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kotegsom
8 days ago
13

Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the ea

st coast, to $3 in the mid-US, to $5 on the west coast. B On their way back they had more baggage in the car and spend $601 for 174 gallons of gas. Based on the same ratio as in Part (a), how many gallons of gas did they buy at each price?
Mathematics
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Last year, sales at a book store increased from $5,000 to $10,000. This year, sales decreased to $5,000 from $10,000. What perce
Svet_ta [12734]
1. 200% =2
5000 multiplied by 2 equals 10000
2.50% = 0.5
10000 multiplied by 0.5 equals 5000
4 0
2 months ago
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What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.
lawyer [12517]

Answer:

x=-2.38

x=-4.62


Step-by-step explanation:

The question is (2x+3)^2+8(2x+3)+11=0

We let u=2x+3, so the equation becomes:

u^2+8u+11=0

Where a=1, b=8, c=11


By applying the quadratic formula, we arrive at:

Quadratic formula: \frac{-b+-\sqrt{b^2-4ac} }{2a}

Substituting yields: \frac{-8+-\sqrt{(8)^2-4(1)(11)} }{2(1)}\\=\frac{-8+-\sqrt{20} }{2}\\=\frac{-8+-2\sqrt{5} }{2}\\=-4+\sqrt{5}, -4-\sqrt{5} }

We let u=2x+3, thus x calculates to:

u=2x+3\\(-4+\sqrt{5})=2x+3\\x=\frac{-7+\sqrt{5}}{2}=-2.38

and

u=2x+3\\(-4-\sqrt{5})=2x+3\\x=\frac{-7-\sqrt{5}}{2}=-4.62


The solutions to the equation are x=-2.38 (rounded to 2 decimal places) and x=-4.62 (rounded to 2 decimal places)

6 0
1 month ago
On his 13th birthday, Josh’s aunt put some money in an account for him. The account pays 4% simple interest annually. She said,
Leona [12618]

Answer:

I’m not completely certain, but it could be $6.00

Step-by-step explanation:


4 0
1 month ago
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Nik needs to estimate how many books will fit in a bin. Each book is 1 ft tall, 0.5 ft wide, and 0.1 ft thick. The bin is 5 feet
lawyer [12517]

Answer:

600 books

Step-by-step explanation:

The dimensions of the bin are

5 by 2 by 3

The volume of the bin is found by multiplying these three dimensions.

Volume of Bin = 5 * 2 * 3 = 30 cubic feet

To find the volume of each book, we use the same method. The dimensions of one book are:

1 by 0.5 by 0.1

Volume of 1 book = 1 * 0.5 * 0.1 = 0.05 cubic feet

The total number of books fitting into the bin is calculated by:

30/0.05 = 600 books

6 0
3 months ago
The figure shows a kite inside a rectangle. Which expression represents the area of the shaded region? 2x2 4x2 6x2 8x2
lawyer [12517]
The area calculation for the shaded section, as seen in the attached diagram, involves subtracting the area of the kite from that of the rectangle. The area of the rectangle is calculated as (3x+x)*(x+x), which simplifies to 4x*2x, equating to 8x². The area of the kite is determined using the formula (1/2)*[d1*d2], where d1 and d2 represent the diagonals, specifically d1=4x and d2=2x. Therefore, the area of the kite becomes (1/2)*[4x*2x], leading to 4x². Consequently, the area of the shaded region can be computed as 8x²-4x², resulting in 4x². Thus, the solution is 4x².
5 0
2 months ago
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