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4 years ago

If RT=36, find the value of x

1 answer:

8 0

Answer:

Step-by-step explanation:

So we know that RT is 36.

Note that RT is the combined length of RS and ST. Therefore:

$RT=RS+ST$

Substitute. RT is 36, RS is 6x+1 and ST is x+7:

$36=(6x+1)+(x+7)$

Combine like terms and add:

$36=7x+8$

Subtract 8 from both sides:

$28=7x$

Divide by 7:

$x=4$

So, our answer is 4 :)

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Ipatiy [6.2K]

Using the combination formula, it is found that photos of 9 different chairs were shown to the home owner.

The order in which the chairs are chosen is important, hence, the <em>permutation formula </em>is used to solve this question.

<h3>What is the permutation formula?</h3>

$P_{n,x}$ is the number of different permutations of x objects from a set of n elements, given by:

$P_{n,x} = \frac{n!}{(n-x)!}$

In this problem, two chairs are chosen from a set of n, and there are 72 different outcomes, hence:

$P_{n,x} = 72, x = 2$

$P_{n,x} = \frac{n!}{(n-x)!}$

$72 = \frac{n!}{(n-2)!}$

$72 = \frac{n(n - 1)(n - 2)!}{(n-2)!}$

$n^2 - n = 72$

$n^2 - n - 72 = 0$

Which is a quadratic function with coefficients $a = 1, b = -1, c = -72$ , hence:

$\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-72) = 289$

Taking the positive root:

$x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{289}}{2} = 9$

Photos of 9 different chairs were shown to the home owner.

You can learn more about the permutation formula at brainly.com/question/25925367

3 0

3 years ago

Leni [432]

The transformations which can lead to the red square image of the blue Square are; Translation, Reflection, Rotation.

<h3>What transformations lead to the image?</h3>

Translation is when we slide a figure in any direction. The translation of the shape can be by moving the blue leftward or rightward and the then downward.
Reflection is when we flip a figure over a line. The reflection involves reflect the blue Square over the line; y = x.
Rotation is when we rotate a figure a certain degree around a point. The rotation is by rotating the blue Square over 180⁰.