More plainly, the sequence is defined recursively by
[tex]a_{n+1} = \begin{cases} 3a_n - 9 & \text{if } a_n \text{ is odd} \\ 2a_n - 7 & \text{if } a_n \text{ is even} \end{cases}[/tex]
and some starting value [tex]a_1[/tex].
We're given that the sequence alternates between two constants, [tex]a[/tex] and [tex]b[/tex], so that [tex]a_1 = a[/tex].
• If [tex]a[/tex] is even, then the second term [tex]b[/tex] must be odd, since
[tex]a_2 = 2a_1 - 7[/tex]
by the given rule, and 2×(even) - (odd) = (odd). So
[tex]a_2 = 2a-7 = b[/tex]
In turn, the third term is even, since we jump back to [tex]a[/tex]. From the given rule,
[tex]a_3 = 3a_2 - 9[/tex]
and so
[tex]3b-9 = 3(2a-7)-9 = a \implies 6a-30=a \implies 5a=30 \implies a=6[/tex]
[tex]3b-9 = 6 \implies 3b = 15 \implies b = 5[/tex]
Then the sum of the two integers is [tex]a+b=\boxed{11}[/tex]
• You end up with the same answer in the case of odd [tex]a[/tex], so I'll omit this part of the solution. (It's almost identical as the even case.)
What’s the answer helppppppp
Answer:
the answer is d........
I need the answer to
y = -x - 3
y=-x-5
Answer:
if you're supposed to be solving for x then the top one is x=-y+3 and the bottom is x=-y+5
Find the slope of the line
Answer:
-3
Step-by-step explanation:
The points (3,-4) and (1,2) lie on the line.
m = (-4-2)/(3-1) = -3
Does the table of values below represent a proportional relationship?
x
2
3
4
5
y
10
15
24
25
Answer:
No
Step-by-step explanation:
The constant of proportionality is k = y/x. In this case, k is 5. When you multiply k which is 5 with the x value you should get the y value. You will see that 2 X 5 = 10, 3 X 5 = 15, and 5 X 5 = 25 but 4X 5 is not equal to 24. This means the ordered pair (4, 24) does not lie on the straight line that is formed where all the other ordered pairs (2,10), (3,15), and (5,25) lie.
For a proportional relationship in a table, the k is constant for all the ordered pair x and y values. All the ordered pairs in the table should also lie on the same straight line.
So the answer is no.
What is 2 1/2 x 1 3/4 x 3/4
Answer:
45/32 or 1.40
Step-by-step explanation:
Answer:
3 9/32 or 105/32
Step-by-step explanation:
2 1/2 = 5/2, 1 3/4 = 7/4
5/2 * 7/4 = 35/8
35/8 * 3/4 = 105/32
105/32 = 3 9/32
Brainliest, please :)
Can you translate that into slope intercept form
Answer:
y = (5/3)x + 4
Step-by-step explanation:
The general equation for slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. Since you have been given both of these values, you can plug them into the formula to find your answer.
slope (m) = 5/3
y-intercept (b) = 4
y = mx + b
y = (5/3)x + 4
find the maxium value of 16x+ 96y
follow p
Find the measure of each missing angle.
Answer:
Step-by-step explanation:
Angle sum property of triangle: Sum of all the angles of a triangle is 180
Alternate interior angles: When two parallel lines are intersected by a transversal, the pair of angles on the inner side of each of these lines but on the opposite side of the transversal are called alternate interior angles
In ΔABC,
∠1 + 90 + 38 = 180 {angle sum property of triangle}
∠1 + 128 = 180
∠1 = 180 - 128
[tex]\sf \boxed{\bf \angle 1 = 52^ \°}[/tex]
AB // CD and AC is transversal.
[tex]\sf \boxed{\bf \angle 3 = 38^\circ}[/tex] {Alternate interior angles are equal}
In ΔACD,
∠2 + ∠3 + 63 = 180 {angle sum property of triangle}
∠2 + 38 +63 = 180
∠2 + 101 =180
∠2 = 180 - 101
[tex]\sf \boxed{\bf \angle 2 = 79^ \°}[/tex]
helppp will give brainliest
Write and graph the inverse variation in which y = 8 when x = –4.
Answer:
Inverse variation here gives out a function [tex]xy=(-32)[/tex].
Step-by-step explanation:
Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases. While direct variation describes a linear relationship between two variables, inverse variation describes another kind of relationship.
An inverse variation can be represented by the equation
[tex]xy=k \\or \\y=kx[/tex]. That is, y varies inversely as x if there is some nonzero constant k.
Here, the product is given by
[tex]xy=(-4)[/tex]×[tex]8[/tex]
[tex]xy=(-32)[/tex]
We will be plotting the graph of the function [tex]xy=(-32)[/tex]
Learn more about inverse variation -https://brainly.com/question/2798700
#SPJ10
Find the midpoint of the segment with the following endpoints. (10, 6) and (4, 9)
Answer:
(10+4/2, 6+9/2)
(7, 7.5)
The Midpoint is (7, 7.5)
Step-by-step explanation:
I just added the x values and divided them by 2 and then the same for the y values.
Answer:
(7,7.5)
Step-by-step explanation:
midpoint formula:
(X1,X2) divided by two and (Y1,Y2) also divided by two.
so you get
10+4/2 and 6+9/2
Add it all up you get
14/2 and 15/2
divide it:
(7,7.5)
Answer the question in the screen shot
Using the continuity concept, as the value of the function has to be equal to the limit, it is found that the value of k is of k = -4.
When a function is continuous?A function is said to be continuous at x = a if, and only if:
[tex]\lim_{x \rightarrow a} f(x) = f(a)[/tex]
In this problem, we have to check at x = -2, hence:
[tex]\lim_{x \rightarrow -2} f(x) = f(-2)[/tex]
[tex]k = \lim_{x \rightarrow -2} f(x)[/tex]
For the limit, we have to check the lateral conditions, hence:
[tex]\lim_{x \rightarrow -2} f(x) = \lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2} = \lim_{x \rightarrow -2} \frac{(x - 2)(x + 2)}{x + 2} = \lim_{x \rightarrow -2} x - 2 = -2 -2 = -4[/tex]
Hence, from the continuity condition, k = -4.
More can be learned about the continuity concept at https://brainly.com/question/24637240
#SPJ1
please help me its math
The value of f(x) = 3x² - 2x at x = 4 is 40.
What is function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math.
Here, the given function;
f(x) = 3x² - 2x
put the value of x = 4, we get
f(4) = 3 X 4² - 2 X 4
f(4) = 3 X 16 - 8
f(4) = 48 - 8
f(4) = 40
Thus, the value of f(x) = 3x² - 2x at x = 4 is 40.
Learn more about Function from:
https://brainly.com/question/12431044
#SPJ1
Assembly of a television set in the factory is set to 45 minutes. Some workers take a shorter time (t) at this while some take longer. However, each varies no more than 8 minutes. Which inequality below represents this scenario?
Answer:
a
Step-by-step explanation:
y>-3x +3
y≥ 2x-2
O (1,0)
O (-1,1)
O(2,2)
(0,3)
Answer:
(1,0)
Step-by-step explanation:
y>-3x +3
y≥ 2x-2
If we plot these two inequalities, we can see where the lines intersect, See attached graph.
They intersect at (1,0)
We can also do this mathematically:
y>-3x +3
- (y≥ 2x-2)
0 [tex]\geq[/tex] -5x + 5
5x [tex]\geq[/tex] 5
x [tex]\geq[/tex] 1
If x = 1:
y≥ 2x-2
y≥ 2(1)-2
y≥ 0
(x,y) = (1,0)
2.2.5a (Part 1): For the graph below, what is the x-intercept? *
-4 -2
2
-2
-4
y
2
4
0 points
X
An x-intercept is the point where the line of a graph passes through the x-axis. Thus, you should look for this point on the given graph.
What is a graph?A graph can be defined as a type of chart that is used for the graphical representation of data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.
In Mathematics, x-intercept refers to the point where the line of a graph passes through the x-axis as shown in the image attached below. Since the graph wasn't provided for this question, you should look for the point where the line passes or crosses through the x-axis.
Read more on x-intercept here: https://brainly.com/question/354683
#SPJ1
what function does this graph represent?
Answer:
D
Step-by-step explanation:
The vertex is at (-2,4), so substituting into vertex form, only C and D match.
Also, the graph opens down, so the coefficient of x² is negative.
This eliminates C, leaving us with D
Eleven upright dominos of increasing height are lined up to be knocked down. The dominos are numbered 0 to 10. The smallest domino, #O, is 3.00 inches tall and will be top- pled by a person to start the chain reaction. Each subsequent domino is 19% taller than the one before. What is the height of domino #10?
The height of domino number 10 is 56.9 inches.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
The exponential function:-An exponential function is given by:
y = abˣ
where a is the initial value of y at x = 0, y, x are variables and b is the multiplication factor
Let y represent the height of the number x domino
Since the height of the smallest domino no 0 is 3 inches, hence a = 5. b = 100% + 19% = 1.19
y = 10(1.19)ˣ
For x = 10:
y = 10(1.19)¹⁰= 56.9 inches
Therefore the height of domino number 10 is 56.9 inches.
To know more about function follow
https://brainly.com/question/2833285
#SPJ1
[tex]\huge\fbox\purple{Question}[/tex]
1)find L.C.M of the following set of numbers by listing multiplies
a)6 and 9
b)8 and 12
c)4,6 and 8
2)find L.C.M of the following set numbers by using divison method
a)6 and 15
b)20 and 30
c)25,30 and 75
The LCM of the given numbers have been determined.
What is LCM ?LCM stands for Least Common Multiple .
For two numbers , LCM is the number that is the smallest number of which they both are a factor.
It is asked to determine
LCM of 6 and 9
6 = { 6 , 12 , 18 , 24 , 30 , 36 , 42 .....}
9 = { 9 , 18 ,27 .....}
The LCM of 6 , 9 is 18
LCM of 8 and 12
8 = { 8,16,24,32....}
12 = {12 , 24 ,36....}
The LCM of 8 and 12 is 24
LCM of 4 , 6 and 8
4 = {4 , 8 , 12 , 16 , 20,24,28 ....}
6 = { 6 ,12 ,18,24......}
8 = {8 , 16,24 .....}
The LCM of 4,6 and 8 is 24
The LCM of 6 and 15 is 30
The LCM of 20 and 30 is 60
The LCM of 25,30 and 75 is 150
The image of the solution is attached .
To know more about LCM
https://brainly.com/question/20739723
#SPJ1
What is the value of x in the following equation?
11-2x+6x+5=32
Answer:
The value of x is 4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
11−2x+6x+5=32
11+−2x+6x+5=32
(−2x+6x)+(11+5)=32
4x+16=32
4x+16=32
Step 2: Subtract 16 from both sides.
4x+16−16=32−16
4x=16
Step 3: Divide both sides by 4.
((4x)/4) = (16/4)
x = 4
Answer:
11-2x+6x=32-5
-2x+6x=27-11
-2x+6x=16
4x÷4=16÷4
x=4
Please help me find the answer to this problem
-2/3.
That is the slope because this equation is written in slope-intercept form (y=mx+b) where...
m= slope
b = y-intercept
Each staple is made from 0.21 g of metal.
How many staples can be made from 1 kg of metal?
Answer:
4762
Step-by-step explanation:
0.21g x 10,000= 2100
0.21 x 5,000= 1050
0.21 x 4,000= 840
0.21 x 4700 = 987
0.21 x 4760 = 999.6
0.21 x 4762= 1000.02
( how much it's made from x the quantity = the grams or kg)
Fernando purchased 1 pound of dried cranberries and 4 pounds of almonds to make a trail mix. Cranberries cost $4 per pound and almonds cost $5 per pound. What is the price per pound of the trail mix? $
Answer:
$24
Step-by-step explanation:
Cranberries needed: 1 pound
Cost of 1 pound = $4
Almonds needed: 4 pound
Cost of 1 pound = $5
4 x 5 = $20
20 + 4 = $24
Answer:
4.80
Step-by-step explanation:
work out the equation of the line
Step-by-step explanation:
Hi there!
According to the question;
The gradient of line is 1/2 and passes through the point (4,-2).
Since, It has one point and gradient we use one point formula to find the equation of the line.
Note:
One point formula: (y-y1) = m (x-x1)
(4,-2) = (x1,y1)
So, using this formula we get;
(y+2) = 1/2(x-4)
Multiply both sides by 2.
2(y+2) = (1/2)*2(x-4)
2y+4 = x-4
Take 2y+4 in right side
0 = x-4 - (2y+4)
Therefore, x-2y-8 = 0 is the required equation.
Hope it helps!
Hi there!
We're given the following information:
Slope (gradient) = ¹/₂Point = (4,2)With this information, we can go ahead and plug the data into the point slope equation: y - y₁ = m(x - x₁).
Plug in 1/2 for m, and (4,2) for x1 and y1:
[tex]\sf{y-y_1=m(x-x_1)}[/tex]
[tex]\sf{y-(-2)=\dfrac{1}{2}(x-4)}[/tex]
[tex]\sf{y+2=\dfrac{1}{2}(x-4)}[/tex]
[tex]\sf{y+2=\dfrac{1}{2}x-2}\\\sf{y=\dfrac{1}{2}x-2-2}\\\\\sf{y=\dfrac{1}{2}x-4}[/tex]
Hence, y = 1/2x - 4.
I hope that helps! :)
For my math assessment, I need to apply trigonometry in a real life situation and explain about it. I've been thinking of 1. trigonometry applied in cricket 2. music (sound waves)... but still not quite sure how to. If anyone has knowledge on how I could work on these or any other new ideas that would be relevant, PLEASE help me!!! Thank you!! <3
Answer:
I know you said relevant so i have two answers.
1) (not so relevant).
You could use it to show how NASA and astronomers use it to calculate the distance between planets and connect it to building rockets and all that cool stuff.
2) (relevant).
For the one about music, you could connect it to sound engineers and use sine and cosine graphs to calculate wavelengths
Answer: Answers below.
Step-by-step explanation: Suppose you want to find the best angle to kick a soccer ball so that it enters the goal. A triangle can be formed with angle ζ facing the goal. Increasing ζ or decreasing ζ will allow you to see the best angle that is the maximum amount of time that you should wait until scoring the ball.
Sine, Cosine, and Tangent waves are used everyday in phones, tablets, computers, and in quantam and normal technology by imitating and creating waves that can be sent to a destination.
You can use inverse trigonometric functions to find the height of a roof, the height of a tree, the height of a pole, and more.
Light waves are, in reality, sine and cosine waves intertwined together.
You can even use trigonometry every day in work places, such as in software engineering. In fact, calculus 1 and 2, as well as Multivariate Calculus, which heavily and fundamentally uses trigonometry, is used widely across computer science. These help you to get $100,000 jobs.
Jose bought 750 bags of peanuts for $375.00. He intends to sell each bag for $0.15. More than he paid . How much should he charge?
The amount of charge for one bag of peanuts will be $0.65.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Jose bought 750 bags of peanuts for $375.00.
He intends to sell each bag for $0.15 more than he paid.
Then the amount of charge for one bag of peanuts will be
⇒ $375 / 750 + $0.15
⇒ $0.5 + $0.15
⇒ $0.65
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x? 1. The distributive property: 4x – 12 + 4 < 10 + 6x 2. Combine like terms: 4x – 8 < 10 + 6x 3. The addition property of inequality: 4x < 18 + 6x 4. The subtraction property of inequality: –2x < 18 5. The division property of inequality: ________ x < –9 x > –9 x < x is less than or equal to negative StartFraction 1 Over 9 EndFraction. x > –x is greater than or equal to negative StartFraction 1 Over 9 EndFraction.
The inequality 4(x – 3) + 4 < 10 + 6x is solved as x > -9. Then the variable x is greater than the negative 9. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The inequality equation is given below.
4(x – 3) + 4 < 10 + 6x
Then the steps of solving are given below.
1. The distributive property: 4x – 12 + 4 < 10 + 6x
2. Combine like terms: 4x – 8 < 10 + 6x
3. The addition property of inequality: 4x < 18 + 6x
4. The subtraction property of inequality: –2x < 18
5. The division property of inequality: x > –9
Then x is greater than the negative 9.
Then the correct option is B.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ1
There are 130 people in a
sport centre.
73 people use the
gym.
62 people use the swimming pool.
58 people use the track.
22 people use the gym and the pool.
29 people use the pool and the track.
25 people use the gym and the track.
11 people use all three facilities.
A person is selected at random.
What is the probability that this
person doesn't use any facility?
Answer:
If 11 people use all three facilities, this means:
22 − 11 or 11 are using the gym and the pool but no the track,
29 − 11 or 18 are using the pool and the track but no the gym,
25 − 11 or 14 are using the gym and the track but no the pool.
How many people use the gym only?
130 − (14 + 11 + 11) = 94
How many people use the pool only?
62 − (18 + 11 + 11) = 22
How many people use the track only?
58 − (14 + 11 + 18) = 15
How many people go in for sports?
94 + 22 + 15 + 11 + 14 + 18 + 11 = 185
How many people use exactly one of the facilities?
94 + 22 + 15 = 131
What is the probability that the person uses exactly one of the facilities?
= 131/185 ≈ 0.7081
Step-by-step explanation:
its a bit confusing
Hope It Helps !!!!
Question 4) Identify the surface area of the composite figure.
The surface area of the composite figure is 714 sq. in.
What is formula of surface area of cube ?
Let, a be the edge of the cube.
Then, surface area of the cube = 6a² square unit
What is formula of surface area of cuboid ?Let, length of the cuboid = l unit
Width of the cuboid = w unit
Height of the cuboid = h unit
Then, surface area of the cuboid = 2(lw+lh+hw) square unit
What is the required surface area ?Given, edge of cube = 4 in.
∴ Surface area of cube = (6×4²) sq. in. = 96 sq. in.
Now, given, length of cuboid = 15 in.
Width of the cuboid = 10 in. & height of the cuboid = 7 in.
∴ Surface area of the cuboid = 2{(15×10)+(15×7)+(10×7)} sq. in.
= 2{150+105+70} sq. in.
= 2{325} sq. in. = 650 sq. in.
Here, we have to find the surface area of the composite figure.
We have to subtract the surface area from both of cube & cuboid, where they are attached.In that case, we have to subtract (4×4) from both.
So, we have to subtract 2(4×4) sq. in. = 32 sq. in.
∴ The surface area of the composite figure = (650+96-32) sq. in.
= 714 sq. in.
Learn more about composite figure here :
https://brainly.com/question/27915109
#SPJ10
the radis of the cylinder is (2/7) units and height of the cylinder is (8/11 units find the volume of the cylinder use =22/7
The volume of the cylinder is 64/3773 cubic units
Volume of a cylinderThe formula for calculating the volume of a cylinder is expressed as:
V = πr²h
where
r is the radius
h is the height
Given the following parameters
r = 2/7units
h =8/11 units
Substitute
V = 22/7 * 2/7 * 2/7* 8/11
V = (2/7)³ * 8/11
V = 8/343 * 8/11
V = 64/3773 cubic units
Hence the volume of the cylinder is 4/3773 cubic units
Learn more on volume of cylinder here: https://brainly.com/question/9554871
#SPJ1
Is (x + 7) a factor of f(x) = x³ - 3x² + 2x - 8?
Answer:
x=-7
0=(-7)³-3(-7)²+2(-7)-8
=-343-147-14-8
0≠-512
x+7 isn't a factor
