The Sum is 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)
What is Series?A finite series is one that has a finite number of terms.
If the series [tex]a_1[/tex]+ [tex]a_2[/tex] + [tex]a_3[/tex] +... + a has n terms and is a finite series with n terms.
As a result, [tex]S_n[/tex] is used to represent the series' sum as follows:
[tex]S_n[/tex]=∑ [tex]a_n[/tex]
Given:
1 + x + x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex]
let P= 1/ 1-x
P - Px= 1
P= 1+ Px
= 1 + (P)x
= 1 + (1+ Px) x
= 1+ x + Px²
= 1+ x + (1+ Px)x²
= 1+ x + x² + Px³ and so on
So, 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)
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The zeros of the expression j2 - 4j-21 are the solutions of the equation
j²-4j-21.
j² - 4j-21 = 0
(+3_) (+5) = 0
j+ 3 = or j+ = -3
Set the expression equal to 0.
Write the equation in factored form
Use Zero Product Property.
j=7 or j = N
Solve.
The zeros of the expression j2 - 4j - 21 are 2 and .
The solutions of the quadratic equation is j = -3 and j = 7 .
In the question ,
it is given that the quadratic equation is j² - 4j - 21 = 0,
we need to find the solution of the given equation .
to find the solution , we use splitting the middle term method .
j² - 4j - 21 = 0
j² - 7j + 3j - 21 = 0 .... splitting the middle term -4j = - 7j + 3j
taking j common form first wo terms and 3 common from last two terms ,
we get
j(j - 7) +3(j - 7) = 0
(j + 3)(j - 7) = 0
j + 3 = 0 and j - 7 = 0
j = -3 and j = 7
Therefore , The solutions of the quadratic equation is j = -3 and j = 7 .
The given question is incomplete , the complete question is
Find the solutions of the quadratic equation j² - 4j - 21 = 0 ?
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The light in a lighthouse flashes every 20 seconds.
How many times will it flash in one hour?
Answer:
180 flashes
Step-by-step explanation:
The lighthouse flashes 3 times in a minute then multiplied by 60 which is 180 flashes.
A square root function has a domain of x≥15 and a range of y≤10.
What is the range of its inverse?
y≤10
x≤15
x≥10
y≥15
Answer:
[tex] y \geq 15[/tex]
Step-by-step explanation:
The range of the inverse is the same as the domain of the original function.
Answer:y>15
Step-by-step explanation:
Consider the equation and the following ordered pairs: (1,y) and (x,3).
6x+1.2y=−2.4
Step 1 of 2: Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Pair (1,y)
[tex]6(1)+1.2y=-2.4 \\ \\ 1.2y=-8.4 \\ \\ y=-7[/tex]
Pair (x,3)
[tex]6x+1.2(3)=-2.4 \\ \\ 6x=-6 \\ \\ x=-1[/tex]
Solve the system of equations by graphing.
x-y=-4
x+y=8
Select all of the following that are quadratic equations. 2 x2+ 12 x = 0, x2 - 2 x = 4, x + 1 x3 - 6 x2 + 8 = 0, 5 x - 3 = 0, 5 x - 1 = 3x + 8, 9 x2 + 6 x - 3 = 0
2x²+12x=0 , x²-2x=4 and 9x²+6x-3=0 are Quadratic equation
Quadratic equations are polynomial equations whose degree is of 2 in one of the variable.
The standard form of quadratic equation is ax²+bx+c = d where a, b and c are real numbers and a ≠ 0.
In general form of quadratic equation , "a" is known as leading coefficient and "c" is known as absolute term of function.
In the given question,
Equation whose max. degree will be 2 will be quadratic .
2x²+12x=0 , equation is quadratic as degree of equation is 2
x²-2x=4 , equation is quadratic as degree of equation is 2
x³-6x²+8=0 , Degree of equation is 3
Therefore , equation is not quadratic
5x-3=0 , Degree of equation is 1
Therefore , equation is not quadratic
5x-1=3x+8 , Degree of equation is 1
Therefore , equation is not quadratic
9x²+6x-3=0 , Degree of equation is 2
It is quadratic equation.
Hence , 2x²+12x=0 , x²-2x=4 and 9x²+6x-3=0 are quadratic equation
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A cookie recipe uses 0.75 cups of sugar for every 1.25 cups of flour
How many cups of sugar will the recipe need if it uses 5 cups of
flour?
Which fraction is greater of 8/400 or 8/10
Two angles whose sum is 180° are supplementary angles. find the measure of the supplementary angle shown in the figure
Step-by-step explanation:
together they are 180°.
so,
(11x + 2) + (8x + 7) = 180
11x + 2 + 8x + 7 = 180
19x + 9 = 180
19x = 171
x = 171/19 = 9
and the angles are
(11x + 2) = 11×9 + 2 = 99 + 2 = 101°
(8x + 7) = 8×9 + 7 = 72 + 7 = 79°
another way to write 6axbcx2d without using multiplication sign
????
Answer:
Step-by-step explanation:
(6a)(b)(c)(2d)
can somebody please help me
Answer: D
Step-by-step explanation: I believe this the correct answer. If you start by looking at the "right 3 units", going right on a coordinate plane is - and left is +, so right 3 units is -3. Then, down 4 units is -4 (on coordinate plane, up is + and down is -).
So then, plug it into the equation: h(x)= {x-3}-4
I hope this helps and you get it right :)
The given quadrilateral ABCD is an isosceles trapezoid. Which choice is NOT true about ABCD?
A) 2x + 10 = 4x - 30
B) angle A+ angle B+ angle C+ angle D=180^
C) angle A+ angle B+ angle C+ angle D=360^
D) AR = CD
Answer: B
Step-by-step explanation:
What is an isosceles trapezoid?
An isosceles trapezoid is a type of quadrilateral in which the non-parallel sides have equal length and angle measure.
Let's address each answer to see which are true:
A) True: By definition of an isosceles trapezoid, the non-parallel sides have equal length and angle measure. 2x+10 and 4x-30 are written as equations to represent the unknown measurement of the angles A and D. Because this is an isosceles trapezoid, these angles would have the same measurement, meaning they are equal to each other.
B) False: A trapezoid is a quadrilateral. Quadrilaterals are four-sided figures which angles add up to 360°. Some other shapes that are quadrilaterals are squares, rectangles rhombuses and trapezoids. Because a trapezoid is a quadrilateral, the angles do not and can not add up to 180°
C) True: A trapezoid is a quadrilateral, which is a shape which angles add up to 360°. This means that Angles A, B, C, D of this shape should also add up to 360°.
D) True: An isosceles trapezoid is a type of trapezoid whose non-parallel sides have equal side lengths and angles measurements. Due to this definition, AB and CD would have the same length.
Newton earns $195 for
working 15 hours as a radio host. How
much money does Newton earn in
3 hours?
Newton earns $39 for working 3 hours as a radio host.
What is meant by time and work?In terms of time and work, it refers to how long it takes a person or group of individuals to perform a task and how well each of them does it. A crucial concept that time and labour have in common with other arithmetic topics is the concept of proportionality. Efficiency is inversely proportional to time required while the amount of work is constant.
Efficiency serves as the proportionality constant, and work and time are directly proportional.
Given,
As a radio host, Newton puts in 15 hours and makes $195..
For a one hour the employee earns $13
So with this information we can put:
13×3=39
In 3 hours Newton earns $39 for working as a radio host.
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Find slope of line please no links
Answer:
Step-by-step explanation:
Using
Point A: x= 1 and y=3
And point B: x=-2 and y=-6
use equation of slope and substitute the values
Slope= YB-YA/Xb-Xa
= -6-3/-2-1
=3
In ΔJKL, m∠J = 67° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.
23°
113°
157°
78.5°
Answer:
[tex]157^{\circ}[/tex]
Step-by-step explanation:
Using the exterior angle theorem,
[tex]m\angle K=m\angle J+m\angle L=157^{\circ}[/tex]
A vehicle is running at a constant speed on a highway. Ignore the initial acceleration at the start and final acceleration when the vehicle runs out of gasoline and comes to halt. Its gas consumption per mile is also constant. The amount of gasoline, in gallons, in the vehicle can be modeled as a linear function G ( t ) = 10 -- 2t, where t is time, in hours. Select all the true statements.le
The correct statements regarding the linear function G(t) = 10 - 2t are given as follows:
Initially, the tank has 10 gallons of gasoline.The rate of consumption is of 2 gallons per hour.The slope of G(t) represents the fuel consumption of the vehicle.The t-intercept represents the time it takes for the vehicle to run out of gas.What are the parameters of the linear function?The linear function is defined as follows:
G(t) = 10 - 2t.
In which the variables are:
G(t) is the amount of gasoline that the car has after t hours.t is the time in hours.The slope and the intercept are presented as follows:
Slope of -2: 2 gallons are consumed each hour.Intercept of 10: The initial fuel in the car is of 10 gallons.The t-intercept is:
10 - 2t = 0
2t = 10
t = 5.
Which is the time it takes for the car to run out of fuel.
Missing InformationThe options are given by the image shown at the end of the answer.
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18) In the Pie Chart Example below, the city of Miami is trying to determine how many new visitors visit their beaches each month in the summer. If the total number of visitors in the entire summer is 300,000 how many visitors come in June? A. 30,000 B. 60,000 C. 135,000 D. 72,000
The number of visitors to the beach in June is B. 60000.
How to calculate the value?Since the pie chart isn't given, let the assumed percentage for the visit to the beach in June be 20%.
In this case, the new visitors visit their beaches each month in the summer. If the total number of visitors in the entire summer is 300,000 will be:
= Percentage for visits × Total people
= 20% × 300000
= 60000
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If 2 is added to a number and the sum is tripled, the result is 16 more than the number. Find the number.
Using simplification, the number is −1.
Given that, If 2 is added to a number and this sum is tripled, the result is 4 more than the number.
Let the number is x.
Therefore from given information we get
2 is added to a number.
Then it is x+2.
Sum is tripled.
So 3(x+2)
4 more than number means x+4.
So according to the given statement equation should be
3(x+2)=x+4
Simplifying the expression
3x+6=x+4
Subtract 6 on both side
3x+6−6=x+4−6
3x=x−2
Subtract x on both sie
3x−x=x−2−x
2x=−2
Divide by 2 on both side we get
x=−1
Hence, the number is −1.
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If 56 apples were placed in each bag instead how many bags would be left over
Its 112 bags how much?
Answer:
56
Step-by-step explanation:
one apple = one bag
the 56 apples = 56 bags
112 -56 =56
Is there enough information to prove the two triangles congruent? If so, write the
congruence statement and name the postulate you would use. If not, write not
possible and tell what other information you would need.
Check the picture below.
decreased by 4
58
gallons in 4 minutes. What will be the change in the volume of water after 1 minute
Answer:
14.5 gallons will be gone in 1 minute
Step-by-step explanation:
just divide 58 by 4 and thats how much water will be gone in 1 minute
3. Harry also paid $14.50 for three T-shirts at the sale. The sale price saved Harry 30% of the
original price of the three T-shirts.
What is the original total price of his three T-shirts?
Show your calculations.
The cost price of three T-shirts is $11.2. Since, the cost price is less than the perchage price hence it is profit.
What is profit and loss?
When perchaging price is less than the original price then it is known as profit. But if it is more than the original price than it is known as loss.
Consider the original price of the three T-shirts is [tex]x[/tex]. Now, the percent saving is given by the following expression:
[tex]\textnormal{Percent saving}=\frac{\textnormal{Total amount without saving-Total amount after saving}}{\textnormal{Total amount without saving}} \times 100\\30=\frac{\$14.50-x}{x}\times 100\\\frac{30x}{100}=14.5-x\\0.3x=14.5-x\\0.3x+x=14.5\\1.3x=14.5\\x=\frac{14.5}{1.3}\\x=11.2[/tex]
Hence, the price of three T-shirts is $11.2.
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y’all can help me with this one pleaseI need to write an equation for each line
The equation of the line m is y = -2x + 4, for n is y = x - 1, for p is x = -4, and for l is y = 4.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The graph on which the straight line is shown:
The equation of the line m
(2, 0) and (0, 4)
y = (4)/(-2)[x - 2]
y = -2(x - 2)
y = -2x + 4
The equation the line n:
(1, 0) and (0, -1)
y = (-1)/(-1)[x - 1]
y = x - 1
The equation of the line p:
x = -4
The equation of the line l:
y = 4
Thus, the equation of the line m is y = -2x + 4, for n, is y = x - 1, for p is x = -4, and for l is y = 4.
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Graph the function. f(x)=-3(x+1)^2+5f(x)=−3(x+1) 2 +5
Answer:
See attachment.
Step-by-step explanation:
1. Use the slope-intercept form to find the slope and y-intercept.
y = mx + b ; m= slope b= y-intercept
2. Find the values.
m = 0
b = 7
slope: 0
y-intercept: ( 0, 7)
3. Find two points on the line, then graph them.
x = 0, 1
y = 7, 7
Alexis biked a distance of 6 miles each day for 3 days. Then, she biked 7 miles each day for the next
5 days. What was the total distance in miles that Alexis biked during these 8 days?
O 35 miles
o 40 miles
o 19 miles
O 54 miles
The Anwser to this question
Write y = 4x in function form
Can you please show the equation or rewrite the equation?
Simply 9/24 fraction
Answer: [tex]\frac{3}{8}[/tex]
Step-by-step explanation: dividing the top and bottom of the fraction [tex]\frac{9}{24}[/tex]by 3 will give you the simplest form. Your welcome
Answer:
3/8
Step-by-step explanation:
The fraction 9/24 simplifies to 38. The way to arrive at this solution is to find the greatest common multiple for both the numerator and the denominator. In this case, the greatest common multiple is 3.
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The legend on a map states that
1 inch is 500 miles. If you measure
8 inches on the map, how many
miles would the actual distance be?
The actual distance will be 4000 miles.
According to the question,
We have the following information:
The legend on a map states that 1 inch is 500 miles.
So, this statement can be rewritten in the form of following expression:
1 inch = 500 miles
Now, in order to find the actual distance for 8 inches, we will multiply the distance in 1 inch with 8.
(More to know: measurements like this are used in daily life to find the actual distance between two places.)
So, we have the following expression:
8 inches = 500*8 miles
8 inches = 4000 miles
Hence, the actual distance will be 4000 miles if it measures 8 inches on the map.
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¿De cuántas formas puede un juez otorgar el
primero, segundo y tercer premio en un
concurso que tiene ocho concursantes?
Hay 336 formas diferentes en las que se pueden entregar los 3 premios.
¿De cuantas formas se pueden otorgar los premios?
Sabemos que hay 8 participantes y de estos se elegiran a 3 para darles 3 premios diferentes.
Para el primer premio, hay 8 posibles concursantes que lo pueden recibir.Para el segundo premio, hay 7 concursantes que lo pueden recibir (hay uno menos por que uno ya recibio el primer premio)Para el tercer premio, hay 6 concursantes que lo pueden recibir.El numero total de combinaciones es lo que obtenemos cuando tomamos el producto entre los números de opciones:
C = 8*7*6 = 336
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How many work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 95.5 percent if a pilot study yielded these times (in minutes): 6.1, 6.9, 6.9, 6.7, 6.8, and 6.4?
The number of work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 95.5 percent if a pilot study yielded these times is 23.
What are Sample Mean?
The average value of the provided sample data is determined using the sample mean formula. Instead of expressing them using actual terms, it is occasionally essential to calculate the sample term average. The ratio of the sum of terms to the total number of terms can be used to describe the sample mean formula. The center of the data is measured by the sample mean. The sample mean is used to estimate the mean of any population. Many times, without surveying the entire population, we must make educated guesses about how the population as a whole is behaving or what variables are affecting the population as a whole. In these situations, the sample mean is helpful. The sample mean is the average value obtained from the sample. The variance and subsequently the standard deviation are determined using the sample mean that was so obtained.
For the given data,
Standard Deviation = 0.3204
Mean =(6.1+6.9+6.9+6.7+6.8+6.4)/6=6.633
The margin of error = 2% of mean
Z score for 95.5 confidence interval = 1.96
Number of cycles, sqrt(n)
= (1.96× 0.3204) / (6.633×0.02)
= 4.7337
n = 22.408
Rounding to the next integer, then work cycles = 23
Hence,
The number of work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 95.5 percent if a pilot study yielded these times is 23.
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