Please hurry .... Point Z is equidistant from the sides of RST which must be true?

Mathematics

2 answers:

Tanya [424]3 years ago

5 0

Answer:

The last answer is right

Step-by-step explanation:

Because zs cuts the shape in half

brilliants [131]3 years ago

3 0

Answer with explanation:

In Δ R ST, Z C ⊥ RT, Z B ⊥TS, and Z A ⊥ RS.

Draw a circle Passing through points A,B and C.

→→Z A=Z B=Z C=Radius of the circle having center Z.

The Angle between Radius and tangent line measures 90°.

Also, The theorem which we will use here to find out which option is true among four options is:

⇒Length of tangent from external point to a circle are equal.

In Δ ZAS and Δ ZBS

∠ ZAS = ∠ ZBS→→→Each being 90°

ZA=ZB→→→Radii of circle

SA=SB→→Length of tangent from external point to a circle are equal.

Δ ZAS ≅ Δ ZBS→→→→→[SAS]

∠ ASZ ≅ ∠BSZ→→→→→→[CPCT]

Option D: ∠ ASZ ≅ ∠BSZ is correct among four options.

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The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 27 more than the original num

Gwar [14]

Answer: 47

Step-by-step explanation: To solve this problem, let's use t to represent our tens digit and u to represent our units digit so that the value of our number can be represented as 10t + u.

If we represent the value of our number as 10t + u, the value of the number with the digits reversed can be represented as 10u + t.

Since the first sentence states that the sum of the digits of a two-digit number is 11, that's t + u = 11.

Reading through our second sentence, when the digits are reversed, the new number is 27 more than the original number, that's 10u + t "is" which means equals 27 more than the original number that's 10t + u + 27.

So 10t + u = 10t + u + 27.

Before solving this system however, let's rearrange our second equation so that the t's and u's are on the same side by subtracting 10t and u from both sides to get 9u - 9t = 27 and when we rewrite our first equation above it, instead of writing it as t + u = 11, let's write it as t + u = 11 so that our u's and t's will match up in the system.

To solve this system, let's use addition so multiply the top equation by 9 to get 9u + 9t = 99 and 9u - 9t = 27 so that when we add the equations together the t's cancel and we get 18u = 126. Dividing both sided by 18, u = 7.

To find t, plug 7 back in for u in our first equation to get t + 7 = 11. Subtract 7 from both sides and t = 4.

Since our tens digit is 4 and our units is 7, our number must be 47.

I have also attached my work on a whiteboard.