Solution:
we are given that
In the image, shape ABCD is similar to shape WXYZ.
we have been asked to find the measure of side ZW.
As we know that when two shapes are similar then the ratios of their corresponding sides are equal.
So we can write
Hence ZW=4.5 Inches.
Answer:
The values of x for which the model is 0 ≤ x ≤ 3
Step-by-step explanation:
The given function for the volume of the shipping box is given as follows;
V = 2·x³ - 19·x² + 39·x
The function will make sense when V ≥ 0, which is given as follows
When V = 0, x = 0
Which gives;
0 = 2·x³ - 19·x² + 39·x
0 = 2·x² - 19·x + 39
0 = x² - 9.5·x + 19.5
From an hint obtained by plotting the function, we have;
0 = (x - 3)·(x - 6.5)
We check for the local maximum as follows;
dV/dx = d(2·x³ - 19·x² + 39·x)/dx = 0
6·x² - 38·x + 39 = 0
x² - 19/3·x + 6.5 = 0
x = (19/3 ±√((19/3)² - 4 × 1 × 6.5))/2
∴ x = 1.288, or 5.045
At x = 1.288, we have;
V = 2·1.288³ - 19·1.288² + 39·1.288 ≈ 22.99
V ≈ 22.99 in.³
When x = 5.045, we have;
V = 2·5.045³ - 19·5.045² + 39·5.045≈ -30.023
Therefore;
V > 0 for 0 < x < 3 and V < 0 for 3 < x < 6.5
The values of x for which the model makes sense and V ≥ 0 is 0 ≤ x ≤ 3.
<span>2h + 4 = m (twice the value of Helena's age plus 4 will equal Mark's age)
3j - 6 = g (three time John's age minus 6 will equal Glenn's age)
3.35s + .80b = 11.75</span>
Five consecutive integers are:
n, n+1, n+2, n+3, n+4 the sum of which is:
5n+10=265 subtract 10 from both sides
5n=255, divide both sides by 5
n=51
Our fifth number was n+4 so the fifth number is 55
3x^2 = 2(x + 4)
3x^2 = 2x + 8
3x^2 - 2x - 8 = 0
(3x + 4)(x - 2) = 0
3x + 4 = 0
3x = -4
x = -4/3
x - 2 = 0
x = 2
solution is : x = -4/3 or x = 2 <==
