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2 years ago

In ANOP, NP is extended through point P to point Q, m_OPQ = (9x – 19)°,

Mathematics

1 answer:

jarptica [38.1K]2 years ago

5 0

Answer:

The values of x and y are x = 6 and y = 9Step-by-step explanation:

MNOP is a parallelogram its diagonal MO and PN intersected at point A

In any parallelogram diagonals:

Bisect each other

Meet each other at their mid-point

In parallelogram MNOP

∵ MO and NP are its diagonal

∵ MO intersect NP at point A

- Point A is the mid-point pf them

∴ MO and NP bisect each other

∴ MA = AO

∴ PA = AN

∵ MA = x + 5

∵ AO = y + 2

- Equate them

∴ x + 5 = y + 2 ⇒ (1)

∵ PA = 3x

∵ AN = 2y

- Equate them

∴ 2y = 3x

- Divide both sides by 2

∴ y = 1.5x ⇒ (2)

Now we have a system of equations to solve it

Substitute y in equation (1) by equation (2)

∴ x + 5 = 1.5x + 2

- Subtract 1.5x from both sides

∴ - 0.5x + 5 = 2

- Subtract 5 from both sides

∴ - 0.5x = -3

- Divide both sides by - 0.5

∴ x = 6

- Substitute the value of x in equation (2) to find y

∵ y = 1.5(6)

∴ y = 9

The values of x and y are x = 6 and y = 9

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3 years ago

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Math quest after a winter storm, the depth of the snow on cherry street was 10 \text{ cm}10 cm10, space, c, m. but then, the sno

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Answer:

9 cm.

Step-by-step explanation:

Let x be the number of hours.

We have been given that after a winter storm, the depth of the snow on cherry street was 10 cm. Then, the snow started melting at a rate of $\frac{1}{3}$ , so the snow melted in x hours will be $\frac{1}{3}x$ .

Since initially there was 10 cm of snow, so the depth of snow after x hours will be:

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3 years ago

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Which angle determines whether or not quadrilateral SVUT is a trapezoid? What measure would the angle need to be for SVUT to be

Lorico [155]

Answer: The answer is ∠TUV.

Step-by-step explanation: Given in the question a quadrilateral SVUT with ∠SVU = 112°. We need to determine the angle whose measure will decide whether or not the quadrilateral SVUT is a trapezoid.

We know that for a quadrilateral to be a trapezoid, we need only one condition that one pair of opposite sides must be parallel.

So, in quadrilateral SVUT, since the measure of ∠SVU is given, so we can decide it is a trapezoid or not if we know the measure of ∠TUV. As ST and UV cannot be parallel, so its meaningless to determine ∠TSV.

For SV and TU to be parallel to each other, we need

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Thus, we need to determine ∠TUV and its measure shoul be 68°.

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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amm1812

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3 years ago

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