If triangle ghj is congruent to triangle lmk, with a scale factor of 5:6, find the perimeter of triangle ghj

Mathematics

1 answer:

3241004551 [841]3 years ago

6 0

Answer: 35

Step-by-step explanation:

1. By definition, the perimeter of a triangle is the sum of the lenght of each side.

2. Then, the perimeter of the triangle LMK is:

$P_{LMK}=14+17+11\\P_{LMK}=42$

3. If both triangles are congruent and the scale factor is 5:6 (Which you can rewrite as a fraction: 5/6), you must multiply the perimeter of the triangle LMK by this scale factor.

4. Then, you have that the perimeter of the triangle GHJ is:

$P_{GHJ}=42*\frac{5}{6}=35$

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A business executive bought 40 stamps for

alekssr [168]

Answer:

32 33-cent stamps, 8 23-cent stamps

Step-by-step explanation:

In order to solve this question, we need to set up a system of equations. Also known as solving for two variables (the number of each stamp).

Let's set x to be the number of 33-cent stamps. Similarly, let's set y to be the number of 23-cent stamps.

To make our first equation, let's think about the number of stamps total we have. We can say:

$x + y =40$

(AKA - The number of 33-cent stamps, plus the number of 23-cent stamps, equals 40 stamps.)

Now, let's make an equation for the cost of these stamps.

$0.33x + 0.23y = 12.40$

(AKA - The cost of the stamps in total, should equal $12.40).

So now, we have our two equations:

$x + y =40\\0.33x+0.23y=12.40$

If you have a TI-84 graphing calculator, you can go to apps -> polysmlt2 -> simultaneous eqn solver, and then input these equations into the menu. This will solve the problem for you.

If you need to do this manually, let's use substitution. Condense our first equation to make it more substitutable.

$x+y=40\\x=40-y$