Which of the following is equivalent to the complex number i8?
Choose 1 answer:
mi
1
-1
pl
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Answer:
1
Step-by-step explanation:
note that i² = - 1
Thus
[tex]i^{8}[/tex]
= i² × i² × i² × i²
= - 1 × - 1 × - 1 × - 1
= 1 × 1
= 1
The value of complex number is 1. Therefore, the option B is the correct answer.
What is the complex number?A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.
The given complex number is i⁸.
We know that, i²=-1
Now, i⁸ can be written as i²×i²×i²×i²
= -1×(-1)×(-1)×(-1)
= 1
Therefore, the option B is the correct answer.
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Area and perimeter please
Answer:
185.68 for perimeter
1652.16 for area
Step-by-step explanation:
Please give me brainliest i hope you do well.!
What is the slope line through (-5,-10) and (-1,5)
Answer:
5
Step-by-step explanation:
Can someone help with step by step
Answer:
See explanation
Step-by-step explanation:
[tex] In\: \triangle ABC \:\&\: \triangle EDC\\
\angle ABC \cong \angle EDC... (Right \: \angle s) \\
\angle ACB \cong \angle ECD... (Vertical \: \angle s) \\\therefore \triangle ABC \sim \triangle EDC... (By\: AA\: Postulate) \\[/tex]
Hey, I need some help with this:
Give an example of what an inverse operation is and how they are used in solving equations
Inverse operations are an operation that undoes each other. For example, addition and subtraction, multiplication and division, squares and square roots.
For example, we have the equation:
2 + 2 = 4
The inverse of this equation is:
4 - 2 = 2
Best of Luck!
Can someone help and explain A and B please...
Please Help!!! Explain how to solve!!! Extra points and brainiest will be given
Answer:
2,493.796 => 2493.8
Step-by-step explanation:
Answer:
2,492.5 mm^2
Step-by-step explanation:
The formula to find the Surface area is 2 pi r^2 + 2 pi r x h
So, 2 pi 14.7^2 + 2 pi 14.7 x 12.3
2 pi 216.09 + 2 pi 180.81
2 x 678.5226 + 2 x 567.7434
1,357.0452 + 1,135.4868
2,492.532
The surface area of this cylinder is 2,492.5 mm^2
Find the interquartile range (IQR) of the data plot below
Answer:
3.5
Step-by-step explanation:
0 1 1 3 3 3 4 5 7
median= 3
Q1= 1
Q3= 4.5
4.5-1= 3.5
Answer:3.5
0,1,1,3,3,3,4,5,7
Tomas selects one of these garments at random. Let AAA be the event that he selects a blue garment and let BBB be the event that he chooses a shirt.
Please help!!!
Answer:
can u explain it more lol
Step-by-step explanation:
1)The probability of choosing a blue garment is 1/2
2)The probability of choosing a shirt is 1/3.
Thomas has 1 blue shirt
Thomas has 1 green shirt
Thomas has 1 blue hat
Thomas has 1 green scarf
Thomas has 1 blue pair of pants
Thomas has 1 green pair of pants
So, number of blue garments = 3
Number of shirts = 2
Total garments =6
What is probability?Probability is the measure of the likelihood of an occurrence.
P(event) = Favorable outcomes / Total outcomes
P(blue garment) = 3/6 =1/2
P(shirt) = 2/6 =1/3
Hence, 1)The probability of choosing a blue garment is 1/2
2)The probability of choosing a shirt is 1/3.
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What is the area of the triangle shown below?
Answer:
65
Step-by-step explanation:
In order to find the area you have to complete a formula for triangles going Area = 1/2 bh ( bh means base time the height height is the 13 and the base is the 10 in the photo.)
can someone help with this please,, also explain if you can..
Answer:
story 1
Step-by-step explanation:
because it says 2 higher than -2 so -2+2 is 0
Select the table that represents a linear function.
Answer:
D
Step-by-step explanation:
A linear function has a constant slope. Meaning that for any equal change in x, there will be an equal change in y.
A running track is 1/4 of a kilometre. What is the
total distance a runner travels if he goes three
times round the track?
How many times would you have to go round the
track to run 2 kilometres?
Willow has read 1/7 of the books in the library.
Answer:
If a runner went around the track 3 times, he would have ran 3/4 of a kilometre. He would have to run around the track 8 times to run 2 kilometres.
Step-by-step explanation:
Answer:He would have to go around the track 8 times to get 2 kilometers
Step-by -step explanation:
what is the 50th term of the sequence that begins -2, 4, 10, 16
290
294
292
296
Answer: 292
Step-by-step explanation:
The formula is: [tex]a_n=a_1+(n-1)d[/tex]
Where;
[tex]a_n=[/tex] [tex]n^t^h[/tex] term or the term we're trying to find.
[tex]a_1=[/tex] First term
[tex]d=[/tex] Common difference.
To find the common difference, take [tex]a_2-a_1[/tex], or [tex]a_3-a_2[/tex] or [tex]a_4-a_3[/tex]
4-(-2)=?
4+2=?
6 -> this is our common difference
---------------------------------
10-4=?
6 -> this is our common difference
--------------------------------
16-10=?
6 -> this is our common difference
------------------------------------------------------------
Knowing this, we plug into the formula the number we're trying to find.
[tex]a_n=a_1+(n-1)d\\a_5_0=-2+(50-1)6\\a_5_0=-2+(49)6\\a_5_0=-2+294\\a_5_0=292[/tex]
Answer:
C. 292
Step-by-step explanation:
Find the area. Will mark brainliest.
Answer:
54 in^2
Step-by-step explanation:
9*12/2=54 in^2
Answer:
54
Step-by-step explanation:
The formula is 1/2*base*height which is 1/2*12*9. This is equal to 54.
hope this helps:)
Solve for y :
y/5 + 7 = -3
Y is equal to -50. (y= -50)
Step-by-step explanation: Solve for y
by simplifying both sides of the equation, then isolating the variable.y=−50
Please Help!!! As quickly as possible!!!
Answer: Bristol's heart rate reaches a maximum of 120
bpm
Step-by-step explanation:
Answer:
Bristol's heart rate reaches a maximum of 120 bpm
At the end of yoga class, Bristol's heart rate returned to her resting heart rate
The graph that models Bristol's heart rate is a parabola
Step-by-step explanation:
help me please ( i’ll give 20 points for this )
Answer:
108
Step-by-step explanation:
add 90+68+94, which will give you 252. subtract that from 360 because it‘s a quadrilateral and you will get 108 :)
Answer:
64°
Step-by-step explanation:
See the angle is smaller than 108° and it is not 90° so the answer is 64°
Please help me out! i have a few more of these questions, about 5
Answer: You could plot the points (0,-2) ( 1,0) ( 2,2) (3,4) ( 4,6) (5,8) ( -1,-4) (-2.-6)
Step-by-step explanation:
y= 2x - 2
x y
0 -2
1 0
2 2
3 4
4 6
5 8
-1 -4
-2 -6
WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The cost for a business trip for 3 people is $1,975 per person. The business trip would use 79%
of the company’s travel budget. Find the total amount of money the company has budgeted for
travel. pls show work :)
Answer:
7500
Step-by-step explanation:
3*1975=5925
5925/.79=$7500
Answer:
5175
Step-by-step explanation:
1975*3=5925
5925/79%=7500 (Take one zero off)
750
5925-750=5175
The Company will pay 5175 in total. But 1725 per each person going.
find the measure of arc UT Given
a.168
b.192
c.84
d.96
Answer:
is there supossed to be a picture?
Step-by-step explanation:
Answer:
Can you please give us a picture!
Step-by-step explanation:
Ben makes $39,600 a year. What the maximum amount he can afford for a mortgage each month ?
Answer:825
Step-by-step explanation:
Which choice is equivalent to the quotient shown here for acceptable values of x?
Answer:
(D)
Step-by-step explanation:
Equivalent expressions are expressions that have equal values
The equivalent expression of [tex]\sqrt{8x^2 } \div \sqrt{3x}[/tex] is [tex]\sqrt{\frac{8x}{3}}[/tex]
The expression is given as:
[tex]\sqrt{8x^2 } \div \sqrt{3x}[/tex]
Represent the expression as a quotient
[tex]\sqrt{8x^2 } \div \sqrt{3x} = \sqrt{\frac{8x^2}{3x}}[/tex]
Evaluate the quotient
[tex]\sqrt{8x^2 } \div \sqrt{3x} = \sqrt{\frac{8x}{3}}[/tex]
Hence, the equivalent expression of [tex]\sqrt{8x^2 } \div \sqrt{3x}[/tex] is [tex]\sqrt{\frac{8x}{3}}[/tex]
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Please, someone, help me quickly!!
Answer:
(B)
Step-by-step explanation:
The value of 9 is more than the value than 4.
Therefore,
9 > 4.
4 is not greater than 9, and nine is not less than four.
Brainilest Appreciated!
The change in the x-coordinates of any two points on a line in the xy-plane is
the______
A. rise
B. slope
C. angle
D. run
Answer:
D. run
Step-by-step explanation:
The slope is given by
m = (y2-y1)/ (x2-x1) = rise/ run
The change in the x coordinates is the run
Triangle XYZ is a right triangle.
Use the drop downs to determine the length of the legs of the right triangle.
What is the length of Side X Z?
What is the length of Size Y Z?
Answer:
What is the length of Side X Z?
✔ 5
What is the length of Size Y Z?
✔ 6
The length of side XZ is 5 units.
The length of side YZ is 6 units.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
To find the length of side XZ, we can use the distance formula, which is:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Substituting the coordinates of X (-2, 4) and Z (3, 4), we get:
[tex]d(XZ) = \sqrt{(3 - (-2))^2 + (4 - 4)^2}\\= \sqrt{5^2 + 0^2}\\= \sqrt{25}\\= 5[/tex]
The length of side XZ is 5 units.
To find the length of side YZ, we can again use the distance formula with the coordinates of Y (3, -2) and Z (3, 4):
[tex]d(YZ) = \sqrt{(3 - 3)^2 + (4 - (-2))^2}\\= \sqrt{0^2 + 6^2}\\= \sqrt(36)\\= 6[/tex]
The length of side YZ is 6 units.
Thus,
The length of side XZ is 5 units.
The length of side YZ is 6 units.
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The area of Miguel’s rectangular garden is 450 square feet. The garden is 9 feet wide.
How many feet of fencing will Miguel need to buy to enclose the garden on all four sides?
Answer: 118 feet
Step-by-step explanation:
For a rectangular shape: Area = W × L
450 = 9 × L
450 ÷ 9
L = 50
Perimeter of a rectangular shape = 2L + 2W
Perimeter = (2 × 50) + (2 × 9)
= 100 + 18 = 118 feet
Melanie's bedroom floor has length equal to 6x + 5 and width equal to 9x – 2 points
4. What equation represents the area of the floor?
Answer:
(6x+5)(9x-2)
Step-by-step explanation:
Area = Length x Width
Answer:
54[tex]x^{2}[/tex] +33x - 10
Step-by-step explanation:
you have to use F.O.I.L. First Outter Inner Last
(6x + 5)(9x - 2)
First (6x)(9x) = 54 [tex]x^{2}[/tex]
Outter (6x)(-2) = -12x
Inner (5)(9x) = 45 x
Last (5)(-2) = -10
combine middle terms
54[tex]x^{2}[/tex] +33x - 10
Answer Choices:
y= x + 10; linear
y= x + 10; non linear
y= 10x + 1; linear
y= 10x + 1; nonlinear
C. =10x+1
y-intercept is 1 because it is the start up cost. 10 is the factor because it says "$10 a month" The variable x is the months
bz is tangent to circle o. ac is a diameter. mbc=90. mcd=30. mde=20.
state the theorem(s) that you used to find the measures of angles 1-10.
Answer:
1. Arc angle
2. Angle at circumference
3. Base angle of an isosceles triangle
4. Sum interior of angles in a triangle
5. Sum interior of angles in a triangle
6. The sum of angles on a straight line
7. Sum interior of angles in a triangle
8. Sum interior of angles in a triangle
9. Angle from a tangent to the radius of a circle
10. Alternate angles of line crossing two parallel lines
Step-by-step explanation:
Here, we note that, the angles where derived as follows;
1. mBC = 90°, therefore, angle subtended by the arc BC at the center of the circle = 1 = 90°
2. 90° The angle at the center which is the straight line diameter with angle 180° = 2 × angle at the circumference
∴ The angle at the circumference, angle 2 = 180°/2 = 90°
3. Angle subtended by the sum of arcs CD + DE at the center = 50°, therefore, ∡EOC = 50° and ∡EOA = 180° - 50° = 130° (the sum of angles on a straight line), since ΔAOE is an isosceles triangle, therefore, ∡OAE = ∡OEA = (180° - 130°)/2 = 25°
4. ∡A + ∡E + ∡C = 180° (Sum interior of angles in a triangle)
∴ 25° + 90° + ∡C = 180°
Hence ∡C = 180° - (90° + 25°) = 65°
5. From arc CD = 30°, ∡COD = 30°, ∴ ∡OBD = 30° = base angle of isosceles triangle with sides equal to the radius
Hence ∡8 = 30° from ∡8 + ∡1 + ∡OBD = 180° which gives
∡8 + 90° + 30° = 180°, hence;
∡8 = 180° - (90° + 30°) = 60°
∡8 = opposite ∡8 = 60°
Opposite ∡8 + ∡C + ∡5 = 180° (Sum interior of angles in a triangle)
Therefore ∡5 = 180° - (opposite ∡8 + ∡C) = 180° - (60° + 65°) = 55°
6. Angles 6 plus angle 5 = 180° (The sum of angles on a straight line)
Therefore, ∡6 = 180° - ∡5 = 180° - 55° = 125°
7. ∡7 + opposite ∡5 + ∡E = 180° (Sum interior of angles in a triangle)
∡E + ∡2 = 180° (The sum of angles on a straight line)
∴ ∡E = 180° - ∡2 = 180° - 90° = 90°
Hence, ∡7 + opposite ∡5 + ∡E = 180° = ∡7 + 55° + 90° = 180°
∴ ∡7 = 35°
8. ∡8 = 60° as found above
9. ∡9 = 90° (Angle from a tangent to the radius of a circle)
10. ∡10 = ∡8 = 60° (Alternate angles).