Answer:
The system of equations are
x+y=557
The total pages in shorter book is 245
The total pages in longer book is 312
Step-by-step explanation:
Given that,
Scott has read 407 of the total number of 557 pages, which 
of the shorter book and 
of longer book.
Total number of pages of shorter book be x and longer book be y.
Then,
page of the shorter book 
pages of the longer book = 
So, he has read 
Total number of pages of both book is = x+y
According to the problem,
x+y=557.........(1)
.......(2)
We can write equation (2) as
......(3)
Now 18 times of equation (1) subtract from equation (3)
18x+25y=12210
18x+18y=10026
- - -
_______________
25y-18y=12,210-10,026
⇒7y=2,184
⇒y= 312
Plug y=312 in equation (1)
x+312=557
⇒x=557-312
⇒x=245
The total pages in shorter book is 245
The total pages in longer book is 312
Answer:
65
Step-by-step explanation:
First let's multiply both the numerator and denominator by 100 so that the decimal number becomes a whole number.
15.6 * 100 / 0.24 * 100
= 1560 / 24
= 65
If a sticky note measures 77mm then when converted into meters it is 0.077
Answer:
4 / 9
Step-by-step explanation:
There are 4 reds out of 9 so the probability would be 4 out of 9 or 4 / 9.
Answer:
Step-by-step explanation:
Given the expression cosec (x) = 4 and tan(x)< 0
since cosec x = 1/sinx
1/sinx = 4
sinx = 1/4
From SOH, CAH TOA
sinθ = opposite/hypotenuse
from sinx = 1/4
opposite = 1 and hypotenuse = 4
to get the adjacent, we will use the Pythagoras theorem
adj² = 4²-1²
adj² = 16-1
adj ²= 15
adj = √15
cosx = adj/hyp = √15/4
tanx = opposite/adjacent = 1/√15
since tan < 0, then tanx = -1/√15
From double angle formula;
sin2x = 2sinxcosx
sin2x = 2(1/4)(√15/4)
sin2x = 2√15/16
sin2x = √15/8
for cos2x;
cos2x = 1-2sin²x
cos2x = 1-2(1/4)²
cos2x = 1-2(1/16)
cos2x= 1-1/8
cos2x = 7/8
for tan2x;
tan2x = tanx + tanx/1-tan²x
tan2x = 2tanx/1-tan²x
tan2x = 2(-1/√15)/1-(-1/√15)²
tan2x = (-2/√15)/(1-1/15)
tan2x = (-2/√15)/(14/15)
tan2x = -2/√15 * 15/14
tan2x = -30/14√15
tan2x = -30/7√15
rationalize
tan2x = -30/7√15 * √15/√15
tan2x = -30√15/7*15
tan2x = -2√15/7
