Equations & Expressions
7 + (-5)
2
6x5 times 4x3 equals?
24x8
If two angles have the same measurement, (90 = 90), then what type of relationship do the angles have?
Key: (Complementary Angle, Supplementary Angle, Adjacent Angle, Vertical Angle, Congruent Angle)
Congruent Angle
Bob owns a mechanic shop downtown Marlton. One day, Bob gets a call from a customer that the customer's car might be too big for the garage. Bob disagrees and reassures the customer that he can serve him. If the garage is 20 feet long and 15 feet wide, and the customer's car is 248 feet(in terms of AREA), can Bob serve the customer? If so, explain why.
Yes, the customer's car is 248 feet, but the garage is 300 feet, Bob can help the customer fix his car.
What's the diameter of a circle if the radius is 6 cm long?
12 cm
Is this an infinite, one or no solution?
-6x + 5 = -6x + 18
no D:
Solve for x.
6 = 2(x+2)
x = 1
Saharsh is confused if complementary angles equal 180 or if supplementary angles equal 180. Explain why you chose the answer.
The answer is supplentary angles. Complementary angles equal 90 degrees, not 180.
If the volume of the book is 605 cm, and the width and height are both 10 cm, then what's the length of the book?
The length - 6.05 cm.
What's the slope of this?
(2, 500) - (8, 2,000)
Slope - y = 250x
Sam loves nuts. Sam wants to share some of his nuts to his friends so he decides to buy h packs of nuts. If Sam has a budget of $20, and each package costs $1.20, how many packs can he buy without going over his budget? Write your answer as an inequality.
or
x≤16.66..
Solve for x.
6x + 18 = 5x - 27
x = -45
5x = 7x - 20
x = 10
Ava makes a triangle where the values are: 8m (height), and 19m(base). While cutting the triangle out, Ava cuts the triangle and claims that, if the triangle was a square, the area would be 76m. While Ava starts explaining, she accidently rips a small piece of the triangle, being 5m in area. Since the piece was ripped off, one of her classmates, Joseph, saids the area is now 71m instead of 76m. Who is correct? And why might the other person be wrong?
Joseph is correct. Because Ava rips off a piece of paper from her "square", this decreases the area of the square from 76m to 71 m. Joseph is correct for pointing out that the "square" should be 71m.
What's the slope and linear equation of this?
(3, 17) - (6, 32)
Slope - 5x
Linear Equation - y = 5x + 2
Emma likes to eat salad. Emma goes to her local Saladworks and orders her usual meal: a salad with chicken, spinach, tomatoes, ranch, and a mango juice. Emma spends about $20 for this meal. The mango juice costs $5.98. With the remaining money, all of the ingredients are her salad cost the same price. However, due to new inflations, all of the ingredients cost about 30% more and the mango juice costs 49% more. Using this infomoration, if Emma brings $28, can she still afford this meal?
Yes, Emma can still afford this meal.
New meal price - $27.14(or 27.15), less than 28
4x2 times 6x-6 over 2x3 times 12x8 is what?
1 over x to the power of 15.
Gavin makes two angles which equal up to 180 degrees. If the first angle is 75 less than the second angle, then what's the value of both the first and second angle?
First angle - 52.5
Second Angle - 127.5
Austin decides to go travelling to a country. Austin's travel bag's dimensions are 3 feet by 2 feet by 2 feet. If the travel weight limit was 50 pounds and Austin's bag was 1.5 pounds per feet(surface area), then can Austin go on the flight using his bag? Or will he need to pay a fee?
Note: This problem is unrealistic to real-life scenarios.
Austin can go on the flight using his travel bag. (Travel bag = 48 pounds)
What's the linear equation of this?
(19, 488) - (43, 1208)
Linear Equation - y = 30x - 82
Francis has $2,500 and wants to go to Ireland for a week. However, Francis can only buy a round-trip ticket, yet, when Francis tries to open the airlines website, it is bugged, forcing Francis to go to the airport and buy the ticket instead. Because of this, the cost to buy the ticket is 3x + 16251 = 18672(x is the cost of the ticket). After this, Francis goes to Ireland and stays at a hotel for 4 days which costs $50 a night. Afterwards, Francis goes to another hotel for 3 days which costs $129 a night. Before going, Francis thinks if he should stay at one hotel only. Francis also buys snacks every day for $6.69 each time. Francis spends about $143.27 each day for meals. However, on the last day, Francis goes to an all-you-can eat buffet, costing $100 per person(This is the only meal Francis eats for this day) To remember the trip, Francis buys a souvenir that costs $6. Using all of this infomoration, what's the most amount of money Francis can spend without going over his amount?
- Very Hard Question - use your brain! :D
Francis can spend about $2,406.45 without going over his budget.
x-3 times y-3 times z-3 = 1
Note: x, y, and z must be the same value!
x, y, z = 1
Sarah makes four angles, A, B, C, and D. All of these angles equal 360 degrees. If A = CD, and D = 20, and C equals 18, then what are all of the values?
- Challeneging Question!
David works at a factory which makes toys. The most popular toy, "Woodie" is 6cm by 8 cm. However, the least popular toy, "Buzz" is 8 cm by 15 cm. Both of these toys use wood, however Woodie uses a different type of wood than Buzz. Woodie uses a wood that costs $0.80 to make every 1 cm, but Buzz uses a wood that costs $0.35 to make every 1 cm. Using this, David also makes a box for the toys. "Woodie" uses a box that is 6cm by 7 cm by 10 cm while "Buzz" uses a box that is 20 cm by 9 cm by 3 cm. Woodie's box costs $1.20 to make every 1 cm. Buzz's box costs $0.55 to make every 1 cm, using this information, which toy can make more money for 10 packaged toys? Both toys are charged 50% than their cost to make. Customers are less likely to buy toys that cost more than $500, having only a 60% chance to buy the toy.
Use this information to solve this problem!
- SUPER HARD Question!
Woodie makes $4,881.60 per 10 toys(packaged) while Buzz makes $3,051 per 10 toys(packaged). Woodie has a net loss of -$542.40 while Buzz has a net loss of -$339. This shows that Buzz ultimately makes more money than Woodie despite making less money(in sales)
Lucy draws a shape in class. This shape is a triangle. While making it, Lucy uses a ruler and measures the shape. The drawing is 6 cm(base) and h cm(height), Lucy does not know of the height of the triangle but what she does know is that the height is 3 times fewer than the area. If the area is 24 cm, then what's the height of the triangle?
The height of the triangle is 8 cm.