The 18th term of the sequence is -140
How to determine the term
It is important to note that the formula for the nth term of an arithmetic sequence is expressed with the equation;
an = a + (n - 1) d
Such that the parameters are enumerated as;
an is the nth term of the arithmetic sequencea is the first term of the sequencen is the number of terms in the sequenced is the common differenceFrom the information given, we have;
The sequence is;
-21, -14, -7, 0, 7, ...
Then, the common difference = -14 - (-21) = -14 + 21 = -7
Substitute the value
a18 = -21 + (18 - 1) -7
expand the bracket
a18 =-21 + (17)-7
a18 = - 21 - 119
a18 = - 140
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The drawings above represent the tablecloths margot is thinking about buying. She plans to sew a decorative fringe on the tablecloth. About how much fringe will margot have to sew on the round tablecloth?
Answer:
Step-by-step explanation:
first give me a high five
Help me please and tthanks
Answer:
59
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic charged $45 per hour, and the second mechanic charged $50 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $1150. How long did each mechanic work?
Answer:
First one worked for 20 hours, second one worked for 5 hours.
Step-by-step explanation:
50 times 5 : 250
45 times 20 :900
250+900 = 1150
Factor the trinomial completely
64x² +8x+1/4
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(Factor completely. Simplify your answer. Use integers or fractions for any numbers in the expression)
A. 64x² + 8x + =
B. The polynomial is prime.
A.Factorizing the polynomial is (8x + 1/2)².
B.The polynomial 64x² + 8x + 1/4 is not prime.
define factorizationFactorization is the process of expressing a mathematical expression, such as a number or a polynomial, as a product of its factors or simpler components.
To factorize 64x² + 8x + 1/4, we can use the factoring formula for a quadratic trinomial:
a² + 2ab + b² = (a + b)²
In this case, we have 64x² + 8x + 1/4, so we can rewrite it as:
(8x)² + 2(8x)(1/2) + (1/2)²
Notice that the first and last terms are perfect squares, so we can apply the factoring formula to get:
(8x + 1/2)²
Therefore, the factorization of 64x² + 8x + 1/4 is:
64x² + 8x + 1/4 = (8x + 1/2)²
The polynomial 64x² + 8x + 1/4 is not prime.
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I’ll give braniest to the best answer
Twoskaters are practicing at the same time on the same rink. A coordinate grid is superimposed on the ice. One skater follows
the path y = - 3x + 60, while the other skater follows the curve y = - 3x^2+ 24x. Find all the points where they might collide if they
are not careful.
Answer:
They will collide at (2,28),(8,16)
Step-by-step explanation:
give me branliest
A jet travels 1959 miles against a jetstream in 3 hours and 2289 miles with the jetstream in the same amount of time. What is the rate of the jet in still air and what is the rate of the jetstream?
Therefore, the rate of the jet in still air is 708 mph and the rate of the Jetstream is 55 mph.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides separated by an equal sign (=). The left-hand side of the equation contains one expression and the right-hand side contains another expression. An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Here,
Let's call the rate of the jet in still air "v" and the rate of the Jetstream "w". When the jet travels against the Jetstream, the effective speed of the jet is v-w, and when it travels with the jetstream, the effective speed is v+w.
We can set up two equations based on the given information:
1959 = 3(v - w)
2289 = 3(v + w)
Simplifying these equations, we get:
653 = v - w
763 = v + w
Now we can solve for v and w using elimination or substitution. Let's use elimination:
Add the two equations together:
653 + 763 = 2v
v = 708 mph
Substitute v back into either equation to solve for w:
763 = v + w
763 = 708 + w
w = 55 mph
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find hcf of 24x^3yz^4; 30x^2y^2z^3 and 36x^3y^2z^3
The HCF is 6x^2yz^3
What is HCF?HCF means Highest Common Factor. HCF of two or more numbers is the greatest factor that divides the numbers. It is also the greatest possible number of all their common factors.
To find the HCF of the following,
24x^3yz^4 , 30x^2y^2z^3, 36x^3y^2z^3
To find the HCF among the first value,
24 , 30 and 36
Factors of 24 are 2, 3, 4, 6, 8, 12, 24
Factors of 30 are 2, 3, 5, 6, 10, 15, 30
Factors of 36 are 2, 3, 4, 6, 9, 12, 18, 36.
The highest common factor that it can be divisible with is 6
Among x^3 , x^2 and x^3
The factors of x^3 are x, x^2, x^3
Factors of x^2 are x, x^2
Factors of x^3 are x, x^2, x^3
The highest common factor is x^2
Among y , y^2 and y^2
Factors of y is y
Factors of y^2 are y, y^2
The highest common factor is y
And among z^4 , z^3 and z^3
Factors of z^4 are z, z^2, z^3, z^4
Factors of z^3 are z, z^2, z^3
The highest common factor here is z^3
Therefore, the highest common factor is 6x^2yz^3
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Please help with this one problem at the bottom only
The number of CDs that need to be produced by the company in order to break even would be 685 CDs .
How to find the breakeven point ?To break even, the revenue generated by selling the CDs must equal the total cost of producing them. Let's denote the number of CDs produced and sold as a.
Revenue = Price per CD × Number of CDs = 52a
Total Cost = Fixed Cost + Variable Cost × Number of CDs = 26000 + 14a
To break even, we set Revenue equal to Total Cost:
52a = 26000 + 14a
Now, we can solve for a:
52a - 14a = 26000
38a = 26000
a = 26000 / 38
a = 685 CDs
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James is 13 and lily is 5. how old would jacob be when lily's 10? How old would jacob be when lilys 16?
(Im super confused lol, 35 points)
Answer: When Lily is 10, Jacob will be 18. When she is 16, he will be 24.
Step-by-step explanation: This is because Jacob is 8 years older than Lily, as seen by subtracting her age from his age (13 - 5 = 8). From there, we just add 8 to Lily's ages from then on. 10 + 8 = 18, and 16 + 8 = 24.
What are the intercepts and asymptote of h(x)? Explain how to find these using the graph.
The value of y-intercept = -1 and The value of x-intercept = -4
The value of the vertexes is-
Horizontally vertex: y = -2
Virtically vertex: x = -5
For the y-intercept, you must look at where the graph intersects with the y-axis. In this case, the graph intersects at -1.
For the x-intercept, you must look at where the graph intersects with the x-axis. In this case, the graph intersects at -4.
The horizontal asymptote is a y value the graph approaches but does not pass or touch. In this case, the y value is -2.
The vertical asymptote is an x value the graph approaches but does not pass or touch. In this case, the x value is -5.
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pleaseeee
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
To find the annual rate of change between 1992 and 2006, we can use the formula:
r = [tex](V_2/V_1)^{1/n}-1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.
=>r = -0.0839
Therefore, the rate of change between 1992 and 2006 is -0.0839.
To express the rate of change in percentage form, we can multiply the result from part A by 100:
=>r = -0.0839 x 100
=> r = -8.39%
Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.
To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.
From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:
where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.
=>V = 11792.51
Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).
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Find the equation of the line.
Use exact numbers.
y=y=y, equals
x+x+x, plus
A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, negative nine and one, negative five.
A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, negative nine and one, negative five.
The equation of the line is y=-4x+9. In order to find the equation of the line, we must first calculate the slope (m) of the line.
What is slope?Slope is a measure of the steepness of a line on a graph. It is calculated by finding the ratio of the vertical change between two points, divided by the horizontal change between the same two points.
The slope is calculated by dividing the change in y-coordinates (rise) by the change in x-coordinates (run).
In this case, the rise is -5 – (-9) = 4, and the run is 1 – 0 = 1. Therefore, the slope of the line is m = 4/1 = 4.
Next, we plug the slope and a point on the line into the point-slope form of a line equation: y - y1 = m(x - x1).
We can choose any point on the line, so let's use (0, -9).
Plugging in the values, we get:
y - (-9) = 4(x - 0)
Simplifying, we get:
y = 4x - 9
Therefore, the equation of the line is y = 4x - 9.
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[tex]-7\sqrt[3]{193x^{10} }[/tex]
Answer:
-7\sqrt[3]{193}x^3\sqrt[3]{x}
Step-by-step explanation:
Find the measure of X around to the nearest hundredth.
Answer:
15.36
Step-by-step explanation:
In this equation, we will be using tangent, which is opposite over adjacent. In this case, the "opposite" will be x, and the "adjacent" will be 12. "θ" means the degrees or measurements of the angle.
To find the missing side of the triangle, we will set up a function. The function is:
Tan (θ) = opposite/adjacent
After plugging in the numbers and variables it will be:
Tan(52) = x/12
Then, we would multiply the 12 to both sides.
12 Tan(52) = x
Then we can plug it into a calculator. We should get 15.3592. We would then round it to the nearest hundredth, which is 15.36.
What is the measure of a dekaliter?
Answer: Ten liter, or one tenth of a hectoliter (2.6418 gallons liquid measure or 1.135 pecks dry measure): abbrev.dal.
0 divided by 1 . what is the answer
Answer: 0
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
0 divided by 1 is 0 similarly to other numbers.
For example 5/1 = 5
Although, 1/0 is undefined as it isn't legal.
The county fair charges $10 admission and $2 per ride. What is the cost for one admission and r rides
Considering the definition of an equation, the cost for one admission and r rides is Cost= 10 + 2×r
Definition of equationAn equation in mathematics is defined as an equality established between two expressions, in which there may be one or more unknowns that must be solved.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a raised equation, means to determine by means of certain procedures the value that satisfies it.
Cost in this caseBeing "r" the number of rides, and knowing that:
The county fair charges $10 admission.The county fair charges $2 per ride.the equation in this case is:
Cost= 10 + 2×r
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Joe’s Convenience Store took in $720 last week. According to Example Graph #1, about how much money did he make from selling comic books?
Joe made about $72 from selling comic books last week.
How to solveTo determine how much money Joe made from selling comic books, we need to find the percentage of $720 that corresponds to comic book sales.
According to the graph, comic book sales account for 10% of Joe's total sales.
To calculate this, we can multiply the total sales ($720) by the percentage of comic book sales (10% or 0.1):
$720 x 0.1 = $72
Therefore, Joe made about $72 from selling comic books last week.
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Joe’s Convenience Store took in $720 last week. According to Example Graph #1, about how much money did he make from selling comic books?
From the content of the graph
The amount of money Joe made is given below:
Selling comic books 10%
Selling costumes 25%
Selling hardware 40%
Selling miscellaneous 20%
What’s the pattern of 1/2,2/4, &4/8?
By answering the presented question, we may conclude that Therefore the pattern is that these three fractions are all equal and reflect the same proportion of a whole, which is half.
what is fraction?In mathematics, a fraction is a number that represents a component of a whole or a ratio between two things. It is shown as a top number (numerator) split by a horizontal line, also known as a vinculum, over a bottom number (denominator). For example, the fraction 3/4 indicates three-quarters of a whole split into four equal pieces. A fraction can be expressed using proper fractions, improper fractions, or mixed integers. A appropriate fraction is one with a numerator smaller than the denominator, such as 2/5.
The provided fractions 1/2, 2/4, and 4/8 have the pattern of being comparable fractions.
This indicates that even though they are worded differently, they reflect the same percentage or quantity of a total. Each fraction, in particular, represents half of the whole.
To see that these fractions are comparable, divide the numerator and denominator by the same number. For example, 2/4 may be simplified by dividing both the numerator and denominator by 2, yielding 1/2. Similarly, we may simplify 4/8 by dividing the numerator and denominator by 4, yielding 1/2.
Therefore the pattern is that these three fractions are all equal and reflect the same proportion of a whole, which is half.
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What is 0.35 of 100.00 + 0.5
of 150.50?
Answer:
Step-by-step explanation:
0.35 = 35/100
100.00 = 100
100×(35/100) = 35
0.5 = 5/10 = 1/2
150.50 = 1505/10
(1505/10)×(1/2) = 75,25
35+75.25 = 110.25
14 At the school play, there were a total of 175 tickets sold. Of those, 125 were adult tickets, and the remaining amount was child tickets. What is the ratio of the number of child tickets to the total number of tickets sold? *Simplify A. 2 to 7 B. 2 to 5 C. D. 7 to 2 5 to 7
Answer:
A) 2 to 7
Step-by-step explanation:
Step 1: Determine How Many Child Tickets Were Sold
The question is asking about the ratio of the number of child tickets sold to the number of total tickets sold, but we can't find that unless we know how many child tickets were sold, so let's figure that out first.
We are given that 175 tickets were sold. Of those 175 tickets, 125 were adult tickets, and the rest were child tickets. This means that the number of total tickets sold was equal to the sum of the number of child and adult tickets sold. Therefore, there were 175 - 125 = 50 child tickets sold.
Step 2: Determine the Ratio of Child Tickets to Total Tickets
We now know that 50 out of the 175 total tickets sold were child tickets, so we can find the ratio of the two values. Remember that a ratio just represents the relation between numbers, so we can write the current ratio of child tickets to total tickets as 50 to 175. However, since ratios can be written as fractions, we quickly see that this ratio can be simplified.
In fraction form, this ratio is [tex]\frac{50}{175}[/tex]. Simplifying this fraction by dividing both the numerator and denominator by their greatest common factor, which is 25 in this case, gives us [tex]\frac{2}{7}[/tex], so the final ratio is 2 to 7.
At present, the length of a rectangular soccer field is 55 yards longer than the width. The city council is thinking of rearranging the area containing the soccer field into two square playing fields. A math teacher on the council decided to test the council member's mathematical skills.
He told them that if the width of the current field were to be increased by 5 yards and the length cut in half, the resulting field would be a square. What are the current dimensions of the field?
The current dimensions of the rectangular soccer field are 45 yards by 100 yards.
What is area of the rectangle?
Area = Length × Width
Here let the width be "w" yards.
Then, according to the problem, the length is 55 yards longer than the width, so the length would be "w + 55" yards.
We can use this information to create an equation for the area of the rectangular field:
Area = (w + 55)w
Area = w² + 55w
Next, the problem tells us that if we increase the width by 5 yards and cut the length in half, we get a square. Let's call the side length of this square "s". We can create another equation for the area of this square:
Area = Side length²
Area = s²
We can use algebra to solve for the current dimensions of the rectangular soccer field. First, we need to find an equation for the side length of the square in terms of the current dimensions of the rectangular field:
s = w + 5 (since we increased the width by 5 yards)
s = (w + 55)/2 (since we cut the length in half)
Setting these two equations equal to each other and solving for "w" gives us:
w + 5 = (w + 55)/2
2w + 10 = w + 55
w = 45
So the width of the rectangular soccer field is 45 yards. Using the equation we created earlier for the length, we can find the length:
Length = Width + 55
Length = 45 + 55
Length = 100
Therefore, the current dimensions of the rectangular soccer field are 45 yards by 100 yards.
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anyone have an idea of what this may be?
The values of the segments A'B' and B'B for the similar triangle ∆ABC area 4 and 4 respectively.
How to calculate the for the segments of the similar triangleThe triangles ABC and A'B'C are similar, this implies that the length A'C of the smaller triangle is similar to the length AC of the larger triangle
so for the segment A'B;
3/9 = A'B'/12
A'B' = (3 × 12)/9 {cross multiplication}
A'B' = 4.
Also for the segment B'B;
3/9 = 2/(2 + B'B)
3(2 + B'B) = 2 × 9 {cross multiplication}
6 + 3B'B = 18
3B'B = 18 - 6
B'B = 12/3
B'B = 4
Therefore, the values of the segments A'B' and B'B for the similar triangle ∆ABC area 4 and 4 respectively.
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A car last month was $250 this month its $330. What is the percent increase
Answer:
Step-by-step explanation:
We Know
A car last month was $250 this month its $330
What is the percent increase?
We Take
(330 ÷ 250) × 100 = 132%
Then We take
132 - 100 = 32%
So, 32% increase.
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
A.
h(13) = 18
B.
h(2) = 16
C.
h(-3) = -1
Miguel reads 3 pages in 5 minutes. He reads at a constant rate.
3
What fraction of a page does Miguel read in 1 minute?
O A
OB.
OC.
O D.
15
1
3
2|3
It is obvious that he cannot read an entire page in one minute, meaning D (2/3) is literally the only possible answer.
Four people are standing on line. The tall man is between a woman with a red hat and a little boy. The little boy is next to a teenager who is not last. In what order are they standing?
We can use logical reasoning to conclude that the order is "teenager, little boy, tall man, and woman" as per the explanation below, based on the clues.
What is logical reasoning?Logical reasoning is a process of using rational thinking and deduction to arrive at a conclusion based on available information. In the given problem, logical reasoning is used to analyze the provided clues and determine the order of the four people standing in line.
By carefully examining the clues and using a process of elimination, we can deduce the position of each person in the line. We use logical reasoning to eliminate the possibilities that contradict the given information, and to arrive at the correct sequence that fits all of the provided conditions.
First, we know that the tall man is between the woman and the little boy. So, they can appear in either of the following orders:
woman - tall man - little boylittle boy - tall man - womanHowever, we are told that the little boy is next to a teenager who is not last. So:
woman - tall man - little boy - teenager --> Incorrect, because the teenager would be last.teenager - little boy - tall man - woman --> Correct, because the teenager would be in a different position.Thus, we can conclude that we have correctly answered this question.
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4. The Bagel Factory baked 200 dozen bagels at a cost of R3.60 per dozen. Five dozen bagels become stale and cannot be sold, and 12 dozen are sold at a reduced price of R1.80 dozen. Find the selling price per dozen bagels that will give the bakery their required mark- up of 66% of cost. per
Answer:
R5.98
Step-by-step explanation:
R3.60×66÷100= R2.38 (66% of R3.60)
R3.60+R2.38= R5.98
how to find 66%
R5.98-R3.60
=R2.38÷R3.60
=R0.66×100
=66%
A circular cookie cake costs $14.13. If the diameter of the cookie cake is 6 inches, what is the approximate cost per square inch of the cookie cake? Use π = 3.14.
$0.13
$0.25
$0.50
$0.75
The apprοximate cοst per square inch οf the cοοkie cake is $0.50.
What is the diameter?A line segment cοnnecting twο pοints οn a circle's perimeter and passing thrοugh its center is said tο be the circle's diameter. It is the furthest pοint οn the circle that can be measured.
The equation A=[tex]\pi r^{2}[/tex],where r is the circle's radius, determines the area οf a prοcess. The radius οf the cοοkie cake is equal tο half οf its diameter, οr 6 inches, οr 3 inches. The cοοkie cake's surface area is as fοllοws:
A = [tex]\pi r^{2}[/tex]
= 3.14 x [tex]3^{2}[/tex]
= 28.26 square inches
We divide the tοtal cοst by the area tο determine the apprοximate cοst per square inch οf the cοοkie cake:
Cοst per square inch = $14.13 / 28.26
= $0.50
As a result, the cοοkie cake cοsts abοut $0.50 per square inch.
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The volume of a soap bubble is 1,696.5mm^3. Find the radius and diameter of the soap bubble. Use 3.14 for pie
After solving the question, we can say that diameter of the soap bubble =14.30 mm.
what is sphere ?A sphere, like a ball, is a three-dimensional geometrical object that is completely spherical. It is a symmetrical form with all points on its surface being equidistant from the centre. The radius of a sphere is the distance from its centre to its surface. Spheres can be found in nature in the shape of planets, stars, and bubbles, and they are utilised in a variety of applications including sports equipment, ball bearings, and aesthetic things.
volume of a sphere
[tex]V = (4/3) * \pi * r^3\\ r = (3V / 4 \pi)^(1/3)\\ r = (3 * 1696.5 mm^3 / (4 * 3.14))^(1/3)\\ r = 7.15 mm[/tex]
d = 2r
d = 14.30 mm
diameter of the soap bubble =14.30 mm.
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