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Mathematics

1 answer:

RUDIKE [14]3 years ago

6 0

The data is larger for intermediate values of x, so the parabola opens downward. That leaves only the 2nd and 4th choices, where the x² coefficient is negative.

To determine which of those is appropriate, it is only necessary to consider x=1. The 2nd choice will give a y-value near 100; the 4th choice will give a y-value near 250.

The fourth choice is appropriate:

... y = -9.16x² +73.04x +183.3

_____

Alternatively, you can consider that for the x-coordinate of the vertex to be positive (it's about +4), the coefficients of the x² and x terms must have opposite signs. Using this consideration, you don't even need to evaluate the expression to determine that the 4th choice is the correct one.

You might be interested in

Colin has several bottles of water. Each bottle of water holds 3 cups. During the day, he drinks 7 cups of water. How many bottl

Natasha_Volkova [10]

Divide total cups he drank by the # of cups in each bottle.

7 ÷ 3= 2.3333

Since each bottle only holds 3 cups, he drank 3 bottles of water. He didn't drink all the water in the third bottle, but he started drinking the third bottle.

ANSWER: 3 bottles

Hope this helps! :)

4 0

3 years ago

√180 can be expressed in the form p√q. where p and q are integers. Find the smallest value of p + q.

frutty [35]

Answer:

The smallest value of p+q is 11

It happens when p = 6 and q = 5.

=======================================================

Explanation:

Let's factor 180 in such a way that exactly one factor is a perfect square.

I'll ignore the trivial factor of 1.

Here are the possible factorizations we could go with:

180 = 4*45

180 = 9*20

180 = 36*5

Those factorizations then lead to the following

$\sqrt{180} = \sqrt{4*45} = \sqrt{4}*\sqrt{45}= 2\sqrt{45}\\\\\sqrt{180} = \sqrt{9*20} = \sqrt{9}*\sqrt{20}= 3\sqrt{20}\\\\\sqrt{180} = \sqrt{36*5} = \sqrt{36}*\sqrt{5}= 6\sqrt{5}\\\\$

Then we have

p+q = 2+45 = 47

p+q = 3+20 = 23

p+q = 6+5 = 11

The smallest value of p+q is 11 and it happens when p = 6 and q = 5.

Side note: p+q is smallest when we go with the largest perfect square factor.

6 0

1 year ago

Ricardo took the following steps to simplify the expression below but was surprised to hear that his answer was incorrect. Which

Xelga [282]

You have not given us any of the steps that Ricardo took to simplify the
expression, and you also haven't given us the list of choices that includes
the description of his mistake, so you're batting O for two so far.
Other than those minor details, the question is intriguing, and it certainly
draws me in.

If Ricardo made a mistake in simplifying that expression, I'm going to say that
it was most likely in the process of removing the parentheses in the middle.

Now you understand that this is all guess-work, because of all the stuff that you
left out when you copied the question, but I think he probably forgot that the 3x
operates on everything inside the parentheses.

He probably wrote that 3x (x-3) is

either 3x² - 3
or x - 9x .

In reality, when properly simplified,

3x (x - 3) = 3x² - 9x .

3 0

3 years ago

Clevon forms a triangle with three straws measuring 20, 25, and 18 inches. To the nearest whole

Ne4ueva [31]

Answer:

Step-by-step explanation:

Let's label this triangle as triangle ABC. Side AB is 18, side BC is 20 and side CA is 25 and the angle we are looking for is angle C. Use the Law of Cosines to find the missing angle. You have to use the Law of Cosines because in order to use the Law of Sines you have to have an angle given and we don't so we have no other options. In our case,

$c^2=a^2+b^2-2abcosC$ which for us looks like this: