For each of the arithmetic sequences, we have that:
a)
The next two terms are 29 and 34.The expression for the nth term is of: [tex]a_n = 4 + 5(n - 1)[/tex].The 30th term is: 149.b)
The next two terms are 18 and 20.The expression for the nth term is of: [tex]a_n = 8 + 2(n - 1)[/tex].The 30th term is: 66.c)
The next two terms are 36 and 43.The expression for the nth term is of: [tex]a_n = 1 + 7(n - 1)[/tex].The 20th term is: 134.What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the following rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
For the sequences in this problem, we have that:
The first terms are, respectively, 4, 8 and 1.The common ratios are, respectively, 5, 2 and 7.Then the general rule is applied to find the nth term of the sequence, while the next two terms are found adding the common ratio.
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A rectangular athletic field has an area of 40x² + 190x-50. The width of the athletic field is 8x - 2. What is the length of the athletic field?
Answer:
The length = 5x + 25
Step-by-step explanation:
A = l x w
A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, what is y
A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, then the value y is -2.8889
The general cosine function is given by
f(x)= A cos (B x -C) +D
where A= 1/3 is the amplitude,
period = 2π /B
π/3 =2π/B
B= 2/3
C= -2π is the horizontal shift and D= -3s a downward vertical shift.
If we substitute all these values into the formula we obtain;
f(x)= 1/3 cos (2/3 x +2π ) -3
if x= π then we have to calculate y
y= 1/3*0.3333 -3
y= -2.8889
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Parallelogram ABCD has vertices A(1,1) , B(17,1) , C(22,13) , and D(6,13) what is the area in units of parallelogram ABCD
The vertices of a parallelogram are given, according to which the area of the parallelogram will be equal to 58 units.
What is perimeter?The perimeter of a shape is its boundary's length, regarded as a whole. A form's circumference can be calculated by adding the lengths of all of its sides and edges. Utilizing linear length units like centimeters, millimeters, yards, and feet, it is determined.
The total of all a parallelogram's sides is its perimeter.
Firstly, solve for vertices AB:
AB = √(17- 1)² + (1 - 1)² = 16
Then,
BC = √(22 - 17)² + (13 - 1)² = 13
Then,
CD = √(6 - 22)² + (13 - 13)² = 16
Lastly,
AD = √(6 - 1)² + (13 - 1)² = 13
Add all the values,
P = 16 + 13 + 16 + 13
P = 58 units.
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Find DE, please help me
Step-by-step explanation:
ABC and CDE are similar triangles.
similar shapes means that both shapes have the same angles. and : that there is one scaling factor for all lines of one of the shapes to calculate the lengths of the lines of the other shape.
we see that all the other sides of ABC are scaled 2:1 to the corresponding sides of CDE. that means the sides of ABC are twice a long as the sides of CDE.
the same scaling factor has to apply to AB vs. DE.
therefore,
11x - 25 = 2(4x + 1) = 8x + 2
3x = 27
x = 9
DE = 4x + 1 = 4×9 + 1 = 36 + 1 = 37
if a peregrine falcon dove at its maximum speed for half a mile to catch prey, how many seconds would the dive take? (round your answer to the nearest second.)
The time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.
Who is peregrine falcon dove?It can be found with in Arctic tundra of North America and Greenland, and it migrates to Central and South American countries as during winter.The peregrine falcon is the world's swiftest bird, diving to acquire its prey at speeds of over 321 kph (200 mph). They are also among the most tolerant species and can flourish in populated places.For the given question;
The maximum speed of peregrine falcon dove is 200 mph.
Time of travel = 0.5 miles.
The relation of distance and speed is;
speed = distance/time
200 mph = 0.5 miles / time
Time = 0.5 miles / 200 mph
Time = 0.5 × 60 × 60 miles / 200 m/ sec
Time = 9 sec
Thus, time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.
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a certain insecticide kills 60% of all insects in laboratory experiments. a sample of 9 insects is exposed to the insecticide in a particular experiment. what is the probability that exactly one insect will die? round your answer to four decimal places.
The probability that exactly one insect will die is 142.611.
Define probability.The subject of a random event is covered in the mathematical field of probability. For instance, if a coin is flung into the air, it could land on its Head or Tail. Probability is equal to the number of favorable outcomes (Total number of outcomes) P = n (E) / n (S) (S) E is the event, P is the probability, and S is the sample area.
Given,
P( an insect will die) = 0.60
q = 1 - p
q = 1 - 0.60
q = 0.40
Sample size,
n = 9
Binomial distribution:
P(X) = ⁿCₓ pˣ qⁿ⁻ˣ
Probability that exactly one insect will die = P(X = 1)
= ⁹C₁ × 0.6¹ × 0.4⁸
= 362880 × 0.6 × 0.000655
= 142.611
The probability that exactly one insect will die is 142.611.
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If 4x+5y=−5 is a true equation, what would be the value of 8+4x+5y?
Answer:
3
Step-by-step explanation:
[tex]4x + 5y = - 5 \\ 8 + 4x + 5y = {?} \\ 8 + - 5 \\ = 3 \\ 8 + 4x + 5y = 3[/tex]
A bowling ball is pushed with a force of 22. 0 N and accelerates at 5. 5 m/s2. What is the mass of the bowling ball?
When a bowling ball is propelled with a force of 22. 0 N and accelerates at a rate of 5. 5 [tex]ms^{-2}[/tex], its mass is 4. 0 kg.
Newton's Second Law of Motion states that force is the result of mass times acceleration.
[tex]F=m*a[/tex]
[tex]m = F / a[/tex]
A force of 22.0 Newtons ( [tex]kgms^{-2}[/tex] ) and an acceleration of 5.5 meters per second squared were used to drive the bowling ball.
F = 22.0 [tex]kgms^{-2}[/tex] and
a = 5.5 [tex]ms^{-2}[/tex]
Put the values in the formula as replacements.
M = 22 [tex]kgms^{-2}[/tex]/ 5.5 [tex]ms^{-2}[/tex]
Meters per second squared (m/s2) units cancel each other out.
M = 22 kg / 5.5
= 4 kg
The bowling ball weighs 4 kilogram.
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Can someone at least explain this to me I’m very confused.
For given line segments RS = TR
In this question, we have been given two line segments QS and TU intersected at point R.
Also, we have been given QS = TU, QR = RU
We need to prove, RS = TR
We can observe that,
QS = QR + RS
and UT = UR + RT
QS = TU ................(Given)
QR + RS = UR + RT
QR + RS = QR + RT .............(Given QR = RU )
QR + RS - QR = QR + RT - QR .............(subtraction property of equality)
RS = TR
Hence proved.
Therefore, for given line segments RS = TR
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When is an equation true?
Answer: when the value on each side of the equal sign is the same
Step-by-step explanation: for example, 9=9 is a true equation. 5+4 = 9 is a true equation
the square root of $x$ is greater than 3 and less than 4. how many integer values of $x$ satisfy this condition?
6 integers that satisfy the given condition are 10,11,12,13,14,15.
Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size
we have the number X
Of which the square root is greater than 3 and less than 4
so,
[tex]3 < \sqrt{X} < 4[/tex]
on squaring both sides
[tex]3^2 < (\sqrt{X})^{2} < 4^2[/tex]
[tex]9 < X < 16[/tex]
so the integer that satisfies the condition is 10,11,12,13,14,15.
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Answer:
6
Step-by-step explanation:
Because 4 > √x > 3, we know that 16 > x > 9. Thus, the integers from 10 to 15 inclusive satisfy this inequality, which means 6 integers satisfy the condition in the problem.
7. Hannah invests £750 and after 4 years has £844.13. Find the compound interest rate.
If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.
What is compound interest?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.
Hannah contributes £750 and following 4 years has £844.13. Then the compound interest rate is given as,
844.13 = 750 (1 + r)⁴
(1 + r)⁴ = 1.1255
1 + r = 1.02999
r = 0.0299
r = 2.99%
r ≈ 3%
If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.
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the degree of f(x) is ?
the end behavior is the left side is ?
and the right side is ?
The degree of the polynomial is 5, and the end behavior is:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
How to get the degree of a polynomial?
For any given polynomial, we define the degree as the largest exponent on the polynomial.
On this case we have:
f(x) = 2x^3 - 3x^5 - x^2 + 1
We can see that the largest exponent is 5, so the degree is 5.
Now, for the ending behavior.
If we have an odd degree (like in this case) we will have opposite ending behaviors in both ends of the domain.
If the leading coefficient is negative (like in this case, it is -3) then the end behavior will be:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
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What is the equation of the line that passes through the points (-2, -6) and (1, 2)?
The equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.
According to the question,
We have the following information:
Points through which line is passing = (-2,-6) and (1,2)
Now, we have the following values:
x1 = -2, y1 = -6
x2 = 1 and y2 = 2
We know that the following formula is used to find the slope of the line:
m = (y2-y1)/(x2-x1)
m = (2+6)/(1+2)
m = 8/3
Now, the following formula is used to find the equation of the line:
y-y1 = m(x-x1)
y+6 = 8/3(x+2)
y+6 = 8x/3+16/3
Subtracting 6 from both sides:
y = 8x/3+16/3-6
y = 8x/3-2/3
Hence, the equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.
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Evaluate the expression.
Do not round your answer.
1/5(3+2+ 5)² =
Answer:
20
Step-by-step explanation:
do parenthesis first
1/5(3+2+ 5)² =
1/5(10)² =
then exponent
1/5(10)² =
1/5(100) =
20
pls help!!!
Consider the calculation 2/3 × 5/8 .
Without calculating the product, explain how you know that 3/4 is not the answer.
(p.s. they are fractions)
if
x/y=y/z=z/x
show that x=y=z
Step-by-step explanation:
x/y = y/z = z/x
x = y²/z = zy/x and y = z²/x
x = y²/z
putting this into the 3rd part of the original equation :
z/x = z/ y²/z = z²/y²
now using the y identity of the second part there :
y = z²/x
z²/y² = z² / z⁴/x² = x²/z² (= z/x per previous equation)
so,
x²/z² = z/x
x³/z³ = 1
x/z = 1
x = z
then
y/z = y/x = z/x (= 1)
and therefore,
y/x = z/x meaning
y = z (and therefore = x)
so,
x = y = z
Thank you for those answering!
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Caroline can make eleven lassis out of two mangoes. How many lassis can she make out of twelve mangoes?
Answer
Step-By-Step-Explanation
2 mangoes=eleven lassis
×6 ×6
12 mangoes=66 lassis
Answer=66 lassis
15 ten büyük 25 den küçük tek sayılar
Answer:
Step-by-step explanation:
15 ile 25 arasında toplam 10 tam sayı var,
buna 25-15=10 şeklinde ulaşabiliriz. Ardından tek sayılar sorulduğu için ve bu 10 tam sayı içerisinde hem tek hemde çift olduğu için sayıyı ikiye böleriz
10/2=5 ve ardından en sonda bulunan 25 sayısını çıkarırız yani, 5-1=4
cevaplar: 17, 19,21,23
Which table of values satisfies the linear equation y=−47x−2?
x y
−7 −6
0 −2
7 2
x y
−14 6
0 0
14 −10
x y
−7 2
0 −2
7 −6
x y
−14 −10
0 0
14 6
The values satisfies the linear equation y = −47x−2 is (0, -2).
Describe the word linear equation?an equation where every term has either a constant else includes only one variable, each variable does have an exponent of one, and the graph is always a straight line.The general form of such a linear equation is y = mx + b, where m and b can be any real number.For the given question.
The linear equation is given as;
y = −47x −2
Check the result by putting the values from option.
For : −7 −6
Put x = -7
y = −47(-7) −2
y = 799 -2
y = 498 (incorrect)
For: 0 −2
Put x = 0
y = −47x −2
y = −47(0) −2
y = -2 (correct)
Thus, the values satisfies the linear equation y = −47x−2 is (0, -2).
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Examine the equation below used for determining the balance on a bank account. Look through this chapter and your notes to help you write a problem that could be modeled by the equation.
The balance on the bank account at the end of the third quarter of the year is 2,630.80
How to find the compound interest?
Compound interest is defined as the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest is found using the formula
A=P(1+r/n)ⁿˣ where:
A= Amountr= interest raten= number of interest applied per period and x= number of time periodTherefore, the amount (A)=2630.80
The P=2500
interest rate is 0.17%
Number of interest applied per period is 365 periods and
number of time period is 3.
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Make x the subject of y = 3x-2
You may use the flowchart to help you if you wish.
x 3
- 2
Answer:
x=y/3 + 2/3
Step-by-step explanation:
Is this what you wanted?
The ___ of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.
The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.
What is hyperbola?A hyperbola is a significant conic section in mathematics that is created by the intersection of a double cone with a plane surface, though not always at the center. A hyperbola is symmetric along its conjugate axis and resembles the ellipse in many ways. A hyperbola is subject to concepts like foci, directrix, latus rectus, and eccentricity. Examples of hyperbola that are frequently seen include the path taken by the tip of a sundial's shadow, the scattering trajectory of subatomic particles, etc.Here, we'll use instances that have been solved to better grasp the definition, formula, derivation, and standard forms of hyperbolas.Hence, The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.
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PLS HELP, it’s due tmrw and I need it done
a. The system of inequalities that best represent how much of the agricultural products of soybeans and corn the river barge can carry is
A. 60x + 90y ≤ 4,500,000, x ≥ 0, y ≥ 0b. option A
c. The river barge can safely ship the agricultural products
How to determine the equation the agricultural products of soybeans and corn the river barge can carryinformation gotten from the question include
Corn weighs about 60 pounds per bushel
soybeans weigh about 90 pounds per bushel
A river barge can safely carry up to 4,500,000 pounds of cargo.
Let x = bushels of corn and y = bushels of soybeans.
a. From the statement, it can be deduced that the equation is
A. 60x + 90y ≤ 4,500,000, x ≥ 0, y ≥ 0
b. some interpretation on inequality
shading above a line is greater than and below a line is less thandotted lines mean the inequality do not have equal to while solid lines mean the inequality has equal tofrom the interpretation
The inequality has "equal to" as result the graph must be a solid lineThe inequality used is less than as a result the shading must be below the linethe correct option is A (graph attached)
c. 60 * 24000 + 90 * 24000
= 3,600,000
The value is ≤ 4,500,000 hence the river barge can carry it
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Kelly earned 300 dollars and put 70% of it into the bank. How much did she put into the bank?
Answer:
$210 in bank
Step-by-step explanation:
Kelly earned 300 dollars and put 70% of it into the bank. How much did she put into the bank?
70% = 0.7
300 * 0.7 = $210 in bank
the initial number of views for a reader board was 25. the number of views is growing exponentially at a rate of 18% per week. what is the number of views expected to be four weeks from now? round to the nearest whole number.
The number of views in the four weeks round to the whole number is 48.
Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.
We have to find the number of views in the fourth week.
On the first week the increase = 25 + 25× 18%
= 25 + 25 × 18/100
= 25 + 4.5
= 29.5
The second week increase = 29.5 + 29.5 × 18%
= 29.5 + 5.31
= 34.81
The third week increase = 34.81 + 34.81 × 18%
= 34.81 + 6.2658
= 41.0758
The fourth week increase = 41.0758 + 41.0758 × 18%
= 41.0758 + 7.393644
= 48.469444
Therefore the number of views in the four weeks is 48.
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Can someone please help me
The area of a rectangular floor is 8x² + 6x-20. The width of the floor is 2x + 4. What is the length of the floor?
Answer:
Length = 4x - 5
Step-by-step explanation:
A = length x width
Part A
The graph shows the distance in miles, , a car travels in hours.
Explain why the graph does or does not represent a proportional relationship between the variables and .
Enter your explanation in the box provided.
Part B
Two cars leave from the same city at the same time and drive in the same direction. The table shows the distances traveled by each car.
• Determine whether the relationship between the number of hours traveled and the number of miles traveled is proportional for each car.
• Use the table to explain how you determined your answers.
• Describe how the graph of the distance traveled by each car would support your answers.
Enter your answers and your explanations in the box provided.
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