Answer:
You would have $18
Step-by-step explanation:
Have a good day!
Let's call the distance from the beach to the playground x.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.
Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
There are three right triangles we can work with.
Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation
![x^{2} + 48^{2} = z^{2}](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%2B%2048%5E%7B2%7D%20%3D%20z%5E%7B2%7D%20)
Triangle with sides 27, x and y. Here y is the hypotenuse so we get
![27^{2} + x^{2} = y^{2}](https://tex.z-dn.net/?f=%2027%5E%7B2%7D%20%2B%20x%5E%7B2%7D%20%3D%20y%5E%7B2%7D%20)
Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get
![y^{2} + z^{2} = (27+48)^{2}](https://tex.z-dn.net/?f=%20y%5E%7B2%7D%20%2B%20z%5E%7B2%7D%20%3D%20%2827%2B48%29%5E%7B2%7D%20)
. That is,
![y^{2} + z^{2} = 5625](https://tex.z-dn.net/?f=%20y%5E%7B2%7D%20%2B%20z%5E%7B2%7D%20%3D%205625)
We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation:
![y^{2} + z^{2} = 5625](https://tex.z-dn.net/?f=y%5E%7B2%7D%20%2B%20z%5E%7B2%7D%20%3D%205625)
and replace
![z^{2}](https://tex.z-dn.net/?f=%20z%5E%7B2%7D%20)
and
![y^{2}](https://tex.z-dn.net/?f=%20y%5E%7B2%7D%20)
using expressions that contain an expression in terms of x from the first two equations we came up with.
That gives us:
![48^{2} + x^{2} + x^{2} + 27^{2} =5625](https://tex.z-dn.net/?f=%2048%5E%7B2%7D%20%2B%20x%5E%7B2%7D%20%2B%20x%5E%7B2%7D%20%2B%2027%5E%7B2%7D%20%3D5625)
which we solve for x as follows:
![2 x^{2} + 3033 =5625 2x^{2} =2592 x^{2} =1296 x=36](https://tex.z-dn.net/?f=2%20x%5E%7B2%7D%20%2B%203033%20%3D5625%0A2x%5E%7B2%7D%20%20%3D2592%0A%20x%5E%7B2%7D%20%3D1296%0Ax%3D36)
Now that we know x we can substitute 36 for x into the equation
![48^{2} + x^{2} = z^{2}](https://tex.z-dn.net/?f=48%5E%7B2%7D%20%2B%20x%5E%7B2%7D%20%3D%20z%5E%7B2%7D%20)
and solve for z as follows:
![48^{2} + 36^{2} = z^{2} 2304+1296=z^{2} 3600=z^{2} z=60](https://tex.z-dn.net/?f=48%5E%7B2%7D%20%2B%2036%5E%7B2%7D%20%3D%20z%5E%7B2%7D%20%0A2304%2B1296%3Dz%5E%7B2%7D%20%0A3600%3Dz%5E%7B2%7D%20%0Az%3D60)
This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.
Answer:
18
Step-by-step explanation:
If 100% is 9 then you need to multiply by 2 to get 200% which is 18.
If a^ x = b then:
x = log_{a}b
For:
4^{7} = 16384 \\ log _{4}16384 = 7
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Most of this exercise is looking at different ways to identify the slope of the line. The first attachment shows the corresponding "run" (horizontal change) and "rise" (vertical change) between the marked points.
In your diagram, these values (run=1, rise=-3) are filled in 3 places. At the top, the changes are described in words. On the left, they are described as "rise" and "run" with numbers. At the bottom left, these same numbers are described by ∆y and ∆x.
The calculation at the right shows the differences between y (numerator) and x (denominator) coordinates. This is how you compute the slope from the coordinates of two points.
If you draw a line through the two points, you find it intersects the y-axis at y=4. This is the y-intercept that gets filled in at the bottom. (The y-intercept here is 1 left and 3 up from the point (1, 1).)