Answer: $ 400
Step-by-step explanation:
Amount collected for new library = $ 3,200 and there are 8 classes and they collected the same amount. This means that each class will collect
3200/ 8 = $400
Answer:
188 cm^2.
Step-by-step explanation:
This consists of 3 pairs of rectangles
= 2 * 4*7 + 2 * 4*6 + 2 * 6*7
= 56 + 48 + 84
= 188.
Answer:
equals -43
Step-by-step explanation:
35 because you must substitute the 8 in for n.
Answer: 28x+42y=3
Step-by-step explanation:
Given: The point (x,y) is equidistant from the points
.
By distance formula the distance between
is
![D_1=\sqrt{(x-\frac{-1}{4})^2+(y-(-4))^2} \\=\sqrt{(x+\frac{1}{4})^2+(y+4)^2}](https://tex.z-dn.net/?f=D_1%3D%5Csqrt%7B%28x-%5Cfrac%7B-1%7D%7B4%7D%29%5E2%2B%28y-%28-4%29%29%5E2%7D%20%5C%5C%3D%5Csqrt%7B%28x%2B%5Cfrac%7B1%7D%7B4%7D%29%5E2%2B%28y%2B4%29%5E2%7D)
Similarly, the distance between
is
![D_2=\sqrt{(x-\frac{13}{4})^2+(y-(\frac{5}{4}))} \\=\sqrt{(x-\frac{13 }{4})^2+(y-\frac{5}{4})^2}](https://tex.z-dn.net/?f=D_2%3D%5Csqrt%7B%28x-%5Cfrac%7B13%7D%7B4%7D%29%5E2%2B%28y-%28%5Cfrac%7B5%7D%7B4%7D%29%29%7D%20%5C%5C%3D%5Csqrt%7B%28x-%5Cfrac%7B13%20%7D%7B4%7D%29%5E2%2B%28y-%5Cfrac%7B5%7D%7B4%7D%29%5E2%7D)
Since,
![D_1=D_2\\\\\Rightarrow\ \sqrt{(x+\frac{1}{4})^2+(y+4)^2}=\sqrt{(x-\frac{13}{4})^2+(y-\frac{5}{4})^2}\\\\\text{Squaring on the sides, we get}\\\Rightarrow(x+\frac{1}{4})^2+(y+4)^2=(x-\frac{13}{4})^2+(y-\frac{5}{4})^2\\\\\Rightarrow[x^2+\frac{1}{2}x+\frac{1}{16}]+y^2+8y+16=x^2-\frac{13}{2}x+\frac{169}{16}+y^2+\frac{25}{4}-\frac{5}{2}y\\\\\Rightarrow7x+\frac{21}{2}y=\frac{3}{4}\\\Rightarrow28x+42y=3](https://tex.z-dn.net/?f=D_1%3DD_2%5C%5C%5C%5C%5CRightarrow%5C%20%5Csqrt%7B%28x%2B%5Cfrac%7B1%7D%7B4%7D%29%5E2%2B%28y%2B4%29%5E2%7D%3D%5Csqrt%7B%28x-%5Cfrac%7B13%7D%7B4%7D%29%5E2%2B%28y-%5Cfrac%7B5%7D%7B4%7D%29%5E2%7D%5C%5C%5C%5C%5Ctext%7BSquaring%20on%20the%20sides%2C%20we%20get%7D%5C%5C%5CRightarrow%28x%2B%5Cfrac%7B1%7D%7B4%7D%29%5E2%2B%28y%2B4%29%5E2%3D%28x-%5Cfrac%7B13%7D%7B4%7D%29%5E2%2B%28y-%5Cfrac%7B5%7D%7B4%7D%29%5E2%5C%5C%5C%5C%5CRightarrow%5Bx%5E2%2B%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B1%7D%7B16%7D%5D%2By%5E2%2B8y%2B16%3Dx%5E2-%5Cfrac%7B13%7D%7B2%7Dx%2B%5Cfrac%7B169%7D%7B16%7D%2By%5E2%2B%5Cfrac%7B25%7D%7B4%7D-%5Cfrac%7B5%7D%7B2%7Dy%5C%5C%5C%5C%5CRightarrow7x%2B%5Cfrac%7B21%7D%7B2%7Dy%3D%5Cfrac%7B3%7D%7B4%7D%5C%5C%5CRightarrow28x%2B42y%3D3)