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iren [92.7K]
1 year ago
11

Part 2 of 3

Mathematics
1 answer:
dlinn [17]1 year ago
3 0

Considering that point S splits segment RT, we have that:

a) The value of y is of y = 4.

b) The lengths are: RS = 29, ST = 19.

<h3>How to find the value of variable y?</h3>

Point S splits segment RT into two parts, hence the length of segment RT can be given by the following equation:

RT = RS + ST

The measures are given as follows:

  • RS = 6y + 5.
  • ST = 3y + 7.
  • RT = 48.

Hence we can solve the equation for y, as follows:

RT = RS + ST

6y + 5 + 3y + 7 = 48.

9y = 36.

y = 4.

<h3>What are the lengths of segments RS and ST?</h3>

Considering that y = 4, we have that:

  • RS = 6y + 5 = 6(4) + 5 = 29.
  • ST = 3y + 7 = 3(4) + 7 = 19.

A similar problem, in which a point splits a segment, is given at brainly.com/question/4450896

#SPJ1

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  see below for a graph

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3 years ago
Read 2 more answers
Which of the following represent the values of x, y, and z.
Paraphin [41]

Answer:

Part 1) z=4\sqrt{3}\ units

Part 2) y=4\sqrt{2}\ units

Part 3) x=4\sqrt{6}\ units

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

<em>Find the value of z</em>

In the right triangle DBC

cos(C)=\frac{4}{z} ----> equation A

In the right triangle ABC

cos(C)=\frac{z}{12} ----> equation B

equate equation A and equation B

\frac{4}{z}=\frac{z}{12}

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z=4\sqrt{3}\ units

step 2

In the right triangle DBC

Applying the Pythagoras Theorem

z^{2}=y^{2}+4^{2}

we have

z=4\sqrt{3}\ units

substitute

(4\sqrt{3})^{2}=y^{2}+4^{2}

48=y^{2}+16

y^{2}=48-16

y^{2}=32

y=4\sqrt{2}\ units

step 3

Find the value of x

In the right triangle ABC

Applying the Pythagoras Theorem

12^{2}=x^{2}+z^{2}

we have

z=4\sqrt{3}\ units

substitute

12^{2}=x^{2}+(4\sqrt{3})^{2}

144=x^{2}+48

x^{2}=144-48

x^{2}=96

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