Answer:
[tex]\textsf{23.} \quad c)\;\;y=-2x+7[/tex]
[tex]\textsf{24.} \quad 12[/tex]
[tex]\textsf{25.} \quad -2.33\:\:\sf (2\:d.p.)[/tex]
Step-by-step explanation:
Question 23
Given equation:
[tex]y=\dfrac{1}{2}x-1[/tex]
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:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1=-2(x-3)[/tex]
[tex]\implies y-1=-2x+6[/tex]
[tex]\implies y=-2x+7[/tex]
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:
[tex]\begin{cases}x+y=15\\20x+50y=390\end{cases}[/tex]
Solve the first equation for y:
[tex]\implies y=15-x[/tex]
Substitute the found expression for y into the second equation and solve for x:
[tex]\implies 20x+50(15-x)=390[/tex]
[tex]\implies 20x+750-50x=390[/tex]
[tex]\implies -30x+750=390[/tex]
[tex]\implies -30x=-360[/tex]
[tex]\implies x=12[/tex]
Therefore, Kerry received 12 twenty-dollar bills.
Question 25
Given expression:
[tex]\dfrac{6^2-4^2}{-10+\sqrt{2}}[/tex]
Following the order of operations (PEMDAS), simplify the numerator:
[tex]\implies \dfrac{36-16}{-10+\sqrt{2}}[/tex]
[tex]\implies \dfrac{20}{-10+\sqrt{2}}[/tex]
Calculate the square root:
[tex]\implies \dfrac{20}{-10+1.414213...}[/tex]
Simplify the denominator:
[tex]\implies \dfrac{20}{-8.5857864...}[/tex]
Divide the numerator by the denominator:
[tex]\implies -2.3294313...[/tex]
Therefore:
[tex]\implies \dfrac{6^2-4^2}{-10+\sqrt{2}}=-2.33\:\: \sf (2\:d.p.)[/tex]
