Numbers like 10,100,1000 and so on are called

While on vacation, your family traveled 2040 miles in 6 days. Your average speed was 340 miles

Leviafan [203]

Answer:

a. independent = number of days

dependent = number of miles

b. f(x)=340x

x = number of days

f(x) = number of miles

c. f(x)=850

850 miles

Step-by-step explanation:

a. the number of miles depends on number of days because more days equals more miles traveled.

b. Idk u need y or f(x) but just switch to one u need.

c. 340 × 2.5 = 850

Hope this helps!

4 0

2 years ago

Problems 2.21, 2.22, 2.23

RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

2.21 and 2.23 are proved by contrapositive
2.22 is proved by induction

2.21: If $n^3$ is even, then n is even (By contrapositive)

The contrapositive of the above statement is that:

If n is odd, then $n^3$ is odd

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

$w =4k^3 + 3k^2 + 3k$

So, we have:

$n^3 =2w + 1$

The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

i.e. If n is odd, then $n^3$ is odd

2.22 $3n + 4$ is even, if and only if n is even

We have: $3n + 4$

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

$3n + 4 = 6k + 6 + 4$

$3n + 4 = 6k + 10$

Factorize

$3n + 4 = 2(3k + 5)$

The factor of 2 means that $3n + 4$ is even.

Hence, $3n + 4$ is even, if and only if n is even

2.22: $s \ne -1$ and $t \ne -1$ , then $s + t + st \ne -1$

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

We have:

$s + t + st = -1$

Substitute the values of s and t in: $s + t + st = -1$

$-1 -1 -1 \times -1 = -1$

$-1 -1 + 1 = -1$

$-1 = -1$

Hence, by contrapositive:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

Read more about proofs at:

brainly.com/question/19643658

7 0

2 years ago

The speed limit on a highway is 70 miles per hour about how fast is this in miles per minute

Kruka [31]

$\frac { 70 \textrm{ miles}}{1 \textrm{ hour}} = \frac {70 \textrm{ miles}}{60 \textrm{ minutes}} = \frac{70}{60} \frac{\textrm{ miles}}{ \textrm{ minute}} = 1.167 \textrm{ mile per minute }$

7 0

3 years ago

Show That <img src="https://tex.z-dn.net/?f=%20%7Ba%20%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%208" id="TexFor

Zigmanuir [339]

Answer:

Please see the attached picture for the full solution.

*From the 4th line of the 1st image, you could also expand it using

(a +b)²= a² +2ab +b² and

(a -b)²= a² -2ab +b².

When squaring a fraction, square both the denominator and numerator.

➣(a/b)²= a²/b²

3 0

3 years ago

Solve. (2/3) (1/4) =

stellarik [79]

You multiply the numerators (top numbers) and separately multiply the (bottom numbers) denominators.

numerator (top number): 2 * 1 = 2

denominator (bottom number): 3 * 4 = 12

Now, we have 2/12 which can be simplified to 1/6.

6 0

3 years ago