Answer:
(2,4)
Step-by-step explanation:
When graphed the lines intersect at point (2,4) which is the solution.
Answer:
80 m^2
Step-by-step explanation:
The given information lets you write two equations involving length (x) and width (y).
- 2(x +y) = 36 . . . . the perimeter is 36 m
- (x+1)(y+2) -xy = 30 . . . . increasing the length and width increases area
The second of these equations simplifies to another linear equation, giving a system of linear equations easily solved.
xy +y +2x + 2 -xy = 30
2x +y = 28 . . . . . . . subtract 2
Dividing the first equation by 2 gives
x +y = 18
and subtracting this from the above equation gives ...
(2x +y) -(x +y) = 28 -18
x = 10
Then
y = 18 -10 = 8
The area of the original rectangle is xy = 10·8 = 80 m^2.
Answer:
Step-by-step explanation:
Given that the hartford insurance company has hired you to poll a sample of adults about their car purchases.
Here the insurance company is using convenience sampling to select customers so they resorted to taking the names from telephone directories.
But this may not be reliable since persons owning cars need not have telephones and similarly persons having telephones need not own cars
Owning a car and name appearing in telephone directory need not be associated at all
So taking random sample of names from telephone directories may not give the required accurate result since here sample cannot be assumed to represent the population of car owners.
It has been proven that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
<h3>How to prove a Line Segment?</h3>
We know that in a triangle if one angle is 90 degrees, then the other angles have to be acute.
Let us take a line l and from point P as shown in the attached file, that is, not on line l, draw two line segments PN and PM. Let PN be perpendicular to line l and PM is drawn at some other angle.
In ΔPNM, ∠N = 90°
∠P + ∠N + ∠M = 180° (Angle sum property of a triangle)
∠P + ∠M = 90°
Clearly, ∠M is an acute angle.
Thus; ∠M < ∠N
PN < PM (The side opposite to the smaller angle is smaller)
Similarly, by drawing different line segments from P to l, it can be proved that PN is smaller in comparison to all of them. Therefore, it can be observed that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Read more about Line segment at; brainly.com/question/2437195
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Answer: 24 cups.
Step-by-step explanation:
Let be "x" the amount of cups of peaches that Fred will need to make 60 cups of fruit salad.
According to the information given in the exercise, you know that the ratio of cups of peaches to cups of cherries is the one shown below:

Which can also be written as a fraction:

Then, if he uses 2 cups of peaches and 3 cups of cherries, he will get 5 cups of fruit salad.
Knowing the above, you can set up the following proportion:

Now you must solve for "x" in order to find its value. This is:
