4(d-8)-5 = 9(d+2)+1
Assuming you're looking for d:
Use Distributive Property for both sides
4d-32-5 = 9d+18+1
Combine like terms
4d-37 = 9d+19
Take all d's to one side & numbers to other
-37-19 = 9d-4d
Simplify
-56 = 5d
Divide both sides by 5
d = -56/5
So the equation of the red graph is already given to us: 
. I assume you meant the blue graph?
We can use the vertex form: 
, where 
is the vertex. (We can ignore 
because is 1 for this graph.) Remember that the vertex is the maximum or minimum of a parabola and the point that the line of symmetry passes through. For f(x) the vertex is (0,0).
The vertex for 
is at 
on the coordinate plane. (4 left, 2 down)
Plug into the vertex form:
The double negative becomes a positive, and then you're done:
Let the three consecutive integers be x, x+1 and x+2.
According to the question, x+x+1+x+2=51
=>3x+3=51
=>3x+3-3=51-3
=>3x=48
=>x=16
Hence, first integer = 16,
second integer = 16 + 1 = 17 and
third integer = 16 + 2 = 18.
Answer:
<h3>1</h3>
Step-by-step explanation:
simplify:
1/1-x^(b-a)+1/1-x^(a-b)
Hence the required answer is 1
It looks like you are good up to problem 4 so I will start there. I believe this is practice worksheet featuring the pyth. theorem. The pyth. theorem is used to find the length of sides in a right triangle notable the hypotenuse (side opposite of 90 degree angle).
4. The monitor is a rectangle but that does not stop you from constructing a right triangle. The smaller lengths are 16 in and 12 in respectively. The hypotenuse of the triangle is the diagonal of the rectangle. To find the length use the pyth. theorem.
diagonal^2 = 16^2+12^2
diagonal = 20 in
7. You know the speeds of both trains and the time spend traveling. You know they are traveling at a 90 degree angle so you can use pyth. theorem. But wait... you need to find the distances traveled for both trains. You can find that though because speed x time = distance.
50mph x 3hrs = 150mi
40mph x 3hrs = 120mi
The distance between the trains after 3 hours is the hypotenuse which can be determined by pyth. theorem.
distance^2 = 150^2+120^2
distance = 192 mi approx.
8. First find length of one piece of wiring. Use pyth theorem. Actually 3,4,5 pyth. triplet in which 5 is the hypotenuse. So you have 5 ft for the length of one piece of wiring. How many pieces of wiring do you need? Well, each tree needs 3 pieces and there are 6 trees so you need 18 pieces.
18 x 5 = 90 ft of wiring
From the work I see, you have a great understanding of the pyth. theorem. Keep it up!
