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30.05.2023

for what values of x and y is quadrilateral ABCD a parallelogram?

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Mathematics

For what values of x and y is quadrilateral ABCD a parallelogram

Step-by-step answer

P Answered by PhD

6

The value of x is 6 and y is 3.

Given that,

ABCD is a parallelogram in which sides of parallelogram are,

AB = 8x- 34, BC = 6x- 4

CD = 9x-40, AD = 4y+20

We have to find,

The value of x and y in a quadrilateral ABCD ?

According to the question,

By the property of a parallelogram,

The opposite sides of a parallelogram are equal and parallel to each other.

AD = BC

CD = AB

Substitute the values of AD and BC and solve for the value of x and y,

$\rm 4y +20 = 6x -4 \\\\4y - 6x = -4 -20\\\\4y -6x = -24\\\\ Divide \ by \ 2 \ on \ both \ the \ sides\\\\ 2y - 3x = -12$

And

$CD = AB \\\\9x-40=8x-34\\\\9x-8x = 40-34\\\\x = 6$

Substitute the value of x in equation 1,

$2y-3x = -12\\\\2y - 3(6) = -12\\\\2y = -18=-12\\\\2y = -12+18\\\\2y = 6\\\\y = \dfrac{6}{2}\\\\y = 3$

Hence, The value of x is 6 and y is 3.

For more details refer to the link.

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Mathematics

For what values of x and y is quadrilateral ABCD a parallelogram

Step-by-step answer

P Answered by PhD

6

The value of x is 6 and y is 3.

Given that,

ABCD is a parallelogram in which sides of parallelogram are,

AB = 8x- 34, BC = 6x- 4

CD = 9x-40, AD = 4y+20

We have to find,

The value of x and y in a quadrilateral ABCD ?

According to the question,

By the property of a parallelogram,

The opposite sides of a parallelogram are equal and parallel to each other.

AD = BC

CD = AB

Substitute the values of AD and BC and solve for the value of x and y,

$\rm 4y +20 = 6x -4 \\\\4y - 6x = -4 -20\\\\4y -6x = -24\\\\ Divide \ by \ 2 \ on \ both \ the \ sides\\\\ 2y - 3x = -12$

And

$CD = AB \\\\9x-40=8x-34\\\\9x-8x = 40-34\\\\x = 6$

Substitute the value of x in equation 1,

$2y-3x = -12\\\\2y - 3(6) = -12\\\\2y = -18=-12\\\\2y = -12+18\\\\2y = 6\\\\y = \dfrac{6}{2}\\\\y = 3$

Hence, The value of x is 6 and y is 3.

For more details refer to the link.

link

Mathematics

The diagonals of quadrilateral ABCD intersect at E . If EC=4, BD=12, AE=x, and BE=y , what values of x and y would prove that the quadrilateral is a parallelogram?

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

16 ae =x

The diagonals of quadrilateral ABCD

intersect at E
. If EC=4, BD=12, AE=x,
and BE=y
, what values o

Mathematics

The diagonals of quadrilateral ABCD intersect at E . If EC=4, BD=12, AE=x, and BE=y , what values of x and y would prove that the quadrilateral is a parallelogram?

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

16 ae =x

The diagonals of quadrilateral ABCD

intersect at E
. If EC=4, BD=12, AE=x,
and BE=y
, what values o

Mathematics

For what values of x and y is a quadrilateral ABCD a parallelogram.. help plz

Step-by-step answer

P Answered by PhD

2

Step-by-step explanation:

correct correct answer of this question is option A , x equals to 6 and y equals to 3

please mark my answer and also vote me

Mathematics

For what values of x and y is a quadrilateral ABCD a parallelogram.. help plz

Step-by-step answer

P Answered by PhD

2

Step-by-step explanation:

correct correct answer of this question is option A , x equals to 6 and y equals to 3

please mark my answer and also vote me

Mathematics

Quadrilaterals ABCD and PQRS shown below are two similar figures. Find the values of x and y.

Step-by-step answer

P Answered by PhD

2

x = 12, y = 16

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

$\frac{AD}{PS}$ = $\frac{DC}{SR}$ , substitute values

$\frac{20}{2x+6}$ = $\frac{18}{27}$ ( cross- multiply )

18(2x + 6) = 540 ( divide both sides by 18 )

2x + 6 = 30 ( subtract 6 from both sides )

2x = 24 ( divide both sides by 2 )

x = 12

-------------------------------------------

and

$\frac{AB}{PQ}$ = $\frac{DC}{SR}$ , substitute values

$\frac{y}{24}$ = $\frac{18}{27}$ ( cross- multiply )

27y = 432 ( divide both sides by 27 )

y = 16

Mathematics

Quadrilaterals ABCD and PQRS shown below are two similar figures. Find the values of x and y.

Step-by-step answer

P Answered by PhD

2

x = 12, y = 16

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

$\frac{AD}{PS}$ = $\frac{DC}{SR}$ , substitute values

$\frac{20}{2x+6}$ = $\frac{18}{27}$ ( cross- multiply )

18(2x + 6) = 540 ( divide both sides by 18 )

2x + 6 = 30 ( subtract 6 from both sides )

2x = 24 ( divide both sides by 2 )

x = 12

-------------------------------------------

and

$\frac{AB}{PQ}$ = $\frac{DC}{SR}$ , substitute values

$\frac{y}{24}$ = $\frac{18}{27}$ ( cross- multiply )

27y = 432 ( divide both sides by 27 )

y = 16

Mathematics

Will give 100 points to ! 5. what is the value of x? (the 1st picture) 6. what is the value of x? (the 2nd picture) a.53 b.61 c.119 d.114 7.a cylinder has a radius of 5 cm and a height of 12 cm. what is the volume of the cylinder? a.60π cm^3 b.300π cm^3 c.720π cm^3 d.1200 cm^3 8. a cone has a diameter of 12 in. and a height of 16 in. what is the volume of the cone? use 3.14 as an approximation for π and express your final answer in hundredths. in3 9. rectangle abcd is similar to rectangle fghi. what is the value of x? (the 3rd picture) 10. given

Step-by-step answer

P Answered by PhD

1

Part 5) ∠x=122°

Part 6) Option D. ∠x=114°

Part 7) Option B.300π cm^3

Part 8) The volume of the cone is $V=602.88\ in^{3}$

Part 9) The value of x is 12 cm

Part 10) BC=21 units

Part 11) Option D.reflection across the y-axis

Part 14) $x=15.6\ cm$

Part 15) B. 5, 12, 13

Step-by-step explanation:

Part 5) What is the value of x?

we know that

∠x+58°=180°------> by supplementary angles

solve for x

∠x=180°-58°=122°

Part 6) What is the value of x?

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

The measure of the third interior angle of the triangle is equal to

180°-61°-53°=66°

so

66°+∠x=180° -----> by supplementary angles

solve for x

∠x=180°-66°=114°

Part 7) A cylinder has a radius of 5 cm and a height of 12 cm. What is the volume of the cylinder?

we know that

The volume of the cylinder is equal to

$V=\pi r^{2} h$

we have

$r=5\ cm$

$h=12\ cm$

substitute

$V=\pi (5)^{2} (12)$

$V=300\pi\ cm^{3}$

Part 8) A cone has a diameter of 12 in. and a height of 16 in. What is the volume of the cone?

we know that

The volume of the cone is equal to

$V=(1/3)\pi r^{2} h$

we have

$r=12/2=6\ in$ ------> the radius is half the diameter

$h=16\ in$

substitute

$V=(1/3)(3.14)(6)^{2} (16)$

$V=602.88\ in^{3}$

Part 9) Rectangle ABCD is similar to rectangle FGHI. What is the value of x?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem

AB/FG=BC/GH

substitute the values

8/6=x/9

x=9*8/6

x=12 cm

Part 10) Given quadrilateral ABCD ~ quadrilateral JKLM and AD = 14, JM = 6, and KL = 9, what is BC?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

AD/JM/BC/KL

substitute the values

14/6/BC/9

BC=14*9/6

BC=21 units

Part 11) What transformation was performed on triangle ABC to create triangle A'B'C' ?

we know that

The rule for a reflection over the y -axis is (x,y)→(−x,y)

so

When reflecting across the y- axis the x-values will be multiplied by negative one, but the y-values will not change

This problem is a reflection across the y-axis

Part 14) What is the value of x? Round to the nearest tenth

we know that

Applying the Pythagoras Theorem

$x^{2}=10^{2}+12^{2}\\ \\x^{2}=244\\ \\x=15.6\ cm$

Part 15) Which set of side lengths defines a right triangle?

we know that

If the set of side lengths defines a right triangle, then must satisfy the Pythagoras Theorem

Verify each case

case A. 6, 8, 11

$11^{2}=6^{2}+8^{2}\\ \\121=100$

Is not true

therefore

Is not a right triangle

case B. 5, 12, 13

$13^{2}=5^{2}+12^{2}\\ \\169=169$

Is true

therefore

Is a right triangle

case C. 7, 9, 13

$13^{2}=7^{2}+9^{2}\\ \\169=130$

Is not true

therefore

Is not a right triangle

case D. 6, 9, 11

$11^{2}=6^{2}+9^{2}\\ \\121=117$

Is not true

therefore

Is not a right triangle

Mathematics

Will give 100 points to ! 5. what is the value of x? (the 1st picture) 6. what is the value of x? (the 2nd picture) a.53 b.61 c.119 d.114 7.a cylinder has a radius of 5 cm and a height of 12 cm. what is the volume of the cylinder? a.60π cm^3 b.300π cm^3 c.720π cm^3 d.1200 cm^3 8. a cone has a diameter of 12 in. and a height of 16 in. what is the volume of the cone? use 3.14 as an approximation for π and express your final answer in hundredths. in3 9. rectangle abcd is similar to rectangle fghi. what is the value of x? (the 3rd picture) 10. given

Step-by-step answer

P Answered by PhD

1

Part 5) ∠x=122°

Part 6) Option D. ∠x=114°

Part 7) Option B.300π cm^3

Part 8) The volume of the cone is $V=602.88\ in^{3}$

Part 9) The value of x is 12 cm

Part 10) BC=21 units

Part 11) Option D.reflection across the y-axis

Part 14) $x=15.6\ cm$

Part 15) B. 5, 12, 13

Step-by-step explanation:

Part 5) What is the value of x?

we know that

∠x+58°=180°------> by supplementary angles

solve for x

∠x=180°-58°=122°

Part 6) What is the value of x?

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

The measure of the third interior angle of the triangle is equal to

180°-61°-53°=66°

so

66°+∠x=180° -----> by supplementary angles

solve for x

∠x=180°-66°=114°

Part 7) A cylinder has a radius of 5 cm and a height of 12 cm. What is the volume of the cylinder?

we know that

The volume of the cylinder is equal to

$V=\pi r^{2} h$

we have

$r=5\ cm$

$h=12\ cm$

substitute

$V=\pi (5)^{2} (12)$

$V=300\pi\ cm^{3}$

Part 8) A cone has a diameter of 12 in. and a height of 16 in. What is the volume of the cone?

we know that

The volume of the cone is equal to

$V=(1/3)\pi r^{2} h$

we have

$r=12/2=6\ in$ ------> the radius is half the diameter

$h=16\ in$

substitute

$V=(1/3)(3.14)(6)^{2} (16)$

$V=602.88\ in^{3}$

Part 9) Rectangle ABCD is similar to rectangle FGHI. What is the value of x?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem

AB/FG=BC/GH

substitute the values

8/6=x/9

x=9*8/6

x=12 cm

Part 10) Given quadrilateral ABCD ~ quadrilateral JKLM and AD = 14, JM = 6, and KL = 9, what is BC?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

AD/JM/BC/KL

substitute the values

14/6/BC/9

BC=14*9/6

BC=21 units

Part 11) What transformation was performed on triangle ABC to create triangle A'B'C' ?

we know that

The rule for a reflection over the y -axis is (x,y)→(−x,y)

so

When reflecting across the y- axis the x-values will be multiplied by negative one, but the y-values will not change

This problem is a reflection across the y-axis

Part 14) What is the value of x? Round to the nearest tenth

we know that

Applying the Pythagoras Theorem

$x^{2}=10^{2}+12^{2}\\ \\x^{2}=244\\ \\x=15.6\ cm$

Part 15) Which set of side lengths defines a right triangle?

we know that

If the set of side lengths defines a right triangle, then must satisfy the Pythagoras Theorem

Verify each case

case A. 6, 8, 11

$11^{2}=6^{2}+8^{2}\\ \\121=100$

Is not true

therefore

Is not a right triangle

case B. 5, 12, 13

$13^{2}=5^{2}+12^{2}\\ \\169=169$

Is true

therefore

Is a right triangle

case C. 7, 9, 13

$13^{2}=7^{2}+9^{2}\\ \\169=130$

Is not true

therefore

Is not a right triangle

case D. 6, 9, 11

$11^{2}=6^{2}+9^{2}\\ \\121=117$

Is not true

therefore

Is not a right triangle

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