Answer: The required value of the first term is 8.
Step-by-step explanation: We are given to find the first term of the arithmetic sequence for which the third term is 126 and sixty fourth term is 3725.
We know that
the nth term of an arithmetic sequence with first term a and common difference d is given by
[tex]a_n=a+(n-1)d.[/tex]
According to the given information, we have
[tex]a_{3}=126\\\\\Rightarrow a+(3-1)d=126\\\\\Rightarrow a+2d=126~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]a_{64}=3725\\\\\Rightarrow a+(64-1)d=3725\\\\\Rightarrow a+63d=3725~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Subtracting equation (i) from equation (ii), we get
[tex](a+63d)-(a+2d)=3725-126\\\\\Rightarrow 61d=3599\\\\\Rightarrow d=59.[/tex]
From equation (i), we get
[tex]a+2\times59=126\\\\\Rightarrow a=126-118\\\\\Rightarrow a=8[/tex]
Thus, the required value of the first term is 8.
When the factors of a trinomial are (x - p) and (x - q) then the constant term of the trinomial is:
A. The quotient of -p and -q
B. The product of -p and -q
C. The difference of -p and -q
D. The sum of -p and -q
The constant term will be the product of -p and -q.
What is a trinomial?A trinomial is an algebraic expression that has three non-zero terms and has more than one variable in the expression.
Given that the factors of a trinomial are (x - p) and (x - q) we need to determine the constant term of the trinomial:
We know that a trinomial in its factors form can be written as,
x² + (α+β)x + αβ, where α and β are factors.
So, here the constant term of the trinomial will be (-p) × (-q) = pq.
Hence the constant term will be the product of -p and -q.
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the table represents a function. what is the value of f(-1)?
f (-1) = - 3
f (-1) = - 1
f (-1) = 0
f (-1) = 6
The value of f(-1) from the table given is 0
Table of functionsTable of functions are used to find the relationship between variables. The variables x and y can be written as coordinate (x, y)
In order to determine f(-1), we need the value of f(x) at the point where x is 1. From the table, the value of f(-1) is 0
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For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year. The third year, he invested $1,000 more than 1/5 of the amount he invested the first year.
During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than 3/2 times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year.
If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ and the amount Sally invested the last year is $ .
If there are 11 apples and I eat one and split half of the rest with my friend. How many do i have?
The height of a ball thrown directly up with a velocity of 10 feet per second from a initial height of of 100 feet is given by the equation h(t) = -16tsquared + 10t + 100, where t is the time in seconds and h is the ball’s height, measured in feet. When will the ball hit the ground? Round your answer to the nearest tenth.
Answer:
The ball will hit at 2.83 seconds.
Step-by-step explanation:
It is given that,
Velocity with which a ball is thrown up is, v = 10 ft/s
Initial height, h = 100 ft
The equation for the height of an object as a function of t is given by :
[tex]h(t)=-16t^2+10t+100[/tex]...............(1)
Where
t is the time in seconds
h is the ball's height measured in feet
We have to find the time when the ball hits the ground. It can be calculated by solving the quadratic equation of equation (1). On solving we get the value of t as :
t = 2.832 seconds
So, at 2.83 seconds the ball will hit the ground. Hence, this is the required solution.
What are the factors of 60a
Answer:
Factors of 60 are:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
Simplify the following expression: 2x − 6y + 3x2 + 7y − 14x. 3x2 + 12x + y 3x2 − 12x − y 3x2 − 12x + y 3x2 − 12x − 13y
The required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.
Given that,
To simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
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,
= 2x − 6y + 3x² + 7y − 14x.
= 3x² + 2x -14x + 7y -6y
= 3x² -12x + y
Thus, the required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.
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jackson bikes 2 miles in 15 minutes. At this rate, how many miles will he bike in 45 minutes?
Which of these expressions is equal to 6 + (2 + 3) × 5
Solve the equation by completing the square. Round to the nearest hundredth if necessary? X^2+3x=24
What is the value of x in the equation 8 + x = 3? −5 5 11 24
Look at the cups shown below (please note that images are not drawn to scale): A cone is shown with width 3 inches and height 6 inches, and a cylinder is shown with width 3 inches and height 5 inches How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tent
Amount of juice that cup B will hold than cup A when both are completely full is A: 18.8 cubic inches. therefore, Option A: 18.8 cubic inches.
Amount of juice hold by Cup B which is in the shape of a cylinder having width 2 inches that is radius 1 inches and height 7 inches
πr^2h = π × 1^2 ×7 = 7π cubic inches
Amount of juice hold by cup A which is in the shape of a cone having width 2 inches that is radius 1 inches and height 3 inches
1/3 × π × r^2 h
1/3 × π × 1^2 × 3 = πcubic inches
Amount of juice that cup B will hold than cup A when both are completely full = 7π - π = 6π cubic inches
= 6 × 3.14
= 18.84 cubic inches
Option A: 18.8 cubic inches
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Question
Look at the cups shown below (please note that images are not drawn to scale):
A cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches.
How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.
18.8 cubic inches
21.9 cubic inches
25.1 cubic inches
32.6 cubic inches
c+1/c-2 = 4/7 please show how you got the answer
Your class is holding elections to choose a leadership committee of 4 students. If there are 30 students in the class, how many different leadership committees would it be possible to elect?
810,000
27,405
120
657,720
Using the combination formula, it is found that it would be possible to elect 27,405 different leadership committees.
The order in which the students are selected to the committee is not important, which means that the combination formula is used to solve this question.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 4 students are chosen from a set of 30, thus:
[tex]C_{30,4} = \frac{30!}{4!26!} = 27405[/tex]
It would be possible to elect 27,405 different leadership committees.
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The sum of 74 and four times a number is 258. Find the number
The unknown number is 46.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Let the number be x.
The sum of 74 and four times a number is 258,
⇒ [tex]74+4x=258[/tex]
⇒ [tex]4x=258-74[/tex]
⇒ [tex]x=\frac{184}{4}[/tex]
⇒ [tex]x=46[/tex]
Hence we can conclude that the unknown number is 46.
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Answer ALL if u cant see all the answers it don't matter all u need is the question
Polygon ABCD has the following vertices:
A(−4, 2), B(3, 2), C(3, −5), and D(−4, −2)
Calculate the area of the polygon.
To be able to solve clearly this problem, the best thing to do is to plot the graph (see attached pic). From the graph we can see that the points form a trapezoid.
The base is formed by the segment connecting point A and point B.
While the two heights: shorter one by the segment connecting points A and D, and the longer one by the segment connecting points B and C.
The formula for area of trapezoid is given as:
A = b (h1 + h2) / 2
Where,
b = base of the trapezoid = 3 – (-4) = 7
h1 = shorter height = 2 – (-2) = 4
h2 = longer height = 2 – (-5) = 7
Therefore the area is:
A = 7 (4 + 7) / 2
A = 77 / 2
A = 38.5
The answer is 38.5. I took this exam and I chose 38.5 and got it right, I hope this helps!
3 times what gives me a sum of 24? im trying to finish my homework so please help.
Erika and Rita have added a 1-mile walk to their daily exercise schedule. The table lists the time each of them took to walk the 1-mile distance over the past five days. Erika’s Time (in minutes) Rita’s Time (in minutes) 20 21.25 21.5 24.75 22.75 23 23.25 23 20.25 20.75 On average, it takes Erika about minute(s) per mile less than Rita.
What is the area of the polygon shown below?
ini earned $160 during the summer doing chores. She bought 3 dresses worth $12 each using her chore money. How much money was left after she bought the dresses?
steps in how to solve
If the family has three pets, what is the theoretical probability that they have three dogs or three cats?
The probability helps us to know the chances of an event occurring. The theoretical probability that they have three dogs or three cats is 0.25.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As it is given that the pet can either be a dog or a cat, therefore,
The probability that all the three pets are dogs is:
[tex]\rm P(X= 3\ dogs) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]
The probability that all the three pets are cats is:
[tex]\rm P(X= 3\ Cats) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]
Now, we need to calculate the probability that all three pets are either dogs or cats, therefore, the probability can be written as,
[tex]\rm P(3\ Dogs\ or\ 3\ Cats) = P(X = 3\ dogs) + P(X = 3\ cats)[/tex]
[tex]= \dfrac{1}{8}+\dfrac{1}{8}\\\\=\dfrac{2}{8}\\\\ = \dfrac{1}{4} = 0.25[/tex]
Hence, the theoretical probability that they have three dogs or three cats is 0.25.
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Write 2.95 as the quotient of two integers
o graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
a.-5/2
b.-2/5
c.2/5
d.5/2
we have
[tex] 2x + 5y = 10 [/tex]
we know that
the formula to calculate the slope is equal to
[tex] m=\frac{(y2-y1)}{(x2-x1)} [/tex]
Let
[tex] A( 5,0)\\B( 0,2) [/tex]
Step [tex] 1 [/tex]
Find the slope AB
[tex] mAB=\frac{(2-0)}{(0-5)} \\ \\ mAB=-\frac{2}{5} [/tex]
therefore
the answer is the option B
[tex] -\frac{2}{5} [/tex]
the graph in the attached figure
What is 3^ 2/3 equal to?
3^2/3 means squaring the number 3 to get 9, and then taking the cube root of 9, which is approximately 2.08008.
Explanation:To calculate 3^2/3, we are dealing with an exponential expression where 3 is the base and 2/3 is the exponent. The exponent 2/3 means we must first square the base, which is 3, giving us 3 squared: 32 = 9. Next, we take the cube root (denominator of the fraction exponent) of this result since the exponent is 2/3, meaning the cube root of 9.
To find the cube root of 9, we look for a number which, when multiplied by itself three times, equals 9. Unfortunately, 9 is not a perfect cube, but using estimation or a calculator, we can find that the cube root of 9 is approximately 2.08008. Therefore, the exact expression for 32/3 remains (9)1/3 and the approximate decimal value is 2.08008.
In italy about 74 of every 100 people use celular telephones. Write the fraction of celular phone users in italy. Then write it as a decimal.
The cost of producing key chains with the company logo printed on them consists of a onetime setup fee of $205.00 plus $0.70 for each key chain produced. This cost can be calculated using the formula C=205.00+0.70p, where p represents the number of key chains produced and C is the cost. Use the formula to calculate the cost of producing 1700 key chains
on every 3rd day Ivan goes to the gym. On every fifth day Gavin goes to the gym. What day will Ivan and Gavin will see each other.
how to write place value 35 thousand,26hundredand 16 tens and 12 ones