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3 years ago

Which expression represents the algebraic phrase “nine times a number plus thirteen”? A. 9 - y + 13

Mathematics

2 answers:

kirza4 [7]3 years ago

5 0

C. 9y + 13
9y is the same as 9 times y (a variable representing a number), + 13

lesantik [10]3 years ago

4 0

Answer: The correct option is (C) 9y + 13.

Step-by-step explanation: We are given to select the expression that represents the following statement :

“nine times a number plus thirteen”

Let the number be represented by y.

Then, nine times the number is written as follows :

$9\times y=9y.$

Since we are to add 13, so the final expression is given by

$E=9y+13.$

Thus, the required expression is $9y+13.$

Option (C) is CORRECT.

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3 years ago

Two lighthouses are located 60 miles from one another on a north-south line. If a boat is spotted S 21o E from the northern ligh

jasenka [17]

Answer:

(A)The northern lighthouse is 8.2 miles closer than the southern lighthouse.

Step-by-step explanation:

The triangle attached represents the given problem.

First, let us determine the distance of the Boat from each of the lighthouse.

In Triangle ABC,

∠A+∠B+∠C=180 degrees

21+∠B+16=180

∠B=180-37=143 degrees.

Using Law of Sines

$\frac{a}{Sin A}=\frac{b}{Sin B}\\\frac{a}{Sin 21^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\a*sin143=60*sin21\\a=60*sin21\div sin143\\a=35.73 miles$

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$\frac{c}{Sin C}=\frac{b}{Sin B}\\\frac{c}{Sin 16^0}=\frac{60}{Sin 143^0} \\\text{Cross Multiply}\\c*sin143=60*sin16\\c=60*sin16\div sin143\\c=27.48 miles$