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3 years ago

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Mathematics

1 answer:

polet [3.4K]3 years ago

4 0

5(6x+5)-2(4x-1) = 30x+25-8x+2 = 22x+27

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2. Why are the triangles congruent?

Lady bird [3.3K]

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

6 0

2 years ago

Read 2 more answers

The perimeter of a triangular field is 120m. Two of the sides are 21m and 40m.Calculate the largest angle of the field.

Mama L [17]

Answer:

the largest angle of the field is 149⁰

Step-by-step explanation:

Given;

perimeter of the triangular filed, P = 120 m

length of two known sides, a and b = 21 m and 40 m respectively

The length of the third side is calculated as follows;

a + b + c = P

21 m + 40 m + c = 120 m

61 m + c = 120 m

c = 120 m - 61 m

c = 59 m

↓ ↓

A → → → → → → → → → → → C

Consider ABC as the triangular field;

Angle A is calculated by applying cosine rule;

$a^2 = b^2 + c^2 - 2bc \ Cos A\\\\Cos \ A = \frac{b^2 + c^2 - a^2}{2bc} \\\\Cos \ A = \frac{40^2 + 59^2 - 21^2}{2 \times 40 \times 59} \\\\Cos \ A = 0.983\\\\A = Cos ^{-1} (0.983)\\\\A = 10.6 \ ^0$

Angle B is calculated as follows;

$Cos \ B = \frac{a^2 + c^2 - b^2}{2ac} \\\\Cos \ B = \frac{21^2 + 59^2 - 40^2}{2 \times 21 \times 59} \\\\Cos \ B = 0.937\\\\B= Cos ^{-1} (0.937)\\\\B = 20.5 \ ^0$

Angle C is calculated as follows;

$Cos \ C = \frac{a^2 + b^2 - c^2}{2ab} \\\\Cos \ C = \frac{21^2 + 40^2 - 59^2}{2 \times 21 \times 40} \\\\Cos \ C = -0.857\\\\C = Cos ^{-1} (-0.857)\\\\C = 149\ ^0$

Therefore, the largest angle of the field is 149⁰.

8 0

3 years ago

What is the 22nd term of the arithmetic sequence 12 , 17 , 22 , 27 , .... , .... , ....

11Alexandr11 [23.1K]

Answer: 117

Step-by-step explanation:

Formula for arithmetic sequence is:

= a + (n - 1)d

22nd term = a + (n - 1)d

= a + (22 - 1)d = a + 21d

where, a = 12

d = 17 - 12 = 5.

Therefore, 22nd term will be:

= a + 21d

= 12 + 21(5)

= 12 + 105

= 117

The 22nd term is 117

5 0

3 years ago

Write in standard form (×+4)(×-5)=4 find the value of a,b,c

Alex17521 [72]

Answer:

$x^{2}$ - x - 24 = 0

a = 1

b = 1

c = -24

Step-by-step explanation:

(x + 4)(x - 5) = 4

x(x - 5) = $x^{2}$ - 5x

4(x - 5) = 4x - 20

$x^{2}$ - 5x + 4x - 20 = 4

$x^{2}$ - x - 20 = 4

$x^{2}$ - x - 20 - 4 = 0

$x^{2}$ - x - 24 = 0

a = 1

b = 1

c = -24

4 0

2 years ago

3. Two quantities, x and y, are in a

frez [133]

Answer:

y = x + 1.8

Step-by-step explanation:

6 0

2 years ago