Answer:
a. 0, -6, -18, -21, -90
b. 3, 0, -6, -18, -42
c. A starting point of any number ≥ 6 will result in a sequence of positive values
Step-by-step explanation:
Here the sequence is governed by the rule:
[tex]\sf a_{n} = 2(a_{n-1} - 3)[/tex]
[tex]\textsf {where $a_n$ is the nth term and $a_{n-1}$ is the previous term}}[/tex]
1) Starting with a₁ = 0 we get
a₂ = 2(a₁ - 3) = 2(0 - 3) = -6
a₃ = 2(a₂ - 3) = 2(-6 -3) = 2(-9) = -18
a₄ = 2(a3 - 3) = 2(-18 - 3) = 2(-21) = -42
a₅ = 2(a₄ - 3) = 2(-42- 3) = 2(-45) = -90
So the first 5 numbers in the sequence starting with 0 are:
0, -6, -18, -21, -90
2) I will approach this slightly differently
We have the relationship:
[tex]\sf a_{n} = 2(a_{n-1} - 3)[/tex]
Expanding the brackets we get
[tex]\sf a_{n} = 2a_{n-1} - 6[/tex]
We have a₁ = 3
a₂ = 2(a₁) - 6 = 2(3) - 6 = 6 - 6 = 0
a₃ = 2(a₂) - 6 = 2(0) - 6 = -6
a₄ = 2(a₃) - 6 = 2(-6) - 6 = -18
a₅ = 2(a₄ ) - 6 = 2(-18) - 6 = -42
The sequence starting with 3 is:
3, 0, -6, -18, -42
Both methods work exactly the same, some students find expanding the brackets easier to deal with
c. We can see that as a₁ increases, the number of negative numbers decreases by 2. So, in order for all numbers to be positive (> 0) we should start with a sufficiently large number so that all numbers are positive
The smallest such number is 6.
When a₁ = 6, the sequence is all 6s because
a₂ = 2(6) - 6 = 12 - 6 = 6
So the next number is a₃ = 12(6) - 6 = 6 and so on
So any starting point ≥ 6 will yield positive values. At 5 the sequence would be: 5, 4, 2, -2, -10 so starting point of 5 will not work
the sum of the lengths of any two sides of a triangle is greater than the third side find the 3rd side
The given statement is false.
Given, that the sum of two sides of a triangle is greater than or equal to the third side.
considering 2 cm, 3 cm, 4 cm
Let the two sides be 2 cm and 3 cm
Let the third side be 4 cm
Now, sum of two sides = 2 + 3 = 5 cm
So, 5 > 4
Therefore, the given statement is false.
What do you mean by Triangle?A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property. There are three sides and three angles in every triangle, some of which may be the same. Triangles are three-sided shapes. The various kinds of triangles go by various names. The size of the angles and the length of the sides determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.
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Add or subtract use place-value blocks to help $1.33 - $0.35
Answer:
$0.98
Step-by-step explanation:
$1.33-$0.35=$0.98.
Answer:
The answer is 0.98 cents
Step-by-step explanation:
Hope it helps!
Use the Quadratic Formula to solve the equation x2 - 2x = - 9
The required solution of the given quadratic equation is [tex]{\displaystyle x={\frac {2\ - {\sqrt {(-32)}}}{2}}[/tex] and [tex]{\displaystyle x={\frac {2\ + {\sqrt {(-32)}}}{2}}[/tex]
What is Quadratic Formula?In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation.
Given a general quadratic equation of the form
ax^2 + bx + c = 0
with x representing an unknown, with a, b and c representing constants, and with a ≠ 0, the quadratic formula is:
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}[/tex]
and,
Now the given quadratic equation is,
x^2 - 2x = - 9
or, x^2 - 2x + 9 = 0
here, a = 1
b = -2
c = 9
Thus quadratic formula is given as,
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}[/tex]
[tex]{\displaystyle x={\frac {-(-2)\pm {\sqrt {(-2)^{2}-4*1*9}}}{2*1}}[/tex]
[tex]{\displaystyle x={\frac {2\pm {\sqrt {4-36}}}{2}}[/tex]
[tex]{\displaystyle x={\frac {2\pm {\sqrt {(-32)}}}{2}}[/tex]
Thus,we get,
[tex]{\displaystyle x={\frac {2\ - {\sqrt {(-32)}}}{2}}[/tex]
[tex]{\displaystyle x={\frac {2\ + {\sqrt {(-32)}}}{2}}[/tex]
Thus,the required solution of the given quadratic equation is [tex]{\displaystyle x={\frac {2\ - {\sqrt {(-32)}}}{2}}[/tex] and [tex]{\displaystyle x={\frac {2\ + {\sqrt {(-32)}}}{2}}[/tex]
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35892 rounded to the nearest ten thousand
Answer:
40,000
Step-by-step explanation:
some jobs pay a commission plus a bonus at the end of the year. the bonus may be a percent of the salesperson's total commission. madelyn carr is a sales representative for a luxury home builder. she receives 7% commission on all sales. at the end of the year, she receives a bonus of 5% of her commission.
a) If Sales = $6412454, then Gross Pay = $471315.369.
If Sales = $412454, then Gross Pay = $30315.369.
b) If Sales = $316250, then Gross Pay = $23244.375.
What is a commission?Commissions are a type of variable-pay compensation for services or items sold. Salespeople are frequently motivated and rewarded through commissions.
Commissions can also be structured to incentive specific sales activities. For example, commissions may be decreased when offering substantial discounts
The remuneration paid to an employee after fulfilling a task, which is generally selling a particular amount of products or services, is referred to as a commission.
A sales commission is money provided to an employee for completing a task, typically selling a specified number of goods or services.
Sales commissions are occasionally used as incentives by employers to boost worker productivity. A commission can be paid in addition to or in place of a wage.
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The complete question is:
Some jobs pay a commission plus a bonus at the end of the year. The bonus may be the percent of the salesperson's total commission. Madelyn Carr is a sales representative for a luxury home builder. She receives 7% commission on all sales. At the end of the year, she receives a bonus of 5% of her commission, (a) What is her gross pay for a year in which she had sales totaling 6412,454? (b) What would be Madelyn's gross pay be if her sales were $316,250?
if i get one point each 2 minutes how long until i get 50 points?
Like how long in time.
a fire truck is called to a scene. three minutes later, a second truck is called. the first truck averages only 30 miles per hour, but the second averages 60 miles per hour. the truckcs travel a total of 12 miles and arrive at the same time.
The trucks arrive 10 minutes after the first call. The first and the second truck travel for 5 miles and 8 miles respectively.
In a time difference of 3 minutes, two fire trucks are called.
The average speed of the first truck is 30 miles per hour.
The average speed of the second truck is 60 miles per hour.
The trucks totally travel for 12 miles and arrive at the same time.
Let d be the number of miles the first truck drove.
Let t be the number of minutes it took the first truck to travel.
Now, Convert 30 miles per hour to a half mile per minute and 60 miles per hour to a mile per minute as we are measuring time in minutes.
For the first truck:
d = 0.5t
The second truck traveled 12 - d miles if the first truck traveled d miles. In the event where the first truck traveled for t minutes and was called 3 minutes later, the second vehicle would have gone for t - 3 minutes.
For the second truck:
12 - d = t - 3
Therefore,
12 - 0.5t = t - 3
15 = 1.5t
t = 15 / 1.5
t = 10 minutes
The trucks arrive after 10 minutes after the first call.
Then,
d = 0.5t = 0.5(10) = 5 miles
And 12 - d = 12 - 5 = 8 miles.
Hence, the first truck traveled for 5 miles and the second truck traveled for 8 miles.
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The complete question is mentioned below:
A fire truck is called to a scene. Three minutes later, a second truck is called. The first truck averages only 30 mph, but the second averages 60 mph. The trucks travel a total of 12 miles and arrive at the same time. How long from the first call did the trucks take to arrive? How far did each travel? We must first remember to change miles per hour to miles per minute.
-6(a+8) i need help ASAP i have to show my work
Answer
-6a - 48
Solution
-6 x a= -6a
8 x -6= 48
-6a - 48
What is a number that is divisible by 2 and 3 that is greater than 50 but less than 60? is there more than one answer?
Answer:
54 can be divided by both 2 and 3. And yes there is more than one answer.
Step-by-step explanation:
54 is less than 60 but greater than 50, and it can also be divided by 2 and 3 without there being a remainder. All the other answers could be: 52, 54, 56, and 58 (all of which could be divided by 2) and 51, 54, and 57 (all of which could be divided by 3).
Hope this helps!!! :)
Solve for x and y, then find m
The value of x is 40 degree and y is 105 degree.
What is Linear pair?Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
2x - 5 + 75=180
2x+70=180
x= 110/2
x= 55 degree.
Now, y= 2x-5 = 2(55)-5 = 110- 5 = 105 (Vertically opposite angle)
Hence, the value of x is 40 degree and y is 105 degree.
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What is the solution set to the equation 2/7-m=4/m - 5-m/7-m
The equation given as 2/(7 - m) = 4/(m - 5) - m/(7 -m) has no real solution for m
How to determine the solution set to the equation?The equation is given as
2/(7 - m) = 4/(m - 5) - m/(7 -m)
Take the like terms of the above equation
So, we have
m/(7 -m) + 2/(7 - m) = 4/(m - 5)
Evaluate the like terms in the above equation
So, we have
(m + 2)/(7 -m) = 4/(m - 5)
Cross multiply the above equation
So, we have
m^2 + 2m - 5m - 10 = 28 - 4m
Evaluate the like terms
m^2 + m + 18 = 0
Using a graphing tool, we have no solution for m
Hence, the equation given as 2/(7 - m) = 4/(m - 5) - m/(7 -m) has no real solution for m
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Nine yards of ribbon are cut into 8 equal pieces. what is the length of each piece of ribbon? write a division expression to represent the problem solve
Answer:
1.125 yards. Division expression: 9 ÷ 8
Step-by-step explanation:
Division expression: 9 ÷ 8
9 is the total length of ribbon and 8 is number of pieces you are cutting the ribbon
Solve the expression:
9 ÷ 8 = 1.125
{y=-2x-1
{4x+2y-12
Answer:
x = -14
Step-by-step explanation:
ez I GOTCHU (pls give brainliest :D)
alr so we got y = -2x-1. we need to substitute that into the equation
4x + 2 (-2x-1) - 12 is ur equation
4x + -4x -2 - 12
-14 = x
pls branliest
what is the range of h(x) = |x| − 2?
Answer: 69
Step-by-step explanation: 59+10=69
Which number line shows the solution to 3 + (−3)?
Answer:
The answer is A.
Because...
[tex]3-3[/tex]
[tex]=3+-3[/tex]
[tex]=0[/tex]
Here's photo as well.
Answer:
The First Image!
Step-by-step explanation:
Given
[tex]\boxed{3+(-3}[/tex]
This gives:
[tex]\boxed{3+(-3)=3-3=0}[/tex]
You were given 3+ (-3).
This means that we count 3 places forward, then count 3 places backward.
We stop at zero.
This implies that 3+(-3) is zero
Which tells you The first option/Image is correct!
Answered by:
AshTheNeko
Where will the hour hand of clock stops if it starts from 7 and goes through 3right angles
The hour hand that goes through 3 right angles and starts from 7 will stop at 4.
We can assume that the numbers in a clock are positioned in a circle. The angle in a circle is 360⁰, while the numbers in a clock is 12.
Hence, from each clock number to its consecutive number, the hour hand must travel 30⁰ as shown in the attached picture.
A right angle is equal to 90⁰. This is equal to 3 ⨉ 30⁰. In other words, to travel 90⁰ means to travel 3 hours.
3 right angles = 3 ⨉ 90⁰
= 3 ⨉ 3 hours
= 9 hours.
Thus, the hour hand will go to:
7 + 9 = 16
16 is equal to number 4 in a clock number.
Conclusion: If the hour hand start from 7, it will stop at clock number 4.
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I really need help I don't know how to solve this. : (
An object is traveling at a steady speed of 9 9/10 mi/h. How long will it take the object to travel 2 1/10 mi? First round to the nearest integer to find the estimated answer. Then find the exact answer.
Answer:
12.73 mins
Step-by-step explanation:
velocity: 9.9 mi/h
distance: 2.1 mi
d=vt
t = d/v = 2.1/9.9 = 0.21h
convert to minutes: 2.1/9.9 x 60 = 12.73 min
The weights of 9-ounce bags of a particular brand of potato chips can be modeled by a normal distribution with mean μ = 9.12
ounces and standard deviation = 0.05 ounce.
What bag weight is at the 84th percentile of the distribution?
Use the empirical rule and do not round.
ounces
It should be noted that the bag weight that is at the 84th percentile of the distribution is 9.17 ounce.
How to illustrate the information?It's important to vompute the z-score for 84th percentile then find the 84th percentile of the distribution for bag weight.
From the standard normal table, the indicated z score for the area of 0.8400 and indicative area 0.8400 is 0.99.
The z-score is 0.99.
The 84th percentile (P) of the distribution for bag weight will be:
= 9.12 + (0.09 × 0.05)
= 9.12 + 0.05
= 9.17.
Therefore, the 84th percentile of the distribution for bag weight will be 9.17.
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Write 7,250,000,000 in scientific notation.
725 × 10−7
725 × 107
7.25 × 10−9
7.25 × 109
Answer:
7.25 x 10⁹
Step-by-step explanation:
The steps are as follows:For 7,250,000,000 , you have to move 9 places to the left to get 7.25 so the number in scientific notation is 7.25 x 10⁹
Use the definition of vampire numbers to determine if the product is a vampire.
15x93=1395
Select the correct answer below and fill in the answer box to complete your choice.
(Use a comma to separate answers as needed.)
OA. The product is not a vampire.
OB. The product is a vampire. The surviving digit(s) is/are
it's a vampire !
the surviving digits are 1, 3, 9 ,and 5.
unless i have the wrong definition of a vampire number.
nikki and kelly can create math problems for a particular course in 20 hours. alone, nikki can do write all of the problems 4 hours faster than kelly could if she were to work alone. how long would it take each person to write the problems if they worked alone?
Nikki alone can do work to write the problem in 43 hours, and Kelly can work in 39 hours.
What are work and time?
Work is the energy expended to complete a task or produce a deliverable. It takes a specific amount of time (T) to finish a particular task (W). The rate of work is the number of units of work completed per unit of time (R). Therefore, Work (W) = Rate (R) Time (T), and Work = Force Distance can be used to determine Work.The joule (J), sometimes known as the Newton meter (N m), is the SI unit for work. When an object is moved across a distance of 1 m with 1 N of force, one joule is equal to the amount of work that is accomplished.
Work and time are proportionate to one another. Because of this, more work can be done with more time, and vice versa.
Nikki can do the part of this problem in 1 hour = 1/x
And, Kelly can do the part of this work in 1 hour = 1/(x - 4)
So, Nikki and Kelly both can do this work in 1 hour = (1/x) + [1/(x - 4)] = 120
= 40x - 80
= x² - 4x
= x = 43, 2
Hence,
Nikki alone can do work to write the problem in 43 hours, and Kelly can work in 39 hours.
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A computer store
charges $45 for materials and $50 an hour for service to install two new programs and a connection. The cost C(h) is a function of the number of hours a it takes to do the job. Graph the function
CCh) = 45 4 50h. How much will instaletion cost?
The cost for a 3-hour installation is $195.
A relation between a collection of inputs and outputs is known as a function. A relationship between inputs and outputs in which each input is connected to only one output is called a function. Each function has a codomain, range, and domain.
The hourly charge to install two new programs and a connection is $50.
The computer store charge $45 for the materials.
The function for the cost of the number of hours it takes to complete the job is given as:
C(h) = 45 + 50h
Therefore, the cost for a 3-hour installation is:
C(3) = 45 + 50 × 3
C(3) = 45 + 150
C(3) = $195
The 3-hour installation cost is $195.
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Please help me out! With this question
Answer:
yessir
jimmy jhon
TROOOOOOOOOOOOOOOOOOOOOP
STARING NOW
Answer:
15.25
do 40.75-25.5 i think
Greatest common factor of 16
Answer:
16
Step-by-step explanation:
The GCF of any number is itself. The GCF of 5 is 5. The GCF of 10 is 10. The GCF of 16 is 16.
5x+y/a=2 for a CAN YOU HELP ME PLEASE
Answer:
pls rate as brainliest it will really go along way
Solve the following system of linear equations by elimination. answer the questions provided.
6x + 8y = -28
-3x - 4y = 14
How many solutions does the system have?
Answer:
(x, y) = (x 7/2, -3/4x m) x € R
Identify the range of the function y=-3x+6 when the domain is {-1,2,4}
A. {-6,0,9}
B. {-9}
C. {3,-12,-18}
D. {-3,12}
E. {-6,9}
the following test have all been ordered at the same time on different inpatients. there is only one phlebotomist on duty. which test should the phlebotomist collect first?
The phlebotomist should first collect STAT electrolytes in the ER.
A medical professional who is trained to draw blood samples from patients is known as phlebotomist. The process of taking blood from vein with the help of a needle is known as phlebotomy. An electrolyte test is a blood test that give information about an electrolyte imbalance in the body.
Electrolytes are minerals and salts, such as sodium, Chloride, potassium, and bicarbonate which are found in the blood. These are responsible for conducting electrical impulses in the body. STAT is a short form of a Latin word 'Statim' which means immediately. The phlebotomist should first collect STAT electrolytes in the ER.
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what is the formula of sin90degree
Answer:
hypotenuse 2 is the answer
You can walk 4/5 of a mile in 1/4 of an hour (15 minutes). How far can you walk in an hour?
Answer:
0.2
Step-by-step explanation:
Multiply 4/5 and 1/4: Decimal form
.8 • .25
Answer:
3.2 miles in one hour
Step-by-step explanation:
You can walk 4/5 of a mile in 1/4 of an hour (15 minutes). How far can you walk in an hour?
If you can walk 4/5 of a mile in 1/4 of an hour the equation would be:
4/5x = 1/4
multiply both sides by 4:
4(4/5x) = 4(1/4)
3.2 miles per 1 hour