Answer:
a +(b -c) = -9i +10j
Step-by-step explanation:
You can use the distributive property to remove the parentheses:
a +(b -c) = a + b - c
Add the vectors as though they were binomials.
a + b - c = (3 -2 -10)i +(4 +5 -(-1))j = -9i +10j
Answer:
h=14
Step-by-step explanation:
So since the triangular shape is a right triangle, we can use a Pythagorean triple. For this question, lets use (5,12,13). But, if you just want to use the formula:
5^2+x^2=13^2
25=x^2=169
x^2=144
x=12
That means a part of h is 12. BUT, we also have an extra two ft on top of the triangle, so h=12+2=14.
Answer: a = -2 and c = 7
Step-by-step explanation:
(this answer uses some basic calculus)
We know that 
, and since 
is a maximum of 
, then 
. That means 
, so 
. Then since 
, we have 
, so 
.
Answer:
x = -1 ± √109
Step-by-step explanation:
2x • 3x + (2 • 3)x + 6x = 648
According to PEMDAS (parentheses/exponents | multiplication/division | addition/subtraction), we should solve the parentheses first.
(2 • 3) = 6
Now we have:
2x • 3x + (6)x + 6x = 648
Now let's multiply.
2x • 3x = 6x²
6 • x = 6x
Now we have.
6x² + 6x + 6x = 648
Combine like terms.
6x² + 12x = 648
Let's factor out a 6.
6(x² + 2x) = 648
Divide both sides by 6.
x² + 2x = 108
Let's use completing the square.
Our equation is in a² + bx = c form.
Divide b by 2.
2/2 = 1
Then square it.
1² = 1
Add 1 to both sides.
x² + 2x + 1 = 108 + 1
Simplify.
x² + 2x + 1 = 109
Now we want to factor the left side. A shortcut is just to use b/2.
(x + 1)² = 109
Take the square root of both sides.
x + 1 = ±√109
The square root is as simplified as possible.
Subtract 1 from both sides.
x = -1 ± √109
Hope this helps!
Answer:
75
Step-by-step explanation:
We have a 90 degree angle and a 15 degree angle that add up to 105. The angle that is missing can be found by doing 180 - 105 = 75 (since it's a straight line). X is vertical from the 75 degree angle, so 75 is your answer.
