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2 years ago

Solve the system of equations -x+y=15−x+y=15 and -5x-3y=27−5x−3y=27 by combining the equations

Mathematics

1 answer:

Genrish500 [490]2 years ago

8 0

Answer:

<em>Solution: x= -36, y=51</em>

Step-by-step explanation:

Solve the system:

x + y = 15

-5x - 3y = 27

By using the reduction method.

Multiply the first equation by 3:

3x + 3y = 45

Add it to the second equation:

3x - 5x = 45 + 27

Simplifying:

-2x = 72

Dividing by -2:

x = 72/(-2)

x = -36

From the first equation:

-36 + y = 15

Adding 36:

y = 15 + 36 = 51

y = 51

Solution: x= -36, y=51

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3 years ago

Quadrilateral CAMP below is a rhombus. the length PQ is (x+2) units, and the length of QA is (3x-14) units. Which statements bes

valentinak56 [21]

Answer:

<h3>Q cuts the diagonal PA into 2 equal halves, since the diagonals of rhombus meet at right angles.</h3><h3>The value of x is 8.</h3>

Step-by-step explanation:

Given that Quadrilateral CAMP below is a rhombus. the length PQ is (x+2) units, and the length of QA is (3x-14) units

From the given Q is the middle point, which cut the diagonal PA into 2 equal halves.

By the definition of rhombus, diagonals meet at right angles.

Implies that PQ = QA

x+2 = 3x - 14

x-3x=-14-2

-2x=-16

2x = 16

dividing by 2 on both sides, we will get,

$x =\frac{16}{2}$

<h3>∴ x=8</h3><h3>Since Q cuts the diagonal PA into 2 equal halves, since the diagonals of rhombus meet at right angles we can equate x+2 = 3x-14 to find the value of x.</h3>

The line segment $\overrightarrow{PA}=\overrightarrow{PQ}+\overrightarrow{QA}$

$\overrightarrow{PA}=x+2+3x-14$

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3 years ago

A family is driving 600 miles. Assuming they stop to get gas 3 times and eat 2 times, how many hours will it take them to reach

Umnica [9.8K]

Lets assume that they are driving at an average of 70mph, and getting gas takes 10 minutes, and stopping to eat takes 30.

t=d/s

t=600/70
t=8.57

Stopping to eat twice is 30 x 2 = 60 (another hour)

and Gas is 10 x 3 = 30 minutes (0.5 hours)

Total time is,

8.57+1+0.5 =10.07

So the trip will take approx 10.7 hours total.

(This is using my assumptions, from my experience!)

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