three bags of potatoes and four cases of corn cost $40. Five bags of potatoes and two cases of corn cost $34. Find the cost of one bag of potatoes and the cost of one case of corn.

Answers

Answer 1

Answer: Use variables and set up equations.

$3p + 4c = 40 \n 5p + 2c = 34$

Next, get one variable with equal coefficients.

$3p + 4c = 40 \n 10p + 4c = 68\ (multiplied\ both\ sides\ by\ 2)$

Then get it alone on one side.

$4c = 40-3p \n 4c = 48-10p$

Now we can use substitution. Since $40-3p = 4c$ , substitute $40-3p$ for $4c$ in the other equation and you'll get an equation with just one variable to simplify and solve.

$40-3p = 68-10p \n 40+7p = 68 \n 7p = 28 \n \boxed{p = 4}$

We can then use $p = 4$ in an earlier equation to find $c$ .

$5p + 2c = 34 \n 5*4 + 2c = 34 \n 20 + 2c = 34 \n 2c = 14 \n \boxed{c=7}$

Answer 2

Answer: 3p + 4c = 40 ⇒ 15p + 20c = 200
5p + 2c = 34 ⇒ 15p +   6c = 102
      14c = 98
   14    14
      c = 7
          5p + 2(7) = 34
      5p + 14 = 34
      - 14 - 14
      5p = 20
   5 5
      p = 4
      (p, c) = (4, 7)

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Is this correct? The answer I picked was the only one that had no limit. If I did it correctly the other choices limit was zero.

Find the equation of the circle that satisfies the given conditions. Radius 2 and center (4, -7)?

Answers

$The\ equation\ of\ the\ circle:\n\n(x-a)^2+(y-b)^2=r^2\n\nwhere\n\ncenter:(a;\ b)\n\nradius:r$

$Center:(4;-7);\ radius:r=2\n\n(x-4)^2+(y+7)^2=2^2\n\n(x-4)^2+(y+7)^2=4$

The gcf of 135 225 270

Answers

The greatest common factor of 135 225 and 270 is 135/225 = 3/5

hope you found this helpful ;)

The GCF of 135, 225, and 270 is 45.

The GCF (Greatest Common Factor) is the largest number that divides evenly into two or more numbers. To find the GCF of 135, 225, and 270, we need to find the common factors of the three numbers and choose the largest one.

The factors of 135 are: 1, 3, 5, 9, 15, 27, 45, 135.

The factors of 225 are: 1, 3, 5, 9, 15, 25, 45, 75, 225.

The factors of 270 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.

The common factors of 135, 225, and 270 are: 1, 3, 5, 9, 15, 45.

The largest common factor is 45. So, the GCF of 135, 225, and 270 is 45.

Learn more about GCF here:

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Lisa is asked to draw a quadrilateral with the following specifications. adjacent angles are supplementary opposite angles are supplementary the measures of two adjacent sides are both 5 inches Which of the following statements about this quadrilateral is true.

Answers

Answer:

B (i do also slightly lean towards C, but i'm pretty sure it would be B because it gives a specific measurement)

Step-by-step explanation:

If all angles that are either adjacent or opposite are supplementary, all angles must be 90°

If at all times adjacent sides are 5 inches, all sides are equal.

Knowing this, it has to be a square because all angles would be 90° and all sides would be equal.

What is 370,000 as a decimal?

Answers

It's 370,000.00000... with as many zeros as you want after the decimal point.

370,000 no need for a decimal point because there are only zeros after it. they don't exist necessarily unless there was another number after the decimal point i.e. 1

What number should be placed in the box to help complete the division calculation?

Answers

Answer:

160

Step-by-step explanation:

226

-160

____

-64 (4 in the quotient)

____

The hcf of two numbers is 7and their lcm is 210. If one of these numbers is 35,find the other

Answers

Answer:

Step-by-step explanation:

The relation between HCF and LCM is that the product of 2 numbers is equal to the product of the HCF of two numbers and the product of LCM of the two numbers.

(7)(210) = (35)(x)

1470 = 35x

x = 42

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