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3 years ago

How do you subtract fractions?

2 answers:

6 0

Make sure the bottom numbers (the denominators) are the same.
Subtract the top numbers (the numerators). Put the answer over the same denominator.
Simplify the fraction (if needed).

fredd [130]3 years ago

6 0

Answer:

When subtracting factions you need to have both denominators be the same

Let's use an example. . .

Step-by-step explanation:

1. $\frac{3}{4} -\frac{1}{3}$

We can see here our denominators aren't the same. To get them to be equal, we have to multiply them by each other.

2. $\frac{3}{3} \cdot\frac{3}{4} -\frac{1}{3}\cdot \frac{4}{4}$

Notice that when we do multiply, we also have to multiply the top! What's done to the bottom needs to be done to the top.

3. Let's go into the multiplication:

On the left side

Numerator: 3 · 3 = 9

Denominator: 3 · 4 = 12

On the right side

Numerator: 4 · 1 = 4

Denominator: 4 · 3 = 12

4. $\frac{9}{12} -\frac{4}{12}$

Now all we do here is subtract the numerator. The denominator does not get subtracted, it stays the same.

5. $\frac{9}{12} -\frac{4}{12} =\frac{5}{12}$

Tada!

The most important thing to remember is

The denominator needs to be the same, multiply each other to get a like term
What's multiplied at the bottom must also be multiplied at the top
When you get to subtracting, the denominator doesn't subtract, it stays the same

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A ball is thrown into the air with an upward velocity of 38 ft/s. Its height h(t) in feet after t seconds is given by the functi

Karo-lina-s [1.5K]

Answer:

Step-by-step explanation:

In a quadratic modeling free fall, h(t) = -16t² + v₀t + h, h(t) is the height of the object AFTER the fall while h is the initial height of the object. To answer a:

a. The initial height of the object is 7 feet

To find the height, h(t), after 1.5 seconds for b., evaluate the quadratic at h(1.5):

h(1.5) = -16(1.5)² + 38(1.5) + 7 so

b. h(1.5) = 29.5 feet

In order to determine the max height of the object, we need to put this quadratic into vertex form. This is an upside down (negative) parabola, so the vertex represents a max height. It is at the vertex values of (h, k) that we will find the answers to both c and d. To put this into vertex form, we need to complete the square on the quadratic. Do this by first setting the quadratic equal to 0 then moving over the constant to get:

-16t² + 38t = -7

The first rule for completing the square is that leading coefficient has to be a positive 1. Ours is a -16, so we have to factor it out:

-16(t² - 2.375t) = -7

The next rule for completing the square is to take half the linear term, square it, and then add that to both sides. Our linear term is 2.375. Half of that is 1.1875, and 1.1875 squared is 1.41015625. BUT we cannot forget about that -16 sitting out front of those parenthesis. It is a multiplier. That means that we did not just add in 1.41015625, we added in -16(1.41015625):

-16(t² - 2.375t + 1.41015625) = -7 - 22.5625

The reason we do this is to create a perfect square binomial on the left. Writing the left side in terms of our binomial and at the same time simplifying the right:

-16(t - 1.1875)² = -29.5625

We finish it off by adding 29.5625 to both sides and setting the vertex form of the quadratic back equal to y:

y = -16(t - 1.1875)² + 29.5625

From this we can ascertain that the vertex is located at (1.1875, 29.5625)

The answer to c is found in the h coordinate of the vertex which 1.1875.

c. 1.1875 seconds to reach its max height

The answer to d is found in the k coordinate of the vertex which is 29.5625

d. The max height is 29.5625 feet

For e, we will look back to the original function. We determined that h(t) is the height of the object AFTER it falls. If the object falls to the ground, it goes to follow that the height of the object while it is on the ground is 0. We sub in 0 for h(t) and factor to find the times at which the object hits the ground.

Plugging our values into the quadratic formula gives us the times of -.017 seconds and 2.5 seconds. Since we know that time can't EVER be negative, the object hits the ground 2.5 seconds after it was dropped.

Good luck with your quadratics!

6 0

3 years ago

The temperature of magnesium must be at least 650 degrees for the metal to melt. A sample of magnesium is currently 255 degrees.

Agata [3.3K]

The total temperature of the magnesium sample is its original temperature plus the temperature increase which is dependent on time. This total should exceed 650 degrees. Thus, the inequality that best describes the condition is,
255 + 10m ≥ 650
m ≥ 39.5
The answer is letter b.

8 0

4 years ago

Suppose that a random variable X is continuously uniform between the values of 3 and 8. Find the variance of the distribution of

Korolek [52]

The formula of the variance of the distribution of sample mean of a random variable X, which it will denoted by $V(\bar{X}),$ is