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Anvisha [2.4K]
2 years ago
5

Find the area of the triangle. Round to the nearest tenth. .

Mathematics
1 answer:
Maslowich2 years ago
8 0

Answer: 60 square meters

Step-by-step explanation:

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Write the equation of each line using the given information.
Leni [432]

a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8

<h3><u>Solution:</u></h3>

<em><u>a. The points (-4,1) and (2,4) both lie on the line</u></em>

The general line equation on which (a, b) and (c, d) lies is:

y-\mathrm{b}=\frac{d-b}{c-a}(x - a)

Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)

Thus the required equation is:

y-1=\frac{4-1}{2-(-4)}(x-(-4))

On solving we get,

\begin{array}{l}{\rightarrow y-1=\frac{3}{2+4}(x+4)} \\\\ {\rightarrow y-1=\frac{3}{6}(x+4)} \\\\ {\rightarrow 2(y-1)=1(x+4)} \\\\ {\rightarrow 2 y-2=x+4} \\\\ {\rightarrow x-2 y+6=0}\end{array}

<em><u>b.) m= -1 and the point (2, -1) lies on the line</u></em>

The equation of line in point slope form is y – b = m(x – a)  

where m is slope and (a, b) is a point on it

Here m = -1 and (a, b) = (2, -1)

Thus the required equation is:

y – (-1) = -1(x - 2)  

y + 1 = -x + 2  

y = -x + 2 -1  

y = -x + 1

<em><u>c. )It has the same slope as y = 5 and passes through (1, 1)</u></em>

our line has same slope with y = 5, then our equation would be y = k  and it passes through (x, y) = (1, 1) so, then by substitution

1 = k

k =1  

Then our equation will be y = k

y = 1

<em><u> d. ) m= -3 and it has a y-intercept of (0, 8)</u></em>

line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept.

Then, our equation will be y = -3x + 8

We took y- intercept = 8 as it is the value of y when x = 0

6 0
3 years ago
2y = x + 3 5y = x - 7 What is the solution set of the given system?
olga_2 [115]
-3=2x+10=  -13=2x = -0.153
5 0
3 years ago
Ron, Kent, and Sharon assembled 734 newsletters. Ron could assemble 124 per hour, Sharon 132 per hour, and Kent 118 per hour. On
vitfil [10]
Hi there!

So If Ron worked 2 hours he collected a total of 248 newspapers.
Sharon worked one hour collecting 132 newspapers.
Kent worked 3 hours collecting 354 newspapers.
248+132+354=734

Therefore Kent worked 3 hours and Sharon worked 1 hour.

Hope this helps!
8 0
3 years ago
2+3**1342=? Someone please trust trade me
svp [43]

Answer:

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the area of a trapezoid ABCD with bases AB and CD ,
Mrrafil [7]

check the picture below on the top side.


we know that x = 4 = b, therefore,  using the 30-60-90 rule, h = 4√3, and DC = 4+8+4 = 16.


\bf \textit{area of a trapezoid}\\\\&#10;A=\cfrac{h(a+b)}{2}~~&#10;\begin{cases}&#10;a,b=\stackrel{bases}{parallel~sides}\\&#10;h=height\\[-0.5em]&#10;\hrulefill\\&#10;a=8\\&#10;b=\stackrel{DC}{16}\\&#10;h=4\sqrt{3}&#10;\end{cases}\implies A=\cfrac{4\sqrt{3}(8+16)}{2}&#10;\\\\\\&#10;A=2\sqrt{3}(24)\implies \boxed{A=48\sqrt{3}}


now, check the picture below on the bottom side.


since we know x = 9, then b = 9, therefore DC = 9+6+9 = 24, and h = b = 9.


\bf \textit{area of a trapezoid}\\\\&#10;A=\cfrac{h(a+b)}{2}~~&#10;\begin{cases}&#10;a,b=\stackrel{bases}{parallel~sides}\\&#10;h=height\\[-0.5em]&#10;\hrulefill\\&#10;a=6\\&#10;b=\stackrel{DC}{24}\\&#10;h=9&#10;\end{cases}\implies A=\cfrac{9(6+24)}{2}&#10;\\\\\\&#10;A=\cfrac{9(30)}{2}\implies \boxed{A=135}

7 0
3 years ago
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