Answer:
An explicit rule for the nth term of the sequence will be:
[tex]a_n=-4\cdot \:2^{n-1}[/tex]
Thus, option (A) is true.
Step-by-step explanation:
Given the sequence
[tex]-4, -8, -16, -32, ...[/tex]
A geometric sequence has a constant ratio r and is defined by
[tex]a_n=a_0\cdot r^{n-1}[/tex]
Computing the ratios of all the adjacent terms
[tex]\frac{-8}{-4}=2,\:\quad \frac{-16}{-8}=2,\:\quad \frac{-32}{-16}=2[/tex]
As the ratio 'r' is the same.
so
[tex]r=2[/tex]
as
[tex]a_1=-4[/tex]
Hence, the nth term of the sequence will be:
[tex]a_n=a_0\cdot r^{n-1}[/tex]
substituting the values [tex]r=2[/tex] and [tex]a_1=-4[/tex]
[tex]a_n=-4\cdot \:2^{n-1}[/tex]
Therefore, an explicit rule for the nth term of the sequence will be:
[tex]a_n=-4\cdot \:2^{n-1}[/tex]
Thus, option (A) is true.
A town has a population of 10000 and grows at 5% every year. What will be the population after 5 years, to the nearest whole number?
Answer:12500
Step-by-step explanation:
10000 x 5% = 500. 500 x 5 = 2500. 10000 + 2500 = 12500
Answer:
12763
Step-by-step explanation:
Got it right on deltamath.
Kevin found his average number of text messages sent over three days using the expression below. Which statement best describes the number of the expression?
Answer:
option C.
Step-by-step explanation:
well the numerator is three. So I don't see why not.
Starting from the same place a plane took 1 hr longer to fly 705 mi to Atlanta, than to fly 470 mi to New Orleans. If the plane flew at the same rate for the entire trip, what was the flying time for the shorter leg? a. 1 2 hr c. 1 1 2 hrs b. 1hr d. 2 hrs
Answer: d. 2 hrs
Step-by-step explanation:
Let x = Time taken(in hours) to fly 470 mi to New Orleans. (Shorter leg)
Then Time taken to fly 705 mi to Atlanta= x+1 (longer leg)
Since the plane flew at the same rate for the entire trip.
i.e. Speed 705 mi to Atlanta = Speed to fly to New orleans
[tex]\Rightarrow\ \dfrac{705}{x+1}=\dfrac{470}{x}\ \ \ \ \ \ \ [\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}]\\\\\Rightarrow\ 705x=470(x+1)\\\\\Rightarrow\ 705x=470x+470\\\\\Rightarrow\ 705x-470x=470 \\\\\Rightarrow\ 235x=470\\\\\Rightarrow\ x=\dfrac{470}{235} \\\\\Rightarrow\ x=2[/tex]
hence, the flying time for the shorter leg = 2 hours
So (d) is the correct option.
One number is eight more than another. If their sum is increased by 17, the result is 95. Find the numbers.
Answer:
No. are 35&43
Step-by-step explanation:
Let the one no. Be= X
Then the other no.= X+8
Sum of both no.= X+ X+8= 2X+8
When sum is increased by 17 = 2X+8+17=95
2X+25=95
2X=70
X=35
Other no=X+8= 35+8=43
all poets are loners. All loners are taxi drivers. therefore, all poets are taxi drivers
is this valid or invalid?
Answer:valid
Step-by-step explanation:
The graph of the function B is shown below. If B(x) = -1, then what is x?
1
2
-1
Answer:
x = 2
Step-by-step explanation:
B(x) = - 1 means what is the value of x for y = - 1
This is the dot positioned at (2, - 1 )
with x = 2
Answer: its the first one
Step-by-step explanation:
hope thats what your lookinf for
A triangle is translated by using the rule (X.Y) =(x-4.y+1). Which describes how the figure is moved?
2
four units left and one unit down
O four units left and one unit up
one unit right and four units down
O one unit right and four units up
Heather has a bag with 3 marbles, 7 tennis balls, 3 apples, and 3 books. What is the ratio of books to tennis balls?
A.
(3/7) or 3:7
B.
(7/8) or 7:8
C.
(4/7) or 4:7
Answer:
B
Step-by-step explanation:
I hope it's correct and I'm thinking it is,. Sorry if it's not
Answer:
I think A
Step-by-step explanation:
3/7. Or 3:7
Cause there are 3 books and 7 tennis balls
Please help!!!!!!!!!!!
Answer:
6/72
Step-by-step explanation:
6/72 =0.0833333333
Answer: 2/9 X 3/8
NOW'
2 X 3 = 6 THIS IS THE ANSWER WHEN U MULTIPLY NOW AS PER
9 8 72
THE QUESTION WE NEED TO SIMPLIFY IT....
SOOOOOO LETS SEE FIRST IF WE CAN SIMPLIFY IT......
my method)
6/72 (lets divide num nd deno by 2)
3/36( Ahh! we cn simplify it further now divide by 3)
1/12
Other metthod
6/72 ( DIVIDE BY 6)
1/12
Step-by-step explanation:
-3y-2=7 what is the value of y
Answer:
y = -3
Step-by-step explanation:
Add 2 to each side to isolate the -3y. Doing this leaves you with -3y=9. You then divide each side leaving you with y = -3
Answer:
The equation has one solution at which y = -3.
Step-by-step explanation:
To find the value of y, we need to isolate it from the rest of the equation.
Add 2 to both sides of the equation.Divide by -3 on both sides of the equation.Simplify the equation if necessary.[tex]\displaystyle{-3y-2=7}\\\\-3y = 9\\\\\bold{y = -3}[/tex]
We can check to make sure that y = -3 by substitution.
[tex]\displaystyle{-3(-3)-2 = 7}\\\\9-2=7\\\\7= 7 \ \checkmark[/tex]
Because we got a true statement, we can determine that y = -3.
Which ordered pair can be removed so that the resulting graph represents a function?
(–2, 2)
(1, 3)
(5, –4)
(–4, –4)
Answer:
(1,3)
Step-by-step explanation:
HELPPP
Solve the equation
log (2x-3)=2
Answer:
2.5 or 5/2
Step-by-step explanation:
2x-3=2
2x=5 (both sides plus 3)
x=5/2 or 2.5(divid by 2 on both sides)
idenify the slope and y-intercept of the function y=-2x+3
Answer:
The y-interept is 3 and the slope is -2.
Step-by-step explanation:
The y-intercept is always the "b" in y=mx+b
Answer:
Slope: − 2
y-intercept: ( 0 , 3 )
Step-by-step explanation:
Can someone help me with this geometry proof?
Answer:
Step-by-step explanation:
IM LEARNING THIS TOO LOL
angle one and angle 2 are congruent because of the corresponding angles theorem
angles 2 and 3 are linear pair so 1 plus 2 equals 180
i believe you can use the transitive property
The length of a rectangle is 10 more than 10 twice the width , if the perimeter is 80inches find the length the width
Answer:
The width is 10 inches
The length is 30 inches
Step-by-step explanation:
Perimeter of a Rectangle
The perimeter of a rectangle of length L and width W is calculated as follows:
P = 2L + 2W
It's given the length of a rectangle is 10 more than twice the width:
L = 2W + 10
Substituting into the formula of the perimeter:
P = 2(2W + 10) + 2W
Operating:
P = 4W + 20 + 2W
P = 6W + 20
It's given this perimeter is 80 inches, thus
6W + 20 = 80
Subtracting 20:
6W = 80 - 20 = 60
Dividing by 6:
W = 60 /6 = 10
Since :
L = 2W + 10
L = 2*10 + 10
L = 30
The width is 10 inches
The length is 30 inches
"Just look at the graph," the player's agent said. "Phil's hits have doubled since last year. We are looking for a large raise and a long contract." Look at the graph. A bar graph titled Phil's hits has this year and last year on the x-axis, and number on the y-axis, from 100 to 200 in increments of 20. This year is 180, and last year is 120. How can you redraw this graph so it appears that Phil's hits have quadrupled since last year. a. Use the same scale and make the top bar twice as thick as the bottom bar. b. Alter the scale so the top bar appears four times as long as the bottom bar. c. Both a and b. d. Neither a or b.
Answer:
Awnser is C
Step-by-step explanation:
We just have to make the top bar seem bigger then it actually is
Denis orders a large pizza for $16.50 plus $2 for each topping. Sheng orders a medium pizza for $13.25 plus $2 for each topping.
Their bills will never be the same because the toppings cost the same.
Question must probably wants to know the number of toppings it would take for their bills to be equal.
Assume the number of toppings is x, Dennis's bill will be:
= Cost of Pizza + Cost of toppings x number of toppings
= 16.50 + 2x
Sheng's bill will be:
= 13.25 + 2x
Equate their bills to find the number of toppings that would equate their costs:
16.50 + 2x = 13.25 + 2x
16.50 - 13.25 ≠ 2x - 2x
3.25 ≠ 0
In conclusion, their bill will never be the same because the toppings are the same price.
Find out more at https://brainly.com/question/5607279.
ASAP 30 points and BRAINLIEST!! PLS!
Answer:
[tex]y+3=\frac{2}{5} (x+5)[/tex]
Step-by-step explanation:
First, let's find the slope using the 2 given points and the slope equation.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Enter in the points:
[tex]m=\frac{-3--1}{-5-0}[/tex]
Simplify:
[tex]m=\frac{-2}{-5}[/tex]
[tex]m=\frac{2}{5}[/tex]
Now that we have slope we can just use one of the points given. Remember point-slope form:
[tex]y-y1=m(x-x1)[/tex]
I'll use the point (-5,-3) in this case.
So, your solution is
[tex]y+3=\frac{2}{5} (x+5)[/tex]
Hope this helps!
y+1=2/5(x+0) should be it
What is the range of the function graphed below?
An airplane traveled 108 miles in 20 minutes? How long will it take to fly 162 miles?
a
30 min
b
25 min
c
8.1min
d
35 min
omg pls help me im giving like all my points out for this
Answer:
poopy
Step-by-step explanation:
Tee Hee
Answer:
a, 30 minutes
Step-by-step explanation:
108 divided by 20 is 54
162 divided by 54 is 30
101.101 correctly written out in words
Answer:
One hundred one and one hundred one thousandths
Step-by-step explanation:
Answer:
Step-by-step explanation:
basicliy he's saying c
wich is true:)
Graph a scatter plot using the given data.
Answer:
Here is the answer.
Step-by-step explanation:
General admission tickets to the fair cost $5 per person. Ride passes cost an
additional $7.50 per person. Parking costs $16 for the family. The total costs for
ride passes and parking was $103.50. How many people in the family attended
the fair?
I need help someone please
Answer: [tex]\frac{6}{2}[/tex]
Step-by-step explanation:
1. Use this [tex]\frac{f(b)-f(a)}{b-a}[/tex] to find the average rate of change
2. Average rate of change = [tex]\frac{f(8)-f(6)}{8-6}[/tex]
3. [tex]f(8) = - 4[/tex] and [tex]f(6) = -10[/tex] (To find these you will need to look at the points on the graph. So the points (8,-4) and (6,-10))
4. Replace -4 to f(8) and -10 to f(6)
5. So it will look like[tex]\frac{-4-(-10)}{8-6}[/tex]
6. Solve [tex]\frac{6}{2}[/tex]
Simplify to create an equivalent expression. 617 - 3y) + 6(y + 1)
Answer:
623+3y
Step-by-step explanation:
You distribute the 6 then you add the ys and the numbers together
A population of kangaroos is growing at a rate of 2% per year, compounded continuously. If the rate continues, how many years will it take of the population to reach 150% of its current size according to the exponential growth function?
Answer:
75 years.
Step-by-step explanation:
Divide 150 by 2, that gives you the years.
Desarrolla el siguiente cuadrado de binomio (2x³ - 6x)²
Answer:
[tex]4x^{6} - 24x^{4} + 36x^{2}[/tex]
Step-by-step explanation:
Find the measure of the indicated arc.
i really hate math so please
Answer:
personally i think c
Step-by-step explanation:
its because for the graph there is 90 and it has a point and when i used a calc i put the points and the a=18 so 90 eould be 18 again this what i think i am not really AMAZING at it but i get some of it for ex the chart equals it only equals a=5
Help Really quick
The table shows data collected from 14 people.
Shoe Size, x 8.5 9 9 9.5 10 10 10.5 10.5 11 11 11 12 12 12.5
Height (inches), y 66 68.5 67.5 70 70 72 71.5 70 71 71.5 73 73.5 74 74
Determine the correlation coefficient for the data. Round to the nearest hundredth.
r=
Answer:
i need the answer ;(
Step-by-step explanation: