80% of the students voted for John as class president. If he received 128 votes, how many students voted?
Let's use a proportion to solve for the total number of students who voted:
80% = 128/x
Here, x represents the total number of students who voted. To solve for x, we'll cross-multiply:
0.8x = 128
And now we'll divide both sides by 0.8:
x = 160
So there were 160 students who voted in the election.
Which equation represents the line that passes through the points (0, 3) and (4, 2)
We can use the point-slope form of a linear equation to find the equation of the line that passes through the points (0, 3) and (4, 2).
Point-slope form: y - y1 = m(x - x1)
We first need to find the slope of the line using the two points:
slope = (y2 - y1) / (x2 - x1)
slope = (2 - 3) / (4 - 0)
slope = -1/4
Now we can choose either point and substitute the values into the point-slope form:
y - 3 = (-1/4)(x - 0)
Simplifying:
y - 3 = (-1/4)x
y = (-1/4)x + 3
So the equation that represents the line passing through the points (0, 3) and (4, 2) is:
y = (-1/4)x + 3.
Which equation represents the line that passes through the points (0, 3) and (4, 2) ?
A. (y - 2) = - 1/4 * (x - 4)
B. (y + 2) = - 1/4 * (x + 4)
C. (y - 4) = - 1/4 * (x - 2)
D. (y + 4) = - 1/4 * (x + 2)
The correct equation is A. (y - 2) = - 1/4 * (x - 4).
Estimate: 20 is 22% of what number?
To solve the problem, we can use the formula:
part/whole = percentage/100
where "part" is the number we are trying to find, "whole" is the total number we're looking for (in this case), and "percentage" is 22.
So, we can write:
20/whole = 22/100
To solve for "whole", we can cross-multiply:
20 * 100 = 22 * whole
2000 = 22 * whole
To isolate "whole", we can divide both sides by 22:
whole = 2000/22
whole ≈ 90.91
Therefore, 20 is approximately 22% of 90.91.
Determine the vertex form and the maximum or minimum value of the function. f(x) = 2x ^ 2 + 8x + 3
We can convert the quadratic function f(x) = 2x^2 + 8x + 3 to vertex form by completing the square:
f(x) = 2(x^2 + 4x) + 3
f(x) = 2(x^2 + 4x + 4 - 4) + 3
f(x) = 2((x + 2)^2 - 4) + 3
f(x) = 2(x + 2)^2 - 5
Therefore, the vertex form of the function is f(x) = 2(x + 2)^2 - 5, and the vertex is (-2, -5).
Since the coefficient of the x^2 term is positive, the parabola opens upwards. Therefore, the vertex is the minimum point of the function, and the minimum value of the function is -5.