Answer:
The ratio of all the adjacent terms is the same and equal to
[tex]r=-4[/tex]
The next three terms after the last one will be:
[tex]a_5=-1024[/tex][tex]a_6=4096[/tex][tex]a_7=-16384[/tex]Step-by-step explanation:
Given the sequence
-4, 16, -64, 256, …
Finding the common ratio
An arithmetic sequence has a constant ratio 'r' and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
computing the ratios of all the adjacent terms
[tex]\frac{16}{-4}=-4,\:\quad \frac{-64}{16}=-4,\:\quad \frac{256}{-64}=-4[/tex]
The ratio of all the adjacent terms is the same and equal to
[tex]r=-4[/tex]
Finding the next three terms
Given the sequence
-4, 16, -64, 256, …
here
[tex]a_1=-4[/tex]
[tex]r=-4[/tex]
substituting [tex]a_1=-4[/tex] and [tex]r=-4[/tex] in the nth term
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=-4\left(-4\right)^{n-1}[/tex]
substituting n = 5 to determine the 5th term
[tex]a_5=-4\left(-4\right)^{5-1}[/tex]
[tex]a_5=-4^4\cdot \:4[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}[/tex]
[tex]a_5=-4^{1+4}[/tex]
[tex]a_5=-4^5[/tex]
[tex]a_5=-1024[/tex]
substituting n = 6 to determine the 6th term
[tex]a_6=-4\left(-4\right)^{6-1}[/tex]
[tex]a_6=-4\left(-4^5\right)[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]a_6=4\cdot \:4^5[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}[/tex]
[tex]a_6=4^{1+5}[/tex]
[tex]a_6=4^6[/tex]
[tex]a_6=4096[/tex]
substituting n = 7 to determine the 6th term
[tex]a_7=-4\left(-4\right)^{7-1}[/tex]
[tex]a_7=-4^6\cdot \:4[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}[/tex]
[tex]a_7=-4^{1+6}[/tex]
[tex]a_7=-4^7[/tex]
[tex]a_7=-16384[/tex]
Therefore, the next three terms after the last one will be:
[tex]a_5=-1024[/tex][tex]a_6=4096[/tex][tex]a_7=-16384[/tex]1.509 rounded to the nearest ones
Answer:
2
Step-by-step explanation:
Because It pases the half point
Does anyone know the answer to this question??
Ahmed wrote two numbers. The first number has a 7 in its tenth place. The second number has a 7 with a value that’s is 1,000 times greater than the value of the 7 in the first number. In which place is the 7 in the second number?
Answer:
in the thousands place
Step-by-step explanation:
Answer:
Hundreds
Step-by-step explanation:
Ahmed wrote two numbers.The first number has 7 in it's tenth place.The second number has a 7 with a value that's 1,000 times greater than the value of the 7 in the first number.This is how we can represent it:
*The symbol 'x' represents the numbers that we don't know.
7xx.7
The first 'x' has a place value of ones.
The second 'x' has a place value of tens.
And the second number (7) has a place value of hundreds.
Evaluate ƒ(x) when x = 3. 6x^2+2
Answer: f(x)=56
Step-by-step explanation:
We are given the equation f(x)=6x²+2. Since we are asking for x=3, we can plug that into the equation and solve.
f(3)=6(3)²+2 [exponent]
f(3)=6(9)+2 [multiply]
f(3)=54+2 [add]
f(3)=56
Now, we know that f(x)=56 when x=3.
What is 1/5 expressed as a percent?
WEIG
The scale on a map states that 2 cm = 15 km. If two cities are 85
kilometers apart in real life, how far apart would they be on the
map?
Answer:
5.66666666667
Step-by-step explanation:
85÷15=5.66666666667
Answer:
11.22cm
Step-by-step explanation:
2cm=15km
0.66km= 5km(17)
11.22cm= 85km
please give me a brainliest!!<3
HELP I WILL GIVE BRANLIEST!!!!!!!!
Mr Binnix wife is older than her sister by 2 years if their ages add up to 52 how old is each sister? Let c represent Leigh Ann’s age and let y represent Larisa s age
Answer:
the older sister is 27 and the younger is 25.
Step-by-step explanation:
C+2=Y
C+Y=52
2C+2=52
2C=50
C=25
25+2=Y
Y=27
help me with this question, thanks!!!
Answer:
Gavin is incorrect,
divide 4
multiply 1/4
each get 1/12
Step-by-step explanation:
Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary style cabinets sell for $90 and farmhouse style cabinets sell for $85. Each cabinet produced must go through carpentry, painting, and fiishing processes. The following table summarizes how much time in each process must be devoted to each style of cabinet.
Hours per process
Style Carpentry Painting Finishing
Contemporary 2.0 1.5 1.3
Farmhouse 2.5 1.0 1.2
Carpentry costs $15 per hour, painting costs $12 per hour, and fiishing costs $18 per hour, and the weekly number of hours available in the processes is 3000 in carpentry, 1500 in painting, and 1500 in fiishing. Brooklyn also has a contract that requires the company to supply one of its customers with 500 contemporary cabinets and 650 farmhouse style cabinets each week.
Let
x = the number of contemporary style cabinets produced each week
y = the number of farmhouse style cabinets produced each week
Develop the objective function, assuming that Brooklyn Cabinets wants to maximize the total weekly profit.
The objective function is maximize
Show the mathematical expression for each of the constraints on the three processes.
Hours available in carpentry: x1 + y1 ≤
Hours available in painting: x2 + y2 ≤
Hours available in fiishing: x3 + y3 ≤
Show the mathematical expression for each of Brooklyn Cabinets' contractual agreements.
x ≥
y ≥
Answer:
See Step by step explanation
Step-by-step explanation:
Objective Function: z
x = number of contemporary style
y = number of farmhouse style
Costs
Carpentry costs:
15*2*x + 15*2,5*y = 30*x + 37,5*y
Painting costs
12*1,5*x + 12*1*y = 18*x + 12*y
Finishing costs
18*1,3*x + 18*1,2*y = 23,4*x + 21,6*y
Total costs:
30*x + 37,5*y + 18*x + 12*y + 23,4*x + 21,6*y
71,4*x + 71,1*y
z = 90*x + 85*y - ( 71,4*x + 71,1*y ) to maximize
z = 18,6*x + 13,9*y to maximize
Subject to:
First constraint:
Hours available in carpentry 3000
2*x + 2,5*y ≤ 3000
Second constraint
Hours available in painting 1500
1,5*x + 1*y ≤ 1500
Third constraint
Hours available in finishing 1500
1,3*x + 1,2*y ≤ 1500
Fourth constraint
Minimum quantity of contemporary style 500
x ≥ 500
Fifth constraint
Minimum quantity of farmhouse style 650
y ≥ 650
General constraints:
x ≥ 0 y ≥ 0 x , y integers
Model:
z = 90*x + 85*y - ( 71,4*x + 71,1*y ) to maximize
Subject to:
2*x + 2,5*y ≤ 3000
1,5*x + 1*y ≤ 1500
1,3*x + 1,2*y ≤ 1500
x ≥ 500
y ≥ 650
x ≥ 0 y ≥ 0 x , y integers
The mathematical expression for each of the constraints on the three processes.
Model z = 90*x + 85*y - ( 71,4*x + 71,1*y )
Subject to
2*x + 2,5*y ≤ 3000
1,5*x + 1*y ≤ 1500
1,3*x + 1,2*y ≤ 1500
x ≥ 500
y ≥ 650
x ≥ 0 y ≥ 0 x , y integers.
We, wants to maximize the total weekly profit.
What is the meaning of constraints?a constraint is a condition of an optimization problem that the solution must satisfy.
Objective function: z
x = number of contemporary style
y = number of farmhouse style
We have to find the cost
The carpentry costs is,
15*2*x + 15*2,5*y = 30*x + 37,5*y
The painting costs is
12*1,5*x + 12*1*y = 18*x + 12*y
The finishing costs is
18*1,3*x + 18*1,2*y = 23,4*x + 21,6*y
Therefore the total costs is,
30*x + 37,5*y + 18*x + 12*y + 23,4*x + 21,6*y
71,4*x + 71,1*y
z = 90*x + 85*y - ( 71,4*x + 71,1*y ) to maximize
z = 18,6*x + 13,9*y to maximize
Subject to the constraint;
The first constraint is,
The hours available in carpentry 3000
2*x + 2,5*y ≤ 3000
The second constraint is,
Hours available in painting 1500 so,
1,5*x + 1*y ≤ 1500
The third constraint is,
Hours available in finishing 1500 so,
1,3*x + 1,2*y ≤ 1500
Fourth constraint is,
The minimum quantity of contemporary style 500 so,
x ≥ 500
The fifth constraint is
The minimum quantity of farmhouse style 650 so,
y ≥ 650
The general constraints are,
x ≥ 0 y ≥ 0 x , y integers,
Therefore the Model z = 90*x + 85*y - ( 71,4*x + 71,1*y ) to maximize,
Subject to
2*x + 2,5*y ≤ 3000
1,5*x + 1*y ≤ 1500
1,3*x + 1,2*y ≤ 1500
x ≥ 500
y ≥ 650
x ≥ 0 y ≥ 0 x , y integers,
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ON wednesday Eddy goes to a velodrome to train. He cycles the first lap of the track in 25 seconds. Each lap Eddy cycles takes him 1.6 seconds longer thatn the previous lap.
Required:
a. Find the time in seconds, Eddy takes to cycle his tenth lap 2
b. Eddy cycles his last lap in 55.4 seconds. Find how many laps he has cycled on wednesday.
c. Find the total time in minutes, cycled by Eddy on Sunday.
Answer:
Step-by-step explanation:
The data of timing for each lap will form a arthmetic progression ( AP ) with first term as 25 s and common difference of 1.6 s .
a )
first term a = 25
common difference d = 1.6 .
10 th term of the series can be given by following formula
a₁₀ = 25 + ( 10-1 ) x 1.6
= 25 + 1.6 x 9
= 39.4 s
b )
Let n th be the last lap
a(n) = a + ( n-1 ) x d
55.4 = 25 + ( n- 1 ) x 1.6
n - 1 = 19
n = 20 .
c )
sum of all the term of AP
=( first term + last term ) x no of term / 2
= (25 + 55.4 ) x 20 / 2
= 804 s .
= 804 / 60 min
= 13.4 min .
I need some help with this
What 9+1 please answer
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
OMG I finally know one on here!
A video game is on sale for 20% off. The sale price of the game is $35.00. How much did the game ORIGINALLY cost?
Answer:
$43.75
Step-by-step explanation:
To find how much the game would have been 20% off from 43.75, you would have needed the expression
43.75*0.8
So to go from 35 to 43.75, you need the expression
35/0.8.
This expression in simpler terms means What is 38, 80% of?
That is how we get 43.75.
35/0.8 = 43.75.
Find the equation for the circle with center (4,3) and passes through (−3,−1).
answer:
(x−3)2+(y−6)2=20
Step by step problem
How do you find area of a trapezoid I will mark brainliest for the most explained and simple answer!!!!
Answer:
A = ((a+b)/2)h
Step-by-step explanation:
a and b are base (the top and bottom)
h is height
Together a chair, a table, and a lamp cost $562. The chair costs 4 times as much as the lamp, and the table costs $23 less than the chair. Find the cost of the table.
Answer:
Cost of table is $237
Step-by-step explanation:
Cost of chair, table and lamp = $562
Cost of lamp = x
Cost of chair = 4x (The chair costs 4 times as much as the lamp)
Cost of table = 4x-23 (the table costs $23 less than the chair.)
We need to find the cost of table.
We know that:
Cost of chair, table and lamp = $562
We can write:
[tex]x+4x+4x-23=562[/tex]
First, we need to find value of x by solving the equation.
[tex]x+4x+4x-23=562\\9x=562+23\\9x=585\\x=\frac{585}{9}\\x=65[/tex]
So, we get x = 65
Now, we can find cost of table:
We are given:
Cost of table = 4x-23
Cost of table = 4(65)- 23 = 237
So, Cost of table is $237
Find the general solution of
dy/dx + 2y =6
Answer:
ye^(2x) - 3e^(2x) = C or (y - 3)e^(2x) = C
Step-by-step explanation:
dy/dx + 2y = 6
This is a first order linear ODE.
p(x) = 2
Integrating factor: I(x) = e^(∫ 2 dx) = e^(2x)
e^(2x)(dy/dx + 2y) = 6e^(2x)
e^(2x) dy + 2ye^(2x) dx = 6e^(2x) dx
Integrate both sides of the equation.
ye^(2x) = 3e^(2x) + C
Thus, the general solution is ye^(2x) - 3e^(2x) = C or (y - 3)e^(2x) = C.
If A={w,h,i,t,e,b,o,a,r,d} and U ={a,b,c,d,e,f,g,h,i,j,k,l,m,,n,o,p,r,s,t,u,v,w,x,y,z}
Answer:
Answer = 1234567890
Step-by-step explanation:
The depth of an underwater camera on a cable anchored to the sea floor is proportional to the time. The table records the time in seconds (s) and depth in meters (m) of the camera. What are the missing values in the table?
Answer:
20=-1
60=-3
100=-5
240=-12
Step-by-step explanation:
divide time and depth by 20
When time is 20 the depth is -1, when time is 60 the depth is -3 and time is 240 the depth is -12.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
The depth of an underwater camera on a cable anchored to the sea floor is proportional to the time.
From the table let us take the values of time and depth which both are given.
Time=100 and depth is -5.
From this we can find the other values.
Depth=-1 when time is x
100/-5=x/-1
100=5x
Divide both sides by 5
x=20
So when time is 20 the depth is -1.
Now we have to find the depth when time is 60.
60/x=100/-5
-300=100x
x=-3
So when time is 60 the depth is -3.
Now we have to find the depth when time is 240.
240/x=100/-5
-1200=100x
Divide both sides by 100
x=-12
when time is 240 the depth is -12.
Hence, when time is 20 the depth is -1, when time is 60 the depth is -3 and time is 240 the depth is -12.
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#SPJ5
5 1/5-1 3/4 answer soon
Answer:3 9/20
Step-by-step explanation:
The graph of a linear function is shown.
Answer:
Step-by-step explanation:
y=1/5+0 is the answer to your problem I very much believe
to multiply/divide fractions the denominator has to be the same.
a) true
b) false
anyone please this answer fast for grade6
Answer:
1 round = 220 meter wire
2 rounds = 440 meter wire
3 rounds = 660 meter wire
Step-by-step explanation:
Given that:
Perimeter of squared garden = 220m
As the perimeter is given, the length of the wire would be calculated with it.
The length of wire to fence with 1 round = 220 * 1 = 220m
The length of wire to fence with 2 rounds = 220 * 2 = 440m
The length of wire to fence with 3 rounds = 220 * 3 = 660m
Hence,
1 round = 220 meter wire
2 rounds = 440 meter wire
3 rounds = 660 meter wire
Han used 1 1/2 gallons of paint to paint 3/5 of a shed. How many gallons of paint will it take to paint the whole shed? Write a multiplication equation or a division equation to represent this situation then find the answer. Show your reasoning
Answer:
2 gallons
Step-by-step explanation:
If Han used 1 1/2 gallons of paint to paint 3/5 of a shed, this can be expressed as;
1 1/2 gallons = 3/5 of the shed
3/2gallons = 3/5 of the shed
To find the number of gallons that will paint the whole shed, we will say;
x gallons = 1 shed
Divide both expressions
3/2/x = 3/5
3/2x = 3/4
2x * 3 = 3*4
6x = 12
x = 12/6
x = 2
Hence 2 gallons will be needed for the whole shed
An experiment started with 100 bacteria. they double in number every hour. find the number of bacteria after 6 hours.
I NEED HELP ASAP PLS :(
Answer:
7
Step-by-step explanation:
A recipe says, "3 parts water to 1 part milk." How much
water will you need If you use 2 Ilters of milk?
Answer:
9 parts water
Step-by-step explanation:
How do u solve this plzzzz helppp
It’s called multi step equations
Answer:
x=6
Step-by-step explanation:
7x-9=3x+15
4x-9=15
4x=24
x=6
Answer:
x=6
Step-by-step explanation:
7−9=3+15
7−9+9=3+15+9
7−3=3+24−3
4=24
x=6
Tina collects stuffed animals. She has 8 teddy bears, 9 dogs, 10 frogs, and 6 monkeys. What is the ratio of monkeys to teddy
bears?
A. 3:7
B. 3:4
O C. 8:6
O D. 7:4
Plssss help ASAP giving away lost of branlist
Answer:
it's c
Step-by-step explanation:
there are 8 bears and 6 monkeys!
hope this helps:)