(8)
since ΔPRS is right isosceles then PR = RS
let PR = RS = x, then using Pythagoras' identity on the triangle
x² + x² = (3√2)²
2x² = 18 ( divide both sides by 2 )
x² = 9 ( take the square root of both sides )
x = 3
that is RS = PR = 3 cm
MNPQ is a square hence PQ = = 5
and QR = PQ - 3 = 5 - 3 = 2 cm
area of rectangle RSTQ = 3 × 2 = 6 cm²
(9)
Since one of the diagonals is an altitude , then right triangle is formed
let one side be x then the other side is x - 2
perimeter = (2 × length ) + (2 × width ) = 2x + 2(x - 2 ) = 4x - 4
now given perimeter = 40, then
4x - 4 = 40 ( add 4 to both sides )
4x = 44 ( divide both sides by 4 )
x = 11
hence sides ( legs of right triangle ) are 11 and 9
Using Pythagoras' identity on the right triangle with hypotenuse (x) being the altitude
x = √(11² + 9²) = √(121 + 81) = √202 ≈ 14.21 in ( to 2 dec. places )
Answer:
first, add 6 to both sides to get..
y+6=5x
then divide each side by 5 to isolate the variable x. you get..
x = y+6
By flipping the fraction of -3/7, you will get the fraction of -7/3 or - 2 1/3.
Therefore, the reciprocal of -3/7 is - 2 1/3.
Hope this helps!
Answer:
To find 2/3 of an hour first we will divide 1 hour that is 60 minutes into 3 parts. So we will get 20 minutes. So we 2parts out of 3 parts of an hour so we get 20X2=40minutes
Step-by-step explanation:
Hey there!
You should not expect more than 34 times to be favorable, because favorable outcomes are about 28% of outcomes, and 28% of 100 is 28, which is less than 34.
6/21 outcomes will be favorable.
Here is a list of all possible out comes:
1 - 1
1 - 2
<u>1 - 3</u>
1 - 4
1 - 5
1 - 6
2 - 2
<u>2 - 3</u>
2 - 4
2 - 5
2 - 6
<u>3 - 3</u>
<u>3 - 4</u>
<u>3 - 5</u>
<u>3 - 6</u>
4 - 4
4 - 5
4 - 6
5 - 5
5 - 6
6 - 6
The underlined ones have one or two 3's in their outcome. There are 21 outcomes total, and 6 of them have 3's in them. We will find the percentage by doing 6/21 = .286, or 28.6%. This means that for every 100 outcomes, you should expect about 29 of them to be favorable.
I hope it helps and have an amazing day! You've got this!