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.)
Which of the following is the solution to 3I x-1 I≥ 12?
A. x≤ -3 or x≥ 5
B. x≤ -3 and x≥ 5
C. x≥ 5
D. x≥ -3 or x≥ 5
The solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
For the given inequality the solution can be found as,
When the value of x is negative,3|x-1| ≥ 12
x-1 ≥ 4
x ≥ 5
When the value of x is positive,3|x-1| ≥ 12
- x + 1 ≥ 4
-x ≥ 3
x ≤ -3
Hence, the solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.
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Question 3 of 10
Evaluate: (4/5) 1/2
O A. 2/25
O B. 2/5
O C.4:5
O D.4/25
Answer:
2/5
Step-by-step explanation:
HELP !!!
A taxi driver uses this formula to work out the price of a journey, in pounds. price of journey = 3 + 2 x distance in miles. Leah has £5, the journey to her home is 2.5 miles. She asks the taxi driver to take her as near to home as possible. How far will she need to walk to arrive home?
The distance Leah would have to walk home is 1.5 miles
Calculating distanceFrom the question, we are to determine the distance Leah will have to walk home
From the given information,
Price of journey in pounds = 3 + 2 × distance in miles
Let the distance be d
Then,
Price of journey in pounds = 3 + 2d
Since Leah has £5, we can write that
5 = 3 + 2d
5 - 3 = 2d
2 = 2d
∴ d = 2/2
d = 1 mile
This means her money can only cover 1 mile
But the journey to her home is 2.5 miles
Therefore, she will have to walk
2.5 mile - 1 mile = 1.5 miles
Hence, the distance Leah would have to walk home is 1.5 miles
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Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
Answer:
From the graph in the attachment, it is clear that Option A is correct.
Step-by-step explanation:
The given inequalities are x - 4y ≤ 4 and y < x + 1.
Let us take the first line x - 4y ≤ 4 and remove the inequality and add equality, x - 4y = 4.
Now, we will find the intercept points. Putting y = 0 we will get x = 4 and putting x = 0 we will get y = -1. So, the points are (4,0) and (0,-1).
When we will solve the inequality, we find that portion above the graph satisfies this inequality.
Let us take the second line y < x + 1 and remove the inequality and add equality, y = x + 1.
Now, we will find the intercept points. Putting y = 0 we will get x = -1 and putting x = 0 we will get y = 1. So, the points are (-1,0) and (0,1).
When we will solve the inequality, we find that portion below the graph satisfies this inequality.
All these conditions satisfy the Option A.
The diagram is in the attachment.
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A local candy shop sells boxes of chocolate for $3.45 each. If a customer purchases five or more boxes, the cost is only $3 per box, plus the customer has an additional $1 fee per order. If C(x) represents the total cost and x represents the number of boxes, which of the following functions best models this scenario?
C of x equals 3.45 times x if x is less than 5 and 3.00x plus 1 if x is greater than or equal to 5.
C of x equals 3.45 times x if x is less than 5 and 3.00 plus x if x is greater than 5.
C of x equals 3.45 times x if x is less than or equal to 4 and 3.00x minus 1 if x is greater than 5.
C of x equals 3.45 times x if x is less than 4 and 3.00x minus 1 if x is greater than or equal to 5
The function that best models the scenario is as follows;
x < 5 : C(x) = 3.45x + 1
x ≥ 5 : C(x) = 3x + 1
How to find an equation?A local candy shop sells boxes of chocolate for $3.45 each.
This is when the consumer purchase less than 5 boxes of chocolates.
Therefore,
x = number of boxes
when x < 5
C(x) = 3.45x + 1
If a customer purchases five or more boxes, the cost is only $3 per box. Therefore,
when x ≥ 5
C(x) = 3x + 1
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1
2
4
10
01:28:2
solve x2 + 12x = -11 by completing the square. which is the solution set of the equation?
be
o {-11, -1}
o {-11, 1}
{11, -1}
o {11, 1}
Answer:
11
Step-by-step explanation:
A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
Answer:
The first statement is true so Shannon is incorrect.
Step-by-step explanation:
Volume of the pyramid with base 20 and h = 6
= 1/3 * base area * height
= 1/3 * 20 * 6
= 40 unit^3.
evaluate 2x^2-1 when x=3
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's evaluate ~
[tex]\qquad \sf \dashrightarrow \: 2 {x}^{2} - 1[/tex]
plug in the value of x :
[tex]\qquad \sf \dashrightarrow \: 2(3) {}^{2} - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 2(9) - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 18 - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 17[/tex]
The required value is 17
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option B, 17}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{2x}^2\textsf{ - 1}[/tex]
Find: [tex]\textsf{When x = 3}[/tex]
Solution: In order to find the value when x is equal to 3 we just need to equate any x to the value of 3 and simplify.
Plug in the values
[tex]\textsf{2x}^2\textsf{ - 1}[/tex][tex]\textsf{2(3)}^2\textsf{ - 1}[/tex]Simplify the expression
[tex]\textsf{2(3 * 3) - 1}[/tex][tex]\textsf{2(9) - 1}[/tex][tex]\textsf{18 - 1}[/tex][tex]\textsf{17}[/tex]Therefore, the answer that would make most sense would be option B, 17.
please hurry its due in 5 mins
Answer:
Divide the shape in two pieces:
A rectangle and a triangle
Find area of rectangle:
A=length*width=5*4=20m^2
Find area of triangle:
base of triangle=5-2=3m
height of triangle=8-4=4m
Area=(1/2)*base*height
=(1/2)(4)(3)=6m^2
Total area=6+20=26m^2
Hope it helps!
simplify 26a7 + (-25a7)
Answer:
1a7
Step-by-step explanation:
26+-25=1
write the faction in the simplest form 28/36
Answer:
7/9
Step-by-step explanation:
Divide the numerator and denominator by 4.
28/36 = 7/9
Answer:
7/9
Step-by-step explanation:
28 and 36 are both divisible by 4.
28÷4 is 7 and
36÷4 is 9
28/36 = 7/9
Identify two angles that are marked
congruent to each other on the diagram
below. (Diagram is not to scale.)
Answer:
Angles G and H are congruent.
Step-by-step explanation:
is this correct ?-?
I need to get this done lol
Answer:
6
Explanation:
[tex]\textsf {The range of a data representation refers to difference of the smallest and }\\\textsf {greatest possible values. }[/tex]
[tex]\textsf {Here :}[/tex]
[tex]\textsf {smallest value = 5}\\\textsf {greatest value = 11}[/tex]
[tex]\textsf {Then the range will be :}\\\implies \textsf {greatest value - smallest value}\\\implies \mathsf {11 - 5}\\\implies \mathsf {6}[/tex]
Round 38.856 to the nearest tenth
Answer:38.9
Step-by-step explanation:
A certain species of virulent bacteria is being grown in a culture. It is observed that the rate of growth of the bacterial population is proportional to the number present. If there were 1000 bacteria in the initial polulation and the number doubled after the first 30 minutes, how many bacteria will be present after 4 hours
Answer:
256,000
Step-by-step explanation:
If the culture doubles in size every 30 minutes, it doubles 2 times per hour. In 4 hours it will have doubled 2×4 = 8 times. Each doubling multiplies the number by 2, so 8 doublings will multiply the number by 2^8.
The population will be ...
1000×2^8 = 256,000 . . . bacteria present after 4 hours
If c = 16, solve for b
Answer:
Step-by-step explanation:
given
cos(30°) = [tex]\frac{adjacent}{hypotenuse} \\[/tex]
cos(30°) = [tex]\frac{b}{c} \\[/tex]
cos(30°)=[tex]\frac{b}{16}[/tex]
b = 16cos(30°)
b [tex]16(\frac{\sqrt{3} }{2})\\ = 8\sqrt{3}[/tex]
Please please help what is equivalent to this??
The correct option is Option A: [tex]16^{3x/4}[/tex] is equivalent to the expression [tex](\sqrt[4]{16})^{3x[/tex].
The rules of the exponent are
(a) [tex]a^m*a^n=a^{m+n[/tex]
(b)[tex]a^m/a^n=a^{m-n[/tex]
(c)[tex](a^b)^c=a^{bc}[/tex]
(d) [tex]\sqrt[n]{a}=a^{1/n[/tex]
here the given expression is [tex]16^{3x/4}[/tex]
we can rewrite the expression as
[tex]16^{3x/4}[/tex]
as we know by the rule of the exponent that [tex](a^b)^c=a^{bc}[/tex]
=[tex](16^{1/4})^{3x[/tex]
as we know by the rule of the exponent [tex]\sqrt[n]{a}=a^{1/n[/tex]
=[tex](\sqrt[4]{16})^{3x[/tex]
Therefore the correct option is Option A: [tex](\sqrt[4]{16})^{3x[/tex]
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can someone please help me
Answer:
Domain: All real numbers
Range: y≤4
need help on this ASAP! please
Step-by-step explanation:
x=66°
180-118=62°
180-52+62=66°
hope this helps
solve log7(x+9)-log7(10)
[tex]\log_7(x+9)-\log_710=\log_77\qquad(x > -9)\\\log_7\dfrac{x+9}{10}=1\\\dfrac{x+9}{10}=7\\x+9=70\\x=61[/tex]
2. The wind blows the pinwheel below clockwise 180 degrees. What positions would the ribbon labeled A end up in after the wind blows it?
Answer: In between the red and yellow ribbons
Step-by-step explanation:
When something is rotated 180 degrees, you basically just mirror it. Since this pinwheel has an uneven amount of ribbons, there isn't a ribbon opposite of it, so it would be between red and yellow.
fill in the blank
83 x 391 - 83 x ____ = 83 x (391 - 15)
Answer:
83 x 391 - 83 x 15 = 83 x (391 - 15)
Step-by-step explanation:
BODMAS is stands for Bracket Of Division Multiplication Addition and Subtraction.
left hand side:
83 × 391 - 83 × ____ = 32453 - 83 × ____
right hand side:
83 × (391 - 15) = 83 × 376 = 31208
equating both sides
32453 - 83 × ____ = 31208
32453 - 31208 = 83 × ____
1245 ÷ 83 = 15
hence the answer is 15.
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Convert 0.50 sen /g to RM/kg
the conversion is:
0.50 sen /g = 5 RM/kg
How to change the units?
First, we know that
1sen = 0.01RM
Then we can change:
0.50 sen /g = 0.50*(0.01 RM) /g = 0.005 RM/g
Now we use the relation:
1g = 0.001kg
So we can rewrite:
0.005 RM/g = 0.005 RM/(0.001kg) = 5 RM/kg
So the conversion is:
0.50 sen /g = 5 RM/kg
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Bronze is a mixture of copper and tin.
The copper and tin are in the ratio 9:1.
a) How much tin is there in a bronze bracelet
weighing 260 grams?
6
Answer:
26 gm
Step-by-step explanation:
Tin is 1 out of (9+1) = 1/10 th
1/10th * 260 gm = 26 gm
The volume of a cylinder is 8177 cm³. If the radius is 3 cm, what is the height
of the cylinder?
OA. 9 cm
OB. 18 cm
O C. 12 cm
O D .6cm
Answer:
None of the options are correct
О E. 289.2 cm
Step-by-step explanation:
Volume of a cylinder = v = л r² h
л = 3.1416 (aprox)
r = radius
h = height
8177 = 3.1416 * 3² * h
8177 = 3.1416 * 9 * h
8177 = 28.2744 * h
8177/282744 = h
h = 289.2 cm
Which shows all the exact solutions of 2sec^2 (x)-tan^4 (x)=-1? Give your answer in radians.
a) pi/3 + kpi and 2pi/3 + kpi
b) pi/3 +2kpi and 5pi/3 +2kpi
c) pi/4 +2kpi, 3pi/4 + 2kpi, 5pi/4 +2kpi, and 7pi/4 +2kpi
d) pi/3 + kpi, 2pi/3 +kpi, 4pi/3 +kpi, and 5pi/3 +kpi
Answer:
a. 1/3pi+kpi and 2/3pi+kpi
Step-by-step explanation:
2Sec²x
=2+2tan²x-(tan²x)²=-1
Let tan²x=u
-u²+2u+2=-1
-u²+2u+3=0
u²-2u-3=0
(u+1)(u-3)=0
u=-1,u=3
(tan x)²=-1(No solution)
(tan x)²=3
>>tan x=±sqrt(3)
I) tan x=sqrt(3)
>>tan(pi/3)=sqrt 3
Tan(pi+A) =tanA
Tan(pi+pi/3)=tan(pi/3)
>>tan(4/3pi)=sqrt(3)
>>x=4/3pi and 1/3pi
General solution: 1/3pi+kpi
ii) tan x=-sqrt(3)
x=2/3pi(At 2nd quadrant)
x=5/3pi(at 4th quadrant)
General solution: 2/3pi+kpi
Please helpppppppppppppp
Answer:
Inequality would be the answer
two ships leave a port sailing 18km/h and 26 km/h. Their angle between their directions of travel from the port is 39 °. How far part are the skips to the nearest km after 2 hours
A road is 450 metres long . It takes a woman 5 minutes to walk along the road . Work out the average speed of the woman . Give your answer in metres per second .
Use the graphs below to answer the following questions: a. g(f(2) b. f(f(1)) c. f(g(2))
Answer:
19-73 19-73 and a very nice little
Step-by-step explanation:
19-73 19-73 and he changed
