19. The base of a triangle is four less than three times the height. The area of the triangle is 38 square centimeters. A=(b×h)2
An expression for the base of the triangle:
Equation for the area of the triangle, substituting in for the base:
The first step in solving for h:
Expression for the base of the triangle: Let the height of the triangle be h. According to the given information, the base is four less than three times the height. Therefore, the expression for the base of the triangle would be 3h - 4.
Equation for the area of the triangle, substituting in for the base: The formula for the area of a triangle is A = (1/2)bh, where A is the area, b is the base, and h is the height. Substituting the expression for the base into the formula, we get A = (1/2)(3h - 4)(h).
The first step in solving for h: Start by substituting the given value of the area (38 cm^2) into the equation: 38 = (1/2)(3h - 4)(h).
From here, one can solve this quadratic equation for h using various methods such as factoring, completing the square, or using the quadratic formula.
20. Solve the equation for y: 3x+5y=60
(1 point)
Responses
y=57x5
y is equal to 57 x over 5
y=−35x+12
y is equal to negative 3 fifths x plus 12
y=60+3x5
y is equal to 60 plus 3 x over 5
y=60−3x
To solve for y in the equation 3x + 5y = 60, we can rearrange the equation to isolate y.
Here are the steps:
1. Start with the equation 3x + 5y = 60.
2. Subtract 3x from both sides of the equation to isolate y:
3x + 5y - 3x = 60 - 3x
Simplify the equation:
5y = 60 - 3x
3. Divide both sides of the equation by 5 to solve for y:
y = (60 - 3x) / 5
So, the solution for y is y = (60 - 3x) / 5.
Let's start by defining the variables in the problem:
Let b be the base of the triangle.
Let h be the height of the triangle.
According to the problem, the base of the triangle is four less than three times the height. This can be expressed as:
b = 3h - 4
The formula for calculating the area of a triangle is A = (1/2)bh, where A is the area, b is the base, and h is the height.
We are given that the area of the triangle is 38 square centimeters. We can substitute the expression for the base (3h - 4) into the formula:
38 = (1/2)(3h - 4)(h)
Now, let's move on to solving for the height (h).
The first step in solving for h is to simplify the expression:
38 = (3/2)h^2 - 2h
To make the equation easier to solve, let's multiply through by 2 to get rid of the fraction:
76 = 3h^2 - 4h
Now, let's rearrange the equation to set it equal to zero:
3h^2 - 4h - 76 = 0
This is a quadratic equation. To solve it, we can either factor or use the quadratic formula.
To find the expression for the base of the triangle, let's first assign variables. Let's say the height of the triangle is 'h' centimeters.
According to the information given, the base of the triangle is four less than three times the height. So, we can write the expression for the base as "3h - 4".
Now, let's move on to the equation for the area of the triangle, substituting in for the base. The formula for the area of a triangle is given as:
Area = (base * height) / 2
Plugging in the expression for the base, we get:
Area = ((3h - 4) * h) / 2
According to the problem, the area of the triangle is 38 square centimeters. So, we can write the equation as:
38 = ((3h - 4) * h) / 2
Now, let's move on to solving for the height (h).
The first step in solving for h is to multiply both sides of the equation by 2 to eliminate the fraction:
2 * 38 = (3h - 4) * h
Simplifying the left side:
76 = (3h - 4) * h
Now, let's expand the equation:
76 = 3h^2 - 4h
This is a quadratic equation. To solve it, we need to set it equal to zero:
3h^2 - 4h - 76 = 0
From here, you can solve the quadratic equation using factoring, completing the square, or the quadratic formula. Once you find the values for h, you can substitute them back into the expression for the base to find its value.