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natka813 [3]
3 years ago
9

A system of equations is shown:

Mathematics
1 answer:
Harrizon [31]3 years ago
6 0

Answer:

<h2>(1, 4)</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}2x=-y+6&(1)\\-4x+3y=8&(2)\end{array}\right\\\\(1)\\-y+6=2x\qquad\text{subtract 6 from both sides}\\-y=2x-6\qquad\text{change the signs}\\y=6-2x\\\\\text{substitute it to (2):}\\\\(2)\\-4x+3(6-2x)=8\qquad\text{use the distributive property}\\-4x+(3)(6)+(3)(-2x)=8\\-4x+18-6x=8\qquad\text{subtract 18 from both sides}\\-10x=-10\qquad\text{divide both sides by (-10)}\\x=1\\\\\text{put the value of x to (1):}\\\\y=6-2(1)\\y=6-2\\y=4

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The walking distance that is saved by cutting across the lot is
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Using the Pythagorean Theorem, we have x^2+(x+2)^2=51^2, and
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8 0
3 years ago
i f N(-7,-1) is a point on the terminal side of ∅ in standard form, find the exact values of the trigonometric functions of ∅.
Natali [406]

Answer:

sin\ \varnothing = \frac{-1}{10}\sqrt 2

cos\ \varnothing = \frac{-7}{10}\sqrt 2

tan\ \varnothing = \frac{1}{7}

cot\ \varnothing = 7

sec\ \varnothing = \frac{-5}{7}\sqrt 2

csc\ \varnothing = -5\sqrt 2

Step-by-step explanation:

Given

N = (-7,-1) --- terminal side of \varnothing

Required

Determine the values of trigonometric functions of \varnothing.

For \varnothing, the trigonometry ratios are:

sin\ \varnothing = \frac{y}{r}       cos\ \varnothing = \frac{x}{r}       tan\ \varnothing = \frac{y}{x}

cot\ \varnothing = \frac{x}{y}       sec\ \varnothing = \frac{r}{x}       csc\ \varnothing = \frac{r}{y}

Where:

r^2 = x^2 + y^2

r = \sqrt{x^2 + y^2

In N = (-7,-1)

x = -7 and y = -1

So:

r = \sqrt{(-7)^2 + (-1)^2

r = \sqrt{50

r = \sqrt{25 * 2

r = \sqrt{25} * \sqrt 2

r = 5 * \sqrt 2

r = 5 \sqrt 2

<u>Solving the trigonometry functions</u>

sin\ \varnothing = \frac{y}{r}

sin\ \varnothing = \frac{-1}{5\sqrt 2}

Rationalize:

sin\ \varnothing = \frac{-1}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}

sin\ \varnothing = \frac{-\sqrt 2}{5*2}

sin\ \varnothing = \frac{-\sqrt 2}{10}

sin\ \varnothing = \frac{-1}{10}\sqrt 2

cos\ \varnothing = \frac{x}{r}

cos\ \varnothing = \frac{-7}{5\sqrt 2}

Rationalize

cos\ \varnothing = \frac{-7}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}

cos\ \varnothing = \frac{-7*\sqrt 2}{5*2}

cos\ \varnothing = \frac{-7\sqrt 2}{10}

cos\ \varnothing = \frac{-7}{10}\sqrt 2

tan\ \varnothing = \frac{y}{x}

tan\ \varnothing = \frac{-1}{-7}

tan\ \varnothing = \frac{1}{7}

cot\ \varnothing = \frac{x}{y}

cot\ \varnothing = \frac{-7}{-1}

cot\ \varnothing = 7

sec\ \varnothing = \frac{r}{x}

sec\ \varnothing = \frac{5\sqrt 2}{-7}

sec\ \varnothing = \frac{-5}{7}\sqrt 2

csc\ \varnothing = \frac{r}{y}

csc\ \varnothing = \frac{5\sqrt 2}{-1}

csc\ \varnothing = -5\sqrt 2

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Answer:

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Step-by-step explanation:

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Null hypothesis: The average number of crisps per can of Pringles is 100.

Alternative hypothesis: The average number of crisps per can of Pringles is less than 100.

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mario62 [17]

Answer:

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Step-by-step explanation:

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3 years ago
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