The rule for the nth term of arithmetic sequence is a + (n - 1)d.
What is the nth term of arithmetic sequence?The difference between consecutive terms in an arithmetic sequence is always the same.An arithmetic sequence's nth term is given by a = a + (n - 1)d. The number d is known as the common difference because any two consecutive terms of an arithmetic sequence differ by d, and it can be found by subtracting any two terms a and an+1.Here also,
We use the definition for the nth term of an arithmetic sequence:
an = a1 + (n - 1) d
Here first term (a1) = 51
common difference (d) = a2 - a1
= 48 - 51
= -3
We have to find 20th term,
a[20] = a1 + (20 - 1) d
= 51 + 19 x -3
= 51 - 57
= - 6
Therefore 20th term of the sequence 51,48,45,42,... is -6.
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Graph the line with y-intercept -7 and slope 3/2
We are given the slope and the y-intercept so using the slope-intercept form:
y = mx + b, where m- slope, b- y-intercept.Substitute values to get:
y = (3/2)x - 7To graph a line we need two points, one is given, (0, - 7) - the y-intercept.
Find one more point, take even value of x to cancel the fraction, let it be x = 4, find its y-coordinate:
y = (3/2)*4 - 7 = 6 - 7 = - 1So our points are:
A(0, - 7) and B(4, - 1)Plot the points and connect to graph the line.
See below.
The graph of the linear equation:y = (3/2)*x - 7 can be seen in the image at the end.
How to graph the linear equation?A general linear equation is written as:y = a*x + b
Where a is the slope and b is the y-intercept. Then our linear equation is:y = (3/2)*x - 7
To graph it, we need to know two points in our line, to do so, we evaluate it in two different values of x. if x = 0y = (3/2)*0 - 7y = -7So we have the point (0, -7)
And if x = 2 then:y = (3/2)*2 - 7y = 3 - 7y = -4So we have the point (2, -4)
Now we just need to graph these two points and connect them with a line. You can see the graph below.
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A cricket 11 is to be chosen from 16 players of whom 7 are bowlers, 4 can keep the wicket. Number o
ways this can be done to contain exactly 5 bowlers, 2 wicketkeepers is
1) 945
2) 885
3) 630
4) 715
Answer:630
Step-by-step explanation:
We have to pick 11 players including 5 bowlers and 2 keepersThe number of ways in which we can choose 5 bowlers out of 7 are 7C5 = 7!/(5!*2!) =21The no. of ways in which 2 keepers can be selected out of 4 are 4C2 = 4!/(2!*2!) =6The number of ways to select remaining (11-5-2=) 4 players out of remaining (16-7-4=) 5 players are 5C4 = 5! /(4!*1!) = 5So, the total number of ways to select the team of 11 is 21 * 6 * 5 = 630A glass holds 3/4 cup of milk. A jug
contains 12 cups of milk. How many
glasses can be filled from the milk in the jug?
Answer: 16 glasses of milk
Step-by-step explanation: To find how many glasses can be filled with milk, we must know that this is a division problem. So, we divide 12 by 3/4 to get 16. When dividing, the answer will be greater than the number it is being divided by, because the reciprocal will be found, and it will be greater when multiplied. I hope this helped. Please mark brainliest (If can)
Find the median and mode of the following data: 34,21,56,33,34,12,53,72,45,23,11
Answer:
see explanation
Step-by-step explanation:
Median -
To find the median: Arrange the data points from smallest to largest. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.
Answer: 34
Mode -
The most frequent number—that is, the number that occurs the highest number of times.
Answer: 34
Answer:
I think
Mode = 34
Median = 34
Step-by-step explanation:
PLEASE HELP 20 POINTS
Graph
A
B
C
D
it is the 1st graph.
Graph A.
someone help me I need a good grade my mom gonna yell at my if i don't get it ):
AB¯¯¯¯¯¯¯¯ with endpoints A(4,4) and B(5,−1) is reflected in the line y=x to create its image A′B′¯¯¯¯¯¯¯¯¯¯. Graph A′B′¯¯¯¯¯¯¯¯¯¯. Then find the perimeter of the figure formed by the segments AB¯¯¯¯¯¯¯¯, B′B¯¯¯¯¯¯¯¯¯, and AB′¯¯¯¯¯¯¯¯¯ to the nearest tenth.
The perimeter of the figure is 5.0.
What is a perimeter?
The perimeter of a two-dimensional shape is the distance around the outside of the shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is the sum of the lengths of all four sides. The perimeter of a triangle is the sum of the lengths of all three sides.
To reflect a point across the line y=x, we can use the following formula:
(x', y') = (y, x)
Where (x', y') is the reflected point and (x, y) is the original point.
Using this formula, we can find the coordinates of the reflected points A' and B':
A' = (4, 4) -> (4, 4) -> (4, 4)
B' = (5, -1) -> (-1, 5) -> (-1, 5)
Therefore, the image of AB is A'B' with endpoints A'(4, 4) and B'(-1, 5).
To find the perimeter of the figure formed by the segments AB, B'B, and A'B', we can add up the lengths of these three segments. The length of AB can be found using the distance formula:
[tex]AB = \sqrt{((5-4)^2 + (-1-4)^2)}\\\\= \sqrt{(1^2 + (-5)^2)}\\\\= \sqrt{(1 + 25)}\\\\= \sqrt{26}[/tex]
The length of B'B can be found using the same formula:
[tex]B'B = \sqrt{((-1-(-1))^2 + (5-5)^2)}\\\\= \sqrt{(0^2 + 0^2)}\\\\= 0[/tex]
The length of A'B' can also be found using the distance formula:
[tex]A'B' = \sqrt{((-1-4)^2 + (5-4)^2)}\\\\= \sqrt{(-5)^2 + (1)^2}\\\\= \sqrt{25 + 1}\\\\= \sqrt{26}[/tex]
The perimeter of the figure is AB + B'B + A'B' = √26 + 0 + √26 = 2√26. To the nearest tenth, this is 5.0.
Hence, the perimeter of the figure is 5.0.
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find the coordinates of the centroid of DEF with vertices (0,4) (6,6) (2,2)
The coordinates of the centroid of triangle DEF with the vertices (0,4) (6,6), and (2,2) is calculated as: (8/3, 4).
How to Find the Coordinates of the Centroid of a Triangle?The formula for finding the coordinates of the centroid of a triangle is given as:
C(x, y) = [tex]( \frac{(x1+x2+x3)}{3}, ( \frac{(y1+y2+y3)}{3})[/tex].
Given the vertices of triangle DEF as follows:
D (0, 4) = [tex](x_1, y_1)[/tex]
E (6, 6) = [tex](x_2, y_2)[/tex]
F (2, 2) = [tex](x_3, y_3)[/tex]
Substitute the values into the centroid formula to find the coordinates:
C(x, y) = [(0 + 6 + 2)/3, (4 + 6 + 2)/3]
C(x, y) = (8/3, 12/3)
C(x, y) = (8/3, 4)
Therefore, the centroid has the coordinates that are calculated as: (8/3, 4).
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Kay uses 4 pints of broth to make a soup. How many quarts of broth does Kay use to make the soup?
Answer:
2 quarts
Step-by-step explanation:
1 quart = 2 pints
4 pints × (1 quart)/(2 pints) = 2 quarts
Answer:
2 quarts
Step-by-step explanation:
1 quart=2 pints
2 quarts=4 pints
Have a great day
Graph the function y=log(x-2)
HELP SO EASY!!!!!! ASAP
A polygon is said to be equilateral if all of its sides are the same length. Find the perimeter of the equilateral polygon whose vertices are as follows.
(−2,−4), (1,0), (1,5), (−2,9), (−7,9), (−10,5), (−10,0), (−7,−4)
The perimeter of the equilateral polygon with the given vertices is given as follows:
40 units.
How to obtain the perimeter of the polygon?The perimeter of a polygon is composed by the sum of the lengths of the outer edges of the figure.
From the figure given at the end of the answer, the parameters for the polygon with these given vertices are given as follows:
8 side lengths.Each side length is of 5 units. (as the polygon is equilateral, meaning that the side lengths are equal).Then, considering the 8 side lengths and the fact that they measure 5 inches, the perimeter of the polygon is given as follows:
Perimeter = 8 x 5 = 40 units.
(sum of 8 times the number 5 is equals to the multiplication of eight by five).
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Rectangle jklm is similar to rectangle wxyz. What is the scale factor of a dilation from jklm to wxyz ? enter your answer as a decimal in the box.
WXYZ to JKLM
JM is equal to 9, ZW is 13.5, JK is 12, and WX is 18.
To obtain the coordinates of the other shape, multiply the original shape by the scale factor
What is the scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
13.5 / 9 = 1.5
9 * 1.5 = 13.5 \s12 * 1.5 = 18
You have a scale factor of 1.5. (because if u multiply 1.5 by the original shape, u get the new shape)
JKLM ~ WXYZ
So JK ~ WX
So the scale factor = WX / JK
Scale Factor = 18 / 12 = 3 / 2 = 1.5
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Formula: B1+B2=2(Midsegemt) Solve for X
2x-4+3x+2=2(2x+4)
if possible please explain/ show work!
thank you so so much!
The mid term is 2,Accordingly, if n is even, there will only be one middle term, and if n is odd, there will be two middle terms.
How does the Midsegment Theorem work?According to the midsegment theorem, the third side of a triangle is parallel to the first two sides, and the length of the third side's midsegment is equal to half of that side's length.The Binomial Expansion is in its middle term. We are aware that (a + b)n has an extension that has (n + 1) words. We can write the middle term(s) of (a + b)n depending on the value of n. Accordingly, if n is even, there will only be one middle term, and if n is odd, there will be two middle terms.Explanation:
2x - 4 + 3x + 2 = 2(2x+4)
The mid term is 2.
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a high school offers these statistics: 25% of incoming students come from single-parent homes. 75% of incoming students come from two parent homes. 42% of incoming students from single parent homes eventually go on to get a college education.58% of incoming students from two parent homes eventually go on to get a college education. what percent of incoming students eventually go on to get a college education? group of answer choices
Whereas students from single parent or two parent homes make up 54% of new students, these students eventually go on to complete their college studies..
what is percentage ?By dividing the value by the entire value and multiplying the result by 100, one can compute the percentage. The formula for calculating percentage is (value/total value)100%.When a piece of a whole is stated as a percentage, it is not a fraction but rather a number between 0 and 100. There are three percentages: 100% for everything, 50% for half of it, and 0% for the remaining portion.
calculation
25% of new students come from one-parent households, which equals 0.25;
75% of new students come from two-parent households, which is 0.75.
42% of incoming students from homes with only one parent go on to complete their college studies = 0. 42
58 percent of incoming students who come from two-parent households go on to complete their education =0.58
= 0.25 * 0.42 + 0.75 * 0.58 = 0.54 = 54%.
Whereas students from single parent or two parent homes make up 54% of new students, these students eventually go on to complete their college studies..
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what is the answer i need them now I will give brainliest if correct
Answer:
5 6/7 or C option
Step-by-step explanation:
5 6/7 is equal to 5.857 and rounded it is 6
While all the others round to 5
Hopes this helps please mark brainliest
Solve the equation $32.001647(x-9.87)=31.999897(x-9.87)+0.000847.$ Enter your answer as an integer or decimal.
Solving the given equation, we calculate the value of x to be 10.369
What is equation?An equation is a mathematical statement that shows that two expressions are equal. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What is simplification?Simplification is the process of reducing an expression or equation to its simplest form by applying the rules of algebra. Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.
By isolating the variable x and using calculator, we find the answer = 10.369.
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answer my question what is the ?
Answer:
18
Step-by-step explanation:
for the first one, 2(5+1)+10=22
for the second one, 2(6+4)+10=30
using the same concept, 2(3+1)+10=18
?=18
im not sure if im right or not lol
Multiplying and Dividing Integers MC) What is the product of (−16)(−4)(−24)? −40 −44 −1,536 −448
The required product of the given product numeral is -1536. Option C is correct.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
= (−16)(−4)(−24)
= 64(-24)
= -1536
Thus, the required product of the given product numeral is -1536. Option C is correct.
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the scatter plot shows the number of days since several people filled their cars with gas and the gallons of gas in their tank. which is the most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up?
The most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up is 17 gallons.
On plotting the graph we will get ,
The most reasonable value of y corresponding to x = 3 is approximately 17 gallons.
A plot is a graphical technique for representing a data set, typically in the form of a graph that depicts the relationship between two or more variables. The plot can be created either by hand or by computer. Previously, mechanical or electronic plotters were used.
Graphs are a visual representation of the relationship between variables that are very useful for humans because they allow them to quickly derive an understanding that would not have been possible from lists of values. Graphs can also be used to read off the value of an unknown variable plotted as a function of a known variable given a scale or ruler, but this can also be done with data presented in tabular form. Function graphs are used in mathematics, science, engineering, and technology.
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Write the polynomial so that the powers of x are in descending order, -3x + 8x² - 11 +
9x³
Answer:
9x³+8x²-3x-11
Step-by-step explanation:
1. You can move sections around throughout the equation.
^Note: Be sure to keep the same signs (either positive or negative) for each section.
In this problem, the sections are (-3x), (8x²), (-11), and (9x³).
^Note: I kept the subtraction/negative sign
2. Rearrange the exponents in order from largest to smallest in the equation.
largest 9x³ +8x² -3x -11 smallest
^Note: -3x has an exponent of 1
Tanvi Is attending a school orchestra concert. She sees her math teacher seated 5 m ahead of her and her science teacher seated 12 m to her right. How far apart are the 2 teachers
Answer:
The two teachers are 13 feet apart
Step-by-step explanation:
Right Triangles
Ava, her math teacher, and her science teacher form a right triangle in which she is at the 90° vertex.
The distances from the three people must satisfy the Pythagora's theorem, where the distance between the two teachers (D) is the hypotenuse, thus:
D = 13 feet
Step-by-step explanation:
Tyler's savings account pays a simple annual interest rate of 3.25%. Suppose he deposits $5,000 in the
account and makes no additional deposits or withdrawals for 3 years. What will the total value of the account
be after 3 years?
Answer:
The total value of the account after 3 years will be $5,503.52.
Step-by-step explanation:
A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Tyler's bank account pays a straightforward yearly financing cost of 3.25%. Assume he stores $5,000 in the record and sets aside no extra installments or withdrawals for a long time.
The total value of the account after 3 years will be calculated as,
A = $5,000(1 + 0.0325)³
A = $5,000 x (1.0325)³
A = $5,000 x 1.1007
A = $5,503.52
The total value of the account after 3 years will be $5,503.52.
12, 18,27,...
Find the 8th term.
Check the picture below.
Answer:
205.03125
Step-by-step explanation:
You want the 8th term of the sequence that begins 12, 18, 27, ....
DifferencesThe first differences of the given terms are ...
18 -12 = 6
27 -18 = 9
These are not constant, so the sequence is not an arithmetic sequence.
RatiosThe ratios of sequential terms are ...
18/12 = 1.5
27/8 = 1.5
These are constant, suggesting the sequence is an exponential sequence. The equation for the n-th term is ...
an = 12(1.5^(n-1))
Then the 8th term is ...
a8 = 12(1.5^7) = 205.03125
__
Additional comment
The sequence could be quadratic if the second differences are all 9-6=3. In that case, the equation for the n-th term is ...
an = 1.5n(n +1) +9
and the 8th term is ...
a8 = 1.5·8(8+1) +9 = 117
<95141404393>
I need help with the statement and reason part. (Its ok if just one of the questions is answered.)
The triangles consist in rectangles ΔABD and ΔCDB are congruent triangles.
Given that,
To prove ΔABD ≅ ΔCDB.
In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
Here,
consider ΔABD and ΔCDB
1. AB = CD [opposite sides of a rectangle]
2. ∠A = ∠C [each angle of the rectangle is 90°]
3. AD = BC [opposite sides of a rectangle]
ΔABD ≅ ΔCDB
Thus, Both triangles ΔABD ≅ ΔCDB are congruent triangles, hence proved.
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Y==-2x+8 find x, if y is 16
Answer:
x = –4
Step-by-step explanation:
y = –2x + 8
16 = –2x + 8
2x = 8 – 16
2x = –8
x = –4
Amy needs to write a paper that contains more than 3,305 words for school. She has already written 1,450 words and writes at a rate of 265 words per day. Which of the following inequalities could be used to solve for x, the number of days it will take Amy to finish her paper?
Inequality that could be used to solve for x is;
1450 words + (265 words / day)x = 3305 words
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given that Amy has already written 1450 words out of 3305 words.
And she writes at the rate of 265 words per day.
To establish the inequality which could be used to solve for x,
Then Firstly, we will form an equation for the total number of days required to write her paper,
1450 words + (265 words / day)x = 3305 words.
Simplifying the above expression,
(265 words / day)x = 3305 words - 1450 words
To solve this linear equation, we'll find x = 7.
x = { 3305 words - 1450 words} / 265 words
x = 7 days.
Hence, inequality that could be used to solve for x is;
1450 words + (265 words / day)x = 3305 words
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Examine the parallelogram below. Given m/ABC = (3x + 1) and m /BCD = (8x - 8), then
m
HELP PLEASE IM BEGGING
The value of the angle m ∠ DAB in the parallelogram is 128 degrees
Angles in a ParallelogramIn a given parallelogram, the opposite sides and angles are equal to one another.
In the question given;
m∠ ABC = 3x + 1
m∠ BCD = 8x - 8
m∠ DAB = ?
m ∠ ABC + m∠ BCD = 180°
The sum of the two angles is equal to 180 degrees
3x + 1 + 8x - 8 = 180
11x - 7 = 180
11x = 187
x = 17
However, m∠ DAB = m∠ BCD
Two opposite angles are equal
m∠ DAB = 8x - 8
m ∠ DAB = 8(17) - 8
m ∠ DAB = 128 degrees
The angle is 128 degrees
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f(x)=−x−4, find f(-2)
By evaluating the function in x = -2, we will get:
f(-2) = -2
How to find f(-2)?To do that, we need to evaluate the given linear equation:
f(x) = -x - 4
We want to find f(-2), so we need to evaluate the linear equation in x = -2, this means that we just need to replace the variable by the corresponding number.
Then we will get:
f(-2) = -(-2) - 4
f(-2) = +2 - 4
f(-2) = -2
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AABC ~ AQRS
Find the missing side length, m.
R
B
3/
A
C
1
m = [?]
m
5
S
The value of missing side length(m) in ΔQRS is 15 cm.
How to solve the sides of triangle?
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them.Two triangles must have the same angles and, as a result, must be congruent if their sides are the same. If two triangles are congruent or not, we may determine this simply by looking at their sides.These two triangles are also equivalent if we know that two sides of one triangle and the angle between them are congruent to two sides and the angle between them of another triangle.ΔABC ~ ΔQRS
The sides of the triangle will be in equal ration of one another.
i.e., AB/AC = QR/QS
3/1 = m / 5
m = 15 cm
Hence, The value of missing side length(m) in ΔQRS is 15 cm.
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PLEASE ANSWER ASAP!
In February, 7 tulips bloom in a garden. In March, 18 tulips bloom. Find the percent change to the nearest percent.
Answer:
Step-by-step explanation:
157.1429% but you can round it down