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2 years ago

In a question like: 3 − (2x − 5) < −4(x + 2)

Mathematics

1 answer:

Viefleur [7K]2 years ago

4 0

Answer:

Step-by-step explanation: I think -5 would change to a positive 5 because of the distributive property. In the part -(2x-5), there is a invisible 1 next to the left parenthesis, so it would be -1(2x-5). Then you would distribute the -1 one to the 2x and the -5. So the thing would look like this: -2x+5.

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Please Help. I really don’t get this concept, if you could explain it in detail it would be very appreciated

Dafna11 [192]

<h3>Answer: 24/25</h3>

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Explanation:

Sine is given to be negative, and so is tangent. This only happens in quadrant Q4

Recall that y = sin(theta), so if sin(theta) < 0, then we're below the x axis.

If tan(theta) < 0, then this means cos(theta) > 0

So we have y < 0 and x > 0 which places the angle somewhere in Q4.

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Draw a right triangle as shown below in the attached image. We have AC = 25 and BC = 7. Use the pythagorean theorem to find that AB = 24

So this is what your steps may look like

a^2+b^2 = c^2

7^2+b^2 = 25^2

b^2+49 = 625

b^2 = 625-49

b^2 = 576

b = sqrt(576)

b = 24

So because AB = 24, we know that the cosine of the angle is adjacent/hypotenuse = 24/25

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As an alternative, you could use the trig identity

sin^2(x) + cos^2(x) = 1

and plug in the given value of sine to solve for cosine. The cosine value result will be positive since we're in Q4.

So,

sin^2(x) + cos^2(x) = 1

(-7/25)^2 + cos^2(x) = 1

(49/625) + cos^2(x) = 1

cos^2(x) = 1 - (49/625)

cos^2(x) = (625/625) - (49/625)

cos^2(x) = (625-49)/625

cos^2(x) = 576/625

cos(x) = sqrt(576/625)

cos(x) = sqrt(576)/sqrt(625)

cos(x) = 24/25

This is effectively a rephrasing of the previous section since the pythagorean trig identity is more or less the pythagorean theorem (just in a trig form)

6 0

4 years ago

THE SUM OF THE DIGITS OF A CERTAIN TWO-DIGIT NUMBER IS 13. REVERSING ITS DIGITS INCREASED THE NUMBER BY 9. WHAT IS THE NUMBER?

KonstantinChe [14]

Answer:

Step-by-step explanation:

Adding 6 and 7 together equate to 13. You then switch the digits of 67 to 76 and the number is increased by 9.

5 0

3 years ago

When a measurement in inches is converted to centimeters, will the number of centimeters be greater or less than the number of i

krek1111 [17]

Answer:
The number of centimeters will be greater than the number of inches.

Explanation:
The conversion between an inch (British Units) and centimeter (Metric Units) is
1 inch = 2.54 centimeters.

According to the conversion, every inch is equivalent to more than 2.5 centimeters.

7 0

3 years ago

-2.1b +5.3= b -- 3.1b + 5.3<br><br> does is have one solution or infinitely many solutions ? Why ?

pychu [463]

Answer: infinitely many solutions.

Step-by-step explanation:

Ok, our equation is:

-2.1*b + 5.3 = b - 3.1*b + 5.3

now, simplifyng the right side, we have:

b - 3.1*b + 5.3 = (1 - 3.1)*b + 5.3 = -2.1*b + 5.3

Then our initial expression is:

-2.1*b + 5.3 = -2.1*b + 5.3

So in both sides of the equality we have the exact same thing, so this is a trivial equality.

This means that the equality will remain true for any value of b, which means that we have infinitely many solutions.

6 0

3 years ago

The slope of the line passing through the points (0, 0) and (2, 3) is

MArishka [77]

You can use the equation to find the slope of a line given two points. This equation is y2 - y1 divided by x2 minus x1. The y2 is represented by the y coordinate of the second ordered pair, but it really doesn't matter, either way you get the same answer. The same way the x2 is represented by the x coordinate of the second ordered pair. For this problem, I will just use the normal coordinates. So the second y coordinate is 3. 3 -0 = 3. So your numerator is 3. The second x coordinate is 2. 2-0 = 2. So the denominator is 2. This is 3/2. So your slope would be 3/2. Hope this helps. :D Let me know if you didn't understand something in my explanation.

4 0

3 years ago