find the 12th term of the geometric sequence 1,3,9,...
we have
a1=1 ------> first term
a2=3
a3=9
Find the value of r (common ratio)
we have that
a2/a1=3/1=3
a3/a2=9/3=3
so
the common ratio is
r=3
we know that the general equation for a geometric sequence is
[tex]a_n=a_1\cdot r^{(n-1)}[/tex]we have
a1=1
r=3
substitute
[tex]\begin{gathered} a_n=1\cdot3^{(n-1)} \\ a_n=3^{(n-1)} \end{gathered}[/tex]Find the 12th term
so
For n=12
substitute in the equation
[tex]\begin{gathered} a_{12}=3^{(12-1)} \\ a_{12}=3^{(11)} \\ a_{12}=177,147 \end{gathered}[/tex]therefore
the answer is177,147I have one more question
Answer: 19
Step-by-step explanation:
[tex]49-6(5)=19[/tex]
Answer:
19
Step-by-step explanation:
a=49,b=5
a-6b
we will just substitute for the values
=49 – 6(5)
= 49 – 30
= 19
What is the Area of a circle with the radius of 5
Answer:
Answer is 78.5
Step-by-step explanation:
the formula for the Area of a cirlcle is [tex]\pi[/tex][tex]r^{2}[/tex]
using it:
area = 3.14 * 5^2
area = 78.5
What value of p satisfies the inequality shown below?
Answer:
7
Step-by-step explanation:
-8(7+2)<-56
-56-16<-56
-72<56
-72 is less than -56
four friends are baking bread . they equally share 3 sticks of butter. write an equation to find the fraction of a stick of butter that each friend uses.
The equation will be 4x = 3 and the fraction of the butter stick that each friend will use is x = 3/4.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the equation will be:
A Number of friends are 4.The number of butter sticks is 3.Then, the equation is:
4x = 33 sticks equally shared by 4 friends:
4x = 3x = 3/4Therefore, the equation will be 4x = 3 and the fraction of the butter stick that each friend will use is x = 3/4.
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Clare has
$102.38 in her savings account. At the ATM, she deposits 3 checks she received for
her birthday. Each check was written for $15.00. Then, she withdraws $20 in cash.
What is Clare's new account balance?
The new account balance of Clare is calculated as $127.38 by using the given data.
What exactly are operations in mathematics?A mathematical operation is a mathematical action. A mathematical operation includes addition, subtraction, multiplication, division, and computing the root.
What exactly is a word problem in mathematics?In math, a word problem is a question expressed in one or more sentences that asks learners to apply their arithmetic skills to a'real-life' scenario. This implies that in order to understand the word problem, students must be conversant with the terminology linked with the mathematical symbols to which they are used.
Given:
Clare has a savings account balance of $102.38. She uses the ATM to deposit three cheques she received for her birthday. Each check was made out for $15.00. She then takes out $20 in cash.
Amount in her savings account = 102.38
Amount after depositing 3 checks = 102.38 + 3(15)
= 147.38
Amount after withdrawing $20 in cash = 147.38 - 20
= 127.38
Therefore, the new account balance of Clare is calculated as $127.38 by using the given data.
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Which plane in the rectangular prism is parallel to plane ABC?
plane ABH
plane EFG
plane CDF
plane BCE
The plane EFG in the rectangular prism is parallel to plane ABC.
In this question, we have been given the rectangular prism ABCDEFGH
We need to find the plane which is parallel to plane ABC.
We can observe that in given rectangular prism,
plane ABH is parallel to the plane CDF
plane BCE is parallel to the plane AGF
plane EFG is parallel to plane ABC.
Therefore, the plane EFG in the rectangular prism is parallel to plane ABC.
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13 In August, 85% of the middle school students voted in a school election. The number of students who voted was 544.
How many students are in the middle school?
(A) 462 students
(B) 544 students
(C)629 students
(D) 640 students
Answer:
D. 640 students
Step-by-step explanation:
hope this helps
The perimeter of the quadrilateral ABCD is 105 inches
what is the Lenght of segment BC
Answer:
Hello, I would need to see an image of the quadrilateral at hand to be able to answer your question.
Step-by-step explanation:
Just let me know, here to help!
Solve the equation. Check the solution.
10-3x-6-12x = 7
X =
(Type an integer or a simplified fraction.)
Answer:
12x5-3a sishanaauanshsushss
Step-by-step explanation:
zhsuzjskakakagshs
Answer:
x=15
Step-by-step explanation:
The ratio of second graders to third graders at the spelling bee was 2 to 7. If there were 204 second graders, how many third graders were there?
There are 714 third-graders.
What is ratio?A ratio is a way to show a relationship or compare two numbers of the same kind.
Given that, the ratio of second-graders to third-graders at the spelling bee was 2 to 7 and there are 204 second-graders
Let the number of third-graders be x, then,
2/7 = 204/x
x = 714
Hence, There are 714 third-graders.
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A wheel on Amanda's bicycle is 0.3 m in diameter. Amanda rides the bicycle in a race, and the wheel turns 50 times during the course of the race. How long is the race?Use the value 3.14 for pie. Round your answer to the nearest tenth. Do not round any intermediate steps.
To be able to determine how long the race that Amanda took, let's multiply the circumference of Amanda's bicycle wheel by 50 times since it turns 50 times during the course of the race.
The formula of the circumference of a circle is,
[tex]\text{Circumference = }\pi d[/tex]Where,
pi = 3.14
d = diameter = 0.30 m
Let's determine the Circumference of Amanda's bicycle wheel,
[tex]\text{ Circumference = }\pi d\text{ = (3.14)(0.30)}[/tex][tex]\text{ Circumference = 0.942 m}[/tex]Let's now determine how long the race is,
[tex]\text{ Distance}_{Race}\text{ = (Circumference)(50) = (0.942)(50)}[/tex][tex]\text{ Distance}_{Race}\text{ = 47.10 m}[/tex]Therefore, the bicycle race that Amanda took is 47.10 m long.
Determine the property, definition, postulate, or theorem that bestjustifies each statement.Given: AC = BD; AB = 3x - 2; CD = 10ABсD If AC = AB + BC and AC = BD.then AB + BC =BD
The given statement is
[tex]AC=AB+BC\rightarrow AC=BD,then,AB+BC=BD[/tex]As you can observe, the observe, we made a substitution. However, the exact property used here is the transitive property of equalities, that's the property responsible for the substitution in mathematics.
Therefore, the answer is the transitive property of equalities.On average, Logan drinks 3/4 of a 12-ounce glass of water in 1 3/4 hours. How many glasses of water does he drink in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
Answer:
4.5 ounce or 3/4 of 6-ounce glass.
Step-by-step explanation:
I don't know -_- I'm too lazy for this.
10 points and brainliest to first correct answer! please answer both!
An explicit formula for the sequence -2,3,8,13,18 is aₙ = 7 - 5n.
The express method for a mathematics collection is an = a + (n - 1)d, and any time period of the collection can be computed, without knowing the opposite terms of the collection. In preferred, the explicit method is the nth time period of mathematics, geometric, or harmonic sequence.
Calculation:-
a₁ = 2
a₂ = 2 - 5 = -3
a₃ = -3 - 5 = -8
a₄ = -8 -5 = -13
a₅ = -13 -5
= -18
The formula for the nth term of explicit sequence is aₙ = a₁ +(n - 1)d
where a₁ = 2 and d = 5
So,
aₙ =2 + (n - 1)(-5) using distributive property
aₙ = 2 + n (-5)+(-1)(-5)
aₙ = 2 - 5n + 5
aₙ = 7 - 5n
The explicit formulae for L-capabilities are members of the family between sums over the complicated variety zeroes of an L-characteristic and sums over prime powers, introduced by Riemann for the Riemann zeta feature.
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ASAP PLEASE
Show how we can use the factors method to find the value of 53 × 20
Write it Step by step.
Answer:
1060
Step-by-step explanation:
I am assuming the factors method is the distributive property:
We can break 53x20 into 50x20+3x20
50x20=1000 and 3x20 is 60
1000+60=1060
Please give me brainiest.
Question
Solve for x.
5(x−225)=−5.2
Enter your answer as a decimal or simplified mixed number in the box.
x =
Answer:
x=223.96
Step-by-step explanation:
Answer as a decimal: x=223.96
Answer as a fraction: x= 223 24/25
Let's solve this equation step-by-step!
5(x−225)=−5.2
Step 1: Simplify both sides of the equation.
5(x−225)=−5.2
(5)(x)+(5)(−225)=−5.2 (Distribute)
5x+−1125=−5.2
5x−1125=−5.2
Step 2: Add 1125 to both sides.
5x−1125+1125=−5.2+1125
5x=1119.8
Step 3: Divide both sides by 5.
5x/5=1119.8/5
x=223.96
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
4+( ) Rewrite the expression 4-11 as the sum of two numbers
Answer:
4+(-11)
Step-by-step explanation:
you need to put the negative 11 in ()
The area of a triangle is 50
the length is x+10 and the width is x
solve for x.
In a rectangle of area 50 the value of x is 5
How to solve for xArea of a rectangle is given by multiplication of the length and the width
Area was given as 50
length = x + 10
width = x
Area = L * w
50 = (x + 10) * x
50 = x^2 + 10x
rearranging the equation
x^2 + 10x - 50
factorizing gives
x - 5x + 10x - 50
x(x- 5) + 10(x - 5)
(x - 5)(x + 10)
therefore
x = 5 or x = -10
taking the positive value
x = 5
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Question
The area of a rectangle is 50 the length is x+10 and the width is x
solve for x.
find the error & explain why it is wrong: jon had to solve the equation below. what did he do wrong?
Answer:
Step B is incorrect because the factors of [tex]x^2 + 4x + 3[/tex] should be:
[tex](x + 3)(x + 1)[/tex]
true or flase? Any method (elimination, substitution, or graphing) can be used to any possible system of linear equations.
Answer:
Step-by-step explanation:
Yes, you can use either the system of elimination, substitution, or graphical method to solve linear equations
Find the area of the shaded sector QRS
The diagram given is a sector, and from the diagram
Radius(r) = 9 in
[tex]\theta=120^{\cdot}[/tex][tex]\begin{gathered} \text{Area of a sector = }\frac{\theta}{360}\times\pi r^2 \\ \\ \text{Area of a sector = }\frac{120}{360}\times\frac{22}{7}\times9^2 \\ \text{Area of a sector =}\frac{19440}{2520}=7.71in^2 \end{gathered}[/tex]let p represenst "angke A is an obtuse angle" and q represent " the measure of angle A = 75 degrees. convert the symbolic statement to a sentence.
In this scenario, we are considering if-then statements. Looking at the given statement,
p = angle A is an obtuse angle
q = the measure of angle A = 75 degrees
A statement of if q, then p would be
q - p
where - is an arrow pointing to the right
Looking at the picture, the symbol before p represents negation. It tells us that
if q, then not p. By translation, the correct answer would be
If the measure of angle A = 75 degrees, then angle A is not an obtuse angle
calculus ! find the equation of the normal line to the curve `f(x) = (1)/(x)` at the point (1,1)
The slope of the tangent line at the point x = a of the function f(x) is f'(a).
We are given the function:
[tex]f(x)=\frac{1}{x}[/tex]Computing the first derivative:
[tex]f^{\prime}(x)=-\frac{1}{x^2}[/tex]The slope of the tangent line at (1, 1), that is, where x = 1 is:
[tex]f^{\prime}(1)=-\frac{1}{1^2}=-1[/tex]The tangent line and the normal line are perpendicular to each other. If their respective slopes are m1 and m2, then:
[tex]m_1\cdot m_2=-1[/tex]We have calculated m1 = -1, calculate m2:
[tex]m_2=-\frac{1}{m_1}=-\frac{1}{-1}=1[/tex]Now we know the slope of the normal line. We need to find its equation. Use the point-slope formula:
y - k = m(x - h)
Where m is the known slope and (h, k) is a point of the line. We are given the point (1, 1), thus:
y - 1 = 1(x - 1) = x - 1
Adding 1:
y = x
Answer: D. x
pls help me out I really need to sleep
Answer:
4
Step-by-step explanation:
Point 1: (-2, 0)
Point 2: (3, 4)
(4-0) ÷ (3-2) = 4 ÷ 1 = 4
How to substitute 8x-4y=-12, 8x+y=-17
we have the system
8x-4y=-12 -----> equation A
8x+y=-17 -----> y=-17-8x -----> equation B
substitute equation B in equation A
8x-4(-17-8x)=-12
solve for x
8x+68+32x=-12
40x=-12-68
40x=-80
x=-2
Find the value of y
y=-17-8(-2)
y=-17+16
y=-1
the solution is x=-2y=-1Example8x-4y=-12 -----> equation A8x+5y=-17 -----> equation B
isolate the variable y in equation B (or equation A)
5y=-17-8x
y=-(17/5)-(8/5)x
substitute in equation A
8x-4[-(17/5)-(8/5)x ]=-12
solve for x
Write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence The sequence is 7,9,11,13,15
7,9,11,13,15
First, find the common difference (d)
9-7 = 11-9 = 13-11 = 15-13 = 2
d= 11
a1 = first term = 7
apply the formula:
an = a1 + (n-1) d
an = 7 + (n-1) 2
an = 7 + 2n-2
an = 2n + 5
help me with this im really confused lol please
Answer:
Here is the equation in quadratic form:
x= 3±i√47/4
What is the slope of this line?
A. - 1/3
B. 1/3
C. 2/3
D. - 2/3
Answer:
2/3
Step-by-step explanation:
rise/run=slope
2 up and 3 to the right to it is 2/3
Solve the equations and check for extraneous solutions5^3^x + 14 = 78
we have the equation
[tex](5^3)^x+14=78[/tex]Solve for x
[tex]\begin{gathered} (5^3)^x=78-14 \\ (5^3)^x=64 \end{gathered}[/tex]Applying log on both sides
[tex]log((5^3)^x=log(64)[/tex][tex]\begin{gathered} xlog(5^3)^=log(64) \\ x=\frac{log64}{2log5} \end{gathered}[/tex]