MATHEMATICS HIGH SCHOOL

Determine the slope from the following order pairs:
(5, 7) (6,3)

Answers

Answer 1
Answer:

Answer:

Step-by-step explanation:

(3-7)/(6-5)= -4/1= -4

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A certain microscope is able to magnify an object up to 100,000 times its original size. In scientific notation, 100,000 is _____.

Answers

Answer: In scientific notation, 100,000 is 1.0*10^5

Step-by-step explanation:

We know that the scientific notation is a technique to describe a very large or a very small number in the product of a decimal form of number [generally between 1 and 10] and powers of ten.

The given number = 100,000

Here the number of zeroes = 5

Then, in scientific notation, 100,000 =1.0*10^5
shift 5 decimal places to the left, so the exponent for base 10 is 5. Therefore, the number in scientific notation is: 
1.0 x 105

How do I factor out a constant before factoring out a quadratic? 
Factor completely: 3w^2-3w-90

Answers

3w^2-3w-90 =0 \ \ \:3 \n \nw^2- w-30 =0 \n \na=1 , \ b= -1 , c= -30 \n \n\Delta =b^2-4ac = (-1)^2 -4\cdot1\cdot (-30) =1+120=121 \n \nw_(1)=(-b-√(\Delta) )/(2a)=(1-√(121))/(2 )=( 1-11)/(2)=(-10)/(2)=-5

w_(2)=(-b+√(\Delta) )/(2a)=(1+√(121))/(2 )=( 1+11)/(2)=(12)/(2)=6 \n \n Answer:\n \n w^2- w-30 =(x+5)(x-6)
 

Jeremy is 5 years younger than his older sister. His older sister is 9 years older than his younger sister. The total of their age is 49. Write and solve an equation to find the ages of Jeremy and his sisters. I need help please!

Answers

Jeremy=x
Older sister=x+5
younger sister=x+5-9 or x-4
x+(x+5)+(x-4)=49
combine like terms
3x+5-4=49
3x+1=49
subtract 1 from both sides
3x=48
divide both sides by 3
x=16
Jeremy=16
Older sister=16+5=21
younger sister =16-4 or 16+5-9=12
J=16
OS=21
YS=12
Jeremy - x
Older sister - x+5
Younger sister - x-4
3x+1=49
3x=48
X= 16

Jeremy: 16
Older sister: 21
Younger sister: 12

Which is greater 6.8 or 8.6?

Answers

8.6 because 8 is bigger than 6
8.6 is greater than 6.8 because the whole number in front of the decimal point (8) is greater than the whole number in front of the decimal point (6).

Simplifying rational expressions1. (c+8)(c-8)/(c-8)(c+3)
2. n^2+4n-12/n^2+2n-8
3. 42x^2y^3/28x^3y
4. m^2-3m-10/m-5

Answers

1. ((c + 8)(c - 8))/((c - 8)(c + 3))_,_
    (c + 8)/(c + 3)_,_

2. (n^(2) + 4n - 12)/(n^(2) + 2n - 8)_,_
    (n^(2) + 6n - 2n - 12)/(n^(2) + 4n - 2n - 8)_,_
    (n(n) + n(6) - 2(n) - 2(6))/(n(n) + n(4) - 2(n) - 2(4))_,_
    (n(n + 6) - 2(n + 6))/(n(n + 4) - 2(n + 4))_,_
    ((n - 2)(n + 6))/((n - 2)(n + 4))_,_
    (n + 6)/(n + 4)_,_

3. (42x^(2)y^(3))/(28x^(3)y)_,_
    (3y^(2))/(2x)_,_

4. (m^(2) - 3m - 10)/(m - 5)_,_
    (m^(2) - 5m + 2m - 10)/(m - 5)_,_
    (m(m) - m(5) + 2(m) - 2(5))/(m - 5)_,_
    (m(m - 5) + 2(m - 5))/(m - 5)_,_
    ((m + 2)(m - 5))/(m - 5)_,_
    m + 2_,_

Plz help what is 2x4+3x5(5x6)+2x6

Answers

2x4+3x5(5x6)+2x6 =
2x4+3x5x30+2x6=
8+15x30+12=
8+450+12=
470
Order of operations:
P parentheses
E exponents
MD multiplication/division
AS addition/subtraction

Start with parentheses
2x4+3x5(5x6)+2x6
2x4+3x5(30)+2x6
The 5 next to the 30 in parentheses means the 5 and 30 have a multiplication sign between them
2x4+3x5x30+2x6

Now exponents - we don't have any, so no worries

Now multiplication and division, in order from left to right
2x4+3x5x30+2x6
8+3x5x30+2x6
8+450+2x6
8+450+12

Now addition and subtraction, in order from left to right
8+450+12
458+12
470
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