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3 years ago

7

What is - 3 + ( - 4 ) evaluated??

2 answers:

Zepler [3.9K]3 years ago

8 0

You would add them together and you would get -7 because when you add 2 negative numbers together you come out with a negative number.

-3+(-4)=-7

dimaraw [331]3 years ago

4 0

-7 is the answer to that question

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Jose prefers to walk to work when the weather

stich3 [128]

Answer:

independent: time (hours)

dependent: distance (miles)

Step-by-step explanation:

The independent variable would be time because it can be changed depending on his walking speed.

The dependent variable would be distance

6 0

2 years ago

Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference

Bezzdna [24]

Since $a_1,a_2,a_3,\cdots$ are in arithmetic progression,

$a_2 = a_1 + 2$

$a_3 = a_2 + 2 = a_1 + 2\cdot2$

$a_4 = a_3+2 = a_1+3\cdot2$

$\cdots \implies a_n = a_1 + 2(n-1)$

and since $b_1,b_2,b_3,\cdots$ are in geometric progression,

$b_2 = 2b_1$

$b_3=2b_2 = 2^2 b_1$

$b_4=2b_3=2^3b_1$

$\cdots\implies b_n=2^{n-1}b_1$

Recall that

$\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n$

$\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2$

It follows that

$a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n + n(n-1)$

so the left side is

$2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n$

Also recall that

$\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}$

so that the right side is

$b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)$

Solve for $c$ .

$2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}$

Now, the numerator increases more slowly than the denominator, since

$\dfrac{d}{dn}(2n(n-1)) = 4n - 2$

$\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2$

and for $n\ge5$ ,

$2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2$

This means we only need to check if the claim is true for any $n\in\{1,2,3,4\}$ .

$n=1$ doesn't work, since that makes $c=0$ .

If $n=2$ , then

$c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0$

If $n=3$ , then

$c = \dfrac{12}{2^3 - 6 - 1} = 12$

If $n=4$ , then

$c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N$

There is only one value for which the claim is true, $c=12$ .

3 0

2 years ago

Plz help with question I added a photo☝️

salantis [7]

Answer: C, 4 gallons per minute.

Step-by-step explanation: To find the unit rate of the faucet, we must make the units an even gallons/minute. Thus, we multiply each rate by 5 to get 4 gallons/minute.

6 0

2 years ago

How can u solve this by system of equations by elimination 4x-5y=6;2x+5y=-28

gayaneshka [121]

Answer:

x=17/3, y=10/3. (17/3, 10/3).

Step-by-step explanation:

4x-5y=6

2x+5y=-28

-----------------

4x-5y=6

-2(2x+5y)=-2(-28)

--------------------------

4x-5y=6

-4x-10y=56

------------------

-15y=-50

15y=50

y=50/15

y=10/3

4x-5(10/3)=6

4x-50/3=6

4x=6+50/3

4x=18/3+50/3

4x=68/3

x=(68/3)/4

x=(68/3)(1/4)=68/12=17/3

4 0

2 years ago

A fence on a hill uses vertical posts L and M to hold parallel rails N and P. ∠10 and ∠14 are alternate interior angles. What is

kherson [118]

The answer is B. Thank you:$))

7 0

3 years ago