If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?
1 answer:
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The Type B trees produces 120 pears.
<h3>What is meant by percentage?</h3>A percentage is a number or ratio expressed as a fraction of 100 in mathematics. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement.
<h3>How many pears did the Type B trees produce?</h3>- Type A trees produced 20 percent more pears than Type B trees did
- Type A trees produced 144 pears.
Let us consider, Type B produced 100% pears.
So, Type A will produce 120%of B, that is 144
144 = 120/100 B
simplifying the above equation, we get
144 100 = 120B
B = 14400/120
B = 120
The value of B = 120.
Hence, the Type B trees produces 120 pears
Therefore, the correct answer is option B) 120.
To learn more about percentage, refer to:
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<span>f(x) = 2(3x)
Exponential functions represent the initial value outside of the parentheses so if 2 is the initial value it has to be on the outside of the parentheses.
Exponential growth formula.
</span>
<span>a represents the initial value.</span>
Exponential functions represent the initial value outside of the parentheses so if 2 is the initial value it has to be on the outside of the parentheses.
Exponential growth formula.
</span>
<span>a represents the initial value.</span>
<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)