Answer: A. x ≤ -3
x/3 - x-1/2 ≥ 1 would make x ≤ -3
It should be acute because if A and B are complementary then B and A added together should be 90 so 90-30=60 and 60 would be an acute angle
Answer:
The height is 4.5ft
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Step-by-step explanation:
Given
yearly
Required
Determine the height in 3 years
First, we need to determine the growth equation.
Represent the height with h and the years with x
So:
To solve the required, we have that:
becomes
<em>Hence, the height is 4.5ft</em>
Answer:
4b. −6x + y = −4
4a. 7x + 4y = −12
3b. y = ½x + 3
3a. y = −6x + 5
2b. y + 2 = −⅔(x + 3)
2a. y - 3 = ⅘(x - 5)
1b. y = -x + 5
1a. y = 5x - 3
Step-by-step explanation:
4.
Plug the coordinates into the Slope-Intercept Formula first, then convert to Standard Form [Ax + By = C]:
b.
2 = 6[1] + b
6
−4 = b
y = 6x - 4
-6x - 6x
_________
−6x + y = −4 >> Standard Equation
a.
4 = −7⁄4[-4] + b
7
−3 = b
y = −7⁄4x - 3
+7⁄4x +7⁄4x
____________
7⁄4x + y = −3 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]
4[7⁄4x + y = −3]
7x + 4y = −12 >> Standard Equation
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3.
Plug both coordinates into the Slope-Intercept Formula:
b.
5 = ½[4] + b
2
3 = b
y = ½x + 3 >> EXACT SAME EQUATION
a.
−1 = −6[1] + b
−6
5 = b
y = −6x + 5
* Parallel lines have SIMILAR <em>RATE OF CHANGES</em> [<em>SLOPES</em>].
__________________________________________________________
2.
b. y + 2 = −⅔(x + 3)
a. y - 3 = ⅘(x - 5)
According to the <em>Point-Slope Formula</em>, <em>y - y₁ = m(x - x₁)</em>, all the negative symbols give the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.
__________________________________________________________
1.
b. y = -x + 5
a. y = 5x - 3
Just write out the Slope-Intercept Formula as it is given to you.
I am joyous to assist you anytime.
The number of lionfish after 6 years will be 85,609. The recursive equation for f(n) will be f(n) = 4242.42(1.65)ⁿ - 1300n.
<h3>What is an exponent?</h3>
Consider the function:
y = a (1 ± r) ˣ
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
lionfish are considered an invasive species, with an annual growth rate of 65%.
Then the equation will be
f(n) = P(1.65)ⁿ
P = initial polulation
A scientist estimates there are 7,000 lionfish in a certain bay after the first year.
7000 = P(1.65)
P = 4242.42
Then the equation will be
f(n) = 4242.42(1.65)ⁿ
The number of lionfish after 6 years will be
f(n) = 4242.42(1.65)⁶
f(n) = 85608.58
f(n) ≅ 85,609
If scientists remove 1,300 fish per year from the bay after the first year.
Then the recursive equation for f(n) will be
f(n) = 4242.42(1.65)ⁿ - 1300n
More about the exponent link is given below.
brainly.com/question/5497425
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