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Alexxx [7]
2 years ago
14

An artisan wants to split his equilateral triangular-shaped piece of glass into four equally sized pieces as part of a window de

sign. Explain to him, with a diagram, how to design an inscribed triangle, and show him that the pieces all have equal area.
Mathematics
1 answer:
jeka942 years ago
8 0

The triangle QPR having inscribed triangle STU will allow the artisan to divided his glass piece into four equal triangular pieces.

In order to divide an equilateral triangle into four equal triangular glass pieces, the artisan must;

  • Take S as the mid-point on PA, T as the mid-point on PR, and U as the mid-point on QR. Thus, S, T, and U are the three mid-points on each side of the equilateral triangle QPR.
  • Now, by joining these mid-points S, T, and U, four equal triangles are made(as shown in the figure).

Since the triangle is equilateral,

PQ = QR = RP

Mid-point divides the lines into equal parts. So,

PS = SQ = QU = UR = RT = TP

Thus, it is proved that

ΔPST = ΔSTU = ΔTUR = ΔQSU

Learn more about 'Equilateral Triangle' here:

brainly.com/question/2855144

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Which points of the following points are solutions to the equation 3x-4y-8=12
Natali [406]

Answer:

(0, -5), (4, -2), (-16, -17)

Step-by-step explanation:

I attach your full question in the image below

The equation is

3x-4y-8=12

Which can be rewritten as

3x-4y =12 +8

3x-20 = 4y

y = (3/4)*x - 5

We need to check each individual case

(0,-5)

y = (3/4)*(0) - 5  

y = -5

True

(4,-2)

y = (3/4)*(4) - 5  

y = -2

True

(8,2)

y = (3/4)*(8) - 5  

y = 1

False

(-16,-17)

y = (3/4)*(-16) - 5  

y = -17

True

(-1,-8)

y = (3/4)*(-1) - 5  

y = -23/4

False

(-40,-34)

y = (3/4)*(-40) - 5  

y = -35

False

(0,-5) (4,-2) and (-16,-17) are the solutions

8 0
3 years ago
UUUUUUUURRRRGGGGEEENNTTTT! WILL GIVE BRAINLIEST! PLEASE SHOW WORK
nikklg [1K]

Answer:

C. Ted will gain $7,532 more from the rent than from the appreciation.

Step-by-step explanation:

Yes

6 0
3 years ago
The angles listed from largest to smallest are __________________
photoshop1234 [79]

Answer:

B, A, C

Step-by-step explanation:

That's a 30-60-90 triangle.

7 0
3 years ago
The length of time that an auditor spends reviewing an invoice is approximately normally distributed with a mean of 600 seconds
Bumek [7]
Answer: 11.5% 

Explanation:


Since 1 minute = 60 seconds, we multiply 12 minutes by 60 so that 12 minutes = 720 seconds. Thus, we're looking for a probability that the auditor will spend more than 720 seconds. 

Now, we get the z-score for 720 seconds by the following formula:

\text{z-score} =  \frac{x - \mu}{\sigma}

where 

t = \text{time for the auditor to finish his work } = 720 \text{ seconds}
\\ \mu = \text{average time for the auditor to finish his work } = 600 \text{ seconds}
\\ \sigma = \text{standard deviation } = 100 \text{ seconds}

So, the z-score of 720 seconds is given by:

\text{z-score} = \frac{x - \mu}{\sigma}
\\
\\ \text{z-score} = \frac{720 - 600}{100}
\\
\\ \boxed{\text{z-score} = 1.2}

Let

t = time for the auditor to finish his work
z = z-score of time t

Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:

P(t \ \textgreater \  720) 
\\ = P(z \ \textgreater \  1.2)
\\ = 1 - P(z \leq 1.2)
\\ = 1 - 0.885
\\  \boxed{P(t \ \textgreater \  720)  = 0.115}

Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice. 
8 0
3 years ago
The least common multiple of two numbers is 60 and one of the numbers is 7 less than the other number.What are the numbers.Justi
denis-greek [22]

Answer:

As the least common multiple of two numbers is 60 , the two numbers are factors of 60 . Among {1,2,3,4,5,6,10,12,15,20,30,60} , 3 & 10 and 5 & 12 are the only two pair of numbers whose difference is 7 . But Least common multiple of 3 and 10 is 30

6 0
2 years ago
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