Answer:
(1 + 3i)(1 - 3i)
Step-by-step explanation:
The product of a complex number and its conjugate produce a real number.
given a ± bi the conjugate is a ∓ bi ← where a and b are real, then
(a + bi)(a - bi)
= a² - b² ← a real number
The only pair of conjugate complex numbers in the list is
(1 + 3i)(1 - 3i)
The pair of complex numbers that has a real-number product is:
(1 + 3) (1-3) = -8
Option C is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
For a pair of complex numbers to have a real-number product, their imaginary parts must cancel out when the product is expanded.
Let's expand each pair of complex numbers and see which one has a
real-number product:
(1 + 3) x (61) = 61 + 183i
This product has a non-zero imaginary part, so it is not a real number.
(1 + 3) x (2-3) = -5 + 5i
This product has a non-zero imaginary part, so it is not a real number.
(1 + 3) x (1-3) = -8
This product has no imaginary part, so it is a real number.
(1 + 3) x (31) = 124 + 124i
This product has a non-zero imaginary part, so it is not a real number.
Therefore,
The pair of complex numbers that has a real-number product is:
(1 + 3) (1-3) = -8
Learn more about expressions here:
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Help with proofs (10 points) please help will give brainliest
??please help me solve
Answer:
y = -4x - 6
Step-by-step explanation:
slope-intercept form: y = mx + b
Given: Slope: -4
Point: (-2, 2)
To write an equation in slope-intercept form, we need to know the slope(m) and the y-intercept(b). Since we were given the value of the slope, all we have to do now is find b. To do this, input the given values of m and the point into the equation and solve for b:
y = mx + b
2 = -4(-2) + b
2 = 8 + b
-6 = b
The y-intercept is -6.
Now that we know the slope and the y-intercept, we can write the equation:
y = -4x - 6
Which number line shows the solution to 11x + 14 <-8
Answer:
The answer is D
Step-by-step explanation:
I did it on edg
Find the required annual interest rate, to the nearest tenth of a percent, for $ 1170 to grow to $ 1708
if interest is compounded quarterly for 6 years.
A) 6.4%
B) 1.6%
C) 3.2%
D) 7.9%
Answer:
Step-by-step explanation:
The formula you need for this is
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]
where A(t) is the final amount after the compounding is done, P is the initial investment, r is the interest rate in decimal form, n is the number of times per year that the money is compounded, and t is the time in years. Filling in accordingly:
[tex]1708=1170(1+\frac{r}{4})^{(4)(6)}[/tex]
First things first. Simplify by division and then multiply the n by the t to get the exponent:
Divide 1708 by 1170 to get the equation:
[tex]1.45982906=(1+\frac{r}{4})^{24}[/tex]
Undo the 24th power by taking the 24th root of both sides to get:
[tex]1.015888202=1+\frac{r}{4}[/tex] Now subtract 1 from both sides to get
[tex].0158882024=\frac{r}{4}[/tex] Multiply both sides by 4 to finish it off and get that
r = .0635528 but since we want the percentage, we move the decimal 2 places to the right and round to r = 6.4% which is choice A.
A function has the function rule y = -7x - 2. If the input is -4, what is the output?
-30
26
-26
14
Answer:
y=-7x-2
input -4 (x)
y=-7(-4)-2
y=28-2
y=26
PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
Answer:
i got 3 1/2 hours
Step-by-step explanation:
Answer: 1.5 or 5
Step-by-step explanation:
You have to add 1/4 and 3/4 and I mean you do 3+1=4 then add 4+1=5
Or you can add 1/4+3/4 which is 4/8 then do 4/8+1 whole that equals 1.5
But try both steps and see which one you like best
A parallelogram has a length of 4 inches and a width of 9 inches. What is it's area?
Answer:36
Step-by-step explanation:
State the point on the line y - 18 = 71.3(x +98)
Please explain how you got your answer, thank you.
9514 1404 393
Answer:
(-98, 18)
Step-by-step explanation:
We recognize the equation as being in the "point-slope" form.
y -k = m(x -h) . . . . . . . a line with slope m through point (h, k)
__
Comparing this form to the given equation, we identify the parameters as ...
k = 18, m = 71.3, h = -98
The point on this line is (h, k) = (-98, 18).
somebody help please
Answer:
if that says plus 60 cents then she pledged 455 dollars
Step-by-step explanation:
The track is 3/5 of a mile long. If Tyrone jogged around it twice, how far did he run?
He ran for 6/5 miles long.
What is multiplication?In maths, to multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem.
Given that, Tyrone run on a 3/5 long track for twice.
3/5*2 = 6/5
Hence, He ran for 6/5 miles long.
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Find the solution to the system of equations: x + 3y = 7 and 2x + 4y = 8 1. Isolate x in the first equation: 2. Substitute the value for x into the second equation: 3. Solve for y: 4. Substitute y into either original equation: 5. Write the solution as an ordered pair: x = 7 – 3y 2(7 – 3y) + 4y = 8 14 – 6y + 4y = 8 14 – 2y = 8 –2y = –6 y = 3 x + 3(3) = 7
Answer:
(-2,3)
Step-by-step explanation:
Hi can you guys help me please?!
Answer:
7B, 8C, 9D, 10A
Step-by-step explanation:
evaluate the expression. |13| + | -2|
Answer:
(13 + 2) = 15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
6s-4=8 (2+ 0.25s)
solve for s
Answer:
s=5
Step-by-step explanation:
6s-4=16+2s
6s=20+2s
4s=20
s=5
Answer:
S=5
Step-by-step explanation:
explain relationship between how radical expressions and rational (fractional) exponents
are written.
Answer:
Any radical in the form can be written using a fractional exponent in the form . The relationship between and works for rational exponents that have a numerator of 1 as well. For example, the radical can also be written as , since any number remains the same value if it is raised to the first power.
Step-by-step explanation:
the mass, m, of an object varies directly as the cube of its length, l. m=72 when l=2. Find m when l=5.
Answer:
M=180 when L=5
Step-by-step explanation:
If m is 72 when mass is 2 then 2.5×2 =5 and so m when 2.5×72=180 :)
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Answer:
??
Step-by-step explanation:
i am so confused... love ur pfp tho
Answer:
:D
Step-by-step explanation:
thank
2(4x - 1)+ 1 = 2x + 6x – 2
How many solutions do you get when you solve ?
Answer:
Step-by-step explanation:
2(4x-1)+1=2x+6x-2
8x-2+1=2x+6x-2
8x-1=8x-2
No solution
Please need this now Hurry!
Rectangle ABCD is transformed to A’B’C’D’ by a dilation
What is the scale factor used for the dilation
1/6
1/3
3
6
Answer:
1/3 the rectangle was dilated by a factor of 1/3
Step-by-step explanation:
9/3 = 3 and 6/3= 2
Answer:
1/3 the rectangle was dilated by a factor of 1/3
Step-by-step explanation:
9/3 = 3 and 6/3= 2
Find the midpoint of each line segment with the given endpoints: (2,0) and (-2,4)
Answer:
(0,2)
Step-by-step explanation:
Kate wants to buy a new bicycle from a sporting goods store. The bicycle she wants normally sells for $540. The store has a sale where all bicycles cost
7
9
of the regular price. What is the sale price of the bicycle?
Answer:
21%
Step-by-step explanation:
The sale price is 21%
47.9 is what percent of 152?
A)3.2%
B)31.5%
C)0.32%
D)317.3%
Answer: B
Step-by-step explanation:
Step 1: We make the assumption that 152 is 100% since it is our output value.
Step 2: We next represent the value we seek with x
Step 3: From step 1, it follows that 100%=152
Step 4: In the same vein, x%=47.9
Step 5: This gives us a pair of simple equations:
100%=152(1).
x%=47.9(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
100%/x% = 152/47.9
x= 31.5
Jason has 34 strawberry scones and 85 raspberry scones.He wanted to make as many identical bags of scones as possible.Each bag should have an equal number of strawberry scones and an equal number of raspberry scones.What is the greatest number of bags Jason can fill?
Answer: 17
Step-by-step explanation:
We are told Jason has 34 strawberry scones and 85 raspberry scones and that he wanted to make as many identical bags of scones as possible and that each bag should have an equal number of strawberry scones and an equal number of raspberry scones.
To calculate greatest number of bags Jason can fill, we find the factor of 34 and 85 and choose the highest that's common to both.
Factor of 34 = 1, 2 , 17, and 34
Factor of 85 = 1, 5, 17, and 85.
Highest common factor = 17
The answer is 17
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Find an expression which represents the difference when (9x-10y) is subtracted from (-8x-8y) in simplest terms.
Basically what is (9x-10y)-(-8x-8y)?
Consecutive interior angles are...
A. Complementary
B. Supplementary
C. Congruent
D. Colinear
Answer:
Consecutive interior angles will be supplementary
Step-by-step explanation:
As we know that a transversal line is a straight line which tends to intersect two or more parallel lines.
Consecutive interior angles are interior angles that are on the same side of the transversal line. Their sum is 180°.
Hence, Consecutive interior angles will be supplementary
For example, let ∠A and ∠B be the two consecutive interior angles.
As the sum of Consecutive interior angles is 180°, hence they are supplementary.
so the equation becomes
∠A + ∠B = 180°
Let suppose <A and <B are both consecutive interior angles.
Let ∠A is 110°, and we have to determine ∠B.
As the sum of Consecutive interior angles is 180°,
110° + ∠B = 180°
∠B = 180° - 110°
= 70°
so 70° + 110° = 180°
Therefore, Consecutive interior angles will be supplementary
please help due in 2 min
and I can't get another one wrong
Answer:
True
Step-by-step explanation:
Both functions are straight lines. This means they will continue in both directions forever. So the both have a range and domain of all real numbers. Linear functions commonly have range and domains of all real numbers.
The price of a toy usually costing £50 is increased to £65
Work out the percentage increase.
Answer:
30%
Step-by-step explanation:
£50 -- 100%
£65 -- ?
Do cross multiply:
(60 X 100) divided by 50
= 130%
130% - 100% = 30%
34. The amount of money in an account with continuously compounded interest is given by the formula 1
4 Por, where is the principal, / is the annual interest rate, and / is the time in years, Calculate to the
nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded
continuously at 6,2%Round to the nearest tenth,
11.2 y
A
1 0.0 %
O
4
Answer:
Step-by-step explanation:
I have no idea what formula that is you're using but the one I teach in both algebra 2 and in precalculus for continuous compounding is
[tex]A(t)=Pe^{rt}[/tex]
where A(t) is the amount after the compounding, P is the initial investment, ee is Euler's number, r is the interest rate in decimal form, and t is the time in years. If our money doubles, we just have to come up with a number which will be P and then double it to get A(t). It doesn't matter what number we pick to double, the answer will come out the same regardless. I started with 2 and then doubled it to 4 and filled in the rest of the info given with time as my unknown:
[tex]4=2e^{(.062)(t)}[/tex]
Begin by dividing both sides by 2 to get
[tex]2=e^{.062t}[/tex]
The only way we can get that t out of its current position is to take the natural log of both sides. Natural logs have a base of e, so
[tex]ln_e(e)=1[/tex] This is because they are inverses of one another. Taking the natural log of both sides:
[tex]ln2=.062t[/tex] Now divide by .062 to get
t = 11.2 years
40°
140°
mz1 = _°
50
90
70
Answer:
0.0
Step-by-step explanation:
70degress i think hsodisnshdhddhdtdhdhuehejshdydjdjbddbdjksisj8s