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].
Erin is testing how a component used in a manufacturing process responds to rapid changes in temperature over a period of 30 seconds. During the test, the temperature of the component in degrees Fahrenheit at seconds is modeled by the quadratic function () -- +241 fort=0 tr = 30
Using this model, which statements are true about the test? Choose all that are correct
The initial temperature of the component is o"
The temperature is increasing for the duration of the experiment
The temperature of the component is never less than zero degrees
The component has the same temperature att and t 24
The maximum temperature reached by the component during the experiment is 144"
Answer:
The answer will be A and D and E
Step-by-step explanation:
list the factors of 5i^2+12i−32 i need help fast
Answer:
Step-by-step explanation:
5i² + 12i - 32i = 5i² - 20i
= 5i² - (5*4*i)
= 5i(i - 4)
I NEED HELP IM BEGGING WILL MARK BRAINLEST
JUST ANSWERS NO WORK NEEDED
Answer:
a = 5 c =11
Step-by-step explanation:
Answer:
sqrt[(80^2) + (20^2)] = (bottom base of the entire rectangle)
= 20(sqrt(17)) units or about 82.46211 units
find angle at bottom corner
arctan(20/80) = about 14.04624 degrees
cos(14.04624) = 20(sqrt17) / (80+a)
solve for a: --> a = 5 units
use pythag for side c
(20^2) + (5^2) = c^2
c is about 20.6155 units or 5(sqrt17)
Step-by-step example:
which table and graph represents the equation y=2x i give brainly wjo ever it correct
Answer:
graph a and table a=B
Step-by-step explanation:
This is because for table a, if you subsite the numbers of x it would give you the answer for y such as y=2x, and since x is 2 y is 4, which is shown on the graph. And since it does not have any add ons, if you make x 0 it would be 0 so it would also be proportional through the orgin. so graph A is also correct.
Which expressions are polynomials? Select each correct answer. x2−x√+2 2 + s 4x³ + y
Answer:
Answers are
Y
2+s
4x^3+y
Step-by-step explanation:
[tex]81 \frac{1}{2} \times 121 \frac{1}{2} [/tex]
Solve the following equation:
1/3(y - 2) -5/6 (y + 1) =3/ 4(0 - 3) - 2
Answer:
11/5
Step-by-step explanation:
If you need help with more problems like this you can use m a t h w a y. (remove the spaces) :)
3) In Carter's math class, 20\% of students earned an A on a test. If there were 30 student in the class, how many did not get an A.
Answer:
24 students did NOT get an A
Step-by-step explanation:
30x.20=6
30-6=24
Someone help and plz make sure it’s right
Answer:
80 degree angle is the right answer
Help help help help help help help
Answer:
35/14
Step-by-step explanation:
Volume = 4 * h * 7 / 2 = 14h
35/14 = h
Somebody help me ASAP noww
Answer:
65
Step-by-step explanation:
That is a 180 split so 180-115=65
please help this is due soon
the answer is 60degree..hope it helps u
Help pls show brainly
Answer:
10
Step-by-step explanation:
125 divided by 12.5
Answer: 10 dresses
Step-by-step explanation:
125/12.5=10
For every dress she needs 12 1/2 yards of fabric so what multiple of 12.5 is equal to or less than 125 and thats 10
can some help me pick the right answer for (9 + t) /12 = -3
45
-45
36
-36
Answer:
(9 + t)/12=-3
(9-45)/12
-36/12
= -3
answer = -45
Which temperature is greater, -20F or -60F
Answer:
-20
Step-by-step explanation:
Answer:
It's -20F :)
Step-by-step explanation:
hsbshehehebvdhshhakakkanabsbxh
The population of a city is 250,000 and the annual growth rate is 2.2% Write an equation to model the population y after x years.
Answer:
bueno, es 3.70 así que espero que ayude um buena suerte ~ nena ~
Step-by-step explanation:
Factor 35y+40z please help.
Answer:
i judt want points
Step-by-step explanation:
What is the distance between (3,5) and (7,3)
Evaluate: 5*5/7
enter your answer as a proper fraction or mixed number
Answer:
3 4/7
Step-by-step explanation:
5 times 5/7 = 25/7
= 3 4/7
Answer:
3 4/7
Step-by-step explanation:
5/1 x 5/7 = 25/7 = 3 4/7
Can someone help me pls
If x/5 = 4/15, what is the value of x? Please hurry and answer!!! In a test!!!!
Answer:
x= [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
(✿◡‿◡) <-- she helped u on your test, the least you can do is give her brainliest
HELP ANSWER GETS BRANLIEST ANSWER!
Answer: -5/4
Step-by-step explanation: You can use the graph to count the slope. The change in y is -5 and the change in x is 4, and slope is change in y over change in x.
en una encuesta a 200niños sobre el programa de T.V. que más les gusta ver ,se encontró que a 30 niños ven dibujos animados 45 niños miran películas animadas solamente 55niños miran programas sobre animales 38 niños miran programas sobre animales y dibujos animados 32 niños miran los tres tipos de programas encuentra el porcentaje de cada grupo
Answer:
15% de los niños solo ven dibujos animados, 22.5% solo ven películas animadas, 27.5% ven programas sobre animales, 19% miran programas sobre animales y dibujos animados, y 16% ve los tres tipos de programas.
Step-by-step explanation:
Dado que en una encuesta a 200 niños sobre el programa de TV que más les gusta ver se encontró que 30 niños ven dibujos animados, 45 niños miran películas animadas, 55 niños miran programas sobre animales, 38 niños miran programas sobre animales y dibujos animados y 32 niños miran los tres tipos de programas, para determinar el porcentaje de cada grupo se deben realizar los siguientes cálculos:
30/200 = 15/100 = 15%
45/200 = 22.5/100 = 22.5%
55/200 = 27.5/100 = 27.5%
38/200 = 19/100 = 19%
32/200 = 16/100 = 16%
Así, 15% de los niños solo ven dibujos animados, 22.5% solo ven películas animadas, 27.5% ven programas sobre animales, 19% miran programas sobre animales y dibujos animados, y 16% ve los tres tipos de programas.
Plz help me Jen can jump rope 80 times in 60 seconds. If she jumps at a constant ratio of seconds to jumps, how many jumps can she make in 15 seconds?
Answer:
The answer is 4
Step-by-step explanation:
You just divide 80 by 15.
She can jump rope 20 times in 15 seconds
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
Given that Jen can jump rope 80 times in 60 seconds.
We have to determine the number of jumps can she make in 15 seconds.
Let the number of jumps would be x she can make in 15 seconds
Since she jumps at a constant ratio of seconds to jumps
So according to proportionality,
⇒ 80/60 = x/15
⇒ x = 15(80/60)
⇒ x = 20
Hence, she can jump rope 20 times in 15 seconds.
Learn more about the Ratio here:
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Orlando wants to buy a new TV. The price was $985. When he goes to the store a second time, he found that price was marked down by 35%. What is the new price of the TV?
Will give brainliest
Answer:
The third option
Step-by-step explanation:
-1 - 3 = -4
1 - 3 = -2
3 - 3 = 0
5 - 3 = 2
Which figures appear to be congruent?
An image of 5 triangles on a 14 by 12 grid is shown.Triangle 1 has a base that is 4 units long. The upper vertex is 4 units above the midpoint of the base. To the right, triangle 2 has a horizontal leg that is 3.5 units long and a vertical leg that is 4 units long. A small square is positioned in the triangle at the lower left vertex. Below triangle 1, triangle 3 has a horizontal leg that is 3.5 units long and a vertical leg that is 4 units long. A small square is positioned inside this triangle at the upper right vertex. Triangle 4 is toward the center of the grid. It has a horizontal leg that is 1 unit long and a vertical leg that is 4 units long. A small square is positioned inside this triangle at the upper right vertex. Triangle 5 is to the lower right. It has a horizontal leg that is 6 units long and a vertical leg that is 4 units long. A small square is positioned inside this triangle at the lower left vertex.
A. 1, 2, and 3
B. 1 and 4
C. 1 and 5
D. 2 and 3
Answer:
D
Step-by-step explanation:
Mei has 2 yellow teacups and 5 brown teacups Which ratio compares the number of brown teacups to the total number of teacups
Answer: 5: 7
Step-by-step explanation:
The total number for teacups: 2 yellow teacups + 5 brown teacups = 7 teacups
the ratio compares the number of brown teacups to the total number of teacups is :
5: 7
The ratio that compares the number of brown teacups to the total number of teacups is 5: 7
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that Mei has 2 yellow teacups and 5 brown teacups.
The total number for teacups is;
2 yellow teacups + 5 brown teacups = 7 teacups
Therefore, the ratio compares the number of brown teacups to the total number of teacups can be;
5: 7
Learn more about the ratio here:
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2 people working at the same rate will take 9 hours to paint a room.
a) Assuming that they all work at this rate, how long will it
take 3 people to paint the room?
hours
(2)
b) In fact, the third person works at a faster rate.
How does this affect the time to paint the room?
Will it be
A faster?
B slower?
or
Answer:
a)6 hrs
b)faster
Step-by-step explanation:
a) 9*2/3=6
5 cm 7 cm 15 cm What is the surface area of the figure? by square centimeters