How to break down 29

How many non-congruent triangles can you draw with the given properties? a. Sides measuring 7 inches, 8 inches, and 16 inches b.

Leno4ka [110]

Answer:

The answers are;

a. None

b. None

c. Infinite

d. None

e. None

Step-by-step explanation:

The number of non congruent triangles that can be drawn depends on the uniqueness of the triangle

The parameters of a unique triangle are;

Knowing the Side Side Side (SSS)

Knowing the Side Angle Side (SAS)

Knowing the Angle Side Angle (ASA)

Knowing the Angle Angle Side (AAS)

However, knowing only the Side Side Angle it is possible to draw two non-congruent triangles

Therefore, considering each of the triangles gives;

a. Sides 7 inches, 8 in., and 16 in. which is of the form SSS hence the triangle is well defined and it is not possible to draw two non-congruent triangle with the provided properties

b. Similarly, the given triangle parameters are 4 in., 4 in., and 6 in. which is of the form SSS hence the triangle is well defined and it is not possible to draw two non-congruent triangle with the provided information

c. The parameters of the triangle given here are angles 30°, 60°, and 90° which is of the form Angle Angle Angle, or AAA for which the sides can be scaled to form an infinite number of non-congruent triangles

d. The parameters given are three angles measuring 120° which does not form a triangle as the sum of triangles in a triangle = 180°

Hence the number of non-congruent triangles that can be drawn in this case = 0

e. The parameters given are two angles measuring 45° and one side length of 10 in., hence the parameter is of the forms AAS or ASA hence the triangle is unique and it is not possible to draw two non-congruent triangle with the provided properties.

6 0

3 years ago

GET THIS RIGHT GET BRAINLYEST!!!<br><br> whats 4 plus 4?????

nirvana33 [79]

Answer:

8

Step-by-step explanation:

4+4=8

8 0

3 years ago

the davis' backyard measures 40 ft x90 ft. find the area of their backyardand show how the area could be written using exponents

drek231 [11]

2,100 is the real number. 1,050² is exponent form.

8 0

3 years ago

Mary takes 9 grapes from Robin and then decides to give 4 back Write a subtraction problem to describe how many grapes Robin has

GuDViN [60]

Answer:-9-(-4)

Step-by-step explanation:

You start with -9 and then then when u distribute the - to the -4 it will become - 9+ 4

5 0

4 years ago

Read 2 more answers

A stereo store is offering a special price on a complete set ofcomponents (receiver, compact disc player, speakers, cassette dec

Korvikt [17]

Answer:

Step-by-step explanation:

(a)

The number of receivers is 5.

The number of CD players is 4.

The number of speakers is 3.

The number of cassettes is 4.

Select one receiver out of 5 receivers in $5C_1$ ways.

Select one CD player out of 4 CD players in $4C_1$ ways.

Select one speaker out of 3 speakers in $3C_1$ ways.

Select one cassette out of 4 cassettes in $4C_1$ ways.

Find the number of ways can one component of each type be selected.

By the multiplication rule, the number of possible ways can one component of each type be selected is,

The number of ways can one component of each type be selected is

$=5C_1*4C_1*3C_1*4C_1\\\\=5*4*3*4\\\\=240$

Part a

Therefore, the number of possible ways can one component of each type be selected is 240.

(b)

The number of Sony receivers is 1.

The number of Sony CD players is 1.

The number of speakers is 3.

The number of cassettes is 4.

Select one Sony receiver out of 1 Sony receivers in ways.

Select one Sony CD player out of 1 Sony CD players in ways.

Select one speaker out of 3 speakers in ways.

Select one cassette out of 4 cassettes in $4C_1$ ways.

Find the number of ways can components be selected if both the receiver and the CD player are to be Sony.

By the multiplication rule, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is,

Number of ways can one components of each type be selected

$=1C_1*1C_1*3C_1*4C_1\\\\=1*1*3*4\\\\=12$

Therefore, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is 12.

(c)

The number of receivers without Sony is 4.

The number of CD players without Sony is 3.

The number of speakers without Sony is 3.

The number of cassettes without Sony is 3.

Select one receiver out of 4 receivers in 4C_1 ways.

Select one CD player out of 3 CD players in 3C_1 ways.

Select one speaker out of 3 speakers in 3C_1 ways.

Select one cassette out of 3 cassettes in 3C_1 ways.

Find the number of ways can components be selected if none is to be Sony.

By the multiplication rule, the number of ways can components be selected if none is to be Sony is,

$=4C_1*3C_1*3C_1*3C_1\\\\=108$

[excluding sony from each of the component]

Therefore, the number of ways can components be selected if none is to be Sony is 108.

(d)

The number of ways can a selection be made if at least one Sony component is to be included is,

= Total possible selections -Total possible selections without Sony

= 240-108

= 132

Therefore, the number of ways can a selection be made if at least one Sony component is to be included is 132.

(e)

If someone flips the switches on the selection in a completely random fashion, the probability that the system selected contains at least one Sony component is,

$= \text {Total possible selections with at least one Sony} /\text {Total possible selections}$

= 132 / 240

= 0.55

The probability that the system selected contains exactly one Sony component is,

$= \text {Total possible selections with exactly one Sony} /\text {Total possible selections}$ $\frac{1C_1*3C_1*3C_1*3C_1+4C_11C_13C_13C_1+4C_13C_13C_13C_1}{240} \\\\=\frac{99}{240} \\\\=0.4125$

Therefore, if someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains at least one Sony component is 0.55.

If someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains exactly one Sony component is 0.4125.

6 0

4 years ago