iReady (math) final diagnostic of the year, can anyone help? I have to type all of these questions manually.....
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The expression c - 0.25c can be used to find the cost of an item on sale for 25% off. Which expression below is equivalent to c - 0.25c?
A.) 1.12c
B.) 0.25c
C.) 0.75c
D.) 0.75
The expression c - 0.25c can be simplified as follows:
c - 0.25c = 0.75c
Therefore, the expression that is equivalent to c - 0.25c is option C, 0.75c.
Solve:
3 (2d - 1) - 2d = 4 (d - 2) + 5
A.) d = 4
B.) d = 0
C.) no solution
D.) infinitely many solutions
Let's begin by simplifying both sides of the equation:
3(2d - 1) - 2d = 4(d - 2) + 5
6d - 3 - 2d = 4d - 8 + 5
4d - 3 = 4d - 3
We can see that both sides of the equation are equal, and so the solution is true for all values of d.
Therefore, there are infinitely many solutions, and the correct answer is option D.
The expression below reperesents the cost, c, of an item that is on sale for 25% off.
c - 0.25c
Which expression is also equivalent to the cost of the item?
A.) 1 - 0.75c
B.) 1 - 0.25c
C.) 0.25c
D.) 0.75c
The expression c - 0.25c can be simplified as follows:
c - 0.25c = 0.75c
Therefore, another expression that is equivalent to the cost of the item is 0.75c.
Therefore, the correct answer is option D, 0.75c.
If a and b represent positive real numbers, what is the inequality when solved for x?
ax/2 - bx/3 > 10
A.) x < 3ax - 60/2b
B.) x > 3au - 60/2b
C.) x > -3au - 60/2b
D.) x < ax - 60/b
To solve for x, we will begin by clearing the fractions in the inequality:
ax/2 - bx/3 > 10
Multiplying both sides by 6, the least common multiple of 2 and 3, we get:
3ax - 2bx > 60
Adding 2bx to both sides, we get:
3ax > 2bx + 60
Dividing both sides by 3a, we get:
x > (2bx + 60)/3a
Simplifying the expression on the right, we get:
x > (2b/3a)x + 20
Subtracting (2b/3a)x from both sides, we get:
(1 - 2b/3a)x > 20
Dividing both sides by (1 - 2b/3a), we need to be careful since the value 1 - 2b/3a could be negative.
If 1 - 2b/3a is positive, we can divide both sides by the positive value without flipping the inequality. If 1 - 2b/3a is negative, we must divide both sides by the negative value and flip the inequality.
So,
If 1 - 2b/3a > 0, then:
x > 20/(1 - 2b/3a)
Simplifying, we get:
x > 60/(3a - 2b)
which matches with option A, x < (3ax - 60)/2b, after taking the reciprocal of both sides of the inequality.
If 1 - 2b/3a < 0, then:
x < 20/(2b/3a - 1)
Simplifying, we get:
x < 60/(2b - 3a)
which does not match with any of the given options.
Therefore, the correct answer is option A, x < (3ax - 60)/2b, if 1 - 2b/3a > 0.