Simplify 10(0.4x+0.2y)+21(0.6x-0.8y) BRAINLIEST
1 answer:
You might be interested in
Answer:
Distance between cars rounded to the nearest foot is : 1903 ft
Step-by-step explanation:
Notice that two right triangles can be used to represent the diagram of this situation. One between the car whose angle of depression is , and the other with the car with angle of depression
(see attached image)
Each triangle in the attached image is depicted with a different color. and as one can see, the distance between both cars is the addition of the side "x" in one triangle, to the side "y" in the other.
Notice as well that the information known for both right-angle triangles is one acute angle, and the side opposite to it. And what one needs to find is the side adjacent to this acute angle. Then, the function to use in both triangles, is the tangent:
a) For the [orange] triangle :
b) For the [green] triangle:
Therefore the total distance between cars is:
1081.42 ft + 821.19 ft = 1902.61 ft
which to the nearest foot can be rounded as: 1903 ft
There are a lot of steps involved in this, so pay attention. First step is to expand the squared quantity and FOIL it out, like this:
and
We are going to combine all the like terms now and get them all on one side of the equation:
Now we are going to complete the square on the polynomial in order to find the vertex. Do this by first setting the equation equal to 0 and then moving the constant over to the other side of the equals sign, like this:
and now factor out the negative sign (cuz negative signs are a pain):
. To complete the square, you take half the linear term, square it, and add it in to both sides. Our linear term is 6x. Half of 6 is 3, and 3 squared is 9. That's easy to add in on the left side, but we cannot forget that fact that we factored out a negative 1, and that the negative 1 is still there and has to be taken into consideration when we "add" in a 9 to the other side. We actually multiply the negative 1 times the 9 and that's what's added in to the right:
What you do when you complete the square is create a perfect square binomial on the left, which we have and which looks like this:
When we move the 3 back over to be with its mates (the 3 is the y coordinate for the vertex), we have the actual sign of the y coordinate. The number inside the parenthesis with the x is the x coordiante of the vertex in the form
. So the vertex of your problem is (-3, 3). The negative outside the parenthesis just indicates to us that the parabola is an upside down one, like a mountain instead of a valley.
We are going to combine all the like terms now and get them all on one side of the equation:
Now we are going to complete the square on the polynomial in order to find the vertex. Do this by first setting the equation equal to 0 and then moving the constant over to the other side of the equals sign, like this:
What you do when you complete the square is create a perfect square binomial on the left, which we have and which looks like this:
When we move the 3 back over to be with its mates (the 3 is the y coordinate for the vertex), we have the actual sign of the y coordinate. The number inside the parenthesis with the x is the x coordiante of the vertex in the form