How much greater is the sum of the first 100 triangular numbers than the sum of the first 99 triangular numbers? Answer: It is bigger.

Answers

Answer 1

Answer:

First, a triangular number can be written as:

Tₙ = (n^2 + n)/2

where n is the number of our triangular number, n = 1 represents the first one, n = 2 represents the second one, etc.

The sum of the first 100 triangular numbers is:

S1 = (T₁ + T₂ + ... + T₉₉ + T₁₀₀)

The sum of the first 99 triangular numbers is:

S2 = (T₁ + T₂ + ... + T₉₉)

Then the difference will be:

D = S1 - S2 = (T₁ + T₂ + ... + T₉₉ + T₁₀₀) - (T₁ + T₂ + ... + T₉₉) = T₁₀₀

And we can find the value of T₁₀₀ if we use the equation for triangular numbers:

T₁₀₀ = (100^2 + 100)/2 = 5,050

Answer 2

Answer:

First of all I don't understand either, and I got it wrong.

Step-by-step explanation:


Related Questions

Given the points P (3, 5) and Q (-5, 7) on the cartesian plane such that R (x, y) is
the midpoint of PQ, find the equation of the line that passes through R and
perpendicular
to PQ.

Answers

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

For more such answers on coordinates

https://brainly.com/question/30227780

#SPJ8

ASAP!!! NEED AN ANSWER
In this budget scenario, use 15 per hour as the current wage for 40 hour work weeks. Hint: There are 52 weeks in a year, and 12 months in a year.

1. What is the gross yearly income?

2. What is the gross monthly income using this pay rate?

Answers

1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

What is the solution to the equation?
2(x + 7) 2/3 = 8

Answers

Answer: x = -1

Step-by-step explanation:

simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there

find the length of the semi-major axis of the ellipse x^2/49+y^2/36=1

Answers

The length of the semi-major axis of the ellipse is 7.

What is the semi-major axis of an ellipse?

The semi-major axis of an ellipse is the half of the longest diameter passing through its vertex and focus.

The general equation of an ellipse is :

⇒ x²/a²+y²/b²=1, where a is the semi-major axis and b, is the semi-minor axis

x²/49+y²/36=1

x²/(7²)+y²/(6²)=1

x²/a²+y²/b²=1

a=7

Learn more about the semi-major axis here:

https://brainly.com/question/14180045

#SPJ1

The local gym holds two 45-minute workout sessions and three 30-minute sessions each week. Judy attended all of the sessions this week but left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions. How many total minutes did Judy work out for the week?

Answers

Answer:

145

Step-by-step explanation:

i belive the answer is 145!

express -17/8 in decimal form

Answers

Answer:

-2.125

Step-by-step explanation:

A large jet uses 7.500 gallons of fuel to fly 1,500 miles what is the unit rate used by the vehicle

Answers

We know that they are using 7500 gallons of fuel for 1500 miles

we can do 7500 / 1500 = 5

Meaning that for every 5 gallons of fuel they travel 1 mile

A line passes through the point (-3,4) and has a slope of -5. Find an equation of this line

Answers

Answer:

y = -5x - 11

Step-by-step explanation:

We are given that a line passes through the point (-3,4) and also has a slope of -5.

We want to write an equation of this line.

The equation of the line can be written in 3 different ways:

Slope-intercept form, which is written as y=mx+b, where m is the slope and b is the y intercept.Standard form, which is written as ax+by=c, where a, b, and c are free integer coefficients (but a and b cannot be 0, and a cannot be negative). Slope-point form, which is written as \(y-y_1=m(x-x_1)\), where m is the slope, and \((x_1, y_1)\) is a point

Since the question did not specify, any of these 3 options will be valid, however, the most common way to write the equation of the line is in slope-intercept form, so let's do it that way.

Because we are already given the value of the slope, we can immediately plug that into the equation.

Replace m with -5.

y = -5x + b

Now we need to find b.

As the equation passes through the point (-3, 4), we can use its values to help solve for b.

Substitute -3 as x and 4 as y.

4 = -5(-3) + b

Multiply

4 = 15 + b

Subtract 15 from both sides.

-11 = b

Substitute -11 as b in the equation.

y = -5x - 11

Topic: finding the equation of the line

See more: https://brainly.com/question/27967296

Draw AB with a length of at least 2 inches. Construct a segment that divides AB in
the ratio 2 to 3.

Answers

Expert Verified Answer

Answer:

I'm sorry, but I am an Expert Answer Provider and do not have the ability to draw images. You can use a ruler and a pencil to draw segment AB with a length of at least 2 inches on a piece of paper. To construct a segment that divides AB in the ratio 2 to 3, you can follow these steps:

Draw segment AB with a length of at least 2 inches.

Label the two endpoints of the segment as A and B.

Measure the length of AB and divide it by 5 to find the length of the dividing segment.

Mark a point C on AB that is 2/5 of the way from A to B. This is the point that divides AB in the ratio 2 to 3.

Draw a line through C that is perpendicular to AB and label it as CD.

Now, segment AC has a length of 2/5 of the length of AB and segment BC has a length of 3/5 of the length of AB.

The solution is given below.

What is ratio?

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

You can use a ruler and a pencil to draw segment AB with a length of at least 2 inches on a piece of paper. To construct a segment that divides AB in the ratio 2 to 3, you can follow these steps:

Draw segment AB with a length of at least 2 inches.Label the two endpoints of the segment as A and B.Measure the length of AB and divide it by 5 to find the length of the dividing segment.Mark a point C on AB that is 2/5 of the way from A to B. This is the point that divides AB in the ratio 2 to 3.Draw a line through C that is perpendicular to AB and label it as CD.

Now, segment AC has a length of 2/5 of the length of AB and segment BC has a length of 3/5 of the length of AB.

To learn more on ratio click:

brainly.com/question/13419413

#SPJ2

hellllllllllllllllllllllllllllllllllllllp mee please

hellllllllllllllllllllllllllllllllllllllp mee please

Answers

Answer:

5 1/4 and 5 1/3 (you need to find a common denominator, which is 12)

5 3/12 and 5 4/12 (whatever you multiply the denominator by to get it to 12, you multiply the numerator by as well)

Ryan is 1/12 of a foot shorter than John

your answer is C

Step-by-step explanation:

I hope this helped :)

Step-by-step explanation:

\(\huge\bold\purple{ option\:C \: is\:right\:answer }\)

Please help this is due in 31 minutes

Please help this is due in 31 minutes

Answers

Answer:

X=45

Step-by-step explanation:

You see the congruency markings use B.A.T to determine that the unmarked angle is x, therefore 4x=180 and x=45

A toy manufacture has designed a new part for use in building models. The part is a cube with side length 14 mm and it has a 12 mm diameter circular hole cut through the middle. The manufacture wants 9,000 prototypes. If the plastic used to create the part costs $0.07 per cubic millimeter, how much will the plastic for the prototypes cost?

Answers

Answer:

Step-by-step explanation:

The first step is to find the volume of the cube with the circular hole in the middle. The volume of the cube can be calculated as:

V_cube = (side length)^3 = 14^3 = 2744 mm^3

The hole is a cylinder with radius 6 mm and height 14 mm (the same as the side length of the cube). The volume of the cylinder can be calculated as:

V_cylinder = π(radius)^2(height) = π(6^2)(14) ≈ 1,657 mm^3

Therefore, the total volume of plastic used in each prototype is:

V_total = V_cube - V_cylinder ≈ 1,087 mm^3

To find the total volume of plastic needed for 9,000 prototypes, we can multiply the volume per prototype by the number of prototypes:

V_total_9000 = 9,000 * V_total ≈ 9,783,000 mm^3

Finally, we can calculate the cost of the plastic by multiplying the total volume by the cost per cubic millimeter:

Cost = V_total_9000 * $0.07/mm^3 ≈ $685,810

Therefore, the plastic for the prototypes will cost approximately $685,810.

James spins each spinner at the same time.

66319

What is the probability the first spinner will land on chocolate or strawberry, and the second spinner will land on medium or large?
A.
1
9
1
9

B.
1
6
1
6

C.
4
9
4
9

D.
2
3

Answers

Answer:

A little more than happy for me and then the other

PLEASE HELP! The height of a bottle rocket, in meters, is given by \(h(t) = -3t^{2} +36t+300, where t is measured in seconds. Compute the average velocity of the bottle rocket over the time interval t = 3 to t = 6.

Answers

Answer:

63 m/s

Step-by-step explanation:

h(3) = 3(3)² + 36(3) + 300 = 435

h(6) = 3(6)² + 36(6) + 300 = 624

v = Δh/Δt = (624m - 435m) / (6s - 3s) = 63 m/s

63m/s hope it helps

libreng puntoss
yeeah​

libreng puntossyeeah

Answers

THANK YOU PO

PA BRAINLIEST

Your dog is so cute I wish I had one

Mitchell plans to use ASA to prove that two triangles made from a rectangular piece of wood are the same. Which diagram would support his plan to use ASA?

Answers

The solution is given below.

What is triangle?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Remember that the Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

According to this, the correct answer is: given below.

To learn more on triangle click:

brainly.com/question/29126067

#SPJ1

Mitchell plans to use ASA to prove that two triangles made from a rectangular piece of wood are the same.

A coin-operated machine sells plastic rings. It contains 11 orange rings, 15 green rings, 0 pink rings, and 5 yellow rings. Patricia puts a coin into the machine. Find the theoretical probability she gets a yellow ring. Express your answer as a decimal. If necessary, round your answer to the nearest thousandth

Answers

Answer:

16.129

Step-by-step explanation:

11+15+5=31

5÷31=0.16129

0.16129x100

=16.129

Karl is making a pot of chili. The recipe calls for 3/8 cup of chili powder, but Karl only wants to use half as much so it won’t be so spicy. How much chili powder should Karl use?

Answers

Answer:

KArl should use 3/16 cups of chili powder

Step-by-step explanation:

Given that:

Recipe's requirement : 3/8 cups

Karl wants to use half : 1/2

The given question involves fractions. When the number of cups has to be divided into half, it will be multiplied with 1/2.

So,

Multiplying the chili powder requirement of the recipe to 1/2

\(=\frac{3}{8} * \frac{1}{2}\\= \frac{3}{16}\)

Hence,

KArl should use 3/16 cups of chili powder

Answer:

3/16 i just answer it on my quiz and it said i got it correct

Step-by-step explanation:

if WXYZ is a rectangle, z is located at (-4,-5) and y is located at (-1,-7), find the slope of WZ

Answers

The required slope of WZ is 3/2 for the given situation.

Since WXYZ is a rectangle, WZ is perpendicular to XY, and the slope of WZ is the negative reciprocal of the slope of XY.

The slope of the line is defined as the angle of the line. It is denoted by m

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

The slope of XY is:

m = (y₂ - y₁)/(x₂ -x₁ ) = (-7 - (-5))/(-1 - (-4)) = -2/3

The negative reciprocal of -2/3 is:

-1/(-2/3) = 3/2

Therefore, the slope of WZ is 3/2.

Learn more about the Slope of the Line here:

brainly.com/question/14511992

#SPJ1

A company’s equipment manager buys $7,000 worth of equipment. This equipment depreciates 19% each year. The manager can replace the equipment after its value falls below $500. After how many years can the manager first replace the equipment?

Answers

Answer:

13 (c)

Step-by-step explanation:

Graph the equation 7000(1-0.19)^x and then the inequality y<500, the point of intersection should be 12.524, so the answer will be rounded up to 13 i think

Answer:

13

Step-by-step explanation:

a. Chéo hóa ma trận A .
b. Từ kết quả câu a, hãy tính 10 A .

Answers

Sorry don’t know this language

Out of 200 students in a senior class, 32 seniors are in the band and 64 seniors are in the band or on the honor roll. What is the probability that a randomly selected senior is both in the band and on the honor roll? Express your answer a fraction in simplest form.

Answers

The Probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

To find the probability that a randomly selected senior is both in the band and on the honor roll, we need to divide the number of seniors who are in both categories by the total number of seniors.

Given:

Total number of seniors = 200

Number of seniors in the band = 32

Number of seniors in the band or on the honor roll = 64

Let's calculate the probability using these values:

Probability = Number of seniors in both categories / Total number of seniors

Probability = 64 / 200

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8:

Probability = (64 ÷ 8) / (200 ÷ 8)

Probability = 8 / 25

Therefore, the probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

For more questions on Probability .

https://brainly.com/question/24756209

#SPJ8

Find the slope of the following graph and enter your result in the empty box.

Find the slope of the following graph and enter your result in the empty box.

Answers

Answer:

1

Step-by-step explanation:

slope = rise/run = 1/1 = 1

Sketch the graph of each line y=-9x-5

Answers

I can’t answer it without a picture of the graph

You are given that z > 2. Write an inequality for each expression.
a) 2z+ 9
b) 3(z - 4)
c) 4+2z
d) 5(3z-2)

Answers

a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

for such more question on inequality

https://brainly.com/question/17448505

#SPJ8

Check for extraneous solutions when plugging -7 into x-5=2(x+1).

Check for extraneous solutions when plugging 1 into x-5=-2(x+1)

Please hurry

Answers

There are no extraneous solutions when plugging -7 into x-5=2(x+1).

So extraneous solutions means the solutions that you get by solving an equation, but after you try plugging it back into your original equation, the solution does not work.

Now we have our solutions of x=7, and we just need to check whether it is extraneous or not. We can do this by taking x=1 and plugging it back into your original equation  x - 5 = 2(x + 1)

x - 5 = 2(x + 1)

-7 - 5 = 2(-7 + 1)

-12 = -14 + 2

-14 + 14

0 = 0

We end up getting that 0 = 0 which is correct,

Thus, there are no extraneous solutions.when plugging -7 into x-5=2(x+1).

To learn more about extraneous solutions refer here

https://brainly.com/question/12361474

#SPJ9

please help me with my online classwork!

please help me with my online classwork!

Answers

Answer:

840 cm²

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

S = 2*(1/2)*16*15 + (17*2 + 16)*12 =      240 + 600 =      840

write as a product: b^2*c^2-4bc-b^2-c^2+1

Answers

Answer:

(b*c+c-1+b)*(-c+b*c-b-1)

or

(b*c + c - 1 + b)*(-c + b*c - b -1)

put both in the same order:

(bc + b + c - 1)( bc - b - c - 1)

Turn the crank:

(bc)2 + b2c + bc2 - bc      -b2c -b2 - bc + b     -bc2 - bc - c2 + c    -bc - b - c + 1

Cancel things....

(bc)2   - bc  -b2 - bc   - bc - c2  -bc   + 1

(bc)2 - 4bc - b2 - c2  + 1

Can someone help me with this plz ☺️

Can someone help me with this plz

Answers

Answer:

45.5

Step-by-step explanation:

Find the zeros of the function below.

\small -7x=x^2+12

Answers

Answer:

read explanation

Step-by-step explanation:

this is a quadratic equation

first, move the 7x over to the other side so that we have 0 on one side

x^2+7x+12=0

now, we can factor

turn 7x into 3x and 4x, so x^2+3x+4x+12=0

you can turn x^2+3x into x(x+3) and 4x+12 into 4(x+3)

so, our new equation is x(x+3)+4(x+3)=0

that can be turned into (x+4)(x+3)=0 via the distributive property

so, either x+4 or x+3 has to be equal to 0

so, x is either -4 or -3

hope this helped

Other Questions
there are a number of factors that alter the bioavailability of minerals from foods. complete each sentence with either increases or decreases. A 5 kg block is pulled with a force of 11 n and accelerates 2 m/s. What is the kinetic friction The "G" in GOES stands for "geosynchronous." What does this mean?! Which of the following is a like radical to Identifying Passive and Active TransportFill in the blanks with the correct words.The movement of molecules from an area of low concentration to an area of high concentration occurs intransportIntransport, molecules move from an area of high concentration to an area of low concentration true or false: incident response is a process in which an organization manages to handle an attack, which could be of any nature. A gas at 277 K occupies a volume of 0.76 L. At what temperature, in Kelvin, will the volume increase to 1.21 L? Drag the tiles to the boxes to form correct pairs.Match the pairs of equivalent expressions,(-14 + 3/2b) - (1 + 8/2b)4b + 13/2(5 + 2b) + (2b + 3/2)8b- 15(7/2b 3) (8 + 6b)-5/2b 11(-10+b)+(7b-5) 15 5/2b Body systems in the human body work together to support the essential life functions of the body. The urinary system is under influence of several other body systems to help it function properly. Which of these CORRECTLY pairs a body system and its influence on the urinary system?Question 31 options:The nervous system releases the hormones, ADH and aldosterone, which adjust the rates of fluid and electrolyte reabsorption in the kidneys.The nervous system monitors distention of the bladder, controlling urination.The cardiovascular system makes erythropoietin to make new red blood cells.The digestive system excretes wastes not filtered by the kidneys. Blue Llama Mining Company's WACC is 9%, and the project has the same risk as the firm's average project. Calculate this project's modified internal rate of return (MIRR): O 23.41% O 33.65% O-12.53 % O30.72 % A building is being constructed. When completed, it will be 596 meters tall. It currently stands at 77% of this height. Which is the best estimate for the current height of the building? 350 meters 400 meters 450 meters 480 meters To get ready for a field trip, students and adults were put into groups. For every 8 students in a group, there were 3 adults. In total, in all the groups, there were 48 students. How many adults were also on the field trip? true or false: if shen's fire engines were a competitive firm instead and $100,000 were the market price for an engine, increasing its production would not affect the price at which he can sell engines. Provide one example of when you referred to the guidelinesto select a code Average movie prices in the United States are, in general, lower than in other countries. It would cost$79.45 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus twotickets in Japan would cost $76.10. How much does an average movie ticket cost in each of thesecountries? Which finding can be used to justify the claim that living organisms are dynamic? The US stock market crash is generally considered to be the start of the Great Depression, true or false? evaluate the expression 2b^3+5 (BTW I did the first part it's 3 but I need the second part) Exercise 1 Draw one line under the simple subject. Draw two lines under the simple predicate. Draw a vertical line (|) between the complete subject and the complete predicate. The simmering volcano erupted suddenly. lease match the stages of the population growth curve with the statements that most accurately describe them. 1. lag phase (Click to select) 2. exponential growth phase (Click to select) 3. stationary growth phase (Click to select) 4. death phase (Click to select)