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3 years ago

Select the property of equality used to arrive at the conclusion.

Mathematics

1 answer:

Naya [18.7K]3 years ago

6 0

Answer:

addition property of equality

Step-by-step explanation:

This is because the addition property of equality means

if $a=b$ then $a+c=b+c$

So if, $x=2$ then $x+8=2+8$

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.The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 s

Citrus2011 [14]

Answer:

The constant of variation is 1/9

The equation representing the direct variation is y/x= 1/9

Step-by-step explanation:

In direct variation, y/x=k denotes the equation, with k being the constant of variation. Here, y is the number of square yards and x is the number of square feet. Therefore, as we know that 27 square feet = 3 square yards, we can write one point (x₁, y₁) as (27 square feet, 3 square yards). Plugging x₁ and y₁ into our equation, we get

y/x = k

3 / 27 = k

(3/27) / (3/3) = 1/9* = k

Therefore, the constant of variation is 1/9

Next, as stated previously, y/x = k represents the equation of direct variation. Therefore, y / x = 1/9 as our equation

* because 3 is a factor of both 3 and 27, we can divide both the numerator and denominator by 3 to keep the fraction the same but also simplify it. One way to find the greatest common factor is to list the factors of each number and see the highest number that is a factor of both

5 0

3 years ago

Find the midpoint of PQ<br><br> P(4 1/3, 3 1/6), Q(-2 1/5, 3 2/3)

Paha777 [63]

Answer:

$(1\frac{1}{15},3\frac{5}{12})$

Step-by-step explanation:

To find the midpoint, you must average the x's then average the y's.

So the x's are $4 \frac{1}{3}$ and $-2\frac{1}{5}$ .

The y's are $3\frac{1}{6}$ and $3\frac{2}{3}$ .

To find an average of a data with 2 elements you must add the two elements then take that sum and divide it by 2.

So this is what we will do with the x's then the y's.

So first x:

$\frac{4\frac{1}{3}+-2\frac{1}{5}}{2}$

Write as improper fractions:

$\frac{\frac{13}{3}+\frac{-11}{5}}{2}$

Division by 2 is the same as multiplying by 1/2:

$\frac{13}{6}+\frac{-11}{10}$

The least common multiple of 6 and 10 is 30. We will multiply first fraction by 5/5 and 3/3 for the second so we can have the same denominator.

$\frac{65}{30}+\frac{-33}{30}$

Now that the bottoms are the same we can write as one fraction:

$\frac{65+-33}{30}$

Simplify:

$\frac{32}{30}$

If you want the answer as a mix fraction like your question began as we can do that by first figuring out how many 30's are in 32 and what is the remainder of that division.

There is one 30 and 32 and so 32-30=2 is the remainder.

$1\frac{2}{30}$