MATHEMATICS HIGH SCHOOL

FOR 10 POINTS
Which of the following arithmetic sequences have a common difference of 2 1/2

Answers

Answer 1
Answer:

Answer: -4,-1.5,1,3.5,6,8.5

Step-by-step explanation: You can check that the difference of any of its consecutive terms is always equal to 2.5.

8.5 - 6 = 2.5

-1.5 - (- 4) = 2.5

3.5 - 1 = 2.5

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What multiplys to 40 and adds to -13

Answers

-5 and -8 both multiply to 40 -5 x -8 = 40 and both add up to -13. -5 + -8 = -13. two negative numbers when added together the answer is still negative. ex: if i owe 2 dollars to someone and 2 to another i owe 4 in total
We know that both of our numbers will need to be negative so that they multiply to get a positive number (the double negatives cancel) but add to get a negative one.
Consider factor pairs of 40.

-40 × -1 = 40 (adds to -41)
-20 × -2 = 40 (adds to -22)
-10 × -4 = 40 (adds to -14)
-5 × 8 = 40 (adds to -13)

Your numbers are -5 and -8.

Simplify 2 over squareroot 5

Answers

Square Root cannot be in the Denominator, therefore:

2 / √5
2 × √5 / √5 × √5
2√5 / 5

Hope this helps! 

2/5 / 2/3 how to divide fractions?

Answers

you use KCF- keep change flip 
2/5 X 3/2 = 6/10 = 3/5

What is the value of the system determinant for the following system of equations? 6x + y = 4 5x + y - 7 = 0

Answers

Answer:  The value of the determinant is 1.

Step-by-step explanation:  The given system of linear equation is as follows:

6x+y=4~~~~~~~~~~~~~~~~(i)\n\n5x-y-7=0\n\n\Rightarrow 5x-y=7~~~~~~~~~~~(ii)

The first column of the determinant gives the coefficients of 'x' and the second column gives the coefficients of y in the two equations.

Therefore, the determinant for the given system is

D=\begin{vmatrix} 6& 1\n  5& 1\end{vmatrix}=6* 1-5* 1=6-5=1.

Thus, the required value of the determinant is 1.

Yolanda spends 8/23 hours per month playing soccer. Approximately how many hours does she play soccer in a year

Answers

Given:
8 2/3 hours per month
12 months in a year.

Number of hours she play soccer in a year.

8 2/3 must be converted to improper fraction.

((8*3)+2)/3 = 26/3

26/3 * 12 = (26 * 12)/3 = 312/3 = 104 

Yolanda spends 104 hours in a year playing soccer.
(8+2/3)*12=96+2*12/3=96+2*4=96+8=104
Approximatively 104h per year

What does | 3+i | equal

Answers

The straight lines are asking to find the modulus or the size of the complex number.
For a complex number  z = x + iy,  [z] = √(x^2 +y^2)
Where x = Real Number, y = Imaginary number.
For 3 +i,  x = 3, y = 1    (Note y is what number that is attached to i)

[3 + i] = √(3^2 +1^2) = √10 = 3.162
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