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galina1969 [7]
3 years ago
6

Lines l and m are parallel. lines t1 and t2 are transversals.

Mathematics
1 answer:
Lorico [155]3 years ago
7 0
I think it is an acute angle
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Are the following statements equivalent:
san4es73 [151]

<u>Answer:</u>

all statements discuss the multiplication of two numbers (we can say they are equivalent based on this context)

first three statements are exactly the same

last three statements are exactly the same


<u>Explanation:</u>

<u>Let's go through the statements one by one:</u>

1) ab > 0 and “a>0, b>0”

We know that when multiplying two positive numbers, the result is always a positive number.

Examples:

2 * 3 = 6

\frac{1}{4} * \frac{2}{5} = \frac{2}{20} = \frac{1}{10}

We can note that when the two operands are positive, the result is also positive


2) ab > 0 and “the numbers a and b are of the same sign”

We know that when multiplying two positive numbers or two negative numbers, the result will always be positive

Examples:

2 * 3 = 6

-2 * -3 = 6

We can note that when the two operands have the same sign, the result is positive


3) ab > 0 and “a>0, b>0 or a<0, b<0”

This choice is actually the same as the previous one.

When the two numbers are positive: a > 0 and b > 0

Wen the two numbers are negative: a < 0 and b < 0

Therefore, it is just a paraphrasing of statement 2


4) ab < 0 and “a>0, b<0”

We know that when we multiply numbers of different signs, the result will always be negative

Examples:

2 * -3 = -6

\frac{-1}{4} * \frac{2}{5} = \frac{-2}{20} = \frac{-1}{10}

We can note that when the two operands have different signs, the result is negative


5) ab < 0 and “a<0, b>0 or a>0, b<0”

This is the same as statement 4 as it shows that the two operands have different signs (one is greater than zero while the other is less than zero), their product will be a negative number (less than zero)


6) ab < 0 and “the numbers a and b are of different signs”

This is the same as statement 5. It is only a paraphrase of the words.


<u>Based on the above, we can conclude that:</u>

1- all statements discuss the multiplication of two numbers

2- first three statements are exactly the same

3- last three statements are exactly the same


Hope this helps :)




3 0
3 years ago
Which equation best describes the line shown on the graph?
maksim [4K]

Answer:

x = -2

Step-by-step explanation:

4 0
2 years ago
Solve for x. 1/15+x=3/10
ValentinkaMS [17]

Answer:

x=7/30

Step-by-step explanation:

3/10-1/15

7 0
3 years ago
Read 2 more answers
Someone smart help me please
mafiozo [28]
Pretty sure it is
shift 1 left
i might be wrong
7 0
3 years ago
a toy manufacturer has designed a new piece for use in building models. It is a cube with side lengths 7 mm and has a 3 mm in di
Ray Of Light [21]

Given that the cubical piece has side (s) 7 mm, and a cylindrical hole of diameter (d) as 3 mm.

The volume of the piece can be calculated as,

\begin{gathered} \text{Volume of piece}=\text{ Volume of cube}-\text{ Volume of cylinder} \\ V=s^3-\frac{\pi}{4}d^2s \\ V=7^3-\frac{\pi}{4}(3)^2(7) \\ V=343-\frac{63\pi}{4} \\ V\approx293.52mm^3 \\ V\approx293.52\times10^{-9}\text{ }m^3 \end{gathered}

It is mentioned that the material costs $207 per cubic meter, so the cost (c) of 1 piece is calculated as,

\begin{gathered} \text{Cost of 1 piece}=\text{ Cost per unit volume}\times\text{ Volume of 1 piece} \\ c=207\times293.52\times10^{-9} \\ c\approx60758.64\times10^{-9} \end{gathered}

This is the cost (in dollars) for 1 piece.

Given that the manufacturer wants to produce 1,000,000 such pieces, so the total cost (TC) is calculated as,

\begin{gathered} \text{Total Cost}=\text{ Cost per piece}\times\text{ No. of pieces} \\ TC=60758.64\times10^{-9}\times1,000,000 \\ TC=60758.64\times10^{-9}\times10^6 \\ TC=60758.64\times10^{-3} \\ TC=60.75864 \\ TC\approx60.75 \end{gathered}

Thus, the total prototypes will cost around $60.75

7 0
1 year ago
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