All categories

3 years ago

Find the 97th term of the arithmetic sequence 25,29,33

Mathematics

1 answer:

notka56 [123]3 years ago

6 0

D = 4
Formula: an = a1 + (n-1)d
a97 = 25 + (97-1) * 4
a97 = 25 + 384
a97 = 409
The 97th term is 409

You might be interested in

4minutes 45seconds=_____seconds

Elodia [21]

1 minute = 60 second

60 * 4 = 240

240 + 45

285 seconds

5 0

3 years ago

Read 2 more answers

How many elements are in the union of four sets if

12345 [234]

Answer:

Step-by-step explanation:

Let A, B, C and D sets.

Let |A| the number of elements of A.

Remember, the quantity of elements that have the set $A\cup B\cup C\cup D$ is

$|A\cup B\cup C\cup D|=|A|+ |B|+ |C|+|D|-|A\cap B|-|A\cap C|-|A\cap D|-|B\cap C|-|B\cap D|-|C\cap D|-|A\cap B\cap C|-|A\cap B\cap D|-|B\cap C\cap D|-|A\cap B\cap C \cap D|$

1. Since each set has 100 elements,

2. each pair of the sets shares 50 elements

3. each three of the sets share 25 elements,

4. the four sets share 5 elements

Then

$|A\cup B\cup C\cup D|=100+100+100+100-50-50-50-50-50-50-25-25-25-5=20$

So, there are 20 elements in the union of the sets A, B, C and D

6 0

3 years ago

The Rutgers University and Princeton University soccer teams scored goals in a

Schach [20]

I know the answer is that Princeton scores 15 goals but I don’t know how the work is supposed to be shown. I did it in my head. I multiplied both 8 and 5 by 3 so 8 would become 24(the goals Rutgers scored) and then you would find the number of goals Princeton scored. Sorry I couldn’t show the work but the answer is 15 goals.

5 0

3 years ago

Which expression is equivalent to log Subscript w Baseline StartFraction (x squared minus 6) Superscript 4 Baseline Over RootInd

zysi [14]

Option b: $4 \log _{w}\left(x^{2}-6\right)-\frac{1}{3} \log _{w}({x^{2}+8})$ is the correct answer.

Explanation:

The expression is $\log _{w}\left(\frac{\left(x^{2}-6\right)^{4}}{\sqrt[3]{x^{2}+8}}\right)$

Applying log rule, $\log _{c}\left(\frac{a}{b}\right)=\log _{c}(a)-\log _{c}(b)$ , we get,

$\log _{w}\left(\left(x^{2}-6\right)^{4}\right)-\log _{w}(\sqrt[3]{x^{2}+8})$

Again applying the log rule, $\log _{a}\left(x^{b}\right)=b\cdot\log _{a}(x)$ , we get,

$4 \log _{w}\left(x^{2}-6\right)-\log _{w}(\sqrt[3]{x^{2}+8})$

The cube root can be written as,

$4 \log _{w}\left(x^{2}-6\right)-\log _{w}({x^{2}+8})^{\frac{1}{3} }$

Applying the log rule, $\log _{a}\left(x^{b}\right)=b\cdot\log _{a}(x)$ , we have,

$4 \log _{w}\left(x^{2}-6\right)-\frac{1}{3} \log _{w}({x^{2}+8})$

Thus, the expression which is equivalent to $\log _{w}\left(\frac{\left(x^{2}-6\right)^{4}}{\sqrt[3]{x^{2}+8}}\right)$ is $4 \log _{w}\left(x^{2}-6\right)-\frac{1}{3} \log _{w}({x^{2}+8})$

Hence, Option b is the correct answer.

3 0

4 years ago

Read 2 more answers

9/16 = x/12<br>x-3/18 = 12/9<br>7/11 = 18/x+1<br>3x-4/14 = 9/10<br>Simplify

hjlf

Answer:

Step-by-step explanation:

9/16=x/12

cross product

16x=9*12

16x=108

x=108/16

simplify

x=27/4

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

x-3/18=12/9

x=12/9+3/18

x=24/18+3/18

x=27/18

x=3/2

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

7/11=18/x+1

18/x=7/11-1

18/x=7/11-11/11

18/x=-4/11

x=18/(-4/11)=(18/1)(-11/4)=-198/4=-99/2

x=-99/2

4 0

4 years ago