Rationalize the numerator of the expression

the teacher separated her class of twenty-eight student into two group. one group has 4 more than twice as many students as the

mina [271]

For this case, the first thing we must do is define variables:

x: students of group 1

y: students of group 2

We now write the system of equations that models the problem:

$x + y = 28\\y = 2x + 4$

Solving the system by substitution we have:

$x + (2x + 4) = 28\\3x + 4 = 28\\3x = 28-4$

$3x = 24$

$x = \frac{24}{3}\\x = 8$

Then, the value of y is given by:

$y = 2 (8) +4\\y = 16 + 4\\y = 20$

Answer:

8 students of group 1

20 students of group 2

3 0

3 years ago

Read 2 more answers

Veronique found the difference of a number and 8. Which expression models the situation? n minus 8 StartFraction 8 Over n EndFra

Katyanochek1 [597]

Answer:

n-8

Step-by-step explanation:

4 0

3 years ago

A counter top is 18 feet long and 3 feet wide. What is the area of the counter top in square meters? Use the conversion 1 foot =

podryga [215]

Answer:

Area of the counter top is $5.02\ m^2$ .

Step-by-step explanation:

Given:

Length of the Counter top = 18 feet

Width of the counter top = 3 feet

We need to find the area of the counter top is square meter;

Solution:

Now we need to find the area of the counter top is square meter.

But given data is in feet so we will first convert feet into meters.

1 foot = 0.305 meter.

So 18 feet = Number of meters in 18 feet.

By Using Unitary method we get;

Number of meters in 18 feet = $18\times 0.305 = 5.49\ m$

Length of the Counter top = 5.49 m

Also 3 feet = Number of meters in 3 feet.

Again Using Unitary method we get;

Number of meters in 3 feet = $3\times 0.305 = 0.915\ m$

Width of the counter top = 0.915 m

Now we know that;

Area of the counter top can be calculated by multiplying Length of the counter top with width of the counter top.

framing in equation form we get;

Area of the counter top = $5.49\times 0.915 = 5.0233\ m^2$

Rounding up to 2 decimals we get;

Area of the counter top = $5.02\ m^2$

Hence Area of the counter top is $5.02\ m^2$ .

3 0

4 years ago

Graph the circle which is centered at (-5,1) and has a radius of 4 units

Elden [556K]

(y+5)^2 + (x-1)^2 = 16
[^2 meaning squared]

7 0

3 years ago

Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root min

Cloud [144]

$7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}$ simplified as $11\sqrt{3}- 7\sqrt{6}$ or $1.909$ .

<u>Step-by-step explanation:</u>

We need to Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four. Which is equivalent to $7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}$ :

$7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}$

⇒ $7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{44}$

⇒ $7\sqrt{3}- 4\sqrt{6} + \sqrt{16(3)} - \sqrt{9(6)}$

⇒ $7\sqrt{3}- 4\sqrt{6} + 4\sqrt{(3)} - 3\sqrt{(6)}$

⇒ $11\sqrt{3}- 4\sqrt{6}- 3\sqrt{(6)}$

⇒ $11\sqrt{3}- 7\sqrt{6}$

$\sqrt{3} = 1.732 , \sqrt{6} = 2.449$

⇒ $11(1.723)- 7(2.449)$

⇒ $1.909$

Therefore, $7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}$ simplified as $11\sqrt{3}- 7\sqrt{6}$ or $1.909$ .

6 0

3 years ago