2x+3 + 3x-4 + 2x+3 + 3x-4 = 78
10x -2 = 78
10x = 80
x=8
deck is 2(8)+3 by 3(8)-4, or 19 by 20
Solution: For finding QR we need to apply Pythagoras Theorem
What is Pythagoras Theorem ?
ans : Pythagoras Theorem is the sum of square of two sides which is equal to the third side or the hypotenuse. This formula is valid oy incase of Right-Angled Traingle because one of three angles here is 90°
According to this law let's apply it in the diagram shown here.
- (Hypotenuse)² = (Adjacent)² + (Opposite)²
- (5x - 2)² = (QR)² + (3x - 1)²
- (QR)² = (5x - 2)² - (3x - 1)²
After factorising both of them we get
- (QR)² = 25x² - 20x + 4 - (9x² - 6x + 1)
- (QR)² = 25x² - 20x + 4 - 9x² + 6x - 1
So, QR is √(16x² - 14x + 3)
Answer:
D 36
Step-by-step explanation:
<em>Write the information algebraically</em>
c = 3a
c + a = 48
c = children, a = adults
<em>In the second sentence (in bold), we can replace c with 3a</em>
c + a = 48 → 3a + a = 48
<em>Simplify</em>
3a + a = 48 → 4a = 48 → a = 12 (divide both sides by 4)
<em>We can then substitute or plug in a = 12 into the original equation:</em>
c + a = 48 → c + 12 = 48 → c = 36 (subtract 12 from both sides)
<h3>There are 36 children</h3>
Answer:
(x − 5)² + (y − 4)² = 4²
(x − 5)² + (y + 4)² = 4²
Step-by-step explanation:
x=1 and x=9 are vertical lines. If both are tangent to the circle, then the circle has a diameter of 8, or a radius of 4, and the center of the circle is on the line x=5.
y=0 is the x-axis. Since the circle is tangent to that, the center of the circle is either 4 units above the x-axis or 4 units below.
So two possible equations of the circle are:
(x − 5)² + (y − 4)² = 4²
(x − 5)² + (y + 4)² = 4²
Here's a graph: desmos.com/calculator/9e4lxx731u
