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3 years ago

Since we know U is the midpoint, we can say TU equals BLANK? Substituting in our values for each we get BLANK? =12x - 1

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

5 0

Answer:

x = 3

Length of each segment = 3

Step-by-step explanation:

Since point U is the midpoint of the line segment TV, that means both the parts of the segment UV and TU will be equal in measure.

m(TU) = m(VU)

(8x + 11) = (12x - 1)

By further solving this,

8x + 11 + 1 = 12x - 1 + 1

8x + 12 = 12x

8x + 12 - 8x = 12x - 8x

12 = 4x

x = $\frac{12}{4}$

x = 3

(12x - 1) = 12×3 - 1

= 35

And the length of each segment will be 35 units.

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1. The diagonal of a quadrilateral

zalisa [80]

Consider the length of diagonal is 8.5 cm instead of 8.5 m because length of perpendiculars are in cm.

Given:

Length of the diagonal of a quadrilateral = 8.5 cm

Lengths of the perpendiculars dropped on it from the remaining opposite vertices are 3.5 cm and 4.5 cm.

To find:

The area of the quadrilateral.

Solution:

Diagonal divides the quadrilateral in 2 triangles. If diagonal is the base of both triangles then the lengths of the perpendiculars dropped on it from the remaining opposite vertices are heights of those triangles.

According to the question,

Triangle 1 : Base = 8.5 cm and Height = 3.5 cm

Triangle 2 : Base = 8.5 cm and Height = 4.5 cm

Area of a triangle is

$Area=\dfrac{1}{2}\times base \times height$

Using this formula, we get

$Area(\Delta 1)=\dfrac{1}{2}\times 8.5\times 3.5$

$Area(\Delta 1)=14.875$

and

$Area(\Delta 2)=\dfrac{1}{2}\times 8.5\times 4.5$

$Area(\Delta 2)=19.125$

Now, area of the quadrilateral is

$Area=Area(\Delta 1)+Area(\Delta 2)$

$Area=14.875+19.125$

$Area=34$

Therefore, the area of the quadrilateral is 34 cm².

6 0

3 years ago

I need advice!

g100num [7]

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4 0

3 years ago

Read 2 more answers

The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width

Delicious77 [7]

Answer:

Length is 90yards and width is 60yards

Step-by-step explanation:

Perimeter= 2( length+width)

let the width be x

then the length will be 30 + x

300 = 2(30+x+x)

150 = 30 + 2x

120= 2x

x = 120/2

x = 60 yards

length= 30+x

= 30 + 60

= 90yards

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2 years ago

The first step to solve 2x - 5 = 13 is:

Triss [41]

Answer: First add 5 to both sides

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3 years ago

Complete this expression using the distributive property

Aneli [31]

Answer:

5(4) + 5(8)

Step-by-step explanation:

Through destributive property, 5 is multiplied by both 4 and 8

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3 years ago