Step 2: x = 30 – 5
Step 3: x = 25
Part A: Is Charlie's solution correct or incorrect? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation. (6 points)
Part B: How many solutions will this equation have? (4 points)
Part A: Charlie's answer is incorrect. Part B: There is only 1 solution for this equation.
A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
Charlie solved an equation;
Step 1: 5x = 30
Step 2: x = 30 – 5
Step 3: x = 25
Part A: Charlie's answer is incorrect.
In step 2 of Charlie's answer he subtracted 5 from each side. Since 5x is multiplication so, he must divide each side by 5 to get x by itself.
Step 1: 5x = 30
Step 2: x = 30/5
Step 3: x = 6
Part B: There is only 1 solution for this equation.
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The dimensions that give the maximum area is 5 cm by 5 cm.
Given:
The perimeter of this rectangle is 20 cm, and formula for perimeter is
P= 2(W+L)
P = 20 cm = 2W + 2L.
Then W + L = 10 cm,
or W = (10 cm) - L.
The area of the rectangle is A = L·W, and is to be maximized.
On substituting the values, we get A = L[ (10 cm) - L ], or A = 10L - L²
Note that this is the equation of a parabola that opens down. With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is
x = -b / (2a). Subbing 10 for b and -1 for a, we get:
x = -[10] / [2·(-1)] = 10/2, or 5.
This tells us that one dimension of the rectangle is 5 cm.
Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:
20 cm = 2(5 cm) + 2W, or
10 cm = W + 5 cm, or W = 5 cm.
Therefore, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.
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Answer:
5 cm by 5 cm
Step-by-step explanation:
The perimeter of this rectangle is 20 cm, and the relevant formula is
P = 20 cm = 2W + 2L. Then W + L = 10 cm, or W = (10 cm) - L.
The area of the rectangle is A = L·W, and is to be maximized. Subbing (10 cm) - L for W, we get A = L[ (10 cm) - L ], or A = 10L - L²
Note that this is the equation of a parabola that opens down. With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is
x = -b / (2a). Subbing 10 for b and -1 for a, we get:
x = -[10] / [2·(-1)] = 10/2, or 5.
This tells us that one dimension of the rectangle is 5 cm.
Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:
20 cm = 2(5 cm) + 2W, or
10 cm = W + 5 cm, or W = 5 cm.
Thus, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.
3x + y = 18
Answer:
40 minutes
Step-by-step explanation:
We have a load and a discharge, given by a speed that would be a barrel / minute.
Which means that the loading rate is: 1/20
And the discharge rate: 1/40
Since they are contrary, the result would be the subtraction between these two rates:
1/20 - 1/40 = 1 / x
1 / x = 0.025
x = 1 / 0.025
x = 40
Which means it will take 40 minutes to fill under the mentioned conditions
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Answer:
1. Divide This Fraction 9/3 / 2/5
A. 6 1/2
B. 4 1/3
C. 2 1/2
D. 6 3/4
2. Max had purchased 25 apples for $15. How much did each apple cost?
A. $0.80
B. $1
C. $0.60
D. $0.40
C. What is the square root of 81?
A. 9
B. 27
C. 18
D. 36
Step-by-step explanation:
1. A is the correct answer. 9/3 / 2/5, reciprocal is the one you use to solve it. 5/2 x 9/3
45/6 = 6 3/6
6 1/2
2. You need to divide $15/25 as a number, to find the unit rate, giving you $0.60. 6 is the correct answer.
3. A is the correct answer. 9 x 9 equals 81, so therefore 9 is the correct answer.