Consuelo and James are writing an algebraic expression for three times the sum of n squared and 3. Is either of them correct?

1 answer:

8 0

Yes, the initial response is valid because n squared denotes n with an exponent of 2, and adding 3 to it yields the first result. The three outside indicates multiplication, confirming that the original response is indeed accurate.

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replace each star with a digit to make the problem true.Is there only one answer to each problem? ****-***=2

babunello [11817]

Answer: We discover two outcomes:

1000 - 998 = 2

1001 - 999 = 2

Step-by-step explanation:

The problem can be stated as:

****-*** = 2

Where each asterisk symbolizes a distinct digit; here with a 4-digit number subtracting a 3-digit number to yield a difference of 2.

This can be represented as 99*, where we can increase any digit from 1 to 9 and we will achieve a 4-digit result:

So we rewrite it this way:

1000 - 998 = 2

When we add one to each side, the difference remains preserved, maintaining equal digit counts:[

1000 - 998 + 1 - 1 = 2

(1000 + 1) - (998 + 1) = 2

Thus, 1001 - 999 = 2

A simple case would also yield further solutions where digits can be zeros, for instance:

0004 - 0002 = 2

However, this trivial solution may be disregarded. This leads us to conclude that we have two unique solutions.

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2 months ago

"a guest orders a drink that contains 1½ ounces of 80-proof vodka and 12 ounces of beer. approximately how many drinks does this

Leona [12618]

A patron orders a drink consisting of <span>1½ ounces of 80-proof vodka and 12 ounces of beer
indicating it has a total of 2 drinks.
This is because 3 ounces of 80-proof vodka is categorized as 2 drinks, so half of that is regarded as 1 drink, and since 12 ounces of beer counts as one drink, the total number of drinks in this mix equals two.</span>

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2 months ago

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For every 1 litre of water used to make a medicine, 300 ml of sucrose and 750ml of saline solution are used. Express the amount

PIT_PIT [12445]

Answer: The ratio needed will be 20:6:15.

Step-by-step explanation:

Given that

For every 1 liter of water used to create the medicine, 300 ml of sucrose and 750 ml of saline solution are required.

We should simplify the quantities of water, sucrose, and saline solution to their lowest terms.

All amounts should be converted to the same unit, which is ml.

As per the information provided,

$1\ liter=1000\ milimeter\\$

Thus, the ratio will be expressed as

$\text{Amount of water: Sucrose: saline solution}\\\\=1000:300:750\\\\=200:60:150\\\\=40:12:30\\\\=20:6:15$

Consequently, the required ratio is 20:6:15.

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2 months ago

Hector is competing in a 42 mile bicycle race. He has already completed 18 miles of the race and is traveling at a constant spee

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Wanda encounters Hector after 4.5 hours. Wanda will not be able to reach Hector before the end of the race because at his current pace (16m/h), he would finish when both reach mile 72, while the race is only 42 miles.
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