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katrin2010 [14]
2 years ago
9

—— ——

Mathematics
1 answer:
blsea [12.9K]2 years ago
5 0

Given: NQ = NT , QS Bisect NT(∴ NS=ST ) , TV Bisects QN (∴ NV=VQ )

To Prove: QS=TV

Proof: In ΔNQT

NQ=NT

\frac{1}{2}NQ=\frac{1}{2}NT

∴ VQ=ST

In a isosceles triangle, If two sides are equal then their opposites angles are equal.

∴ ∠NQT=∠NTQ       ( ∵ NQ=NT)

In ΔQST and TVQ

ST=VQ                    (sides of isosceles triangle)

∠NQT=∠NTQ          (Prove above)

QT=TQ                    (Common)

So, ΔQST ≅ TVQ  by SAS congruence property

∴ QS=TV  (CPCT)

CPCT: Congruent part of congruence triangles.

Hence Proved

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Step-by-step explanation:

in such a case the easiest approach might be using the point-slope form of a line equation :

y - y1 = m(x - x1)

with m being the slope, and (x1, y1) being a point on the line.

so, in our case that would be

y - 8 = 8(x - 4)

simplified this would be

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FYI - this would be then the slope-intercept form (-24 would be the intercept point on the y-axis).

3 0
1 year ago
Leslie has a rectangular patio. She measures it and finds out it is 2135 feet long by 1115 feet wide. She wants to know how many
larisa86 [58]

Answer: (1) Leslie will need 2,380,525 square tiles (1 foot by 1 foot each)

(2) She will have to spend $1,785,393.75 to cover her patio.

Step-by-step explanation: Please refer to the picture attached.

The rectangular patio has been designed and as shown in the diagram has on side measuring 2135 ft and the other side measuring 1115 ft. This means, in order to cover the entire patio, she would have to cover an entire area defined as 2,135 feet into 1,115 feet. If one tile measures 1 foot long by 1 foot wide, the total number of tiles to cover the patio can simply be derived as;

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Where the length is 2135 and the width is 1115,

Area = 2135 x 1115

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(1) The above calculation shows that Leslie would be using up a total of 2,380,525 square tiles to completely cover her patio.

(2) Having been told that each square foot of tile costs 75 cents ($0.75), the total amount spent to cover her patio would be calculated as follows;

Cost = Area x cost per tile

Cost = 2380525 x 0.75

Cost = 1785393.75

The total cost therefore is $1,785,393.75

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3 years ago
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Ivan

Answer: I would say 135

Step-by-step explanation:

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2 years ago
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