Four times a number +3: 4n+3 is the same as:= 5+ the number.: 5+n 4n+3=5+n
4n-n=5-3
3n=2
N=2/3
The equivalent expression is 8t+32
Answer:
<u>1. 3x^2 + 4x - 5 = 0</u>
<u>x₁ = (-2 + √19)/3</u>
<u>x₂ = (-2 - √19)/3</u>
<u>2. X^2 - 13x + 42 = 0</u>
<u>x₁ = 7</u>
<u>x₂ = 6</u>
Step-by-step explanation:
1. Let's solve for x using the quadratic formula this way:
3x^2 + 4x - 5 = 0
x = [-4 +/- √(4² - 4 * 3 * -5)]/2 * 3
x = [-4 +/- √(16 + 60)]/6
x = [-4 +/- √76]/6
x = [-4 +/- 2√19]/6 (√76 =√4 * 19)
x = -2 +/- √19/3
<u>x₁ = (-2 + √19)/3</u>
<u>x₂ = (-2 - √19)/3</u>
2. Let's solve for x, factoring this way:
X^2 - 13x + 42 = 0
(x - 7) (x - 6) = 0
<u>x₁ = 7</u>
<u>x₂ = 6</u>
Answer:4
Step-by-step explanation:
34-30=4
Answer:
Given :
The diagonal of a rectangle is 2 ✓13 cm.
The length and breadth are in the ratio
3:2.
To find :
The Area of the rectangle.
Solution :
Given that
The ratio of the length and breadth of a rectangle = 3:2
Let they be 3X cm and 2X cm
We know that
The diagonal of a rectangle = √(1²+b³)
units
The diagonal of the rectangle
= √[(3X)³+(2X)³] cm
= √(9x³+4x²) cm
=> √(13X²) cm
=> √13 X cm
According to the given problem
The diagonal of the rectangle = 2√13 cm
=> ✓13 X = 2 √13
=> X = 2√13/√13
=> X = 2 cm
If X = 2 cm then 3X=3(2) = 6 cm
If X = 2 cm then 2X = 2(2)=4 cm
Length = 6 cm
Breadth = 4 cm
We know that
Area of a rectangle = length breadth sq.units
Area of the given rectangle = 6 cm x 4 cm
= 24 cm²