An <em>algebraic expression</em> is one that consists of both <u>number(s)</u> and an <u>alphabet(s)</u>. The <em>required</em> answers are:
i. Distance from Chenoa's <u>house</u> to the <em>coffee shop</em> = 6.0 miles
ii. D<u>istance</u> from <em>coffee shop</em> to Chenoa's <u>school</u> = 1.5 miles
iii. <em>Distance</em> from Chenoa's <u>house</u> to her <u>school</u> = 7.5 miles
An <em>algebraic expression</em> is one that consists of both <u>number(s)</u> and an <u>alphabet(s)</u>. The <em>alphabet</em> is referred to as the <u>unknown</u> whose <u>value</u> has to be <em>determined</em>.
In the given question, let the <u>distance</u> from the <em>coffee shop</em> to Chenoa's <u>school</u> be represented by y.
So that;
The <u>distance</u> from Chenoa's house to the <em>coffee shop</em> = (2y + 3) miles.
The <em>total distance</em> from Chenoa's <u>house</u> to her <u>school </u>= 5y.
This implies that:
(2y + 3) + y = 5y
3y + 3 = 5y
3 = 5y - 3y
2y = 3
y = 
= 1.5
The <em>distance</em> from the <em>coffee shop</em> to Chenoa's <u>school</u> is 1.5 miles.
Thus;
(2y + 3) = ( 2(1.5) + 3)
= 6
The <u>distance</u> from Chenoa's <u>house</u> to the <em>coffee shop</em> is 6 miles.
And,
5y = 5(1.5)
= 7.5
The <em>total distance</em> from Chenoa's <u>house</u> to her <u>school</u> is 7.5 miles.
For more clarifications on algebraic expressions, visit: brainly.com/question/12792264
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<h3>Answer: A. 5/12, 25/12</h3>
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Work Shown:
12*sin(2pi/5*x)+10 = 16
12*sin(2pi/5*x) = 16-10
12*sin(2pi/5*x) = 6
sin(2pi/5*x) = 6/12
sin(2pi/5*x) = 0.5
2pi/5*x = arcsin(0.5)
2pi/5*x = pi/6+2pi*n or 2pi/5*x = 5pi/6+2pi*n
2/5*x = 1/6+2*n or 2/5*x = 5/6+2*n
x = (5/2)*(1/6+2*n) or x = (5/2)*(5/6+2*n)
x = 5/12+5n or x = 25/12+5n
these equations form the set of all solutions. The n is any integer.
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The two smallest positive solutions occur when n = 0, so,
x = 5/12+5n or x = 25/12+5n
x = 5/12+5*0 or x = 25/12+5*0
x = 5/12 or x = 25/12
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Plugging either x value into the expression 12*sin(2pi/5*x)+10 should yield 16, which would confirm the two answers.