Molly Long

12) Solve the unknown y in this question: 3(y+4) = 19

Solution:

y = 2.33

y = 3.23

y = 2.00

y = 3.33

Every measurement has a measurement uncertainty. Discuss how precise and accurate measurement can be achieved in spite of the inherent measurement uncertainty.

a. Take a ruler and measure the height of the textbook three times. Record the three measurements, and discuss the uncertainty in your measurements. Remember to report the smallest markings on your ruler.

Identify and discuss the differences between the terms ‘theories,’ ‘laws,’ and ‘hypotheses.’ Describe ‘controlled conditions.’

Solving by factoring

2a^2-3a =5

Please show your work so I can break it down for my self. Thank you!

Car trips; Stuart’s Subaru travels 280 mi averaging a certain speed. If the car had gone 5 mph faster, the trip would have taken 1 hr less. Find Stuart’s average speed.

I suppose the time taken was t, so the average speed is 280/t

If the average speed had been (280/t) + 5, the trip would have taken t - 1, therefore:

280 / (t - 1) = (280/t) + 5

Multiply through by t(t - 1):

280t = 280(t - 1) + 5t(t - 1)

280t = 280t - 280 + 5t^2 - 5t

5t^2 - 5t - 280 = 0

t^2 - t - 56 = 0

t^2 - 8t + 7t - 56 = 0

t(t - 8) + 7(t - 8) = 0

(t + 7)(t - 8) = 0

t + 7 = 0 or t - 8 = 0

t = -7 or t = 8

But time can't be negative, therefore t = 8

So the average speed is 280/8 = 35mph as his average speed.

The real question is:

How would you check your average speed of 35 is correct?

Also explain how you obtained the important equation:

280 / (t - 1) = (280/t) + 5

using rates.

Please help???

Solve:

t2 + 4t = 1

t^2 + 4t - 1 = 0

using the quadratic formula:

t = [- 4 ± √(20)]/2 = [- 4 ± 2√5]/2 = - 2 ± √5

Can the equation

t2 + 4t = 1

be solved by factoring or not?

Please help?????

Solve by factoring: 4x2 − 12x + 9 = 0

4x² – 12x + 9 = (2x – 3)² = 0

x = 3/2

This is a perfect square trinomial... but how would you check the proposed solution of x = 3/2?

Please help?????

Solve by factoring: 2a^2 + 1 = -3a

Use the discriminate to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.

3x2 + 6x – 5 = 0

Two different imaginary solutions

Two different irrational solutions

Exactly one rational solution

Two different rational solutions

If a stone is tossed from the top of a 230 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 230, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.

In solving the equation (x + 4)(x – 4) = 9, Eric stated that the solution would be

x + 4 = 9 => x = 5

or

(x – 4) = 9 => x = 13

However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.

Factor completely. If a polynomial is prime, state this. Would you also show the important steps leading to your factoring of (2x + 5)(3x + 2). Also which method (e.g. reverse FOIL) was used and the steps in that method?

6x2 + 19x + 10

(2x + 5)(3x + 2)

To check it I use FOIL –

First: 2x • 3x = 6x²

Outside + Inside: 2x • 2 + 5 • 3x = 4x + 15x = 19x

Last: 5 • 2 = 10

which tells me I was right.

So again which factoring method did I use?

Factor completely. Remember to look first for a common factor. If a polynomial is prime, state this.

6p2 − 6q2

6(p² – q²) = 6(p + q)(p – q)

What factoring method did I use here with the whole p^2- q^2?

4x^2 − 12x + 9 = 0

Factor completely. Remember to look first for a common factor. If a polynomial is prime, state this.

6p2 − 6q2

Factor completely. If a polynomial is prime, state this.

6x2 + 19x + 10

Factor: Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative.

10x4 − 30x3 − 50x − 20

Find the product: (2x^2-9y)(2x^2+9y)

Please explain the proceedure.

64x^2-96xy-36y^2

64x^2+36y^2

64x^2-36y^2

64x^2-96xy+36y^2

x^3-1

x^3-x-1

-x^3-x^2-x

x^2+2x