What would a equal if 4(a+12) was 32?
What is the 10th term of the sequence?
Answer: 23
Explanation: First of all, let's make sure we have an arithmetic sequence. An arithmetic sequence is a sequence that has a common difference which is the number repeatedly added or subtracted to reach the next term.
To get from -4 to -1, we're adding 3.
To get from -1 to 2, we're adding 3.
To get from 2 to 5, we're adding 3.
So we know that this is an arithmetic sequence because it has a common difference or the number that is repeatedly added which is 3.
Now, we want to determine the 10th term in this sequence.
There are 2 ways that you can determine the 10th term. You can keep on adding 3 until you get to the 10th term or you can use the explicit formula. I will show you the explicit formula which is shown below.
Now we want to determine what the 10th term is so we're trying to determine . Now, we know what is because it's our first term or -4. Now, n will be the number of terms we're solving for or 10. Lastly, we have the d which represents the common difference which is 3.
So plugging into the formula, we have .
Now, make sure we apply order of operations because this is where many students make mistakes.
(10 -1) is going to be 9. Then we want to make sure we multiply before we add so 9 x 3 is going to be 27 and then -4 + 27 is 23.
So the 10th term in this sequence is 23.
b. 5.4
c. 6.3
d. 7.2
3. Find the value of x.
a. 7
b. 7.5
c. 8
d. 8.5
4. FG ⊥ OP, RS ⊥ OQ. FG=40, RS=40, OP=15. Find x.
a. 15
b. 17
c. 20
d. 21
5. Find the value of x to the nearest tenth.
a. 7.5
b. 7.9
c. 8.1
d. 8.9
Answer:
Part 2) Option b. 5.4
Part 3) Option c. 8
Part 4) Option a. 15
Part 5) Option d. 8.9
Step-by-step explanation:
Part 2) Find the value of x to the nearest tenth
we know that
x is the radius of the circle
Applying the Pythagoras Theorem
Part 3) Find the value of x
In this problem
x=8
Verify
step 1
Find the radius of the circle
Let
r -----> the radius of the circle
Applying the Pythagoras Theorem
step 2
Find the value of x
Applying the Pythagoras Theorem
substitute
Part 4) Find the value of x
In this problem
x=OP=15
Verify
step 1
Find the radius of the circle
Let
r -----> the radius of the circle
In the right triangle FPO
Applying the Pythagoras Theorem
step 2
Find the value of x
In the right triangle RQO
Applying the Pythagoras Theorem
Part 5) Find the value of x
Applying the Pythagoras Theorem
Answer:
C
Step-by-step explanation:
work shown below