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3 years ago

Solve the system of linear equations below 2x-y=0 3x-2y=-3

Mathematics

1 answer:

Lynna [10]3 years ago

3 0

2x - y = 0
2x = y

3x - 2(2x) = -3
3x - 4x = -3
-x = -3
x = 3

2(3) = y
6 = y

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In a shipment of 56 vials, only 13 do not have hairline cracks. If you randomly select 3 vials from the shipment, in how many wa

Elden [556K]

Answer: 27434

Step-by-step explanation:

Given : Total number of vials = 56

Number of vials that do not have hairline cracks = 13

Then, Number of vials that have hairline cracks =56-13=43

Since , order of selection is not mattering here , so we combinations to find the number of ways.

The number of combinations of m thing r things at a time is given by :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

Now, the number of ways to select at least one out of 3 vials have a hairline crack will be :-

$^{13}C_2\cdot ^{43}C_{1}+^{13}C_{1}\cdot ^{43}C_{2}+^{13}C_0\cdot ^{43}C_{3}\\\\=\dfrac{13!}{2!(13-2)!}\cdot\dfrac{43!}{1!(42)!}+\dfrac{13!}{1!(12)!}\cdot\dfrac{43!}{2!(41)!}+\dfrac{13!}{0!(13)!}\cdot\dfrac{43!}{3!(40)!}\\\\=\dfrac{13\times12\times11!}{2\times11!}\cdot (43)+(13)\cdot\dfrac{43\times42\times41!}{2\times41!}+(1)\dfrac{43\times42\times41\times40!}{6\times40!}\\\\=3354+11739+12341=27434$

Hence, the required number of ways =27434

5 0

2 years ago

A flower bed has a shape of a rectangle 9yards long and 3 yarss wide what is the area in square feet

Maslowich

It should be 81 square feet.

3 yards x 9 yards = 27 yards squares.

It asks for your answer in square feet, so you multiply by 3. This is because there are 3 feet in ever yard.

27 x 3 feet = 81 square feet.

8 0

2 years ago

A vehicle is moving at a constant speed travels 45 miles in 3/4 hour. The driver thinks he will be late to a meeting that is sti

Ivahew [28]

The unit rate is 60 miles per hour and the driver will reach before time with the calculated constant speed

Step-by-step explanation:

Given

Distance = d = 45 miles

Time = t = 3/4 hour

The unit rate is defined as the distance per unit time. In this case, the unit rate can also be called speed.

So,

$s = \frac{d}{t}\\s = \frac{45}{\frac{3}{4}}\\s = 45 * \frac{4}{3}\\s = 60\ miles\ per\ hour$

Using this unit rate we can see if the car can travel 65 miles in 1.25 hours or not

Given

Distance = d1 = 65 miles

Speed = s = 60 miles per hour

Putting the values in the formula for speed

$s = \frac{d_1}{t_1}\\60 = \frac{65}{t_1}\\t_1 = \frac{65}{60}\\t_1 = 1.08\ hours$

As we can see that 1.08 is less than 1.25 so the driver will reach the meeting before time if he drives on a constant speed of 60 miles per hour

Hence,

The unit rate is 60 miles per hour and the driver will reach before time with the calculated constant speed

Keywords: Speed, unit rate

Learn more about speed at:

#LearnwithBrainly

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2 years ago

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Answer:

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