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2 years ago

Q5. Solve for x and y using elimination method.10x +3y = 75, 6x - 5y = 11

Mathematics

1 answer:

sleet_krkn [62]2 years ago

8 0

Answer:

16x - 2y = 86

Step-by-step explanation:

10x + 3y = 75

+ 6x - 5y = 11

16x -2y =86

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In a parallelogram ABCD point K belongs to diagonal BD so that BK:DK=1:4. If the extension of AK meets BC at point E, what is th

olya-2409 [2.1K]

Answer:

$\frac{BE}{EC} =\frac{1}{3}$

Step-by-step explanation:

In the diagram below we have

ABCD is a parallelogram. K is the point on diagonal BD, such that

$\frac{BK}{CK} =\frac{1}{4}$

And AK meets BC at E

now in Δ AKD and Δ BKE

∠AKD =∠BKE ( vertically opposite angles are equal)

since BC ║ AD and BD is transversal

∠ADK = ∠KBE ( alternate interior angles are equal )

By angle angle (AA) similarity theorem

Δ ADK and Δ EBK are similar

so we have

$\frac{AD}{BE} =\frac{DK}{BK}$

$\frac{AD}{BE} =\frac{4}{1}$

$\frac{BC}{BE}=\frac{4}{1}$ ( ABCD is parallelogram so AD=BC)

$\frac{BE+EC}{BE}=\frac{4}{1}$ ( BC= BE+EC)

$\frac{BE}{BE} +\frac{EC}{BE}=\frac{4}{1}$

$1+\frac{EC}{BE}=4$

$\frac{EC}{BE}=3$ ( subtracting 1 from both side )

$\frac{EC}{BE}=\frac{3}{1}$

taking reciprocal both side

$\frac{BE}{EC} =\frac{1}{3}$

8 0

3 years ago

the perimeter of a rectangle is 160ft. One fourth the length is the same as twice the width. Find the dimensions of the rectangl

Hitman42 [59]

Answer:

w = 80/9 ft.

L = 640/9 ft.

Step-by-step explanation:

L = length w = width

2w = L/4 so 8w = L

160 = 2L + 2w

160 = 2(8w) + 2w

160 = 16w+2w

160 = 18w

80/9 = w

5 0

2 years ago

Q5. Solve for x and y using elimination method.10x +3y = 75, 6x - 5y = 11​

Q5. Solve for x and y using elimination method.10x +3y = 75, 6x - 5y = 11