Answer:
(a) [tex]U_1 =5[/tex]; [tex]U_2 = 8[/tex]; [tex]U_{18} = 328[/tex]
(b) [tex]U_1 = 11[/tex]; [tex]U_2 =17[/tex]; [tex]U_{18} = 113[/tex]
Step-by-step explanation:
Required
1st, 2nd and 18th terms
To do this, we simply substitute 1, 2 or 18 for n in the given equations
Solving (a):
[tex]U_n =n^2 + 4[/tex]
1st term: n = 1
[tex]U_1 =1^2 + 4[/tex]
[tex]U_1 =1 + 4[/tex]
[tex]U_1 =5[/tex]
2nd term: n = 2
[tex]U_2 = 2^2 + 4[/tex]
[tex]U_2 = 4 + 4[/tex]
[tex]U_2 = 8[/tex]
18th term: n = 18
[tex]U_{18} = 18^2 + 4[/tex]
[tex]U_{18} = 324 + 4[/tex]
[tex]U_{18} = 328[/tex]
Solving (b):
[tex]U_n = 6n + 5[/tex]
1st term: n = 1
[tex]U_1 = 6*1 + 5[/tex]
[tex]U_1 = 6 + 5[/tex]
[tex]U_1 = 11[/tex]
2nd term: n = 2
[tex]U_2 = 6*2 + 5[/tex]
[tex]U_2 =12 + 5[/tex]
[tex]U_2 =17[/tex]
18th term: n = 18
[tex]U_{18} = 6*18 + 5[/tex]
[tex]U_{18} = 108 + 5[/tex]
[tex]U_{18} = 113[/tex]
Serenity invested $1300 in an account that pays 4.5% interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Serenity would have in the account 10 years after her initial investment. Round to the nearest tenth (if necessary).
Answer: 2018.9
Step-by-step explanation:
A construction crew is paving a road. The crew has already paved 1,000 square feet and can pave at a rate of 300 square feet of road per hour. The function f(x) = 300x
Answer:
Step-by-step explanation:
i go to southwind what’s the answer ??
The crew would spend 3.33 hours to pave a road that is 1,000 ft².
A linear equation is in the form:
y = mx + b;
where y, x are variable, m is the slope of the line and b is the y intercept.
Let f(x) represent the amount of space paved in x hours.
Given the function:
f(x) = 300x
Therefore to pave 1000 ft²:
1000 = 300x
x = 3.33 hours
The crew would spend 3.33 hours to pave a road that is 1,000 ft².
Find out more at: https://brainly.com/question/21105092
The sum of 2/3m and 1/5
50 Points Help will give brainliest
1. To transform from standard form to vertex form you need to complete the square.
To transform from vertex form to standard form multiply the equation out and combine all the like terms.
2. The attributes from vertex form would be the roots ( zeros)
From standard form the attribute would be the lowest point, also known as the vertex.
enter the length of PQ to the nearest tenth.
Answer:
[tex]\displaystyle PQ \approx 5.2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] cosθ = adjacent over hypotenuseStep-by-step explanation:
Step 1: Identify
Angle θ = 55°
Adjacent Leg = PQ
Hypotenuse = 9
Step 2: Solve
Substitute in variables [cosine]: [tex]\displaystyle cos55^\circ = \frac{PQ}{9}[/tex][Multiplication Property of Equality] Isolate PQ: [tex]\displaystyle 9cos55^\circ = PQ[/tex]Evaluate: [tex]\displaystyle 5.16219 = PQ[/tex]Rewrite: [tex]\displaystyle PQ = 5.16219[/tex]Round: [tex]\displaystyle PQ \approx 5.2[/tex]What is the value of x when angle 1 is74° and angle 2 is 6x + 8° ?
Answer:
74 + 6x + 8 = 180
6x + 82 = 180
6x = 180 - 82
6x = 98
x = 98/6
x = 16.3
this answer is only correct
when angles in linear pair
Find the volume of a right circular cone that has a height of 3.2 m and a base with a
radius of 14.1 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
what's the question i need more info
ASAP plz I’m being times 40 point + Brainly for correct find slope and rate of change
Answer:
slope: -30x
rate of change: -30
Step-by-step explanation:
[tex] \frac{change \: in \: y}{change \: in \: x} [/tex]
[tex] \frac{ - 30}{1} [/tex]
slope = -30x
rate if change: -30
Find the sum
(7x^6 + 2x^5 – 3x^2 + 9x) + (5x*5 + 8x^3 – 6x² + 2x - 5) =
Answer:
i think
7x^6+7x^5+8x^3-9x^2+7x-5
Write the ratios for sin A and cos B. 10 AC, 24 CB, 26 BA
Answer:
acdc
Step-by-step explanation:
Using the graph, determine the equation of the circle
Answer:.
Step-by-step explanation:
Well if you look at the graph and first look at the
joe nuts
In 1998 there were 305 students who graduated from high school. In 2019, there were 356 students. What is the rate of change in the number of students?
1. About 1 student per year
2. about 51 students per year
3. about 2 students per year
4. about 5 students per year
Answer:
3. about 2 students per year
Step-by-step explanation:
The rate of change would be the difference in the number of students divided by the number of years passed.
So, rate of change = [tex]\frac{356-305}{2019-1998}[/tex]
= [tex]\frac{51}{21} = 2.43[/tex]
So it's around 2 students per year.
I hope this is correct and helps!
1,000 cm = 0.01 km
Correct or incorrect
Answer:
Correct
Step-by-step explanation:
Answer:
Correct
Step-by-step explanation:
Hope this helps
Can someone please solve this it's very important thank you
The size of a TV is usually given by the length of the screen diagonal. If the screen dimensions of a TV are 16 inches by 12 inches, what size is this TV?
A)28 inch
B)20 inch
C)16 inch
D)12 inch
Answer:
A
Step-by-step explanation:
You have to do step by step
Applying the Pythagorean Theorem, the size of the TV that is 16 inches by 12 inches is: B)20 inch
Recall:
Diagonal of a rectangle can be found using the Pythagorean Theorem given as: [tex]d = \sqrt{l^2 + w^2}[/tex]Where, d = diagonal, l and w are the dimensions of the shape.Given:
l = 16 inches
w = 12 inches
Therefore,[tex]d = \sqrt{16^2 + 12^}\\[/tex]
[tex]d = \sqrt{400} \\\\\mathbf{d = 20 inches}[/tex]
Therefore, applying the Pythagorean Theorem, the size of the TV that is 16 inches by 12 inches is: B)20 inch
Learn more here:
https://brainly.com/question/11239816
What is md enter your answer in the box
Mr Abraham is able to divide the learners in his mathematics class into equal groups of 2, 5 or 6 without leaving any learners out. What is the smallest possible number of learners in the class
Answer:
30
Step-by-step explanation:
Find the lowest number divisible by both 6, 5, and 2.
To start, let's list off the numbers divisible by six, and see if we can check any of them off for 5. Since both 2 and 6 are even numbers, we know that if a number is divisible by 6, it's divisible by 2.
6 12 18 24 30 36 42 48 54 60
All of these numbers are divisible by two. Let's find the lowest one that is divisible by 5. We know this by either the umber ending in 5 or 0.
30 is the lowest number that is divisible by 2, 5, or 6.
5x - 9y = -13
-2x + 3y = 4
Can you explain more? if your looking for the slope of both it is 5/9 for the fist one and 2/3 for the second. If your looking for y and x -intercept for the first one x intercepts at (-2,0) and y intercepts at (0, 4/3) and, for the second one x intercepts at ( -13/5, 0) and y intercepts at (0, 13/9)
A construction company wants to hire x carpenters for $220 a day and y plumbers for $260 a day. the company wants to hire at least 18 workers. it wants to pay no more than $4500 each day.
write a system of inequalities to model the situation (use >, <, <=, =>)
Answer:6
Step-by-step explanation:
$220 × 6 = $1320 this is how much it cost to pay 6 carpenters for one day. Now lets find how much it cost to 12 plumbers at $260 a day. $260 × 12 = $3120 this is how much it costs to pay 12 plumbers a day.
Under his cell phone plan, Owen pays a flat cost of $67.50 per month and $4 per gigabyte. He wants to keep his bill at $71.90 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Owen can use while staying within his budget.
Answer:
1 gig im preety sure i might be wrong
Step-by-step explanation:
HELPPP MEE PLSSS
Find m∠2
Answer:
Step-by-step explanation:
180-68=112
1= 68
2=112
What does 2 (p -q) +5 (p+q) equal when p = 7 and q = -2? Answer:
Answer:
43
Step-by-step explanation:
Given
2(p - q) + 5(p + q) ← substitute p = 7 and q = - 2 into the expression
= 2(7 - (- 2)) + 5(7 + (- 2))
= 2(7 + 2) + 5(7 - 2)
= 2(9) + 5(5)
= 18 + 25
= 43
A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1938 mailboxes this week. If each mailbox has dimensions as shown in the figure below, how many square meters of aluminum will be needed to make these mailboxes? In your calculations, use the value 3.14 for pi, and round up your answer to the next square meter.
Step-by-step explanation:
Area = Area of sides + area of semicircle thing
= (2*0.21*0.31) + (2*0.31*0.61) + (0.21*0.61) + ( 3.14*0.105*0.61) + (3.14*0.105*0.105) = 0.872 m^2
Total area = 0.872 *1106 =964.43 m^2
Answer =965 m^2
A local artist, Sally, had a total of $2,610 at the end of the State Art Fair. She sold each of her paintings for $45. How many paintings did she sell?
Can someone please help me with math.
please help with this!!!
Can someone help me with this. Will Mark brainliest.
Answer: [tex]\sqrt{89}[/tex]
Step-by-step explanation:
[tex]d=\sqrt{(x_{2}-x_{1)} ^{2} } +(y_{2} -y_{1} )^{2} }[/tex]
(-1, 9) and (7,4)
[tex]d=\sqrt{(7-(-1))^{2}+ (4-9)^{2} }[/tex]
[tex]d= \sqrt{8^{2} +(-5)^{2} }[/tex]
[tex]d=\sqrt{64+25} \\d=\sqrt{89}[/tex]
Jesse read 98 pages of a book in one week. What was his unit rate of
pages read per day?
Answer:
14 per day
Step-by-step explanation:
Please mark brainliest
Find the distance between the pair of points.
(-14, 11) and (-7,5)
Answer: 13 units or whatever measurement you're using.
Step-by-step explanation: First get -14 to -7 by adding 7. Then get 11 to 5 by subtracting 6 then adding 6 and 7 together I'm pretty sure.
A composite figure is shown below.
What is the area of the figure?
A 6
B 8
C 9
D 10
Answer:
option C 9 unit².
Step-by-step explanation:
option C 9 units ²
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you if you find it useful.