If we look at the series, one third of the current term gives the numerical value of the next term.
If we need to express it algebraically, we can write the following equation.
[tex]a_{n+1}=\frac{a_{n}}{3}[/tex]Therefore, our common multiplier can be found as follows. Because this sequence is a geometric sequence.
[tex]\frac{a_{n+1}}{a_{n}} =r=\frac{1}{3}[/tex]In geometric sequences, any term can be written in terms of the first term. Below is an example.
[tex]a_{n}=a_{1}.r^{n-1}[/tex]Since we know the numerical values of the first term and the common factor of the series, we can easily find the seventh term.
[tex]a_{7}=a_{1}.r^{7-1}[/tex][tex]a_{7}=18.(\frac{1}{3} )^6[/tex][tex]a_{7}=\frac{2}{81}[/tex]Can someone help me find the slope???
Answer:
The slope is -1/3.
Step-by-step explanation:
When you count the rise/run, which is how much it goes up/down and left/right, you get -4/12. Simplify -4/12 and you'll get -1/3.
g + 3 < 6
please help me
The solution to the given inequality expression is g <3
Linear inequalityInequality are expressions not separated by an equal sign. They are separated by a less than, greater than, less than or equal to and greater than or equal to.
Given the linear equation below:
g + 3 < 6
We are determine the unknown variable "g"
First, we need to subtract 3 from both sides to have;
g + 3 - 3 < 6-3
g < 6 - 3
g < 3
Hence the solution to the given inequality expression is g < 3
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Write each number as a power of 4
a) 1/4
b) 1/64
Answer: I am going to assume that 1/4 is 1 over 4 ( a fraction ) and that it is the same for 1/64
A) 0.00390625
B) 0.015625^4 <------( Here is the equation. when i put it in a calculator it was too long. here is the answer that gave me: 5.96046448 e-8 )
Which postulate could we use to prove that the angles
The angle postulate that best defined angles CAB and CAD is; Supplementary Angles
What is the Angle Postulate?We know that there are different angle postulates such as Corresponding angles, complementary angles, supplementary angles and others.
Now, in this case we want to find the angle theorem that best describes angles CAB and CAD. Now, from the given image, it is clear that both angles form a straight line and we know that the sum of angles on a straight line equals 180 degrees.
Since both angles sum up to 180 degrees and we know that these angles are defined as supplementary angles which are linear pairs.
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Pancakes are made with 1½ cups water and 1/2
What is the ratio of water to milk?
cup milk.
1 1/2 : 1/2 is the rario of wayer to milk
The ratio of water to milk is 3:1.
What are ratios ?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other is called ratio.
Water = 1½ cups
= 3/2 cups
Milk = 1/2 cup
Ratio of Water to milk
= 3/2 : 1/2
= 3/2 ÷ 1/2
= 3/2 x 2/1
= 3/1
so, the ratio of water to milk is 3:1.
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Solve y3 = 1.
answers are
y = −1
y = 1
y = ±1
y = 3
Answer:
Is y3 supposed to be y^3? Is so, the answer is 1.
Step-by-step explanation:
If the equation is correct as written, 3y = 1, then y = 1/3
y^3 = 1
This can also be written as y^2*y = 1
1. If y = -1, then y^2y would be (1)*(-1) = -1
2. If y = 1, then (1)^3 * (1) = 1 This works.
3. If y = ±1, then -1 is a possible answer and -1 does not work as per #1
4. 3^3 = 27
Which of the following is equal to (2x/5 - 9) +9?
Answer:
I don't see any answer options, and the equation doesn't look correct.
I'll assume the equation is meant to be:
(2x/5 - 9) = 9, not (2x/5 - 9) +9Step-by-step explanation:
(2x/5 - 9) = 9
2x/5 = 18
2x = 90
x = 45
if the modified equation is correct.
the third term in the sequence is 11
the term-to-term rule is "take away 4"
write an expression on in terms of n for the nth term of the sequence
An expression, in terms of n, for the nth term of this arithmetic sequence is aₙ = 23 - 4n.
What is an arithmetic sequence?An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.For the second term, we have:
a₂ = a₃ - d
a₂ = 11 - (-4)
a₂ = 11 + 4
a₂ = 15.
For the first term, we have:
a₁ = 4 + second term
a₁ = 4 + 15
a₁ = 19
Substituting the given parameters into the formula, we have;
aₙ = a₁ + (n - 1)d
aₙ = 19 + (n - 1)(-4)
aₙ = 19 - 4n + 4
aₙ = 23 - 4n
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what is the common ratio for the geometric sequence 35/2, 7, 14 / 5, 28 / 25, enter your answer as a decimal
Given:
The geometric sequence is
[tex]\begin{gathered} a_1,a_2,a_3,a_4 \\ \frac{35}{2},7,\frac{14}{5},\frac{28}{25} \end{gathered}[/tex]To find the common ratio,
[tex]\begin{gathered} Ratio=\frac{a_2}{a_1} \\ =\frac{7}{\frac{35}{2}} \\ =\frac{7\cdot2}{35} \\ =\frac{14}{35} \end{gathered}[/tex]Hence the common ratio, r is 14/35.
Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the force exerted on the object. If an object accelerates at a rate of 3 m/s2, it will exert a force of 15 N. How much force will the same object exert if it accelerates at a rate of 7 m/s2 ?
Answer: 35N
Step-by-step explanation:
Cross multiply and divide to find the missing value
Answer: 35N :)))))))))))))))))))))))))))))
Write an explicit formula for an, the nth term of the sequence
6, -12, 24,....
Answer:
6,12,24,48,96
Step-by-step explanation:
Katie bought 4 sweaters that each cost the same amount and 1 skirt that cost 20$ . The items she bought cost a total of 160 before tax was added. What was the cost of each sweater?
A
$20\$ 20$20
Using simple linear equation we calculate the cost of a sweater as $35 .
A linear polynomial over a field, from which the coefficients are taken, can be equalised to zero to produce a linear equation.
The numbers that, when used to replace the unknowns in such an equation, result in the equality, are the solutions.There is just one possible answer when there is only one variable (providing that. The term "linear equation" frequently alludes indirectly to this specific situation, in which the variable is appropriately referred to as the "unknown."Let the cost of each sweater be x.
Cost of the skirt = $20
Let us form a linear equation to calculate the required cost
4x + 20 = 160
solving we get :
x = 35
Therefore the cost of a skirt is $35.
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Please help I have no clue what I’m doing! Grade is getting low and this was due awhile ago!
Given the function below, determine the following.
f(x) = 10x + 13
Find f(3).
f(3)
Find f(-8).
f(-8)
Find x if f(x) = 53.
x=
Answer:
see explanation
Step-by-step explanation:
f(3) means what is the value of f(x) when x = 3
substitute x = 3 into f(x)
f(3) = 10(3) + 13 = 30 + 13 = 43
similarly for x = - 8
f(- 8) = 10(- 8) + 13 = - 80 + 13 = - 67
given f(x) = 10x + 13 and f(x) = 53 , equate the right sides
10x + 13 = 53 ( subtract 13 from both sides )
10x = 40 ( divide both sides by 10 )
x = 4
Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation. Average Cycling Speed A graph titled Average Cycling Speed has minutes on the x-axis and miles per hour on the y-axis. Points are at (5, 15), (10, 13), (15, 11), (20, 10), (25, 9). a. no correlation b. negative; as time passes, speed decreases c. positive; as time passes, speed increases d. positive; as time passes, speed decreases Please select the best answer from the choices provided A B C D Mark this and return
Step-by-step explanation:
5,15 can accord to be an sciencetistic teachers, the 15,11 which means you can appear to combine them together and be an 100 then you do the abcd and boom
Help ASAP, will mark brainliest!
If triangle ABD is congruent to triangle CBD, angle ADB = 49 degrees and angle CDB = 7x.
Answer:
x = 7 degrees
Step-by-step explanation:
Angle CDB = 49 degrees (corresponding angles triangle ABD congruent to triangle CBD)
Angle CDB = 49 degrees = 7x
7x = 49 degrees
x = 7 degrees
The telephone company offers two billing plans for local calls. Plan 1 charges $31 per
month for unlimited calls and Plan 2 charges $13 per month plus $0.03 per call.
a. Use an inequality to find number of monthly calls for which Plan 1 is more
economical than Plan 2.
b. Explain the meaning of the answer to part a.
Answer:
i think is (a)
because i zay do
Step-by-step explanation:
anyways...... i want more pictures of math problems
the world population was 6.9 billion at the end of 2010 and is predicted to reach 9 billion by the end of 2050.1 (a) assuming the population is growing exponentially, what is the continuous growth rate per year? round your answer to three decimal places.
The continuous growth rate per year of the world population is 0.664%.
What is defined as Exponential Growth?Exponential growth occurs when the growth of a quantity at any point in time has been proportional towards its value at that point. If we have a few numbers, we could use simple exponential growth models to determine the population.We've been told to assume that population is growing at an exponential rate. As a result, we can employ the population model shown below.
N(t) = N₀ e∧(kt)
Here, N(t) represents the population after t years, N₀ represents the initial population, and k represents the continuous growth rate.
We've been told that initial population of 6.9 billion will increase to 9 billion in 40 years (2050-2010).
To use this information, we calculate the growth rate using the model described below.
N(40) = 6.9 e∧(40k)
N(40) = 9 (given)
9 = 6.9 e∧(40k)
Taking ㏑ both side
㏑ 9 = ㏑ 6.9 e∧(40k)
40k = ㏑(9/6.9)
k = 0.00664
k = 0.664%
Thus, the continuous growth rate per year of the world population is 0.664%.
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write the equation of a circle given the center (2, 9) and radius r = 3
Answer: x^2 + y^2 - 4x + 18y = 76 = 0
The center of the circle given is (2, 9)
radius = r
The equation of a circle for a given point is
(x - h)^2 + (y - k)^2 = r^2
Where h = 2, and y = 9
(x - 2)^2 + (y - 9)^2 = 3^2
Expand the parentheses
(x - 2) (x - 2) + (y - 9) (y - 9) = 9
(x - 2) (x - 2 ) = x* x - 2*x - 2*x + 2* 2
= x^2 - 4x + 4
(x - 2) (x - 2) = x^2 - 4x + 4
(y - 9) (y - 9) = y*y - y*9 - 9*y + 9*9
= y^2 - 18y + 81
(y - 9) (y - 9)= y^2 - 18y + 81
Therefore, the equation becomes
x^2 - 4x + 4 + y^2 - 18y + 81 = 9
Re-arrange the equation
x^2 + y^2 - 4x - 18y + 4 + 81 = 9
x^2 + y^2 - 4x - 18y = 9 - 81 - 4
x^2 + y^2 - 4x - 18y = -76
x^2 + y^2 - 4x - 18y + 76 = 0
The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0
Answer:
The equation of a circle given the center (2, 9) and radius 3 is x^2 + y^2 - 4x + 18y = 76 = 0
Step-by-step explanation:
HELP ME PLEASE!!! THANK U SO MUCH IF U HELP ME, UR HELP WILL BE APPRECIATED <3
Answer:
1b) in first image
1c) in second image
The measures of the exterior angles of a quadrilateral are 2x°, 3x°, 9x°, and 10x°. Find the measure of the largest exterior angle.
The measures of the angles of a triangle are shown in the figure below. Solve for x.
54°
(7x+1)°
Answer:
54 + (7x + 1) + 90 = 180° (sum of angles in triangle=180)
7x = 35
x = 5
Answer:
x = 5
Step-by-step explanation:
Geometry TheoryThis question deals with a right-angled triangle. The sum of the angles in a triangle is equal to 180 degrees. A right angle is equal to 90 degrees which means that the other two angles must equal to 90 degrees as well.
AlgebraForm the equation.
( 7x + 1 ) + 54 + 90 = 180;
Subtract 90 from both sides.
7x + 1 + 54 + 90 - 90 = 180 - 90;
7x + 1 + 54 = 90;
Simplify left-hand side.
7x + 55 = 90;
Subtract 55 from both sides.
7x + 55 - 55 = 90 - 55;
7x = 35;
Divide both sides by 7.
x = 35 / 7;
x = 5;
You are on the prom decorating committee and are in charge of buying balloons. you want to use both latex and mylar balloons. The latex balloons cost $.10 each and the mylar balloons cost $.50 each. You need 125 balloons and you have $32.50 to spend. how many of each can you buy?
I can buy 75 latex balloons and 50 mylar balloons.
This is a problem from an algebraic equation. We can solve this problem by following a few steps.
We need 125 balloons. Let's assume we have to purchase x latex balloons.
So, mylar balloons are ( 125 - x ).
Our total budget is $32.50.
The cost of x latex balloons is ($.10 × x) = $.10x , as the latex balloons cost $.10 each.
The cost of ( 125- x) mylar balloons is $[( 125- x) × 0.50] , as the mylar balloons cost $.50 each.
So the total cost is,
$[( 125- x) × 0.50] + $.10x = 32.50
Now, we have to solve this equation, Let's simplify it.
62.50 - 0.50x + .10x = 32.50
Or, 62.50 - 0.40x = 32.50
Or, -0.40x = 32.50 - 62.50 [ deduce 62.50 from both side ]
Or, -0.40x = -30 [ we should devide both sides 0.40 ]
Or, x = 30/0.40 = 75
So, the number of latex balloons is 75. Therefore, the number of remaining mylar balloons is ( 125 - 75) = 50
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I WILL GIVE BRAINLIEST!! HELP PLEASE NOW!!
A conjecture and the flowchart proof used to prove the conjecture are shown.
Drag an expression or phrase to each box to complete the proof.
yes thank you very muchGiven: Measure of angle D E G equals 51 degrees. Measure of angle G E F equals 39 degrees. Prove: Triangle D E F is a right triangle. Art: A right angle triangle D E F. Angle D E F is a right angle. Point G is on segment D F, and segment E G is drawn.
Deshaun invested in a savings bond for 4 years and was paid simple interest at an annual rate of 2%. The total interest that he earned was $160. How much did he invest?
For a Simple Interest of $160, the amount that he invested is $2000.
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Given:
Simple Interest (S.I.) = $160
Rate of Interest (R) = 2%
Time Period (T) = 4 Years
Let the Principal Amount be $P
We know,
[tex]S.I. =\frac{P*R*T}{100}[/tex]
Putting the given values in the formula, we get:
[tex]S.I. =\frac{P*R*T}{100}\\S.I. =\frac{P*2*4}{100} =\frac{P*8}{100}\\ 160 =\frac{P*8}{100} \\P = \frac{160*100}{8} =\frac{16000}{8} = 2000[/tex]
Hence, He Invested $2000
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Answer:
$2,000
Step-by-step explanation:
Simple Interest Formula
[tex]\large\boxed{\sf I = Prt}[/tex]
where:
I = Total interest accrued.P = Principal.r = Interest rate (in decimal form).t = Time (in years).Given values:
I = $160r = 2% = 0.02t = 4 yearsSubstitute the given values into the formula and solve for P:
[tex]\implies \sf 160=P \cdot 4 \cdot 0.02[/tex]
[tex]\implies \sf 160=0.08P[/tex]
[tex]\implies \sf P=\dfrac{160}{0.08}[/tex]
[tex]\implies \sf P=2000[/tex]
Therefore, the amount Deshaun invested was $2,000.
Put the following equation of a line into slope-intercept form, simplifying all fractions. 6x-3y=15
Answer: y=2x-5
Step-by-step explanation:
6x-3y=15
6x-6x-3y=-6x+15
-3y=-6x+15
-(3y=6x-15)
3y=6x-15
3y/3=(6x-15)/3
y=6x/3-15/3
y=2x-5
Reasoning 5 Jack calculates 6 x 102 + 3 x 10³ = 9 × 105 Explain Jack's mistake, and write in the correct answer in standard index form.
Answer:
3.6*10³
Step-by-step explanation:
Jack cannot add the powers of 10 because they are in addition. We can apply the exponent rule only when they are in multiplication.
[tex]\sf 6 *10^2 + 3*10^3= 6*100 + 3*1000\\[/tex]
= 600 + 3000
= 3600
[tex]\sf = 3.6 * 10^3[/tex]
Standard to slope intercept form
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - 6x+ 6[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given equation is :
[tex]\qquad\displaystyle \tt \rightarrow \: 24x + 4y = 24[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 4y =24 - 24x [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ 24}{4} - \frac{24x}{4} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - 6x + 6[/tex]
And this the equation of same line in its slope intercept form, where slope (m) = -6 and y - intercept = +6
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Georgia is given a rectangular piece of paper. If the
length of Georgia's piece of paper is represented by
x - 5 and the width is represented by 7x - 3, then
what is the area of the paper represented by?
Answer:
i will answer in 2050 my bad
i just need the points rq
Step-by-step explanation:
n/a
Write an equation in slope-intercept form of the line that passes through $\left(1,-9\right)$ and $\left(-3,-9\right)$ . An equation is
The equation of line is y = -9.
What is a equation of line?These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
Given that,
(1, -9) = ( [tex]x_{1}, y_{1}[/tex])
(-3, -9) = [tex](x_{2},y_{2})[/tex]
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
= [tex]\frac{-9+9}{-3-1}[/tex]
Slope = 0
Then the equation of line
[tex]y-y_{1} = m(x-x_{1})[/tex]
y+9 = 0
y = -9
Hence, The equation of line is y = -9.
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49 = 7/6u solve for u simplify your answer as much as possible
Answer:
Step-by-step explanation:
49 = 7/6u
49 * 6/7 = 7/6u * 6/7
42 = u