x + 7 = 2(3x - 4) Remove the brackets
x + 7 = 2*3x - 4*2
x + 7 = 6x - 8 Subtract 7 from both sides.
x + 7 - 7 = 6x - 8 - 7
x = 6x - 15 Subtract 6x from both sides
x - 6x = - 15
-5x = - 15 Divide by -5
-5x/-5 = -15/-5
x = 3
Answer:
Step-by-step explanation:
The formula for the dot product of vectors is
u·v = |u||v|cosθ
where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.
which is 
which is 
I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.
We also need the angle, which of course has its own formula.
where uv has ITS own formula:
uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.
uv = 96.
To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:
which returns an angle measure of 30.7. Plugging that all into the dot product formula:
gives you a dot product of 96
Answer:
x=4 x=10
Step-by-step explanation:
(x - 6) (x - 8) =8
We need to multiply out the left side
x^2 -8x -6x+48 = 8
x^2 -14x +48 = 8
Subtract 8 from each side
x^2 -14x +48-8 = 8-8
x^2 -14x+40 =0
We need to factor the left side. What two numbers multiply to give 40 and add to give -14
-4*-10 = 40
-4+-10 = -14
(x-4) (x-10) =0
Using the zero product property
x-4=0 x-10 =0
x=4 x=10
The depth of the joist that was drilled by Freddy is 5 1/3 inches.
From the information given, we are informed that Freddy drilled into a piece of wood and a joist to attach them and that be drilled 4 inches and the wood was 1 1/3 inches thick.
Therefore, to get the depth that was drilled, we'll need to add the fractions given together. This will be:
= 4 + 1 1/3
= 5 1/3 inches.
Therefore, the depth of the joist that was drilled by Freddy is 5 1/3 inches.
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