MATHEMATICS HIGH SCHOOL

Follow the directions to solve the system of equations by elimination.8x + 7y = 39
4x – 14y = –68

Answers

Answer 1
Answer: To solve a system of equation by elimination, the coefficients of the  same variable of both equations must be equal. In this case, let's choose y.
In order to make the coefficient of y of the second equation be equal to 7, we divide it by 2. Resulting to:
2x - 7y = -34

Next, add the two solutions so that the y term is eliminated. The result is:
10x = 5
Then solve for x
x = 1/2

Substitute x to either of the solution to solve for y. The result is:
y = 5
Answer 2
Answer:

Final answer:

The solution to the system of equations 8x + 7y = 39 and 4x – 14y = -68 via elimination is x = 0.5 and y = 5.

Explanation:

The two given equations are 8x + 7y = 39 and 4x – 14y = -68. The method for solving this is elimination.

  1. First, modify the second equation by multiplying every term by 2.
  2. This will give 8x - 28y = -136.
  3. Now, you have two equations 8x + 7y = 39 and 8x - 28y = -136 that can be combined by subtraction: 8x - 8x + 7y - (-28y) = 39 - (-136).
  4. Simplification gives 35y = 175, so y = 5.
  5. Substituting y = 5 into the first equation, 8x + 7*5 = 39, which simplifies to 8x + 35 = 39, and then to 8x = 4, so x = 0.5.

Learn more about Systems of equations here:

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The mass of a computer

Answers

the mass of a computer uses kilogram (kg) so the weight of a computer is between .68 kg and .73... Hope it helps ur out..

in a two digit number the tens digit is 6 more than the units digit. if the digits are interchanged, the sum of the new and the original number is 132. Determine the original number.​

Answers

Given:

In a two digit number the tens digit is 6 more than the units digit.

If the digits are interchanged, the sum of the new and the original number is 132.

To find:

The original number.

Solution:

Let the unit digit of the original number be x. So, the tens digit is (x+6) and the value of the number is:

m=(x+6)* 10+x* 1

m=10x+60+x

m=11x+60

If we interchange the digits, then the value of new number is:

n=x* 10+(x+6)* 1

n=10x+x+6

n=11x+6

The sum of the new and the original number is 132.

m+n=132

11x+60+11x+6=132

22x+66=132

22x=132-66

22x=66

Divide both sides by 22.

x=(66)/(22)

x=3

So, the unit digit of the original number is 3 and the tens digit is:

x+6=3+6

x+6=9

Therefore, the original number is 39.

Suppose you roll a number cube. What is the theoretical probability of rolling a 2

Answers

Answer:  (1)/(6)

Step-by-step explanation:

We know that a cube has six faces , if we roll a cube then we have chances to roll six different faces  with six different number if it is not biased.

Let the number on cube be  1,2,3,4,5,6.

Thus total outcomes = 6

Then the theoretical probability of rolling a 2 is given by :-

P(2)=\frac{\text{favorable outcome}}{\text{total outcomes}}\n\n\Rightarrow\ P(2)=(1)/(6)
if theres six sides to the dices then the answer will be 1/6 

What is x+4/5=2/3- x-3/6

Answers

x+(4)/(5)=(2)/(3)-x-(\not3^1)/(\not6_2)\n\nx+(4)/(5)=(2)/(3)-x-(1)/(2)\n\nfind\ LCD((4)/(5);\ (2)/(3);\ (1)/(2))=2*3*5=30\n\nmultiply\ both\ sides\ by\ LCD=30\n\n30x+30\cdot(4)/(5)=30\cdot(2)/(3)-30x-30\cdot(1)/(2)\n\n30x+6\cdot4=10\cdot2-30x-15\cdot1\n\n30x+24=20-30x-15

30x+24=5-30x\ \ \ \ |subtract\ 24\ from\ both\ sides\n\n30x=-19-30x\ \ \ \ \ |add\ 30x\ to\ both\ sides\n\n60x=-19\ \ \ \ \ |divide\ both\ sides\ by\ 60\n\n\boxed{x=-(19)/(60)}



(x+4)/(5)=(2)/(3)-(x-3)/(6)\n\n(x+4)/(5)=(2\cdot2)/(3\cdot2)-(x-3)/(6)\n\n(x+4)/(5)=(4)/(6)-(x-3)/(6)\n\n(x+4)/(5)=(4-(x-3))/(6)\n\n(x+4)/(5)=(4-x+3)/(6)\n\n(x+4)/(5)=(7-x)/(6)\ \ \ \ |cross\ multiply

6(x+4)=5(7-x)\n\n6(x)+6(4)=5(7)-5(x)\n\n6x+24=35-5x\ \ \ \ \ |subtract\ 24\ from\ both\ sides\n\n6x=11-5x\ \ \ \ \ |add\ 5x\ to\ both\ sides\n\n11x=11\ \ \ \ \ |divide\ both\ sides\ by\ 11\n\n\boxed{x=1}

Carlos bought a $235 water heater with his credit card. He used the water heater for five years before replacing it. He paid off the water heater after two years, making monthly payments. The water heater cost him an average of $1.56 per week in electricity, and $0.78 per week in water. If Carlos’s credit card has an APR of 14.15%, compounded monthly, and he made no other purchases with it, what percentage of the lifetime cost of the water heater was interest? (Round all dollar values to the nearest cent.)

Answers

First we will find the interest on:


P = $235 principal


t = 2 years


r = 0.1415 annual rate


A = future value 


I = A - P the interest


A = P(1 + r)^t


A = 235(1 + 0.1415)^2


A = $306.21


I = A - P


I = $306.21 - $235


I = $71.21


the interest was $71.21.



Next lets find the lifetime cost value:


Lifetime cost value = 306.21 + 5*1.56*52 + 5*0.78*52 = $914.61 (considering that 1 year = 52 weeks)



Now lets find the percentage what percentage the interest is of the lifetime cost:


(71.21/914.61)*100 = 7.79%

Answer:

C. 4.12%

Step-by-step explanation:

Give the inequality (-3 -2 -1 0 1 2 3)

Answers

The answer is -10128
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