Question 1 :
3(x + y) = y
If (x, y) is a solution to the equation above, and y ≠ 0, what is the ration x/y?
(A) -4/3 (B) -2/3 (C) 1/3 (D) 2/3
Answer :
3(x + y) = y
Use the distributive property.
3x + 3y = y
Subtract 3y from each side.
3x = -2y
Divide each side by 3y.
3x/3y = -2y/3yB)
x/y = -2/3
The correct answer is (B).
Question 2 :
A grocery store sells a brand of juice in individual bottles and in packs of 6 bottles. On a certain day, the store sold a total of 281 bottles of the brand of juice, of which 29 were sold as individual bottles. Which equation shows the number of packs of bottles, p, sold that day?
(A) p = (281 - 29)/6
(B) p = (281 + 29)/6
(C) p = 281/6 - 29
(D) p = 281/6 + 29
Answer :
Out of the total 281 bottles sold, 29 were sold individually. The rest (281 - 29) were sold in packs of 6 bottles.
So, the number of packs of bottles, p, sold that day in the store is :
p = (281 - 29)/6
The correct answer is (A).
Question 3 :
Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width. What is the perimeter of Janice’s fence if the area of her garden is 5,670 square feet?
(A) 342 ft (B) 318 ft (C) 300 ft (D) 270 ft
Answer :
Let x be the width of the rectangular garden.
Then, the length is (3x - 9).
Given : Area is 5,670 square feet.
A = 5670
l ⋅ w = 5670
Substitute (3x - 9) for l and x for w.
(3x - 9)x = 5670
3x^{2} - 9x = 5670
3x^{2} - 9x - 5670 = 0
Divide each side by 3.
x^{2} - 3x - 1890 = 0
Find two factors of -1890 such that the sum of the factors is equal to -3 and product of the factors is equal to -1890. If you find it difficult to find such two factors, use quadratic formula.
Here, the two factors of -1890 are -45 and +42.
x^{2} - 45x + 42x - 1890 = 0
x(x - 45) + 42(x - 45) = 0
(x - 45)(x + 42) = 0
x - 45 = 0 x = 45 |
x + 42 = 0 x = -42 |
Because the dimension of the rectangle can not be negative, x = -42 can be ignored.
So, x = 45.
Then, the width and length are :
width = 45
length = 3(45) - 9 = 126
Perimeter of the rectangular garden :
= 2(l + w)
= 2(126 + 45)
= 2(171)
= 342 ft
The correct answer is (A).
Question 4 :
A truck enters a stretch of road that drops 4 meters in elevation for every 100 meters along the length of the road. The road is at 1,300 meters elevation where the truck entered, and the truck is traveling at 16 meters per second along the road. What is the elevation of the road, in meters, at the point where the truck passes t seconds after entering the road?
(A) 1,300 - 0.04t
(B) 1,300 - 0.64t
(C) 1,300 - 4t
(D) 1,300 - 16t
Answer :
Given : The elevation of the road drops 4 meters for every 100 meters along the length of the road.
Then, the elevation of the road drops for 1 meter is
= 4/100
= 0.04 meters
Given : The truck is traveling at 16 meters per second along the road.
Then, the distance it has traveled t seconds after entering the road is 16t meters.
The elevation of the road drops for 16t meters is
= 0.04 ⋅ 16t
= 0.64t meters
Given : The truck entered the road that is at 1,300 meters elevation.
The elevation of the road, in meters, at the point where the truck passes t seconds after entering the road is
= 1300 - 0.64t
The correct answer is (B).
Question 5 :
The equation y = 36 + 18x models the relationship between the height y, in inches, of a typical golden delicious apple tree and the number of years, x, after it was planted. If the equation is graphed in xy-plane what is indicated by the y-intercept of the graph?
(A) The age, in years, of a typical apple tree when it is planted.
(B) The height, in inches, of a typical Apple tree when it is planted.
(C) The number of years it takes a typical apple tree to grow.
(D) The number of inches a typical apple tree grows each year.
Answer :
y = 36 + 18x
For any line or curve, y-intercept is the value at where the line or curve intersects y-axis. At that point, x-coordinate is zero.
In the equation above, to get y-intercept, we have to substitute x = 0.
y = 36 + 18(0)
y = 36
When the number of years is zero, the height of the tree is 36 inches. That is, the height of the tree is 36 inches when it is planted.
So, y-intercept in the equation y = 36 + 18x indicates the height of the tree when it is planted.
The correct answer is (B).
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