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3 years ago

Can the set of numbers 8,12,4 make a triangle? And if it can, does it make a right triangle

Mathematics

1 answer:

bagirrra123 [75]3 years ago

4 0

Answer:

Step-by-step explanation:

The sum of the shorter two lengths is exactly equal to the longer length. The "triangle" made by these segments will look like a line segment of length 12. It will have zero area.

Many authors would tell you this is <em>not a triangle</em>. (Others will tell you it is a triangle—a degenerate case.)

_____

These numbers are an arithmetic sequence. The ratio of lengths is 1 : 2 : 3. The only arithmetic sequence of side lengths that makes a right triangle are those in the ratio 3 : 4 : 5.

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Describe how you would estimate the square root of 100

max2010maxim [7]

I am not completely sure but Khan Academy might show how to do that. Or it might at least give an example.

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3 years ago

A regular hexagonal prism has an edge length 12 cm, and height 10 cm. Identify the volume of the prism to the nearest tenth.

Alexeev081 [22]

Check the picture below.

so the volume will simply be the area of the hexagonal face times the height.

$\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\stackrel{\qquad degrees}{\cot\left( \frac{180}{n} \right)}~~ \begin{cases} n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{side}\\[-0.5em] \hrulefill\\ n=6\\ s=12 \end{cases}\implies A=\cfrac{1}{4}(6)(12)^2\cot\left( \frac{180}{6} \right) \\\\\\ A=216\cot(30^o)\implies A=216\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the hexagon}}{(216\sqrt{3})}~~\stackrel{height}{(10)}\implies 2160\sqrt{3}~~\approx ~~3741.2~cm^3$

6 0

1 year ago

Jackson is starting an exercise program. The first day he will spend 30 minutes on the treadmill. He will increase his time on t

yulyashka [42]

Answer:

40 minutes.

Step-by-step explanation:

time spent on the thread mill as a function of d(day) = t(d)

= 30 +2(d-1) minutes

[where d represents day number]

(when d is 1 the time spent should be 30

so substitute d=1 and check it will be 30 only.

on first day he will spend 30 minutes so, I added 30 .

and on every additional day( these additional days are excluding first day), he will increase the time by 2 minutes.so, I added 2(d-1) to initial 30 minutes)

so, T(6), the minutes he will spend on the treadmill on day 6=

=30+2(6-1)

=30+2(5)

=30+10

=40 minutes

3 0

3 years ago

Rachel is 40 cm taller than Lucy. Rachel is 25 percent taller than Lucy. How tall is Lucy? Explain

tatyana61 [14]

What is 40cm 25% of?
The answer is 160cm.

Rachel is 160cm. 160 - 40 = 120.

Lucy is 120cm tall.

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2 years ago

Complete the sentence below. A function f is _____ on an open interval I if, for any choice of x1 and x2 in I, with x1less th

mojhsa [17]

Answer:

Increasing if f' >0 and decreasing if f'<0

Step-by-step explanation:

Difference quotient got by getting

$\frac{f(x+h)-f(x)}{h}$ will be greater than 0 if function is increasing otherwise negative

Here h is a small positive value.

In other words, we find that whenever first derivative of a function f(x) is positive the function is increasing.

Here given that for x1, x2 where x1<x2, we have

if f(x1) <f(x2) then the function is decreasing.

Or if x1<x2 and if f(x1) >f(x2) for all x1, and x2 in I the open interval we say f(x) is decreasing in I.

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3 years ago