A sequence is shown in the graph.
points at 1 comma 48, 2 comma 12, 3 comma 3, and 4 comma 75 hundredths
Assuming the pattern continues, what is the formula for the nth term?
an = 48(4n)
an = 48(0.25n + 1)
an = 4(48n − 1)
an = 48(0.25n − 1)
Answers
Answer:
(d) 48(0.25^(n-1))
Step-by-step explanation:
The points shown on the graph have y-values that decrease by a factor of 4 as x-values increase by 1. The first couple are (1, 48), (2, 12). You want the formula for the n-th term.
Geometric sequenceThe terms of a geometric sequence have a common ratio (r). If the first term is a1, the general term is ...
an = a1(r^(n-1))
ApplicationThe given sequence has first term a1 = 48. The common ratio is ...
r = 12/48 = 1/4 = 0.25
Using these value in the formula for the general term, we find the n-th term to be ...
an = 48(0.25^(n-1)) . . . . n-th term of the pattern
[tex]\begin{array}{ccccccccc} 1&&2&&3&&4&&5\\\cline{1-9} \\48&,&12&,&3&,&\underset{0.75}{\frac{3}{4}}&&\underset{0.1875}{\frac{3}{16}}\\[2em]\cline{1-9} &&48\left( \frac{1}{4} \right)&&12\left( \frac{1}{4} \right)&&3\left( \frac{1}{4} \right)&&\frac{3}{4} \end{array}~\hfill \begin{array}{llll} a_1=48\\\\ r=\frac{1}{4} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\stackrel{\textit{first term}}{48}\\ r=\stackrel{\textit{common ratio}}{\frac{1}{4}\to 0.25} \end{cases}\implies a_n=48\left( 0.25 \right)^{n-1}[/tex]
Related Questions
write a quadratic function in standard form whose graph passes through (-5 0) (0,-8) and (4,0).
Answers
The required quadratic function in the standard form is f(x) = -1.25 x² + 5x.
What is a quadratic equation ?
A quadratic equation is an equation which contains a single variable of degree 2 and its general form is ax² + bx + c = 0.
The x - intercepts of the quadratic equation are (-5, 0) and (0 , -8). That meant (x + 5) and (x -0) are two factors of quadratic equation.
f(x) = a (x + 5) (x - 0)
f(x) = ax² + 5x
The graph of quadratic equation passes through (4 , 0). So we need to substitute x = 4 , f(x) = 0 in equation 1.
0 = a × 4² + (5 × 4)
0 = a × 16 +20
a = -20/16
We know that quadratic equation is in form ax² + bx + c = 0.
f(x) = [tex]\frac{-20}{16}[/tex] × x² + 5x
f(x) = [tex]\frac{-5}{4}[/tex]x² + 5x
f(x) = -1.25 x² + 5x
Therefore , the required quadratic function in the standard form is f(x) = -1.25 x² + 5x.
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The school is planning a field trip. there are 2652 students and 78 seats on each school bus. How many buses are needed to take the trip
Answers
2652÷78=34 so I think it's 34
Convert (1/3)^x=27 to logarithmic form, with work worked out!
Answers
[tex] {a}^{x} = m \\ log_{a}(m) = x[/tex]
[tex]( \frac{1}{3} )^{x} = 27 \\ log_{ \frac{1}{3} }(27) = x[/tex]
That's the logarithmic form. Do you need with solving the equation too?
please solve for j: j+17=8
Answers
Answer:
-9
Step-by-step explanation:
8-17=-9
Answer: -9
Check: -9 + 17 = 8 (Check)
I hope this helps, and Happy Holidays! :)
Is 0.46 terminating number
Answers
Answer:
Yes because the decimal doesn't go on forever
Answer:
Yes
Step-by-step explanation:
0.46 is a terminating number because it has a finite number of decimal digits. Hence the name terminating, there is a terminated or ending to the decimal.
The length of a rectangular floor is 5m longer than its width. The area of the floor is 84m^. What is the width of the floor? How about its length
Answers
Step-by-step explanation:
I give you answer later ..........
Answer:
The width is 16.8 m
Step-by-step explanation:
A = l * w
w = A/l
w = 84m^2 / 5m
w = 16.8m
Don’t worry about number three just tell me the answer to number 1
Answers
Answer 3 1 /2 in decimal it is -3.5
Step-by-step explanation:
I need help finding an eqaution for this.
Answers
Answer:
x>7
Step-by-step explanation:
Answer
7 is less than x
Type the correct answer in each box.
Elena has 32 hair ties. Melanie has 8 hair ties.
The ratio of Elena’s hair ties to Melanie’s hair ties is
: 1. If, Melanie gets 4 more hair ties, the new ratio of Elena’s hair ties to Melanie’s hair ties is 8 :
.
Answers
Answer step by step explanation:
The ratio of Elena's hair ties to Melanie At first is 32/8 divide by eight is 4:1
The new hair ties after Melanie gets 4 is 12 ,so the new ratio of Elena's hair ties to Melanie that is 32/12 divided by four will be 8:3
Each of the 27 turtles in the pet store needs to be fed. There is one bag of turtle food that weighs 84 ounces. If each turtle gets the same amount of food, how many ounces of turtle food will each turtle get?
3 ounces
3.1 ounces
3.ModifyingAbove 1 with bar
3.12 ounces
Answers
Answer:
3.1 Modifying Above 1 with bar is the correct answer .
Answer: 3.1 modifying ounces
Step-by-step explanation:
84/27 = 3.11111111
If x2 = 50, what is the value of x
Matemáticas
Answers
Answer:
x=25
Step-by-step explanation:
Triangles XYZ and EFG are given and ΔXYZ≅ΔEFG by SAS. If YZ=2n−5, YX=2n−1, EG=n+8, and FG=n+5, then which of the following statements is true.
Answers
Answer:
ZY = 15
Step-by-step explanation:
ZY is congruent to GF, so you set the equation up as
2n-5 = n+5
+5 +5
-----------------
2n = n+10
-n -n
------------------
n = 10
After you get n, you plug it in to 2n-5 (ZY)
2(10)-5
20-5
15
ZY=15
Explain if the following is a proportional relationship: Sam used 6 gallons of gas to drive 50 miles and 4 gallons of gas to drive 100
miles.
Answers
Answer:
it's not a proportional relationship. ..............
The word particle can be used to describe a speck of dust, molecule, an atom or an electron. How can we avoid confusion in using the word particle?
Answers
Answer:
To avoid confusion in using the word "particle," one must state that a particle is an identifiable part of dust, a molecule, an atom, or an electron. This means that particles form these elements.
Step-by-step explanation:
For example, atoms are made up of three particles: protons, neutrons and electrons. These particles are each composed of even smaller particles known as quarks. Since quarks cannot be broken down further, they are the smallest particles known to mankind.
What is -2/3 divided 4/5
Answers
Answer:
-5/6
Step-by-step explanation:
-2/3 / 4/5 =
-2/3 * 5/4 =
-10/12 =
-5/6
Answer:
-5/6
Step-by-step explanation:
just divide it you will get the answer
What is the missing reason???
Answers
Given that,
AD is parallel to EC, BD is congruent to BC.
Solution,
Here,
[tex]\angle D=\angle C[/tex] = the reason for this is that the two angles are alternate interior angle. So, by alternate interior angle theorem [tex]\angle D=\angle C[/tex].
As [tex]\angle ABD=\angle EBC[/tex] = due to vertically opposite theorem
It means,
[tex]\triangle ABD \cong \triangle EBC[/tex] (angle-side-angle)
Hence, the correct option is (c).
[tex]\sqrt{18} is between which two whole numbers[/tex]
Answers
You need to find which two perfect squares is the sqrt{18} between.
sqrt{16} is a perfect square = 4
sqrt{25} is a perfect square = 5.
We conclude the sqrt{18} lies between the sqrt{16} and sqrt{25}.
A 12 count box of Ouaker Instant Grits has a UPCof 00030000047606. What is the check number?
A)0
B)4
C)6
D)7
Answers
Answer:
6
Step-by-step explanation:
CAN YOU HELP ME WOTH GEOMETRY! It's due TONIGHT!
Answers
Answer:
look down below
Step-by-step explanation:
We know that AB = DC, and BC = AD, ∠B = ∠D because they are given
So, ΔABC ≅ ΔCDA because of SAS congruency
graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation y=−3x
Answers
The graph of the line is shown below
Graph of a Linear equationFrom the question, we are to determine the graph of the line by plotting any two ordered pairs
First, we will find two ordered pairs on the line
y = -3x
When x = 1
y = -3x
y = -3(1)
y = -3
(1, -3)
When x = 2
y = -3x
y = -3(2)
y = -6
(2, -6)
Using the ordered pairs, the graph of the line is shown below
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Hi help me please wit the equation i need help
Answers
Answer:
the y-intercept is (0,8)
please help me! math stuff
Answers
Answer:
C.
Step-by-step explanation:
64+56=120
189-120=C. $69
match each equation with a value of x that satisfies it
options are:
5 , 9 , 18, 2, 1, -3
(x-2)^1/4=2 --->___
√x^2+7=4. --->___
^3√1-x=-1. --->___
Answers
Answer:
(x-2)^1/4=2 ---> 18
√x^2+7=4. ---> -3
^3√1-x=-1. ---> 2
Step-by-step explanation:
just did it on plato
The numerical expression [tex]\rm (x - 2)^{1/4} = 1[/tex], √x² + 7 = 4, and ∛(1 - x) = -1 are correctly matched with 18, -3, and 2.
What is simplification?Simplification is to make something easier to do or understand and to make something less complicated.
The expressions are given below.
[tex]\rm (x - 2)^{1/4} = 1[/tex], √x² + 7 = 4, and ∛(1 - x) = -1
Then By simplification, we have
x - 2 = 2⁴
x = 16 + 2
x = 18
√x² + 7 = 4
x + 7 = 4
x = -3
∛(1 - x) = -1
1 - x = -1³
x = 2
The numerical expression [tex]\rm (x - 2)^{1/4} = 1[/tex], √x² + 7 = 4, and ∛(1 - x) = -1 are correctly matched with 18, -3, and 2.
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Plz help me, i will mark u brainliest!!!
Answers
Answer:
Step-by-step explanation:
To find out how much should he drive more = 7/8 - 1/8 = 6/8
6/8
Both have table of 2 in common so
3/4 is the simplest form
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
No. of remaining days = [tex]\frac{7}{8}[/tex] - [tex]\frac{1}{8}[/tex]
If the denominators are the same, you can directly do the working for the numerators while leaving the denominator alone.
[tex]\frac{7}{8}[/tex] - [tex]\frac{1}{8}[/tex] = [tex]\frac{6}{8}[/tex]
6 and 8 both have a common factor of 2, so we can further simplify this fraction.
[tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
Thus, he must drive for [tex]\frac{3}{4}[/tex] more days.
9+6d+c
whats the answer
Answers
Answer:
15d I think
Step-by-step explanation:
Because 9+6 is 15 and then you add the d to 25
Answer:
You can't solve this question unless you have an subject to solve for. This equation is in its simplest form.
If I got your question wrong, please leave a comment! :D As I might be wrong.
Stay safe and Merry Christmas! :)
Need help with number 11 ASAP!!!!
Answers
Answer:
78%, no he didn't score high enough
Step-by-step explanation:
What is HL? Trapezoid
Answers
Answer:
HL = 21
Step-by-step explanation:
HL is the midsegment of the trapezoid shown above. Thus, it follows that:
HL = (JK + GF)/2
JK = 12
GF = 2.5(JK) = 2.5(12) = 30
Plug in the values:
HL = (12 + 30)/2
HL = 42/2
HL = 21
Find the balance of the account.
$1600 at 5% for 1 year
This is simple interest btw. I also need a explanation too
Answers
Answer:
$1680
Step-by-step explanation:
I = 5%
P = $1600
period = 1 year
$1600 + 15% = $1680
Answer:
$1680.
Step-by-step explanation:
The interest for 1 year = 1600 * 5%
= 1600 * 0.05
= $80.
So the new balance = old balance + interest
= 1600 + 80
= $1680.
which of the following inequalities matches the graph?
Answers
Since the area shaded is left of x = -3, x has to be less than -3.
7) What is the equation of a circle with the center (-8, 9) and the radius of 10?
Answers
Answer:
(x+8)² + (y - 9)² = 100Step-by-step explanation:
The general equation of a circle is expressed as;
(x-a)² + (y - b)² = r² where;
(a, b) is the centre of the circle
r is the radius
Given
Centre (-8, 9) where a = -8, b = 9
radius r = 10
Substitute into the formula to get the required equation;
(x-(-8))² + (y - 9)² = 10²
(x+8))² + (y - 9)² = 10²
(x+8)² + (y - 9)² = 100
Hence the required equation is (x+8)² + (y - 9)² = 100