Answer:
When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Vertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex
Answer:
y = 312x + 2
Step-by-step explanation:
According to y = mx + b, m stands for slope and b stands for y-intercept. Let us find the y-intercept. To find the y-intercept, the x should be zero in (x, y).
(x, y)
(0, 2) ---> y-intercept (b)
Now that we have found the y-intercept, we will now find the slope by using its formula.
Slope formula:-
m = y2 - y1 / x2 - x1
Pick two random (x, y). I will pick the first and last pairs.
(0, 2) and (4, 1250)
Now plug these two pairs in the formula.
m = y2 - y1 / x2 - x1
m = 1250 - 2 / 4 - 0
m = 1248 / 4
m = 312
This means that the slope (m) is 312. Now put that in y = mx + b form.
y = mx + b
y = 312x + 2
Both of the forms are the same. Hope this helps, thank you :) !!
Answer:
5:6
Step-by-step explanation:
20/4=5
24/4=6
20:24 ratio simplified is 5:6
sorry if wrong
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.
I believe the answer is 6
