Answer:
Step-by-step explanation:
I've attached a pic, I used y for sin(theta) and x for cos(theta). Shows all steps. See image.
Step 1: use "factoring sum of cubes" to factor the numerator.
Step 2: in the trinomial, in the numerator, rearrange terms to use the sin^2 + cos^2 = 1 .
Step 3: cancel that factor with the denominator.
Answer:
$2.50
Step-by-step explanation:
Let's set up a proportion using the following setup.
price / pens = price / pens
We know that it costs $4.00 for 8 pens.
$4.00 / 8 pens = price / pens
We don't know how much it costs for 5 pens. Therefore, we can say it costs $x for 5 pens.
$4.00 / 8 pens = $x / 5 pens
4/8=x/5
We want to solve for x (the cost for 5 pens). Therefore, we must get x by itself on one side of the equation. x is being divided by 5. The inverse of division is multiplication, so multiply both sides of the equation by 5.
5*(4/8)=(x/5)*5
5*(4/8)=x
5*0.5=x
2.5=x
x= $2.50
Ivan should pay $2.50 for 5 pens.
Lining up the trapezoids you need to notice that you have measurements for the LEFT side of both trapezoids. These measurements will be used to set up the ratio of small to large. 8/12 = 2/3 is the ratio of small trapezoid to large trapezoid.
To find a: 8/12 = 12/a; cross multiply; 8a = 144, divide both sides by 8; a = 18
To find b: 8/12 = b/6; cross multiply; 12b = 48, divide both sides by 12; b = 4
To find c: 8/12 =c/15; cross multiply; 12c =120, divide both sides by 12; c = 10
Instead of using 8/12 you could have used the reduced version, 2/3.
Answer:
581 square centimeters
Step-by-step explanation: