Question

HELP WITH ALLLLL PLEASE THIS IS ALGEBRA II BTWWW:))

Answer 1

`\textsf{23.} \quad c)\;\;y=-2x+7`

`\textsf{24.} \quad 12`

`\textsf{25.} \quad -2.33\:\:\sf (2\:d.p.)`

Explanation:

Question 23

Given equation:

`y=(1)/(2)x-1`

If two lines are perpendicular to each other, the slopes are negative reciprocals.

Therefore, the slope of a line perpendicular to the given equation is -2.

Substitute the found slope and the given point (3, 1) into the point-slope formula to find the equation of the line:

`\implies y-y_1=m(x-x_1)`

`\implies y-1=-2(x-3)`

`\implies y-1=-2x+6`

`\implies y=-2x+7`

Question 24

Define the variables:

• Let x = number of $20 bills.
• Let y = number of $50 bills.

Given information:

• Total amount cashed = $390
• Total number of bills = 15

Create two equations with the given information:

`\begin{cases}x+y=15\\20x+50y=390\end{cases}`

Solve the first equation for y:

`\implies y=15-x`

Substitute the found expression for y into the second equation and solve for x:

`\implies 20x+50(15-x)=390`

`\implies 20x+750-50x=390`

`\implies -30x+750=390`

`\implies -30x=-360`

`\implies x=12`

Therefore, Kerry received 12 twenty-dollar bills.

Question 25

Given expression:

`(6^2-4^2)/(-10+√(2))`

Following the order of operations (PEMDAS), simplify the numerator:

`\implies (36-16)/(-10+√(2))`

`\implies (20)/(-10+√(2))`

Calculate the square root:

`\implies (20)/(-10+1.414213...)`

Simplify the denominator:

`\implies (20)/(-8.5857864...)`

Divide the numerator by the denominator:

`\implies -2.3294313...`

Therefore:

`\implies (6^2-4^2)/(-10+√(2))=-2.33\:\: \sf (2\:d.p.)`