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Radda [10]
4 years ago
10

I need 10x+3y=19 and y=2x+5 solved algebraically

Mathematics
1 answer:
taurus [48]4 years ago
8 0
Y=2x+5
sub 2x+5 for y in other equaiton
10x+3(2x+5)=19
distribute
10x+6x+15=19
minus 15 from both sides
16x=4
divide both sides by 16
x=1/4
sub back

y=2x+5
y=2(1/4)+5
y=1/2+5
y=5.5=11/2

solution is (1/4,11/2) or in decimal, (0.25,5.5)
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DaniilM [7]
5\sin2x=3\cos x\iff10\sin x\cos x=3\cos x

by the double angle identity for sine. Move everything to one side and factor out the cosine term.

10\sin x\cos x=3\cos x\iff10\sin x\cos x-3\cos x=\cos x(10\sin x-3)=0

Now the zero product property tells us that there are two cases where this is true,

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In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of \dfrac\pi2, so x=\dfrac{(2n+1)\pi}2 where n[/tex ]is any integer.\\Meanwhile,\\[tex]10\sin x-3=0\implies\sin x=\dfrac3{10}

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4 years ago
Gordon types 43 3/4 pages in 3 1/2 hours. What is his rate in pages per hour
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Answer:

His rate is 12 1/2 pages per hour.

Step-by-step explanation:

Given that,

Gordon types 43 3/4 pages in 3 1/2 hours or Gordon types 175/4 pages in 7/2 hours./ We need to find its rate in pages per hour. So,

R=\dfrac{\dfrac{175}{4}\ \text{pages}}{\dfrac{7}{2}\ \text{hour}}\\\\R=\dfrac{175}{4}\times \dfrac{2}{7}\\\\R=12.5\ \text{pages per hour}\\\\R=12\dfrac{1}{2}\ \text{pages per hour}

Hence, his rate is 12 1/2 pages per hour.

8 0
3 years ago
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