Answer:
They have the same x-value
f(x) has the greater minimum
Step-by-step explanation:
To find the vertex of a second degree equation, in this case the minimum value, we can use the following equation:
x = -b / 2a
Remember that a second degree equation has the following form:
ax^2 + bx + c
so a = 1, b = -8 and c = 7. Now you have to substitute in the previous equation
x = - (-8) / 2(1)
x = 8 / 2
x = 4
This means that the two functions have the same x-value.
The y value of f(x) would be
f(4) = (4)^2 - 8(4) + 7
f(4) = 16 - 32 + 7
f(4) = -9
So the vertex, or minimun value of f(x) would be at the point (4, -9).
The vertex, or minimun value of g(x) is at the point (4, -4).
So f(x) has a minimum value of -9 and g(x) a minimum value of -4.
Answer:
All represent the three sides of the triangle.
Step-by-step explanation:
The question seeks to test your knowledge of the Triangle Inequality Theorem.
The Triangle Inequality Theorem states that the summation of any 2 sides of a triangle must be greater than the measure of the third side.
Note: This rule must be satisfied for all 3 conditions of the sides.
The answer is all can represent the three sides of the triangle.
Options (6 cm, 22 cm, 10 cm), (7 cm, 25 cm, 11 cm), (9 cm, 22 cm, 11 cm) and (10 cm, 14 cm, 23 cm) satisfies the Triangle Inequality Theorem and all represent the three sides of the triangle.
Answer:
(a) 4.148 x 10^(12) ways
(b) 5,827,360 ways
Step-by-step explanation:
Number of Demonstrators (D) = 44
Number of Repudiators (R) = 56
(a)
5 senate members must be Repudiators and 5 must be demonstrators, assuming that the order at which they are selected is irrelevant:
![N= C^{D}_{5} * C^{R}_{5}\\N=\frac{56!}{5!(56-5)!} *\frac{44!}{5!(44-5)!} \\N=3,819,816*1,086,008\\N=4.148 *10^{12}](https://tex.z-dn.net/?f=N%3D%20C%5E%7BD%7D_%7B5%7D%20%2A%20C%5E%7BR%7D_%7B5%7D%5C%5CN%3D%5Cfrac%7B56%21%7D%7B5%21%2856-5%29%21%7D%20%2A%5Cfrac%7B44%21%7D%7B5%21%2844-5%29%21%7D%20%5C%5CN%3D3%2C819%2C816%2A1%2C086%2C008%5C%5CN%3D4.148%20%2A10%5E%7B12%7D)
(b)
Since there are two different positions, (speaker and vice speaker), order is important in this situation, and the total number of ways to select two senators from each party is:
![N= P^{D}_{2} * P^{R}_{2}\\N=\frac{56!}{(56-2)!} *\frac{44!}{(44-2)!} \\N=3,080*1,892\\N=5,827,360](https://tex.z-dn.net/?f=N%3D%20P%5E%7BD%7D_%7B2%7D%20%2A%20P%5E%7BR%7D_%7B2%7D%5C%5CN%3D%5Cfrac%7B56%21%7D%7B%2856-2%29%21%7D%20%2A%5Cfrac%7B44%21%7D%7B%2844-2%29%21%7D%20%5C%5CN%3D3%2C080%2A1%2C892%5C%5CN%3D5%2C827%2C360)
Point Form:
(5/7, 12/7)
Equation Form:
x= 5/7, y= 12/7
22×2= 44 (for the pants)
92-44= 48 (total for shirts)
48÷4 (total number of shirts)= 12 per shirt