PART A:
The given quadratic equation is 2x²-10x-8=0
The radicand is given by b²-4ac where a, b, and c are the constants in a quadratic form ax²+bx+c
From the given equation, we have
a = 2
b = -10
c = -8
Radicand b²-4ac = (-10)² - 4(2)(-8) = 100 + 64 = 164
The radicand is >0 hence the quadratic equation has two distinct roots
PART B:
4x²-12x+5 = 0
We can use the factorization method to solve the equation
Firstly, we multiply 4 by 5 to get 20
Then we find the pair of numbers that multiply gives 20 and sum gives -12
The pair of number is -2 and -10
Rewriting the equation
4x²-2x-10x+5 = 0
2x(2x-1)-5(2x-1) = 0
(2x-1)(2x-5) = 0
2x-1 = 0 and 2x-5 = 0
x = 1/2 and x = 5/2
Lets calculate how much she walks each weeks and then we multiply that by the number of weeks.
weekWalk = 5(2) + 3 = 10 + 3 = 13
therefore, she walks 13 miles per week, if she walked for 29 weeks then we have:
total walked =(29)(13) = 377
so she walked 377 miles total, so her original estimate is not reasonable
The volume of a rectangular prism is L * W * H.
We are looking for whole numbers that multiply to 28.
There are 10 possible molds.
L, W, H
-------------
28, 1, 1
1, 1, 28
14, 2, 1
1, 14, 2
1, 2, 14
7, 4, 1
4, 1, 7
7, 1, 4
7, 2, 2
2, 2, 7
Answer:
<h2>The volume of water in the vase is 339.33 in^3</h2>
Step-by-step explanation:
To calculate the volume of water in the vase we need the following parameters
1. the diameter/radius of the vase
2. the height /level of water in the vase
Given data
diameter d= 6 in
radius = d/2= 6/2 = 3 in
height of water h= 12 in
we know that the expression for the volume of a cylinder is given as
Inserting our data we have
