yx2 +yx4 +yx6 +yx8 +...+ yx100 =5100
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\(a,=x\left(x^2-10x+25\right)=x\left(x-5\right)^2\\ b,=y\left(x+y\right)-\left(x+y\right)=\left(y-1\right)\left(x+y\right)\\ c,=\left(x-5\right)^2\\ d,=\left(x-8\right)\left(x+8\right)\)
Y x 1 + Y x 2 + Y x 3 + ... + Y x 100 = 12625
Y x (1+2+3+...+100) = 12625
Y x (100+1) x (100:2) = 12625
Y x (101 x 50) = 12625
Y x 5050 = 12625
Y= 12625 : 5050
Y= 2,5
219,1 + y:y < y \(\times\) 2 + y \(\times\) 4 - y < 230,2 - y + y
219,1 + 1 < y \(\times\) 2 + y \(\times\) 4 - y \(\times\) 1 < 230,2 - ( y - y)
210,1 < y \(\times\) ( 2 + 4 - 1) < 230,2
210,1 < y \(\times\) 5 < 230,2
210,1 : 5 < y < 230,2: 5
42,02 < y < 46,04
y * 1 + y * 2 + y * 3 + y * 4 + y *1 = 825
y * ( 1 + 2 + 3 + 4 + 1) =825
y * 11 = 825
y = 825 / 11
y = 75
a) \(\dfrac{3}{4}+\dfrac{9}{5}\div\dfrac{3}{2}-1=\dfrac{3}{4}+\dfrac{18}{15}-1=\dfrac{39}{20}-1=\dfrac{19}{20}\)
b) \(\dfrac{6}{7}\cdot\dfrac{8}{13}+\dfrac{6}{13}\cdot\dfrac{9}{7}-\dfrac{4}{13}\cdot\dfrac{6}{7}=\dfrac{48}{91}+\dfrac{54}{91}-\dfrac{24}{91}=\dfrac{48+51-24}{91}=\dfrac{78}{91}=\dfrac{6}{7}\)
c) \(\dfrac{-3}{7}+\left(\dfrac{3}{-7}-\dfrac{3}{-5}\right)\)\(=\dfrac{-3}{7}+\left(\dfrac{-3}{7}-\dfrac{-3}{5}\right)=\dfrac{-3}{7}+\dfrac{6}{35}=-\dfrac{9}{35}\)
3. are there any eggs?-No, there aren't some
4.is there any salt?- yes, there is any
5.are there any carrots?-yes, there are some
6.are there any apples?-no there aren't some
7.is there any suger?-yes, there is any
8.are there any cakes?-no there aren't some
9.is there any butter?-no. there isn't any
10. is there any mineral water?- yes. there is any
\(=>y\times\left(2+4+6+8+...+100\right)=5100\\ =>y\times\left(100+2\right)\times50:2=5100\\ =>y\times2500=5100\\ =>y=\dfrac{5100}{2500}=2\)
\(y.2+y.4+y.6+y.8+...+y.100=5100\\ \Rightarrow y.\left(2+4+6+8+...+100\right)=5100\\ \Rightarrow y.\dfrac{\left(100+2\right).\left[\left(100-2\right):2+1\right]}{2}=5100\\ \Rightarrow y.\dfrac{102.50}{2}=5100\\ \Rightarrow y.2550=5100\\ \Rightarrow y=5100:2550\\ \Rightarrow y=2\)