5,7,12,20,31 what’s the pattern
Answers
Answer:
To identify the pattern in the given sequence of numbers (5, 7, 12, 20, 31), we can try finding the differences between consecutive terms:
7 - 5 = 2
12 - 7 = 5
20 - 12 = 8
31 - 20 = 11
We notice that the differences themselves form a sequence of consecutive odd numbers: 2, 5, 8, 11. This suggests that the pattern in the original sequence might involve adding consecutive odd numbers to the previous term.
Starting with 5, we can add the first odd number (1) to get 6, then the next odd number (3) to get 9, then the next odd number (5) to get 14, and so on. Continuing this pattern, we get:
5, 7, 12, 20, 31, 45, 62, 82, ...
Therefore, the pattern in the given sequence is that each term is obtained by adding consecutive odd numbers to the previous term, starting with 5 and the first odd number (1).
Related Questions
Joyce saved $220 on an item that was 75% off what was the original price
Answers
Answer:
$880
Step-by-step explanation:
Use the equation:
\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.
220=(1-0.75)x
simplify parenthesis terms
220=0.25x
divide both sides by 0.25
880=x
So, the original price was $880.
Hope this helps! :)
Fill in the blank with the correct number. the number____ is divisible by 2,3,5,6 and 10.
Answers
Answer: hope this helps! have a great day!
god bless!
Step-by-step explanation:
If the last digit is even (0, 2, 4, 6, or 8) then it is divisible by 2.
Sum the digits. The result must be divisible by 3.
The last two digits form a number that is divisible by 4.
If the last digit is 0 or 5 then it is divisible by 5.
It is divisible by 2 and by 3 then it is divisible by 6.
Sum the digits. The result must be divisible by 9.
If the ones digit is 0 the the number is divisible by 10
through: (-5,1), parallel to y = -2/3x +2
Answers
Answer:
y = -2/3x-1
Step-by-step explanation:
Consider the relationship 7r+2t=7. a. Write the relationship as a function r=f(t).
Answers
Answer: r = 2/7 -t
Step-by-step explanation: solve r from equation
7r = 2-7t l:7. r = 2/7 - t
The relationship as a function r=f(t) is \(\rm f(t)=\dfrac{7-2t}{7}\\\\\).
What is the equation?In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
Consider the relationship;
7r+2t=7
Substitute r = f(t) in the equation
\(\rm 7r+2t=7\\\\7f(t)+2t=7\\\\ 7f(t)=7-2t\\\\f(t)=\dfrac{7-2t}{7}\\\\\)
Hence, the relationship as a function r=f(t) is \(\rm f(t)=\dfrac{7-2t}{7}\\\\\).
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
Answers following the rounding instructions: see below for details
BC = 5.1
m∠B = 23°
m∠V = 116°
Step-by-step explanation:
Givens:
AC = 3
AB = 7
m∠A = 41°
Unknowns:
BC = ?
m∠B = ?
m∠C = ?
Find side BC using the law of cosines: c² = a² + b² - 2ab cos(C)
a² = 3² + 7² - 2(3)(7)(cos41)
a = √9 + 49 - 42(cos41)
a = 5.128 ≈ 5.13
side BC = 5.13
Use the law of sines to find m∠B: sin(A) / a = sin(B) / b = sin(C) / c
m∠B = sin⁻¹[sin41/5.13 x 3] = sin⁻¹(0.3837) = 22.56 ≈ 22.6°
Sum of interior angles of a triangle is 180, so now you can find m∠C:
m∠C = 180 - 22.6 - 41 = 116.44 ≈ 116.4°
Rounding side BC to nearest tenth: BC = 5.1
Rounding angles to nearest whole degree:
m∠B = 23°
m∠V = 116°
8. What is the value of x in the diagram?
A
E
429
B
49
D
32°C
Answers
Answer:
D. \(10^{\circ}\)
Step-by-step explanation:
Let the measure of minor arc \(AE\) be \(\alpha\) and the measure of minor arc \(BD\) be \(\beta\).
Using the secant-secant theorem, \(\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}\).
By the inscribed angle theorem, \(\alpha=84^{\circ}\).
Thus, \(\beta=20^{\circ}\).
By the inscribed angle theorem, \(x=10^{\circ}\).
Fill in the table 'using this function rule.
y = -5x+2
x
-1
0
1
2
y
0
0
0
X
4
S
Answers
Answer:
7, 2, -3, -8
Step-by-step explanation:
y = -5x + 2 Substitute in -1 for x
y = -5(-1) + 2
y = 5 + 2
y = 7
y = -5x + 2 Substitute in 0 for x
y = -5(0) + 2
y = 0 + 2
y = 2
y = -5 + 2 substitutes in 1 for x
y = -5(1) + 2
y = -5 + 2
y = -3
y = -5x + 2 Substitute in 2 for x
y = -5(2) + 2
y = -10 + 2
y = -8
Helping in the name of Jesus.
transformation of the graph of f(x)=x^3 for the graph of g(x)=-x^3
Answers
The transformation was a reflection over the x-axis. This is because \(g(x)=-f(x)\).
The price of an item has been reduced by 45%. The original price was $85.
Answers
Answer:
$38.25
Step-by-step explanation:
Answer:
Sale Price: $85 * 0.55 = $46.75
Step-by-step explanation:
how many times can 0.3 be found in 900
Answers
Answer:
How many times does 3 go into 900 you ask? Here we will explain two ways of looking at this problem to solve it.
"How many times does 3 go into 900?" is the same as asking "How much is 900 divided by 3?" Thus, the answer can be calculated as follows:
900/3 = 300
"How many times does 3 go into 900?" is also the same as asking "What (x) do you multiply by 3 to get 900?" We solve the problem with an easy algebra equation:
3(x) = 900
x = 300
Tip: When you get a question like "How many times does 3 go into 900?", just think of it as how many times you can fit 3 into 900.
The answer on this page is rounded to the nearest decimal if necessary.
Step-by-step explanation:
~Izuku Midoriya~
Gayla’s mom bought 9.5 gallons of gas for $21.85 . What is the cost of a gallon of gas?
Answers
Answer:
$2.30
Step-by-step explanation:
Magic Realm, Inc., has developed a new fantasy board game. The company sold 15,000 games last year at a selling price of $20 per game. Fixed costs associated with the game total $182,000 per year, and variable costs are $6 per game. Production of the game is entrusted to a printing contractor. Variable costs consist mostly of payments to this contractor.
Required:
1) Prepare a contribution format income statement for the game last year and compute the degree of operating leverage.
2) Management is confident that the company can sell 18,000 games next year (an increase of 3,000 games, or 20%, over last year).
Compute:
a) The expected percentage increase in net operating income for next year.
b) The expected total dollar net operating income for next year.
Answers
The expected total dollar net operating Income for next year = $70,000
1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:
Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000
Variable expenses (15,000 × $6) = $90,000
Contribution margin = $210,000
Fixed expenses = $182,000Net operating income = $28,000
Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)
The expected percentage increase in net operating income for next year:
The expected sales in next year = 18,000
games selling price per game = $20
Therefore, Total sales revenue = 18,000 × $20 = $360,000
Variable expenses = 18,000 × $6 = $108,000
Fixed expenses = $182,000
Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses
= $360,000 – $108,000 – $182,000= $70,000
The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%
The expected total dollar net operating income for next year = $70,000
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Construct a parallelogram PQRS such that PQ = 8.1 cm, QR = 6.9 cm and the diagonal QS = 10.4 cm. Measure and write down the length of the diagonal PR.
Answers
Answer:
10.4 it is the correct answer please mark me as a brainlist
Is the point (7,0) located on the x axis
Answers
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Yes. As the y value is 0, this point would be on the x axis
Have A Nice Day ❤
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bonsoir pouvez vous m'aidez
Answers
Answer:
Treatment for HIV/AIDS involves taking highly effective medicines called antiretroviral therapy (ART) that work to control the virus [1][2]. ART involves taking a combination of HIV medicines (called an HIV regimen) to suppress the virus and stop the progression of the disease [1]. The goal of treatment is to reduce the amount of HIV in the body and keep it at a low, undetectable level to help prevent further damage to the immune system and reduce the risk of transmitting HIV to others.
Help me please I beg if you can
Answers
Answer: The mean is 3780
Step-by-step explanation:
Mean is found by adding all values and dividing the sum by how many values were added.
4250+4019+3895+3739+3401+3376=22680
22680/6=3780
Evaluate: 2 • [(6 + 1)2 + 1]
Answers
Answer:
20
Step-by-step explanation:
2•[(6+1)2+1]
2•[(7)3]
2•10
• means times
2×10
20 answer
Answer:
p
Step-by-step explanation:
2 • [(6 + 1)2 + 1]
First The Brackets :
[(6 + 1)
->>> 6 + 1
= 7
But there's a bracket around 6 + 1 so now we multiply
-->>> [(7)2 + 1]
->>> 7 x 2
= 14
So now we add :
-->>> 14 + 1
= 15
And now we multiply:
->>> 15 • 2
--->>> 30
Hope it helps :))))
1. Find the equation of the image of the circle x² + y2 + 16x-24y + 183 = 0 by rotated the line mirror 4x + 7y + 13 = 0. 2. The image of the circle (x - 3)² + (y-2)² = 1 in the line mirror ax + by = 19 is (x-1)³ + (y-16)2 = 1 then, find the values of (a, b). 3. Find the equation of a line passing through the origin and making an angle with the 4 line y-3x-5. 4. A parabola is drawn with its focus at (3,4) and vertex at the focus of the parabola y²-12x - 4y + 4 = 0. The n find equation of the parabola. 5. If the line ax + by + c = 0 touches the circle x² + y² - 2x = and is normal to the circle x² + y² + 2x - 4y + 1 = 0, then find the value of (a, b). 6. If the line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x. -3 7.1² 14 231= [] then find the matrix A 8. Find the equation of the ellipse having its center at the point (2,-3), one and one vertex at (4, -3). 3 9. Find the value of x if-1 0 10. Solve the linear system using Cramer's rule a) 2 1 2 4 (6x - 4y = -12 8x - 3y = -2 X = 16 -21 3x + 2y = z = 5 b) x-y+3z = -15 (2x + y +7z = -28 one focus at (3,-3) 11. Find the value of k for which the following system of linear equations has infinite solutions: x + (k+1)y = 5 ((k+1)x + 9y = 8k - 1
Answers
Answer:
-72x - 53y + 287 = 0.
Step-by-step explanation:
To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.
The line mirror equation is given as 4x + 7y + 13 = 0.
The reflection of a point (x, y) in the line mirror can be found using the formula:
x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)
y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)
where A, B, and C are the coefficients of the line mirror equation.
For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.
Now, let's find the equations of the image of the circle.
The original circle equation is x² + y² + 16x - 24y + 183 = 0.
Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':
x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)
= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)
= (x - 8y - 8(4x + 7y + 13)) / 65
= (x - 8y - 32x - 56y - 104) / 65
= (-31x - 64y - 104) / 65
y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)
= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)
= (y - 14x + 8(Ax + By + C)) / 65
= (y - 14x + 8(4x + 7y + 13)) / 65
= (57x + 35y + 104) / 65
Therefore, the equation of the image of the circle is:
(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0
Simplifying the equation, we get:
-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0
-72x - 53y + 287 = 0
So, the equation of the image of the circle is -72x - 53y + 287 = 0.
The graph is supposed to represent this system of inequalities y>}(-2 y
Answers
We notice that the boundary lines seem to divide the appropriate regions , but the problem is that inequalities that do NOT contain the "=" sign in the inequality symbol (like in this case y< and y> ) should be graphed with DASHED lines.
Both lines appear as solid lines. and should be drawn with DASHED lines.
So please select option B which states exactly this.
You are most welcome!
1) Define theoretical probability.
possible outcomes times favorable outcomes
favorable outcomes times possible outcomes
favorable outcomes divided by possible outcomes
possible outcomes divided favorable outcomes
2) On a spinner with equal pie shapes of red, blue, green, yellow, and orange. What is the theoretical probability you will land on blue when you spin?
4/5
5
1
1/5
3) In a sample of 1,000 coffee drinkers, 450 said they like the taste of the new coffee. Predict how many out of 10,000 will like the new coffee.
4500
450
100
45
Answers
The correct answer is: favorable outcomes divided by possible outcomes. The theoretical probability is a mathematical concept that represents the likelihood of an event occurring based on the ratio of favorable outcomes to the total number of possible outcomes.
The correct answer is: 1/5. Since there are five equally-sized pie shapes on the spinner, and only one of them is blue, the probability of landing on blue when you spin is 1 out of 5 or 1/5.
To predict how many out of 10,000 coffee drinkers will like the new coffee, we can use the concept of proportion. Since we know that 450 out of 1,000 coffee drinkers like the new coffee, we can set up the proportion:
450/1,000 = x/10,000
Cross-multiplying, we get:
1,000x = 450 * 10,000
Simplifying further:
1,000x = 4,500,000
Dividing both sides by 1,000:
x = 4,500
Therefore, out of 10,000 coffee drinkers, we can predict that approximately 4,500 will like the new coffee.
Find the sum of the first 27 terms
of the arithmetic sequence.
First, fill in the equation.
a₁
= 5 and a27
Sn = 2/(a₁ + an)
Sn
=
[?]
2
+
=
83
Answers
Answer:
S₂₇ = 1188
Step-by-step explanation:
using the given formula for \(S_{n}\) , that is
\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )
with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then
S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188
Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
Answers
The equation given in slope-intercept form does not represent the graph because the y-intercept of the graph is equal to 4 while the y-intercept of the equation is equal to 5.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
m represents the slope.c represents the y-intercept.x and y are the data points.What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
Based on the information provided regarding the equations and graphs, the y-intercept are as follows:
The y-intercept of y = 4x + 5 is equal to 5.The y-intercept of this graph with point (0, 4) is 4.Read more on y-intercept here: brainly.com/question/19576596
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9. A has some amount of money with him. He gave one half of one third from that amount One half of the amount received by B is 20. What is the amount that A originally had?
Answers
Using the expression 5x/12 = 20, the amount that A originally had was $48.
We have,
Let x be the amount of money that A originally had.
Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.
The amount received by B is 1/2 of the remaining amount,
which is (x - x/6)/2 = 5x/12.
We know that 5x/12 = 20,
Solving for x.
5x/12 = 20
5x = 240
x = 48
Therefore,
The amount that A originally had was $48.
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A bank gives an interest of 12% per annum.How long will it take to double one's interest?
Answers
Divide 72 by your rate and you get the amount of years.
Write an equation for the line parallel to the line -7x - 7y= 7 through the point (-1,2)
Answers
Answer:
\(y=-x+1\)
Step-by-step explanation:
Slope-Intercept Formula:It helps to write the equation in slope-intercept formula to find the slope of an equation in the form: \(y=mx+b\) where "m" is the slope of the equation. We can take the equation given: \(-7x-7y=7\) and solve for "y" to get the equation in slope-intercept form:
\(-7x-7y=7\)
add 7x to both sides:
\(-7y=7x+7\)
Divide both sides by -7
\(y=-x-1\)
Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:
\(y=-x+b\text{ where b }\ne -1\)
We're given the point (-1, 2) and we can use it to solve for that "b" value.
We plug in -1 as x and 2 as y
\(2=-1(-1)+b\implies 2=1+b\implies 1=b\)
Now we just plug this into the general equation to get: \(y=-x+1\)
Solve the inequality below. Use the drop-down menus to describe the solution and its graph. 7 13 11 Click the arrows to choose an answer from each menu. The solution to the inequality is Choose.... Choose... A graph of the solution should have Choose.... and be shaded to the
Answers
Answer:
\(x \leq -4\)
There will be a filled-in hole at -4.
Step-by-step explanation:
We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)
\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)
The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.
For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.
In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.
A filled-in hole means the number is included in the inequality, while an empty one means it isn't.
In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.
02:26:0
Researchers compare the body composition of cattle feeding on a grain diet with that of cattle feeding on a grass diet.
This method of gathering data is classified
Answers
Answer:
C on Edge 2021
Step-by-step explanation:
Answer
Your answer should be C.
Step-by-step explanation:
Explain two attributes that a rectangle and a square have in common.
Answers
Answer:
All angles and opposite angle are equal;opposite sides are parallel.
Step-by-step explanation:
Answer:
they both have 4 sides and they both have paralell sides.
Step-by-step explanation:
Select the correct answer from each drop-down menu.E22 Edmentum. All rights reserved.AThere are seven lines of reflection across which the regular polygon ABCDEFG can reflect to map onto itself. One of them is aofBC
Answers
There are seven lines of reflection across which the regular polygon ABCDEFG can reflect to map onto itself. One of them is a perpendicular bisector of line segment
The final answer
The function h(t) = -16t2 + 48t + 28 models the height (in feet) of a ball where t is the time (in seconds).
What is the maximum height that the ball reaches? Just write the numerical answer - do not include h = or any units in your
answer.
Answers
Answer:
64
Step-by-step explanation:
[using calculus] When the function h(t) reaches its maximum value, its first derivative will be equal to zero (the first derivative represents velocity of the ball, which is instantaneously zero). We have \(h'(t) = -32t + 48\), which equals zero when \(t = 3/2 = 1.5\). The ball therefore reaches its maximum height when t = 1.5. To find the maximum height, we need to find h(1.5), which is 64 feet.
[without calculus] This is a quadratic function, so its maximum value will occur at its vertex. The formula for the x-coordinate of the vertex is -b/2a, so the maximum value occurs when t = -48/(2*16), which is 1.5. The maximum height is h(1.5), which is 64 feet.
