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3 years ago

Find a number that has exactly 7 different prime factors. Explain how you found it.

1 answer:

5 0

The first seven prime numbers are 2, 3, 5, 7, 11, 13, 17
If you multiply all those numbers together, you'll have a product with 7 different prime factors (each of the numbers you multiplied).
So, 2 x 3 x 5 x 7 x 11 x 13 x 17 = 510,510

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Semenov [28]

Your answers are a and d hope this helps

4 0

3 years ago

For each give the correct METRIC unit of measure. Do NOT use the abbreviation. a. My foot is 21 (fill in blanks) long. b. My lar

Nataly [62]

Answer:

Inches

Gallons

Kilometers

Yards

Step-by-step explanation:

We are to proffer the appropriate unit of measurement for each scenario given below :

a. My foot is 21 inches long. (unit for measuring length which are usually small such a a person's foot)

b. My large aquarium holds 55 gallons of water. (volume measurement of liquid in a large container)

c. My dad drives 27 kilometers to work each day. (distance measurement which are moderately long)

d. I just bought 12 yards of carpet to cover my family room floor. (length measurement used for materials such as cloth, carpet, rugs e.t.c).

7 0

3 years ago

What is the opposite of -9.7?

kondor19780726 [428]

Answer:

9.7..................

4 0

2 years ago

Read 2 more answers

Car rentals involve a $130 flat fee and an additional cost of $31.67 a day. What is the maximum number of days you can rent a ca

Elanso [62]

With a $500 budget you can rent a car for 11 days as $500-$130 is $370 which you then divide by $31.67 which gives you 11.682

3 0

3 years ago

which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!

coldgirl [10]

9514 1404 393

Answer:

(a) -(x+7)/y

(b) (x+7)/-y

Step-by-step explanation:

There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.

The given expression with -1 factored out is ...

$\dfrac{-x-7}{y}=\dfrac{1(x+7)}{y}=\boxed{-\dfrac{x+7}{y}} \quad\text{matches A}$

Likewise, the expression of (b) with the minus sign factored out is ...

$\dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}$

On the other hand, simplifying expression (c) gives something different.

$\dfrac{-x-7}{-y}=\dfrac{-(x+7)}{-(y)}=\dfrac{x+7}{y} \qquad\text{opposite the given expression}$

Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).

Given: (-x-7)/y = (-x/y) +(-7/y)

(a) -(x+7)/y = (-x/y) +(-7/y)

(b) (x+7)/(-y) = (-x/y) +(-7/y)

Of course, you need to know the use of the distributive property and the rules of signs.

a(b+c) = ab +ac

-a/b = a/(-b) = -(a/b)

-a/(-b) = a/b

<u>Summary</u>: The given expression matches (a) and (b).

_____

<em>Additional comments</em>

Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...

$\left(\dfrac{-x-7}{y}\right)-\left(\dfrac{x+7}{-y}\right)=\dfrac{-y(-x-7)-y(x+7)}{-y^2}\\\\=\dfrac{xy+7y-xy-7y}{-y^2}=\dfrac{0}{-y^2}=0$

Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.

The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.

(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given

(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given

3 0

2 years ago