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eduard
3 years ago
13

(ASAP!!) Given that point M is the midpoint of TS and UR which of the following triangle congruence methods could be used to pro

ve TUM SRM? T R M U S Do O ASA 0 O AAA O 0 O Qo O SAS 0 O SSS​

Mathematics
1 answer:
Natalka [10]3 years ago
3 0

Answer: SAS or Side-Angle-Side

Step-by-step explanation: Two triangles are congruent if they have the same exactly 3 sides and same exactly 3 angles.

There are methods to help prove congruence.

For example:

  • <u>ASA</u> or <u>Angle-Side-Angle</u>: when two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle;
  • <u>SAS</u> or <u>Side-Angle-Side</u>: when two sides and the included angle of one triangle is congruent to the corresponding parts of the other triangle;
  • <u>SSS</u> or <u>Side-Side-Side</u>: if three sides of one triangel are congruent to the three sides of the other triangle, they are congruent;

The triangles TUM and SRM are congruent because:

Lines RU and TS intersect at point M forming two pair of opposite angles, which are vertical and therefore, the same.

Being midpoint, point M divides RU into two equal segments: UM = MR. The same happens to TS: TM = MS.

Two sides and the included angle of one triangle is congruent to the corresponding parts of the other triangle, which means ΔTUM and ΔSRM are congruent and proved by SAS method.

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A bag contains a total of 60 marbles. A marble is to be chosen at random from the bag. If the probability that a blue marble wil
valkas [14]

Answer:

There are 21 blue marbles

Step-by-step explanation:

In this question, we are asked to calculate the number of blue marbles in a bag that contains a total of 60 marbles, given the probability of choosing a blue marble.

Mathematically, the probability of choosing a blue marble can be represented as:

P(B) = number of blue marbles/ Total number of marbles

From the question, we can identify that P(B) is 0.35, number of Marbles is unknown while the total number of marbles is 60.

We insert these values in the equation;

0.35 = number of blue marbles/60

Hence, number of blue marbles = 60 * 0.35 = 21

4 0
3 years ago
Find the solution to the system of equations: x + 3y = 7 and 2x + 4y = 8
mojhsa [17]
{ x + 3 y = 7      * ( - 2)
 2 x + 4 y = 8 

{ - 2 x - 6 y = - 14
    2 x + 4 y = 8
_______________
             -2 y =  - 6   * ( -1)

 2 y = 6

y = 6 / 2

y = 3

For x :

2 x + 4 y = 8

2 x + 4 * ( 3) = 8

2 x + 12 = 8

2 x = 8 - 12

2 x = - 4

x = - 4 / 2

x = - 2

Solution:   x = -2    and  y = 3 

hope this helps!

8 0
3 years ago
Find the value of x in each case:<br><br><br> PU ∩ RT = S, Q ∈ PR
Eddi Din [679]

Answer:

x=34

Step-by-step explanation:

When we look triangle SQR, we have angles 3x and 68, we know that sum angles of triangle is 180.

<R=180-(3x+68)

Now, we look at the PQS:

<PQS=180-68=112°

Then :

<PSQ=180-(112+x)=68-x

Then we have :

Angles PSR= 68-x+3x=68+2x and angles TSU=4x.

We have that

PSR=TSU

68+2x=4x

4x-2x=68

2x=68

x=34

3 0
3 years ago
Find the value of yy in each equation. Explain how you determined the value of y.
Hitman42 [59]

Answer:

a) 3

b) 9

c) 81

d) x

Step-by-step explanation:

We know the properties of log function as:

1) log(AB) = log(A) + log(B)

2) \log(\frac{A}{B}) = \log(A)+\log(B)

3) log(aᵇ) = b × log(a)

also,

4) \log_b(a)=\frac{\log(a)}{\log(b)}

Given:

a. y = 3^{\log_3(3)}

Now,

taking log both sides, we get

log(y) = \log(3^{\log_3(3)})

using 3, we get

log(y) = log₃(3) × log(3)

using 4, we get

log(y) =  \frac{\log(3)}{\log(3)} × log(3)

or

log(y) =  1 × log(3)

taking anti-log both sides

y = 3

b. y = 3^{log_3(9)}

Now,

taking log both sides, we get

log(y) = \log(3^{\log_3(9)})

using 3, we get

log(y) = log₃(9) × log(3)

using 4, we get

log(y) =  \frac{\log(9)}{\log(3)} × log(3)

or

log(y) = log(9)

taking anti-log both sides

y = 9

c. y = 3^{\log_3(81)}

Now,

taking log both sides, we get

log(y) = \log(3^{\log_3(81)})

using 3, we get

log(y) = log₃(81) × log(3)

using 4, we get

log(y) =  \frac{\log(81)}{\log(3)} × log(3)

or

log(y) =  log(81)

taking anti-log both sides

y = 81

d. y = 3^{\log_3(x)}

Now,

taking log both sides, we get

log(y) = \log(3^{\log_3(x)})

using 3, we get

log(y) = log₃(x) × log(3)

using 4, we get

log(y) =  \frac{\log(x)}{\log(3)} × log(3)

or

log(y) =  log(x)

taking anti-log both sides

y = x

3 0
3 years ago
Please help me with this question! #10
Finger [1]
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4 0
4 years ago
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