Questions posted in Mathematics

Answer:

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!!

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.

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.

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 

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

Answer:

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      ...[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

Simplify we get;

⇒

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

On simplify, we get;

y = 5.

-3/4 +5/8
= 5/8-3/4
= 5-6/8
= -1/8

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

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.

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.

Answer:

-1 good luck guys

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

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.

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

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.

Round off to one decimal.

q = 11.9

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)

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

Answer: 102

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 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.

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:

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

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.

Is there mor information on this picture i cant see

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

Answer:

That there is no definite answer

Step-by-step explanation:

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.

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 

D) the triangles are not similar 

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