The area of the triangle is 10 sq units
<u>SOLUTION:
</u>
Given, we have to find the area of a triangle whose vertices are D(3, 3), E(3, −1) and F(−2, −5)
We know that,
![\text { Area of triangle }=\frac{1}{2}\left[x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right]](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Area%20of%20triangle%20%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%5Bx_%7B1%7D%5Cleft%28y_%7B2%7D-y_%7B3%7D%5Cright%29%2Bx_%7B2%7D%5Cleft%28y_%7B3%7D-y_%7B1%7D%5Cright%29%2Bx_%7B3%7D%5Cleft%28y_%7B1%7D-y_%7B2%7D%5Cright%29%5Cright%5D)
Where,
are vertices of the triangle.
Here in our problem, ![\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=(3,3),\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)=(3,-1) \text { and }\left(\mathrm{x}_{3}, \mathrm{y}_{3}\right)=(-2,-5)](https://tex.z-dn.net/?f=%5Cleft%28%5Cmathrm%7Bx%7D_%7B1%7D%2C%20%5Cmathrm%7By%7D_%7B1%7D%5Cright%29%3D%283%2C3%29%2C%5Cleft%28%5Cmathrm%7Bx%7D_%7B2%7D%2C%20%5Cmathrm%7By%7D_%7B2%7D%5Cright%29%3D%283%2C-1%29%20%5Ctext%20%7B%20and%20%7D%5Cleft%28%5Cmathrm%7Bx%7D_%7B3%7D%2C%20%5Cmathrm%7By%7D_%7B3%7D%5Cright%29%3D%28-2%2C-5%29)
Now, substitute the above values in the formula.
![\begin{aligned} \text { Area of triangle } &=\frac{1}{2}\left|x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right| \\\\ &=\frac{1}{2}|3(-1-(-5))+3(-5-3)+(-2)(3-(-1))| \\\\ &=\frac{1}{2}|3(-1+5)+3(-8)-2(3+1)| \\\\ &=\frac{1}{2}|3(4)-24-2(4)| \\\\ &=\frac{1}{2}|12-24-8| \\\\ &=\frac{1}{2}|12-32|=\frac{1}{2}|-20|=\frac{20}{2}=10 \text { sq units } \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Ctext%20%7B%20Area%20of%20triangle%20%7D%20%26%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%7Cx_%7B1%7D%5Cleft%28y_%7B2%7D-y_%7B3%7D%5Cright%29%2Bx_%7B2%7D%5Cleft%28y_%7B3%7D-y_%7B1%7D%5Cright%29%2Bx_%7B3%7D%5Cleft%28y_%7B1%7D-y_%7B2%7D%5Cright%29%5Cright%7C%20%5C%5C%5C%5C%20%26%3D%5Cfrac%7B1%7D%7B2%7D%7C3%28-1-%28-5%29%29%2B3%28-5-3%29%2B%28-2%29%283-%28-1%29%29%7C%20%5C%5C%5C%5C%20%26%3D%5Cfrac%7B1%7D%7B2%7D%7C3%28-1%2B5%29%2B3%28-8%29-2%283%2B1%29%7C%20%5C%5C%5C%5C%20%26%3D%5Cfrac%7B1%7D%7B2%7D%7C3%284%29-24-2%284%29%7C%20%5C%5C%5C%5C%20%26%3D%5Cfrac%7B1%7D%7B2%7D%7C12-24-8%7C%20%5C%5C%5C%5C%20%26%3D%5Cfrac%7B1%7D%7B2%7D%7C12-32%7C%3D%5Cfrac%7B1%7D%7B2%7D%7C-20%7C%3D%5Cfrac%7B20%7D%7B2%7D%3D10%20%5Ctext%20%7B%20sq%20units%20%7D%20%5Cend%7Baligned%7D)
Answer: x = -.63, -2.37
Step-by-step explanation:
x=−32±3–√2
x=−0.633975
x=−2.36603
Find the Solution for
2x2+6x+3=0
using the Quadratic Formula where
a = 2, b = 6, and c = 3
x=−b±b2−4ac/√2a
x=−6±62−4(2)(3)/√2(2)
x=−6±36−24/√4
x=−6±12−−√4
The discriminant b2−4ac>0
so, there are two real roots.
Simplify the Radical:
x=−6±23–√4
x=−64±23–√4
Simplify fractions and/or signs:
x=−32±3–√2
which becomes
x=−0.633975
x=−2.36603
Answer:
s = 6 m
Step-by-step explanation:
The value of the velocity v is given as:
m/s
To find s, we have to integrate and apply the initial values of s = o when t = 0:
![\frac{ds}{dt} = 6 sin(2t)\\\\\int\limits^s_0 {ds} = \int\limits^t_0 {6sin(2t)} \, dt\\\\s|^s_o = -3cos(2t)|^t_o\\\\s - 0 = -3cos(2t) -(-3cos(0))\\\\s = -3cos(2t) + 3(1)\\\\s = -3cos(2t) + 3](https://tex.z-dn.net/?f=%5Cfrac%7Bds%7D%7Bdt%7D%20%3D%206%20sin%282t%29%5C%5C%5C%5C%5Cint%5Climits%5Es_0%20%7Bds%7D%20%3D%20%5Cint%5Climits%5Et_0%20%7B6sin%282t%29%7D%20%5C%2C%20dt%5C%5C%5C%5Cs%7C%5Es_o%20%3D%20-3cos%282t%29%7C%5Et_o%5C%5C%5C%5Cs%20-%200%20%3D%20-3cos%282t%29%20-%28-3cos%280%29%29%5C%5C%5C%5Cs%20%3D%20-3cos%282t%29%20%2B%203%281%29%5C%5C%5C%5Cs%20%3D%20-3cos%282t%29%20%2B%203)
When t = π/2, s will be:
s = -3cos(2 * π/2) + 3
s = -3cos(π) + 3
s = -3(-1) + 3
s = 3 + 3
s = 6 m
Answer:
Step-by-step explanation:
Y = 3.2x + 5 is a linear function with slope 3.2 and y-intercept 5.
For any x value you choose to substitute for x, you'll obtain a unique y value. For example, if we were to substitute -3 for x, we'd get:
f(-3) = y = 3.2(-3) + 5, or y = -9.6 + 5 = -4.6
There is only one y result for each choice of x.
Y=3.2x+5 alone does not have an "answer." Again: You must pick your own x values and for each such value you must calculate y.
Answer: The total cost of computer would be $719.95
Step-by-step explanation:
I use proportions for these types of problems so we begin with a proportion!
20/100=x/849
100x=16980
x=169.80
Then, after finding how much the discount is, we would subtract it.
849-169.80=679.20
Next, we would find the tax amount with another proportion to find what 6 percent of 679.20 is.
6/100=x/679.20
100x=4075.2
x=40.75
Lastly, we would add the tax, $40.75, plus the total after the discount, $679.20!
Hope this helps! Good luck! (: