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eimsori [14]
3 years ago
7

The following table shows the length and width of two rectangles:

Mathematics
2 answers:
Irina-Kira [14]3 years ago
8 0
The correct answer is 4x-10

Svetlanka [38]3 years ago
3 0

Answer:

Option A (4x-10)

Step-by-step explanation:

we know that

The perimeter of a rectangle is equal to

P=2(L+W)

where

L is the length

W is the width

Step 1

Find the perimeter of rectangle A

Substitute the values

PA=2((2x+4)+(x-1))

PA=2(3x+3)

PA=(6x+6)\ units

Step 2

Find the perimeter of rectangle B

Substitute the values

PB=2((3x+1)+(2x-3))

PB=2(5x-2)

PB=(10x-4)\ units

Step 3

Find the result of the perimeter of rectangle B minus the perimeter of rectangle A

PB-PA=(10x-4)-(6x+6)=(4x-10)\ units


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3 years ago
O is the centre of the circle, EF is a tangent, angle BCE = 28°, angle ACD = 31°
andriy [413]

Answer

a. 28˚

b. 76˚

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d. 56˚

Step-by-step explanation

Given,

∠BCE=28°  ∠ACD=31°  &  line AB=AC .

According To the Question,

  • a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°

  • b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚

        thus , ∠ABC=76° .

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Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°

Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)

∠DAB = 180° - 107° ⇔ 73°

& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°

Now, In Triangle ADC Sum of angles in a triangle is 180°

∠ADC = 180° - (31° + 45°)  ⇔  104˚

   

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For Diagram, Please Find in Attachment  

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