Percent means parts out of 100
20%=20/100=2/10=1/5
a mixed number is a fraction over 1 expressed in the form (whole number) and (fraction part)
since this is less than one, it techinally is not a mixed number but we can do this
0 and 1/5
Answer:
k = 9.
Step-by-step explanation:
2x + 3y -8=0
3y = -2x + 8
y = -2/3 x + 8/3
So the slope of this line is -2/3.
Therefore the slope of a line perpendicular to the above is -1 /-2/3
= 3/2.
kx - 6y = 9
6y = kx - 9
y = k/6x - 3/2
But the slope is 3/2,
So k/6 = 3/2
2k = 18
k = 9.
Answer:
Step-by-step explanation:
Let the length and breadth of the rectangle be a,b units respectively.
Then the area will be ab square units.
Now if the length of the rectangle is reduced by 5 units and breadth is increased by 2 units then new length and breadth will be (a−5) units and (b+2) units.
Then new area will be (a−5)(b+2).
Then according to the problem,
(a−5)(b+2)−ab=−80
or, 2a−5b=−70.......(1).
Now if length of the rectangle is increased by 10 units and breadth is decreased by 5 units then new length and breadth will be (a+10) units and (b−5) units.
Then new area will be (a+10)(b−5).
Then according to the problem,
(a+10)(b−5)−ab=50
or, 10b−5a=100
or, 2b−a=20
or, 4b−2a=40......(2).
Now adding (1) and (2) we get
−b=−30
or, b=30.
Putting the value of b in (1) we get, a=40.
Now a+b=40+30=70.
Answer:
Hence, m∠R=95°.
Step-by-step explanation:
We are given that ΔABC is similar to the ΔRST i.e. ΔABC~ΔRST.
Aslo m∠A=6x+17, m∠B=3x+9, and m∠C=37
We know that sum of all the angles of a triangle is 180°.
⇒ ∠A+∠B+∠C=180
⇒ 6x+17+3x+9+37=180
⇒ 9x+63=180 (As 6x+3x=9x and 17+9+37=63)
⇒ 9x=180-63
⇒9x=117
⇒ x=13. (on dividing both side by 9)
Hence m∠A=6x+17=6×13+17=95°
m∠B=3x+9=3×13+9=48°
m∠C=37°
Also as ΔABC~ΔRST so this implies m∠R=m∠A=95°
Hence, m∠R=95°.
