2x2-5x-18=0
Two solutions were found :
x = -2
x = 9/2 = 4.500
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2x2 - 5x) - 18 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2-5x-18
The first term is, 2x2 its coefficient is 2 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -18
Step-1 : Multiply the coefficient of the first term by the constant 2 • -18 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -5 .
-36 + 1 = -35
-18 + 2 = -16
-12 + 3 = -9
-9 + 4 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4
2x2 - 9x + 4x - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-9)
Add up the last 2 terms, pulling out common factors :
2 • (2x-9)
Step-5 : Add up the four terms of step 4 :
(x+2) • (2x-9)
Which is the desired factorization
Equation at the end of step 2 :
(2x - 9) • (x + 2) = 0
Step 3 :
Theory - Roots of a product :
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Answer:
Step-by-step explanation:
Fibro dndhdjdjdjudjdhdhdjd
Answer:
Girls to boys = 1:2
Girls to students = 1:3
Boys to students = 2:3
Step-by-step explanation:
So, let's subtract the number of girls from the number of students in the class:
60 - 20 = 40
This means that for every 20 girls there are 40 boys in the ratio of girls to boys:
20:40
This can be simplified down by factoring, here we can divide by 20:
(20 ÷ 20) : (40 ÷ 20)
1:2
So the ratio of girls to boys is 1:2
The ratio of boys to students can be calculated via:
40:60
This can be simplified by dividing by 20 again:
(40 ÷ 20) : (60 ÷ 20)
2:3
So the ratio of boys to students is 2:3
The ratio of girls to students can be put in a ratio of:
20 : 60
This can be simplified down by dividing by 20:
(20 ÷ 20) : (60 ÷ 20)
1:3
So the ratio of girls to students is 1:3
Hope this helps!
Answer:
what is the question?
Step-by-step explanation:
Given:
Big cone : diameter = 12 cm ; height = 18 cm ; base = 14 cm
Small cone: diameter = 12 cm ; height = 6 cm ; base = 14 cm
Volume of a cone-shaped container = π r² h/3
Big cone:
V = 3.14 * (6cm)² * 18cm/3
V = 3.14 * 36cm² * 6cm
<span>V = 678.24 cm³
</span>Small cone:
V = 3.14 * (6cm)² * 6cm/3
V = 3.14 * 36cm² * 2cm
<span>V = 226.08 cm³
</span>Big cone - small cone = volume of water
678.24 cm³ - 226.08 cm³ = 452.16 cm³
