1. 29.16
2. 3.5
3. a=0.32
4. 2/15
5. d= 23.33333333 ( am assuming this is a repeating decimal)
Answer: Choice C) 2
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Explanation:
Using the law of sines, we get
sin(B)/b = sin(C)/c
sin(18)/7 = sin(C)/11
0.0441452849107 = sin(C)/11
11*0.0441452849107 = sin(C)
0.4855981340177 = sin(C)
sin(C) = 0.4855981340177
C = arcsin(0.4855981340177) or C = 180-arcsin(0.4855981340177)
C = 29.0516679549861 or C = 150.948332045013
There are two possibilities for angle C because of something like sin(30) = sin(150) = 1/2 = 0.5
Those approximate values of C round to
C = 29.05 and C = 150.95
If C = 29.05, then angle A is
A = 180-B-C
A = 180-18-29.05
A = 132.95
Making this triangle possible since angle A is a positive number
If C = 150.95, then angle A is
A = 180-B-C
A = 180-18-150.95
A = 11.05
making this triangle possible since angle A is a positive number
There are two distinct triangles that can be formed.
One triangle is with the angles: A = 132.95, B = 18, C = 29.05
The other triangle is with the angles: A = 11.05, B = 18, C = 150.95
The decimal values are approximate
<span> FOIL is a mnemonic rule for multiplying binomial (that is, two-term) algebraic expressions. </span>
<span>FOIL abbreviates the sequence "First, Outside, Inside, Last"; it's a way of remembering that the product is the sum of the products of those four combinations of terms. </span>
<span>For instance, if we multiply the two expressions </span>
<span>(x + 1) (x + 2) </span>
<span>then the result is the sum of these four products: </span>
<span>x times x (the First terms of each expression) </span>
<span>x times 2 (the Outside pair of terms) </span>
<span>1 times x (the Inside pair of terms) </span>
<span>1 times 2 (the Last terms of each expression) </span>
<span>and so </span>
<span>(x + 1) (x + 2) = x^2 + 2x + 1x + 2 = x^2 + 3x + 2 </span>
<span>[where the ^ is the usual way we indicate exponents here in Answers, because they're hard to represent in an online text environment]. </span>
<span>Now, compare this to multiplying a pair of two-digit integers: </span>
<span>37 × 43 </span>
<span>= (30 × 40) + (30 × 3) + (7 × 40) + (7 × 3) </span>
<span>= 1200 + 90 + 280 + 21 </span>
<span>= 1591 </span>
<span>The reason the two processes resemble each other is that multiplication is multiplication; the difference in the ways we represent the factors doesn't make it a fundamentally different operation. </span>
Step-by-step explanation and answers:
300 articles at a total cost of $1500:
$1500 / 300 = $5 / article
Sells 260 articles at a price 20% above this ^ price:
20% of $5 is $1, so $5 + $1 = $6
Then he sells 260 articles at the price of ^ $6
260 * $6 = $1560
Each of the remaining articles is sold at a price that's 50% of the 260 he sold.
He sold those for $6, so he would now sell the last 40 for $3
From the remaining 40 articles, he makes 40 * $3, or $120
The shopkeeper made $1560 + $120 = $1680, which is $180 more than he bought them for ($1500)
Therefore, he made a profit percentage of $180 / $1500, (the amount of profit over the amount spent).
He made a profit percentage, compared to the cost price, of 12%.
