Given:
[tex]h(1)=9[/tex]
[tex]h(n)=h(n-1)\cdot (-3)[/tex]
To find:
The explicit formula for h(n).
Solution:
We have,
[tex]h(n)=h(n-1)\cdot (-3)[/tex] ...(i)
It is the recursive formula of a geometric sequence. It is of the form
[tex]a(n)=a(n-1)\cdot r[/tex] ...(ii)
where r is the common ratio.
On comparing (i) and (ii), we get
[tex]r=-3[/tex]
We have, [tex]h(1)=9[/tex] so the first term of the geometric sequence is [tex]a=9[/tex].
The explicit formula for a geometric sequence is:
[tex]h(n)=ar^{n-1}[/tex]
Substitute a=9 and r=-3 to get the explicit formula for the given sequence.
[tex]h(n)=9(-3)^{n-1}[/tex]
Therefore, the required explicit formula is [tex]h(n)=9(-3)^{n-1}[/tex].
Two Forest Ranger stations are located 9.8 miles apart. They both receive the same distress call. They determine that from Ranger Station 1 the distress call is at an angle of 46° and from Ranger Station 2 it is at angle of 52°. Which ranger station is closer to the distress call and by how much?
Answer:
Ranger station 2 is closer by 3.47 miles
Step-by-step explanation:
tan(46)=O/9.8
O (ranger station 2 to distress call)=10.15 miles
sin(46)=9.8/H
H (ranger station 1 to distress call)=13.62 miles
13.62-10.15=3.47 miles
So, ranger station 2 is closer by 3.47 miles
Given the system of equations, what is the value of the system determinant?
2x + y = 8
x - y = 10
0-1
0-2
0-3
Given:
The system of equation is
[tex]2x+y=8[/tex]
[tex]x-y=10[/tex]
To find:
The value of the system determinant.
Solution:
If two equations of a system of equations are [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex], then the system determinant is
[tex]D=\left|\begin{matrix}a_1&b_1\\a_2&b_2\end{matrix}\right|[/tex]
[tex]D=a_1b_2-b_1a_2[/tex]
The given two equations are [tex]2x+y=8[/tex] and [tex]x-y=10[/tex].
Here, [tex]a_1=2,b_1=1,c_1=8, a_2=1,b_2=-1,c_2=10[/tex].
[tex]D=\left|\begin{matrix}2&1\\1&-1\end{matrix}\right|[/tex]
[tex]D=(2)(-1)-(1)(1)[/tex]
[tex]D=-2-1[/tex]
[tex]D=-3[/tex]
The value of the system determinant is -3. Therefore, the correct option is C.
Answer:
-3
Step-by-step explanation:
2x+-3=8
x-3=10
when mark was 2 years old his parents invested 2,000 in a money market account with annual average interest rate of 8% after 15 years how much money will he have in the account
Answer:
$4400
Step-by-step explanation:
I=PRT
I=(2000)(8%)(15)
I=4400
-2/7 ÷ (-8/21) step by step answer
please this homework is due today its benchmark practice and i have to sleep like in 10 or 7 min like no joke
Answer:
1.3
Step-by-step explanation:
first, divide the parentheses:-8/21= -0.380952
second, dived -2/7= -0.285714
now divide both of them -0.380952 ÷ -0.285714 = 1.3
SOMEONE PLZ HELP!!
Round answer to the nearest hundredth
Answer:
17 i think
Step-by-step explanation:
help me please. Translate the description below as an algebraic expression:
half the quotient of p and 11
Answer:
try this
Step-by-step explanation:
1/2 (p/11)
slash is the dividing sign
Answer:
( p ÷ 11) ÷ 2
Or
1/2 (p ÷ 11)
Step-by-step explanation:
Half the quotient of p and 11
"the quotient of p and 11" signifies that you have to divide p by 11. And "half the.." signifies that you have to divide the quotient of p/11 in half
Every month, Mr. Jones pays his school loans through automatic payments (withdrawals) from his savings account. He pays the same amount on his school loan each month. At the end of the year, his savings account balance changed by -$3,183 from payments made on his school loan. What is the change in Mr. Jones savings account balance each month due to his school payment?
Answer:
i think the answer is 265.25
Step-by-step explanation:
because there are 12 months in a year so 3,183 ÷ 12 = 265.25
If the circle below is cut from the square of plywood below, how many square inches of plywood would be left over? Use π = 3.14, and round your answer to the nearest hundredth
Answer:
86in²
Step-by-step explanation:
Find the complete question attached
Area of the circle = πr²
Area of the square = L²
Length of the side of the square
r is the radius of the circle
r = L/2 = 20/2 =10in
Given
Length of the side of the circle = 20in
Area of the square = 20²
Area of the square = 400in²
Area of the circle =π(10)²
Area of the circle = 3.14(100)
Area of the circle= 314in²
Amount of plywood left over = 400in²-314in² = 86in²
what would be the coordinates marked wrong
Answer:
R: (-3, -4)
S: (-3, -1)
T: (1, -4)
Step-by-step explanation:
You would subtract 1 from all the initial x values, and 5 from all the initial y values
Laura goes to a Mexican restaurant for lunch she's planning to order either a chicken or beef dish if there are a choices for chicken and 12 choice es for beef how many options does Laura have to choose from
A. 4
B. 8
C. 12
D. 20
Look at picture.........
Step-by-step explanation:
jJJshzysyqvsudishw wjs87eye
Fill in the blanks to the picture above
Answer:
The answer is B, 6x^2 - 21x + 15
Step-by-step explanation:
= (3x + − 3) (2x + − 5)
= (3x) (2x) + (3x) (− 5) + ( − 3) (2x) + ( − 3) ( − 5)
= 6x^2 − 15x − 6x + 15
= 6x^2 − 21x + 15
- I don't know how you want me to fill the boxes exactly but here's the step by step explanation. I hope I helped.
The function f (x) = 4(3) can be used to determine the number of
bacteria in a petri dish after x weeks. How much bacteria will there be in 4
weeks?
Find the value of the variable. Write all answers in simplest radical form. Show your work
Answer:
x = 4.5
Step-by-step explanation:
By geometric mean theorem:
[tex] {3}^{2} = 2 \times x \\ \\ 9 = 2x \\ \\ x = \frac{9}{2} \\ \\ x = 4.5[/tex]
15 - 1.5(y - 5) - 7.5 simplified
Answer:
I hope that is useful for you :)
Step-by-step explanation:
[tex]15 - 1.5y + 7.5 - 7.5 \\ 15 - 1.5y \\ 1.5(10 - y)[/tex]
solve liner equation for they variable
-6x+7=2x+10-8x-3
Answer:
x is infinite
Step-by-step explanation:
-6x+7=2x+10-8x-3
reduce:
-6x+7=7-6x
7-6x = 7-6x
x = x
x is infinite
Which inequality represents all values of x for which the quotient below is defined? √x+2÷√5-x
Answer:
The answer is C -2<x<5 ihope its help-2 ≤ x < 5
represents all values of x which the quotient √(x+2) ÷ √(5-x) is defined.
Find the probability that the team will win exactly one of the two matches
Answer:
The probability is 0.341
Step-by-step explanation:
Here, we want to calculate the probability that the student will win exactly one of the two matches
This means that;
If they win on Saturday, they lose on Sunday
or
If they lose on Saturday, they win on sunday
So either of the two scenarios will give that the team will win on either of the two days
Mathematically, we have that;
(0.45 * 0.33) + (0.55 * 0.35)
= 0.1485 + 1925
= 0.341
Four cards labeled A, B, C, and D are randomly placed in four boxes labeled A, B, C, and D. Each box receives exactly one card.
In how many ways can the cards be placed in the boxes?
Answer: 16 different ways
Step-by-step explanation:
mhanifa or someone else can you PLZ answer this
Answer:
[tex] \frac{7 {n}^{2} - 41n + 8 }{ {n}^{2} - 1 } [/tex]
Step-by-step explanation:
[tex] \frac{7n}{n + 1} + \frac{8}{n - 7} \\ \\ = \frac{7n(n - 7) + 8(n + 1)}{(n + 1)(n - 1)} \\ \\ = \frac{7 {n}^{2} - 49n + 8n + 8 }{ {n}^{2} - 1 } \\ \\ = \frac{7 {n}^{2} - 41n + 8 }{ {n}^{2} - 1 } [/tex]
Answer:
Simplified:
[tex]\frac{7n}{n + 1} + \frac{8}{n - 7}[/tex] =[tex]\frac{7n(n - 7) + 8(n + 1)}{(n + 1)(n - 7)}[/tex] =[tex]\frac{7n^2 - 49n + 8n + 8}{n^2 + n - 7n - 7}[/tex] =[tex]\frac{7n^2 - 41n + 8}{n^2 - 6n - 7}[/tex]This can be further simplified if required
[tex]\frac{7n^2 - 42n -49 + n + 57}{n^2 - 6n - 7}[/tex] =[tex]7 + \frac{n + 57}{n^2 - 6n - 7}[/tex]Mean
Vasquez read 5 books in January, 8 books in February,
4books in March, and 7 books in April. What is the
average number of books Vasquez reads per month?
A customer deposits $1275 in a savings account that pays 4% interest compounded quarterly. How much money will the customer have in the account after 2 years? (Round to the nearest cent-- 2 decimal places)
$13777.00
Step-by-step explanation:
What is the measure of angle b in degrees?
Answer:
119
Step by Step:
180-112=68, 68+51=119, 180-119=61, 180-61=119
If you spent 58 minutes doing English homework and 47 minutes doing math homework how much more time did you need to spend doing English homework?
Answer:
58 minutes
Step-by-step explanation:
Please brainliest me
There are 11 minutes more time to spend doing English homework.
What is mean by Subtraction?
Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
If you spent 58 minutes doing English homework and 47 minutes doing math homework.
Now,
Since, The time for doing English homework = 58 minutes
And, The time for doing Math homework = 47 minutes
So, The time more to spend doing English homework = 58 - 47
= 11 minutes
Thus, There are 11 minutes more time to spend doing English homework.
Learn more about the subtraction visit:
https://brainly.com/question/28467694
#SPJ5
There are 7 students in cara art club . They need to share 2 rolls of clay equally . Cara wants to know how much clay she will get?
Answer:
2/7
Step-by-step explanation:
What is the range of the function y= 5-2x when the domain is {0,1,2,3}
Answer:
The range for the function y=5-2x is all real numbers, but the numbers corresponding the the domain values of 0, 1, 2, and 3, are 5, 3, 1, -1.
Step-by-step explanation:
if m< 3=3x+20 and m <6=x+50 , what is x?
Since you said they are supplementary, 3x+20+x+50=180
Since the definition of supplementary angles are they adds up to 180 degrees.
Now we just need to solve the equation
4x+70=180
4x=110
x=27.5
which numeration system is also known as 10 base numeration system
Answer:
decimal system
..........
NEED HELP ASAP 2 questions WORTH 50
Answer:
The first question tan(24) = x/12 because tan(x) = opposite/adjacent
so x in radians ≈ -25.618....
x in degrees ≈ 5.342....
For the second question tan(72) = x/20
x in radians ≈ -5.248....
x in degrees ≈ 61.553....
Answer:
for first one
relationship between base and perpendicular is given by tan angle
tan24=p/b
tan24=x/12
x=tan24×12=5.34
Step-by-step explanation:
for second one
relationship between base and perpendicular is given by tan angle
tan72=x/20
x=tan72×20=61.55
What is 7/10 of 650?
Answer:
455
Step-by-step explanation:
I answered first, but forgot to answer here.