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ira [324]
3 years ago
10

If S lies between R and T, RT=21, RS=2X+5, and ST=3x-4. Find RS and ST

Mathematics
2 answers:
Snowcat [4.5K]3 years ago
8 0
The answer is c so pick it so I can get answers
zepelin [54]3 years ago
8 0

Answers:

RS = 13

ST = 8

==================================================

Explanation:

S is between R and T. I'm assuming also that S is on line RT.

If that's the case, then by the segment addition postulate, we can say  RS+ST = RT.

In other words, the longest segment RT is broken into two smaller pieces RS and ST (not necessarily equal but they may be). Gluing the pieces back together should get us the original longest segment.

---------------

Apply substitution and solve for x.

RS+ST = RT

(2x+5)+(3x-4) = 21

(2x+3x)+(5-4) = 21

5x+1 = 21

5x = 21-1

5x = 20

x = 20/5

x = 4

--------------------

If x = 4, then,

  • RS = 2x+5 = 2*4+5 = 13
  • ST = 3x-4 = 3*4-4 = 8

Then notice how RS+ST = 13+8 = 21, which is is the length of RT

This confirms that RS+ST = RT is true and it confirms our answers.

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Which sequence of transformations confirms congruence by mapping shape I onto shape II?
Lubov Fominskaja [6]

Answer:

  • Neither of the choices is correct.

Explanation:

<u>1. Coordinates of the vertices of the figure I (preimage):</u>

  • (10, - 5)
  • (15, -5)
  • (10, - 10)
  • (15, -10)

<u />

<u>2. Coordinates of the vertices of the figure II (image):</u>

  • (0,10)
  • (0,15)
  • (-5,10)
  • (-5, 15)

Since many different rigid transformations can map the figure I into the figue II, you will need to use trial and error.

The most important is to do it in an educated way.

I will start by eliminating some options.

The first option, a reflection across the x-axis and 15 units left, does not work, because the reflection across the x-axis would shift the figure to a lower position than what you need.

The third option, a 90º counterclokwise rotation about the origin then a translation 10 units up, would move the figure to the second quadrant, and we need it in the third quadrant.

I will try now with the second choice, a 90º clockwise rotation and then 25 units up:

First, a 90º clockwise rotation, which is the same that a 270º counterclockwise rotation, follows the rule (x, y) → (y, -x)

Then, that results in:

  • (10, - 5) → (-5, -10)
  • (15, -5) → (-5, -15)
  • (10, - 10) → (-10, -10)
  • (15, -10) → (-10, -15)

Now, you can see that shifting 25 units up will not work, because you need that two x-coordinates become 0 (zero). So, this is not the correct set of transformations either.

A 180º rotation about the origin and a translation 10 units right follow this chain of rules:

  • (x, y) → (-x, -y) → (-x + 10, -y)

That means:

  • (10, - 5) → (-10,5) → (-10 + 10, 5) = (0, 5)
  • (15, -5) → (-15, 5) → (-15 + 10, 5) = (-5, 5)
  • (10, - 10) → (-10, 10) → (-10 + 10, 10) = (0, 10)
  • (15, -10) → (-15, 10) → (-15 + 10, 10) = (-5, 10)

        These last points do not coincide either with the vertices of the figure II.

In conclusion, neither of the choices gives the correct answer to the question.

8 0
3 years ago
Read 2 more answers
Can someone help me with this?? - Linear Functions
BlackZzzverrR [31]

Answer:

1.) two points are (1,6)(2,4)

2.) slope= -2

3.) y intercept= (0,8)

4.) x-intercept= (4,0)

5.) two points are (1,4)(2,5)

6.) slope=1

7.) y-intercept=(0,3)

8.) x-intercept=(-3,0)

Step-by-step explanation:

you can use a desmos caluclator online or

m a t h w a y

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4 0
3 years ago
What is the measure of 3? triangle on right has angles labeled forty-four degrees, sixty-six degrees, and three.?
sveta [45]
[1] First, remember that the sum of the angles in a triangle must add up to 180*.

[2] We are told two of the angles, 44* and 66*, but we are missing the third.

[3] Combining [1] and [2], we know that 44* + 66* + ? = 180*. In other words,
110* + ? = 180*
so,
? = 70*

The missing angle 3 is equal to 70 degrees.
4 0
3 years ago
Twice the sum of two numbers is 24. if one number is 2 times larger than the other, what is the smaller of the two numbers?
Vikki [24]
2(x+y)=24
2x=y

Use substitution. If y=2x, than we can substitute 2x for it in the other equation, because x and y equal the same things in both equations. 

So using that we get 2(x+2x)=24

SIMPLIFY
2(3x)=24

DISTRIBUTE
6x=24. 

DIVIDE: x=4.

If we substitute x into the original equations we get x=4 and y=8. Those are your two numbers. 

Have a nice day! :)


4 0
3 years ago
MULTIPLE CHOICE HELP ASAP! Brainliest for correct answer.
N76 [4]

Answer:

An equation of the circle with centre (-2,1) and radius 3 is \mathbf{(x+2)^2+(x-1)^2=9}

Option D is correct.

Step-by-step explanation:

Looking at the figure we get centre of circle C (-2,1) and radius of circle r = 3

The equation of circle is of form: (x-h)^2+(x-k)^2=r^2 where (h,k) is centre and r is radius.

We have centre C (-2,1) so, we have h = -2 and k = 1

We have radius = 3 so, r = 3

Putting values in the equation and finding the required equation:

(x-h)^2+(x-k)^2=r^2\\(x-(-2))^2+(x-1)^2=(3)^2\\(x+2)^2+(x-1)^2=9

So,  an equation of the circle with centre (-2,1) and radius 3 is \mathbf{(x+2)^2+(x-1)^2=9}

Option D is correct.

7 0
3 years ago
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