Given:
The sequence is 29, 22, 15, 8, 1, ...
To find:
The common difference.
Solution:
We have,
29, 22, 15, 8, 1, ...
It is an AP.
First term : [tex]a_1=29[/tex]
Second term : [tex]a_2=22[/tex]
Now,
Common difference : [tex]d=a_2-a_1[/tex]
[tex]d=22-29[/tex]
[tex]d=-7[/tex]
Therefore, the correct common difference is -7.
Note: Here calculation by student is not given, so we cannot find the error of the student.
Solve the system using Gaussian elimination. 6x−y+3z=−9 5x + 5y−5z = 20 3x−y+4z = −5 A (2,12,−3)open paren 2 comma 12 comma negative 3 close paren B (2,2,0)open paren 2 comma 2 comma 0 close paren C (−1,6,1)open paren negative 1 comma 6 comma 1 close paren D (−2,6,3)
Answer:
C. (-1,6,1)
Step-by-step explanation:
Given the system of equation
6x−y+3z=−9 ...... 1
5x + 5y−5z = 20 ...... 2
3x−y+4z = −5 ...... 3
Reduce the equations to two variables with 2unknown
Multiply equation 3 by 2 and add to 1.
Equation 3×2; 6x−2y+8z = −10 ...... 4
Subtract 4 from 1
-y-(-2y)+3z-8z = -9-(-10)
-y+2y-5z = -9+10
y-5z = 1 ...... 5
Also multiply eqn 2 by 3 and 3 by 5
Equation 2×3; 15x+15y-15z= 60
Equation 3×5; 15x-5y+20z = -25
Subtract
15y+5y-15z-20z = 60+25
20y-35z = 85
Divide through by 5:
4y-7z = 17 ...... 6
...................................
Solve 5 and 6
y-5z = 1 ...... 5 × 4
4y-7z = 17 ...... 6 × 1
....................................
4y-20z = 4
4y-7z = 17
Subtract
-20z+7z = 4-17
-13z = -13
z = -13/-13
z = 1
Substitute z = 1 into equation 5 to get y:
From 5: y-5z = 1
y - 5(1) = 1
y-5 = 1
y = 1+5
y = 6
Substitute y = 6 and z = 1 into equation 3 to get x;
From 3: 3x−y+4z = −5
3x-6+4(1) = -5
3x -6+4 = -5
3x-2 = -5
3x = -5+2
3x = -3
x = -3/3
x = -1
Hence x = -1, y = 6 and z = 1
The correct answer is (-1, 6, 1)
Please help me answer this question on congruent triangles. 30 points available.
Answer:
Pair A are not congruent.
To prove two triangles are congruent, 3 equal angles aren't sufficient.
Pair B are not congruent as well.
To prove they are congruent using ASA we have to make sure the given equal side lies between the 2 angles, which it is not.
They are not congruent
For this sequence describe (in words) a way to produce each new term from the previous term.
Find common ratio:-
1/9/(1/3)=31/3(3)=11(3)=33(3)=9Just Multiply 3 with previous term to get next one
Please help with homework
The drawing shows how to___?
A. Construct an angle congruent to a given angle
B. construct an equilateral triangle
C. draw an angle bisector
D. draw a perpendicular line through a point on the line
Answer:
C. draw an angle bisector
Step-by-step explanation:
which of the following lines are perpendicular to the line y= 3/4x - 8? select all that apply
a. y=4/3x+8
b.y=-4/3x-12
c.y+4/3x=2
d.y-3/4x=1
e.6y=-8x+12
Answer:
B and C that's the answers
600 people attended a football game. If 25% of the people who attended were teenagers, how many teenagers attended the game?
Answer:
150 Teenagers would have attended the game
What is the £ to € exchange rate?
a car travelled 300km and used 24 litres of petrol.
1) ) how many litres of petrol is needed by the car to travel 400km?
2) how far can the car travel if it's petrol tank has 36 litres of petrol?
Answer:
1. 8liters
2.5
Step -by - step explaination:
8litres= 100
16litres=200
24litres=300
32litres=400
and so on
Find the approximate radius of a circle with a circumference of 7.92 centimetres. Use 3.14 for Π. Round to the nearest hundredth if needed.
Answer:
1.26
Step-by-step explanation:
Using the equation that the of the circumference:
C = 2Πr, you can plug in the given circumference:
7.92 = 2(3.14)r | Now you can isolate r:
7.92 = 6.28r
7.92/6.28 = r
r =1.26
Write a word problem using rational numbers and using at least two of the operations (add, subtract, multiply, divide).
Alicia had - $11.00 in her checking account. She did a few chores and made $44.50. She decided to pay for her and a friend to go to the movies and each ticket costs $6.25. How much money does she have left in her account?
There are 30 students in Mrs.
Woodward’s class and 15 of the class has their own cell phone. Of this group of students, 12 of them
are allowed to use social media. How many of the students have a cell phone and can use social media?
There are two up there
What is the ratio 15 : 24 written in lowest terms? 0 3:4 07:8 0 3:5 c 5:8
Answer 5:8
Step-by-step explanation:
Question in the photo :) (Please help with my other questions!)
Answer:
a
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]u_{n}[/tex] = u₁ + (n - 1)d
given u₂₀ = 100 and u₂₅ = 115 , then
u₁ + 19d = 100 → (1)
u₁ + 24d = 115 → (2)
subtract (1) from (2) term by term to eliminate u₁
0 + 5d = 15
5d = 15 ( divide both sides by 5 )
d = 3
substitute d = 3 into (1) and solve for u₁
u₁ + 19(3) = 100
u₁ + 57 = 100 ( subtract 57 from both sides )
u₁ = 43
Answer:
a) u₁ = 43, d = 3
Step-by-step explanation:
Given :-
u₂₀ = 100
u₂₅ = 115
To Find :-
u₁ and d
Solving :-
u₂₀ = u₁ + 19d = 100 -(1)
u₂₅ = u₁ + 24d = 115 -(2)
(2) - (1)
5d = 15
d = 3
u₁ + 19(3) = 100
u₁ + 57 = 100
u₁ = 43
Solution :-
a) u₁ = 43, d = 3
A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 8 faculty members and 13 students eligible to serve on the committee. In how many ways can the committee be formed?
Answer:
Step-by-step explanation:
This question bothers on combination. combination has to do with selection.
If 4 faculty members are chosen from total of 8 faculty members, this can be done in 8C4 number of ways.
8C4 = 8!/(8-4)!4!
8C4 = 8!/4!4!
8C4 = 8*7*6*5*4!/4!*4*3*2
8c4 = 8*7*6*5/24
8C4 = 7*5*2
8C4 =70 ways
Similarly, 5 students are to be selected from a pool of 13 students, this can be done in 13C5 number of ways.
13C5 = 13!/(13-5)!5!
13C5 = 13!/8!5!
13C5 = 13*12*11*10*9*8!/8!*5*4*3*2
13C5 = 13*12*11*10*9/120
13C5 = 1,287 ways
The total number of ways the committee can be formed is 8C4 * 13C5 = 70*1287
The total number of ways the committee can be formed is 90,090 ways
Choose the best selection for the
quadrilateral with vertices at the
following points:
(0,0), (0,4), (8,4), (8,0)
A. Rectangle
B. Square
C. Rhombus
D. Trapezoid
The quadrilateral with vertices (0, 0), (0, 4), (8, 4) and (8,0) makes the rectangle.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
The given points are,
(0, 0), (0, 4), (8, 4) and (8,0).
To determine the section for the quadrilateral,
Find distance between points.
The distance between two points A(x₁, y₁) and B(x₂, y₂)
Distance
= √(x₂ - x₁)² + (y₂ - y₁)²
The distance between (0, 0) and (0, 4)
= √(0-0)² + (4-0)² = √(0)² + (4)² = √(4)² = 4
The distance between (0, 4) and (8, 4)
= √(8-0)² + (4-4)² = √(8)² + (0)² = √(8)² = 8
The distance between (8, 4) and (8, 0)
= √(8 - 8)² + (0 - (4))² = √(0)² + (4)² = √(4)² = 4
The distance between (8, 0) and (0, 0)
= √(0 - 8)² + (0- 0)² = √(-8)² + (0)² = √(8)² = 8
Since, the opposite sides are equal,
Therefore, the quadrilateral is rectangle.
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when is the temperature constant?
Answer:
From 11 am until 2 pm
Step-by-step explanation:
The line is straight meaning its constant throughout the time 11pm - 2pm, it is neither rising nor falling like the other two.
The roaming cell phone company charges $15.00 per month plus $0.20 per minute of airtime usage. If Juanita uses x minutes of airtime, what is an equation that can be used to determine her monthly cell phone bill (C)?
Answer:
$63.00
Step-by-step explanation
Since you have sales tax, you would do a 10% sales tax for 15 dollar
10/100 = x/15
Therefore you will calculate x and 100 divided by 15 which would be 6.6 repeated
You would round to the nearest tenth and get 6.6 then you would add 56.4 as in the tip+ month airtime usage and get 63 dollars
brainly please...maybe
Answer with step-by-step explanation:
x = $63.00
Since you have sales tax, you would do a 10% sales tax for 15 dollar
Equation = 10/100 = x/15
Therefore you will calculate x and 100 divided by 15 which would be 6.6 repeated
You would round to the nearest tenth and get 6.6 then you would add 56.4 as in the tip+ month airtime usage and get 63 dollars.
Hope this helped! (brainliest please)
PLEASE ANSWER THIS QUESTION I WILL GIVE BRAINLIEST!!!
Find the value of x in this case-
Already answered here: https://brainly.com/question/26946183
EASY POINTS
Thomas has some leftover paint that he would like to sell. He mixes
4 3/8
gallons of blue paint with 6 5/8
gallons of white paint. Then, he pours this light-blue mixture into
1/4
gallon containers. To find out how many of these
1/4
gallon containers he can fill, which two equations would you need?
Answer:
4 3/8+6 5/8=x and x÷1/4=number of gallons
Answer:
4 3/8+6 5/8=x and x÷1/4=number of gallons
Step-by-step explanation:
1. What is the correct reason for statement #3?
2. What is the correct reason for statement #4?
3.What is the coolest reason for statement #5?
Answer:
1) B. Combine-like terms
2) A. Subtraction Property of Equality
3)D. Division Property of Equality
Step-by-step explanation:
Write the equation y=3/4x-4 in standard form
The equation 3x - 4y = 16 is now in standard form, where A = 3, B = -4, and C = 16.
To convert the equation y = (3/4)x - 4 into standard form, we need to eliminate any fractions and rewrite it in the form Ax + By = C, where A, B, and C are integers.
The given equation is already almost in standard form, but we can proceed with the following steps:
Step 1: Multiply both sides by 4 to eliminate the fraction:
4y = 3x - 16
Step 2: Move all terms to one side of the equation to have zero on the other side:
3x - 4y = 16
The equation 3x - 4y = 16 is now in standard form, where A = 3, B = -4, and C = 16.
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Aline etlea, deux coiffeuses contactent le même. fournisseur . Aline commande 10 lots de champoing à 15,60 l,unite et paie la meme somme que lea qui a commande 2 tondeuses et 2 lots dechampoing. Combien coûte une tondeuse? c,est undm note aidez moi reponse
Answer:
on my screen it sayes its 50938
Step-by-step explanation:
Add. Enter a number only as your answer in the space provided
Please I really need help
Answer:
0 is the answer okay
Step-by-step explanation:
0 is the answer okay
in an election, candidate a got 75% of the total valid votes. if 15% of the total votes were declared invalid and the total numbers of votes is 560 000, find the number of valid votes polled in favor of candidate.
Answer:
357000Step-by-step explanation:
in an election, candidate a got 75% of the total valid votes. if 15% of the total votes were declared invalid and the total numbers of votes is 560 000, find the number of valid votes polled in favor of candidate.
find total valid votes
560000 - 15% = 476000
find 75% of valid votes
476000 : 100 * 75 = 357000
Match each equation to the situation it represents.
Answer:
I believe you need to switch the equations from the top and middle problems.
Step-by-step explanation:
I hope this helps
Which line matches the equation below? *
f(x) = 31
O
Red
Blue
Green
Purple
Step-by-step explanation:
there is a mistake in your question for sure.
because none of the lines match the function.
f(x) = 31
is a constant function represented by a straight horizontal line going through y = 31.
there is no such line in the graph.
Create a word problem using the numbers -6 and 3.
Answer:
Aaron has 3 red cubes and 15 yellow cubes in his bag. If he subtracts six yellow cubes, how many cubes of each color does he have?
Answer:
Jake from state farm lost 3 dollars from buying McDonalds it cost him dollars 6 how much money does he still have to pay
Step-by-step explanation:
The Stock Market alexzander is a stockbroker. Earns 12% commission each week. Last week, he sold $5,400 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011?
Answer:
Commission in March = $648
Commission in 2011 = $33696
Step-by-step explanation:
Given
[tex]Stocks = \$5400[/tex]
[tex]Commission = 12\%[/tex]
Required
- Determine the amount of commission
- Determine the amount of commission in 2011
This is calculated as
[tex]Amount = Commission * Stocks[/tex]
[tex]Amount = 12\% * 5400[/tex]
[tex]Amount = 0.12 * 5400[/tex]
[tex]Amount = \$648[/tex]
Since the number of weeks in a year is 52.
[tex]Yearly\ Commission = 52 * \$648[/tex]
[tex]Yearly\ Commission = \$33696[/tex]
4.678
written to one decimal point would be
Answer:
hello
4.678 = 4 678 / 1000
Step-by-step explanation:
What number makes the equation true enter the answer in the text box
Answer:
2
Step-by-step explanation:
because 2x4=8
so 2/8=4
Answer:
32
Step-by-step explanation:
firstly do the inverse which is 4 times 8 which is 32
then to check if ur answer is correct do 32 ÷8 which is 4