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2 years ago

Write for the system 3x - 5y = 9,3x+y=3, which variable should we eliminate first?

Mathematics

1 answer:

murzikaleks [220]2 years ago

7 0

Answer:

Step-by-step explanation:

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Find the solution using a tape diagram H + 12 = 34

Mnenie [13.5K]

The answer is H=22 and the tape diagram is below with the step by step explanation

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3 years ago

Math Correct answers only please!!

aksik [14]

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Rewrite and add each vector:

$p=\langle40cos70^\circ,40sin70^\circ\rangle\\q=\langle50cos270^\circ,50sin270^\circ\rangle\\r=\langle60cos235^\circ,60sin235^\circ\rangle\\p+q+r=\langle40cos70^\circ+50cos270^\circ+60cos235^\circ,40sin70^\circ+50sin270^\circ+60sin235^\circ\rangle\\p+q+r\approx\langle-20.73,-61.56\rangle$

Find the magnitude of the resulting vector:

$||p+q+r||=\sqrt{x^2+y^2}\\||p+q+r||=\sqrt{(-20.73)^2+(-61.56)^2}\\||p+q+r||\approx64.96$

Therefore, the best answer is D) 64.959

Problem 2

Think of the vectors like this:

$t=\langle7cos240^\circ,7sin240^\circ\rangle\\u=\langle10cos30^\circ,10sin30^\circ\rangle\\v=\langle15cos310^\circ,15sin310^\circ\rangle$

By adding the vectors, we have:

$t+u+v=\langle7cos240^\circ+10cos30^\circ+15cos310^\circ,7sin240^\circ+10sin30^\circ+15sin310^\circ\rangle\\t+u+v\approx\langle14.8,-12.55\rangle$

Since the direction of a vector is $\theta=tan^{-1}(\frac{y}{x})$ , we have:

$\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{-12.55}{14.8})\\\theta\approx-40.3^\circ$

Don't forget to take into account that the resulting vector is in Quadrant IV since the horizontal component is positive and the vertical component is negative, so we will add 360° to our angle to get the result:

$\theta=360^\circ+(-40.3)^\circ\\\theta=319.7^\circ$

Therefore, the best answer is D) 320°

Problem 3

Again, rewrite the vectors and add them:

$u=\langle30cos70^\circ,30sin70^\circ\rangle\\v=\langle40cos220^\circ,40sin220^\circ\rangle\\u+v=\langle30cos70^\circ+40cos220^\circ,30sin70^\circ+40sin220^\circ\rangle\\u+v\approx\langle-20.38,2.48\rangle$

Using the direction formula:

$\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{2.48}{-20.38})\\\theta\approx-6.94^\circ$

As the vector is located in Quadrant II, we need to add 180° to our angle:

$\theta=180^\circ+(-6.94)^\circ\\\theta=173.06^\circ$

Therefore, the best answer is D) 173°

Problem 4

Using scalar multiplication:

$-3u=-3\langle35,-12\rangle=\langle-105,36\rangle$

Find the magnitude of the resulting vector:

$||-3u||=\sqrt{x^2+y^2}\\||-3u||=\sqrt{(-105)^2+(36)^2}\\||-3u||=111$

Find the direction of the resulting vector:

$\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{36}{-105})\\\theta\approx-18.92^\circ$

As the vector is located in Quadrant II, we need to add 180° to our angle:

$\theta=180^\circ+(-18.92)^\circ\\\theta=161.08^\circ$

Therefore, the best answer is C) 111; 161°

Problem 5

Using scalar multiplication:

$5v=5\langle25cos40^\circ,25sin40^\circ\rangle=\langle125cos40^\circ,125sin40^\circ\rangle$

Since the direction of the angle doesn't change in scalar multiplication, it only affects the magnitude, so the magnitude of the resulting vector would be $||5v||=125$ , making the correct answer C) 125; 200°

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3 years ago

Which number is the best approximation for 45√−23√ ?

forsale [732]

I think it would be 6.7 - 4.8
Which would also equal 1.9

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4 years ago

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What is the range of the function on the graph?

STALIN [3.7K]

Answer:

the answer is D. all real numbers greater than or equal to 2.

Step-by-step explanation:

looking at the graph, half of a parabola is curved upwards, and will never stop going up. looking at (1, 2), the dot (instead of circle) indicates the range is greater than or equal to itself, which is 2.

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3 years ago

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A store sells ice cream with assorted toppings. they charge $ 3.00 for ice cream plus 0.50 per ounce of toppings.

aev [14]

Answer:7 ounces

Step-by-step explanation:

If they charge 0.50 cents per ounce then u would take the 50 cents and add that up until it gets to 3.50 and that will give u 7 so the answer is 7 ounces.

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3 years ago

Write for the system 3x - 5y = 9,3x+y=3, which variable should we eliminate first?​

Write for the system 3x - 5y = 9,3x+y=3, which variable should we eliminate first?