b) Here are the first four terms of another sequence.
7
11 15 19
Write an expression for the nth term of this sequence.
Answers
Answer:
[tex]a_{n}[/tex] = 4n + 3
Step-by-step explanation:
There is a common difference between consecutive terms, that is
11 - 7 = 15 - 11 = 19 - 15 = 4
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 7 and d = 4 , then
[tex]a_{n}[/tex] = 7 + 4(n - 1) = 7 + 4n - 4 = 4n + 3
Related Questions
Solve these simultaneous equations:
2x + 4y = 38
7x - 4y =7
Answers
Answer:
Step-by-step explanation:
Answer:
x=5, y=7
Step-by-step explanation:
2x+4y= 38
+7x-4y= 7
9x= 45
9x/9= 45/9
x=5
2x+4y=38
2(5)+4y= 38
10+4y= 38
-10 -10
4y= 28
4y/4= 28/4
y=7
PLS USE the information given! DONT GUESS!
Write the equation of the circle.
A: (x+3)2+(y−6)2= 2
B: (x−3)2+(y+6)2= 2
C: (x+3)2+(y−6)2= 4
D: (x−3)2+(y+6)2= 4
Answers
Answer:
C. (x + 3)² + (y - 6)² = 4Step-by-step explanation:
Get the center and radius from the graph.
Center is: (-3, 6)Radius is: 2Use the circle formula:
(x - h)² + (y - k)² = r²We have:
h = -3, k = 6, r = 2Substitute and get the equation:
(x - (-3))² + (y - 6)² = 2² ⇒(x + 3)² + (y - 6)² = 4Correct choice is C
solve each system by substitution y=2x-1. 3x+8y=11
Answers
Answer:
x=1, y=1
Step-by-step explanation:
Sub y=2x-1 into 3x+8y=11
3x+8(2x-1)=11
3x+16x-8=11
19x=11+8
19x=19
x=1
Sub x=1 into y=2x-1
y=2(1)-1
y=2-1
y=1
A study is done on the population of a certain fish species in a lake. Suppose that the population size P(1) after years is given by the following exponential
function.
P(t) = 400(1.22)
Find the initial population size.
Does the function represent growth or decay?
O growth O decay
By what percent does the population size change each year?
Answers
Answer:
Growth22%Step-by-step explanation:
Given function:
[tex]P(t) = 400(1.22)^{t}[/tex]Initial population size is when t = 0
P(0) = 400(1.22)⁰ = 400(1) = 400The multiple of 1.22 is applied every year, so the ratio of change is:
1.22 = 122% = 100% + 22%This is an exponential growth which represents 22% annual growth.
The function is
y=400(1.22)^tAs per y=ab^x
1.22 is the rate of changeIts growth as it's greater than 1
The percentage increase is
1.22-10.2222%how do you find the circumference of a circle
Answers
Answer:
circumference = pi (3.14 or 22/7, whatever your teacher wants or whatever the problem asks) x the diameter
Step-by-step explanation:
Answer:
To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14).
Step-by-step explanation:
I hope the images help!!
Please help me give Brain
Answers
Answer:168
Step-by-step explanation:
Which shape shows the cross-section of the square pyramid when it is cut by a plane parallel to the base?
Answers
Answer:
Triangle
Step-by-step explanation:
A pyramid is a strong-solid shape that is comprised of triangles, square shapes, squares, and different polygons. Pyramids are arranged depending on the state of their base. For instance, the outline given is a square-based pyramid in light of the state of its base(which is a square). Different sorts incorporate the three-sided based pyramid, three-sided based pyramid, and other polygon-based pyramids.
In the event that this square pyramid is cut with a plane that is corresponding to the base of the pyramid, the state of its cross-area will be a triangle since the shapes that are corresponding to the base are altogether triangles. So slicing the plane corresponding to the base is like removing one side of the triangle making up the pyramid.
help help
Prove the following:
[tex] \sf\frac{ \tan( \theta) }{1 - \cot( \theta) } + \frac{ \cot( \theta) }{ 1 - \tan( \theta) } = \sec( \theta) \cdot \: \csc( \theta) + 1[/tex]
[tex]\text{note: explanation is obvious}[/tex]
Answers
Answer:
the pictures are attachedplease see the explanation in the attached pictureAnswer:
note:[tex]\theta =y[/tex]
Your answer is in the attachment.
we have
siny(cosy-siny)
taking - common from this
-siny(-cosy+siny)
-sin y(siny-cosy)
The circle graph below shows the results of a survey about the number of TV's in a household. If you surveyed 250 households, how many would you predict to have 3 TV's?
Answers
Answer: answer
Step-by-step explanation: joe nuts
Write an equation when the two angles together are supplementary. solve for x
Answers
lol ur from trms
Step-by-step explanation:
What is the total surface area??? Please help me I’m confused
Answers
Answer:
136+56 ig
Step-by-step explanation:
If h:k = 2:5, x:y=3:4 and 2h+x:k+2y = 1:2, find the ratio h-x: k-y.
Answers
Given:
[tex]h:k=2:5,x:y=3:4,2h+x:k+2y=1:2[/tex]
To find:
[tex]h-x:k-y[/tex]
Solution:
We have, [tex]h:k=2:5[/tex] and [tex]x:y=3:4[/tex].
Let the values of h and k are 2a and 5a respectively.
Let the values of x and y are 3b and 4b respectively.
We have,
[tex]2h+x:k+2y=1:2[/tex]
It can be written as
[tex]\dfrac{2h+x}{k+2y}=\dfrac{1}{2}[/tex]
[tex]\dfrac{2(2a)+(3b)}{5a+2(4b)}=\dfrac{1}{2}[/tex]
[tex]\dfrac{4a+3b}{5a+8b}=\dfrac{1}{2}[/tex]
[tex]2(4a+3b)=1(5a+8b)[/tex]
On further simplification, we get
[tex]8a+6b=5a+8b[/tex]
[tex]8a-5a=8b-6b[/tex]
[tex]3a=2b[/tex]
[tex]a=\dfrac{2b}{3}[/tex]
Now,
[tex]h-x:k-y=\dfrac{h-x}{k-y}[/tex]
[tex]h-x:k-y=\dfrac{2-3b}{5a-4b}[/tex]
[tex]h-x:k-y=\dfrac{2\times \dfrac{2b}{3}-3b}{5\times \dfrac{2b}{3}-4b}[/tex]
[tex]h-x:k-y=\dfrac{\dfrac{4b}{3}-3b}{\dfrac{10b}{3}-4b}[/tex]
On further simplification, we get
[tex]h-x:k-y=\dfrac{\dfrac{4b-9b}{3}}{\dfrac{10b-12b}{3}}[/tex]
[tex]h-x:k-y=\dfrac{-5b}{-2b}[/tex]
[tex]h-x:k-y=\dfrac{5}{2}[/tex]
[tex]h-x:k-y=5:2[/tex]
Therefore, the ratio [tex]h-x:k-y[/tex] is [tex]5:2[/tex].
A bag contains 24 discs.
8 are red and 16 are blue.
One disc is taken out at random and replaced by two of the other colour.
Another disc is then taken out at random and replaced by two of the other colour.
Another disk is taken out at random
Work out the probability that all three discs are taken out red
Answers
Answer:
Step-by-step explanation:
8/24 are Red
Pick and return 2
So it will be 7/25
Again pick and return 2
Then it is 6/26
Now multiply the results
8/24 × 7/25 × 6/26 = 7/ 325
The probability that all three discs are taken out of red will be 7/ 325.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that a bag contains 24 discs. 8 are red and 16 are blue. One disc is taken out at random and replaced by two of the other colour. Another disc is then taken out at random and replaced by two of the other colour.
The probability will be calculated as,
Red = 8/24
Pick and return 2 it will be 7/25
Again pick and return 2 then it is 6/26
Now the overall probability will be,
P = 8/24 × 7/25 × 6/26 = 7/ 325
Therefore, the probability that all three discs are taken out of red will be 7/ 325.
To know more about probability follow
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A child has a box of colored building blocks. He will choose one block without looking. The odds against choosing a blue block are 13/4. What is the probability of choosing a blue block?
Answers
Answer:
The answer is "0.2352".
Step-by-step explanation:
Given:
The chance of selecting a odds blue block [tex]= \frac{13}{4}[/tex]
[tex]=\frac{\text{Amount of unfavourable blue block evets} \ (13)}{\text{Amount of unfavourable blue block evets} \ (4)}[/tex]
total number of events are 13+4= 17
Calculating the probability of choosing the blue block
[tex]=\frac{\text{Amount of unfavourable blue block evets} }{\text{Amount of unfavourable blue block evets} } \\\\ = \frac{4}{17} \\\\ =0.2352[/tex]
If the value of y varies inversely with x , which function represents the relationship between x and y if y = 48 when x = 3?
A. Y= 144/x
B. Y= 16/x
C. Y= x/16
D. Y= x/144
Answers
Answer:
A. Y = 144/x
Step-by-step explanation:
Inversely means y = 1/x
If y = 48, when x = 3
so 144/3 = 48
Therefore the answer is A
If the value of y varies inversely with x then the function Y= 144/x represents the relationship between x and y if y = 48 when x = 3
What is a function?A relation is a function if it has only One y-value for each x-value.
If y varies inversely with x, it means that y is inversely proportional to x, or y=k/x, where k is a constant of proportionality.
To find k, we can use the given values of y and x:
y = k/x
48 = k/3
k = 144
Now that we know k, we can write the function that represents the relationship between x and y:
y = 144/x
Therefore, if the value of y varies inversely with x then the function Y= 144/x represents the relationship between x and y if y = 48 when x = 3
To learn more on Functions click:
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A cake weights 900 g. Paul cuts it in 4 pieces. The biggest piece weighs as much as the 3 other pieces weigh together. What is the weight of the biggest piece?
Answers
Answer:500 g
Step-by-step explanation:
what is the distance between -a and a
Answers
Answer:
2a
Step-by-step explanation:
-a + a = 0, 0 + a = a. Therefore -a + 2a = a
Plz help
Rewrite the fraction in the sentence below as a percentage.
In a certain class,
23/25
of the students got problem 10 wrong on Friday's math test.
Answers
Explanation: 23/25 is same as 92/100, so we can easily know that it's 92% :D
What is the value of x rounded to the nearest hundredth?
ps this is a pythlly therom
Question 2 options:
68
92
54
75
Answers
Step-by-step explanation:
60x60+32x32=4624
✓4624
68
Part A: Xavier needs to collect at least 120 cans for a food drive to earn community service credit. He has already collected 64 items. Choose the correctly written inequality to represent the number of cans, c, that Xavier must still collect (before solving)
A 64 + c ≥ 120
B 64 + c < 120
C c - 120 ≤ 64
Answers
Answer:
A
Step-by-step explanation:
He needs to collect at least 120 so if c is what he must still collect
64 +c must be greater than or equal to 120
A
B
C
D
Help please
Answers
Heeeelp me Asp need this
Answers
Answer:
False; True; True
Step-by-step explanation:
If the radius is 4, the area of the circle is
pi*r*r = pi * 4 * 4 = 16pi; The second statement is true.
The entire circle's "angle" is 2pi, so the sector takes (2pi/3) / 2pi of it all, equal to 1/3 of the entire circle - hence the area of the sector is
16pi * 1/3 = 16pi/3; the first statement is false
The length of the entire circle is 2 * pi * r = 2 * pi * 4 = 8pi
The sector is 1/3 of that, so 8pi/3; the third statement is true.
Apply the Pythagorean Theorem to find the distance between points A and B
Answers
Lucas read 30% of his book containing 480 pages. What page is he going to read next?
Answers
Step-by-step explanation:
[tex]480 \div 100 \times 3 0 = \\ = 4.8 \times 30 = \\ = 48 \times 3 \\ = 144[/tex]
145
I WILL GIVE BRAINLIEST!!!
Answers
Answer:
Step-by-step explanation:
Determine if the two triangles are congruent. If they are, state how you know.
Answers
Answer:
No, these 2 triangles are not congruent as not even 1 side in the triangles has been marked as equal.
Hence, the answer is f) not enough information.
Cody hits a baseball. The highest distance it travels is represented by the ______ of the parabola.
A. Maximum
B. Minimum
C. x-intercept
D. y-intercept
Answers
Answer:
A
Step-by-step explanation:
Not B and Not C
Express the ratio as a fraction in simplest form.
18:24
1/2
2/3
3/4
6/7
Answers
reduce it
it’ll be 3/4
In the school election James ran against Ben for
secretary. James received 75% of the votes. If 240
students voted, how many votes did James
receive?
Answers
Choose the system of equations to solve the following: Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. Determine the total number of adult and student tickets.
Answers
Answer:
3 student tickets and 5 adult tickets
Step-by-step explanation:
Students= 3 tickets
Adults: 7.25 • 5 = 36.25
Students: 5.50 • 3 = 16.5
36.25 + 16.5 = 52.75
