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Mathematics, 14.02.2022 01:00 Arelysoqui91

Hello help me with this question thanks in advance

Hello help me with this question thanks in advance

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Answers: 3

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Answer from: annadel742

$\bold{\huge{\purple{\underline{ Solutions}}}}$

Answer 5 :-

We have,

$\sf{ HE = 2x cm \: and \: OR = ( x + 5)cm}$

We know that,

Parallelogram has opposite sides parallel and equal.

From above property,

$\sf{ HE = OR }$

$\sf{ 2x = x + 5}$

$\sf{ 2x - x = 5}$

$\sf{ x = 5}$

Thus, The value of x is 5cm

Therefore,

The value of HE

$\sf{ = 2x}$

$\sf{ = 2× 5}$

$\sf{\red{ = 10 cm}}$

The measurement of HE is 10 cm

Hence, Option A is correct

Answer 6 :-

We have,

$\sf{m}{\sf{\angle{HER = 5y - 26° \: and\: m }}}{\sf{\angle{ ROH = 2y + 40°}}}$

In parallelograms, Opposite angles are equal

From above property,

$\sf{m}{\sf{\angle{HER = }}}{\sf{\angle{ ROH}}}$

$\sf{ 5y - 26° = 2y + 40°}$

$\sf{ 5y - 2y = 40 + 26}$

$\sf{ 3y = 40 + 26}$

$\sf{ y = 66/3}$

$\sf{ y = 22°}$

Thus, The value of y is 22°

Therefore,

The measurement of Angle HER

$\sf{ = 5 × 22 - 26 }$

$\sf{ = 110 - 26 }$

$\sf{\red{= 84° }}$

The measurement of angle HER is 84°

Hence option D is correct

Answer 7 :-

We have,

$\sf{ HZ = 4a - 5 \:and \:RZ = 3a + 5 }$

The diagonals of parallelogram are equal in length Here, RZ is the bisector of diagonal HR

$\sf{ 4a - 5 = 3a + 5 }$

$\sf{ 4a - 3a = 5 + 5}$

$\sf{ a = 10}$

Thus, The value of a is 10

Therefore,

The measurement of HZ

$\sf{ = 4 × 10 - 5 }$

$\sf{ = 40 - 5 }$

$\sf{\red{= 35 \: cm }}$

The measurement of HZ is 35 cm

Hence, Option C is correct

Answer 8 :-

We have ,

One diagonals = 5x - 47

Another diagonal = 2x + 34

In isosceles trapezoid, Diagonals are equal in length.

From above property,

$\sf{ 5x - 47 = 2x + 34 }$

$\sf{ 5x - 2x = 34 + 47}$

$\sf{ 3x = 81 }$

$\sf{ x = 81/3 }$

$\sf{ x = 27}$

Thus, The value of x is 27

Hence, Option A is correct

Answer 9 :-

We have,

The sides of parallelogram GAME are (7x - 1 ) , ( 5x + 10 ) , (6x) , ( 7x - 2 )

In parallelogram, Opposite sides are equal

From above property,

$\sf{ 7x - 1 = 6x }$

$\sf{ 7x - 6x = 1 }$

$\sf{ x = 1 }$

$\sf{ 5x + 10 = 7x - 2}$

$\sf{ 7x - 5x = 10 + 2 }$

$\sf{ 2x = 12}$

$\sf{ x = 12/2 }$

$\sf{ x = 6 }$

Thus, measurements of parallelogram GAME in inches is 1 and 6 .

Hence, Option B is correct

Answer 10 :-

We have,

$\sf{ ES = 18 cm}$

The diagonals of rectangle are equal in length. Here, NP = OE PS and NS act as a bisector in OE and OS and ES act as a bisector in NP

From above we can say that,

$\sf{ OE = OS + ES }$

$\sf{ OE = 2ES ( OS = ES bisector}$

$\sf{ OE = 2 × 18 }$

$\sf{ OE = 36cm }$

Thus, The value of OE is 38 cm

Therefore,

$\sf{ OE = NP }$

[ Diagonals of the given rectangle ]

$\sf{\red{NP = 36 cm }}$

Thus , The value of NP is 36 cm

Hence, Option C is correct

ansver

Answer from: Quest

answer: the answer is (b) amie should have multiplied

$54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

$v_s=\pi r^2h=\pi r^3,$

and the volume of the cylinder will be

$v_c=\dfrac{4}{3}\pi r^3=54~\textup{m}^3.$

therefore, we have

$v_c=\dfrac{4}{3}v_s=\dfrac{4}{3}\times 54=72~\textup{m}^3.$

thus, ammie should have multiplied the volume of the sphere $54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

ansver

Answer from: Quest

That’d be 9 years or something

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