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chubhunter [2.5K]
3 years ago
14

2y = x - 4 4x + 3y = 5

Mathematics
1 answer:
MakcuM [25]3 years ago
8 0

Answer:

the answer is, {x,y} ={2,1}

Step-by-step explanation:

1) 4x - 3y = 5     2) x + 2y = 4   3) 4•(-2y+4) - 3y = 5     4) - 11y = -11                         5) 11y = 11   y = 1    6)   x = -2y+4 y = 1    7)   x = -2(1)+4 = 2 = {x,y} = {2,1} !!!

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Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below. 18.75 93.75 581.25 145.3125
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we have that

300 + 150 + 75 +...

Let

a1=300\\ a2=150\\ a3=75

we know that

\frac{a2}{a1} =\frac{150}{300} \\\\ \frac{a2}{a1}=0.5 \\ \\ a2=a1*0.50

\frac{a3}{a2} =\frac{75}{150} \\\\ \frac{a3}{a2}=0.5 \\ \\ a3=a2*0.50

so

a(n+1)=an*0.50

Is a geometric sequence

Find the value of a4

a(4)=a3*0.50

a(4)=75*0.50

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Alternative Method

Applying the formula

S_n=\frac{a_1 (1-r^n)}{1-r} \\\\a_1=300 \\ r=\frac{1}{2}\\\\ S_5=\frac{300(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}\\\\=\frac{300(1-\frac{1}{32})}{\frac{1}{2}}\\\\=\frac{300 \times \frac{31}{32}}{\frac{1}{2}}\\\\=\frac{75 \times \frac{31}{8}}{\frac{1}{2}}\\\\=\frac{\frac{2325}{8}}{\frac{1}{2}}\\\\=\frac{2325}{8} \times 2\\\\=\frac{2325}{4}\\\\=581 \frac{1}{4}\\\\=581.25

therefore

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581.25

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