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avanturin [10]
1 year ago
7

Lucas is keeping track of the total number of miles he runs each week. During the second week, he ran four more than twice as ma

ny miles as he did during the first week.
(A) If “m” represents the number of miles that he ran during the first week, write an equation in terms of “m” for the number of miles he ran during the second week.

(B) The total number of miles that Lucas ran during the first two weeks is equal or eight less than four time the number of miles he ran during the first week. Determine the number of miles Lucas ran in the first week.
Mathematics
1 answer:
Novosadov [1.4K]1 year ago
4 0

(A) The equation represents the number of miles he ran during the second week is (2m + 4) miles.

(B) The total number of miles that Lucas ran during the first two weeks is m + (2m + 4) ≤ 4m ⇒ m ≥ 4

<h3>What is an equation?</h3>

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, Lucas is keeping track of the total number of miles he runs each week.

In the first week, he ran m miles, and in the second week, he ran 4 miles more than twice the miles he ran in the first week.

∴ The equation in terms of m represents the number of miles he ran during the second week is (2m + 4) miles.

Also given, The total number of miles that Lucas ran during the first two weeks is equal to or eight less than four times the number of miles he ran during the first week which is,

m + (2m + 4) ≤ 4m.

3m - 4m ≤ - 4.

- m ≤ - 4.

m ≥ 4.  (think of moving the terms to other sides to make m positive).

learn more about inequalities here :

brainly.com/question/28823603

#SPJ1

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Answer:

Step-by-step explanation:

The distributive property affects both terms.

1/2 * 10x + 1/2 * 20 y

5x + 10 y <===== Answer

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How do I slove this eqaution, and whats the answer?<br> -3(n+6)+10=-9
Sauron [17]

Answer:

n = \frac{1}{3}

Step-by-step explanation:

  1. Apply the distributed property, so it now looks like this: -3n + -18 + 10 = -9
  2. Combine like terms: -3n + -8 = -9
  3. Simplify: -3n - 8 = -9
  4. Add 8 to each side, so it now looks like this: -3n = -1
  5. Divide each side by -3 to cancel out the -3 next to n. It should now look like this: n = 1/3

I hope this helps!

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Question 1,2, and 3 how do i factor those? Can you show the work and explain how?
DiKsa [7]

1: 3n^{2}+9n+6

notice that each part is divisible by 3

3n^{2} ÷ 3 = n^{2}

9n ÷ 3 = 3n

6 ÷ 3 = 2

so it becomes 3(n^{2} +3n+2)

3n can be rewritten as 2n+n

-you want to rewrite it into two numbers that multiply to the number that's alone (in this case 2)

which would get you

3(n^{2} +2n+n+2)

Now that it's rewritten, you can factor out n + 2 from the equation.

<u><em>the answer is </em></u>

3(n+2)(n+1)

And you can check that by multiplying (n+2)(n+1) which is n^{2} +2n+n+2 and then each of those by 3, which is 3n^{2} +6n+3n+6 or 3n^{2}+9n+6, our origional equation

2: 28+x^{2} -11x

So I rewrote this as x^{2} -11x+28 (it's the same thing, just reordered using the commutative property)

now -11x can be rewritten as -4x-7x

(remember, the two numbers should multiply to equal 28, which is our constant.)

x^{2} -4x-7x+28

now we can factor out x from the first expression and -7 from the second

x(x-4)-7(x-4)

and lastly you factor out x-4,

<u><em>which would give you</em></u>

(x-4)(x-7)

Make sure to check your work and make sure it multiplies to x^{2} -11x+28

3: 9x^{2} -12x+4

The first thing I notice when looking at this problem is that both 9 and 4 are perfect squares. Not only that, but they are the squares of 2 and 3, which are products of -12

So if you rewrite 9 as 3^{2} and 4 as 2^{2}, the equation becomes

3^{2} x^{2} -12x+2^{2}

now that 3^{2} x^{2} is ugly so it can be turned into (3x)^{2}

and -12x can be rewritten as -2*3x*2

so our equation now looks like (3x)^2-2*3x*2+2^{2}

There's a rule that says a^{2} -2ab+b^{2} = (a-b)^{2}

In our case, a=3x and b=2

<u><em>so the final answer is</em></u>

(3x-2)^2

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Step-by-step explanation:

B' stands for the complement of B.

B' means set elements in the universe that aren't in B.

Here is the universe:

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(The dots mean it continues with that pattern forever and ever.)

And the elements we taking out:

B={13,15,17,19,21,23,...}

So we taking out the odd numbers from U that are odd and greater than or equal to 13. (The dots mean it continues with that pattern forever and ever.)

So B' is the set of natural odd numbers that are less than 13:

{1,3,5,7,9,11}

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