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Match each power of i with its multiplicative inverse. 1) i 2) i^2 3) i^3 4) i^4 Each number has one of the following answers answers cannot be used more than once. Answer 1) i Answer 2) 1 Answer 3) -i Answer 4) -1

Mathematics 18/01/2020 10:31 AM answersmine

Answer:

  1. i=\frac{1}{i}*\frac{-i}{-1}=-i
  2. i^2=\frac{1}{i^2}*\frac{-i^2}{-i^2}=-1
  3. i^3=\frac{1}{i^3}*\frac{-i^3}{-i^3}=i
  4. i^4=\frac{1}{i^4}*\frac{-i^4}{-i^4}=1

Step-by-step explanation:

To find the multiplicative inverse of a complex number, you do as follows:

The inverse is found by reciprocating the original complex number. (\frac{1}{complex number}) Multiply the numerator and denominator of the reciprocal by conjugate of the denominator and simplify.

Hope this helps!!

Between which two consecutive integers does square root 147 lieA. 146 and 148B. 10 and 11C. 11 and 12D. 12 and 13

Mathematics 18/01/2020 10:31 AM answersmine
12² = 144
13² = 169

147 lies between 144 and 169, so √147 lies between
  D. 12 and 13

_____
It can be helpful to memorize the squares of positive integers up to 20 or 25.

Which of the following is the correct factorization of the polynomial below? 2x^2-8x+8

Mathematics 18/01/2020 10:30 AM answersmine

Answer:

2(x-2)²

Step-by-step explanation:

We have to factorize the given expression.

2x² - 8x + 8  =  2[x²- 4x + 4]

                    = 2(x - 2)²       [since (a-b)² = a² + b² - 2ab]

Therefore, 2(x-2)² is the correct factorized form.

What is the recursive formula for this geometric sequence? –4, –24, –144, –864, ... a. b. c. d.

Mathematics 18/01/2020 10:30 AM answersmine

the question does not present the options, but this does not interfere with the resolution

Let

a1=-4

a2=-24

a3=-144

a4=-864

a5=?


we know that

a2/a1=-24/-4----> 6-------> a2=6*a1

a3/a2=-144/-24---> 6-----> a3=6*a2

a4/a3=-864/-144---> 6----> a4=6*a3

therefore

a5=6*a4-----> a5=6*(-864)------> a5=-5184


hence 

the formula is

an=6*a(n-1)

n and (n-1) are subscripts 

The sum of two numbers is 12. their difference is 2. find the numbers

Mathematics 18/01/2020 10:29 AM answersmine

Answer:

The numbers are 7 and 5.

Step-by-step explanation:

Let two  unknown numbers be x and y .

Assume  x>y.

The first expression is given : The sum of two numbers is 12.

we have,

x+y =12      ...[1]

The second expression  states that : The difference of  two numbers is 2 , i.e,

we have;

x- y =2      .....[2]

Now, adding the equations, term by term on both sides,  we will eliminate y leaving an equation in x that we can solve:

then,  [1]+[2] gives

x+y+x-y = 12 +2

Simplify we get;

2x = 14

x= 7

Substitute the value of  x =7 in equation [1];

7+y =12

On simplify, we get;

y = 5.




What is -3/4 + 5/8 using adding and subtracting fractions

Mathematics 18/01/2020 10:29 AM answersmine
-3/4 +5/8
= 5/8-3/4
= 5-6/8
= -1/8

Find two numbers whose sum is 19 if the sum of their squares is 185

Mathematics 18/01/2020 10:29 AM answersmine
the first number:8
the second number: 11
x+y=19
-y -y
-----------
x=19-y substitute the values in
x^2+y^2=185
(19-y)^2+y^2=185
361-38y+y^2+y^2=185
361-38y+2y^2=185
-185 -185
-----------------------------------
361-38y+2y^2-185=0 combine like terms
176-38y+2y^2=0 commutative property
2y^2-38y+176=0 divide both sides by 2
------------------------
2
y^2-19y+88=0 solve the quadratic equation
y= -(19)+square root of (-19)^2-4(1)(88)
---------------------------------------------------- simplify
2(1)
y= (19)+ square root of 361-4(88)
----------------------------------------------
2
y=19+square root of 361-352
---------------------------------------
2
Y=19 square root of 9
------------------------------
2
Y=19+3
-
------
2
y=19-3 16
---------- ---- = 8
2 2
y=19+3 22
------- ------ =11
2 2



Kora uses the following ingredients to make 1 s'more. Ingredient Graham crackers 1 Chocolate squares 8 Marshmallo How many s'mores can Kora make if she has 20 graham crackers

Mathematics 18/01/2020 10:29 AM answersmine

Answer:

Kora can prepare 20 s'mores.

Step-by-step explanation:

There is some info missing. I think this is the original question.

Kora uses the following ingredients to make  1  s'more.

Ingredient                  amount

graham crackers           1

chocolate squares        8

marshmallows               3

How many s'mores can kora make if she has  20  graham crackers?

According to the cooking recipe, each s'more requires 1 graham crackers. This is our conversion factor. We can find the number of s'mores that can be prepared using 20 graham crackers using proportions.

20 graham cracker × (1 s'more / 1 graham cracker) = 20 s'more

Kora can prepare 20 s'mores, assuming she has enough of the other ingredients.

What is another name for the point located at (0 0)?

Mathematics 18/01/2020 10:27 AM answersmine
The horizontal axis in the coordinate plane is called the x-axis. The vertical axis is called the y-axis. The point at which the two axes intersect is called the origin. The origin is at 0 on the x-axis and 0 on the y-axis.



Which pair of undefined terms is used to define the term parallel lines?point and lineplane and linepoint and rayray and line

Mathematics 18/01/2020 10:27 AM answersmine

Answer:

the answer is plane line i just took a quiz and i was really helpful.!

Step-by-step explanation:


Where c is an oriented simple curve connecting (1, 1, 1) to (1, 3, 9)?

Mathematics 18/01/2020 10:26 AM answersmine
Maximum 0.027%. As a result, since the variance is less than 5%, it is clear that the experimental results are consistently executed. Therefore, these data are reliable in carrying out numerical analysis.

Solve the following equation. Then place the correct mixed number in the box provided. 5x/7=22

Mathematics 18/01/2020 10:26 AM answersmine
We have that
 5x/7=22
multiply by 7 both sides
5x=22*7-------> 5x=154
divide by 5 both sides
x=154/5
x=30.8--------> x=30 4/5

the answer is
x=30 4/5

What is the length of side q, given r = 20, s = 30, and Q = 15°? Round the answer to the nearest tenth. mc022-1.jpg [Not drawn to scale] 11.9 40.7 140.9 1659.1

Mathematics 18/01/2020 10:26 AM answersmine

Answer:

Option a)

11.9 is correct answer.

Step-by-step explanation:

Given that in a triangle QRS, we have side r =20, s=30 and Q= 15 degrees

We have to find the side length q.

Use cosine formula for triangles.

q^2=r^2+s^2-2rs cos Q\\     = 20^2+30^2-2(600)cos 15\\     =1300-1159.11\\    q = 11.911

Round off to one decimal.

q = 11.9

What is the volume of the given prism? round the answer to the nearest tenth of a centimeter. 9.4 cm 5.4 cm 11.7 cm?

Mathematics 18/01/2020 10:26 AM answersmine

Answer:

Volume of the prism = 593.9 cm^3

Step-by-step explanation:

Length =9.4 cm

width=5.4 cm

height =11.7 cm

Volume of the prism = Length * width * height

Plug in the values and multiply the numbers to get volume of the prism

Volume of the prism = Length * width * height

Volume of the prism = 9.4 * 5.4 * 11.7

= 593.892 cubic cm

Harlon recorded this set of data, which contains an outlier. 163, 97, 184, 199, 169, 175 What is the range of this set of data? 12 97 102 172

Mathematics 18/01/2020 10:26 AM answersmine

Answer: 102

Step-by-step explanation:

The given data set :  \text{163, 97, 184, 199, 169, 175}

We know that the range of a data set is the difference between maximum value and the minimum value of the data set .

In the given data set, Maximum value = 199

Minimum value =97.

Then , the range of this set = 199-97=102

Hence ,the range of the given data set = 102.

The graph shows the relationship between the volume of a rectangular prism and the volume of a square pyramid with an identical base and height. What is the slope of the line?

Mathematics 18/01/2020 10:26 AM answersmine
The picture in the attached figure

we know that
volume of a rectangular prism=area of the base*h
area of the base=B
volume of a rectangular prism=B*h-----> equation 1

volume of a square pyramid=(1/3)*area of the base*h
area of the base=B
volume of a square pyramid =(1/3)*B*h-----> equation 2

substitute equation 1 in equation 2
volume of a square pyramid =(1/3)*volume of a rectangular prism
volume of a rectangular prism/volume of a square pyramid=3

therefore
the slope of the line must be 3

let's check it
To solve for the slope of the line, you must choose two coordinates first and use the formula m = (y₂-y₁)/(x₂-x₁). 
Choosing the points (2,6) and (3,9) :m = (9-6)/(3-2) = 3.

the answer isThe slope of the line is 3.

Convert the following measurements. Round your answers to two decimal places. a. 14,974 pounds to tons b. 8,047 ounces to pounds c. 64 ounces to pounds d. .27 ton to pounds

Mathematics 18/01/2020 10:25 AM answersmine

Answer:

A. 6.79 tons

B. 502.94 pounds

C. 4 pounds

D. 59524.74 pounds

hope this helps have a good day

Step-by-step explanation:

Convert the following measurements. a. 22 tons to pounds b. 13 pounds to ounces c. 90,320 ounces to pounds d. 24,000 pounds to tons

Mathematics 18/01/2020 10:25 AM answersmine
For this case we have to know the following conversions:
 1 ton = 2204.62 pounds
 1 oz = 0.0625 pounds
 Now we apply the conversions:

 22 tons to pounds:
 
(22)*(2204.62) = 48501.64 pounds

 13 pounds to ounces:
 
(13)*(1/0.0625) = 208 oz

 90,320 ounces to pounds:
 
(90320)*(0.0625) = 5645

 24,000 pounds to tons:
 
(24000)*(1/2204.62) = 10.88 tons

Solve the following multiplication and division problems. a. 10 yd. × 3 yd. b. 15 ft. × 18 ft. c. 13 yd. 2 ft. 6 in. × 15 d. 198 sq. yd. 8 sq. ft. × 7

Mathematics 18/01/2020 10:25 AM answersmine
A. 10 yd.×3 yd.=30 square yards;
b. 15 ft.×18 ft.=279 square feets;
c. 13 yd.=13×3 ft.=39 ft.=39×12 in.=468 in., 2 ft. 6 in.=2×12+6 in.=30 in., then 13 yd. 2 ft. 6 in.×15=498 in. × 15=7470 in.;
d. 198 sq. yd.=198 ×9 sq. ft.=1782 sq. ft.
198 sq. yd. 8 sq. ft. =1782+8 sq. ft.=1790 sq. ft.
Then 1790 sq. ft. × 7=12530 sq. ft.


SEE PIC ON TOP FIRST Need answers for number:10,11,12 and 13

Mathematics 18/01/2020 10:25 AM answersmine
Is there mor information on this picture i cant see

Solve the following problems. a. 2 ft. 5 in. + 9 in. b. 4 yd. 8 in + 6 yd. 6 in. c. 29 yd. 2 ft. 11 in. + 55 yd. 1 ft. 10 in. + 13 yd. 1 ft. 3 in. d. 4,839 sq. yd. 8 sq. ft. 139 sq. in. + 7 sq. ft. 124 sq. in.

Mathematics 18/01/2020 10:24 AM answersmine
a. 2 ft. 5 in. + 9 in.=2 ft 14 in.=2 ft. (12+2) in.=3 ft. 2 in. (since 1 ft.=12 in.);

b. 4 yd. 8 in + 6 yd. 6 in. =(4+6) yd. (8+6) in.=10 yd. 14 in.=10 yd. (12+2) in.=10 yd. 1 ft. 2 in.;

c. 29 yd. 2 ft. 11 in. + 55 yd. 1 ft. 10 in. + 13 yd. 1 ft. 3 in.=(29+55+13) yd. (2+1+1) ft. (11+10+3) in.=97 yd. 4 ft. 24 in.=97 yd. (3+1)  ft. (12+12) in.=98 yd. 3 ft.=99 yd.


d. 4,839 sq. yd. 8 sq. ft. 139 sq. in. + 7 sq. ft. 124 sq. in.=4,839 sq. yd. (8+7) sq. ft. (139+124) sq. in.=4,839 sq. yd. 15 sq. ft. 263 sq. in. =
4,839 sq. yd. 15 sq. ft. (144+119) sq. in.=4,839 sq. yd. 16 sq. ft. 119 sq. in.=4,839 sq. yd. (9+7) sq. ft. 119 sq. in.=4,840 sq. yd. 7 sq. ft. 119 sq. in.










Convert the following measurements. a. 13 miles to yards b. 67 square feet to square inches c. 4,800 inches to feet d. 87,120 square yards to acres e. 3 miles to yards f. 54 inches to yards g. 12 yards to feet h. 7 acres to square feet

Mathematics 18/01/2020 10:24 AM answersmine
a. 13 miles to yards

1 mile is equal to 1,760 yards, then 13 mi= 13×1,760 yd=22,880 yd.

b. 67 square feet to square inches1 feet is equal to 12 inches and 1 square feet is rqual to 144 square inches, then 67 sq. ft.=67×144 sq. in.=9,648 sq. in.

c. 4,800 in=(4,800÷12) ft.=400 ft.

d. 87,120 square yards to acres
1 Square yard = 0.00020661157 acre, then 87,120 sq. yd.=87,120×0.00020661157 acres=17.9999999784 acres

e. 3 mi=3×1,760 yd=5,280 yd.
f. 54 inches to yards54 in=(48+4) in.=(48÷12)ft 4 in.=4 ft. 4 in.=(3+1) ft. 4 in.=1 yd. 1 ft. 4 in.1 feet is equal to 12 inches and 1 yard is equal to 3 feets

g. 12 yards to feet1 yard is equal to 3 feets, then 12 yd.=12×3 ft.=36 ft.

h. 7 acres to square feet1 acre = 43,560 square feet, then 7 acres=43,560×7 sq. ft.=304,920 sq. ft.









Geometry questions please help asap

Mathematics 18/01/2020 10:24 AM answersmine
The triangles are not similar 

Geometry question please help asap

Mathematics 18/01/2020 10:24 AM answersmine
D) the triangles are not similar 

Write the following decimal number in its equivalent fraction form. Show all work for full credit.0.225

Mathematics 18/01/2020 10:24 AM answersmine
Rewrite the decimal number as a fraction with 1 in the denominator

0.225=0.22510.225=0.2251

Multiplying by 1 to eliminate 3 decimal places, we multiply top and bottom by 103 = 1000

0.2251×10001000=2251000