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Damm [24]
3 years ago
9

How do graphs and equations reveal information about a relationship between two quantities

Mathematics
1 answer:
fiasKO [112]3 years ago
3 0
Graph and equation both shows the proportional comparison between two quantities

for example, equation y = 4x, this means, the value of 'y' will always be 4 times the value of 'x'

More complex equation such as y = 3x + 5, means that the value of 'y' equals to 5 more triples of value of 'x'

Another example is the conversion graph attached below, it shows the relationship between kilometers and miles. For example, we want to find out how many miles are in 10 kilometers, we would draw a line from the point that shows 10 km towards the graph, then across from the graph to miles, and we'd get a reading of 12 miles.

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The length is 2 feet longer than the width. The perimeter is 36 feet, what is the length?
SOVA2 [1]

Answer:

The length would be 10ft and the width would be 8ft

Step-by-step explanation:

For the purpose of this, we'll set the width as x. We can then define the length as x + 2 since we know it is 2 ft longer than the width. Now we can use those along with the perimeter formula to solve for the width.

P = 2l + 2w

36 = 2(x + 2) + 2(x)

36 = 2x + 4 + 2x

36 = 4x + 4

32 = 4x

8 = x

Now since we know that the width is 8ft, we can add 2ft to it to get the length, which would be 10ft.

4 0
3 years ago
Which of the following is a factor of 24x6 − 1029y3?
amid [387]

Answer:

The answer to your question is only the second and the third are factors.

Step-by-step explanation:

Find the factors of               24x⁶ − 1029y³

First find the prime factors of 24 and 1029

  24  2                1029 3

  12   2                  343 7                  Then 24 = 2³3

   6   2                    49  7                         1029 = 7³ 3

   3   3                       7  7

   1                             1

     x⁶ = (x²)³                  y³ = y³

Then

                                  2³3(x²)³  -  7³ 3  y³

Factor 3                    3[  2³(x²)³  -  7³ y³]

Factor                      3 [ (2x² - 7y)(4x⁴ + 14x²y + 49y²)]

Then

24

2x2 + 7y

4x4 + 14x2y + 49y2

All of the above

8 0
3 years ago
Read 2 more answers
Angelita and Cynthia like to play a video game against each other that is scored by round. The goal is to
REY [17]

Answer:

0.80

Step-by-step explanation:

Khan told me

8 0
2 years ago
Please help I’m really confused and need to learn this
egoroff_w [7]

Answer:

2.

Step-by-step explanation:

For #2, another way to word this question is: For which of the following trig functions is π/2 a solution? Well, go through them one by one. If you plug π/2 into sinθ, you get 1. This means that when x is π/2, y is 1. Try and visualize that. When y is 1, that means you moved off the x-axis; so y = sinθ is NOT one of those functions that cross the x-axis at θ = π/2. Go through the rest of them. For y = cos(π/2), you get 0. At θ = π/2, this function crosses the x-axis. For y = tanθ, your result is undefined, so that doesn't work. Keep going through them. You should see that y = secθ is undefined, y = cscθ returns 1, and y = cotθ returns 0. If you have a calculator that can handle trig functions, just plug π/2 into every one of them and check off the ones that give you zero. Graphically, if the y-value is 0, the function is touching/crossing the x-axis.

Think about what y = secθ really means. It's actually y = 1/(cosθ), right? So what makes a fraction undefined? A fraction is undefined when the denominator is 0 because in mathematics, you can't divide by zero. Calculators give you an error. So the real question here is, when is cosθ = 0? Again, you can use a calculator here, but a unit circle would be more helpful. cosθ = π/2, like we just saw in the previous problem, and it's zero again 180 degrees later at 3π/2. Now read the answer choices.

All multiples of pi? Well, our answer looked like π/2, so you can skip the first two choices and move to the last two. All multiples of π/2? Imagine there's a constant next to π, say Cπ/2 where C is any number. If we put an even number there, 2 will cut that number in half. Imagine C = 4. Then Cπ/2 = 2π. Our two answers were π/2 and 3π/2, so an even multiple won't work for us; we need the odd multiples only. In our answers, π/2 and 3π/2, C = 1 and C = 3. Those are both odd numbers, and that's how you know you only need the "odd multiples of π/2" for question 3.

6 0
3 years ago
Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, port
GrogVix [38]

Answer:

a=49.5 -1.28*15=30.3

So the value of height that separates the bottom 10% of data from the top 90% is 30.3.  

If the score is lower than 30.3 we consider this score as risk averse

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X \sim N(49.5,15)  

Where \mu=49.5 and \sigma=15

We are interested in the bottom 10% of the data.

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.9   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.1 of the area on the left and 0.9 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.1 and P(z>-1.28)=0.9

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-1.28

And if we solve for a we got

a=49.5 -1.28*15=30.3

So the value of height that separates the bottom 10% of data from the top 90% is 30.3.  

If the score is lower than 30.3 we consider this score as risk averse

7 0
2 years ago
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