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3 years ago

12

The difference of two is 4. The larger is 8 less than twice the smaller. What are the two numbers ?

1 answer:

siniylev [52]3 years ago

5 0

Answer:

{12, 16}

Step-by-step explanation:

The difference of two <em>numbers (x and y)</em> is 4. Thus, if y is the larger, then y - x = 4. Also, y = 2x - 8.

So we need to solve the system of linear equations

y - x = 4

y = 2x - 8

Subbing 2x - 8 for y, in the first equation, we get (2x - 8) - x = 4, or

x - 8 = 4, and conclude that x = 12. Then, because y - x = 4, y must be 16.

The numbers are 12 and 16.

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Solve the Equation <br> 2x-3=14<br> -x+3y=-6

andriy [413]

Step-by-step explanation:

If you lost "y" in the first equation.

$\underline{+\left\{\begin{array}{ccc}2x-3y=14\\-x+3y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\\\.\qquad x=8\\\\\text{Put the value of x to the first equation:}\\\\2(8)-3y=14\\16-3y=14\qquad\text{subtract 16 from both sides}\\-3y=-2\qquad\text{divide both sides by (-3)}\\y=\dfrac{2}{3}\\\boxed{x=8,\ y=\dfrac{2}{3}}$

If first equation is correct.

$2x-3=14\qquad\text{add 3 to both sides}\\2x=17\qquad\text{divide both sides by 2}\\x=8.5\\\\\text{Put the value of x to the second equation:}\\-8.5+3y=-6\qquad\text{add 8.5 to both sides}\\3y=2.5\qquad\text{divide both sides by 3}\\y=\dfrac{2.5}{3}\\y=\dfrac{25}{30}\\y=\dfrac{5}{6}\\\\\boxed{x=8.5,\ y=\dfrac{5}{6}}$

6 0

2 years ago

How many different simple random sampmes of size 5 can be obtained from a pppulation whose size is 43?

Nesterboy [21]

Answer:

Number of random samples = 962598

Step-by-step explanation:

A random sample represents the responses for a certain survey of a part of the population.

A sample size is the part of the population being surveyed.

For a population $N$ the number of different random samples that can be chosen for a sample size $x$ can be calculated as = $NCx$

This can be calculated as :

$NCx=\frac{N!}{x!(N-x)!}$

Given:

Population size = 43

Sample size = 5

Number of random samples = $43C5$

⇒ $\frac{43!}{5!(43-5)!}$

⇒ $\frac{43!}{5!(38)!}$

⇒ $\frac{43\times42\times41\times40\times39}{5\times4\times3\times2\times1}$ [Canceling out the common terms]

⇒ $962598$ (Answer)

4 0

2 years ago

Now examine |a + bi| and complete the definition below. The absolute value of any complex number a + bi is the from (a, b) to (0

sergejj [24]

Distance

|a+bi| is the length of the vector from origin to (a,b).

$|a+bi| = \sqrt{a^2 + b^2}$

8 0

3 years ago

Read 2 more answers

Suppose that y varies directly with x<br> and y = 10 when x = 20. What is y<br> when x = 15?

tresset_1 [31]

Answer: y = 7.5

Step-by-step explanation:

Suppose that y varies directly with x

That is, y∝x

Convert y∝x to a full equation by introducing a constant k to the right hand side.

Therefore, y = kx

Given that y = 10 and x = 20

Substitute y and x in the equation above. We have;

10 = k(20)

10 = 20k

20k = 10

k = 10/20

k = 0.5

Since k = 0.5, the equation y = kx becomes y = 0.5x

Now, to find y if x = 15, substitute x in equation y = 0.5x

Therefore, y = 0.5(15)

y = 7.5

5 0

2 years ago

Answer please ASAP!!!!!!

weqwewe [10]

<h3>Answer: 282.6 square units</h3>

====================================================

Work Shown:

r = 3 is the radius of the circular base

h = 12 is the height of the cylinder

pi = 3.14 approximately

SA = surface area of the cylinder

SA = 2pi*r^2 + 2pi*r*h

SA = 2*3.14*3^2 + 2*3.14*3*12

SA = 282.6

3 0

2 years ago