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:
First of all I don't understand either, and I got it wrong.
Step-by-step explanation:
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.
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?
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
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
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?
Answer:
145
Step-by-step explanation:
i belive the answer is 145!
express -17/8 in decimal form
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
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
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 pointSince 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.
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
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
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?
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
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.
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
libreng puntoss
yeeah
PA BRAINLIEST
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?
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
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
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?
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
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?
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 .
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.
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.
Answer:
1
Step-by-step explanation:
slope = rise/run = 1/1 = 1
Sketch the graph of each line y=-9x-5
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)
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
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!
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 = 840write as a product: b^2*c^2-4bc-b^2-c^2+1
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 ☺️
Answer:
45.5
Step-by-step explanation:
Find the zeros of the function below.
\small -7x=x^2+12
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