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# Questions posted in Mathematics

## 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

1. 2. 3. 4. 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. ( ) 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

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

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.

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

## There is a bag with 4 red marbles, 2 green marbles, and 2 black marbles. What is the probability that when you pick out three marbles without putting them back in the bag, they are all red?

P(RRR)=4/8*3/7*2/6
=3/42

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

The numbers are 7 and 5.

Step-by-step explanation:

Let two  unknown numbers be x and y .

Assume .

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

we have,

x+y =12      ...

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

we have;

x- y =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,  + gives Simplify we get;  Substitute the value of  x =7 in equation ; On simplify, we get;

y = 5.

-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

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= -(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

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)?

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.

## Substitute the value of x back into the equation x + 3 – 2x = + x + 5 to justify the solution. What value of x is the solution?Edit: Just solved it, it's -1.

-1 good luck guys

Step-by-step explanation:

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

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)?

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

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

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

Option a)

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. Round off to one decimal.

q = 11.9

## A city grid of Anytown, USA is shown on the grid below. The fire department is represented by quadrilateral RSTU. Another fire department is opening in a different part of the city to maximize fire protection. The size of the new department's property must be congruent to the older department. Vertices A and B are plotted on the grid below to represent two vertices of the new fire department quadrilateral ABCD: Map of Anytown. The line y equals 6 is Main Road. The line y equals 3 is Rose Lane. The line y equals negative 5 is Crystal Avenue. The line x equals negative 4 is Brick Street. The diagonal line is Dogwood Drive. Old Fire Department forms quadrilateral with ordered pairs R at negative 4, negative 3, S at negative 4, negative 5, T at negative 8, negative 5, U at negative 8, negative 3, A is at negative 4, 5 and B is at negative 4, 3. What could be the ordered pairs representing vertices C and D of quadrilateral ABCD so that the new fire department

The new fire station seems to be translated north 8 units. However, we don't know the location of Dogwood Drive, so we cannot tell if the missing vertices are
C(-8, 3)
D(-8, 5)

or are
C(0, 3)
D(0, 5)

## 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?

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

Step-by-step explanation:

The given data set : 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 = 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?

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

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

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

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

Is there mor information on this picture i cant see

## Two steamers leave a port on a river at the same​ time, traveling in opposite directions. Each is traveling 28 mph. How long will it take for them to be 168 miles​ apart?

It will take them 6 hours to be 168 miles apart.

## (08.05)What conclusion can be determined from the dot plot below? A dot plot showing five dots above 9, six dots above 10, three dots above 11, and one dot above 12.

That there is no definite answer

Step-by-step explanation:

## 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.

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

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.

The triangles are not similar