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katrin2010 [14]
3 years ago
14

Which pair of triangles appear to be congruent? check all that apply

Mathematics
2 answers:
Ratling [72]3 years ago
7 0
All three sides are the same size
Gala2k [10]3 years ago
3 0
C triangles 1 and triangles
3
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The polygons are regular polygons. Find the area of the shaded region to the nearest tenth.
Paha777 [63]

Answer:

128.8 cm²

Step-by-step explanation:

In the image attached below, the regular polygon is a square which is composed of a small square and a large square. In a square, all the sides are equal.

For the small square, half of the diagonal is 4 cm, therefore the length of the diagonal is 8 cm (2 × 4 cm). Let the length of the side be a cm, using Pythagoras theorem:

a² + a² = 8²

2a² = 64

a² = 32

a = √32 = 5.7 cm

The area of the small square = length × length = 5.7 × 5.7 = 32.5 cm²

For the large square, half of the diagonal is 9 cm, therefore the length of the diagonal is 18 cm (2 × 9 cm). Let the length of the side be b cm, using Pythagoras theorem:

b² + b² = 18²

2b² = 324

b² = 162

b = √162 = 12.7 cm

The area of the large square = length × length = 12.7 × 12.7 = 161.3 cm²

The area of the shaded region = Area of large square - Area of small square = 161.3 cm² - 32.5 cm² = 128.8 cm²

4 0
3 years ago
Dan has a board that is 15/16 yd. How many “Keep out” signs can he make if the length of the sign is changed to half of the orig
CaHeK987 [17]
3 keep our signs. if dan has a board that is 15/16 yd and each is 2.5/8 (half of the original which is actually 5/16) then you can fit 3 signs
5 0
3 years ago
Read 2 more answers
Can you help me solve this question
Serggg [28]

Answer:

t = 32

Step-by-step explanation:

The given equation is :

24=\dfrac{3}{4}t ....(1)

Where

t is the number of guests attending the catered event.

The reciprocal of \dfrac{3}{4} is \dfrac{4}{3}.

Multiplying both sides by the reciprocal of \dfrac{3}{4}.

24\times \dfrac{4}{3}=\dfrac{3}{4}\times \dfrac{4}{3}t\\\\t=8\times 4\\\\t=32

Hence, 32 guests will attend the catered.

3 0
3 years ago
3 5/6 + (-1 1/6)<br> plz help me with this.
ANEK [815]

Answer:

3 5/6 + (-11/6) --> 2 2/3

Step-by-step explanation:

Step 1: 3-1--> 2

Step 2: 5/6 - 1/6 --> 2/3

Final Answ. : 2 2/3

4 0
3 years ago
Read 2 more answers
If the 5th term of a geometric progression is 162 and the 8th term is 4374, find the (i) 1st three terms of the sequence; (ii) s
Alona [7]

Answer:

see explanation

Step-by-step explanation:

The nth term of a geometric progression is

a_{n} = a₁r^{n-1}

where a₁  is the first term and r the common ratio

Given a₅ = 162 and a₈ = 4374 , then

a₁r^{4} = 162 → (1)

a₁r^{7} = 4374 → (2)

Divide (2) by (1)

\frac{a_{1}r^{7}  }{a_{1}r^{4}  } = \frac{4374}{162}

r³ = 27

r = \sqrt[3]{27} = 3

Substitute r = 3 into (1) and solve for a₁

a₁(3)^{4} = 162

81a₁ = 162

a₁ = \frac{162}{81} = 2

Then

a₂ = a₁ × 3 = 2 × 3 = 6

a₃ = a₂ × 3 = 6 × 3 = 18

The first 3 terms are 2, 6, 18

(ii)

The sum to n terms of a geometric progression is

S_{n} = \frac{a_{1}(r^{n}-1)  }{r-1} , then

S_{10} = \frac{2(3^{10}-1) }{3-1}

     = \frac{2(59049-1)}{2}

     = 59049 - 1

     = 59048

   

6 0
3 years ago
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