The 3rd term in the given sequence is 45
What is sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given that, first and nth term of a sequence a₁ = 4 and aₙ = 3aₙ₋₁ + n
a₁ = 4
aₙ = 3aₙ₋₁ + n
So, a₂ = 3a₂₋₁ + 2
= 3a₁ + 2
= 3×4+2
= 14
Therefore,
a₃ = 3a₋₁ + 3
= 3a₂ + 3
= 14×3+3
= 45
Hence, a₃ = 45
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What ordered pairs are the solutions of the system of equations shown in the graph below?
Answer: (-4, 1) (-8, 9)
Explanation: These points are where the two functions meet
One lap around the inide lane of a tandard track i equal to 400 meter. Brad jog one lap around a track in one minute 30 econd. Auming he can maintain thi pace, how long will it take him to run a mile? Round your anwer to the nearet tenth of a minute
Brad takes 6 minutes to run a mile assuming he can maintain the same pace.
Given that,
One lap around the inside lane of a standard track = 400m
Time taken for Brad to jog one lap around a track = 1 minute and 30 secs
We know that one mile = 1609.34 meters = 1600 meters (approximately)
Since Brad can jog 400m in 1 minute and 30 secs
1600 meters = 400*4 meters
Assuming that he can maintain the same pace:
so, the total time taken to run 1 mile = 1 minute 30 secs * 4 = 6 minutes
Hence, Brad takes 6 minutes to run a mile assuming he can maintain the same pace.
Correct question: One lap around the inside lane of a standard track is equal to 400 meters: Brad jogs one lap around a track in one minute and 30 seconds. Assuming he can maintain this pace, how long will it take him to run a mile? Round your answer to the nearest tenth of a minute.
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Last week, Darell spent 5 hours doing homework. Bruce did homework for 1/5 as many hours as Darell did. How many hours did Bruce spend doing homework?
The number of hours Bruce spent doing homework last week if he spent 1/5 of Darell's time is 1 hour.
How to solve fractions?Time Darell spent doing homework last week = 5 hours
Time Bruce spent doing homework last week = 1/5 of Darell's time
= 1/5 of 5
= 1/5 × 5
= (1 × 5) / (5 × 1)
= 5/5
= 1 hour
In conclusion, given the fraction of time Bruce spent doing homework last week, that means, he spent 1 hour doing homework.
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factor each expression. You can check your answer by distributing. 8d + 20e
The factorization of given expression is 4(2d+5e).
What is factorization?The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.
The given expression is 8d+20e.
In the given expression there are two terms and factors them are
8d= 2×2×2×d
20e= 2×2×5×e
So, the greatest common factor is 4
Now, 4(2d+5e)
Therefore, the factorization of given expression is 4(2d+5e).
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A fence post that is 5 feet tall casts a 2-foot shadow at the same time that a tree that is 26 feet tall casts a shadow in the same direction. Determine the length of the tree's shadow.
5.2 feet
10.4 feet
12.2 feet
15.4 feet
Answer:
10.4 feet
Step-by-step explanation:
26/5 = 5.2
5.2(2)=10.4
The length of the tree's shadow is 10.4 feet. Option B is correct.
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
We can use similar triangles to solve this problem.
The ratio of the height of the fence post to its shadow is the same as the ratio of the height of the tree to its shadow.
(height of fence post) / (length of fence post's shadow) = (height of tree) / (length of tree's shadow)
Substituting the given values, we get:
5 / 2 = 26 / x
where x is the length of the tree's shadow.
Cross-multiplying and solving for x, we get:
x = 26 × 2 / 5
= 10.4 feet
Therefore, the length of the tree's shadow is 10.4 feet.
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I need help on filling in the blanks for these shapes
We can see here that the triangles have been attached to the corresponding angles and sides.
(a) ∠A ≅ ∠Y
∠B ≅ ∠Z
∠C ≅ ∠X
(b) Side AB ≅ Side YZ
Side AC ≅ Side YX
Side BC ≅ Side ZY
(c) ΔABC ≅ Δ YZX
What is congruent?Congruent refers to the state of two geometric figures or shapes having the same size and shape. Two figures are congruent if one can be superimposed on the other by a combination of rotation, reflection, and translation.
Congruence is often denoted by the symbol “≅”. Congruence is a fundamental concept in Euclidean geometry, and it applies to many types of geometric figures, including lines, angles, triangles, and polygons.
We can see that the various angles and sides has been shown above.
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In the triangle below, with right angle Q, suppose that m/R= (3x+2) and m/S= (2x+18).
Find the degree measure of each angle in the triangle.
solve each system by substitution
y=4x
x-2y=56
Answer:
-8
Step-by-step explanation:
Since it tells you that y=4x you can use that to replace y in the next equation so now it's
X-2(4x)=56
Distribute the -2
X-8x=56
Subtract -8x from x
-7x=56
Divide by -7
X=-8
Answer:
x=−8
y=−32
pspdwdpvprngbpnrpt
please please
can someone give answers?
Answer:
1. A,2. C, 3. B.-------------------------------
Question 1Opposite leg / hypotenuse is the ratio for sine:
sin 40° = x/20Correct choice is A.
Question 2Opposite leg / adjacent leg is the ratio for tangent:
tan 53° = x/12Correct choice is C.
Question 3Adjacent leg / hypotenuse is the ratio for cosine:
cos 51° = 10/xCorrect choice is B.
The ratio for tangent is opposite leg/adjacent leg,tan 53° is x/12.
The opposing side's ratio to the hypotenuse is what?We'll use the term sine and the symbol sin to denote the ratio of a right triangle's opposing side to hypotenuse. The cosine, denoted by the symbol cos, is the ratio between the neighboring side and hypotenuse of a right triangle.
The cosine, denoted by the symbol cos, is the ratio between the neighboring side and hypotenuse of a right triangle.
Explanation:
The first question is:
Correct answer is A: sin 40° = x/20.
The ratio for tangent is opposite leg/adjacent leg:
tan 53° = x/12
C is the proper selection.
The cosine ratio is the adjacent leg to hypotenuse:
cos 51° = 10/x
B is the proper selection.
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The Chamber of Commerce of a city in central Florida is making brochure to attract tourists. They recorded the high temperatures (in degrees Fahrenheit) for a week in January to be 75, 72, 73, 56, 62, and 71. If you were a tourist planning to visit the area, which of these measures of central tendency would be the best to use as the most accurate indicator of the temperature for planning your wardrobe? Correct mean median mode range
The measure of central tendency that would be the best to use as the most accurate indicator of the temperature for planning your wardrobe is the mean.
What is the mean?The ratio between the sum of all observations and the total number of observations in a data set is known as the mean in statistics. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set.
When a data set is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
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Drag each title
Match the mortgage types with their descriptions
Each of the mortgage types should be matched with the correct description as follows:
Government insured: it requires the buyer to make a 20% down payment.Balloon mortgage: a large portion of principal is paid in a single payment at the end of the loan.Fixed rate: it has the same interest rate for the life span of the loan.Conventional: it requires a lower down payment and allows buyers to have a lower credit score.Hybrid: it initially has a fixed rate for three to five years and then adjusts at a predetermined time.Adjustable: it starts with a low interest rate and then adjusts throughout the duration of the loan.What is mortgage brokering?Mortgage brokering can be defined as a strategic process which typically involves a mortgage broker acting as an intermediary between a financial institution such as a mortgage bank that is offering loans and an individual that seeks to collect (obtain) this loan.
What are the types of mortgage?Generally speaking, there are different types of mortgage and these include the following:
Government insured mortgage.Balloon mortgage.Fixed rate.Conventional mortgage.Hybrid mortgage.Adjustable mortgage.In conclusion, a government insured mortgage is a type of mortgage that requires a buyer making a 20% down payment.
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Complete Question:
Match the mortgage types with their descriptions. it requires the buyer to make a 20% down payment. a large portion of principal is paid in a single payment at the end of the loan. it has the same interest rate for the life span of the loan. it requires a lower down payment and allows buyers to have a lower credit score. it initially has a fixed rate for three to five years and then adjusts at a predetermined time. it starts with a low interest rate and then adjusts throughout the duration of the loan.
8.3 points
What is the leading coefficient in the polynomial 2v³ +4v² + 1?
2
4
1
3
The leading coefficient in the polynomial 2v³ +4v² + 1 will be A. 2
How can you determine a polynomial's leading coefficient?The term with the highest power of x is the leading term in a polynomial. As an illustration, the leading term in 7 + x + 3x² is 3x².
The leading coefficient is the number in front of the variable with the highest power
A polynomial's leading coefficient is the coefficient of the leading term. The leading coefficient in the aforementioned illustration is 3.
In this case, this will be 2v³. The coefficient is 2.
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What is the formula for finding the distance between two parallel lines?
[tex]d=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}[/tex] is the formula used to calculate the distance between two parallel lines. This is derived from the slope-intercept equation.
The two lines that never cross over one another are referred to as parallel lines. When the separation between these two lines is considered constant, then these two lines are parallel.
As a result, the distance between two lines can be determined by considering their perpendicular distance. The two parallel lines can be written using the slope-intercept form as y = mx + c₁ and y = mx + c₂, respectively.
Then, the formula to calculate distance is given by, [tex]d=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}[/tex]. Here, the intercepts of the two lines are c₁ and c₂, and a and b are the constants or integers.
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Which two points on the number line represent numbers that can be combined to make zero?
B and D
A and B
C and D
A and C
Answer:
B and D
Step-by-step explanation:
-2+2=0
What is the y-intercept of y =- 2 5?
Comparing the given expression with the slope-intercept form, the intercept value is calculated. And the value is -2/5.
A line's slope gives information about its steepness or indicates how much y rises as x rises. The equation is typically written as y=mx+b in slope-intercept form. The slope in this equation is represented by the letter m, and the y-intercept is represented by the letter b. The y-intercept is calculated in the subsequent step by comparing the given expression with this.
The given expression is y =- 2/5. Comparing this expression with y=mx+b, we get, m=0, x=0, and b=-2/5. Therefore, the required y-intercept is -2/5.
The complete question is -
What is the y-intercept of y =- 2/5?
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in 2009 the average weekly wage of men exceeded that of a woman by $162. the sum of their average wages equaled $1476. write and solve a system of equations to determine the average wage of men and of women in 2009
Trevor's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 5 coffees in all, 4 of which were regular. What percentage of the coffees were regular? Write your answer using a percent sign (%)
Answer:
80%
Step-by-step explanation:
since there were 5 coffees but 4 out of it were regular
mathematically
that's 4/5
but to percentage
that's times 100
4/5×100
4×100 all divided by 5
400 divided by 5
80%
Nadia is a stockbroker. She earns 12% commission each week. Last week, she sold $5,300 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Nadia made commission of $636 last week
She made $33072 commission in 2011.
What is percentage?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given,
Weekly commission of Nadia = 12%
Cost of stocks Nadia sold last week = $5300
Commission made by Nadia last week = 12% of $5300
= (12/100) × 5300
= 12 × 53
Commission made by Nadia last week = $636
No. of weeks in 2011 = 52 weeks
If she averages that same amount each week
Then commission made by her in 2011 = 52 × $636
= $33072
Hence, $636 is the commission made by Nadia last week,
$33072 is the total commission made by Nadia in 2011.
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What is the exponential form of 5 * 5 * 7 * 7 * 7?
The exponential form of 5 * 5 * 7 * 7 * 7 is [tex]5^{2}[/tex] * [tex]7^{3}[/tex] . Exponential form can be written from the prime factorization of the number.
To get the exponential form of a number we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. We can find the prime factorization of a number using factor trees, which are tools used to repeatedly break a number into products until all of the factors are prime numbers.
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Can you draw a triangle with sides of length 2cm 3cm and 7cm?
It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).
In the given question, we have to check that it is possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.
To check this we firstly add the 2 and 3
2 + 3 < 7
5 > 7
Now we add 2 and 7
2 + 7 > 3
9 > 3
Now we add 3 and 7
7 + 3 > 2
10 > 2
It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).
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what is the square root 15v to the 4th power times square root of 2v
the square root 15v to the 4th power times square root of 2v to the 3rd power is 15v^2 x 2v^3, or 30v^5.
What is square root?The square root of a number is a value that, when multiplied by itself, produces the original number. For example, the square root of 16 is 4 because 4 x 4 = 16. In mathematics, the square root of a number is written as a radical symbol, with the number inside the radical symbol. The square root symbol is also known as the radical symbol or radix.
To calculate this, first take the square root of 15v to the 4th power, which is 3v. Then take the square root of 2v to the 3rd power, which is 2v.
Finally, multiply 3v and 2v together to get the final answer of 30v^5.
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Complete questions as follows-
What is the square root 15v to the 4th power times square root of 2v to the 3rd power?
The function g is defined by the following rule. g(x) = 2x +1
The function g is defined by the following rule. g(x) = 2x +1 can be represented in the method given below-
How does this occur?
The function f with g is written as (fg)(x)=f(g(x)), and is understood as f of g of x. The function g will be used in place of any x in the function f, according to this statement (x)
f(x), where x is the input, is a common way to refer to a function. A function can be conceptualized as y = f in general (x).
x= -3 then g(-3) = 2(-3) + 1 = -5If x = -2 then g(-2) = 2(-2) + 1 = -3if x = -1 then g(-1) = 2(-1) + 1 = -1If x = 1 then g(1) then = 2(1) +1 =3This is how by taking various x value we can find the value of g(x) = 2x +1
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Why can’t astronomers take a picture of a black hole?
Gravity is so strong that even light cannot escape a black hole.
The nearest black hole is too far away to be seen.
There is no way to detect the locations of black holes.
Black holes are too large to photograph.
Answer:
A
Step-by-step explanation:
edge 2023
1. The function that describes the rigid motion could be (x, y) -
A. (2x, y).
C. (y,-22).
B. (x - 3,y).
D. (x,3).
HELP ME PLS
Choose the correct graph of the given systems of equations. y − 2x = −1 2y − x = 4 graph of two lines intersecting at two comma three with text on graph that reads One Solution 2, 3 graph of two lines intersecting at zero comma negative one with text on graph that reads One Solution 0, negative 1 graph of two parallel lines with positive slopes with text on graph that reads No Solution graph of two lines on top of each other with text on graph that reads Infinitely Many Solutions
The correct graph of the given systems of equations include the following: A. graph of two lines intersecting at two comma three with text on graph that reads One Solution 2, 3.
What is a graph?In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis and y-axis respectively.
Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (2, 3) as shown in the graph attached below.
By critically observing the graph of the given system of equations, we can logically deduce that it has only one solution, which is the ordered pair (2, 3);
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When a number greater than 1 is written in scientific notation the exponent is?
When a number greater than 1 is written in scientific notation, the exponent is positive.
Scientific notation is a way of expressing numbers that are very large or very small using a decimal number between 1 and 10, multiplied by a power of 10. For example, instead of writing the number 100,000,000 as 100,000,000, it can be written in scientific notation as 1 x 10^8.
The exponent of a number in scientific notation is the power of 10 that the decimal number is multiplied by, and it gives the number of places the decimal point is moved to the right or left to obtain the original number. In the example above, the exponent is 8, which indicates that the decimal point has been moved 8 places to the right to get the original number 100,000,000.
When the number is greater than 1, the exponent of scientific notation is positive and indicates that the decimal point is moved to the right.
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the graph below represents a linear function. which of the following equations models the linear graph above?
What are these two problems fully simplified?
Answer:
1. 3/2 x m^5 x n
2. 54 x m^11 x n^9
Ellie is 1.75 meters tall. At 3 p.m., she measures the length of a tree's shadow to be 20.25 meters. She stands 16.2 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
To find the height of the tree, we can use the tangent of the angle between the top of the tree and the tip of Ellie's shadow to find the height of the tree.
Tangent(theta) = Opposite / Adjacent
Opposite = height of tree
Adjacent = distance between Ellie and the tree
Tangent(theta) = height of tree / 16.2
We know that:
Tangent(theta) = 20.25 / 16.2
We can solve for the height of the tree by multiplying both sides of the equation by 16.2:
height of tree = Tangent(theta) * 16.2
height of tree = (20.25 / 16.2) * 16.2height of tree = 20.25
So, the height of the tree is 20.25 meters to the nearest hundredth of a meter.
Answer: the height of the tree is 20.25 meters to the nearest hundredth of a meter.
Step-by-step explanation:
If UV = x + 6 and UY = x - 1, find YV.
(WY INTERSECTS UV AT Y)
The length of YV is equivalent to 7.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that UV = x + 6 and UY = x - 1. Also, WY intersects UV at Y.
We can write that -
UV = UY + YV
YV = UV - UY
YV = (x + 6) - (x - 1)
YV = x + 6 - x + 1
YV = 7
Therefore, the length of YV is equivalent to 7.
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