Answer:
The extremes are 5 and 64.
The middle terms are 80 and 4.
Step-by-step explanation:
Given the proportion:
5 : 80 :: 4 :64
To find:
The extreme and middle terms of the given proportion.
Solution:
The given statement is in proportion if and only if the product of extremes i.e. the numbers at both the ends is equal to the product of middle numbers.
OR
First number 
Fourth number = Second number Third number
First of all, let us check the two products.
5 64 = 320
And the second product:
80 4 = 320
The product is same therefore, the given numbers are in proportion.
The extreme terms are the first and the fourth numbers.
i.e. The extremes are 5 and 64.
The middle terms are 80 and 4.
Answer:
13 cm
Step-by-step explanation:
The diagonal of a rectangle forms a right triangle; where the diagonal is a hypotenuse, and two sides of the rectangle are legs.
Using pythagorean's theorem (
), we can say:
The hypotenuse is equal to 13cm.
Please, use " ^ " to denote exponentiation: p(t) = t^2 + 5t + 6.
To find the critical points, differentiate p(t) with respect to t, set the result = to 0, and then solve the resulting equation for t:
p '(t) = 2t + 5 = 0
Solving for t: 2t = -5, and so t = -5/2. (-5/2, p(-5/2)) is the critical point. That evaluates to (-5/2, -0.25). This happens to be the vertex of a parabola that opens up.
2/5 ≥ x - (4/5). add 4/5 to each side
6/5 ≥ x
X+y = 4, -----> y=4 - x
x² +(4-x)² =16
x² +16-2*4x+x² =16
2x² - 8x = 0
x(2x-8) = 0
2x-4=0, 2x=8, x=4
x=0 or x=4
If x=0, y=4-x=4-0=4.
If x=4, y= 4-x=4-4=0.
(0,4) or (4,0)
Check
x² +y² =16
For (0,4)
0²+4² =16
16 =16 True
For (4,0)
4² +0²=16
16=16 True
Answer (0, 4) and (4,0).
