MATHEMATICS MIDDLE SCHOOL

Solve this system of linear equations. Separatethe x- and y-values with a comma.
20x + 11y = 37
4x + 3y = 13
Enter the correct answer.

Answers

Answer 1

Answer:

Answer: x= -2 and y=7

Step-by-step explanation:

4×20x+11y=37

20×4x+3y=13

Using elimination method

80x+44y=148

80x+60y=260

-16y/-16=-112/-16

Y=7

Substitute for Y in equation (1)

20x+ 11(7)=37

20x+77=37

20x=37-77

20x/20= -40/20

X= -2

therefore, x=-2 and y=7

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The volume of a rectangular prism is 270 cubic centimeters. The height of the prism is 5 centimeters. What should the length and width of the prism be? Explain your solution strategy.

Answers

V=volume h=height l=length w=width
V=h•w•l
w•l=v/5
w•l=270/5
w•l=54
Since this is all we know, we can't tell what the width or length really is but we can give examples: 6 and 9 (or 9 and 6), 4 and 13.5 (or the other way round), 18 and 3 (or 3 and 18), 2 and 27 (or 27 and 2).

5cm (H), 9cm (L), 6cm (W).

5 times 9 is 45 times by 6 (240 plus 30=) 270 CC

Or You could just have numbers for L and W which equal 54 because 5 times by 54 is 270.

Jenny filled 12 pitchers with equal amount of lemonade in each. The total amount of lemonade in the 12 pitchers was 41.4 liters. How many liters of lemonade would be in 7 pitchers

Answers

Answer:

24.15 liters of lemonade would be in 7 pitchers.

Step-by-step explanation:

The total amount of lemonade was 41.4 liters.

Jenny filled 12 pitchers with equal amount of lemonade in each.

So dividing total amount of lemonade by number of pitchers will yield amount of lemonade in each pitcher.

Hence,

$\text{Amount of lemonade in each pitcher}=\frac{\text{Total lemonade}}{\text{Number of pitchers}}$

$=(41.4)/(12)$

$=3.45\ lit$

Then the amount of lemonade in 7 pitchers will be,

$=3.45* 7=24.15\ lit$

24.15 liters of lemonade would be in 7 pitchers

Further explanation

Comparison is an effort to compare two or more objects in terms of shape or size, or number

Proportional Comparisons / Directly proportional are comparisons of two or more numbers where one number increases, the other numbers also increase at the same rate

Can be formulated

$\displaystyle \frac {x1} {y1} = \frac {x2} {y2}$

so that if:

x = 2

then

$\displaystyle y ={ \frac {y} {x} * \: 2}$

While the reversal value comparison / inversely proportional is the comparison of two or more numbers where one number increases, the other number decreases in value

or when one value decreases at the same rate that the other increases

Can be formulated

$\displaystyle \frac {x1} {y2} = \frac {x2} {y1}$

so that if:

x = 2

then

$\displaystyle y = \frac {x} {y} * \: 2$

Known

Jenny filled 12 pitchers with 41.4 liters of lemonade

Asked

lemonade in 7 pitchers

Answer

Because this includes Proportional Comparisons / Directly proportional, the equation becomes:

$\displaystyle (7~pitchers)/(12~pitchers)=(x)/(41.4~liters)$

$\displaystyle x=(7*41.4)/(12)$

$\large{\boxed{\bold{24.15~liters}}}$

Learn more

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Keywords: pitchers, lemonade, liters, Proportional Comparisons / Directly proportional

Which us shorter 1/3 2/5 3/10 or 1/4

Answers

The shortest fraction is 1/4.

The common denominator is 60, so you see how much times the denominator can go into 40 and multiply the numerator by that much. For example 3/4 and the common denominator is 20. Four can go into 20 five times so you multiply 3 five times and the fraction is 15/20

Wayne is going to paint the side of the house shown in the diagram. What is the area that will be painted? Explain how you found your answer.