Answer:
[tex]f(n)=f(n-1)+22[/tex].
Step-by-step explanation:
Note: In the given function it should be (n-1) instead of (n=1).
Consider the given function is
[tex]f(n)=-11+22(n-1)[/tex]
It is the explicit form of an A.P.
For [tex]n=1[/tex],
[tex]f(1)=-11+22(1-1)=-11+0=-11[/tex]
For [tex]n=2[/tex],
[tex]f(2)=-11+22(2-1)=-11+22=11[/tex]
Common difference is
[tex]d=a_2-a_1=11-(-11)=11+11=22[/tex]
The recursive formula of an A.P. is
[tex]f(n)=f(n-1)+d[/tex]
Substitute [tex]d=22[/tex] in the above formula.
[tex]f(n)=f(n-1)+(22)[/tex]
[tex]f(n)=f(n-1)+22[/tex]
Therefore, required recursive formula is [tex]f(n)=f(n-1)+22[/tex].
In the triangle below y= .round to the nearest
Answer:
Step-by-step explanation:
y = atan(10/8) = 51.3 deg
A sports club charges an initiation fee and a monthly fee. At the end of the 5 months, a member had paid a total of $450. At the end of the 10 months, she had paid a total of $500.
a) Write a linear system to model the situation
b) Solve the linear system by substitution to solve the related problem: What are the initiation fee and the monthly fee?
Answer:Initiation fee is $400 while monthly fee is $10
Step-by-step explanation:
Let the initial fee be x which is fixed while the monthly fee be y
At the end of 5 months, 450 was paid
This means that;
x + 5y = 450 ••••••••(i)
At the end of 10 months, $500 was paid
Mathematically, this means that;
x + 10y = 500•••••••••••(ii)
now we solve both equations simultaneously to get the value of x and y
our equation ii can be rewritten as;
x + 5y + 5y = 500
we can now insert equation i directly into this
450 + 5y = 500
5y = 500-450
5y = 50
y = 50/5
y = $10
From x + 5y = 450
let’s insert the calculated value of y
x + 5(10) = 450
x + 50 = 450
x = 450-50
x = $400
Find the volume of the rectangular prism. Express your answer as a simplified mixed number.
Answer:
414 9/16 m³
[tex]414\frac{9}{16}m^{3}[/tex]
Step-by-step explanation:
The volume of a Rectangular prism is calculated as Length × Width × Height
From the attached diagram,we can see that
The length = 8 3/8 m
The width = 6 m
The height =8 1/4 m
Converting the mixed fraction to improper fraction in other to simplify it better
The length = 67/8 m
The height = 33/4 m
The volume of the rectangular prism =
67/8 m × 6m × 33/4m
= (13266/32)m³
= 6633/16 m³
= 414 9/16 m³
= [tex]414\frac{9}{16}m^{3}[/tex]
Sailors on a ship at sea spot the light from a lighthouse at an angle of elevation of 25°. The light of the lighthouse is 30 meters above sea level. How far from shore is the ship? Round your answer to the nearest meter.
The distance between the ship and the shore is 63.83 meters.
We have,
Distance between the ship and the shore = x
Use tangent trigonometric identites.
tan θ = perpendicular / Base
tan 25 = 30/x
tan 25 = 0.47
0.47 = 30/x
x = 30/0.47
x = 63.83
Thus,
The distance between the ship and the shore is 63.83 meters.
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Find the perimeter of the following figure.
x + 13
3x + 2
8
2
X + 5
Answer:
5x+30
Step-by-step explanation:
simply add each side together:
(x+13)+(3x+2)+8+2+(x+5)
=5x+30
Question 1 of 10
2 Points
If f(x)= 2(x)2 +5W/(x+2), complete the following statement:
f(2)=
Answer:
8 + (5W)/ 4
Step-by-step explanation:
Plug in 2 for x
2 * 2 * 2 + (5W)/(2 + 2)
8 + (5W)/ 4
Recall the shipping box scenario from the Introduction. As an employee of a sporting goods company, you need to order shipping boxes for bike helmets. Each helmet is packaged in a box that is n inches wide, n inches long, and 8 inches tall. The shipping box you order should accommodate the boxed helmets along with some packing material that will take up an extra 2 inches of space along the width and 4 inches of space along the length. The height of the shipping box should be the same as the helmet box. The volume of the shipping box needs to be 1,144 cubic inches. The equation that models the volume of the shipping box is 8(n + 2)(n + 4) = 1,144.
Answer:
The dimensions of the helmet box are as follows
Width is 9 inches
Length is 9 inches
Height is 8 inches
The dimensions of the shipping box ordered are as follows;
Width is 11 inches
Length is 13 inches
Height is 8 inches
Step-by-step explanation:
8(n + 2)(n + 4) = 1144
8·n² + 48·n + 64 = 1144
8·n² + 48·n - 1080 = 0
8×(n - 9)×(n + 15) = 0
∴ n = 9 or -15 inches
The dimensions of the helmet box are as follows
Width = 9 in.
Length = 9 in.
Height = 8 in.
The dimensions of the shipping box ordered are as follows;
Width = 9 + 2 = 11 in.
Length = 9 + 4 = 13 in.
Height = 8 in.
Answer:
8 inches x 11 inches x 13 inches
Step-by-step explanation:
I got correct on edmentum
f(x) = (x + 3)(x + 5).
Answer:
Step-by-step explanation:
Answer:y=x+8x+15
Step-by-step explanation:
PLEASE PLEASE HELP ME IM SOOO CONFUSED!!!!!
( show the work MANDATORY)
WRITE EACH FRACTION AS A DECIMAL. USE A BAR TO SHOW REPEATING DECIMAL.
1.) 7/10
2.) 1/4
3.)-3/10
4.)1/8
5.) 7/30
6.) 7/11
7.)-3/5
Answer:
1=0.70 2=0.25 3=-0.30 4=0.125 5=0.233333333 6=0.636363636 7=-0.6
Step-by-step explanation:
Calculator and anything over 10, just move the decimal back one space!
please help for brainliest
Answer:
f = 6, g = 8
Step-by-step explanation:
The area of Δ ADE = 60 - 48 = 12 cm²
Thus
[tex]\frac{1}{2}[/tex] AD × 4 = 12, that is
2AD = 12 ( divide both sides by 2 )
AD = 6 = f
The area of ABCD = 48 cm² , thus
fg = 48 , that is
6g = 48 ( divide both sides by 6 )
g = 8
Thus f = 6 and g = 8
Saturn is 8.867 × 108 miles away from the Sun. Uranus is 1.787 × 109 miles away from the Sun. Approximately how many times farther is Uranus from the Sun than Saturn is?
A. 0.2 times
Answer:
0.2 times
Step-by-step explanation:
Saturn: 8.867 × 108 = 957.636
Uranus: 1.787 × 109 = 194.783
You take (Uranus: 194.783)
& you divide it by (Saturn: 957.636)
You should get a funky number like 0.203399830415732 but since they said approximately you only need to use the first 2 (don't forget to round)
That would make Uranus 0.2 times as far from the sun
Seaside Bike Rental Shop charges a $13 fee plus $7 per hour to rent a bike. Chris paid $62 to rent a bike. How many hours did he pay for?
Answer:
7 hours
Step-by-step explanation:
(62-13)/7=7
What is the area of a circle with a radius of 6 inches?
9 st in?
12 x in.2
36 x in 2
81 x in 2
Answer:
A≈113.1in²
Step-by-step explanation:
Radius: 6in
Solved for area
Shape: Circle
Formula: A=πr2
1: Use the formula πr (r) to calculate the the area.
2: We are looking for the area.
3: 6 inches for radius to find the area
Answer: A≈113.1in²
Hope this helps.
Please help, having trouble figuring out this word problem. Thanks if you do :)
Answer:
-21. -19.-17
Step-by-step explanation:
Let x be the smallest
x+2 next smallest
x+4 be the largest
4*(x) = 18+6(x+4)
Distribute
4x = 18+6x+24
Combine like terms
4x = 42+6x
Subtract 6x from each side
-2x = 42
Divide by -2
-2x/-2 = 42/-2
x = -21
x+2 = -19
x+4 = -17
Answer:
- 21, - 19, - 17
Step-by-step explanation:
Let y be the smallest no.
& y + 2 next smallest no.
& y + 4 be the largest no.
= 4 * (y) = 18 + 6 * (y + 4)
4y = 18 + 6y + 24
4y - 6y = 42
- 2y = 42
= - 21
The other 2 numbers are:
y + 2
= - 19
y + 4
= - 17
Hope this helps!
Mr. Smith plans to serve 200 hamburgers at the company picnic. How many packages of hamburger buns will he need if buns come in packages of 12? How many packages will he need if buns come in packages of 16?
Answer:
34 packages
25 packages
Step-by-step explanation:
He needs a pair of buns for each hamburger.
He needs 200 hamburger. That means that he needs 400 buns for his picnic.
If buns come in a package of 12, the number of packages he needs is:
400 / 12 = 33.33 packages
Because packages come in whole numbers, we have to round up.
That means he needs 34 packages.
If buns come in a package of 16, the number of packages he needs is:
400 / 16 = 25 packages
You owe $225 on your credit card. You make a $55 payment and then purchase $87 worth of clothes at Target. What is the integer that represents the balance owed on the credit card
Answer: 83
Step-by-step explanation:
225 - 55 -87= 83
You have $83 left on the credit card as your balance.
Will mark brianliest !!!!!!!!!!!!! Please answer correctly !!!!!!!!!!!!!
Answer:
9 is the greater x and 2 is the lesser x
Step-by-step explanation:
I really don't know how to explain without simply writing it out for you, which I really can't do. But there's the answer lol
Answer:
x = 2, x = 9
Step-by-step explanation:
Given
x² - 11x + 18 = 0
Consider the factors of the constant term (+ 18) which sum to give the coefficient of the x- term (- 11)
The factors are - 9 and - 2 , since
- 9 × - 2 = + 18 and - 9 - 2 = - 11 , thus
(x - 9)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2 ← lesser value
x - 9 = 0 ⇒ x = 9 ← greater value
3.) The length of a midsegment of a trapezoid is the blank
lengths of the bases. *
Your answer for blank!
Answer:
Average
Step-by-step explanation:
If a and b are the lengths of the bases, then a+b/2 is the length of the midsegment of the trapezoid.
Solve for w. 5w + 9z = 2z + 3w w = w equals negative StartFraction 7 Over 2 EndFraction z.Z w = w equals negative StartFraction 2 Over 7 EndFraction z.Z w = –2z w = –7z
Answer:
w = -7z/2
Step-by-step explanation:
We need to solve for w in terms of z.
The equation given is:
5w + 9z = 2z + 3w
Collect like terms:
5w - 3w = 2z - 9z
2w = -7z
w = -7z/2
Answer:
option A (-7/2z)
Step-by-step explanation:
Evaluate (-B)2 for A= 5, B = -4, and C = 2.
Answer:
8
Step-by-step explanation:
Expression:
(-B)2
Let's substitute the value of B into this expression:
B = -4
(-B)2
[-(-4)]2
Notice how there are two negative signs int this expression:
[-(-4)]2
Well, there is an invisible 1 behind the first negative sign.
[-(-4)]2
[-1(-4)]2
All we have to do now is multiply:
[-1(-4)]2
(4)2
(4)2
= 8
Therefore, the value of the expression is 8.
Imani is buying a new cell phone for $800.00. She has to put down
20% and finance the rest at an exact interest rate of 6% for 275
days. How much is the maturity value of her loan?
. Suppose you plan to make a box that will hold exactly 40 one-inch cubes. Give the dimensions (ex: 1in x 1in x 40in) of 3 possible boxes you can create to hold all cubes.
Answer:
The dimensions of the three possible boxes are;
Box 1: 2 inches length by 4 inches width by 5 inches height
Box 2: 2 inches length by 2 inches width by 10 inches height
Box 3: 8 inches length by 1 inch width by 5 inches height
Step-by-step explanation:
The dimensions of the required box = 40 in³
Therefore, a box that will hold all the cubes will have a dimension given as follows;
Length, l × Width, w × Height, h = 40 in.³
We therefore, look for possible dimensions of l, w, h, however to make is faster, we note that l × w = base area, BA, hence we look for the factors 40 thus;
BA × h ≡ l × w × h
8 × 5 = 40 ≡ 2 × 4 × 5 = 40
4 × 10 = 40 ≡ 2 × 2 × 10 = 40
8 × 5 = 40 ≡ 8 × 1 × 5 = 40
Hence we have our three possible boxes as follows;
Box 1: Length = 2 inches, width = 4 inches and height = 5 inches
Box 2: Length = 2 inches, width = 2 inches and height = 10 inches
Box 3: Length = 8 inches, width = 1 inches and height = 5 inches.
Which explains how to find the quotient of the division below? Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction Write Negative 3 and one-third as Negative StartFraction 13 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 13 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 9 and three-fourths. Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 7 and StartFraction 6 over 12 EndFraction = Negative 7 and one-half. Write Negative 3 and one-third as Negative StartFraction 9 over 3 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 9 over 3 EndFraction times StartFraction 4 over 9 EndFraction. The quotient is Negative 1 and one-third. Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 4 over 9 EndFraction. The quotient is Negative 1 and StartFraction 13 over 27 EndFraction = Negative 1 and StartFraction 13 over 27 EndFraction.
Answer:
(B) Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 7 and StartFraction 6 over 12 EndFraction = Negative 7 and one-half.
Step-by-step explanation:
To find the quotient of the division:
[tex]-3\dfrac13 \div \dfrac49[/tex]
Step 1: [tex]\text{Write}$ $ -3\dfrac13$ as $ -\dfrac{10}{3}[/tex]
[tex]-3\dfrac13 \div \dfrac49 = -\dfrac{10}{3} \div \dfrac49[/tex]
Step 2: Find the reciprocal of [tex]\dfrac94[/tex]
[tex]-\dfrac{10}{3} \times \dfrac94\\=-7\dfrac12[/tex]
Answer:
b
Step-by-step explanation:
What do I do in this question
Step-by-step explanation:
X × 3 + 4 = 22
X × 3 = 22 - 4
X × 3 = 18
X = 18 /3
X = 6
Jordan bought StartFraction 9 Over 16 EndFraction of a pound of sunflower seeds and divided them evenly into 9 snack bags for his lunch. What is the weight of sunflower seeds in each snack bag?
Answer: 1/16 of a pound
Step-by-step explanation:
Here is the complete question:
Jordan bought 9/16 of a pound of sunflower seeds and divided them evenly into 9 snack bags for his lunch. What is the weight of sunflower seeds in each snack bag?
1/16 of a pound
1/9of a pound
16/81 of a pound
81/16 pounds
From the question, we are told that Jordan bought 9/16 of a pound of sunflower seeds and then divided them equally into 9 snack bags for his lunch. To get the weight of sunflower seeds in each snack bag, we will divide 9/16 by 9 snack bags. This can be written mathematically as:
= 9/16 ÷ 9
= 9/16 × 1/9
= 1/16
The weight of sunflower seeds in each snack bag will be 1/16 of a pound.
Answer:
A- 1/16
Step-by-step explanation:
I took the quiz and got it correct :) hope I could help!!!
Bernard is two years older than his sister Therese and four years younger than his sister
Josephine. The product of his sisters' ages is the age of his mother, 40.
A. If x is Bernard's age, write his two sisters' ages in terms of x.
Answer:
B. Write Bernard's mother's age in terms in terms of x and solve this quadratic equation.
Answer:
C. What is Bernard's age?
Answer:
Please show working out
Firstly Bernard = x
A) lets focus on Therese first. Bernard id two years older than her so for Therese’s equation in terms of x it would be x+2. Now for Josephine Bernard is 4 years younger than HER so it would be 4-x.
B) The mother is the PRODUCT of the sisters’ ages so (multiplication)
It would be like this: (x+2)(4-x)= 40 This is all in terms of x.
Solving for the equation (using distributive property) we get:
4x-x+8-2x=40
(Reorganize to group like terms, remember to go in order from the numeral numbers with variables, to variables only then numbers only): 4x-2x-x+8=40 (now combine like terms and simplify): x+8=40 this is his mom’s age in terms of x
C) HERE we can solve for x:
Isolating x to get the answer we move the 8 to the other side of the equation and it becomes a negative 8 so:
x=40-8
x=32
Therefore Bernard is 32 years old.
Hope this helps!
La mama de maximo le pidio que fuera a la tienda dijo que comprara 0.5 litros de leche, el dueño de la tienda le dijo que solo tenia leche en envases de ½ litros ¿Es mas, menos o igual a la capacidad que le pidió su mama?
Answer:
1/2 litros es igual a la capacidad que le pidió su mamá.
Step-by-step explanation:
Para encontrar la respuesta debes escribir 0.5 como fracción. Para hacerlo, el numerador es el número original sin el punto decimal y para definir el denominador debes determinar cuántos digitos decimales tienes. En este caso, el número tiene un dígito decimal, por lo cual el denominador es 10. De acuerdo a esto:
0.5 se escribiría como [tex]\frac{5}{10}[/tex] y esta fracción se puede simplificar porque los dos números son divisibles entre 5:
5/5= 1
10/5= 2
Por esto, 0.5= [tex]\frac{1}{2}[/tex]
Esto significa que 1/2 litros es igual a la capacidad que le pidió su mama.
help me!!
solve for d
Answer:
d =±2sqrt(7) i
Step-by-step explanation:
d^2 = -28
Take the square root of each side
sqrt(d^2) = ±sqrt(-28)
d = ±sqrt(-28)
d = ±sqrt(-1)sqrt(28)
We know that sqrt(-1) = i
d =±i*sqrt(4)sqrt(7)
d =±i 2sqrt(7)
d =±2sqrt(7) i
The picture below has all the questions I need assistance with.
Answer:
11) D, 12) D
Step-by-step explanation:
if you do the math it works
The table gives some information about the heights of 30 plants.
Height, h in cm
Frequency
0<h < 10
1
10 <h < 20
9
20 <h < 30
7
30 <h < 40
13
Which class interval contains the median?
Select your answer.
osh <10 10 sh< 20 20 sh < 30 30 sh<40
А
B
C
D
Answer:
2,8,8
Step-by-step explanation:
The class interval 20 <h < 30 contains the median.
Median :To find the interval in which median is lies, first we have to find the cumulative frequency.
The table is,
Height range frequency Cumulative frequency
0<h < 10 1 1
10 <h < 20 9 1 + 9 = 10
20 <h < 30 7 10 + 7 = 17
30 <h < 40 13 17 + 13 = 30
Sum = 30
Since, the sum of frequency is even. So that the median is ,
[tex]\frac{\frac{n}{2} th +(\frac{n}{2} +1)th}{2} =\frac{15th +16th}{2}[/tex]
From observing table, 15th and 16th term lies in cumulative frequency of 17.
Thus, the class interval 20 <h < 30 contains the median.
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