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3 years ago

Match the property of equality with the corresponding definition given that a = b.

Mathematics

2 answers:

DochEvi [55]3 years ago

7 0

Answer:

See Explanation

Step-by-step explanation:

Given

$a = b$

Required

Match proper type of equality

Each of the equality properties can easily be identified with their names; For multiplication property of equality, same term must be multiplied on both sides;

For addition, same term must be added on both sides;

Same thing implies for division and subtraction

Multiplication:

$a(c) = b(c)$

Subtraction

$a - c = b - c$

Addition

$a + c = b + c$

Division

$a/c = b/c$

dezoksy [38]3 years ago

7 0

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What is 04.151515... into a fraction

Sergio039 [100]

Answer:

$\displaystyle 4.\overline{15} = \frac{137}{33}$ .

Step-by-step explanation:

Start by separating this decimal number into its integer part and its fraction part:

$4.151515\cdots = 4 + 0.151515\cdots$

The most challenging task here is to express $0.151515\cdots$ as a proper fraction. Once that fraction is found, expressing the original number $4.151515\cdots$ will be as simple as rewriting a mixed number as an improper fraction.

Let $x = 0.151515\cdots$ . $(x + 4)$ would then represent the original number.

Note that the repeating digits appear in groups of two. Therefore, if the digits in $x$ are shifted to the left by two places, the repeating part will continue to match:

$\begin{aligned}x = 0.&151515\cdots && \\ 100\, x = 15.& 151515\cdots \end{aligned}$ .

Note, that this "shifting" is as simple as multiplying the initial number by $100$ (same as $10$ raised to the power of the number of digits that needs to be shifted.)

Subtract the original number from the shifted number to eliminate the fraction part completely:

$\begin{aligned}&(100\, x) - x \\ &= 15.151515\cdots\\ & \phantom{=}- 0.151515\cdots\\&=15 \end{aligned}$ .

In other words:

$99\, x = 15$ .

$\displaystyle x = \frac{15}{99} = \frac{5}{33}$ .

Therefore, the original number would be:

$\displaystyle x + 4 = \frac{5}{33} = \frac{132 + 5}{33} = \frac{137}{33}$ .

4 0

3 years ago

How do you do this?<br> Please help, I’ve been staring at this for like 10 min :)

damaskus [11]

Answer & Step-by-step explanation:

The formula is given in the middle. You are supposed to insert the value of x into this formula to find the value of y (like in the first given example):

$x=-2\\y=2(-2)+5\\y=-4+5\\y=1$