1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
irina [24]
2 years ago
10

Find the area of the shaded region in the image below:

Mathematics
1 answer:
grandymaker [24]2 years ago
8 0

9514 1404 393

Answer:

  34 square units.

Step-by-step explanation:

The figure can be decomposed into a trapezoid and a triangle. The point of intersection of the two lines is (6, 4), so a horizontal line at y=4 will create ...

  • a triangle of height 2 and base 6
  • a trapezoid with bases 6 and 8, and height 4.

Using the relevant area formulas, we find ...

  triangle area = 1/2bh = 1/2(6)(2) = 6

  trapezoid area = 1/2(b1 +b2)h = 1/2(6+8)(4) = 28

Total shaded area = 6 + 28 = 34 square units.

__

The equations of the lines can be written as ...

  y = -2x +16

  y = -1/3x +6

Equating y, we get

 -2x +16 = -1/3x +6

  10 = 5/3x . . . . . . . . . add 2x-6

  6 = x . . . . . . . . . multiply by 3/5

  y = -2(6) +16 = 4

The point of intersection is (6, 4).

_____

<em>Alternate solution</em>

Once we know the vertices of the shaded area:

  • (0, 0)
  • (0, 6)
  • (6, 4)
  • (8, 0)
  • (0, 0)

we can form pairwise "determinants" of the form x1y2 -x2y1. Note the first point is repeated at the bottom of the list, and the points are listed in order around the boundary of the area. The points (0, 0) contribute nothing, so we have left them out of the computation below. The area is half the absolute value of the sum of these "determinants".

  1/2|(0·4 -6·6) +(6·0)-(8·4)|

  = 1/2|-36 -32| = 1/2(68) = 34

_____

In the attachment, the equations of the lines are written in intercept form, since the problem statement gives the intercepts of the lines.

You might be interested in
1 of 5
Allisa [31]

Answer:

7/1296

Step-by-step explanation:

Multiply the two probabilities.

7/36 x 1/36 = 7/1296

3 0
3 years ago
Read 2 more answers
A negative value of r means that:
tatuchka [14]

Answer:

(d.) Those who score high on one variable tend to score low on the other.

Step-by-step explanation:

A negative value of correlation coefficient (r) shows a relationship between two variables such that as one variable increases, the other decreases. It shows the inverse relationship between two variables with the dependence determined by the value of the correlation coefficient (r).

It can be observed that for graphs with negative slope, the correlation coefficient (r) is similarly negative. This speaks about its relationship too.

The correlation coefficient being negative doesn't mean the relationship between the two variables in question is bad, it just means that the correlation relationship is inverse (still dependent). A perfectly negative correlation is -1.  

6 0
3 years ago
Evaluate this function at x = 2: f(x)= 3x + 20 *
trasher [3.6K]

Answer:

26

Step-by-step explanation:

Fitst,  you substitute

f(2) = 3(2) + 20

f(2) = 6 + 20

f(2) = 26

your answer is 26

5 0
3 years ago
Read 2 more answers
the price of a small pizza increased from $5 to $8. what is the percent of increase in the cost of the pizza? round to the neare
Ne4ueva [31]
60%

Working

£5:100%
£1:20%
£8:160%

So percentage increase is 60%
6 0
3 years ago
Solve the following system of equations by elimination:
sergeinik [125]

Answer:

x=4

y=5

(4,5)

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • The function f is defined by f(x)=x^2-5 find f(2y)
    10·1 answer
  • I need help with this problem! Please show work so i can get credit for my work
    5·1 answer
  • Anyboady know (-3)-8​
    8·1 answer
  • When Arjun makes hot cocoa, he adds 20ml of chocolate syrup for every 3 ounces of hot water. Arjun's brother, Eli, adds 45mL of
    15·1 answer
  • What is greater then -12/16
    13·1 answer
  • Antonio drops a glass marble into a pond and creates ripples that form concentric circles on the surface of the water. The radiu
    7·1 answer
  • PLEASE HELP ASAP PLEASE
    11·1 answer
  • Find the slope of the following equation y=-6/7x+42? I'm so stuck can someone help?
    5·1 answer
  • If james hand is 0.17 meters and junes is 0.165 who have the Bigger hand
    9·1 answer
  • What is the mean of 4,7
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!