The sequence alternates between letters and squares of integers. The letters seem to follow a particular positional increment pattern, and the numbers are squares of consecutive positive integers. The missing elements in the sequence are R and 36.
The given sequence is: A, 4, D, H, 16, M, 25, _, _. This sequence appears to have two separate patterns interleaved. One pattern is a sequence of letters and the other is a sequence of numbers. For the letters part, A (1st letter), D (4th letter), H (8th letter), M (13th letter), so the next letters might follow an increasing pattern with the position of the letters in the alphabet. For the numbers, we have 4, 16, 25 which are squares of 2, 4, and 5 respectively. To solve for the next elements in the pattern, we would have to decipher the rule that connects the letters with their positions and the next squares of numbers.
The numbers are squares of consecutive positive integers: 2², 4², 5². The next number is 6² which is 36. Following the pattern in letters, after M (the 13th letter), the next letter should be the letter that is five positions ahead because the interval between the previous letters increased by 3 each time (D is 3 letters after A, H is 4 letters after D, M is 5 letters after H), so the next letter should be R (the 18th letter, which is 5 letters after M).
Therefore, the sequence should continue with R, 36.
What two numbers multiply to 80 and add to 28
Final answer:
The task is to find two numbers that multiply to 80 and add to 28. However, after checking possible factors, no such pair of numbers satisfies both conditions. A re-evaluation of the problem may be necessary as the conditions may have been stated incorrectly.
Explanation:
We are looking to find two numbers that when multiplied together equal 80, and when added together equal 28. To solve this problem, we set up a system of equations based on the information given:
By factoring the number 80, we look for factor pairs that also add up to 28. We notice that 16 and 5 are such numbers because:
However, this doesn't meet our second criterion, so we continue searching. Further examination reveals that 20 and 4 are the correct pair because:
In this case, we have not found two numbers meeting both conditions exactly. Therefore, it appears there has been a mistake as no pair of numbers both multiply to 80 and add up to 28. Thus, we either reconsider our pair list or recheck the conditions given.
The ratio of m∠PQR to m∠PQS is 5:9. What is m∠RQS?
10°
40°
50°
80°
Greatest common factor of 12, 60, and 68
Which of the following represent x=1/2y written in general form
1/2x-y=0
2x-y=0
x-1/2y=0
Answer:
Option 2 - [tex]2x-y=0[/tex]
Step-by-step explanation:
Given : Expression [tex]x=\frac{1}{2}y[/tex]
To find : Write the given expression in general form?
Solution :
Step 1 - Write the given expression
[tex]x=\frac{1}{2}y[/tex]
Step 2 - Multiply 2 both side,
[tex]2x=\frac{2}{2}y[/tex]
Step 3 - Solve the expression
[tex]2x=y[/tex]
[tex]2x-y=0[/tex]
Therefore, The general form of given expression is [tex]2x-y=0[/tex]
Hence, Option 2 is correct.
What is the time 23 hours after 8:00 pm
What is the domain of the quadratic function graphed below?
Amelia receives a treat bag. the treat bag contains 10 gumballs, 5 pixie sticks, 2 bracelets, and 3 chocolates. If Amelia selects 3 items from her treat bag without looking and gives them to her sister, which could not represent a possible outcome for the items Amelia selects?
F. gumball, gumball, gumball
G. pixie stick, gumball, chocolate
H. bracelet, bracelet, bracelet
J. gumball, gumball, pixie stick
what is 3/20 as a decimal equivalent
900 students attended the school concert. There were twice as many adults as children in the audience. How many children attended the concert? which let statement would you use?
To solve for the number of children at the concert with twice as many adults present in a total of 900 attendees, we let the number of children be x, set up the equation x + 2x = 900, and solve for x to find that there were 300 children.
Explanation:The question pertains to solving a problem involving proportions in a total population. Assuming there are twice as many adults as children at the school concert, we can use a 'let' statement to express the number of children as 'x'. Thus, the number of adults would be '2x' because there are twice as many adults as children. Since the total number of attendees is 900, we can set up the equation: x + 2x = 900.
To find the number of children, we combine like terms to get 3x = 900, and then divide both sides by 3 to find x. Thus, x = 900 / 3, which means x = 300. So, there were 300 children at the concert.
Step-by-Step Solution:Let the number of children be 'x' (let statement).Write the number of adults as '2x' because there are twice as many adults as children.Set up the equation for the total attendees: x + 2x = 900.Combine like terms: 3x = 900.Divide both sides by 3 to solve for x: x = 300.Conclude that there were 300 children at the concert.
4x + 5x + 12 = -6 (given)
9x + 12 = -6 (simplify)
9x = -18 (subtraction)
x = -2 (addition)
Which reason is incorrect?
A) addition
B) given
C) simplify
D) subtraction
Answer:
Addition
Step-by-step explanation:
USA Testprep
How many grams are in 40 hectograms
There are 4000 grams in 40 hectograms.
To convert from hectograms to grams, you need to know that there are 100 grams in 1 hectogram.
Therefore, to find out how many grams are in 40 hectograms, you can use the conversion factor:
40 hectograms * 100 grams/hectogram = 4000 grams
So, there are 4000 grams in 40 hectograms.
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A software company startes with 2 employees. in 6 months, the company has u employees. the number of employees increased at a steady rate. which equation models the relationship between the number of employees n and the number of months m since the company started?
Eric sells shirts. It costs him $100 to buy all the shirts and $10 to print designs on the shirts. Eric sells each shirt for $4. So far Eric has sold 20 shirts. Eric uses an equation to calculate his total profit.
What is the slope of the equation modeling this situation?
To find the slope of the equation modeling Eric's situation, subtract the total cost from the selling price per shirt, resulting in a loss of $106 per shirt sold.
The slope of the equation modeling Eric's situation can be calculated as follows:
Profit per shirt = Selling price per shirt - Total cost per shirtProfit per shirt = $4 - ($100 + $10)Profit per shirt = $4 - $110 = -$106The slope, which represents the profit per shirt, is -$106, indicating a loss of $106 for each shirt sold.
Carolyn is building a pen for her dog. The perimeter of the pen is 52 ft
a) Explain how you can use a proportion to convert the perimeter into yards and feet.
b) The fencing material is sold by the yard. It costs 10.99 per yard. What is the cost of material before taxes
Carolyn's dog pen with a 52 ft perimeter is approximately 17.33 yards in length. Fencing material costs $10.99 per yard, making the total cost before taxes around $190.44.
Carolyn is constructing a dog pen with a perimeter of 52 feet. To convert the perimeter from feet to yards, we can use the fact that 1 yard equals 3 feet. Since she is purchasing fencing material by the yard, Carolyn needs to know the total length of fencing in yards. This requires setting up a proportion:
1 yard / 3 feet = x yards / 52 feet
Multiplying both sides by 52 gives us x = 52 / 3 yards. Upon calculating, we find that the pen's perimeter is approximately 17.33 yards.
Since the fencing material costs $10.99 per yard, to find the total cost before taxes, we multiply the number of yards needed by the price per yard:
17.33 yards × $10.99/yard = $190.4367
The cost for the fencing materials before taxes is approximately $190.44.
Rewrite with only sin x and cos x.
cos 3x
cos x - 4 cos x sin2x
-sin3x + 2 sin x cos x
-sin2x + 2 sin x cos x
2 sin2x cos x - 2 sin x cos x
Final answer:
To rewrite expressions using only sin x and cos x, we can use trigonometric identities like [tex]cos 2x = 1 - 2sin^2 x[/tex] and sin 2x = 2sin x cos x. By applying these identities, we can simplify the given expressions.
Explanation:
To rewrite the given expressions using only sin x and cos x, we can use the following trigonometric identities:
[tex]cos 2x = 1 - 2sin^2 x[/tex]sin 2x = 2sin x cos x[tex]sin 3x = 3sin x - 4sin^3 x[/tex]Using these identities, we can rewrite the expressions as follows:
cos 3x = [tex]4cos^3 x - 3cos x[/tex]cos x - 4cos x sin^2 x = cos x - 4sin x cos x sin x = [tex]cos x - 4sin^3 x cos x[/tex]-sin 3x + 2sin x cos x = [tex]-(4sin^3 x) + 2sin x cos x[/tex] = [tex]-4sin^3 x + 2sin x cos x[/tex]-sin 2x + 2sin x cos x = -2sin x cos x + 2sin x cos x = 0[tex]2sin^2 x cos x - 2sin x cos x[/tex] = 2sin x cos x (sin x - 1)What is the general form of the equation for the given circle?
x2 + y2 − 8x − 8y + 23 = 0
x2 + y2 − 8x − 8y + 32 = 0
x2 + y2 − 4x − 4y + 23 = 0
x2 + y2 + 4x + 4y + 9 = 0
Answer:
A ) x² + y² - 8 x - 8 y + 23 = 0
Step-by-step explanation:
hope i helped
the ordered pair for an x-intercept has an x-value of 0 A.True or False
The ordered pair for an x-intercept has an x-value of 0 has some value of x and it has zero value for y, So it is a False statement.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
Given statement,
the ordered pair for an x-intercept has an x-value of 0
we can see in graph that when line intersect the x axis, the x coordinate of that point is known as x-intercept,
suppose, we have one line , y = 3x+3
so when we draw graph for it,
and if we see x-intercept
it will come out as, 0 = 3x+3 ⇒ x = -1
It is clear that value of x is not zero
hence, the given statement is false
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Sketch each parabola using the given information.
vertex (3, 6), y-intercept 2
PLEASE HELP BEGGGING YOU
the point Q(9,-1) is reflected across the y axis. Use arrow notation to describe the original point and its reflection
Q(9,-1)----Q(9,1)
Q(9,-1)----Q (-9,1)
Q(9,-1) ------Q(-9,-1)
Q(9,-1) ----Q(9,-1)
Answer:
C is the answer.
Step-by-step explanation:
When you reflect over the y-axis, the y-axis will remain the same and the x-axis will change from either positive to negative, or negative to positive in this case it is positive to negative.
Use the substitution method to solve the system of equations. 2x - y = 10 3x - 2y = 8
Answer:
x=12, y=14
Step-by-step explanation:
[tex]2x - y = 10[/tex]
Solve the equation for y. Subtract 2x from both sides
[tex]- y = -2x+10[/tex]
Divide both sides by -1
[tex]y=2x-10[/tex]
Substitute 2x-10 for y in the second equation
[tex]3x - 2(2x-10)= 8[/tex]
[tex]3x - 4x+20= 8[/tex]
[tex]-1x+20= 8[/tex]
Subtract 20 from both sides
[tex]-1x= -12[/tex]
Divide both sides by -1
x= 12
[tex]y=2x-10[/tex]
Substitute 12 for x
[tex]y=2(12)-10=14[/tex]
y=14
Carla's plant was 10 2/3 inches tall. Yolanda's was 8 3/4 inches tall.
How much taller was Carla's plant than Yolanda's?
A.
1 11/12 in.
B.
2 1/12 in.
C.
2 5/12 in.
D.
2 11/12
Answer: 128/12 > 105/12
Step-by-step explanation:
10 2/3 inches=32/3 inches
8 3/4 inches= 35/4 inches
Find the common denominator, in this case, 12.
128/12 inches is Carla's plant
105/12 inches is Yolanda's plant.
128/12 > 105/12. Therefore, Carla's plant is taller than Yonlanda's
The area of a rectangle painiting is given by the trinomial x^2-9x-36. what are the possible dimensions of the painting ? use factoring
The first term is, x2 its coefficient is 1 .
The middle term is, -9x its coefficient is -9 .
The last term, "the constant", is -36
Step-1 : Multiply the coefficient of the first term by the constant 1 • -36 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -9 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 3
x2 - 12x + 3x - 36
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
3 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x-12)
Which is the desired factorization
What is the equation in point slope form of the line that passes through the point (2, 6) and has a slope of 5?
y−2=5(x−6)
y+2=5(x+6)
y−6=5(x−2)
y+6=5(x+2)
Answer:
The answer is Y-6=5(x-2)
A donut shop is experimenting with two new types of cream-filled treats, one with raspberry filling, and the other with peach. A batch of raspberry donuts cooks in 11 minutes while a batch of peach donuts cooks in only 8 minutes.
Let x represent the number of raspberry-filled donuts and let y represent the number of peach-filled donuts. Write an inequality to represent how many batches of the new type of donuts can be produced in a 10 hour day.
Answer:
The required inequality is [tex]11x + 8y \leq 600[/tex]
Step-by-step explanation:
Given : A donut shop is experimenting with two new types of cream-filled treats, one with raspberry filling, and the other with peach.
A batch of raspberry donuts cooks in 11 minutes while a batch of peach donuts cooks in only 8 minutes.
Let x represent the number of raspberry-filled donuts and let y represent the number of peach-filled donuts.
To write : An inequality to represent how many batches of the new type of donuts can be produced in a 10 hour day.
Solution :
Time taken to cook the raspberry donuts = [tex]11x[/tex] minutes
Time taken to cook the peach donuts = [tex]8y[/tex] minutes
Donuts produced in 10 hours
1 hours = 60 minutes
10 hours = 60 × 10 = 600 minutes
Total time ≤ 600 minutes
Therefore, the required equation is
→ [tex]11x + 8y \leq 600[/tex]
A pack with 6 cans of juice costs 3.48. What it the unit price?
A.0.49 per can B.0.50 per can C.0.58 per can D.0.60 per can**my answer??**
The unit price of one can of juice, when a 6-pack costs $3.48, is $0.58 per can.
The question asks us to calculate the unit price of a juice can when a pack of 6 cans costs $3.48.
To find the unit price, we divide the total cost of the pack by the number of cans in a pack.
In this case, we divide $3.48 by 6, which gives us $0.58.
$3.48 / 6 = $0.58
Therefore, the unit price per can is $0.58.
36% of what number is 180?
The length of a rectangle is 3 meters more than twice its width. the length of this rectangle is 10 meters. write an equation to solve the perimeter of this rectangle
a magazine costs 3.50 how much can you buy with 100$
The seats at a local baseball stadium are arranged so that each row has five more seats than the row in front of it. If there are four seats in the first row, how many total seats are in the first 24 rows?
These are the choices
1,476
2,856
2,952
1,428 ...?
Anne Katz, owner of Katz Sport Shop, loans $8,000 to Shelley Slater to help her open an art shop. Shelley plans to repay Anne at the end of 8 years with interest compounded semiannually at 8 percent. At the end of 8 years, Anne will receive: