Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ
Use the Sum/Difference Identities:
sin(α + β) = sinα · cosβ + cosα · sinβ
cos(α - β) = cosα · cosβ + sinα · sinβ
Use the Unit circle to evaluate: sin45 = cos45 = √2/2
Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
<u />
<u>Proof LHS → RHS</u>
LHS: 2sin(45 + 2A) · cos(45 - 2A)
Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)
Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]
Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]
Distribute: cos²2A + 2cos2A·sin2A + sin²2A
Pythagorean Identity: 1 + 2cos2A·sin2A
Double Angle: 1 + sin4A
LHS = RHS: 1 + sin4A = 1 + sin4A 
Answer:
-7 or 4
Step-by-step explanation:
use foil to get the quadratic equation:
x^2+5x-2x-10=18
x^2+3x-10=18
bring "18" to the left:
x^2+3x-10-18
x^2+3x-28
so what*what= -28
and
what+what=3
factors of -28: -7,4 -4,7 14,-2 -14,2 -28,1 -1,28
factors whose sum is 3: 7,-4
so substitute "7,-4" in place of 3:
x^2+7x-4x-28
2) split it in two groups
group 1) x^2+7x
group 2) -4x-28
x^2+7x has a GCF of "x"
x(x+7)
group 2) -4x-28 has a gcf of "-4"
-4(x+7)
3) (x-4) (x+7)=0
x-4=0
x=4
x+7=0
x=-7
x=4,-7
Hope this helps!
20 cents
just divide $1.60 by 8
The amount of fiber needed in a day is 7.98 grams
<h3>Proportions</h3>
Proportions are parts, in comparative relation to a whole.
In other words, proportions are fractions of a larger dataset
The given parameters from the question are given as:
- Proportion of the daily value of fiber needed = 57%
- Daily serving = 14 grams.
<h3>
Amount of
fiber</h3>
The amount of fiber needed in a day is the product of the proportion and the size of the daily serving.
So, we have:
Hence, the amount of fiber needed in a day is 7.98 grams
Read more about proportions at:
brainly.com/question/1781657
Answer:
19/9
Step-by-step explanation:
We are given repeating decimal number 2.1¯.
We know 2.1¯ = 2.1111..... repeating 1's.
Let us assume x is a fraction equals given repating decimal number.
And set it as a first eqaution.
x = 2.1111..... ------------- (equation 1).
Multiplying equation both side by 10 ( because only one digit is repeating after decimal, we multiply by 10).
On multiplying by 10 we get
10*x = 10*2.1111.....
10x = 21.1111...... ----------------- (equation 2)
Subtracting equation 1 from equation 2, we get
10x = 21.1111......
-x = -2.1111.....
_____________
9x = 19.
Now, dividing both sides by 9. we get
