Put the steps in order to solve the equation: 3n+9+4n=2
. Put the reasoning in the first blank and the simplified equation in the second blank.(6 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Step 1: Response area to get Response area
Step 2: Response area to get Response area
Step 3: Response area to get Response area
.
Step 1: Combine like terms on the left side of the equation.
Reasoning: In order to simplify the equation, we need to combine the terms with the same variable (n).
Simplified equation: 7n + 9 = 2
Step 2: Isolate the variable on one side of the equation.
Reasoning: We want to get the variable (n) alone on one side of the equation to solve for its value.
Simplified equation: 7n = 2 - 9 (subtracting 9 from both sides)
Step 3: Solve for the variable.
Reasoning: Divide both sides of the equation by the coefficient of the variable (7) to find the value of n.
Simplified equation: n = -7/7 (dividing both sides by 7)
The base of a triangle is 4 less than three times the height. The area of the triangle is 38 square cm. A=b × h/2
Step 1: Use the given information to represent the relationship between the base (b) and the height (h) of the triangle.
Reasoning: The problem states that the base is 4 less than three times the height. We can represent this relationship as b = 3h - 4.
Step 2: Substitute the value of the base from step 1 into the formula for the area of a triangle.
Reasoning: The formula for the area of a triangle is A = (b * h) / 2. We can substitute the value of the base (3h - 4) into the formula to get A = ((3h - 4) * h) / 2.
Step 3: Solve the equation for the height (h).
Reasoning: We know that the area of the triangle is 38 square cm, so we can set the equation ((3h - 4) * h) / 2 = 38 and solve for h.
Step 4: Solve the equation for the height (h).
Reasoning: Simplify the equation ((3h - 4) * h) / 2 = 38 and solve for h by multiplying both sides of the equation by 2, distributing, and then rearranging terms to isolate h.
Step 5: Substitute the value of the height obtained in step 4 into the equation for the base from step 1 to find the value of the base.
Reasoning: Substitute the value of h found in step 4 into the equation b = 3h - 4 to solve for the value of b.
Step 6: Check the solution.
Reasoning: Substitute the values of b and h obtained in steps 4 and 5 into the formula for the area of a triangle (A = (b * h) / 2) to check if it equals 38 square cm.
The base of a triangle is 4 less than three times the height. The area of the triangle is 38 square cm. A= b × h/2
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
An expression for the base of the triangle:. Response area
Equation for the area of the triangle: Response area
The first step in solving for h:
An expression for the base of the triangle: 3h - 4
Equation for the area of the triangle: A = (3h - 4) * h / 2
The first step in solving for h: Setting the equation for the area of the triangle equal to 38: (3h - 4) * h / 2 = 38
Step 1: Combine like terms on the left side of the equation: 3n + 4n + 9
Step 2: Simplify the equation: 7n + 9 = 2
Step 3: Move the constant term (9) to the right side of the equation by subtracting 9 from both sides: 7n = 2 - 9
Step 4: Simplify the equation: 7n = -7
Step 5: Solve for n by dividing both sides of the equation by 7: n = -1
Reasoning: We need to simplify the equation and isolate the variable (n) on one side of the equation in order to solve for its value. We do this by combining like terms, moving constants to the opposite side, and performing necessary operations to simplify the equation. In this case, we combined 3n and 4n to get 7n, and then moved the constant term (9) to the right side by subtracting 9 from both sides. Finally, we divided both sides by 7 to solve for n.
Step 1: To solve the equation, we need to isolate the variable (n) on one side of the equation. In this case, we can start by combining like terms on the left-hand side of the equation. So, we add the coefficients of the n terms:
3n + 4n = 7n
The equation now becomes:
7n + 9 = 2
Step 2: Next, we need to isolate the constant term on the other side of the equation. To do this, we can subtract 9 from both sides:
7n + 9 - 9 = 2 - 9
Simplifying, we have:
7n = -7
Step 3: Finally, to solve for n, we need to get rid of the coefficient in front of n. Here, we can divide both sides by 7:
7n/7 = -7/7
Simplifying, we get:
n = -1
Therefore, the steps to solve the equation 3n + 9 + 4n = 2 are as follows:
Step 1: Combine like terms: 7n + 9 = 2
Step 2: Isolate the constant term: 7n = -7
Step 3: Solve for n: n = -1