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ra1l [238]
3 years ago
7

Convert the following equation into standard form. y = -5x + 2 5x + [?]y = [ ]

Mathematics
1 answer:
antiseptic1488 [7]3 years ago
6 0

Answer:

standard form is Ax + by + c = 0

Step-by-step explanation:

add 5x to each side to get 5x + y - 2 = 0

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Katie is buying souvenir.gifts for her big family back home. She wants to buy everyone either a key chain or a magnet. The magne
NikAS [45]
The total number of gifts = x+y.
The inequality is:
x+y  \geq 24

Key chains cost $1, Magnets $0.50
Total Cost = x + 0.5y
Inequality is:
x+0.5y  \leq 20

Without graphing you can solve system by using substitution:
y = 24 - x  \\  \\ x + 0.5(24-x) = 20   \\  \\ 0.5x +12 = 20  \\  \\ x = 16 \\  \\ y = 24-16 = 8

This is one solution where the maximum x value is given.
So the most keychains that can be purchased is 16. However, because magnets are cheaper, more can be purchased as long as cost remains under 20.

If you solve both inequalities for "y", you get the upper and lower bounds for how many magnets can be purchased given a quantity of keychains.

24-x  \leq y  \leq 40 -2x \\  \\ x \leq 16

This is complete solution which gives all possible combinations.
(Graph is Attached)

6 0
3 years ago
Kevin and Randy Muise have a jar containing 73 ?coins, all of which are either quarters or nickels. The total value of the coins
inna [77]

Answer:

24 quarters and 49 nickels

Step-by-step explanation:

This situation has two unknowns - the total number of nickels and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.

  • n+q=73 is an equation representing the total number of coins
  • 0.05n+0.25q=8.45 is an equation representing the total value in money based on the number of coin. 0.05 and 0.25 come from the value of a nickel and quarter individually.

We write the first equation in terms of q by subtracting it across the equal sign to get n=73-q. We now substitute this for n in the second equation.

0.05(73-q)+0.25q=8.45

3.65-0.05q+0.25q=8.45

3.65+0.20q=8.45

After simplifying, we subtract 3.65 across and divide by the coefficient of q.

0.20q=4.8

q=24

We now know of the 73 coins that 24 are quarters. To find the number of nickels, we subtract 24 from 73 and get 49 nickels.

4 0
2 years ago
250 kids go to the local pool on a hot summers day. Each kid dives off the diving board 9 times. How many dives are there altoge
Paraphin [41]
<h3>Answer: </h3>

2250 dives

<h3>Explanation</h3>

If each kid dives off the diving board 9 times, for 250 kids, you need to resolve a simple operation:

9 \times 250 = 2250

4 0
3 years ago
Read 2 more answers
3.541 and 41 is repeated, what would it be as a simplified fraction?
qwelly [4]

Answer: 3.5

Step-by-step explanation: Because the 4 and 1 aren’t big enough to change the 5 to go up the final answer would be 3.5 but if the 4 were to be a 5 or a number higher than the 5 would change to a 6.

8 0
3 years ago
A circle has a diameter of 20 inches and a central angle AOB that measures 160°. What is the length of the intercepted arc AB? U
juin [17]
Calculate the circumference of the full circle:

circumference = PI x diameter = 3.14 x 20 = 62.8 inches
 the arc length is 160 degrees of the full circle

divide 160 by 360 (full circle) and multiply by the circumference:

160/360 x 62.8 = 27.9 inches

5 0
3 years ago
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