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Pavel [41]
2 years ago
14

Determine the number of solutions for the system 6x+9y=9 amd -6x+6y=1

Mathematics
1 answer:
ozzi2 years ago
4 0

Answer:

One solution

Step-by-step explanation:

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PETS Becky wants to buy some fish for her aquarium. She has $20 to spend and the fish cost $2.50 each. Write and solve an inequa
Vilka [71]
To start, you want to determine the inequality. You can do this by setting the number of buying n fish to be less than or equal to her current amount of money, being as it can't go over or she wouldn't be able to afford the fish. This inequality would be written so her amount of money (20) would be greater than or equal to the cost of n fish (2.5n), which would then look as such: 20≥2.5n. To solve this inequality, just solve for n by dividing both sides by 2.5, giving you 8≥n. This would mean that Becky can afford to buy up to 8 fish.
6 0
3 years ago
Ella has 0.5 lb of sugar. how much water should she add to make the following concentrations? Tell Ella how much syrup she will
makkiz [27]

Answer:

For 50% syrup, add 0.5 lb of water for 1 lb of syrup; for 5% syrup, add 9.5 lb of water for 10 lb of syrup; for 75% syrup, add 0.17 lb of water for 0.67 lb of syrup; for 1.5% syrup, add 32.8 lb of water for 33.3 lb of syrup.

Step-by-step explanation:

Let x represent the amount of water added.  This means the total mass of the syrup is represented by 0.5+x.

To find percentages, we divide the part by the whole.  For a 50% syrup, we need the part (sugar) compared to the whole (sugar + water) to equal 50%, or 0.50:

Multiply both sides by 0.5+x:

Using the distributive property, we have

0.5 = 0.5(0.5)+0.5(x)

0.5 = 0.25+0.5x

Subtract 0.25 from each side:

0.5-0.25 = 0.25+0.5x-0.25

0.25 = 0.5x

Divide both sides by 0.5:

0.25/0.5 = 0.5x/0.5

x = 0.5

For 50% syrup, add 0.5 lb of water.  This makes the total mass 0.5+0.5 = 1 lb.

For 5% syrup, we change the equation to equal 0.05 (5% = 5/100 = 0.05) and leave everything else the same:

Multiply both sides by 0.5+x:

Using the distributive property,

0.5 = 0.05(0.5)+0.05(x)

0.5 = 0.025 + 0.05x

Subtract 0.025 from both sides:

0.5-0.025 = 0.025+0.05x-0.025

0.475 = 0.05x

Divide both sides by 0.05:

0.475/0.05 = 0.05x/0.05

x = 9.5

For 5% syrup, add 9.5 lb of water; the total mass will be 9.5+0.5 = 10 lb.

For 75% syrup, set the equation equal to 0.75:

Using the distributive property,

0.5 = 0.75(0.5)+0.75(x)

0.5 = 0.375 + 0.75x

Subtract 0.375 from each side:

0.5 - 0.375 = 0.375 + 0.75x - 0.375

0.125 = 0.75x

Divide both sides by 0.75:

0.125/0.75 = 0.75x/0.75

0.17 = x

For 75% syrup, add 0.17 lb of water; the total mass is 0.17+0.5 = 0.67 lb.

For 1.5% syrup, set the equation equal to 0.015:

Using the distributive property,

0.5 = 0.015(0.5) + 0.015(x)

0.5 = 0.0075 + 0.015x

Subtract 0.0075 from each side:

0.5-0.0075 = 0.0075 + 0.015x - 0.0075

0.4925 = 0.015x

Divide both sides by 0.015:

0.4925/0.015 = 0.015x/0.015

32.8 = x

For 1.5% syrup, use 32.8 lb of water; the total mass is 32.8+0.5 = 33.3 lb.

I hope this is right and have a good day

3 0
2 years ago
Read 2 more answers
Y-2=-3(x-7) written in standard form
uysha [10]
Y=2-3(x-7)
You just add +2 to each side and the positive and negative cancel out and it switches it over
8 0
2 years ago
What is the length of BC in the right triangle below?
gayaneshka [121]

Hey there! :)

Answer:

C. BC = 39 units.

Step-by-step explanation:

Use the Pythagorean theorem to solve for BC. Let BC = c, AB = a, and AC = b.

c² = a² + b²

c² = 15² + 36²

Square and simplify:

c² = 225 + 1296

c² = 1521

c = √1521

c = 39 units.

Therefore:

BC = 39 units.

5 0
3 years ago
Read 2 more answers
Could you help me with this equation:<br> <img src="https://tex.z-dn.net/?f=x%5E%7B3%7D%20%2B%205x%5E%7B2%7D%20-%2018x%20%2B%203
lord [1]

if you want to solve it without a graph you're going to need to use the cubic formula, I'm unsure how else to solve it

3 0
3 years ago
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