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3 years ago

What is the value of y in the solution to the system of equations? 1x + 1y = 1 2x – 3y = -30

Mathematics

1 answer:

nydimaria [60]3 years ago

5 0

Answer:

y=8

Step-by-step explanation:

$\frac{1}{3} x + \frac{1}{4}y= 1\\\\\frac{4x+3y}{12} =1\\4x+ 3y =12\\y = \frac{12-4x}{3}$

let's note this as our equation no. (i)

and let 2x-3y = -30 be the equation no. (ii)

Put value of y from (i) into (ii)

$2x -3y = -30\\2x-3(\frac{12-4x}{3} )=-30\\2x -12+4x = -30\\6x = -30+12\\6x= -18\\x = -3$

Now put x = -3 back in equation (i)

$y = \frac{12-4x}{3}\\y = \frac{12 - 4(-3)}{3}\\y = \frac{12 + 12}{3} \\y = 8$

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Veseljchak [2.6K]

cos θ = $\frac{-4\sqrt{65} }{65}$ , sin θ = $\frac{-7\sqrt{65} }{65}$ , cot θ = 4/7, sec θ = $\frac{-\sqrt{65} }{4}$ , cosec θ = $\frac{-\sqrt{65} }{7}$

<h3>What are trigonometric ratios?</h3>

Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin θ: Opposite Side to θ/Hypotenuse

Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos

Cos θ: Adjacent Side to θ/Hypotenuse

Sec θ: Hypotenuse/Adjacent Side & 1/cos θ

Analysis:

tan θ = opposite/adjacent = 7/4

opposite = 7, adjacent = 4.

we now look for the hypotenuse of the right angled triangle

hypotenuse = $\sqrt{7^{2} + 4^{2} }$ = $\sqrt{49+16}$ = $\sqrt{65}$

sin θ = opposite/ hyp = $\frac{7}{\sqrt{65} }$

Rationalize, $\frac{7}{\sqrt{65} }$ x $\frac{\sqrt{65} }{\sqrt{65} }$ = $\frac{7\sqrt{65} }{65}$

But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.

Therefore, sin θ = - $\frac{7\sqrt{65} }{65}$

cos θ = adj/hyp = $\frac{4}{\sqrt{65} }$

By rationalizing and knowing that cos θ is negative, cos θ = - $\frac{-4\sqrt{65} }{65}$

cot θ = 1/tan θ = 1/7/4 = 4/7

sec θ = 1/cos θ = 1/ $\frac{4}{\sqrt{65} }$ = - $\frac{-\sqrt{65} }{4}$

cosec θ = 1/sin θ = 1/ $\frac{\sqrt{65} }{7}$ = $\frac{-\sqrt{65} }{7}$

Learn more about trigonometric ratios: brainly.com/question/24349828

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1 year ago

-12=3-2k-3k Solving multi-step equations I give Brainliest!

inessss [21]

Answer:

k = 3

Step-by-step explanation:

-12 = 3 - 2k - 3k

-12 = 3 - 5k

5k = 15

k = 3

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3 years ago

Find the mode(s) for the given sample data. The lengths (in inches) of each snake in the Clarmont Zoo's reptile house are shown

Contact [7]

The correct option is : no mode

Explanation

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The mode is the number that is repeated more often than any other number in the data set.

But here we can see that all the numbers in this data set are different. That means they appear only once.

So, there will be 'no mode' in this set.

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3 years ago

Write in a exponent form 2•2•2•3•3•3=_

Dima020 [189]

Answer:

2^3 • 3^2

Step-by-step explanation:

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3 years ago

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Find the highest common factor of 72 and 135

andrey2020 [161]

Answer:9

Step-by-step explanation:

Find the prime factorization of 72

72 = 2 × 2 × 2 × 3 × 3

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135 = 3 × 3 × 3 × 5

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 3 × 3

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2 years ago

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What is the value of y in the solution to the system of equations? 1x + 1y = 1 2x – 3y = -30​

What is the value of y in the solution to the system of equations? 1x + 1y = 1 2x – 3y = -30