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Darya [45]
3 years ago
13

In rectangle abcd, points p and q lie on side AB and DC respectively. Angle PMQ is a right angle, M is the midpoint of side BC a

nd PB=4/3 BC. What is the ration PM: MQ

Mathematics
1 answer:
nirvana33 [79]3 years ago
8 0

Answer:

PM:MQ = 8:3.

Step-by-step explanation:

\rm \angle B\hat{M}P + 90^{\circ} + \angle C\hat{M}Q = 180^{\circ};

\implies \rm \angle B\hat{M}P + \angle C\hat{M}Q = 90^{\circ};

\implies \rm 90^{\circ} - \angle B\hat{M}P = \angle C\hat{M}Q.

Also,

\rm \angle B\hat{P}M = 90^{\circ} - \angle B\hat{M}P in right triangle PBM.

Thus \rm \angle{P\hat{B}M} = \angle C\hat{M}Q.

Additionally \rm \angle \hat{B} = 90^{\circ} = \angle \hat{C}.

Therefore \rm \triangle PBM \sim \triangle MCQ.

\rm \displaystyle BC = 2\;MC for M is the midpoint of segment BC.

\rm \displaystyle PB = \frac{4}{3}BC = \frac{8}{3}MC.

\rm \triangle PBM \sim \triangle MCQ implies that

\displaystyle \rm PM:MQ = PB:MC = 1:\frac{8}{3} = 8:3.

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Answer:

Sasuke     A 2-3

Step-by-step explanation:

4 0
3 years ago
solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. x-2y+
Alekssandra [29.7K]

Answer:

x = -5, y = -6, z = -3

Step-by-step explanation:

Given the system of three equations:

\left\{\begin{array}{l}x-2y+3z=-2\\6x+2y+2z=-48\\x+4y+3z=-38\end{array}\right.

Write the augmented matrix for the system of equations

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)

Find the reduced row-echelon form of the augmented matrix for the system of equations:

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)\sim \left(\begin{array}{ccccc}1&-2&3&|&-2\\0&-14&16&|&36\\0&-6&0&|&36\end{array}\right)\sim \left(\begin{array}{ccccc}1&3&-2&|&-2\\0&16&-14&|&36\\0&0&-6&|&36\end{array}\right)

Thus, the system of three equations is

\left\{\begin{array}{r}x+3z-2y=-2\\16z-14y=36\\-6y=36\end{array}\right.

From the last equation:

y=-6

Substitute it into the second equation:

16z-14\cdot (-6)=36\\ \\16z=36-84\\ \\16z=-48\\ \\z=-3

Substitute y = -6 and z = -3 into the first equation:

x+3\cdot (-3)-2\cdot (-6)=-2\\ \\x=-2+9-12\\ \\x=-5

7 0
3 years ago
The number of cats increased from 1650650 to 2250015. What is the percentage change to the nearest tenth?
Luden [163]
First you have to subtract 2250015 by 1650650 and the answer is 599365

The you add 2250015 to 1650650 and the answer is 3900665 so you divide

599365 by 3900665 and multiply by 100 and the final result is 517.325002

And to the nearest ten is 517.3 because 2 is below five to round up

Final answer— 517.3

Hope this helps
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Sholpan [36]
1056cans/ 8 cans=132 bags
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Which new angle is created by extending one side of a triangle
8090 [49]

Answer: The correct option is (C). an exterior angle.

Step-by-step explanation: We are to select the name of the new angle that is created by extending one side of a triangle.

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∠ABC, ∠ACB and ∠BAC are three interior angles of the triangle ABC.

Let us extend the side BC towards C to point D. The newly created angle is ∠ACD.

∠ACD is called the exterior angle of ΔABC.

Therefore, the newly created angle is an exterior angle.

Thus, option (C) is correct.

7 0
3 years ago
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