Answer:
As the lengths of the two sides is equal. i.e. WY = WX
. Therefore, the triangle WXY is an isosceles triangle.
Step-by-step explanation:
Considering the triangle with the vertices
The distance between the W(-10, 4) and Y(-5, 11) is the length of the side WY.
So,
![\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}](https://tex.z-dn.net/?f=%5Cmathrm%7BCompute%5C%3Athe%5C%3Adistance%5C%3Abetween%5C%3A%7D%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3A%5Cquad%20%5Csqrt%7B%5Cleft%28x_2-x_1%5Cright%29%5E2%2B%5Cleft%28y_2-y_1%5Cright%29%5E2%7D)
![\mathrm{The\:distance\:between\:}\left(-10,\:4\right)\mathrm{\:and\:}\left(-5,\:11\right)\mathrm{\:is\:}](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%5C%3Adistance%5C%3Abetween%5C%3A%7D%5Cleft%28-10%2C%5C%3A4%5Cright%29%5Cmathrm%7B%5C%3Aand%5C%3A%7D%5Cleft%28-5%2C%5C%3A11%5Cright%29%5Cmathrm%7B%5C%3Ais%5C%3A%7D)
![=\sqrt{\left(-5-\left(-10\right)\right)^2+\left(11-4\right)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5Cleft%28-5-%5Cleft%28-10%5Cright%29%5Cright%29%5E2%2B%5Cleft%2811-4%5Cright%29%5E2%7D)
![=\sqrt{\left(-5+10\right)^2+\left(11-4\right)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5Cleft%28-5%2B10%5Cright%29%5E2%2B%5Cleft%2811-4%5Cright%29%5E2%7D)
![=\sqrt{5^2+7^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B5%5E2%2B7%5E2%7D)
![=\sqrt{5^2+7^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B5%5E2%2B7%5E2%7D)
![=\sqrt{74}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B74%7D)
So, the length of the side WY
.
Similarly,
The distance between the W(-10, 4) and X(-3, -1) is the length of the side WX.
![\mathrm{The\:distance\:between\:}\left(-10,\:4\right)\mathrm{\:and\:}\left(-3,\:-1\right)\mathrm{\:is\:}](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%5C%3Adistance%5C%3Abetween%5C%3A%7D%5Cleft%28-10%2C%5C%3A4%5Cright%29%5Cmathrm%7B%5C%3Aand%5C%3A%7D%5Cleft%28-3%2C%5C%3A-1%5Cright%29%5Cmathrm%7B%5C%3Ais%5C%3A%7D)
![=\sqrt{\left(-3-\left(-10\right)\right)^2+\left(-1-4\right)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5Cleft%28-3-%5Cleft%28-10%5Cright%29%5Cright%29%5E2%2B%5Cleft%28-1-4%5Cright%29%5E2%7D)
![=\sqrt{\left(-3+10\right)^2+\left(-1-4\right)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5Cleft%28-3%2B10%5Cright%29%5E2%2B%5Cleft%28-1-4%5Cright%29%5E2%7D)
![=\sqrt{49+5^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B49%2B5%5E2%7D)
![=\sqrt{49+25}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B49%2B25%7D)
![=\sqrt{74}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B74%7D)
So, the length of the side WX
.
As the lengths of the two sides is equal. i.e. WY = WX
. Therefore, the triangle WXY is an isosceles triangle.
Answer:
$20.45
Step-by-step explanation:
Since the Bayside Bugle charges $18 for the first 20 words and there is more than 20 words in the ad you take 27-20 and you get 7 additional words.
Now we know that we already have to pay $18 for the first $20 words.
Since we have 7 additional words we multiply that by 0.35 cents and you get $2.45.
Next we add up our two numbers (2.45+18) we get the total of $20.45 fro a 27-word ad.
I hope this helps :)
Answer:
The correct option is 3. Capacity of smallest tank is 15-gallons.
Step-by-step explanation:
The graph shows the relationship between capacity of tank and combined length of fish it can hold.
The line passing through (0,1) and (1,2).
Slope of the line is
![m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{1-0}=1](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%3D%5Cfrac%7B2-1%7D%7B1-0%7D%3D1)
Slope intercept form of a line is
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where, m is slope and b is y-intercept.
The slope of the line is 1 and the y-intercept is 1, therefore the equation of line is
..... (1)
If we want four 2-inch platys, three 1-inch guppies and a 3-inch loach, then the combined length of fish is
![4\times 2+3\times 1+1\times 3=8+3+3=14](https://tex.z-dn.net/?f=4%5Ctimes%202%2B3%5Ctimes%201%2B1%5Ctimes%203%3D8%2B3%2B3%3D14)
Therefore the combined length of fish is 14.
Put x=14 in equation 1.
Therefore, the capacity of smallest tank is 15-gallons and option 3 is correct.
The correct answer is 40.3 degrees
Answer:
840cm²
Step-by-step explanation:
The two small triangle areas:
b × h / 2 = 12 × 5 = 60 / 2 = 30cm²
So two triangles would be 60cm²
Now, for the top rectangle:
b × h = 26 × 12 = 312cm²
The middle rectangle:
b × h = 26 × 13 = 338cm²
And the bottom last triangle:
b × h = 26 × 5 = 130cm².
Now to add them all: 60 + 312 + 338 + 130 = 840cm²
I advice you to just check to make sure the calculations were right! Good luck with the rest of your finals :)