The sum of finite arithmetic series 1+4+7+ . . . . . .+31 is S(11) = 176
The given arithmetic series is:
1+4+7+ . . . . . .+31
From the above series, we know that:
The first term, a(1) = 1
The last term, a(n) = 31
The common difference, d = 4 - 1 = 3
Recall the formula to find the nth term of an arithmetic sequence:
a(n) = a(1) + (n-1) . d
Substitute a(1) = 1, a(n) = 31, and d = 3:
31 = 1 + (n-1) . 3
31 = 3n - 2
3n = 33
n = 11
In an arithmetic series, the sum of the first n terms is given by:
S(n) = n/2 [ a(1) + a(n) ]
Substitute n = 11, a(1) = 1, and a(n) = 31:
S(n) = 11/2 (1 + 31)
S(11) = 11. 16 = 176
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What is the value of this product
Answer:
The value of the product is 2²
Write a coordinate proof to prove that Δ A B C is an isosceles triangle if the vertices are A(0,0), B(a, b) , and C(2 a, 0) .
An isosceles triangle is one with two equal-length sides. ΔABC is an isosceles triangle.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²] units.
Given that the coordinates of the vertices of the triangle are A(0,0), B(a, b), and C(2a, 0). Now, to prove that the given triangle is an isosceles triangle we need to find the length of each side of the triangle.
AB = √[(x₂-x₁)² + (y₂-y₁)²]
= √[(a - 0)² + (b - 0)²]
= √(a² + b²)
BC = √[(x₂-x₁)² + (y₂-y₁)²]
= √[(2a - a)² + (0 - b)²]
= √(a² + b²)
AC = √[(x₂-x₁)² + (y₂-y₁)²]
= √[(2a - 0)² + (0 - 0)²]
= √4a²
= 2a
Since the length AB and BC are the same, while the length of AC is different, therefore, ΔABC is an isosceles triangle.
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Evaluate x³ for x = 2.
06
02
08
Answer:
8
Step-by-step explanation:
x³; x = 2
2³ or 2 × 2 × 2 = 8
I hope this helps!
Write each number as a percent.
1(2/5)
Tyrone needs 50 volunteers for a concert.
Tyrone has 20% more volunteers than
he needs. Tyrone assigns 15% of the total
volunteers to the stage area. How many
volunteers does Tyrone assign to the
stage area?
Answer:
go
Step-by-step explanation:
i don't understand this shirty app
Answer: 9
Step-by-step explanation:
20% of 50 is 10. So, he has a total of 60 volunteers. He uses 15% of that for the stage area, and 15% of 60 is 9. So, Tyrone assigned 9 volunteers to the stage area.
Problem: using the digits -9 to 9 at most one time each, place a digit on each box to create an equation whose solution is a positive whole number. ("_" is what i need to fill in and the "/" are fractions)
_/_(x)+_/_= _
Considering division signal rules, one possible example of an equation that results in a positive number is:
-9/-3 + 3/1 = 6.
When does a division results in a positive number?A division(fraction) results in a positive numbers if the two terms have the same signal, either both positive or both negative.
Hence, to ensure an expression with a positive result in this problem, the terms in each division got to have the same signal, as the example that follows:
-9/-3 + 3/1 = 6.
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how do i subtract inteargers
Answer:
You remove the difference between the two numbers from each other. E.g., 5-2=3, and 6-4=2.
Step-by-step explanation:
The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $13 per month plus $0.04 per call.
a. Use an inequality to find the 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:
Step-by-step explanation:
The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $15 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
Suppose line l contains points A, B , and C , If A B=7 inches, A C=32 inches, and point B is between points A and C , what is the length of BC? Express your answer in inches.
Length of BC is 25 inches.
Here,
Line l contains points A, B and C.
A B =7 inches, A C = 32 inches, and point B is between points A and C.
We have to find the length of BC in inches.
What are Collinear points?
If two or more points are lie on a straight line then points are called Collinear points.
Now,
Line l contains points A, B and C.
Point B is between points A and C.
Length of A B = 7 inches and A C = 32 inches
Hence, Length of BC = Length of AC - Length of A B
= 32 - 7 = 25 inches.
Therefore, Length of BC is 25 inches.
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3x3 what is the sum to this..?
Answer:
9
Step-by-step explanation:
3x3=9
Answer:
the sum is 9
Step-by-step explanation:
3×1=3
3×2=6
3×3=9
Two different tests to write k/4 +16
Step-by-step explanation:
\begin{gathered}6x - 2y = 6 \\ 6x = 6 + 2y \\ x = \frac{6 + 2y}{6} \end{gathered}
6x−2y=6
6x=6+2y
x=
6
6+2y
The table shows the elevation above sea level of the lowest and highest points in the United States.
Location
Death Valley
Mount McKinley/Denali
Elevation Above Sea Level (feet)
-282
20,310
Choose three correct statements.
A. Death Valley is -282 feet below sea level.
B. Death Valley is 1-2821 feet below sea level.
C. Death Valley is 1-2821 feet above sea level.
D. Mount McKinley/Denali is 120, 310| feet below sea level.
E. Mount McKinley/Denall is-120, 3101 feet below sea level.
F. Mount McKinley/Denali is 1-20, 3101 feet above sea level.
Location Death Valley, Mount McKinley/Denali Elevation Above Sea Level (feet), then the statement B , statement E , statement F are correct.
Death Valley is |-282| feet below sea level. Mount McKinley/Denali is |-20, 310| feet below sea level.Mount McKinley/Denali is |-20, 310| feet above sea level.These three statements are correct.
The table shows the elevation above sea level of the lowest and highest points in the United States.
Location Death Valley
Mount McKinley/Denali
Elevation Above Sea Level (feet)
So, we can write,
Death Valley is |-282| feet below sea level.Mount McKinley/Denali is |-20, 310| feet below sea level.Mount McKinley/Denali is |-20, 310| feet above sea level.You are subtracting the two numbers. Note however, that 282 feet below the sea level = -282
Subtract.
⇒ 20310 - (-282)
Note that two negatives = one positive
⇒ 20310 + 282
⇒ 20592 feet
Therefore, The statement B , statement E , statement F are correct.
Hence,
Death Valley is |-282| feet below sea level. Mount McKinley/Denali is |-20, 310| feet below sea level.Mount McKinley/Denali is |-20, 310| feet above sea level.These three statements are correct.
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Write a relationship for a function whose hx values are 6 less than the cube of x
The mathematical expression from the algebraic expression is a x^3 - 6.
According to the statement
We have to find that the expression of the statement in the mathematical form.
So, For this purpose, we know that the
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
From the given information:
The hx values are 6 less than the cube of x
Then
To convert into the mathematical form:
The cube of the x is in the mathematical form is a x^3
Then
And the 6 less than the cube
And in the mathematical form it becomes the
x^3 - 6.
So, The mathematical expression from the algebraic expression is a x^3 - 6.
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Square root of 9 =3=3=3 and 1 half + 1 half
Write two absolute value functions such that they have a common vertex in Quadrant III and one is the reflection of the other in a horizontal line.
The functions
y = -|x + 4| - 5y=−∣x+4∣−5
y = |x + 4| - 5y=∣x+4∣−5
Both these functions have got a common vertex in the third Quadrant.
They are the reflections of each other in a horizontal line.
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Determine whether each sequence is geometric. If so, find the common ratio. 10,4,1.6,0.64, . . . . .
The given sequence is geometric, with common ratio = 0.4.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Now, Given: 10, 4, 1.6, 0.64, ....
Here, [tex]\frac{4}{10}=\frac{1.6}{4}=\frac{0.64}{1.6}=0.4[/tex]
That is, the given sequence follows the only necessary condition for a sequence to be geometric.
Hence, The given sequence is geometric, with common ratio = 0.4.
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Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
To solve problems, construct one-variable equations and inequalities.
How to use them to solve problems?As opposed to an inequality, which links two different values, an equation declares that two expressions are equal.
Create one-variable equations and inequalities, then utilize them to solve issues.
Include simple rational and exponential equations as well as those resulting from linear and quadratic functions.
In order to answer word problems, students should be able to decipher them and create equations and inequalities.
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You want to buy a new iPhone 50 that costs $1330 including taxes(13%). How many hours will you have to work to be able to buy this new phone if you make minimum wage which is $14.25 per hour?
Answer:
105.47 hours
Step-by-step explanation:
1300x0.13=172.9
172.9+1300=1502.9
1502.9/14.25=105.47
Jan and Dinah both ran for 20 seconds, each at a constant speed. Jan ran 50 mefers and Dingh ran 60 meters. 1. Who was moving faster? Explain how you know. 2. How far did each person move in 1 second?
By calculating speed of each person we can find who is faster.
What is Speed?Speed can be defined as the distance covered with respect to time. It is a scalar quantity. It is calculated as follows
Speed = Distance / Time taken
The time taken by each person is 20 seconds.
Distance covered by Jan = 50 meter
Speed of Jan = Distance / Time taken
Speed of Jan = 50 / 20
Speed of Jan = 2.5 meters per second
Distance covered by Dingh = 60 meter
Speed of Dingh = Distance / Time taken
Speed of Dingh = 60 / 20
Speed of Dingh = 3 meters per second
Since the speed of Dingh is more than Jan, we can say that Dingh is faster.
Distance = Speed × Time taken
Here, time taken = 1 second
This implies Distance Covered = Speed
Therefore, Jan covers 2.5 meters in one second while Dingh covers 3 meters in one second.
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What can you say about and based on the sum of their angles? How are the angles related?
Answer: Do you have a picture of the problem so it will be more sense?
Step-by-step explanation:
What sets (types or categories) of numbers do we use as the input to functions that represent sequences?
Answer:
electrical is a good servant but master
96240 is divisible by 2,3,5,10 true or false
True
It's true, 96240 is divisible by 2,3,5,10
Hope this helps!
50 points
add and write the fraction in its simplest form.
-7/8 + (-2 1/6) =
Answer:-3 1/24
Step-by-step explanation:
I Need help pls i forgot what to do with this math problem
Answer:
-8^3/7^3 = -512/343
Step-by-step explanation:
3√ (-512/343) = 3√-(8/7)^3 = -8/7
-8^3/7^3 = -512/343
Number 7 is the one I need help with please
Answer:
23
Step-by-step explanation:
Two tents are in the shape of hemispheres, with circular floors. The ratio of their floor areas is 9: 12.25 . If the diameter of the smaller tent is 6 feet, what is the volume of the larger tent? Round to the nearest tenth.
The volume of the larger tent in the shape of hemispheres, with circular floors, is 89.8 cubic feet.
If the diameter of the smaller tent is 6 feet, then its radius is 3 feet. Solving for the area of its circular floor,
A = πr^2
A = π(3 feet)^2
A = 9π square feet
Using the ratio of the floor areas of the two tents, calculate the area of the circular floor of the larger tent.
9 : 12.25 = 9π square feet : x
where x = area of the circular floor of the larger tent
9x = 12.25(9π)
x = 12.25 π square feet
If the area of the circular floor of the larger tent is 12.25 π square feet, then solving for its radius,
A = πr^2
12.25 π square feet = πr^2
r = 3.5 feet
Hemisphere refers to half of a sphere and its volume is given by the formula V = 2/3πr^3, where r is the radius.
V = 2/3πr^3
V = 2/3 π (3.5 feet)^3
V = 89.79719002 cubic feet
Rounding off to the nearest tenth.
V = 89.8 cubic feet
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Paul collects comic books. He has 20 books in his collection, and he adds 3 per month. In how many months will he have a total of 44 books in his collection?
F. 5
G. 6
H. 8
J. 15
In 8 months he will have a total of 44 books in his collection.
The correct answer is an option (H)
In this question,
Paul collects comic books. He has 20 books in his collection, and he adds 3 per month.
We need to find the number of months required to have a total of 44 books in his collection.
Let n be the required number of months.
From given information, we get an equation,
20 + 3n = 44
We solve above equation to find the required number of months.
20 + 3n - 20 = 44 - 20
3n = 24
n = 8
Therefore, in 8 months he will have a total of 44 books in his collection.
The correct answer is an option (H)
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identify the inequalities A, B , and C for which the given ordered pair is a solution.
A. x+y ≤ 2
B. y ≤ (3/2)x-1
C. y>-(1/3)x-2
(-8,-11)
The inequality y ≤ (3/2)x-1 satisfies the point (-8, -11) option (B) y ≤ (3/2)x-1 is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The point is (-8, -11)
As we have inequalities shown in the option:
After plotting the inequality in the graph:
From the graph, the point lies in the solution region of the inequality y ≤ (3/2)x-1 which means the point (-8, -11) satisfies the inequality.
Thus, the inequality y ≤ (3/2)x-1 satisfies the point (-8, -11) option (B) y ≤ (3/2)x-1 is correct.
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Simplify.
2 + 8 - 2 [32 + 5 (1 + 2)]}
Your answer should be - 84.
Explanation:
Starting equation: [tex]2\:+\:8\:-\:2\:\left[32\:+\:5\:\left(1\:+\:2\right)\right][/tex]
-Calculate within parentheses [32 + 5 (1+2)] = 47.
Remaining equation: 2 + 8 - 2 x 47
-Multiply and divide (left to right) 2 x 47 = 94
Remaining equation: 2 + 8 - 94
-Add and subtract (left to right) 2 + 8 - 94 = -84
Your final answer is -84
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Hope this helps!
Have a great day and God bless! :)
Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (-2,3)
The equation of the circle that passes through the point (-2 , 3) and has a center at the origin is x^2 + y^2 = 13.
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-2 , 3).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(-2 - 0)^2 + (3 - 0)^2
radius= √4 + 9
radius = √13
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = √13
(x - 0)^2 + (y - 0)^2 = (√13)^2
x^2 + y^2 = 13
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