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adell [148]
3 years ago
7

X + y = 2

Mathematics
1 answer:
liraira [26]3 years ago
8 0

Answer:

D. (3,-1)

Step-by-step explanation:

x + y = 2  \:  \:  \:  \:  \:  \: ..(1) \\ 2x - y = 7 \:  \:  \:  \: ..(2)

from equation 1 we get,

x = 2 - y

now,

put \:  \:  \:  \: x = 2 - y \:  \:  \: in \: (2)

we get,

2(2 - y) - y = 7 \\ 4 - 2y - y = 7 \\ 4 - 3y = 7 \\  - 3y = 7 - 4 \\  - 3y = 3  \\  \\ y =  \frac{3}{( - 3)}  \\  \\ y =  - 1

now,

put \:  \:  \:  \: y =  - 1 \:  \:  \:  \: in \: (1)

we get,

x + ( - 1) = 2 \\ x - 1 = 2 \\ x = 2  + 1 \\ x = 3

hence, the value of x = 3 and y = (-1)

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Prove that (Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A
iVinArrow [24]

Answer:

The answer is below

Step-by-step explanation:

We need to prove that:

(Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A.

Firstly, 1 / cos A = sec A, 1 / sin A = cosec A and tanA = sinA / cosA.

Also, 1 + tan²A = sec²A; sec²A - 1 = tan²A

\frac{\sqrt{secA-1} }{\sqrt{secA+1} } +\frac{\sqrt{secA+1} }{\sqrt{secA-1} } =\frac{(\sqrt{secA-1)}(\sqrt{secA-1})+(\sqrt{secA+1)}(\sqrt{secA+1}) }{(\sqrt{secA+1})(\sqrt{secA-1}) } \\\\=\frac{secA-1+(secA+1)}{\sqrt{sec^2A-secA+secA-1} } \\\\=\frac{2secA}{\sqrt{sec^2A-1} } \\\\=\frac{2secA}{\sqrt{tan^2A} } \\\\=\frac{2secA}{tanA} \\\\=\frac{2*\frac{1}{cosA} }{\frac{sinA}{cosA} }\\\\= 2*\frac{1}{cosA}*\frac{cosA}{sinA}\\\\=2*\frac{1}{sinAA}\\\\=2cosecA

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Data collected over a long period of time show that the length of time x to complete a particular college entrance test is norma
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For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 100

μ = mean = 125

σ = standard deviation = 18

z-score = (100 – 125) / 18

z-score = (-25) / 18

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Find the probability that corresponds to the z-score in the z-table. (see attached images)

-1.39 - (-1.3) : -1.4 - (-1.3) = x - 0.0968 : 0.0808 - 0.0968

-0.09 : -0.1 = x - 0.0968 : -0.016

x - 0.0968 = -0.09(-0.016)/-0.1

x = -0.0144 + 0.0968

x = 0.0824

x = 0.0824

Hence, the probability that a student taking this test will finish in 100 minutes or less is 0.0824 or 8.24%.

Learn more about probability here: brainly.com/question/26822684

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What is the constant in the expression 9x +5y + 12
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Step-by-step explanation:

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