The product of three consecutive positive numbers (x - 1), x and (x + 1) is 96 times their sum.
(i) Use this information to form an equation in x and show that it simplifies to x² - 289x = 0,
(ii) Solve the equation x - 289x = 0 to find the three numbers.
please I need it under 20min
don't answer it if you don't know thanks
Answers
Step-by-step explanation:
their sum is
x - 1 + x + x + 1 = 3x
their product is
(x - 1)x(x + 1) = x(x² - 1)
96 × 3x = x(x² - 1)
96 × 3 = x² - 1
288 = x² - 1
x² = 289
x = 17
so, the solution is 16, 17, 18
Related Questions
convert an effective rate of 14,5% per annum, to a nominal rate per annum compounded half yearly
Answers
The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.
To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:
Nominal rate \(= (1 + r/m)^m - 1\)
Where:
r = effective rate
m = number of compounding periods per year
In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.
Since compounding is done semi-annually, m would be 2.
Plugging in the values:
Nominal rate \(= (1 + 0.145/2)^2 - 1\)
Simplifying the expression inside the parentheses:
Nominal rate \(= (1 + 0.0725)^2 - 1\)
Calculating the exponent:
Nominal rate \(= (1.0725)^2-1\)
Performing the calculations:
Nominal rate = 1.14900625 - 1
Nominal rate = 0.14900625
Converting the nominal rate to a percentage:
Nominal rate = 14.900625%
For similar question on nominal rate.
https://brainly.com/question/28971185
#SPJ8
what percent of 75 is 57?
Answers
Answer:
76%
Step-by-step explanation:
57/75
(57 X 100)/ 75
5700/75
1900/25
76/1
76
If a triangle has side lengths a, b, and c and a² + b2 = c?, then the triable is a........ triangle
Answers
In the diagram, the measures of 23 and 27 are 45°. The measure of 25 is
135°. Are lines cand dparallel?
F
5
8
OA. Yes, because 23 and 27 are congruent.
OB. No, because 27 and 25 are not congruent.
C. Yes, because 25 and 27 are supplementary.
D. No, because 23 and 25 are not supplementary.
Answers
The correct answer is D. No because 23 and 25 are not supplementary.
In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.
If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.
The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.
For more such answers on supplementary angle
https://brainly.com/question/12919120
#SPJ8
The 4th term of an AP is 6. If the sum of the 8th and 9th terms is -72, the com. mon difference is:
Answers
Answer:
t(4) = 6 ---- a + 3d = 6
t(8) + t(9) = -72
a+7d + a+8d = -72
2a + 15d = -72
double the first equation
2a + 6d = 12
subtract them
9d = -84
d = -84/9 = -28/3
Step-by-step explanation:
Ashley’s math average decreased 12 points to 78. Then she completed an extra credit assignment and raised her final average by 5 points. Write an equation to show how Ashley’s average changed.
What was her starting average?
points
How much did her average increase or decrease, overall?
points
What was her final average?
points
Answers
Answer:
1. 90
2. -12 +5
3. 83
Step-by-step explanation:
90 -12 + 5 = 83
PLEASE HELP ASAP, WILL GIVE FIRST ANSWER BRAINLIEST!!!!
Triangle XYZ is drawn with vertices X(1, 2), Y(2, 5), Z(3, 4). Determine the translation direction and number of units if Z′(9, 4).
6 units down
6 units up
6 units to the right
6 units to the left
Answers
Answer:
6 units to the right
Step-by-step explanation:
Z(3,4) → Z'(9,4)
d = √(9-3)² + (4-4)² = √6²+0² = 6 to the right
The translation of point Z of triangle XYZ from (3, 4) to Z′(9, 4) is a move of 6 units to the right.
Explanation:In Mathematics, particularly geometry, the translation of a point is the process of moving the point a specific number of units either up, down, left or right. In the case of your triangle XYZ, the original position of point Z is at (3, 4) and Z′ is positioned at (9, 4). The y-coordinate hasn't changed; it remains at 4. This tells us that the translation is not up or down. However, if we observe the x-coordinate, you’ll see that it went from 3 to 9. Changing the x-coordinate moves the point horizontally, so we know our translation is left or right. Lastly, the difference between 3 and 9 is 6. We can therefore determine that the point moved 6 units to the right.
Learn more about Translation of points here:https://brainly.com/question/32840542
#SPJ2
if the farmer want to stop his soil from the erosion that was happening what would he need to do.
Answers
Answer:
Crop Rotation: Rotating in high-residue crops — such as corn, hay, and small grain — can reduce erosion as the layer of residue protects topsoil from being carried away by wind and water. Conservation Tillage: Conventional tillage produces a smooth surface that leaves soil vulnerable to erosion.
Step-by-step explanation:
Despite how rapidly it progresses, it affects land productivity, soil fertility, degrades water quality, and damages water drainage. ... Erosion, in turn, facilitates the process of groundwater pollution, and the stiffened structure of soil impedes the flow of water in deeper layers.
there are 25 student in a class. five of then scored A and 10 of them score B while the other scored C for Biostatistics. if a student is selected at random, calculate the probability that the selected student scored A or B in biostastics.
Answers
There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.
To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.
Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):
Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.
Therefore, the probability that a randomly selected student scored A or B
in Biostatistics is:
Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.
for more such questions on probability
https://brainly.com/question/25839839
#SPJ8
A finance charge includes which elements?
A) Interest and fees
B) Interest, fees, and principal
D
Fees and principal
192
Interest and principal
Answers
A finance charge includes Interest, fees, and principal, So the correct answer is Option (B) Interest, fees, and principal.
What Is a Finance Charge?A finance charge is a fee incurred when using a credit or extending credit that already exists. A fixed rate or a percentage of borrowings may be used to calculate finance charges; the latter is more common.
A finance charge is usually made up of the cost of carrying the debt as well as any related transaction fees, account management fees, or late fees imposed by the lender.
Finance charges are a way for a lender to get paid for giving a borrower credit or access to funds. These costs could be one-time payments, like the origination fee for a loan, or they could be interest payments that could be repaid daily or monthly. A finance charge includes Interest, fees, and principal
Therefore,
A finance charge includes Interest, fees, and principal, So the correct answer is Option (B) Interest, fees, and principal.
Learn more about Finance Charge at
https://brainly.com/question/2588555
#SPJ1
Can somebody help me with this problem?
Answers
Answer:
You need to use y=mx+b
In this case, m=1.5 so that means that y=1.5x
Now you must find out the y intercept which is "b" in y=mx+b
I think it is the first one (y=1.5x+72)
====================================================
Explanation:
The given slope is m = 1.5
We want the line to go through (x,y) = (6,72). This means x = 6 and y = 72 pair up together.
We'll plug those m, x, and y values into the equation below to solve for b
y = mx+b
72 = 1.5*6+b
72 = 9+b
72-9 = b ... subtract 9 from both sides
63 = b
b = 63 ... y intercept
-------------------
Since m = 1.5 and b = 63, we go from y = mx+b to y = 1.5x+63
NO LINKS!!
Will give brainliest!!!!!
pls help
Answers
Answer:
sec B = \(\frac{15}{8}\)
Step-by-step explanation:
using the identity
sec B = \(\frac{1}{cosB}\)
cos B = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{CD}\) = \(\frac{8}{15}\)
then
sec B = \(\frac{1}{\frac{8}{15} }\) = \(\frac{15}{8}\)
Order the following numbers from least to greatest. Put the lowest number on the left.8-,4,2
Answers
if the first number is 8 and the second number is 4, then it is 2,4,8
if the first number is 8 and the second number is -4, then it is -4,2,8
i didn’t know if the - was supposed to go with the 8 or 4 or neither. hope this helps!
Please help me guys thanks u
Answers
Answer:
B. QT = 18; TR = 8
Step-by-step explanation:
QT = x + 6
SR = 12
PS = 27
TR = x - 4
PR/SR = QR/TR (Similarity theorem)
PR = PS + SR = 27 + 12
PR = 39
QR = QT + TR = x + 6 + x - 4
QR = 2x + 2
Substitute
39/12 = (2x + 2)/(x - 4)
13/4 = (2x + 2)/(x - 4)
Cross multiply
13(x - 4) = 4(2x + 2)
13x - 52 = 8x + 8
Collect like terms
13x - 8x = 52 + 8
5x = 60
x = 60/5
x = 12
✔️QT = x + 6
Plug in the value of x
QT = 12 + 6
QT = 18
✔️TR = x - 4 = 12 - 4
TR = 8
What are the factors of 42 to find it’s prime numbers and how do I put it in a factor tree
Answers
To create a factor tree for 42, we start by finding a pair of factors of 42, such as 2 and 21 and factor each branch until we have prime numbers.
Answer:
See below
Step-by-step explanation:
Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.
Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.
HELP ASAP PLEASE
Given x^2=81, select all possible values of x.
A. -9
B. -3
C. 0
D. 3
E. 9
Answers
Answer:
A and E
Step-by-step explanation:
x² = 81
~Take the square root of both sides
x = ±9
Best of Luck!
Answer:
The answer is a and e
Step-by-step explanation:
(1 point) Let f be a periodic function of period 10 such that f(x)=x2 for −5≤x<5. Then the Fourier series of f is
Answers
Answer:
The answer is "\(\frac{25}{3}\)".
Step-by-step explanation:
please find the complete question in the attached file.
\(a_0=\frac{1}{10}\int^{5}_{x=-5} x^2 dx\\\)
\(=\frac{1}{10} (\frac{x^3}{3})^{5}_{-5}\\\\=\frac{1}{30}[5^3+5^3]\\\\=\frac{2}{30}(125)\\\\=\frac{1}{15} \times 125\\\\=\frac{25}{3}\)
help a girl out :)
could you find the 2 endpoints of the minor axis and show work of how you got it? thank you :)
Answers
Answer:
If a>b then the major axis of the ellipse is parallel to the x -axis (and, the minor axis is parallel to the y -axis)
if a<b then the major and minor axes of the ellipse with respect to the x and y -axes are reversed
Step-by-step explanation:
4(x+8)+9(6-2x)
plz explain me step by step plz answer me fast
Answers
Ans is 86 - 14x
Steps in image :-
Answer:
86-14x
Step-by-step explanation:
4(x+8)+9(6-2x)
4x-18x+54
4x-18x+86
-14x+86
86-14x
Raoul has 72 wristbands and 96 movie passes to put in gift bags. The greatest common factor for the number of wristbands and the number of movie passes is qual to the number of gift bags. Raoul needs to make. Then find how many wristbands and how many movie passes raoul can put in each gift bag if he evenly distributes the items.
Please help I am stuck I am doing work nonstop on all weekends if I don’t get this right and done please help and will give brainlesst for the correct answer
Answers
Answer:
Step-by-step explanation:
I do know give me brainliest first
Answer:
24 gift bags
Step-by-step explanation:
Well first the question says to find the GCF and you find that by finding prime factors in each number. Then you would want to subtract 96-72 and get the answer of 24 so you would be able to make 24 gift bags. Hope this helps!!
May I have heart, 5 star, and brainliest please?
A store pays $50.00 for a coat. Its markup is 25%. Later, it puts the coat on sale at 20%
off. What is the sale price of the Coat. Please help
Answers
Answer:
$50
Step-by-step explanation:
$50 * 25 = 1,250
1,250/100 = 12.5
$50 + $12.5 = $62.5
$62.5 * 20 = 1,250
1,250/100 = 12.5
$62.5 - $12.5 = $50
1. A boat drifted 15 m out into the water off Ocean Beach, where the shore drops off
at 4°. Can Brooke walk out to bring the boat back without getting water over the
tops of her hip boots which are 1 m tall? Explain your reasoning.
2. are the engineer who designed a new branch for the Mountain Railroad
Company. You sent your plans calling for 100 km of track up Bixby Mountain
taking trains 99 km east of the city of Bixby, to the City Council for approval.
But before the Council got around to looking at your plans, they passed a
regulation that no railroad tracks could go up their mountain at an angle of more
than 8°. Will your plans be approved? Why or why not?
3. The residents of Quietville, a little town 9 km from the San Francisco Airport,
insist that any plane flying over their town disturbs them if it is lower than 3 km.
Will a plane that took off at a 21° angle disturb them? Why?
4. You are an air pollution inspector, checking that factories in your city have
chimneys at least 65 m tall. Standing 50 m from the Ore Smelting Company’s
chimney, you find the angle from the ground to the chimney top is 51°. Can the
company use that chimney legally? Explain.
6. River City is offering a $3 million contract to build a bridge between points A and
C on opposite sides of City River. Along the side of the river that makes a right
angle with the line of the bridge at point C, a surveyor walked 72 m to point B
where she measured the 55° angle form B to A. Long Company will build the
bridge for $3 million if it is not more than 103 m from point A to point C. Short
Company agrees to build it if it is no more the 100 m. Which contracting firm
will be awarded the contract? Why?
7. An elderly woman is trapped 17 m up in her burning home. Can a fireman reach
her on his 26 m ladder if it has to make a 43° angle in order to clear the woman’s
greenhouse under her window? Explain your reasoning.
8. A ski lift 1000 m long goes at a 29° angle up Mt. Gentleslope. Does the lift take
skiers all of the way up to the top of the mountain where there is a snack bar at
the 500 m elevation? Explain your reasoning.
9. Mr. Johnson is a jet pilot who just moved with his family to Suburbia, 26 km
from Toledo Airport. His seven-year-old son, Eric, would like to see his father’s
plane as it flies over their new home for the first time today, but there is a layer of
clouds 5 km above the house. Will Eric be able to see his Dad’s plane if it takes
off at a 9° angle? Explain.
10.You are the cost control expert for an engineering firm designing a giant
television tower having several metal braces, each built in 21 m from the base at a
73° angle with the ground. Part of your job is to decide which standard length of
metal brace wastes less metal: the brace that comes 71 m long, or the one that is
73 m long. What is your decision?
Answers
The correct responses found using trigonometric ratios are as follows;
Brooke's cannot bring the boat back without getting water over her boots.The plan will not be approvedThe plane will not disturbThe company can not use the chimney legallyThe Long company will build the bridgeThe fireman can reach her.The lift does not take the skiers up to the bar.Eric will be able to see his Dad's plane.The 73 m. braceHow can trigonometric ratios be used to find the right responses?1. The depth of the water = 15 × tan(4°) = 1.049 m
The height of Brooke's boot = 1 m
Therefore;
Brooke's cannot bring the boat back without getting water over her boots.2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°
Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;
The plan will not be approved.3. Height reached by the plane = 9 × tan(21°) = 3.455
Therefore;
The plane will not disturb.4. Height of the chimney at the factory = 50 × tan(51°) = 61.745
The minimum chimney height = 65 m.
Therefore;
The company can not use the chimney legally.6. Length of the bridge = 72 × tan(55°) ≈ 102.83
Therefore;
The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7
Therefore;
The fireman can reach her.8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8
Therefore;
The lift does not take the skiers up to the bar.9. Height reached by plane = 26 × tan(9°) ≈ 4.12
The plane flies under the cloud therefore;
Eric will be able to see his Dad's plane.10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83
Therefore;
The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.Learn more about trigonometric ratios here:
https://brainly.com/question/24349828
#SPJ1
What is the vertex of the graph of f(x) = |x + 5|– 6? (A) (-6, -5)
(B) (-6, 5)
(C) (-5, -6)
(D) (5.-6)
Answers
Answer:
C
Step-by-step explanation:
Plz mark as brainliest
Answer:
It’s D
Step-by-step explanation:
find the area of the triangular prism
Answers
The total surface area of the triangular prism using the net is 96 square units
Calculating the total surface area using the net.From the question, we have the following parameters that can be used in our computation:
The net of a triangular prism
The surface area of the triangular prism from the net is calculated as
Surface area = sum of areas of individual shapes that make up the net of the triangular prism
Using the above as a guide, we have the following:
Area = 2 * 3 * 7 + 6 * 7+ 2 * 1/2 * 2 * 6
Evaluate
Area = 96
Hence, the surface area is 96 square units
Read more about surface area at
brainly.com/question/26403859
#SPJ1
I need help right now!!!
Answers
1. Figure STUV is congruent to Figure KLMN because rigid motions can be used to map Figure STUV onto Figure KLMN.
2. Figure STUV is also similar to Figure KLMN because rigid motions and/or dilations can be used to map Figure STUV onto Figure KLMN. The scale factor is 2.
What does it mean for figures to be congruent?When it is said that two figures are congruent, like the ones shown on the graph, This means that they have the same shape and size.
Similar figures have the same shape, but they may have different sizes and be located in different positions.
Find more exercises on congruent figures;
https://brainly.com/question/29193622
#SPJ1
Please look at the photo for the question. Thank you!
Answers
The zeros with each multiplicity are given as follows:
Multiplicity one: x = 6.Multiplicity two: x = 11.Multiplicity three: x = -6 and x = -5.How to obtain the multiplicities?The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the linear factors of the function in this problem, the zeros are given as follows:
(x + 6)³ -> zero at x = -6 with multiplicity of 3.(x - 11)² -> zero at x = 11 with multiplicity of 2.x - 6 -> zero at x = 6 with multiplicity of 1.(x + 5)³ -> zero at x = -5 with multiplicity of 3.More can be learned about the Factor Theorem at brainly.com/question/24729294
#SPJ1
Can someone help with this
Answers
Answer:
The missing angle is 50 degrees.
Answer:
50°
Step-by-step explanation:
Knowing that this is a parallelogram, you can infer that the adjacent angles of the polygon must add up to 180 degrees by definition. Using what is given, you would take \(180 - 130\) to get your answer, \(50\)°.
Hoped this helped!
Aiden runs a farm stand that sells apples and strawberries. Each pound of apples sells
for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a
total of 35 pounds of apples and strawberries. Write a system of equations that could
be used to determine the number of pounds of apples sold and the number of pounds
of strawberries sold. Define the variables that you use to write the system.
Answers
Answer:
Step-by-step explanation:
Which set of equations has (-4, 1) as a solution?A and BB and DA and CB and C
Answers
Given two lines that represent sets of equations, we know that the solution is the point where both lines intersect. In this case, the point (-4,1) is located in the intersection between line A and line C.
Therefore, the set of equations that has (-4,1) as a solution are A and C
oven temperature calculation 120
Answers
The oven temperature at 120 degree Celsius is 250 F and the gas is 1/2
what is temperature conversion?A temperature converter helps in the conversion of the measurement units of the temperature recorded in a particular unit
Given:
temperature = 120 Celsius
In Fahrenheit = 250 F
and, the gas is 1/2.
Hence, The oven temperature at 120 degree Celsius is 250 F and the gas is 1/2
Learn more about Temperature conversion here:
https://brainly.com/question/4341833
#SPJ1