Assuming the loan is as described, seven-year loan, which means that Kyle does not repay a cent before seven years.
This is a compound interest problem where n=7 years, interest rate i=0.05, and present value P=8000.
At the end of seven years, Kyle will have to pay
Future value = F = P(1+i)^n = 8000(1.05)^7 = 11256.80 (to the nearest cent)
Simplify
−
3
(
j
+
3
)
+
9
j
-
3
(
j
+
3
)
+
9
j
.
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Simplify each term.
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−
3
j
−
9
+
9
j
<
−
15
-
3
j
-
9
+
9
j
<
-
15
Add
−
3
j
-
3
j
and
9
j
9
j
.
6
j
−
9
<
−
15
6
j
-
9
<
-
15
Move all terms not containing
j
j
to the right side of the inequality.
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Add
9
9
to both sides of the inequality.
6
j
<
−
15
+
9
6
j
<
-
15
+
9
Add
−
15
-
15
and
9
9
.
6
j
<
−
6
6
j
<
-
6
Divide each term in
6
j
<
−
6
6
j
<
-
6
by
6
6
and simplify.
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Divide each term in
6
j
<
−
6
6
j
<
-
6
by
6
6
.
6
j
6
<
−
6
6
6
j
6
<
-
6
6
Simplify the left side.
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j
<
−
6
6
j
<
-
6
6
Simplify the right side.
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j
<
−
1
j
<
-
1
The result can be shown in multiple forms.
Inequality Form:
j
<
−
1
j
<
-
1
Interval Notation:
(
−
∞
,
−
1
)
Answer: The vertical stretch of 5 in the equation y = x is defined by 
.
Explanation:
The given equation is,
It can be written as,
The function is defined as 
.
If 
, then the function has a vertical stretch by a factor of S units.
If 
, then the function has a vertical shrink by a factor of S units.
Since we have to find the vertical stretch of 5 in the equation y = x.
The below figure shows the graph of y = x and .
Let x be the number of pounds of the $1.35 beans. The cost of those beans is $1.35 * x, or 1.35x.
<span>Let y be the number of pounds of the $1.05 beans. The cost of those beans is $1.05 * y, or 1.05y. </span>
<span>We know that 120 pounds of the mix sells for $1.15/pound, for a total of 120 * 1.15 = $138. </span>
<span>x + y = 120 </span>
<span>1.35(x) + (1.05)y = 138 </span>
<span>We can rewrite the first as </span>
<span>x = -y + 120 </span>
<span>Now we can substitute (-y + 120) in for (x) in the second equation, because we just proved they're equal. </span>
<span>1.35(x) + 1.05(y) = 138 </span>
<span>1.35(-y + 120) + 1.05y = 138 </span>
<span>-1.35y + 162 + 1.05y = 138 </span>
<span>-0.3y + 162 = 138 </span>
<span>-0.3y = -24 </span>
<span>y = 80 </span>
<span>And since x + y = 120, that means x = 40. </span>
<span>Check: </span>
<span>40 pounds of x at $1.35 costs 40 * 1.35, or $54. </span>
<span>80 pounds of y at $1.05 costs 80 * 1.05, or $84. </span>
<span>Do those add up to our target total, according to the question, of 120 * 1.15 = $138? </span>
Y= 4 - 4/5x all you have to do is make it go up 4 from 0 and either go down 4 and go right 5 or up 4 and to the left 5... hope this helped!
