Argand diagram, measured in an anticlockwise direction.
[tex]\textsf{For \;$z = x + iy$, \;the argument $\theta$ satisfies\; $\tan \theta = \dfrac{y}{x}$.}[/tex]
[tex]\textsf{Given: \quad $\arg (z-1)=\arg(z+3i)$}[/tex]
[tex]\textsf{If $z$ is a complex number then $z = x + iy$}.[/tex]
[tex]\textsf{Substitute this into the given equation}:[/tex]
[tex]\begin{aligned} \arg(z-1)&=\arg(z+3i)\\\implies \arg(x + iy - 1) &= \arg(x + iy + 3i)\\\implies \arg((x - 1) + iy) &= \arg(x + i(y + 3))\end{aligned}[/tex]
[tex]\textsf{If the argument $\theta$ satisfies\; $\tan \theta = \dfrac{y}{x} \implies \theta=\tan^{-1}\left(\dfrac{y}{x}\right)$}:[/tex]
[tex]\implies \tan^{-1}\left(\dfrac{y}{x-1}\right)=\tan^{-1}\left(\dfrac{y+3}{x}\right)[/tex]
[tex]\implies \tan^{-1}\left(\dfrac{y}{x-1}\right)-\tan^{-1}\left(\dfrac{y+3}{x}\right)=0[/tex]
[tex]\boxed{\begin{minipage}{6.2cm}\underline{Trigonometric identity}\\\\ $\tan^{-1}(a)-\tan^{-1}(b)=\tan^{-1}\left(\dfrac{a-b}{1+ab}\right)$\\ \end{minipage}}[/tex]
Use the arctan identity:
[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{y}{x-1}-\dfrac{y+3}{x}}{1+\left(\dfrac{y}{x-1}\right)\left(\dfrac{y+3}{x}\right)} \right)=0[/tex]
[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{xy-(y+3)(x-1)}{x(x-1)}}{1+\dfrac{y(y+3)}{x(x-1)}} \right)=0[/tex]
[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{xy-(y+3)(x-1)}{x(x-1)}}{\dfrac{x(x-1)+y(y+3)}{x(x-1)}} \right)=0[/tex]
[tex]\implies \tan^{-1}\left({\dfrac{xy-(y+3)(x-1)}{x(x-1)+y(y+3)} \right)=0[/tex]
[tex]\implies \tan^{-1}\left({\dfrac{xy-xy+y-3x+3}{x^2-x+y^2+3y} \right)=0[/tex]
[tex]\implies \tan^{-1}\left({\dfrac{y-3x+3}{x^2-x+y^2+3y} \right)=0[/tex]
[tex]\implies \dfrac{y-3x+3}{x^2-x+y^2+3y}=\tan(0)[/tex]
[tex]\implies \dfrac{y-3x+3}{x^2-x+y^2+3y}=0[/tex]
[tex]\implies y-3x+3=0[/tex]
[tex]\implies y=3x-3[/tex]
[tex]\textsf{Substitute\;\; $y=3x-3$ \;\;into \;\;$\dfrac{x-1}{y}$}:[/tex]
[tex]\begin{aligned}\implies \dfrac{x-1}{y}& =\dfrac{x-1}{3x-3}\\\\ & =\dfrac{x-1}{3(x-1)}\\\\ & =\dfrac{1}{3}\end{aligned}[/tex]
[tex]\textsf{Therefore, the value of\; $\dfrac{x-1}{y}$\; is\; $\dfrac{1}{3}$}.[/tex]
Determine whether the following ratios are equivalent. 3:4 and 12:9
Answer:
no
Step-by-step explanation:
Put them as fractions that have equivalent denominators.
3/4 :27/36 (multiply 9 to both numbers)
12/9 :48/36(multiply 4 to both numbers)
Since the numerators are not the same the answer is no.
If they were equal both numerator and denominator would be the same
A cement mixture calls for 3 pounds of cement for 3 gallons of water. What is the ratio of water to cement? Enter only the missing number.
Based on the calculations, the ratio of water to cement (W:C) is equal to 1:1.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
What is a proportion?A proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Given the following data:
Quantity of cement = 3 pounds.Quantity of water = 3 gallons.Substituting the given parameters into the formula, we have;
Therefore, the ratio of water to cement is given by:
Ratio of water to cement, W:C = 3:3
Ratio of water to cement, W:C = 1:1.
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Any number besides 0 to the zero power evaluates to 0. True or false?
Answer:
True
Step-by-step explanation:
Because anything multiplied by 0 is equal to 0.
Leah wants to divide x by -5/12. What number should she multiply by x to find the answer?
Considering the algorithm to divide a number by a fraction, she must multiply x by -12/5 to find the answer of the division of x by -5/12.
What is the algorithm to divide a number by a fraction?To divide a number, or even another fraction, by a fraction, we need to multiply the numerator by the inverse of the denominator.
Taking the following division of fractions as an example, we have that:
(a/b)/(c/d).
The numerator is given by a/b.The denominator is given by c/d.The inverse of the denominator is d/c. (to find the inverse of a fraction, we exchange the numerator by the denominator).Hence the quotient is:
a/b x d/c.
For this problem, the division is:
x/(-5/12).
Hence:
The numerator is given by x.The denominator is given by -5/12.The inverse of the denominator is -12/5.Thus the quotient is given by:
-12x/5.
Meaning that she must multiply x by -12/5 to find the answer of the division of x by -5/12.
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19/20 divided by 20/30 = 19/20 x ?
A. -30/20
B. 30/20
C. 20/19
D. -20/19
Answer:
19/20*30/20=19/20 x
570/400=19/20 x
57*20=40*19x
1140=760x
x=30/20 or 3/2
You are working on a banner for Friday’s pep
rally. The length of the banner is 6 times the
width. The length is 18 feet.
l
GO WILDCATS! w
What is the width?
Answer in units of feet.
The width of the banner of the Friday’s pep rally is 3 feet.
How do you find the percentage of number?To calculate a percentage, divide the value by total value and multiply the result by 100. (value/total value)100% is the formula for calculating percentage.
Calculating a percentage means determining a portion of a whole in terms of 100. A percentage can be calculated in two ways:
The unitary method is used.By changing the fraction's denominator to 100.For the given expression;
The length of the Friday’s pep rally banner is 18 feet.
Let the width be 'b'.
The given condition is;
The length of the banner is made 6 times the width.
Then,
6 time the width = length
6×w = 18
w = 18/6
w = 3
Therefore, the width of the banner is found as 3 feet.
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Find the 8th term of the geometric sequence 6, 18, 54
Answer:
13122
Step-by-step explanation:
Term multiply by 3
First term is 6
Seven terms remain to be defined
then the 8th term is:
6 * 3⁷ = 6*2187
= 13122
WHICH ONE IS IT
60PTS
Answer:
B. {-4, -2, 0, 2, 4}
Step-by-step explanation:
A definition for the word domain is the "input" of a function, also called the x values.
A definition for the word range is the "output" of a function, also called the y values.
With this knowledge, looking at the question, it is asking for the range of the relation, which means we are looking at the y values.
A is incorrect because it shows all values from -4 to 4, however some are not in the relation shown.
B is correct because it is showing all of the y values given in the table and no others.
C is incorrect because it is just showing the bounds of the relation, but not all values between.
D is incorrect because it is the domain of the function, or the x values.
Therefore, you were correct, and your answer is B.
Answer: B? Although its supposed to be {4, 2, 0, -2, -4}
The difference between two positive numbers is 40 and the ratio of these integers is 1:3.Find the integers.
Answer:
A:B= 1:3
let A=1x,B=3x
A+B = x+3x
x+3x = 40
4x = 40
x=10
A=1(10)=10
B=3(10)=30
Step-by-step explanation:
Dont really know how to explain it well
How do I solve this?
Which of these statements is true?
Answer: WX, ZY and WX and AB.
The 2nd one is correct.
Help asap! and don't answer for the points only if you know for sure it's right
Answer:
Child ticket: 12 dollars
Total price: 64 dollars
Step-by-step explanation(Child ticket price):
[tex]T = X(1 - P\%)\\T = 20(1 - 40\%)\\T = 20(1 - 0.4)\\T = 20(0.6)\\T = 12[/tex]
-----------------------------------------------------------------------------------------------------------
Step-by-step explanation(Total price):
[tex]T(12) * 2 + (20.00 * 2) = \$64[/tex]
Hope this helps.
PLEASE HELP WILL GIVE BRAINLIEST
Answer:
1302 for the first
-194 for second
Step-by-step explanation:
just do the operation
Perforated for Easy
Between which two thousands
does 10,357 fall?
and
Use the number line below to
show how you would round 10,357
to the nearest thousand.
10,357 rounds to
there are 25 boxes of paper, each box has 789 pieces of paper. how many pieces of paper are there in all?
25 times 789 is 19725
the answer:19,725
PLEASE HELP!! I NEED THIS ASAP. I WILL GIVE BRAINLY
Answer:On three of the percentage points you improved your average score.
Step-by-step explanation:I hope this helps.
Answer:
75 + 85 + 90 + 90 + 100 + 75 + 80 + 100 + 90 = 785
785/9 = 87.2
85 + 85 + 100 + 90 + 100 + 85 + 80 + 100 + 90 = 815
815/9 = 90.5
90.5 - 87.2 = 3.3
Round 3.3 to the nearest percent = 3%
easy points. need work shown
Multiply
(2/5)(-5/4)
Enter your answer as a fraction, in simplest form, in the box.
Answer:
-1/2
Step-by-step explanation:
first, we multiply 2 and -5 which is -10, then we multiply 5 and 4 which is 20
so, we get -10/20 then the simplest form is -1/2
MARK ME BRAINLIEST IF IT HELPED :)
i only have one chance to get this right! please help.
Answer:
D. 2z^3/y
Step-by-step explanation:
xyz^2 = 2z^4
z(xyz) = z(2z^3)
xyz = 2z^3
xz = (2z^3)/y
dividing decimals
0.745/ 9.089
Answer:
0.745/9.089
Multiply numerator and denominator by 1000
=745/9089
Polygon EFGH is a scaled copy of polygon ABCD.
Select ALL of the true statements.
(Select all that apply.)
The area of EFGH is twice the area of ABCD.
Segment FG is twice as long as segment CD.
Segment EF is twice as long as segment AB.
The scale factor from EFGH to ABCD is 2.
The length of segment AD is 8 units.
The following statements are true and correct:
Segment EF is twice as long as segment AB
The length of segment AD is 8 units
How to interpret dilation transformation?
Since quadrilateral ABCD is scaled to form quadrilateral EFGH, both are similar polygon.
Now, it is known that;
scale factor = ratio of any of their corresponding side
Thus;
Scale factor = GH/CD = 12/6 = 2
This means quadrilateral EFGH is twice the size of quadrilateral ABCD.
The shape of the original polygon remains the same while the size increases.
This implies that, all segments of quadrilateral ABCD increases proportionally times 2 to give us corresponding lengths of the segments of quadrilateral EFGH.
Since shape remains the same, their corresponding angles are congruent and the same in measure.
Therefore, the following statements are true and correct:
Segment EF is twice as long as segment AB; because (EF = AB*scale factor = 3*2 = 6)
The length of segment AD is 8 units because (EH = AD*scale factor = 8*2 = 16)
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what is the ordered pair for -5, 6
The ordered pair for -5, 6 is (-5, 6)
How to determine the ordered pair for -5, 6?The expression is given as:
-5, 6
Ordered pairs are often represented by the parenthesis i.e. ( , )
Where the variables x and y are in the parenthesis
So, the proper representation of an ordered pair is
(x, y)
Substitute -5, 6 for x and y in (x, y)
(-5, 6)
Hence, the ordered pair for -5, 6 is (-5, 6)
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if four out of every nine trick-or-treaters that came to your house last Halloween were dressed as Snow White, what proportion of trick-or-treaters were not dressed as Snow White?
The proportion of Trick-or-treaters not dressed as Snow white are 5/9.
A proportion may be defined as the way of representation of numbers or letters in the form of ratios which are made equal to each other. For example, if there are 1 mango and 2 bananas then the ratio is written as 1:2 that is for every 1 mango there are 2 bananas and there are 1/3 mangoes and 2/3 bananas.
Total number of Trick-or-treaters = 9
Total number of Trick-or-treaters dressed as Snow white = 4
Total number of Trick-or-treaters not dressed as Snow white = 9-4 = 5
Thus, Proportion of Trick-or-treaters not dressed as Snow white = 5/9
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a travel agent arranges a payment plan for a client it required a down payment of 250 and 15 monthly payment of 582 what was the the total cost if the plan
Answer:
Step-by-step explanation:
it is Payment: Uniform Payment Series: (F/P, i, ∞) = ∞. (A/F, i, ∞) = 0.
36 hundredths divided by 9 tenths
Answer: The answer would be 0.4 or 4/10
Step-by-step explanation:
which shows all the critical points for the inequality x^2-9x/x-5<0
The critical points are 0, 5 and 9 for the inequality (x² - 9 x) / (x - 5) < 0.
The critical point is a single value at which the function is not differentiable
The inequality is given as:
(x² - 9 x) / (x - 5) < 0.
Factorize the numerator
x (x - 9) / (x - 5) < 0.
Equate it to 0, we get that:
x (x - 9) = 0 or x - 5 = 0
x = 0 or x - 9 = 0 or x - 5 = 0
So, the critical points will be:
x = 0 or x = 9 or x = 5.
Therefore, the critical points are 0, 5 and 9 for the inequality (x² - 9 x) / (x - 5) < 0.
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Norma plans to rent a car for her vacation. The cost to rent the car is $39
plus $0.15 per mile she drives. Write a function rule for the total cost of
the rental.
Answer:
$39 + 0.15x
Step-by-step explanation:
$39 is the flat fee no matter what and x is the number of miles driven times cost per mile.
In a 40 hour work week marcie spends 15 hours answering phones what is the ratio of hours spent answering telephones to hours doing other types of work?
Out of 40 hours that Marcie works, 15 of those hours are spent answering phones. The problem asks that the hours spent answering telephones goes first in the ratio, so that will be the first number.
15 :
The last number is the total number of hours Marcie works.
15 : 40