Answer:
B) 23
Step-by-step explanation:
Table: <u> Algebra | No algebra | Total</u>
Physics | 4 Step 1: 8 12
No physics |Step 2: 15
Total | 19 30
We look for the number of people who are in algebra and no physics or physics and no algebra.
1. 12 - 4 = <em>8</em>
2. 19 - 4 = <em>15</em>
3. We find the total of those numbers: <em>15 + 8 =</em> 23
Option A
is one way to determine the factors of 
by grouping
<em><u>Solution:</u></em>
Factoring by grouping means that you will group terms with common factors before factoring
<em><u>Given expression is:</u></em>
Group the first two terms together and then the last two terms together.
We can see that 
is common in first two terms
And 3 is common in last two terms
Factor them out
Thus option A is correct
Answer:
Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis?
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and incresaes into quadrant 1. It goes through the y-axis at (0, 0.25) and goes through (1, 2).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases in quadrant 2. It crosses the y-axis at (0, 0.25) and goes through (negative 1, 2).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It crosses the y-axis at (0, negative 0.25) and goes through (1, negative 2).
On a coordinate plane, an exponential funtion increases in quadrant 3 into quadrant 4 and approaches y = 0. It goes through (negative 1, negative 2) and crosses the y-axis at (0, negative 0.25).
Step-by-step explanation:
Answer:
A + B + C = π ...... (1)
...........................................................................................................
L.H.S.
= ( cos A + cos B ) + cos C
= { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C
= { 2 · cos [ (π/2) - (C/2) ] · cos [ (A-B) / 2 ] } + cos C
= { 2 · sin( C/2 ) · cos [ (A-B) / 2 ] } + { 1 - 2 · sin² ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A -B) / 2 ] - sin ( C/2 ) }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - sin [ (π/2) - ( (A+B)/2 ) ] }
= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - cos [ (A+B)/ 2 ] }
= 1 + 2 sin ( C/2 )· 2 sin ( A/2 )· sin( B/2 ) ... ... ... (2)
= 1 + 4 sin(A/2) sin(B/2) sin(C/2)
= R.H.S. ............................. Q.E.D.
...........................................................................................................
In step (2), we used the Factorization formula
cos x - cos y = 2 sin [ (x+y)/2 ] · sin [ (y-x)/2 ]
Step-by-step explanation:
