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baherus [9]
3 years ago
7

How many different triangles can you make with the following conditions: angles measuring 45 degrees and 90 degrees and an INCLU

DED side that is 1 inch? one more than one none
Mathematics
1 answer:
kotykmax [81]3 years ago
3 0

Answer:

One

Step-by-step explanation:

Clearly, one triangle can be constructed as the angles 45 and 90 do not exceed 180 degrees. (so "None" is not correct)

To show that only one such triangle exists, you can apply the Angle-Side-Angle theorem for congruence.

Since one triangle can be constructed, it remains to be shown that no additional triangle that is not congruent to the first one can be created: I will use proof by contradiction. Let a triangle ABC be constructed with two angles 45 and 90 degree and one included side of length 1 inch. Suppose, I now construct a second triangle that is different from the first one but still has the same two angles and included side. By applying the ASA theorem which states that two triangles with same two angles and one side included are congruent, I must conclude that my triangle is congruent to the first one. This is a contradiction, hence my original claim could not have been true. Therefore, there is no way to construct any additional triangle that would not be congruent with the first one, and only one such triangle exists.

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Rajan had 30 dollars to spend on 3 gifts. He spent 9 1 4 dollars on gift A and 5 4 5 dollars on gift B. How much money did he ha
Lyrx [107]

Answer:

$15 1/10

Step-by-step explanation:

Given that :

Total amount to spend = $30

Amount spent on Gift A = $9 1/4

Amount spent on Gift B = $5 4/5

Amount left to spend on gift C ;

$30 - (9 1/4 + 5 4/5)

$30 - (37/4 + 29/5)

$30 - (185 + 116)/20

$30 - 298/20

30/1 - 298/20

$(600 - 298) / 20

$302/20

$15 2/20

= $15 1/10

3 0
3 years ago
The polynomial 3x2 – 10x + 8 has a factor of 3x – 4. What is the other factor of 3x2 – 10x + 8?
anyanavicka [17]

Answer:

Second factor is (x - 2).

Step-by-step explanation:

The given polynomial is 3x² -10x + 8 has a factor (3x - 4) and we have to find the other factor.

Now we will factorize the given polynomial to get the other factor.

3x² - 10x + 8

[ Here 8×3 = 24( multiplication of constant term 8 and coefficient of highest degree term) and 6 + 4 = 10 ]

= 3x² - 6x - 4x + 8

= 3x(x - 2) - 4(x - 2)

= (3x -4)(x -2)

In this factorized form we get two factors as (3x -4) and (x -2).

Therefore the second factor is (x - 2).

6 0
3 years ago
Read 2 more answers
What are the solutions to the equation below ?<br>6x^2+4x=0
Brrunno [24]
I hope this helps!?!?

5 0
3 years ago
PLEASE HELP 20 POINTS
labwork [276]

Answer:

Step-by-step explanation:

You can simply count the number of unit cubes.

There are 11 cubic units.

6 0
3 years ago
What is the Y intercept of the equation Y equals 8X -24
kiruha [24]

Answer:

24

Step-by-step explanation:

y intercept formula

y=mx+b

b is the y intercept

7 0
3 years ago
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