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1. x + y = 7
2. x * y = -30
Re-arrange 1. to y = -x + 7
Substitute this value for y into 2. gives:
3. x * (-x + 7) = -30
-x2 + 7x = -30
-x2 + 7x + 30 = 0
Now we can factor this quadratic to:
(-x + 10) (x + 3) = 0
Now we can make each bracket equal to 0 in turn.
-x + 10 = 0
-x = -10
x = 10
and
x + 3 = 0
x = -3
So the answer is 10 and -3.
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What two factors of 7 add up to -30?
-23
What number multiplies to get -30 but adds to get -7?
Negative 10 and positive 3
How do you multiply traditionally?
One visualization of multilication is to consider (say 7 x 35) as a grid of dots, 7 dots wide and 35 dots high. Then count up the number of dots in that rectangle. Perhaps simpler is to multiply 7 x (30 +5) = 7 x 30 + 7 x 5; = 210 + 35 = 245.
What multiplies to -60 and adds up to -7?
-12 and +5
What adds up to -33 and multiplies to -280?
-313
What numbers multiply to 30 and adds to 7?
37
What number multiplies by 144 and adds to 7?
Any number can multiply 144 and be added to 7!
What two factors of 7 add up to -30?
-23
What number multiplies to get -30 but adds to get -7?
Negative 10 and positive 3
What is bigger three eighths or seven tenths?
Set up a proportion and multiply up and across. 3/8=7/10 30 ? 56 so 7/10 is bigger
How do you multiply traditionally?
One visualization of multilication is to consider (say 7 x 35) as a grid of dots, 7 dots wide and 35 dots high. Then count up the number of dots in that rectangle. Perhaps simpler is to multiply 7 x (30 +5) = 7 x 30 + 7 x 5; = 210 + 35 = 245.
What adds up to 12?
-7 and -5
What is a number that adds up to 48 that is in between 30 and 40?
The factors of 35 are: 1x35 and 7x5 add the factors 1+35+7+5= 48
What adds up to 7 and multiplies to 6?
6*1
What adds up to -7 and multiplies to 6?
-6 and -1.
What multiplies to -60 and adds up to -7?
-12 and +5
How do you factor this trinomial 5x² plus 6x plus 7?
5x**2+6x+7 Multiply first and third coefficients 5*7=35 Factor result 5*7 1*35 None of these pairs adds up to the second term, cannot be factored
