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borishaifa [10]
2 years ago
6

Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3

. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?
9x + 4y = 36

6x + 2.5y = 24
Mathematics
1 answer:
Arada [10]2 years ago
7 0

Answer:

solving we get Solution set = {4,0}

Step-by-step explanation:

We are given system of equation:

9x + 4y = 36---eq(1)\\6x + 2.5y = 24---eq(2)

Multiply eq(1) by 2 and eq(2) by -3

18x \ \ + 8y \ \ \ = 72\\-18x - 7.5y = -72\\---------\\0.5y=0\\y=0

We get y=0,

Now finding x by putting value of y in eq(1)

9x + 4y = 36\\9x+4(o)=36\\9x=36\\x=\frac{36}{9}\\x=4

So, solving we get Solution set = {4,0}

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Manuel bought 2kg of jelly beans and 2kg of gummy worms for a total of $26. Danny bought 2kg of jelly beans and 3kg of gummy wor
charle [14.2K]

Answer:

Jelly beans: $6 for 1 kg

Gummy worms: $7 for 1 kg

Step-by-step explanation:

In this question, we need to find the cost of 1kg of jelly beans and gummy worms.

To do this, make equations for both scenarios and solve:

2j + 2g = 26

2j + 3g = 33

Turn the bottom equation negative, as we will first solve for gummy worms (g).

2j + 2g = 26

-2j - 3g = -33

Solve:

-g = -7

Divide both sides by -1.

g = 7

We now know that gummy worms cost $7 for 1 kg

To solve for jellybeans (j), plug in 7 to g in one of the equations and solve:

2j + 2(7) = 26

2j + 14 = 26

Subtract 14 from both sides.

2j = 12

Divide both sides by 2.

j = 6

Jellybeans cost $6 for 1 kg.

Check answer by plugging in values to one of the equations:

2(6) + 2(7) = 26

12 + 14 = 26

26 = 26

3 0
2 years ago
Find the point on the line y = 2x +1 that is closest to the point (5, 2).
ELEN [110]
I believe that it's (1,3) 
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7 0
3 years ago
The rule of 72 is used to determine how long it will take an investment to ___. For an Investment of $5,000 earning 7% annually,
Gnom [1K]

Answer:

The rule of 72 is used to determine how long it will take an investment to Double

For an Investment of $5,000 earning 7% annually, this will take about ten years

Step-by-step explanation:

The rule of 72 says that to find the number of years required to double your money at a given interest rate, you just divide 72 by the interest rate

Example:

If you want to know how long it will take to double your money at 9% interest, divide 72 by 9 you will get 8 years

The formula of the rule of 72 is Y = \frac{72}{r}

Let us complete the missing

The rule of 72 is used to determine how long it will take an investment to Double

The missing word is "Double"

∵ The investment is $5,000

∵ The annual interest is 7%

- By using the rule of 72

∵ Y = \frac{72}{r}

∵ r = 7

∴ Y = \frac{72}{7}

∴ Y = 10.29

- Round it to the nearest year

∴ Y ≅ 10 years

For an Investment of $5,000 earning 7% annually, this will take about ten years

The missing word is "ten"

5 0
2 years ago
James has 375 coins. One-fifth of the coins are quarters. How many of his coins are not quarters?
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300 of his coins are not quarters. 
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