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2 years ago

One number is five times another number. Their sum is 42. What are the two numbers?

Mathematics

2 answers:

Amiraneli [1.4K]2 years ago

7 0

Answer:

7 and 35

Step-by-step explanation:

Let one number be x and the other number be y

"one number is five times another number"

Expressed mathematically: y = 5x --- -eq 1

"their sum is 42"

Expressed mathematically : x + y = 42 ------ eq2

Now we have a system of equations with 2 equations and 2 unknowns, we can solve this easily by substitution

From equation 2,

x + y = 42 (substitute eq 1 into eq 2)

x + (5x) = 42

6x = 42 (divide both sides by 6)

x = 42/6 = 7 (answer)

substituting this back into equation 1:

y = 5x

y = 5(7)

y = 35 (answer)

elixir [45]2 years ago

4 0

Answer:

Step-by-step explanation:

x+5x=42

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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 = $\frac{-\sqrt{65} }{7}$

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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

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tan θ = opposite/adjacent = 7/4

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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 = - $\frac{-4\sqrt{65} }{65}$

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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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