The factored form of the expression x² + 5x+6 is (x + 3)(x + 2)
How to determine the factorized formTo factorize the quadratic equation, we need to take the following steps;
Multiply the coefficient of the x squared by the constant value, we have;
6
Now, find the pair factors of the product that would add up to give 5, we have;
2 + 3
Substitute the values into the expression, we have;
x² + 2x + 3x + 6
Now, group the expression in pairs, we have;
(x² + 2x) + (3x + 6)
Factorize the expressions
x(x + 2) + 3(x + 2)
Then, we have;
x + 3
x + 2
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The ratio of cars to people in one country is 300 to 1,000. Write a fraction to represent this ratio in simplest form
Answer:
3/10
Step-by-step explanation:
Question 10(Multiple Choice Worth 2 points)
(11.01 LC)
What is the range of this data set?
The range of this data set include the following: D. 6.
What is a range?In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.
Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph (dot plot) shown in the image attached above, we can reasonably and logically deduce the following range:
Range = {18, 19, 20, 21, 22, 24} = 6.
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pls help fast with this question
Hence, it will take 2.6 hours for the two trains to be 520 miles apart.
What is the distance?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
What is the speed ?In everyday use and in kinematics, the speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity..
The two trains are moving away from each other,
so we can add their speeds to get their relative speed:
relative speed = 95 mph + 105 mph = 200 mph
Now ,we determine the time it takes for the trains to be 520 miles apart,
so we can use the formula:
distance = speed × time
let t be the time it takes for the trains to be 520 miles apart.
Then we get,
520 = 200 × t
Solving for t, we get:
t = [tex]\frac{520}{200}[/tex]
t = 2.6 hours
Therefore, it will take 2.6 hours for the two trains to be 520 miles apart.
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On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. What is the probability that the appliance will work at least six years without requiring repairs?
The probability that the appliance will work at least six years without requiring repairs is 0.2231 or 22.31%.
To find the probability that the appliance will work at least six years without requiring repairs, we need to consider the exponential distribution and the given average repair time. Given that the appliance requires repairs once every four years on average, the rate parameter (λ) for the exponential distribution is 1/4, or 0.25.
Here we want to find the probability that the appliance will work at least six years without requiring repairs, which can be represented as [tex]P(X ≥ 6)[/tex], where X is the time between repairs. Using the complementary probability, we can rewrite this as [tex]P(X ≥ 6) = 1 - P(X < 6)[/tex]
The cumulative distribution function (CDF) of the exponential distribution is given by
[tex]F(x) = 1 - e^{(-λx)}[/tex]
Now, we can plug in the values:
[tex]P(X ≥ 6) = 1 - F(6) \\ P(X ≥ 6) = 1 - (1 - e^{(-0.25 \times 6)}) \\ P(X ≥ 6) = 1 - (1 - e^{(-1.5)}) \\ P(X ≥ 6) = e^{(-1.5)}[/tex]
Therefore, the probability that the appliance will work at least six years without requiring repairs is approximately 0.2231 or 22.31%.
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will give brainliest to quickest answer
Answer:
The vertex is option C: (-6, -2)
Step-by-step explanation:
The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)
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(1 point) a spherical balloon is inflated so that its volume is increasing at the rate of 2.8 ft3/min . how rapidly is the diameter of the balloon increasing when the diameter is 1.5 feet?
The diameter of the balloon is increasing at a rate of approximately 0.79 ft/min when the diameter is 1.5 feet.
We can use the formula for the volume of a sphere to relate the rate of change of volume with the rate of change of diameter
V = (4/3)πr^3 = (1/6)πd^3,
where V is the volume, r is the radius, and d is the diameter.
Taking the derivative with respect to time t, we get
dV/dt = (1/2)πd^2 (dd/dt),
where dd/dt is the rate of change of diameter.
We are given that dV/dt = 2.8 ft^3/min and d = 1.5 ft, so we can solve for dd/dt
dd/dt = (2dV/dt)/(πd^2) = (2(2.8))/(π(1.5)^2) ≈ 0.79 ft/min.
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Anthony has 35 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 132 square meters. List each set of possible dimensions (length and width) of the field.
The two possible sets of dimensions for the rectangular plot are:
Length = 27 meters, Width = 4 meters
Length = 4 meters, Width = 15.5 meters
Let's denote the length of the rectangular plot by L and the width by W. We know that the total length of the fencing needed is 35 m, which we can use to create an equation:
L + 2W = 35
The area of the land is 132 square meters, which we can use to create another equation:
LW = 132
We can solve the first equation for L:
L = 35 - 2W
Substituting this into the second equation, we get:
(35 - 2W)W = 132
Expanding and rearranging, we get a quadratic equation:
2W^2 - 35W + 132 = 0
We can solve for W using the quadratic formula:
W = [35 ± √(35^2 - 4(2)(132))] / (2(2))
W = [35 ± √(841)] / 4
W = [35 ± 29] / 4
Solving for W, we get two possible values:
W = 4 or W = 15.5
If W is 4 meters, then L is:
L = 35 - 2W = 27
If W is 15.5 meters, then L is:
L = 35 - 2W = 4
Therefore, the two possible sets of dimensions for the rectangular plot are:
Length = 27 meters, Width = 4 meters
Length = 4 meters, Width = 15.5 meters
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What is the name corresponding to the metric symbol mL?
A credit card starts new customers at a $2,000 limit when they are approved for a card. The company adds $500 annually to this limit for customers who pay their bill on time. Choose the equation below that gives the credit limit, Ln, of customers who have payed on time every year, and who are in their nth year of having the card. Then, use this equation to find the credit limit of a customer in their 10th year of having the card.
On solving the provided question we can say that As a result, the credit equation limit of a client who has paid on time every year for the past ten years is $7,000.
What is equation?A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions. The equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14, for instance.
The relationship between the two sentences that are located on opposite sides of a letter is explained by a mathematical formula. Frequently, the symbol and the single variable are identical. like in 2x - 4 = 2, for example.
The following equation determines the credit limit, Ln, of customers who have made on-time payments each year and are in the nth year of card ownership:
Ln = $2,000 + $500n
where Ln stands for the credit limit in the nth year and n is the number of years the cardholder has had it.
In the equation above, we substitute n=10 to get a customer's credit limit after ten years of card use:
L10 = $2,000 + $500(10)
L10 = $2,000 + $5,000
L10 = $7,000
As a result, a client with a ten-year history of on-time payments has a credit limit of $7,000.
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solve for x
khan academy solve similar triangles advanced
Value of side CD = x=3
What is similarity of two triangle ?When two triangles are are referred to as similar figures when they share the same shape but different in size.
given that CB and ED are perpendicular to AD,
in triangle ABC and ADE
∠A=∠A (common angle )
∠B=∠D (both are 90 degree)
ΔABC≈ ΔADE by angle-angle similarity .
and we know that when two triangle are similar then their corresponding sides are with in the same ratio or proportional.
so ,here we proved that triangle ABC and ADE are similar,
then ,
[tex]\frac{BC}{ED}=\frac{AB}{AD}[/tex]
[tex]\frac{x}{5}=\frac{9}{9+6}[/tex]
[tex]\frac{x}{5} =\frac{9}{15}\\ X=3[/tex]
x=3
from above result ,value of side CB =x=3
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Bret bought his family lunch. Before tax, the bill came to $42. The sales tax was 6% and Bret tipped the waitress 20% before tax was added. How much money did Bret spend?
Answer: Bret spent $52.92 on the lunch, including tax and tip.
Step-by-step explanation:
Given:
The bill before tax = $42
Sales tax = 6%
Tip = 20% before tax
To find:The total amount of money Bret spent
Solution: Calculate the sales tax:
Sales tax = 0.06 * $42 = $2.52
Calculate the total bill, including tax:
Total bill = $42 + $2.52 = $44.52
Calculate the bill before tax, based on which the tip is calculated:
Bill before tax = $44.52 - $2.52 = $42
Calculate the tip amount:
Tip = 0.2 * $42 = $8.40
Calculate the total amount spent by Bret:
Total spent = $44.52 + $8.40 = $52.92
Therefore, Bret spent $52.92 on the lunch, including tax and tip.
In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About how many times greater was the intensity of the Chilean earthquake? a. 2.5 b. 25 c. 150 d. 316
In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About 316 times greater was the intensity of the Chilean earthquake.
Hence, the correct option is D.
The Richter scale is a logarithmic scale that measures the magnitude of an earthquake. Each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves.
To find out how many times greater the intensity of the Chilean earthquake was compared to the Haitian earthquake, we will have to find the difference in magnitude between the two earthquakes.
9.5 - 7.0 = 2.5
Since each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves, a 2.5 increase represents
10^(2.5) = 316.2
Hence, the intensity of the Chilean earthquake was about 316 times greater than the intensity of the Haitian earthquake.
Hence, the correct option is D.
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Answer:d
Step-by-step explanation:
its d
ruby is using the quadratic formula to solve a quadratic equation. which of the following is the next step for simplifying x=−6±85√2 responses
x=−3±8√5
x=−3±√5
x=−3±4√5
this is fully simplified.
a lot is in the shape of a right triangle. the shorter leg measures 150 m. the hypotenuse is 50 m longer than the length of the longer leg. how long is the longer leg?
Answer:
Starting with the 3-4-5 right triangle, multiply all lengths by 50, obtaining 150, 200, and 250. So the length of the longer leg is 200 meters.
Find the value of x. If a segment looks like a tangent, it is a tangent.
The value of x in the circle is 19.5 .
What is secant line of circle?
A secant is a straight line that intersects a circle at least twice in different places. We can draw an endless number of secants on a circle since a circle has an infinite number of points around its perimeter.
Here the given circle using formula for secant line ,
(A+B).B = (C+D).D
Here A = x , B = 8 , C= 12 and D=10. Then,
=> (x+8).8= (12+10).10
=> 8x+64 = 22*10
=> 8x+64 = 220
=> 8x = 220-64 = 156
=> x = 156/8 = 19.5
Hence the value of x in circle is 19.5.
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Solve the quadratic equation x² +9x = 0 by
factoring the GCF.
Answer: x=0 and x=-9
Step-by-step explanation:
The radius of a circle is 9 millimeters. What is the circle's circumference?
Use 3.14 for л.
Answer:
56.55
Step-by-step explanation:
C=2πr=2·π·9≈56.54867
There is a spinner with 14 equal areas, numbered 1 through 14. If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 4?
Answer:
Okay, let's solve this step-by-step:
There is a spinner with 14 equal areas, numbered 1 through 14
We want to find the probability that the result is a multiple of 3 or a multiple of 4
There are 14 possible outcomes (numbers 1 through 14) when the spinner is spun.
Of these 14 numbers:
4 are multiples of 3: 3, 6, 9, 12
4 are multiples of 4: 4, 8, 12, 16
However, 12 is also a multiple of both 3 and 4, so we have counted it twice.
We need to subtract 1 from each to account for this:
Multiples of 3: 3
Multiples of 4: 4
So there are 3 possible multiples of 3 and 3 possible multiples of 4.
In total, there are 3 + 3 = 6 possible multiples of 3 or 4.
To calculate probability:
Probability = (Number of favorable outcomes) / (Total possible outcomes)
= 6 / 14
= 3/7
Converting to a percent: 3/7 = 42.9%
Rounded to the nearest whole percent: 43%
Therefore, the probability that the result is a multiple of 3 or a multiple of 4 is 43%.
Step-by-step explanation:
You start driving west for 3 miles, turn right, and drive north for another 11 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
Find the volume of the cone. Use 3.14 for pi. Round your answer to the nearest tenths
place.
The volume of the cone is approximately 37.7 cubic units
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
To find the volume of a cone, we use the formula:
V = (1/3) * π * r² * h
where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.
Plugging in the given values, we get:
V = (1/3) * 3.14 * 3² * 4 ≈ 37.7
Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).
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Consider the equation: x² + 10x + 22 = 13 1) Rewrite the equation by completing the square. Your equation should look like (x + c)2 = dor (x - c)² = d. 2) What are the solutions to the equation? Choose 1 answer: A x=5±4 x = -5±4 x = 5±16 x = -5±16
The solutions to the equation x² + 10x + 22 = 13 are: x = -5 ± 4
Solving the equation by completing the squareTo rewrite the equation by completing the square, we need to isolate the constant term on one side and group the x-terms together. Starting with:
x² + 10x + 22 = 13
Subtracting 13 from both sides:
x² + 10x + 9 = 0
Next, we add and subtract the square of half of the coefficient of x (which is 5 in this case) to complete the square:
x² + 10x + 25 - 25 + 9 = 0
x² + 10x + 25 - 16 = 0
Factor the perfect square trinomial:
(x + 5)² - 16 = 0
Now that we have rewritten the equation in the form (x + c)² = d, we can solve for x by taking the square root of both sides:
(x + 5)² - 16 = 0
Taking the square root of both sides and solving for x, we get:
x + 5 = ±4
So, we have
x = -5 ± 4
So the solutions to the equation are:
x = -5 + 4 = -1
x = -5 - 4 = -9
Therefore, the answer is x = -5 ± 4.
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Margo missed 24.6% of her free throw shots in a season. During the season, she shot a total of 90 free throws. Which of the following is the best estimate of the number of free throws Margo missed?
Answer: 22
Step-by-step explanation:
So since Margo missed 24.6% of 90 free throws, you have to find 24.6% of 90. The easiest way to do this is to do 90 multiplied by 0.246.
To multiply by percentages in general, move the decimal point to the left by two places. For example, if it said 82.6, the decimal point would go to the left two places and be 0.826.
Back to the original question...
so 90 multiplied by 0.246 is 22.14. If you can use a calculator, this is easy, if not just do the usual multiplication.
Then, this rounds to 22, and the problem is complete!
Gus is designing a cylinder to ship liquids using the constraints given.
The inside of the cylinder must hold from 475 to 480 cubic centimeters of
liquid.
The diameter must be at least 8 centimeters and at most 10 centimeters.
What are a possible radius and corresponding height, in centimeters, for the inside
of a cylinder that meets the constraints? Round the answers to the nearest tenth.
You will focus your answer on the lower constraints of 475 volume and diameter of 8
cm for our take on this problem. You will fill in the height you find rounded to the
nearest tenth with no cm. Use 3.14 for pi.
Answer:
The possible radius and height for the inside of the cylinder that meets the constraints are r = 4 cm and h = 9.4 cm.
Step-by-step explanation:
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. We want to find a radius and height that will give us a volume between 475 and 480 cubic centimeters, with a diameter between 8 and 10 centimeters. First, we’ll use the lower limits of the constraints: a volume of 475 cubic centimeters and a diameter of 8 centimeters. The diameter is 8 centimeters, so the radius is 4 centimeters. We can plug in these values to the formula for volume and solve for h: 475 = 3.14 x 4^2 x h 475 = 50.24h h = 9.44 So a possible radius and height for the inside of the cylinder that meets the constraints are: r = 4 cm and h = 9.4 cm.
The center of a circle is at (−2, −7) and its radius is 6.
What is the equation of the circle?
Responses
(x+2)2+(y+7)2=3
open parenthesis x plus 2 close parenthesis squared plus open parenthesis y plus 7 close parenthesis squared equals 3
(x+2)2+(y+7)2=36
open parenthesis x plus 2 close parenthesis squared plus open parenthesis y plus 7 close parenthesis squared equals 36
(x−2)2+(y−7)2=3
open parenthesis x minus 2 close parenthesis squared plus open parenthesis y minus 7 close parenthesis squared equals 3
(x−2)2+(y−7)2=36
option B is correct: [tex](x+2)^2+(y+7)^2=36[/tex]
The general equation of the circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where,
(h, k) is the center of the circle and r is the radius of the circle.
As per the statement:
The center of a circle is at (−2, −7) and its radius is 6.
[tex]\implies (h, k) = (-2, -7)[/tex] and [tex]r = 6[/tex] units
Substitute these we have:
[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]
[tex]\implies(x+2)^2+(y+7)^2=36[/tex]
Therefore, the equation of circle is, [tex]\bold{(x+2)^2+(y+7)^2=36}[/tex]
show that,for all value for x
(2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2
Answer:
Therefore, the answer is: (2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2
Step-by-step explanation:
To prove that (2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2 for all values of x, we can simply expand the left-hand side of the equation and simplify it to match the right-hand side.
Expanding the left-hand side using the distributive property, we get:
(2x-1)(x+2)(3x-1) = (2x^2+3x-2)(3x-1)
= 6x^3 + 7x^2 - 9x + 2
This matches the right-hand side of the equation, so we have proven that (2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2 for all values of x.
now, using the above definition, determine if the function below is increasing, decreasing, even, odd, and/or invertible on its natural domain: $$f(x)
f'(x) = 2x - 2 is always positive on (-∞, 1) and always negative on (1, ∞), the function is increasing and decreasing, respectively, and therefore one-to-one. Therefore, f(x) is invertible in its natural domain.
What is the exponential function?
An exponential function is a mathematical function of the form f(x) = aˣ
where "a" is a constant called the base, and "x" is a variable. Exponential functions can be defined for any base "a", but the most common base is the mathematical constant "e" (approximately 2.71828), known as the natural exponential function.
To determine if the function f(x) = x² - 2x + 3 is increasing, decreasing, even, odd, and/or invertible in its natural domain, we need to analyze its derivative and second derivative:
f'(x) = 2x - 2
f''(x) = 2
Increasing/decreasing: Since f''(x) is always positive (i.e., 2 is positive), the function is always concave up and has a minimum at x = 1. Thus, f(x) is increasing on (-∞, 1) and decreasing on (1, ∞).
Even/odd: To determine if f(x) is even or odd, we need to check if it satisfies the properties of even and odd functions.
Even function: A function f(x) is even if f(-x) = f(x) for all x in the domain. Let's check if f(x) satisfies this property:
f(-x) = (-x)² - 2(-x) + 3 = x² + 2x + 3
f(x) = x² - 2x + 3
f(-x) ≠ f(x), so the function is not even.
Odd function: A function f(x) is odd if f(-x) = -f(x) for all x in the domain. Let's check if f(x) satisfies this property:
f(-x) = (-x)² - 2(-x) + 3 = x² + 2x + 3
-f(x) = -(x² - 2x + 3) = -x² + 2x - 3
f(-x) ≠ -f(x), so the function is not odd.
Invertible: To determine if f(x) is invertible, we need to check if it has an inverse function.
A function has an inverse function if it is one-to-one, which means that it passes the horizontal line test.
To check if f(x) is one-to-one, we can analyze its derivative.
Hence, f'(x) = 2x - 2 is always positive on (-∞, 1) and always negative on (1, ∞), the function is increasing and decreasing, respectively, and therefore one-to-one. Therefore, f(x) is invertible in its natural domain.
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Complete question:
For the following, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain: f(x) = x² - 2x + 3.
Right answer gets brainliest and 25 points‼️‼️‼️‼️
Answer: d
Step-by-step explanation:
Answer:
B: Range of round 1 were higher than the range of Round-2.
Step-by-step explanation:
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Ethan had some solid-coloured socks and patterned socks. He had \frac{3}{4} as many solid-coloured socks as patterned socks. He threw away 16 Paris of solid-coloured socks and 16 Paris of patterned socks. \frac{1}{5} of his socks were now solid-coloured socks. How many pairs of patterned socks did Ethan have at first?
If ethan threw away 16 Paris of solid-coloured socks and 16 Paris of patterned socks, Ethan had 140 pairs of patterned socks at first.
Let's start by assuming that Ethan had x pairs of patterned socks. According to the problem statement, Ethan had 3/4 as many solid-coloured socks as patterned socks. Therefore, the number of solid-coloured socks he had can be represented as 3/4*x.
Ethan threw away 16 pairs of solid-coloured socks and 16 pairs of patterned socks. So, after the clean-up, he had (3/4*x)-16 pairs of solid-coloured socks and (x-16) pairs of patterned socks.
The problem states that 1/5 of his socks were now solid-coloured socks. So, we can set up an equation:
(3/4x-16) = (1/5)(3/4*x + x - 32)
Simplifying and solving for x, we get:
x = 140
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Before working through each problem, identify the principal, rate, time. Work with your shoulder-partner to find the solution. • Mr. Jackson deposited $1,250 in a new account at his bank. • The bank pays 3.5% simple interest • Mr. Jackson pays no additional deposits or withdrawals. o What amount is closest to the balance of the account at the end of 2 years?
Thus, the amount of the money in the bank account at the end of 2 years is found to be: $1337.5.
Explain about the term simple interest:Simple interest denotes interest that is simply charged on the principal amount, which is the original amount borrowed or deposited. The interest charge is going to be applied once, regardless of how frequently it is applied. Many loans base their calculations on simple interest, but you should double-check before signing anything.
Given data:
Principal P = $1,250Simple Interest rate R = 3.5%Time T = 2 yearsFormula for the estimating simple interest:
SI = PRT/100
SI = 1250*3.5*2 / 100
SI = 87.5
Amount = principal + simple interest
A = 1250 + 87.5
A = 1337.5
Thus, the amount of the money in the bank account at the end of 2 years is found to be: $1337.5.
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using definition of derivative:lim as h approaches 0f(a+h) - f(a) / h
Using the definition of the derivative, we have:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
We're asked to use the definition of the derivative, which includes the terms:
limit, h, f(a+h), f(a), and the fraction f(a+h) - f(a) / h.
The definition of the derivative of a function f(x) at a specific point x=a is given by:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
f(a+h) represents the value of the function f(x) at the point (a+h).
f(a) represents the value of the function f(x) at the point a.
f(a+h) - f(a) calculates the difference in the function values at these two points.
h is the small change in the x-coordinate (x-axis) between these two points, and we let h approach 0 to ensure we're finding the instantaneous rate of change.
(f(a+h) - f(a)) / h represents the average rate of change between the points (a, f(a)) and (a+h, f(a+h)).
By taking the limit as h approaches 0, we find the instantaneous rate of change at the point x=a, which is the derivative of the function f(x) at x=a.
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