Width = x
Length = x+18
Assuming the table is rectangular:
Area = x(x + 18)
Therefore:
x(x + 18) <span>≤ 175
x^2 + 18x </span><span>≤ 175
Using completing the square method:
x^2 + 18x + 81 </span><span>≤ 175 + 81
(x + 9)^2 </span><span>≤ 256
|x + 9| </span><span>≤ sqrt(256)
|x + 9| </span><span>≤ +-16
-16 </span>≤ x + 9 <span>≤ 16
</span>-16 - 9 ≤ x <span>≤ 16 - 9
</span>-25 ≤ x <span>≤ 7
</span><span>
But x > 0 (there are no negative measurements):
</span><span>
Therefore, the interval 0 < x </span><span>≤ 7 represents the possible widths.</span><span>
</span>
Answer:C
Step-by-step explanation:
For every function; f(x) = y
Each value of 'x' produces only one output 'y'
A,B and D are not functions because this rule is violated. It is observed that on the graphs of A,B and D, there exists a value of x that produces two outputs(y).
Hence, C is the correct option as it produces only one output 'y' for each value of x.
Answer:
15 and 18
Step-by-step explanation:
Create a system of equations. Let x and y represent the numbers:
y = x + 3
x + y = 33
Solve by substitution, by plugging in the first equation into the second equation as y:
x + y = 33
x + (x + 3) = 33
2x + 3 = 33
2x = 30
x = 15
Find the other number by plugging in 15 as x into the first equation:
y = x + 3
y = 15 + 3
y = 18
So, the numbers are 15 and 18
Refer to the figure shown below.
Because the maximum height of the parabola is 50 m, its equation is of the form
y = ax² + 50
This equation places the vertex at (0,50). The constant a should be negative for the vertex to be the maximum of y.
The base of the parabola is 10 m wide. Therefore the x-intercepts are (5,0) and (-5,0).
Set x=5 and y=0 to obtain
a(5²) + 50 = 0
25a = -50
a = -2
The equation of the parabola is
y = - 2x² + 50
At 2 m from the edge of the tunnel, x = 5 - 2 = 3 m.
Therefore the height of the tunnel (vertical clearance) at x = 3 m is
h = y(3)
= -2(3²) + 50
= - 18 + 50
= 32 m
Answer: 32 m
Answer:
<em>2 - 4i</em>
Step-by-step explanation:
Given the complex number 10/1+2i, to write this in the form a + bi, we will rationalize the function as shown;
= 10/1+2i * 1-2i/1-2i
= 10(1-2i)/(1+2i)(1-2i)
= 10-20i/(1-2i+2i-4i²)
= 10-20i/1-4(-1)
= 10-10i/1+4
= 10-20i/5
= 10/5 - 20i/5
= 2 - 4i
<em>Hence the expression in the form a + bi is 2 - 4i</em>