Answer:
Step-by-step explanation:
48:44= 12:11
Answer:
1 - cosΘ
Step-by-step explanation:
using the identity
sin²x + cos²x = 1 , then
sin²x = 1 - cos²x
![\frac{sin^20}{1+cos0}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5E20%7D%7B1%2Bcos0%7D)
=
← factor 1 - cos²Θ as a difference of squares
=
← cancel 1 + cosΘ on numerator/ denominator
= 1 - cosΘ
#1.
For this problem, we can use Pythagorean Theorem (a^2 + b^2 = c^2, where a and b are the legs, and c is the hypotenuse). We are given C, the hypotenuse, and A, a leg of the triangle in this problem.
9^2 + b^2 = 41^2
81 + b^2 = 1681
b^2 = 1600
b = 40 feet
#2.
We will again use Pythagorean Theorem. We are given the height and the length of a leg in this problem.
33^2 + b^2 = 65^2
1089 + b^2 = 4225
b^2 = 3136
b = 56 inches
Hope this helps!! :)
karen 3 more than 2 times of mary amy sold 5 more than karen
(3x)2+5
![\bold{\huge{\underline{ Solution }}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Chuge%7B%5Cunderline%7B%20Solution%20%7D%7D%7D)
<h3><u>Given </u><u>:</u><u>-</u></h3>
- Here, We have given two equations that is ,
![\sf{ x + 2y = 13\:\: and\:\: x + 5y = 28}](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%2B%202y%20%3D%2013%5C%3A%5C%3A%20and%5C%3A%5C%3A%20x%20%2B%205y%20%3D%2028%7D)
<h3><u>To </u><u>Find </u><u>:</u><u>-</u></h3>
- We have to find the value of x and y.
<h3><u>Concept</u><u> </u><u>used </u><u>:</u><u>-</u></h3>
- Linear equations are those equations which having highest power of degree as 1 .
- Linear equations can be solved by subsitute method, elimination method and cross multiplication method.
- Here, I have used substitution method to make calculation easier.
- In subsitute method, you have to subsitute the value of one variable of eq(1) in eq(2) .
<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u></h3>
<u>Here</u><u>,</u><u> </u>
- We have two equations, let consider these two equations as eq(1) and eq(2) that is,
![\sf{ x + 2y = 13 ...eq(1)}](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%2B%202y%20%3D%2013%20...eq%281%29%7D)
![\sf{ x + 5y = 28 ...eq(2)}](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%2B%205y%20%3D%2028%20...eq%282%29%7D)
<u>By </u><u>solving </u><u>eq(</u><u>1</u><u>)</u><u> </u><u>:</u><u>-</u>
![\sf{ x + 2y = 13 }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%2B%202y%20%3D%2013%20%7D)
![\sf{ x = 13 - 2y ...eq(3)}](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%20%3D%2013%20-%202y%20...eq%283%29%7D)
<u>Subsitute </u><u>eq(</u><u>3</u><u>)</u><u> </u><u>in </u><u>eq(</u><u>2</u><u>)</u><u> </u><u>:</u><u>-</u>
![\sf{ (13 - 2y) + 5y = 28 }](https://tex.z-dn.net/?f=%5Csf%7B%20%2813%20-%202y%29%20%2B%205y%20%3D%2028%20%7D)
![\sf{ 13 - 2y + 5y = 28 }](https://tex.z-dn.net/?f=%5Csf%7B%2013%20-%202y%20%2B%205y%20%3D%2028%20%7D)
![\sf{ 13 + 3y = 28 }](https://tex.z-dn.net/?f=%5Csf%7B%2013%20%2B%203y%20%3D%2028%20%7D)
![\sf{ 3y = 28 - 13 }](https://tex.z-dn.net/?f=%5Csf%7B%203y%20%3D%2028%20-%2013%20%7D)
![\sf{ 3y = 28 - 13 }](https://tex.z-dn.net/?f=%5Csf%7B%203y%20%3D%2028%20-%2013%20%7D)
![\sf{ 3y = 15 }](https://tex.z-dn.net/?f=%5Csf%7B%203y%20%3D%2015%20%7D)
![\sf{ y = }{\sf{\dfrac{ 15}{3}}}](https://tex.z-dn.net/?f=%5Csf%7B%20y%20%3D%20%7D%7B%5Csf%7B%5Cdfrac%7B%2015%7D%7B3%7D%7D%7D)
![\sf{ y = }{\sf{\cancel{\dfrac{ 15}{3}}}}](https://tex.z-dn.net/?f=%5Csf%7B%20y%20%3D%20%7D%7B%5Csf%7B%5Ccancel%7B%5Cdfrac%7B%2015%7D%7B3%7D%7D%7D%7D)
![\bold{ y = 5 }](https://tex.z-dn.net/?f=%5Cbold%7B%20y%20%3D%205%20%7D)
Thus, The value of y is 5
<h3><u>Now</u><u>, </u></h3>
<u>Subsitute </u><u>the </u><u>value </u><u>of </u><u>y </u><u>in </u><u>eq(</u><u>1</u><u>)</u><u> </u><u>:</u><u>-</u>
![\sf{ x + 2(5) = 13 }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%2B%202%285%29%20%3D%2013%20%7D)
![\sf{ x + 10 = 13 }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%20%2B%2010%20%3D%2013%20%7D)
![\sf{ x = 13 - 10 }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%20%20%3D%2013%20-%2010%20%7D)
![\bold{ x = 3 }](https://tex.z-dn.net/?f=%5Cbold%7B%20x%20%20%3D%203%20%20%7D)
Hence, The value of x and y are 5 and 3 .
![\bold{\huge{\underline{ Let's \: Verify }}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Chuge%7B%5Cunderline%7B%20Let%27s%20%5C%3A%20Verify%20%7D%7D%7D)
<h3>
<u>Equation </u><u>1</u><u> </u><u>:</u><u>-</u></h3>
![\sf{ x + 2y = 13 }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%2B%202y%20%3D%2013%20%7D)
![\sf{ 3 + 2(5) = 13 }](https://tex.z-dn.net/?f=%5Csf%7B%203%20%2B%202%285%29%20%3D%2013%20%7D)
![\sf{ 3 + 10 = 13 }](https://tex.z-dn.net/?f=%5Csf%7B%203%20%2B%2010%20%3D%2013%20%7D)
![\sf{ 13 = 13 }](https://tex.z-dn.net/?f=%5Csf%7B%2013%20%3D%2013%20%7D)
![\bold{ LHS = RHS }](https://tex.z-dn.net/?f=%5Cbold%7B%20LHS%20%3D%20RHS%20%7D)
<h3>
<u>Equation </u><u>2</u><u> </u><u>:</u><u>-</u><u> </u></h3>
![\sf{ x + 5y = 28 }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%2B%205y%20%3D%2028%20%7D)
![\sf{ 3 + 5(5) = 28 }](https://tex.z-dn.net/?f=%5Csf%7B%203%20%2B%205%285%29%20%3D%2028%20%7D)
![\sf{ 3 + 25 = 28 }](https://tex.z-dn.net/?f=%5Csf%7B%203%20%2B%2025%20%3D%2028%20%7D)
![\sf{ 28 = 28 }](https://tex.z-dn.net/?f=%5Csf%7B%2028%20%3D%2028%20%20%7D)
![\bold{ LHS = RHS }](https://tex.z-dn.net/?f=%5Cbold%7B%20LHS%20%3D%20RHS%20%7D)