Answer:
The numerical length of RS is 22 units
Step-by-step explanation:
∵ Point S is on the line segment RT
→ <em>That means S divide RT into two parts RS and ST</em>
∴ RS + ST = RT
∵ RS = 4x - 10
∵ ST = 2x - 10
∵ RT = 4x - 4
→ <em>Substitute them in the statement above</em>
∴ 4x - 10 + 2x - 10 = 4x - 4
→ <em>Add the like terms in the left side</em>
∴ (4x + 2x) + (-10 + -10) = 4x - 4
∴ 6x + (-20) = 4x - 4
∴ 6x - 20 = 4x - 4
→ <em>Add 20 to both sides</em>
∴ 6x -20 + 20 = 4x - 4 + 20
∴ 6x = 4x + 16
→ <em>Subtract 4x from both sides</em>
∴ 6x - 4x = 4x - 4x + 16
∴ 2x = 16
→ <em>Divide both sides by 2 to find x</em>
∴ 
∴ x = 8
→ <em>Substitute the value of x in Rs to find its length</em>
∵ RS = 4(8) - 10
∴ RS = 32 - 10
∴ RS = 22 units
The numerical length of RS is 22 units
Answer:
$2,820
Step-by-step explanation:
Since, £1 = $1.41
Therefore, £2,000 = 2000*1.41 = $2,820
5(x-2)+7=65-4(5x-8)
We move all terms to the left:
5(x-2)+7-(65-4(5x-8))=0
We multiply parentheses
5x-(65-4(5x-8))-10+7=0
We calculate terms in parentheses: -(65-4(5x-8)), so:
65-4(5x-8)
determiningTheFunctionDomain
-4(5x-8)+65
We multiply parentheses
-20x+32+65
We add all the numbers together, and all the variables
-20x+97
Back to the equation:
-(-20x+97)
We add all the numbers together, and all the variables
5x-(-20x+97)-3=0
We get rid of parentheses
5x+20x-97-3=0
We add all the numbers together, and all the variables
25x-100=0
We move all terms containing x to the left, all other terms to the right
25x=100
x=100/25
x=4
Answer:

with the video game cost of x = $6
This agrees with the last option in the list of possible answers
Step-by-step explanation:
Recall that the maximum of a parabola resides at its vertex. So let's find the x and y position of that vertex, by using first the fact that the x value of the vertex of a parabola of general form:

is given by:

In our case, the quadratic expression that generates the parabola is:

then the x-position of its vertex is:

This is the price of the video game that produces the maximum profit (x = $6). Now let's find the y-position of the vertex using the actual equation for this value of x:

This value is the highest weekly profit (y = $246).
Now, recall that we can write the equation of the parabola in what is called "vertex form" using the actual values of the vertex position
:

Therefore the answer is:

with the video game cost of x = $6