the sum of 5 consecutive integers is equal to the sum of the next three consecutive integers. what is the largest of these eight integers
Answers
we find that x = 2 satisfies both conditions. Therefore, the largest of the eight consecutive integers is 2 + 4 = 6.
Explanation:
Let's assume that the first of the five consecutive integers is x. Then, the sum of the five consecutive integers can be written as x + (x + 1) + (x + 2) + (x + 3) + (x + 4), which simplifies to 5x + 10.
Similarly, let's assume that the first of the next three consecutive integers is y. Then, the sum of the three consecutive integers can be written as y + (y + 1) + (y + 2), which simplifies to 3y + 3.
Now, we are given that the sum of the five consecutive integers is equal to the sum of the next three consecutive integers. Therefore, we can set the two expressions equal to each other and solve for y:
5x + 10 = 3y + 3
5x + 7 = 3y
y = (5x + 7) / 3
Since y represents the first of the next three consecutive integers, we know that y must be an integer. Therefore, (5x + 7) must be divisible by 3.
The largest of the eight consecutive integers will be the last of the five consecutive integers. Since we know that the first of the five consecutive integers is x, we can express the largest integer as x + 4.
We can now try different values of x to find which one satisfies the condition that (5x + 7) is divisible by 3. For example, if x = 1, then (5x + 7) / 3 = 4, which is an integer. Therefore, the largest of the eight consecutive integers is 1 + 4 = 5.
However, we need to check if this value satisfies the condition that the sum of the five consecutive integers is equal to the sum of the next three consecutive integers. We can plug in x = 1 and y = 5 into the expressions we derived earlier:
5x + 10 = 5(1) + 10 = 15
3y + 3 = 3(5) + 3 = 18
Since 15 is not equal to 18, the value x = 1 does not work. We can try different values of x until we find one that satisfies both conditions. After trying a few values, we find that x = 2 satisfies both conditions. Therefore, the largest of the eight consecutive integers is 2 + 4 = 6.
To learn more about expressions click here, brainly.com/question/14083225
#SPJ11
Related Questions
What value is equivalent to 5³ – 2 • 3 – (7² + 50)?
Answers
Answer: -20
Read more at Answer.Ya.Guru – https://answer-ya.com/questions/5043911-5-2-3-7-50.html
Step-by-step explanation: PEMDAS use this ok first you do 7x7 to equal 49 then add 50 to equal 99. then do 5x5x5 to equal 125. the parentheses are gone and the 5x5x5 is gone now the problem is 125-2x3-99. to finish you multiply 2x3 to equal 6 now 125-6-99=20 answer-20
Read more at Answer.Ya.Guru – https://answer-ya.com/questions/5043911-5-2-3-7-50.html
Determine the graph of the polar equation r = 10/4-sin theta
Answer: C
Answers
The Graph of \(r=\frac{10}{4}-\sin\ \theta\) is shown below:
What is Graph?The graphs of trigonometric functions have the domain value of θ represented on the horizontal x-axis and the range value represented along the vertical y-axis.
Since , the function is in polar coordinates.
We know, r = a sin θ is a circle, where “a” is the diameter of the circle
This means, r = 10/4- sin θ is a circle that has edge.
In the graph it is shown that a circle has bottom-most edge.
The Graph of \(r=\frac{10}{4}-\sin\ \theta\) is
Learn more about trigonometric function graph here:
https://brainly.com/question/12249347
#SPJ1
plsssssss help
got 20 mins
the question is: The sin of angle DCB is
Answers
Answer:
i. <DCB = \(53.13^{o}\)
ii. Sin of <DCB = 0.8
Step-by-step explanation:
Let <DCB be represented by θ, so that;
Sin θ = \(\frac{opposite}{hypotenuse}\)
Thus from the given diagram, we have;
Sin θ = \(\frac{4}{5}\)
= 0.8
This implies that,
θ = \(Sin^{-1}\) 0.8
= 53.1301
θ = \(53.13^{o}\)
Therefore, <DCB = \(53.13^{o}\).
So that,
Sin of <DCB = Sin \(53.13^{o}\)
= 0.8
Sin of <DCB = 0.8
Student tickets cost $2.00 and everyone else
is $4.00. If $500 was made by selling 175
tickets, how many student tickets were sold?
Answers
Answer:
Student =100
Step-by-step explanation:
Factor the algebraic expression. 9a + 6
Answers
Given expression is:
\(9a+6\)Take 3 common from it:
\(9a+6=(3)(3a+2)\)So the factor are:
\(3(3a+2)\)Find the volume of radius 7 cm in diameter of 12 cm in 3.14
Answers
The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.
To find the volume of a sphere with a radius of 7 cm, we can use the formula:
V = (4/3) * π * r^3
where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.
The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:
V = (4/3) * π * (6 cm)^3
V = (4/3) * 3.14 * (6 cm)^3
V = (4/3) * 3.14 * 216 cm^3
V = 904.32 cm^3
For more such questions on volume
https://brainly.com/question/463363
#SPJ8
Answer the question in the image below
Answers
Answer:
Here ya go! Have a great day!
A ball is released at the left end of three different tracks. The tracks are bent from equal-length pieces of channel iron.
a. From fastest to slowest, rank the speeds of the balls at the right ends of the tracks.
b. From longest to shortest, rank the tracks in terms of the times for the balls to reach the ends.
c. From greatest to least, rank the tracks in terms of the average speeds of the balls. Or do all the balls have the same average speed on all three tracks?
Answers
a. From fastest to slowest, the speeds of the balls at the right ends of the tracks will depend on the curvature of the tracks.
If the tracks are of equal length but have different curvatures, the ball on the track with the least curvature will have the highest speed, followed by the ball on the track with the next least curvature, followed by the ball on the track with the most curvature.
b. From longest to shortest, the tracks in terms of the times for the balls to reach the ends will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the most curvature will have the longest time for the ball to reach the end, followed by the track with the next most curvature, followed by the track with the least curvature.
c. From greatest to least, the tracks in terms of the average speeds of the balls will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the least curvature will have the highest average speed, followed by the track with the next least curvature, followed by the track with the most curvature.
All the balls will have the same average speed on all three tracks if the track lengths are equal, but will have different speeds at the end of each track due to the different curvatures.
know more about speeds here
https://brainly.com/question/28224010#
#SPJ11
For the past 40 days, Naomi has been recording the number of customers at her restaurant between 10:00 am and 11:00 am. During that hour, there have been fewer than 20 customers on 25 out of the 40 days. What is the experimental probability there will be 20 or more customers on the forty first day?
(Pls help this is due tm)
Answers
Answer: 0.375 or 37.5%.
Step-by-step explanation:
To calculate the number of days with 20 or more customers, subtract the days with fewer than 20 customers from the total number of days:
Day(s) with 20 or more customers = 40 - 25 = 15
So, out of the 40 days, 15 days had 20 or more customers between 10:00 and 11:00 a.m. As a result, the likelihood of 20 or more customers on the forty-first day is:
Probability = number of occurrences of event / total number of trials
15/40 is the probability.
0.375 is the probability.
As a result, the probability of there being 20 or more customers between 10:00 and 11:00 a.m. on the forty-first day is 0.375, or 37.5%.
payments of $1400 each year for 8 years at 6ompounded annually
Answers
If you make annual payments of $1400 for 8 years at a 6% interest rate compounded annually, the total amount accumulated over the 8-year period would be approximately $12,350.
To explain further, when you make annual payments of $1400 for 8 years, you are essentially depositing $1400 into an account each year. The interest rate of 6% compounded annually means that the interest is added to the account balance once a year.
To calculate the total amount accumulated, you can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
where FV is the future value, P is the payment amount, r is the interest rate per compounding period (in this case, 6% or 0.06), and n is the number of compounding periods (in this case, 8 years).
Plugging in the values, we have:
FV = $1400 * ((1 + 0.06)^8 - 1) / 0.06
≈ $12,350
Therefore, the total amount accumulated over the 8-year period would be approximately $12,350.
To learn more about interest rate click here, brainly.com/question/28272078
#SPJ11
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!!!
Answers
Answer:
There were 12 babies and 4 adults
Rick has $8x and Helen has twice that amount. They save $3 each per week. What amount will be the sum of their money 4 weeks from now
Answers
Answer:
Savings total for both = 24x + 24
Step-by-step explanation:
Rick has 8x to start with
Let w = the number of weeks he will save.
Savings = 8x + 3*w
Let w = 4
Savings = 8x + 3*4
Savings = 8x + 12
Helen
Let w = the number of weeks she will save.
Savings = 16x + 3*w
Let w = 4
Savings = 16x + 12
Now we come to the question. It seems to want the total combining both of them.
Rick + Helen = 8x + 12 + 16x + 12 = 24x + 24
The only other possible answer is
Rick = 8x + 12
Helen = 16x + 12
Una escalera está apoyada sobre la fachada de un edificio. Si la escalera mide 10 m de longitud y el pie de la escalera está a 5 m de la pared, ¿a qué altura de la pared llega la escalera? Expresa el resultado con radicales extrayendo todos los factores posibles.
Answers
Answer:
8.66 meters
Step-by-step explanation:
Assuming that the building is completely straight, a right angle is formed and therefore a right triangle.
Thanks to this we can calculate the height at which the ladder reaches the wall using the Pythagorean theorem, this height being one of the legs.
We have to:
c ^ 2 = a ^ 2 + b ^ 2
c = 10
a = 5
replacing
b ^ 2 = 10 ^ 2 - 5 ^ 2
b ^ 2 = 75
b = 8.66
that is to say that the height at which the ladder reaches the wall is 8.66 meters
A publisher prints 1,912 copies of a book in each print run. If they print 305 runs,
the manager wants to know about how many books will be printed. What is a
reasonable estimate?
Answers
Answer:
I belive it is 583,160 books
Step-by-step explanation:
I did 1912 times 305
Finding the rate or time in a word problem on continuous exponential growth or decay
Answers
continuous exponential growth model
\(A=Pe^{r\cdot t}\)since the size of the sample doubled:
A/P = 2
r = 8.5% = 0.085
e: eurler's number = 2.71828...
therefore,
\(\begin{gathered} \frac{A}{P}=e^{r\cdot t} \\ 2=e^{0.085\cdot t} \end{gathered}\)apply the law of exponents
\(\ln \mleft(2\mright)=0.085t\)\(t=\frac{\ln\left(2\right)}{0.085}\)So, t = 8.15467...
rounding to the nearest hundred
t = 8.15
10. John is mixing paint.He uses black, green and blue in the ratio 6:3: 1. How much of black green and blue paint is needed to make a mixture of paint of 500ml.
Answers
The given ratio becomes 6x : 3x : x.
6x = black paint
3x = green paint
x = blue paint
6x + 3x + x = 500
10x = 500
x = 500/10
x = 50
6x = 6(50) = 300
3x = 3(50) = 150
x = 50
Answer:
300 ml of the black paint.
150 ml of the green paint.
50 ml of the blue paint.
A circle has a diameter of 12 inches. what is the best approximation of its area? use 3.14 to approximate for π.
Answers
The best approximation of the area of the circle is 113.04 square inches.
A circle is a shape with all points equidistant from a central point, known as the center. The distance from the center to any point on the edge of the circle is called the radius.
It can be calculated using the formula π \(r^2\), where r is the radius.
Since the diameter of the circle is 12 inches, the radius would be half of that which is 6 inches.
So, the area would be approximately 3.14 * \(6^2\) = 113.04 square inches.
Therefore, The best approximation of the area of the circle is 113.04 square inches.
To learn more about the area of the circle:
https://brainly.com/question/14068861
#SPJ4
Challenge The value of a baseball player's rookie card began to increase once the player retired When he retired in 1996 his card was worth $6.09. The value has increased by $1.08 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2005? can you please answer the circle problem please ❤❤❤❤plsssss
Answers
Answer:
$15.81
Step-by-step explanation:
We see that 9 years pass between 1996 and 2005.
each year it increases by 1.08 dollars
we take the nine years and multiply it by 1.08 getting 9.72
then we add the 9.72 to the original 6.09 to get 15.81 dollars
Please simplify the sum and show work and answer the questions in the picture below
Answers
The simplified form of the expression is written as 11x³ - 39x -2x²/(x²- 9)(x+ 3)
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of terms, variables, constants, factors and coefficients.
These expressions are also made up of arithmetic operations such as addition, multiplication, division, subtraction, etc
From the information given, we have that;
x -2/x + 3 + 10x/x² - 9
Find the lowest common denominator and simplify
(x-2)(x² - 9) + (x-3)(10x) /(x²- 9)(x+ 3)
Now, expand the bracket, we get;
x³ - 9x - 2x² + 10x³ - 30x/(x²- 9)(x+ 3)
collect the like terms of the denominator and that of the numerator, we get;
11x³ - 39x -2x²/(x²- 9)(x+ 3)
Learn more about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
The price of a cell phone is x dollars. sandy bought the phone for x+0.07x dollars after an additional 7%sales tax. what is another expression that represents the same amount, in dollars, that sandy had to pay to buy the cell phone?
Answers
The amount that Sandy has to pay to buy the cell phone is 1.07x dollars.
This is a question of percentages.
Percentage
Percentage means a number or a ratio expressed in terms of fractions of 100. It is denoted using the percentage sign “%”.
It is given in the question that:-
Price of cell phone = x dollars
Additional sales tax = 7 %
We have to find the amount, in dollars, that Sandy had to pay to buy the cell phone.
Total amount Sandy had to pay for the cell phone = x + 7 % of x
x + (7/100)x = x + 0.07x = 1.07x dollars.
To learn more about Percentage, here:-
https://brainly.com/question/28269290
#SPJ1
A. 34
B. 74
C. 106
D. 72
PLEASE HELP I NEED IY
Answers
Answer:
34 degrees
Step-by-step explanation:
m<z = m<s
2/3 = 20/b solve for b.
Answers
2b = 60
b = 30
Which are true of algorithms (in the strict sense of the term)?a. There must be at least one input b. There must be at least one output с. The algorithm should halt after a finite number of steps d. Each step should be clear and unambiguous e. The result should be correct in all cases
Answers
The statement which is strictly true for algorithms is :
Option d. Each step of algorithms should be very clear and unambiguous.
Algorithms is the way of representing the data to solve a problem or performing any computation.It represent exact number of instruction to perform the computation clearly.Algorithms are used in mathematics . computer science to solve the problem step wise without any ambiguity.It simplify the complicated task or computation into simple and clear way.Algorithm has input and output .Therefore, the option d. each step of algorithms represents steps clearly and unambiguous is the true statement of algorithms.
learn more about algorithms here
brainly.com/question/30189645
#SPJ4
Find the perimeter. Simplify your answer.
Answers
Answer:
3z+13
Step-by-step explanation:
Perimeter is found by adding all the sides
z+2+z+2+z+9
3 z variables 2+2+9=13
Simplified equals
3z+13
Hope this helps!
Please mark this answer as brainiest :)
Answer:
Step-by-step explanation:
z+2 + z + 2 + z + 9 = Perimeter Collect like terms
3z + 13 = Perimeter
Can anyone help me with this question ?
I’ll mark you as a brainliest.
Please don’t answer if you do not know.
Answers
Plz help
Will mark brainliest
Answers
Answer:
4567
Step-by-step explanation:
add 2
add 88
sub 99
Cody and Darry each improved their yards by planting day lilies and shrubs. They bought their supplies from the same store. Cody spent $84 on 2 day lilies and 6 shrubs. Darry spent $120 on 6 day lilies and 6 shrubs. What is the cost of one day lily and the cost of one shrub?
Answers
One lily is $9
One shrub is $11
Step-by-step explanation:
Let the lillies be x
Let the shrub be y
2x + 6y= 84.........i
6x + 6y = 120..........ii
Lets make x the subject formula in eq(I)
2x= 84- 6y
x = 42 - 3y........iii
Put the value of x into eq (ii)
6(42-3y) + 6y = 120
252 - 18y + 6y= 120
252 - 12y= 120
12y= 252-120
12y= 132
Y= 11
Put the value of Y into eq (I)
2x + 6(11)= 84
2x + 66= 84
2x= 18
X= 9
Therefore,the cost of one day lily is $9 and the cost of one shrub is $11.
EXTREMELY IMPORTANT HELP ME
Answers
A woman who develops gestational diabetes mellitus has a 3 - 7 times greater probability of developing ____________________________ within 5 - 10 years.
Answers
A woman who develops gestational diabetes mellitus has a 3 - 7 times greater probability of developing type 2 diabetes mellitus within 5 - 10 years.
Gestational diabetes mellitus (GDM) is a type of diabetes that occurs
during pregnancy, and it usually goes away after delivery.
However, women who develop GDM have an increased risk of developing
type 2 diabetes later in life.
This is because GDM is a sign that the body has difficulty processing
glucose, which can lead to high blood sugar levels.
Women who have had GDM should get regular follow-up care and
screening for diabetes to manage their risk.
for such more question on Gestational diabetes mellitus
https://brainly.com/question/12525578
#SPJ11
U7L2 Cool Down
The measure of the arc from B to A not passing through C is 26 degrees.
1. What is the measure of angle BOA ?
2. What is the measure of angle BDA?
3. What is the measure of angle BCA ?
degrees
degrees
degrees
Answers
Using the inscribed angle theorems, the measure of the indicated angles are:
1. m∠BOA = 26°
2. m∠BDA = 13°
3. m∠BCA = 13°
What is the Inscribed Angle Theorems?Based on the inscribed angle theorem, the following relationships are established:
Inscribed angle = 2(measure of intersected arc)Central angle = measure of intersected arcGiven:
Intercepted arc BA = 26°
1. ∠BOA is central angle
Thus:
m∠BOA = 26° (inscribed angle theorems)
2. ∠BDA is inscribed angle.
m∠BDA = 1/2(30) = 13° (inscribed angle theorems)
3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)
Learn more about inscribed angle theorems on:
https://brainly.com/question/30494878