Answer:
x + y = 52
y = x + 12
(soccer team) x = 20, (hockey team) y = 32
Step-by-step explanation:
x = students on the soccer team
y = students on the hockey team
x + y = 52
y = x + 12
Substitute y = x +12 to get:
= x + x +12 = 52
= 2x + 12 =52
Isolate x for 2x + 12 = 52: x = 20.
Now incorporate a new equation with x = 20:
y = 20 +12
y = 32
Therefore:
x = 20, y = 32
Answer:
![\theta=287^o](https://tex.z-dn.net/?f=%5Ctheta%3D287%5Eo)
Step-by-step explanation:
<u>Position in the Plane
</u>
If we place an object in a plane and mesure its x and y coordinates, we are referencig its position according to the rectangular system. Other popular way to reference positions is in polar form or magnitude-angle form. If we have the rectangular coordinates (x,y), we can easily find the polar coordinates
(and vice-versa). We use the formulas
![r=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
![\displaystyle tan\theta=\frac{y}{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20tan%5Ctheta%3D%5Cfrac%7By%7D%7Bx%7D)
We have x=31.4 Km East (a positive coordinate) and y=-102.5 Km South (negative because it's pointing downwards). we need to find the angle respect to the East reference where
. Check the image below for reference.
![\displaystyle tan\theta=\frac{-102.5}{31.4}=-3.264](https://tex.z-dn.net/?f=%5Cdisplaystyle%20tan%5Ctheta%3D%5Cfrac%7B-102.5%7D%7B31.4%7D%3D-3.264)
![\theta=-73^o](https://tex.z-dn.net/?f=%5Ctheta%3D-73%5Eo)
The angle can be also given as a positive quantity by adding 360^o
![\theta=-73^o+360^o](https://tex.z-dn.net/?f=%5Ctheta%3D-73%5Eo%2B360%5Eo)
![\boxed{\theta=287^o}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctheta%3D287%5Eo%7D)
The values of functions are:
a) f( x ) + g( x ) = x² + x - 3
b) f( x ) - g( x ) = x² - x - 5
c) f( x ) / g( x ) = x² - 4/ (x+ 1)
d) f( x ) * g( x ) = x³ + x² - 4x - 4
<h3>what is function?</h3>
In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = x² - 4 and g (x) = x + 1
a) f( x ) + g( x )
= x² - 4 + x+ 1
= x² + x - 3
b) f( x ) - g( x )
= x² - 4 - ( x+ 1)
= x² - 4 - x- 1
= x² - x - 5
c) f( x ) / g( x )
= x² - 4/ (x+ 1)
d) f( x ) × g( x )
= (x²- 4)( x+ 1)
= x³ + x² - 4x - 4
Learn more about function here:
brainly.com/question/12431044
#SPJ1
Answer:
Computational science is a discipline concerned with the design, implementation and use of mathematical models to analyse and solve scientific problems. Typically, the term refers to the use of computers to perform simulations or numerical analysis of a scientific system or process.
Step-by-step explanation:
Answer:
two digits to the right
Step-by-step explanation:
When multiplying a decimal by 102 you would need to move the decimal point two digits to the right. This is because we are multiplying by a hundred number. When multiplying any whole positive number by a decimal, we need to move the decimal point to the right one less than the amount of digits that the positive whole number has. For example, a thousand (1000) has 4 digits so we move the decimal point of the product to the right by 3.
Examples:
102 * 0.02 = 2.04
1000 * 0.02 = 20
10000 * 0.02 = 200