The transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.
The "-2" in the equation of g(x) reflects a vertical stretch by a factor of 2, which causes the graph to become narrower and steeper than f(x).
The "+6" in the equation of g(x) reflects a vertical shift upward by 6 units, which moves the entire graph of g(x) upward by 6 units.
Therefore, the transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.
2. Algebraically determine the initial velocity required in a roller coaster design if the velocity will be 26 m/s at the bottom of a vertical drop of 34 m (Acceleration due to gravity in SI units is 9.8 m/s 2).
The initial velocity required in the roller coaster design is also 26 m/s.
what is an algebraic expression?
An algebraic expression is a mathematical phrase consisting of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
To determine the initial velocity required in a roller coaster design, we can use the conservation of energy principle. At the top of the drop, the total energy of the roller coaster is potential energy, given by mgh, where m is the mass of the roller coaster, g is the acceleration due to gravity, and h is the height of the drop.
At the bottom of the drop, the total energy of the roller coaster is kinetic energy, given by (1/2)mv^2, where v is the velocity of the roller coaster at the bottom.
By equating the two energies, we get:
mgh = (1/2)mv^2
Solving for the initial velocity, we get:
v = sqrt(2gh)
where h is the height of the drop.
Substituting the given values, we get:
v = sqrt(2 x 9.8 m/s^2 x 34 m) = 26 m/s
Therefore, the initial velocity required in the roller coaster design is also 26 m/s.
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4.02 Lesson check ! (4)
We can see that the sequence 1, 3, 9, 27 is not arithmetic.
Is the given sequence arithmetic?An arithmetic sequence is a sequence where the difference between any pair of consecutive terms is a constant knowed as the common difference d.
Generally, the recursive relation for these sequences is:
a(n) = a(n - 1) + d
Here we have the sequence:
1, 3, 9, 27, ...
Taking the differences between consecutive terms of the sequence we get:
3 - 1 = 2
9 - 3 = 6
27 - 9 = 18
The differences are different, so there is no common difference, meaning that this sequence is not arithmetic.
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The wheels on a car have a diameter of 28 inches. How many full revolutions will the wheels need to make to travel 200 feet? Use 3. 14 to approximate π
To get to 200 feet, the car will need to do 27 complete rotations, rounded to the nearest whole number.
The circumference of the wheel, which is determined by: is equal to the distance covered by the vehicle during one rotation of the wheels.
C = πd
where d represents the wheel's diameter. Using the approximate value of as 3.14 and the supplied value of d = 28 inches, we get:
C=3.1428 = 87.92 inches
The vehicle covers 87.92 inches in a single revolution.
As there are 12 inches in a foot, we divide this measurement by 12 to convert it to feet:
12.5"/foot divided by 87.92" equals 7.3267"/revolution (rounded to 4 decimal places)
Hence, one tyre rotation of the vehicle will result in a distance of 7.3267 feet.
The automobile must execute the following moves to move 200 feet:
200 feet multiplied by 7.3267 feet per revolution results in 27.296 revolutions.
To get to 200 feet, the car will need to do 27 complete rotations, rounded to the nearest whole number.
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Work out the value of x :
5x5x5x5x5x5= 5x
Answer:
x=3125
Step-by-step explanation:
5×5×5×5×5=5x
15625=5x
divide by 5 both sides
[tex] \frac{15625}{5} [/tex]
x=3125
Answer:
3125
Step-by-step explanation:
[tex]5 \times 5 \times 5 \times 5 \times 5 \times 5 = 5x \\ {5}^{6} = 5x \\ \frac{ {5}^{6} }{5} = x \\ \frac{15625}{5} = x \\ x = 3125[/tex]
Does anyone know this? I really need help!!
Answer:
measure of arc JL is 170°
Step-by-step explanation:
The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Inscribed angles that intercept the same arc are congruent.
so 85*2 is 170°
For the years 1970-2006, the percent of females in the workforce is given by y=11.596+8.540lnx, where x is the number of years from 1960.(a) What does the model predict the percent to be in 2013? In 2018?(b) Is the percent of female workers increasing or decreasing?If $4000 is invested in an account earning 7% annual interest compounded continuously, then the number of years that it takes for the amount to grow to $8000 is n= ln2 0.07. Find the number of years.The number of periods needed to double an investment when a lump sum is invested at 11% compounded bimonthly is n= log2 0.0079. In how many years will the investment double?
a) The percentage of females in the workforce in the year 2013 and 2018 can be found using the given equation: y = 11.596 + 8.540 ln(x), where x is the number of years from 1960. We need to find the value of y when x is 53 (2013) and 58 (2018), as we know that 1970 was 10 years after 1960.
So, when x = 53 (in the year 2013), the percentage of females in the workforce can be found as: y = 11.596 + 8.540 ln(53)
= 11.596 + 8.540 × 3.970
= 11.596 + 33.8618
= 45.4578 %
Therefore, the model predicts that the percentage of females in the workforce was 45.4578% in 2013.
Similarly, when x = 58 (in the year 2018), the percentage of females in the workforce can be found as:
y = 11.596 + 8.540 ln(58)
= 11.596 + 8.540 × 4.060
= 11.596 + 34.7244
= 46.3204 %
Therefore, the model predicts that the percentage of females in the workforce was 46.3204% in 2018.
b) To determine if the percentage of female workers is increasing or decreasing, we need to look at the coefficient of ln(x) in the given equation. Here, the coefficient of ln(x) is positive (8.540). Hence, the percentage of female workers is increasing over the years.
Therefore, the percentage of female workers is increasing.
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each marble bag sold by susans marble company contains 3 blue marbles for every 4 green marbles. if a bag has 24 blue marbles how many green marbles does it contain
Answer:
18
Step-by-step explanation:
We know that for every 4 green marbles, there are 3 blue marbles.
so if there are 8 green marbles, there are 6 blue marbles.
This continues on until we get 24 blue marbles.
Expression : Taking Green Marbles as 'x' and Blue Marbles as 'y'
4x = 3y
so if there are 24 Blue marbles , this means:
4x = 3 x 24
4x = 72
x = 72/4 = 18 Marbles are green
How is the denominator and numerator of your answer related to the model? Explain
The terms denοminatοr and numeratοr are nοt directly related tο a mοdel unless the mοdel invοlves a fractiοn οr a ratiο.
What is denοminatοr and numeratοr?The denοminatοr and numeratοr are terms οften used in mathematics and fractiοns. In a fractiοn, the numeratοr is the tοp number, and the denοminatοr is the bοttοm number. The numeratοr represents the number οf parts being cοnsidered οr cοunted, while the denοminatοr represents the tοtal number οf parts in the whοle.
The terms denοminatοr and numeratοr are nοt directly related tο a mοdel unless the mοdel invοlves a fractiοn οr a ratiο.
Hοwever, in statistical mοdels, the dependent and independent variables can be thοught οf as the numeratοr and denοminatοr οf a ratiο οr a fractiοn. The dependent variable represents the numeratοr, the number οf events οr οbservatiοns οf interest, while the independent variable represents the denοminatοr, the tοtal number οf events οr οbservatiοns.
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A circular pond has a diameter of 141 feet. If Ricky walks one lap around the perimeter of the pond, how far does Ricky walk? Enter a decimal rounded to the hundredths place.
If Ricky walks οne lap arοund the perimeter οf the pοnd then he walks 443.14 feet far.
What is feet ?The British imperial and American custοmary systems οf measurement bοth use the unit οf length knοwn as the fοοt (plural: feet), standard symbοl: ft. Usually used as an alternate symbοl is the prime symbοl, One yard is equal tο three feet in bοth custοmary and imperial measures; οne fοοt is equal tο 12 inches.
Thrοughοut histοry, the "fοοt" was a cοmpοnent οf a number οf regiοnal systems οf measurement, including the Greek, Rοman, Chinese, French, and English systems. Frοm οne natiοn tο the next, frοm οne city tο the next, and perhaps frοm οne trade tο the next, it varied in length. Its length was οften divided intο 12 inches οr 16 numbers and ranged frοm 250 tο 335 mm in length, thοugh this was nοt always the case.
Hence, The diameter οf pοnd 141 feet
The radius οf pοnd = 141/2 feet
Area οf pοnd = 2πr
Or, Area οf pοnd = 2×(22/7)×(141/2)
Or, Area οf pοnd = 443.14 feet
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An educator is interested in the relationship between how
many hours students spend doing homework and the
scores earned on exams. He gathers data from 12
students and calculates the least-squares regression
line to be y = 68.4 + 1.46x, where y is the score on an
exam and x is the number of hours spent doing
homework. The residual plot is shown.
Based on the residual plot, is the linear model
appropriate?
O No, the residuals are relatively large.
O No; there is a clear pattern in the residual plot.
O Yes, there is no clear pattern in the residual plot.
O Yes, about half of the residuals are positive and half
are negative.
The linear model, based on the residual plot shown and the data from the 12 students is appropriate because D. Yes, about half of the residuals are positive and half are negative.
Why is the linear model best ?When analyzing a residual plot, an appropriate linear model should display the following characteristics:
The residuals should be randomly scattered around the horizontal axis (which represents a residual of zero).There should be no apparent patterns or trends in the plot.The variance of the residuals should be roughly constant across the range of the independent variable.Looking at the residual plot for the hours spent by students doing homework and their performance on exams, we can see that the residuals are scattered randomly, there is no apparent pattern and the number of residuals above and below the line are roughly equal.
The linear model is therefore best.
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If a blouse cost is GH¢ 2. 50 work out the total cost of 15 blouse
The total price of 15 blouses whilst every shirt costs GH¢ 2.50 is GH¢ 37.50.
To calculate the overall price of 15 blouses at a price of GH¢ 2.50 per blouse, you can use multiplication. Multiplying the cost of 1 blouse (GH¢ 2.50) with the aid of the number of blouses (15) offers you the total value of 15 blouses.
Using this approach, the total cost of 15 blouses could be:
Total price of 15 blouses = 15 x GH¢ 2.50 = GH¢ 37.50
Therefore, the full price of 15 blouses whilst every shirt costs GH¢ 2.50 is GH¢ 37.50. This calculation is critical in commercial enterprise and retail settings while figuring out the total price of a buy or order.
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Using technology, what is the slope of the least-
squares regression line and what is its interpretation?
o the slope is 1. 98, which means for each additional
inch in height, the child's weight will increase by 1. 98
pounds.
the slope is 1. 98, which means for each additional
inch in height, the child's weight is predicted to
increase by 1. 98 pounds.
o the slope is 0. 50, which means for each additional
pound in weight, the child's height will increase by
0. 5 inches.
o the slope is 0. 50, which means for each additional
pound in weight, the child's height is predicted to
increase by 0. 5 inches.
The slope of the least-squares regression line is 0.50, which means that for each additional pound in weight, the child's height is expected to increase by 0.5 inches.
The slope of the least-squares regression line can be calculated using the formula:
Slope = (Σxy – (Σx)(Σy)/n) / (Σx2 – (Σx)2/n)
Where n is the number of data points, Σx is the sum of all x-values, Σy is the sum of all y-values, and Σxy is the sum of the products of the x-values and the y-values.
For example, consider a dataset with 10 data points, where the x-values are the heights in inches, and the y-values are the weights in pounds. The sum of the x-values, Σx, would be the total height of all 10 children, the sum of the y-values, Σy, would be the total weight of all 10 children, and the sum of the products of the x-values and y-values, Σxy, would be the total of the products of the heights and the weights for all 10 children. Using these values, the slope of the least-squares regression line would be:
Slope = (Σxy – (Σx)(Σy)/n) / (Σx2 – (Σx)2/n)
= (2098 - (2040)(812)/10) / (4246 - (2040)2/10)
= (98) / (1406)
= 0.50
Therefore, the slope of the least-squares regression line is 0.50, which means for each additional pound in weight, the child's height is predicted to increase by 0.5 inches.
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Sylvie asked, "Do college tennis coaches generally get paid more than college football coaches?"
Is this a statistical question?
Yes, this is a statistical question as the answer involves gathering and analyzing data about college football and tennis coaches' salaries. It's important to remember that a variety of factors could influence these salaries.
Explanation:Sylvie's question, 'Do college tennis coaches generally get paid more than college football coaches?' is considered a statistical question because it anticipates a response based on data analysis. To answer this, one would typically gather data on the salaries of both college tennis and football coaches, process this data, and then perform a comparative analysis. It's important to understand that salaries can vary widely, influenced by factors including the size of the college, the success of the program, and the region of the country.
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Pls help me with this thxsss!!!! <3
The value of s is 107° for this we have know the definition and property of triangle.
What is Triangle?A triangle is a polygon that has three(3) edges and three(3) vertices. It is one of the fundamental(basic) shapes in geometry.
Vertices, A vertex in geometry is a location where two(2) or more curves, lines, or edges come together.
s-37° + s-38° + x = 180° (Sum of three angle is 180°)
2s + x = 180° + 75°
2s + x = 255° ( Equation 1 )
s+32° + x = 180°
s + x = 180° - 32°
s + x = 148° ( Equation 2)
After solving equation 1 and 2 we get,
s = 107°
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How do I solve for "x" with the equation of 2x=10?
Answer:
x=5
Step-by-step explanation:
when to solve an equation which was given as 2x=10 then you have to make x the subject so you will divide 10 by the coefficient of x by 2x=10 then you will get your answer to be 5 as simple as that
Find x. Round to the nearest tenth.
Answer:13.5
Step-by-step explanation:
use sinuses theorem:
[tex]\frac{x}{sina}=\frac{y}{sinb} \\\frac{12}{sin63}=\frac{x}{sin90} \\x=\frac{12}{sin63}=13.5[/tex]
homework pls help me
Answer:
Step-by-step explanation:
Answer: 27.5
Step-by-step explanation:
Hope this helps
please help with this
[tex](ax^{6} )^{\frac{1}{n} } =4x^{2}[/tex]
find the value of a and n
The values of a and n that make the equation[tex](ax^6)^(1/n) = 4x^2[/tex] true for all values of x are a = 4 and n = 3.
What are laws of exponents?The laws of exponents are rules for simplifying expressions with powers, including multiplying powers with the same base, dividing powers with the same base, and raising powers to a power.
The equation is [tex](ax^6)^(1/n) = 4x^2[/tex]. We want to find the values of a and n that make this equation true for all values of x.
We can begin by simplifying the equation using the laws of exponents:
[tex](ax^6)^(1/n) = 4x^2[/tex]
a[tex]ax^6/n = 4x^2[/tex]
Now we can solve for a and n by comparing the exponents of x on both sides of the equation:
The exponent of x on the left side is 6/n, and the exponent of x on the right side is 2. Therefore:
[tex]6/n = 2[/tex]
Multiplying both sides by n, we get:
6 = 2n
Dividing both sides by 2, we get:
n = 3
Now we can solve for a by substituting n = 3 into the equation and simplifying:
[tex]ax^6/3 = 4x^2\\ax^2 = 4x^2[/tex]
a = 4
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Maria decorated her notebook with 4 rectangular stickers. Each sticker was 1/2 inches wide and 11/16 inches long
The total area of the stickers is (1/2) x (11/16) x 4 = 11/8 inches squared.
To calculate the total area of the stickers that were used to decorate the notebook, we need to know the dimensions of each sticker. In this case, the stickers were rectangular and each sticker was 1/2 inches wide and 11/16 inches long. To find the total area, we need to multiply the width of each sticker by the length of each sticker and then multiply this number by the number of stickers used. In this example, we have 4 stickers, so we must multiply (1/2) x (11/16) x 4. When this calculation is done, we end up with 11/8 inches squared as the total area of the stickers.
the complete question is :
Maria decorated her notebook with 4 rectangular stickers. Each sticker was 1/2 inches wide and 11/16 inches long
What was the area of each sticker?
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Show that the roots of the equation 2x + a(x-a)=0 are rational for any real value of a where a*0 Discuss the nature of the roots if a=0.
The root of the equation is rational for any real value of a where a>0. if a=0, the equation has a single root which is real and rational.
What are roots?In mathematics, the number that results in the initial number when multiplied by itself is called the root. For instance, 7 is the square root of 49 since 77=49. Because 49 is created by multiplying 7 by itself twice in this instance, we refer to 7 as the square root of 49. Since 333=27, the cube root of 27 is 3.
According to question:The given equation is 2x + a(x-a) = 0. Simplifying, we get:
[tex]$\begin{align*}2x + ax - a^2 &= 0 \x(2+a) &= a^2 \x &= \frac{a^2}{2+a}\end{align*}[/tex]
Therefore, the root of the equation is [tex]\frac{a^2}{2+a}$[/tex].
To show that this root is rational for any real value of a where a>0, we need to show that [tex]\frac{a^2}{2+a}$[/tex] can be expressed as a ratio of two integers.
Let [tex]$p=a^2$[/tex] and q=2+a. Since a>0, we have p>0 and q>0. Therefore, [tex]\frac{p}{q}$[/tex] is a rational number.
Thus, the root of the equation is rational for any real value of a where a>0.
If a=0, the given equation becomes 2x=0, which has only one root, x=0. Therefore, if a=0, the equation has a single root which is real and rational.
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With a polynomial rule we can substitute values in. For instance if P(x)=x^(4) then P(3)=3^(4)=81 For P(x)=5x^(2) find the value of P(3)
Answer:
Step-by-step explanation:Sure! To find the value of P(3) for the polynomial rule P(x) = 5x^2, we just need to substitute x = 3 into the rule and simplify:
P(3) = 5(3^2) (Substitute x = 3)
= 5(9) (Evaluate 3^2)
= 45 (Multiply 5 by 9)
Therefore, P(3) = 45 when P(x) = 5x^2.
5. How many possible rational roots are there for the polynomial P(x) = 10x³ + 6x² + 4x +4?
a.8
b.10
c.16
d.4
Answer:
By the Rational Root Theorem, the possible rational roots of a polynomial are of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The constant term of P(x) is 4, whose factors are ±1 and ±4. The leading coefficient is 10, whose factors are ±1, ±2, ±5, and ±10.
So, the possible rational roots of P(x) are: ±1/1, ±2/1, ±4/1, ±1/10, ±2/10, ±5/10, and ±10/10. This gives us a total of 8 possible rational roots.
Therefore, the answer is a. 8.
Step-by-step explanation:
Find x to the nearest hundredths place. Q 650 + R 22 cmS
To find the length of the hypotenuse in a right-angled triangle, we can use trigonometry. Using the given values of RS and angle Q, we can solve for QS ≈ 24.08 cm to the nearest hundredths place.
To find the length of the hypotenuse in a right-angled triangle with a given angle and one side, we can use trigonometry. In this case, we are given the angle Q, which is 65°, and the length of one of the sides, RS, which is 22 cm. We can use the sine function to relate the opposite side, RS, to the hypotenuse, QS. Solving for QS gives us QS = RS / sin(65°), which we can then evaluate to find QS ≈ 24.08 cm. Therefore, x ≈ 24.08 cm to the nearest hundredths place.
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The missing figure is in the image attached below
5.1) Discuss why the current account is
account to assess the stability.
used as a better
of the economy.
(8)
A current account is typically ideal to perform day-to-day transactions such as receiving a salary, paying bills, and making purchases.
What is a current account?A current account (or checking account) is an account that, unlike a savings account does not pay interest on the balance. In most cases rather fees may be charged from the available balance, such as overdrafts or international transactions.
It would be ideal to use a current account to perform day-to-day transactions such as receiving as a salary account, to pay for bills, and for making purchases.
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You've asked an incomplete question. However, I assumed you need more information about a current account, thus, they're provided above.
Using the empirical rule, what percentage of the games that Lillian bowls does she score between 119 and 141
Using the Empirical Rule, Lillian should score between 119 and 141 in 68% of the games she bowls.
In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively. the empirical rule states that 99.7% of data occurs within three standard deviations of the mean within a normal distribution. To this end, 68% of the observed data will occur within the first standard deviation, 95% will take place in the second deviation, and 97.5% within the third standard deviation. The empirical rule predicts the probability distribution for a set of outcomes.
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A marketing research company desires to know the mean consumption of meat per week among people over age 49
. They believe that the meat consumption has a mean of 4.2
pounds, and want to construct a 90%
confidence interval with a maximum error of 0.06
pounds. Assuming a variance of 1.44
pounds, what is the minimum number of people over age 49
they must include in their sample? Round your answer up to the next integer.
To calculate the minimum sample size required to construct a 90% confidence interval with a maximum error of 0.06 pounds, we can use the formula:
n = (Z^2 * σ^2) / E^2
where n is the sample size, Z is the z-score corresponding to the desired confidence level (in this case, 90%), σ^2 is the variance, and E is the maximum error.
Substituting the given values, we get:
n = (1.645^2 * 1.44) / 0.06^2
n = 84.934
Rounding up to the next integer, we get a minimum sample size of 85 people over age 49.
Therefore, the marketing research company must include at least 85 people over age 49 in their sample to construct a 90% confidence interval with a maximum error of 0.06 pounds, assuming a variance of 1.44 pounds and a mean consumption of meat per week of 4.2 pounds.
Graph then find the following: a) Domain b) Range c) Vertex d) Axis of symmetry e) Minimum f) Maximum g) Stretch or shrink h) Upward/downward: A) f(x)=x² B) f(x) = -3x²
Step-by-step explanation:
a) Domain of both functions is all real numbers (-∞, +∞), as there are no restrictions on the input (x).
b) The range of A) f(x)=x² /3 is [0, +∞), as the minimum value of the function is 0 and there is no maximum value.
The range of B) f(x) = -3x² is (-∞, 0], as the maximum value of the function is 0 and there is no minimum value.
c) The vertex of A) f(x)=x² /3 is at (0,0).
The vertex of B) f(x) = -3x² is at (0,0).
d) The axis of symmetry of both functions is the vertical line passing through the vertex, which is x = 0.
e) The minimum value of A) f(x)=x² /3 is 0, which occurs at the vertex.
f) The maximum value of B) f(x) = -3x² is 0, which occurs at the vertex.
g) A) f(x)=x² /3 is a horizontally shrunk version of the parent function f(x) = x² by a factor of 1/3.
B) f(x) = -3x² is a vertically stretched version of the parent function f(x) = x² by a factor of 3.
h) A) f(x)=x² /3 opens upward, as the coefficient of x² is positive.
B) f(x) = -3x² opens downward, as the coefficient of x² is negative.
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
∠OPM
Step-by-step explanation:
∠QPR = ∠3 = ∠1 = ∠OPM
Answer:
∠3
Step-by-step explanation:
Find the twenty-third term of an arithmetic sequence that has a common difference
equal to 10 and its eighth term equal to 52
The twenty-third term of the given arithmetic sequence is 192.
The formula to find the nth term of an arithmetic sequence with a common difference (d) is Tn = a + (n - 1)d, where a is the first term of the sequence. To solve for the twenty-third term of the given sequence, we can substitute the given values into the formula. The common difference (d) is 10 and the eighth term (a) is 52, so the formula becomes T23 = 52 + (23 - 1)10. When we solve this equation, we get T23 = 192. Therefore, the twenty-third term of this arithmetic sequence is 192.
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Solve the equation.
4x4 - 40x2 + 36 = 0
A. x=1 , x= 3
B. x= -3, x= -1, x= 1, x= 3
C. x= -3, x= -1
D. no solution
The solutions of the given equation as required to be determined are as given in; +3, -3, +1, and -1.
What are the solutions of the given equation?As evident from the task content; it follows that the solutions of the given equation are to be determined.
Given; 4x⁴ - 40x² + 36 = 0
Therefore, we have;
x⁴ - 10x² + 9 = 0
Let y = x² so that we have;
y² - 10y + 9 = 0
(y - 9) (y -1) = 0
y = 9 Or y = 1
Therefore, since y = x²;
x = ± 3 or ±1
Hence, the solutions for the equation as required are; +3, -3, +1, and -1.
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