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3 years ago

Which dimensions cannot create a triangle?

Mathematics

1 answer:

podryga [215]3 years ago

4 0

Answer:

three angles measuring 109º, 25º, and 145º cannot create a triangle

three angles measuring 40º, 70º, and 65º cannot create a triangle

Step-by-step explanation:

Verify each dimensions

Part 1) three angles measuring 109º, 25º, and 145º

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

In this problem we have

$109^o+25^o+145^o=279^o$

$279^o> 180^o$

therefore

three angles measuring 109º, 25º, and 145º cannot create a triangle

Part 2) three sides measuring 9 m, 15 m, and 9 m

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the triangle inequality theorem

1) 9+15 > 9 ---> is ok

2) 9+9 > 15 ---> is ok

therefore

three sides measuring 9 m, 15 m, and 9 m can create a triangle

Part 3) three angles measuring 40º, 70º, and 65º

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

In this problem we have

$40^o+70^o+65^o=175^o$

$175^o< 180^o$

therefore

three angles measuring 40º, 70º, and 65º cannot create a triangle

Part 4) three sides measuring 6 cm, 8 cm, and 10 cm

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the triangle inequality theorem

1) 6+8 > 10 ---> is ok

2) 8+10 > 6 ---> is ok

3) 6+10 > 8 ---> is ok

therefore

three sides measuring 6 cm, 8 cm, and 10 cm can create a triangle

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Answer:

x = 6

Step-by-step explanation:

Given

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5x - 17 = 13 ( add 17 to both sides )

5x = 30 ( divide both sides by 5 )

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4 years ago

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You could win a giant jar of M&Ms, if only you could guess how many are in the jar. You find a smallerjar such that the gian

sleet_krkn [62]

Answer:

There are 7360 M&Ms in larger jar.

Step-by-step explanation:

We are given the following in the question:

A giant jar is such that it is exactly four times times the smaller jar in dimensions.

If r and h is the radius and height of the cylindrical jar respectively, then the dimensions of the larger are:

$R = 4r\\H=4h$

Number of M&Ms in smaller jar = 115

Volume of smaller jar =

$v = \dfrac{1}{3}\pi r^2 h$

Volume of larger jar =

$V =\dfrac{1}{3}\pi R^2 H=\dfrac{64}{3}\pi r^2 h$

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3 years ago

Let P(1,2,1), Q(1,0,-1), R(2,2,0) be the vertices of a parallelogram with adjacent sides PQ and PR. Find the other vertex S.

ladessa [460]

Given:

The vertices of a parallelogram are P(1,2,1), Q(1,0,-1), R(2,2,0).

PQ and PR are the adjacent sides of the parallelogram.

To find:

The coordinates of vertex S.

Solution:

We know that, the diagonals of a parallelogram bisect each other.

Let the coordinates of the vertex S are (a,b,c).

In the given parallelogram PS and QR are the diagonals. It means their midpoints are same.

$\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{1+2}{2},\dfrac{0+2}{2},\dfrac{-1+0}{2}\right)$

$\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{3}{2},\dfrac{2}{2},\dfrac{-1}{2}\right)$

On comparing both sides, we get

$\dfrac{1+a}{2}=\dfrac{3}{2}$

$1+a=3$

$a=3-1$

$a=2$

Similarly,

$\dfrac{2+b}{2}=\dfrac{2}{2}$

$2+b=2$

$b=2-2$

$b=0$

And,

$\dfrac{1+c}{2}=\dfrac{-1}{2}$

$1+c=-1$

$c=-1-1$

$c=-2$

Hence, the coordinates of vertex S are (2,0,-2).

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