<u>Give</u><u>n</u><u>:</u>
- A ladder is leant against a wall of height 5m.
- The foot of ladder is 12m away from the wall.
<u>To</u><u> </u><u>Find</u><u>:</u>
<u>Conc</u><u>ept</u><u> Used</u><u>:</u>
- We will use Pythagoras Theorem.
<u>An</u><u>swer</u><u>:</u>
Here given
- Vertical height = 5m.
- Base = 12m.
Here the length of ladder is equal to hypotenuse of ∆ so formed.
Now in a right angled ∆ ,
=> (hypotenuse)² = (pependicular)²+(base)².
=> h ² = (12m)²+(5m)²
=> h² = 144m² + 25m².
=> h² = 169m².
=> h = √169m².
=> h = 13m.
<u>He</u><u>nce</u><u> the</u><u> required</u><u> answer</u><u> is</u><u> </u><u>1</u><u>3</u><u>m</u><u>.</u>
Answer: No, She is not right.
Step-by-step explanation:
First question:
Initial number of bison = 550
After increasing 10% than the initial number of bison, the new number of bison after one year= Initial number of bison + 10 % of the initial number of bison
= ![110\% \text{ of the initial number of bison}](https://tex.z-dn.net/?f=110%5C%25%20%5Ctext%7B%20of%20the%20initial%20number%20of%20bison%7D)
= ![110\% \text{ of }550](https://tex.z-dn.net/?f=110%5C%25%20%5Ctext%7B%20of%20%7D550)
= ![\frac{110\times 550}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B110%5Ctimes%20550%7D%7B100%7D)
= ![\frac{60500}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B60500%7D%7B100%7D)
= ![605](https://tex.z-dn.net/?f=605)
Second question:
Let Initial number of bison = x
After decreasing 10% than the initial number of bison, the new number of bison after one year= Initial number of bison - 10 % f the initial number of bison
= ![90\% \text{ of the initial number of bison}](https://tex.z-dn.net/?f=90%5C%25%20%5Ctext%7B%20of%20the%20initial%20number%20of%20bison%7D)
= ![90\% \text{ of } x](https://tex.z-dn.net/?f=90%5C%25%20%5Ctext%7B%20of%20%7D%20x)
= ![\frac{90\times x}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B90%5Ctimes%20x%7D%7B100%7D)
= ![\frac{9x}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B9x%7D%7B10%7D)
According to the question,
![\frac{9x}{10}=550](https://tex.z-dn.net/?f=%5Cfrac%7B9x%7D%7B10%7D%3D550)
![x=\frac{5500}{9}=611.11\approx 611](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B5500%7D%7B9%7D%3D611.11%5Capprox%20611)
Since, 605 ≠ 611
Therefore, Both questions have different answer.
⇒ Noah is not correct.
<u><em>Answer:</em></u>
The x-intercept is -8
The y-intercept is 4
<u><em>Explanation:</em></u>
<u>1- The x-intercept:</u>
The x-intercept of a function is the value of the x at y = 0
Therefore, to get the x-intercept, all we have to do is set y=0 in the given function and solve for x
<u>This is done as follows:</u>
-x + 2y = 8
-x + 2(0) = 8
x = -8 ....................> x-intercept = -8
<u>2- The y-intercept:</u>
The y-intercept of a function is the value of the y at x = 0
Therefore, to get the y-intercept, all we have to do is set x=0 in the given function and solve for y
<u>This is done as follows:</u>
-x + 2y = 8
0 + 2y = 8
2y = 8
y = 8/2 = 4 ....................> y-intercept = 4
<u>Note:</u> The graphical solution is shown in the attached picture
Hope this helps :)
The ans is choice D. since there nothing under 5x, imagine there is a 1 under. After that, you can simply cross multiply, so it would be 1(6+8x)= 2(5x). 6+8x= 10x now combine like terms so subtract 8x from both sides and divide 6 by 2 and you will get 3
A = 71.5 degrees (1 dp)
cos(A) = (21^2 + 16^2 - 22^2) / (2 x 21 x 16)
= 0.31696...
A = cos^-1(0.31696...) = 71.5 degrees