Answer:
The equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:
Step-by-step explanation:
The slope-intercept form of the line equation
where
Given the line
3x - 4y = 7
writing in the slope-intercept form
4y = 3x - 7
dividing both sides by 4
4y/4 = 3/4x - 7/4
y = 3/4x - 7/4
Now, comparing with the slope-intercept form of the line equation
y = 3/4x - 7/4
The slope of the line m = 3/4
We know that parallel lines have the same slopes.
Therefore, the slope of the parallel line is: 3/4
now we have,
The point (-4, -2)
The slope m of parallel line = 3/4
Given the point-slope form of the line equation
where m is the slope of the line and (x₁, y₁) is the point
substituting (-4, -2) and m = 3/4 in the point-slope form of line equation


Thus, the equation in the point-slope form of the line equation is:

Simplifying the equation

Subtract 3 from both sides


Multiplying the equation by 4


Therefore, the equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:
Answer:
"no additional days of food need to be ordered."
Step-by-step explanation:
Suppose initial quantity of food is x units
Assuming each student eats 1 unit of food per day,
x = 30 * 100 = 3000 units of food
In 2 days, food eaten:
100 * 1 * 2 = 200 units
So food left after 2 days is 3000 - 200 = 2800 units
Now, there are 140 students. They stay 2 weeks (14 days) - 2 = 12 more days
So food eaten in 12 days:
140 * 1 * 12 = 1680 units
<u>THus, after total 14 days gone, the amount of food left is:</u>
2800 - 1680 = 1120 units
Half students left, so there are 70 students left for the last 16 days. How much food would they need?
70 * 1 * 16 = 1120 units
And there are exactly 1120 units left. So, no additional days of food need to be ordered.
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Answer:
The height of the tree is about 30 feet.
Step-by-step explanation:
tan(55) = h/21
*21 *21
21*tan(55)=h
29.99=h
h=29.99=30 feet