Algebra
Evaluate:
4Β²+3Β²
16+9=25
A car rental company charges $40 as a flat fee plus $0.20 per kilometre. What is the equation that represents the total cost C to drive d km?
C=0.20d+40
Determine the π₯ and y intercepts of the line: 2π₯+y=6
π₯-int: Let y=0
2x=6
x=3
y-int: Let x=0
y=6
In a triangle, two angles measure 53Β° and 68Β°. What is the measure of the third angle?
Total = 180Β°
180Β°β53Β°β68Β°=59Β°
What is the next number in this pattern?
2, 4, 8, 16, ___
The pattern multiplies by 2 each time: 32
Simplify:
π₯Β³ Γ π₯Β² Γ· π₯
π₯Β³ Γ π₯Β² = π₯β΅
π₯β΅ Γ· π₯ = π₯β΄
Using the equation C=0.20d+40, how much will it cost to drive 250km?
C=0.20(250)+40
= 50+40
= $90
Are the lines y=3x+1 and y=-1/3x-2 perpendicular? Justify.
Yes. Their slopes (3 and -1/3) are negative reciprocals so they are perpendicular.
Two straight lines intersect, forming vertical angles. One angle measures 72Β°. What is the measure of the angle opposite it?
Vertical angles are equal:
Opposite angle=72Β°
Is the number 221 a prime number? If not, name a factor.
No, 221 is not a prime number. 13Γ17=221
3(π₯+4)-2(π₯-1)
3π₯+12-2π₯+2= π₯+14
A school is selling tickets to a talent show. Student tickets cost $5 and adult tickets cost $8.
The school sells π₯ student tickets and y adult tickets and earns $460 in total.
a) Write an equation that represents this situation.
b) If the school sold 40 adult tickets, how many student tickets were sold?
a) 5π₯ +8y =460
b) Substitute y=40
5π₯+8(40)=460
5π₯+320=460
5π₯=140
x=28
The equation of a horizontal line is y=β4. What is the slope, and how does the graph look?
Slope= 0
Itβs a straight line passing through y=β4 and parallel to the π₯-axis
A rectangular garden is 7.5m long and 4.2m wide. What is the perimeter of the garden?
2(7.5+4.2)= 2(11.7)= 23.4m
A shirt is on sale for 25% off. If the original price is $40, what is the sale price?
40Γ0.25=10
40β10=$30
The length of a rectangle is 3 times its width. If the perimeter is 48cm, what are the dimensions?
Let width=π₯ and length=3π₯
Perimeter:=2(π₯+3π₯)= 8π₯ =482(π₯+3π₯)=8π₯= 48 π₯=6π₯=6
Width:= 6cm
Length = 18cm
Rearrange the equation 4π₯β2y=10 into slope-intercept form and state the slope and y-intercept.
-2y=-4π₯+10
y=2π₯-5
slope: 2
y-int:-5
Find the equation of the line that passes through the points (β2, 4) and (2,β4).
Slope: -4-4/2-(-2)=-8/4=-2
Use point-slope:
y-4=-2(x+2)
y=-2x
A triangular sail has a base of 6.2m and a height of 3.5m. What is the area of the sail?
A=1/2x6.2x3.5=10.85mΒ²
A number is divisible by both 2 and 3. What other number is it definitely divisible by?
The least common multiple of 2 and 3 is 6.
A triangle has side lengths: 2π₯+3, π₯+5, and 4π₯β7. Find the perimeter when π₯=4.
Perimeter expression: 2π₯+3+π₯+5+4π₯β7= 7π₯+1
π₯=4:7(4)+1=29
A linear relation passes through the points (1,3) and (5,7). What is the equation of the line?
Slope: 7-3/5-1
Use point-slope form:
y-3=1(π₯-1)
y=π₯+2
A gym offers two pricing plans:
Plan A: $25/month + $5/visit
Plan B: $10/visit only.
Set up the equations and find when both plans cost the same.
A: C=5v+25
B: C=10v
Solve:
5v+25=10v
25=5v
v=5 visits
A rectangular prism has a length of 5cm, width of 4cm, and height of 3cm. What is the surface area of the prism?
SA = 2(lw+lh+wh)=2(20+15+12)=2(47)=94cmΒ²
You roll two six-sided dice. What is the probability of rolling a total of 7?
There are 6 combinations that make 7 out of 36 total rolls:
6/36=1/6