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vladimir2022 [97]
3 years ago
5

Write an inequality that would include the point (3,78), (0,312), (5,10) to be part of the solution.

Mathematics
1 answer:
just olya [345]3 years ago
8 0

Answer:

We want to write an inequality with the points (3, 78), (0, 312) and (5, 10) as solutions.

Then the set of the x-values is {0, 3, 5}

The set of the y-values is {10. 78. 312}

So if we wrote an inequality like:

y > 5

It would include all these solutions, because:

10 > 5

78 >  5

312 > 5

And this has no restriction on the x-variable, so all the x-value range can be a solution, meaning that the points (3, 78), (0, 312) and (5, 10) are solutions to that inequality.

Another one (also trivial) can be:

x < 9

because:

3 < 9

0 < 9

5 < 9

And we have no restriction on the y-values, then the points (3, 78), (0, 312) and (5, 10) are solutions to that inequality.

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The altitude of an equilateral triangle is 5 cm. what is the length of a side of the triangle?
Grace [21]

Answer:

The length side of the triangle is \frac{10\sqrt{3}}{3}\ cm

Step-by-step explanation:

we know that

The equilateral triangle has three equal sides and three equal internal angles of measure of 60 degrees each.

Let

b------> the length side of the equilateral triangle

Applying Pythagoras theorem

b^{2}=(b/2)^{2}+5^{2}\\\\ b^{2}-(b/2)^{2}=25\\\\ (3/4)b^{2}=25\\ \\b^{2} =25*4/3\\ \\b=\frac{10}{\sqrt{3}}\ cm\\ \\b=\frac{10\sqrt{3}}{3}\ cm

3 0
3 years ago
the Olympic record for the men's 100m freestyle is 47 seconds. the Olympic record for the women's 50m freestyle is 24 seconds. w
Nikolay [14]

Answer:

Step-by-step explanation:

The unit rate of the 100m race is 2.12... m/s which you get by dividing the 100 meters by the 47 seconds. The unit rate for the 50m race is 2.08... m/s which you get by dividing the 50 meters by the 24 seconds. This means that the record for the 100m race is faster.

5 0
3 years ago
Solve the following system of inequalities graphically on the set of axes below. State
tankabanditka [31]

Answer:

The answer is definitely C

Step-by-step explanation:

Following the system of inequalities will graph this solution best on the graph, it is the inequality represented in the graph.

ur wlcm :)

correct me if im wrong

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6 0
2 years ago
Which of the following describes the behavior of the graph shown over the interval (-2,2)?
sergejj [24]

Hello!

We are trying to describe the behavior of the graph given in the question.

To help us understand how to solve this question, we would need to understand <u>concavity.</u>

There are two types of concavity:

  • Concave <em>up</em>
  • Concave <em>down</em>

When a graph is concave up, the slope of the line would look like a "U".

When a graph is concave down, the slope of the line would look like a "U" that is flipped upside down.

In this case, we can see that the graph is concave down.

We can tell that the <em>slope</em> is negative due to the fact that the slope is going <u>down,</u> which results in the graph having a negative slope.

We can also tell that the graph is decreasing due to the fact that the line is doing downward.

Answer:

C). negative and decreasing

7 0
1 year ago
For each order pair (x,y) , determine whether it is a solution to the inequality 4x-6y_&lt; - 18
anyanavicka [17]

Solution:

Given:

4x-6y\leq-18

To determine if an ordered pair is a solution, we substitute the x and y-values into the inequality and check if it is true.

Thus,

\begin{gathered} For\text{ the point }(-9,-2) \\ x=-9,y=-2 \\ 4x-6y\leq-18 \\ 4(-9)-6(-2)=-36+12=-24 \\ Since\text{ }-24

\begin{gathered} For\text{ the point }(0,3) \\ x=0,y=3 \\ 4x-6y\leq-18 \\ 4(0)-6(3)=0-18=-18 \\ Since\text{ }-18=-18,\text{ then }(0,3)\text{ is a solution} \end{gathered}

\begin{gathered} For\text{ the point }(5,-3) \\ x=5,y=-3 \\ 4x-6y\leq-18 \\ 4(5)-6(-3)=20+18=38 \\ Since\text{ }38>-18,\text{ then }(5,-3)\text{ is not a solution} \end{gathered}

\begin{gathered} For\text{ the point }(8,5) \\ x=8,y=5 \\ 4x-6y\leq-18 \\ 4(8)-6(5)=32-30=2 \\ Since\text{ }2>-18,\text{ then }(8,5)\text{ is not a solution} \end{gathered}

Therefore, the correct answers are selected as shown below;

7 0
1 year ago
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