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2 years ago

What is the greatest common factor (gcf) of the numerator and denominator in the rational expression below? 7x+14/2x^2+x-6

1 answer:

4 0

The answer is C. The numerator 7x+14 can be factored as 7(x+2). The denominator 2x^2+2x-6 can be factored as (x+2)(2x-3). The greatest common divisor of 7(x+2) and (x+2)(2x-3) is obviously x+2, which is contained in both of the two expressions.

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In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equatio

Nitella [24]

In the game of cornhole, when Sasha tossed a bean bag to the edge of the hole, in which the equations of the hole and bean bag's path are x² + y² = 5 and y = 0.5x² + 1.5x - 4, respectively, she could have tossed her bean bag to the points (1, -2) or (2, 1).

To find the points in which she could have tossed her bean bag, we need to intersect the two equations of the function as follows.

The equation for the hole

$x^{2} + y^{2} = 5$ (1)

The equation for the path of the bean bag

$y = 0.5x^{2} + 1.5x - 4$ (2)

By entering equation (2) into (1) we have:

$x^{2} + (0.5x^{2} + 1.5x - 4)^{2} = 5$

$x^{2} + 0.25x^{4} + 1.5x^{3} - 4x^{2} + 2.25x^{2} - 12x + 16 = 5$

$0.25x^{4} + 1.5x^{3} - 0.75x^{2} - 12x + 11 = 0$

By solving for x, we have:

x₁ = 1

x₂ = 2

Now, for y we have (eq 2):

x₁ = 1

$y_{1} = 0.5(1)^{2} + 1.5(1) - 4 = -2$

x₂ = 2

$y_{2} = 0.5(2)^{2} + 1.5(2) - 4 = 1$

Therefore, the points are (1, -2) or (2, 1).

To find more about intersections, go here: brainly.com/question/4977725?referrer=searchResults

I hope it helps you!

8 0

1 year ago

Estimate the indicated probability by using normal distribution as an approximation to the binomial distribution. Estimate P(6)

lianna [129]

Answer:

P(6) = 0.6217

Step-by-step explanation:

To find P(6), which is the probability of getting a 6 or less, we will need to first calculate two things: the mean of the sample (also known as the "expected value") and the standard deviation of the sample.

Mean = np

Here, "n" is the sample size and "p" is the probability of the outcome of interest, which could be getting a heads when a tossing a coin, for instanc

So, Mean = n × p = (18) ×(0.30) = 5.4

Next we we will find the standard deviation:

Standard Deviation = $\sqrt{npq}$

n = 18 and p = 0.3 "q" is simply the probability of the other possible outcome (maybe getting a tails when flipping a coin), so q = 1 - p

Standard Deviation = $\sqrt{npq} = \sqrt{(18)(0.3)(0.7)}$

= 1.944

Now calculate the Z score for 6 successes.

Z = ( of successes we're interested in - Mean) ÷ (Standard Deviation)

=(6-5.4) ÷ (1.944) = 0.309

we have our Z-score, we look on the normal distribution and find the area of the curve to the left of a Z value of 0.309. This is basically adding up all of the possibilities for getting less than or equal to 6 successes. So, we get 0.6217.

5 0

1 year ago

Tim was given a large bag of sweets and ate one third of the sweets before stopping as he was feeling sick. The next day he ate

mars1129 [50]

Answer: In the beginning he was given 27 sweets.

Step-by-step explanation: The most logical thing to do is to solve it backwards, that is, from what he had at the end of the third day up till the beginning of the first day.

On the third day he ate one-third and had 8 sweets left over. To determine how many he started with on the third day, let the total on day three be called a. If one-third of a is eaten, then the left over which is two-thirds is 8. That is;

8/a = 2/3

By cross multiplication we now have

8 x 3 = 2a

24/2 = a

a = 12

Let the number of sweets he had on day two be called b. If he ate one-third of b and he had 12 left over, then the two-thirds left over is 12 and we now have;

12/b = 2/3

By cross multiplication we now have

12 x 3 = 2b

36 = 2b

36/2 = b

b = 18

Let the number of sweets he had on day one be called x. If he ate one-third of x and he had 18 left over, then the two-thirds left over is 18, and we now have;

18/x = 2/3

By cross multiplication we now have

18 x 3 = 2x

54 = 2x

x = 27

Therefore Tim was given 27 sweets at the beginning.

3 0

2 years ago

Which of the following best describes the slope of the line below? pls help asap

Harlamova29_29 [7]

Answer:

Step-by-step explanation:

Undefined.

3 0

1 year ago

Read 2 more answers

Is the statement ""For every natural number n ≥ 1 there exists a directed graph of n vertices for which every vertex has an inde

Semenov [28]

Answer:

The given statement is false.

Step-by-step explanation:

Reason

let D be a directed graph with 'n' no of vertices and 'E' edges.

where 'n'=1. thus D =(n,E).

In degree: in directed graph the number of incoming edges on a vertex is known as indegree.

it is denoted as deg ⁺(n).

And now we know that in a directed graph

if deg ⁻(n)= deg ⁺(n) for each vertex n.

5 0

1 year ago