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aliya0001 [1]
2 years ago
5

How many unique triangles can be drawn with side lengths 8 in., 12 in., and 24 in.? Explain. A. Any three sides form a unique tr

iangle, so these lengths can be used to draw exactly 1 triangle. B. If you draw two of the sides together, the third side could angle in or out from the existing angle, so these lengths can be used to draw exactly 2 triangles. C. Two of the side lengths add to a sum that is less than the third side length, so these lengths cannot be used to draw any triangles. D. Any three sides form many triangles with different angles, so these lengths can be used to draw infinitely many triangles. i need help quick please
Mathematics
1 answer:
netineya [11]2 years ago
6 0

Answer: C. Two of the side lengths add to a sum that is less than the third side length, so these lengths cannot be used to draw any triangles.

Explanation:

Those two sides in question are 8 and 12. They add to 8+12 = 20, but this sum is less than the third side 24. A triangle cannot be formed.

Try it out yourself. Cut out slips of paper that are 8 units, 12 units, and 24 units respectively. The units could be in inches or cm or mm based on your preference.

Then try to form a triangle with those side lengths. You'll find that it's not possible. If we had the 24 unit side be the horizontal base, so to speak, then we could attach the 8 and 12 unit lengths on either side of this horizontal piece. But then no matter how we rotate those smaller sides, they won't meet up to form the third point for the triangle. The sides are simply too short. Other possible configurations won't work either.

As a rule, the sum of any two sides of a triangle must be larger than the third side. This is the triangle inequality theorem.

That theorem says that the following three inequalities must all be true for a triangle to be possible.

  • x+y > z
  • x+z > y
  • y+z > x

where x,y,z are the sides of the triangle. They are placeholders for positive real numbers.

So because 8+12 > 24 is a false statement, this means that a triangle is not possible for these given side lengths. Therefore, 0 triangles can be formed.

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SashulF [63]
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Adjust the equation so the line passes through the points. Y=x+1
lapo4ka [179]

Answer:

Slope=  

2.000

2.000

​  

=1.000

x−intercept=  

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​  

=−1.00000

y−intercept=  

1

1

​  

=1.00000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-(x+1)=0  

STEP

1

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Equation of a Straight Line

1.1     Solve   y-x-1  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  y-x-1  = 0 and calculate its properties

Graph of a Straight Line :

 

 

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 1/1 so this line "cuts" the y axis at y= 1.00000

 y-intercept = 1/1  =  1.00000  

Calculate the X-Intercept :

When y = 0 the value of x is 1/-1 Our line therefore "cuts" the x axis at x=-1.00000

 x-intercept = 1/-1  = -1.00000  

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 1.000 and for x=2.000, the value of y is 3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 3.000 - 1.000 = 2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  2.000/2.000 =  1.000  

Geometric figure: Straight Line

1.  Slope = 2.000/2.000 = 1.000

2. x-intercept = 1/-1 = -1.00000

3.  y-intercept = 1/1 = 1.00000

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3 years ago
The inequality 7-2/3x &lt; x-8
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Answer:

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Step-by-step explanation:

We know that the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p".

In other words, it is symbolically represented as:

' ~q ~p is the contrapositive of p q '

For example, the contrapositive of "If it is a rainy day, then they suspend the match" is "If they do not suspend the match, then it won't be a rainy day."

Given

p: 2x -5=5

q: 4x-6=14

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Thus, we conclude that:

If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.

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yes

Step-by-step explanation:

um just multiply why am i even here sorry anyway hoped it helped u know u can just google it

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