Answer:
Option 4th is correct.
[tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]
Step-by-step explanation
The explicit sequence of the geometric sequence is given by:
[tex]a_n = a_1r^{n-1}[/tex] ....[1]
where,
r is the common ratio
n is the number of terms
[tex]a_1[/tex] is the first term
As per the statement:
The explicit rule for a sequence is:
[tex]a_n=9(-5)^{n-1}[/tex]
On comparing [1] we have;
[tex]a_1 = 9[/tex] and r= -5
Recursive formula for the geometric sequence is given by:
[tex]a_n = r \cdot a_{n-1}[/tex] for [tex]n\geq 2[/tex]
Substitute the given values we have;
[tex]a_n = -5 \cdot a_{n-1}[/tex]
Therefore, the recursive rule for the sequence is, [tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]
A rug shaped like a rectangle has a width of 3 m. the length of the rug is 2 m greater than its width. what is the perimeter of the rug in meters
Jeanette purchased a concert ticket on a website.The original price of the ticket was $75.She used a coupon code to receive a 20% discount.The website applied a 10% service fee to the discounted price.Jeanettes ticket was less than the original price by what percent?
Please help Over the course of the semester, Kylie made the following scores on her Algebra tests: 92, 88, 95, 82, 75, 82, 96, 78. What is her average test score? A) 82 B) 83 C) 84 D) 86
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. find the probability of the indicated result. 20) both marbles are red.
How can you tell when a quadratic equation has no real solutions?
A. when the radicand is negative
B. when b in the quadratic formula is greater than the radicand
C. when the radicand equals zero
D. when the radicand is not a perfect square
I believe the answer is A? is that right?
helppppppppppppppppppppppppppppppppppppppppp
75°, 75°, 75°, 78° 80°, 80°, 115° The daily temperatures for a week in Brownsville are shown. Which measure of central tendency best represents the data?
A) mean
B) median
C) mode
D) range
Which of the following expression expressions is equivalent to cos3x/sinxcosx?
A.) cscxcos2x-secxsin2x
B.) secxcos2x-cscxsin2x
C.) secxcosx-cscxsinx
D.) cscxcosx-secxsinx
1. (4.8x + 15.5) + (2.1x - 12.2)
2. (7x + 8) - (3x + 12)
3. (0.5x + 0.74) + (0.5x - .25)
What are the possible numbers of positive, negative, and complex zeros of
f(x) = −3x4 − 5x3 − x2 − 8x + 4?
A. Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
B. Positive: 1; negative: 3 or 1; complex: 2 or 0
C. Positive: 3 or 1; negative: 1; complex: 2 or 0
D. Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
Look at changes of signs to find this has 1 positive zero, 1 or 3 negative zeros and 0 or 2 non-Real Complex zeros.
Then do some sums...
Explanation:f(x)=−3x4−5x3−x2−8x+4
Since there is one change of sign, f(x) has one positive zero.
f(−x)=−3x4+5x3−x2+8x+4
Since there are three changes of sign f(x) has between 1 and 3 negative zeros.
Since f(x) has Real coefficients, any non-Real Complex zeros will occur in conjugate pairs, so f(x) has exactly 1 or 3 negative zeros counting multiplicity, and 0 or 2 non-Real Complex zeros.
f'(x)=−12x3−15x2−2x−8
Newton's method can be used to find approximate solutions.
Pick an initial approximation a0 .
Iterate using the formula:
ai+1=ai−f(ai)f'(ai)
Putting this into a spreadsheet and starting with a0=1 and a0=−2 , we find the following approximations within a few steps:
x≈0.41998457522194 x≈−2.19460208831628We can then divide f(x) by (x−0.42) and (x+2.195) to get an approximate quadratic −3x2+0.325x−4.343 as follows:
Notice the remainder 0.013 of the second division. This indicates that the approximation is not too bad, but it is definitely an approximation.
Check the discriminant of the approximate quotient polynomial:
−3x2+0.325x−4.343 Δ=b2−4ac=0.3252−(4⋅−3⋅−4.343)=0.105625−52.116=−52.010375Since this is negative, this quadratic has no Real zeros and we can be confident that our original quartic has exactly 2 non-Real Complex zeros, 1 positive zero and 1 negative one.
Answer:
Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
Find three positive consecutive integers such that the product of the second integer and the third integer is 72
Let xbe a positive integer number. Then x, x+1 and x+2 are three positive consecutive integers (the first one is x, the second is x+1 and the third is x+2).
The product of the second integer and the third integer is (x+1)·(x+2) and is equal to 72. So you have the equation
[tex](x+1)\cdot (x+2)=72.[/tex]
Solve it:
[tex]x^2+2x+x+2=72,\\ \\x^2+3x+2-72=0,\\ \\x^2+3x-70=0,\\ \\D=3^2-4\cdot (-70)=9+280=289,\\ \\\sqrt{D}17,\\ \\x_1=\dfrac{-3-17}{2}=-10,\ x_2=\dfrac{-3+17}{2}=7.[/tex]
Solution [tex]x_1=-10[/tex] is extra because [tex]x_1[/tex] is negative.
Answer: three positive consecutive integers are 7, 8 and 9.
Help Me plz Im stuck
Which is the counterexample to the following conjecture?
If a number is divisible by 3, it must also be divisible by 9.
A.18
B.54
C.21
D.27
Show all work. Calculate and find the x-intercepts of the
following function:
f(x)=x^2+5x-36
Which of the following circles have their centers in the second quadrant? Check all that apply.
A. (x - 5)2 + (y - 6)2 = 25
B. (x + 1)2 + (y - 7)2 = 16
C. (x - 4)2 + (y + 3)2 = 32
D. (x + 2)2 + (y - 5)2 = 9
PLEASE HELP AND EXPLAIN!!!,
If the circumference of a circle is 12.56 ft, what is the length of the diameter? use 3.14 for Ï.
Final answer:
To determine the diameter of a circle with a circumference of 12.56 feet using π as 3.14, divide the circumference by π resulting in a diameter of 4 feet.
Explanation:
The student has asked to find the length of the diameter of a circle if the circumference is 12.56 ft using 3.14 for π (Pi). The formula for the circumference C of a circle is C = π * d, where d is the diameter of the circle. To find the diameter, we rearrange the formula to d = C / π. Substituting the given values, we get:
d = 12.56 ft / 3.14
After dividing the circumference by pi, we find that:
d = 4 ft
Therefore, the length of the diameter is 4 feet.
The brightness of a light bulb in watts, is a type of which Data?
Nominal Qualitative
Ordinal Qualitative
Discrete Quantitative
Continuous Quantitative,
The brightness of a light bulb in watts is considered continuous quantitative data as it represents measurable amounts that can vary and take on any value within a range.
The brightness of a light bulb, measured in watts, represents the power it uses and is an example of quantitative data. Since wattage can take on any positive value and is not restricted to whole numbers (for example, a bulb can be rated at 60.5 watts), it is considered to be continuous quantitative data. Unlike discrete data, which involve counts that must be whole numbers, continuous data can include any value within a range. Hence, when comparing the brightness of light bulbs by their wattage, one is dealing with continuous quantitative data.
which is less -12.05 or -12.5
9, 21, 7, 11, 13, 21, 5, 14, whats the range?
The square of the sum of six and a number
Pleaseee hellpppppppppp
solve for p. 50,000= (25,000*p)/(100-p)
Will give brainliest if correct
The value of a stock share in a new technology company has been increasing at a rate of 8.6% quarterly. The initial price of one share was $102.15. An investor plans to sell once the value of one share reaches $233.10.
If t is the number of quarters since the initial price of one share was set, which equation could be used to determine how long it will take the share to reach $233.10, assuming it continues to grow at the same rate?
A. 102.15 = 233.10(0.086)t
B. 102.15 = 233.10(0.914)t
C. 233.10 = 102.15(1.86)t
D. 233.10 = 102.15(1.086)t
The correct equation to use is D. 233.10 = 102.15(1.086)^t, which represents how the value of the share increases over time assuming consistent growth. The growth factor is represented by (1.086)^t as the share is increasing by 8.6% quarterly.
Explanation:The correct equation to determine how long it will take for the share to reach $233.10 is D. 233.10 = 102.15(1.086)^t.
This equation represents a classic compound interest formula that describes how an investment grows over time, where 102.15 is the initial share price, 1.086 is the quarterly growth rate (1+8.6%), and t is the number of quarters.
The equation shows that the future value, $233.10, is equal to the initial value, $102.15, multiplied by the growth factor, (1.086)^t, raised to the number of quarters.
Learn more about Compound Interest Formula here:https://brainly.com/question/35413403
#SPJ11
What is the rule for the transformation above?
A. (x' , y') = (-x - 6 , -y + 1)
B. (x' , y') = (x - 6 , -y + 1)
C. (x' , y') = (x - 6 , y - 1)
D. (x' , y') = (-x + 6 , -y - 1)
Which of the following best describes how to measure the spread of the data?
Final answer:
To measure the spread of data, you can use the range, variance, or standard deviation, which respectively measure the absolute difference between extremes, the average squared deviation from the mean, and the average deviation from the mean in the same units as the data.
Explanation:
The question refers to the methods used to measure the spread of data in a dataset. The spread, or variability, indicates how much the data points in a set differ from each other and from the central measures like the mean. There are several ways to quantify this spread, including:
The range, which is the difference between the largest and smallest values in the set.
The variance, which is the average of the squared differences from the mean.
The standard deviation, which is the square root of the variance and provides a measure of spread in the same units as the data.
Knowing the spread of data helps in understanding the distribution and consistency of the dataset, which is essential for statistical analysis.
At which angle will the hexagon rotate onto itself?
60°
90°
120°
180°
The optimum angle at which a projectile should be launched to cover maximum distance is 45°. This angle gives the projectile the greatest range by maximizing the time of flight.
Explanation:The optimum angle at which a projectile should be launched in order to cover the maximum distance is 45°. This launch angle gives the projectile the greatest range.
To understand why this angle is optimal, we can consider that the motion of a projectile can be divided into two independent components: horizontal and vertical. The range of a projectile is maximized when the time it spends in the air is maximized. At a launch angle of 45°, the horizontal and vertical components of the projectile's velocity are equal. This means that the time of flight is maximized, resulting in the maximum range.
For example, if a projectile is launched at a shallower angle, such as 30°, the vertical component of the velocity is decreased, reducing the time of flight and therefore the range. Similarly, if the projectile is launched at a steeper angle, such as 60°, the horizontal component of the velocity is decreased, again reducing the time of flight and range.
Learn more about Projectile Motion here:https://brainly.com/question/29545516
#SPJ3
When Katie was born her mother invested $5000 in an account for her college savings. The interest rate is 3.5% compounded annually. To represent this, we can use the formula V = 5000(1 + r)t where r represents the interest rate and t represents the time in years. How much will Katie have in her account when she turns 18
Find the greatest Greatest Common Factors of the following Monomials:
44b^5 and 36b
Hello everybody!! Can somebody help me with this?
"The expression 937(1+x) gives the markup price of a computer, where x is the percent of the markup written in decimal form.
Which part of the expression represents the percent, in decimal form, of the initial price that is being paid?"
Is it (1+x) ? Or just x ? I'm not understanding too well.,
2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work
Would the measure of angle B be x for this??
Scott is beginning racquetball at a club. his equipment will cost $67.95, the fees are $70 membership plus $5.50 per hour for 40 hours, and he will make 30 trips at $1.34 per trip. what are his total costs?
Answer: Total cost will be $398.15.
Step-by-step explanation:
Since we have given that
Cost of his equipment = $67.95
Cost of membership fees = $70
Cost of per hour =$5.50
For 40 hours,
Cost will be [tex]5.50\times 40=\$220[/tex]
Cost of per trip = $1.34
Cost for 30 trips will be
[tex]1.34\times 30=\$40.2[/tex]
According to question,
[tex]\$67.95+\$70+\$220+\$40.2=\$398.15[/tex]
Hence, total cost will be $398.15.