Gerard’s baby brother spends 7/8 of his day sleeping. How many hours does his baby brother sleep? i
Answers
You multiply 7/8 to the number of hours in a day which 24
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Answers
3x+y = 2
4x+y-3x-y = 20-2
x = 18
3x+y = 2
3.18 + y = 2
54 + y = 2
y = -52
Answers
x² - 16 = 0
x² = 16
√x² = √16
x = 4 or -4
Question 7
x² + 3x - 54 = 0
Factorizing
Find two numbers that add to make 3x and multiply to make 54
Write out the factor of -54 in pairs
1, -54
-1, 54
2, -27
-2, 27
3, -18
-3, 18
4, -16
-4, 16
6, -9
-6, 9
Then find the pair that, when added = +3 (in bold)
-6 + 9 = 3
x² + 9 - 6x - 54 = 0
x(x + 9) -6(x + 9)
Use the (x + 9) and the coefficient of these brackets to make double brackets.
(x+9)(x-6) = 0
If the product of two terms =0, at least one must equal 0
x + 9 = 0
x = -9
x - 6 = 0
x = 6
x = -9 or 6
Question 8
2x² -11x - 6 = 0
First, multiply the coefficient of x² by the value of c (the number on its own)2 x -6 = 12
This time, find factors of -12 that equal -11
1, -12
-1, 12
2, -6
-2, 6
3, -4
-3, 4
The pair is in bold
1 + -12 = -11
2x² -12x + x - 6
Split down the middle and factorise in singe brackets
2x(x - 6) 1(x - 6)
Now use the brackets pre-made (x - 6) and put together what is in front of them (2x +1)
(2x + 1)(x - 6)
If the product of two or more terms = 0, at least 1 must equal 0
2x + 1 = 0
2x = -1
2x/2 = x -1/2 = -0.5
x - 6 = 0
x = 6
x = -0.5 or 6
Question #6:
They expect you to remember that the difference
of two squares can be factored as
(the sum of the squared numbers) times (their difference).
So [ x² - 16 = 0 ] can be written as (x + 4) (x - 4) = 0 .
Now, a rule that you've used hundreds of times before
and you'll use thousands of times again:
If the equation says that the product of two things is zero,
then the equation is true if EITHER of them is zero.
So ...
(x+4) = 0 gives you one solution,
and (x-4)=0 gives you the other solution.
__________________________________
Question #7:
Factor the left side of the equation.
(x + 9) (x - 6) = 0 .
Now, use a rule that you heard somewhere VERY recently:
If the equation says that the product of two things is zero,
then the equation is true if EITHER of them is zero.
So ...
(x + 9) = 0 gives you one solution, and
(x - 6) gives you the other one.
_______________________________________
Question #8:
Factor the left side of the equation:
(2x + 1) (x - 6) = 0
Now use the golden rule that you've memorized by now:
If the equation says that the product of two things is zero,
then the equation is true if EITHER of them is zero.
So ...
(2x + 1) = 0 gives you one solution,
and (x - 6) = 0 gives you the other one.
Answers
Answer:
Step-by-step explanation:
There's no answer here. Because -6<21.
Answers
Answer:
12 + 20 = 4 × (3 + 5)
Step-by-step explanation:
12 = 4 × 3
20 = 4 × 5
12 + 20 = 4 × 3 + 4 × 5 = 4 × (3 + 5)
Answers
Declaration
Let the original amount of the paycheck be x
Equation
Paycheck - cost of mower - cost of chainsaw - 180 = 270
x - [(3/8)x + (2/5)x + 180] = 270
Solve
Change 3/8 and 2/5 to a common denominator and add.
3*5/8*5 + 2*8/5*8 = 15/40 + 16/30 = 31/40
x - [(31/40)x + 180] = 270 Remove the outer brackets
x - (31/40)x - 180 = 270 Evaluate the "x"s
40/40x - 31/40x - 180 = 270
9x/40 - 180 = 270 Add 180 to both sides
9x/40 = 180 + 270
9x/40 = 450 Multiply by 40
9x = 18000 Divide by 9
x = 18000/9
x = 2000
His paycheck was 2000 dollars.
b.6/8
c.5/6
d.9/12