Answer:
x = 
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
(leg of Δ ABC )² = (part of hypotenuse below it ) × ( whole hypotenuse )
x² = 3 × (3 + 7) = 3 × 10 = 30 ( take the square root of both sides )
x =
The spoke of the wheel serves as the radius of the circle.
To solve for the circumference of the circle, we use this formula:
C = 2πr
42 inches = 2 * 3.14 * r
42 inches = 6.28 * r
42 inches / 6.28 = r
6.69 inches = r
The length of each spoke is 6.69 inches.
7(2x+5)=4x-9-x
14x+35=3x-9
11x = -44
x = -4
7(2*-4+5)=4*-4-9--4
7(-3)=-21
-21=-21. so it checks out and x = -4
#1. 4x^2 + 17 - 15 = 0
Use the roots given, and plug them in to a factored form. Then, foil! It can also be helpful to multiply the equation to get rid of decimals/fractions.
(x - 3/4)(x + 5) = 0
x^2 - 3/4x + 5x - 3 3/4 = 0
x^2 + 4.25 - 3.75 = 0 (multiply everything by 4)
4x^2 + 17 - 15 = 0
#2. y = 0, -4
Both 4y^2 and 16y contain a 4 in the coefficient and a y in the variables. Therefore, we can factor out a 4y from each.
4y(y + 4) = 0
Then, set both parts of the factored equation equal to 0.
4y = 0
y = 0
y + 4 = 0
y = -4
#3. a = 0, -3
Both 6a^5 and 18a^4 contain a 6 in the coefficient and an a in the variables. Therefore, we can factor out a 6a^4 from each.
6a^4(a + 3) = 0
Then, set both parts of the factored equation equal to 0.
6a^4 = 0
a = 0
a + 3 = 0
a = -3
#4. x = -8
We are looking for two terms that multiply to equal a * c, and add up to equal b. We know that 8 + 8 = 16, and 8 * 8 = 64. There are no negatives in this equation, therefore both signs in our factored form are positive.
(x + 8)(x + 8) = 0
x + 8 = 0
x = -8
#5. x = -8, 8
First, subtract 64 from both sides. The key word here is 'factoring.' If this was not present, there is a different way (which may be easier for some).
x^2 = 64
x^2 - 64 = 0
Next, use the difference of two squares property to factor (x - c)(x + c), and set the two binomials equal to 0.
(x - 8)(x + 8) = 0
x - 8 = 0
x = 8
x + 8 = 0
x = -8
Hope this helps!! :)
