15. A boat travels 30 miles upstream in 4 hours. The trip downstream takes 2.5 hours. Find the rate of the boat in still water.
33. Solve the following: (q + 2)^2 = 25
34. Solve the following: y^2 + 6y + 9 =49
39. How many real roots are there for the equation x^2 + 3x -1?
Thanks
-MC
15.
You have posted this same question before and it was answered for you.
You should make a log of all the questions and their times you post, and check before posting it again.
33. very simple, take √ of both sides to get
q+2 = ± 5
q = 2 ± 5 or 7 and -3
34. the left side is a perfect square so your equation becomes
(x+3)^2 = 49 and now follow the steps of #33
39. You don't have an equation, it should be
x^2 + 3x - 1 = 0 perhaps ?
If so, evaluate b^2-4ac
= 9-4(1)-1) = 13
so you would have two real roots
Please acknowledge so we know that you actually read these replies.
Thank you for your help!
-MC
welcome
15. To find the rate of the boat in still water, we can use the formula: rate of boat in still water = (rate downstream + rate upstream) / 2.
Let's start by finding the rate downstream. The distance traveled downstream is 30 miles and it took 2.5 hours. Therefore, the rate downstream is 30 miles / 2.5 hours = 12 miles per hour.
Next, let's find the rate upstream. The distance traveled upstream is also 30 miles, but it took 4 hours. Therefore, the rate upstream is 30 miles / 4 hours = 7.5 miles per hour.
Now we can find the rate of the boat in still water by adding the rate downstream and the rate upstream, and then dividing by 2:
Rate of boat in still water = (12 miles per hour + 7.5 miles per hour) / 2 = 19.5 miles per hour.
So, the rate of the boat in still water is 19.5 miles per hour.
33. To solve the equation (q + 2)^2 = 25, we can take the square root of both sides of the equation. However, we need to consider both the positive and negative square root.
(q + 2)^2 = 25
Taking the square root of both sides:
q + 2 = ±√25
Simplifying:
q + 2 = ±5
Now, let's solve for q:
q = -2 + 5 = 3
q = -2 - 5 = -7
So, the values of q that satisfy the equation are q = 3 and q = -7.
34. To solve the equation y^2 + 6y + 9 = 49, we can start by subtracting 49 from both sides of the equation:
y^2 + 6y + 9 - 49 = 0
Simplifying:
y^2 + 6y - 40 = 0
Now, we can factor the quadratic equation:
(y + 10)(y - 4) = 0
Setting each factor equal to zero:
y + 10 = 0 or y - 4 = 0
Solving for y:
y = -10 or y = 4
So, the values of y that satisfy the equation are y = -10 and y = 4.
39. To determine the number of real roots of the equation x^2 + 3x - 1, we can use the discriminant, which is the expression inside the square root of the quadratic formula.
The discriminant is given by the formula: b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c.
In this case, the coefficients are a = 1, b = 3, and c = -1. Now, let's calculate the discriminant:
b^2 - 4ac = (3)^2 - 4(1)(-1)
= 9 + 4
= 13
Since the discriminant is positive (13 > 0), the equation x^2 + 3x - 1 has two real roots.
Therefore, the equation x^2 + 3x - 1 has two real roots.