If Reasoning Tommy earned $57.00 in interest after 5 years on a principal of $300. The bank you would rather use is: Jane's, because her bank offers a better interest rate.
What is interest rate?Interest rate can be defined as the rate or percentage that enables a borrower to know the interest they will pay on the amount loaned to them. On the other hand interest rate means the rate a person earn on their saved amount.
Based on the given scenario i would make use of Jane bank based on the fact that Jane bank offers a better interest than Tommy bank.
Therefore Jane bank is better.
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The complete question is:
Tommy earned $30.40 in interest after 4 years on a principal of $200. His simple interest rate is 3.8%. Jane earned $81.90 in interest after 3 years on a principal of $700. Her simple interest rate is 3.9%. Which bank would you rather use? Explain your reasoning.
answer choices
Jane's because her bank offer a better interest rate.
Jane's because her bank accepted a smaller principal.
Tommy's because his bank paid more interest.
Tommy's because his investment took less time.
please answer all of them with a clear answer
See below for the solution to the questions
The parallel side of the trapezoidThe given parameters are:
Area = 138
a = 4x - 1
b = x - 4
Height = 12
The area is calculated as:
Area = 0.5 * (a + b) * height
So, we have:
0.5 *(4x - 1 + x - 4) * 12 = 138
This gives
5x - 5 = 23
Add 5 to both sides
5x = 28
Divide by 5
x = 5.6
Recall that:
a = 4x - 1 = 4 * 5.6 - 1 = 21.4
b = x - 4 = 5.6 - 4 = 1.6
Hence, the short base length is 1.6 meters and the long base length is 21.4 meters
The largest angle in the triangleThe sides are given as:
x = 22
y = 24
z = 25
The largest angle always opposite the largest side.
This means that the largest angle is Z
The CircumferenceThe radius is given as:
r = 29
The circumference is calculated as:
[tex]C = 2\pi r[/tex]
So, we have:
[tex]C = 2\pi *29[/tex]
Evaluate
C = 182.21
Hence, the circumference is 182.21 inches
Measure of angle from arcThe measure of the arc is given as:
[tex]\theta = 69^o[/tex]
The angle LIK is calculated as:
[tex]m\angle LIK = \frac{\theta}2[/tex]
So, we have:
[tex]m\angle LIK = \frac{69^o}2[/tex]
Evaluate the quotient
[tex]m\angle LIK = 34.5^o[/tex]
Hence, the measure of the angle is [tex]m\angle LIK = 34.5^o[/tex]
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A fishing trawler sails 30 km from port on a bearing of 120° until it reaches a submerged reef.
How far (to the nearest km) is the port north of the reef?
From rectangular component, the distance of the port north of the reef is 25.9808 km.
What is the distance of the given point by rectangular component analysis ?It is given that a fishing trawler sails 30 km from port on a bearing of 120° until it reaches a submerged reef.
Thus the direction of the fishing trawler is given to be 120° with respect to the movement of the trawler.
Resolving the direction by the horizontal and vertical components, we get
The horizontal component of distance is |30*cos(120°)| = 15 km
The vertical component of distance is |30*sin(120°)| = 25.9808 km
Thus as we have to find the north direction or the vertical component, the distance is 25.9808 km.
Therefore, from rectangular component, the distance of the port north of the reef is 25.9808 km.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer:
[tex]x^2+(y-3)^2=36\\[/tex] and [tex]x^2+(y+8)^2=36[/tex]
Step-by-step explanation:
So the general formula for a circle is usually represented as: [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.
Since the diameter is 12, the radius is going to be 6, because the radius is half the diameter. We now square that value (since it's squared in the equation), you get 36, which is going to be on the right side.
The last thing to know is since it's on the y-axis, that means h=0, since if h didn't equal 1, it would either be to the right or left of the y-axis. So the equation should look something like this: [tex]x^2+(y-k)^2=36[/tex] where k can be any real number.
So this gives you the two equations:
[tex]x^2+(y-3)^2=36\\[/tex] and [tex]x^2+(y+8)^2=36[/tex]
Part A:
What is the solution to the inequality below?
|x + 6| ≥ 5
Part B:
In 3-4 sentences, write a description of solution as it would look on a number line. Be sure to include the words:
-Shaded or Not Shaded
-Open or closed
-Solution
The solution of the inequality, |x + 6| ≥ 5 is given as follows,
(A) x > -1
(B) It follows that x either belongs to the interval (-∞, -11) or to the interval (-1,∞) for the given absolute inequality.
(A) Solving the Given Inequality:
|x + 6| ≥ 5
x+6 ≥ 5 or x+6 ≤ (-5)
x+6-6 ≥ 5-6 or x+6-6 ≤ (-5)-6
x ≥ -1 or x ≤ -11
Hence the solution of the given inequality is given as,
x ∈ (-∞, -11] or x ∈ [-1, ∞)
(B) Description of the Solution
From the given absolute inequality, it can be concluded that x either belongs to the interval (-∞, -11] or to the interval [-1, ∞). Hence, on the number line, the solution of the inequality will be shown as a shaded region from -∞ to -11 and from -1 to ∞. The area between -1 and -11 will remain unshaded.
In the deduced solution, the interval is either open or closed on both sides. Open interval means the extreme value is not includes. On the other hand, closed interval indicates inclusion of the extreme point in the solution of the inequality.
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An angle has turn through 15 one-degree angle. what is a measurement of this angle in degrees
The measurement of the angle is 15° (if initial angle is 0°).
Turning Through One-degree Angles
An angle is said to have an angle measure of n degrees if it rotates across n one-degree angles. Since turning through one degree means making an angle of one degree, every time you take a turn of one degree, you rotate through one degree more. Thus, turning through n one-degree angles give rise to an angle of n degrees.
Measurement of the Angle
It is given that the angle has turned through 15 one-degree angles. Thus, the angle will turn through 15°.
Let us assume the initial angle to be x°.
Then, the new angle after 15 one-degree turns would be (x+15)°
If initial angle, x = 0°, the measurement of the angle formed is 15°.
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true ir false .
A central angle is equal to half the measure of its intercepted arc.
Answer:
Step-by-step explanation:
Answer
False but close.
The intercept arc and the central angle are equal.
i need help quick!!
you can have brainliest this is algerbra btw
Answer:
Step-by-step explanation:
Day 1 = 2 birds
day 2 = 3 birds
day 3 = 9 birds
day 4 = 8 birds
day 5 = 1 bird
On day 1 the points are (1,2)
On day 5 the points are (5,1)
(I am picking these for the points because I don't know your options for the selecting area.)
we use this formula y2-y1/x2-x1
2-5/1-1
3/0
our answer is infinite which is the relation and this is an infinite function
Answer:
◘ (1, 2)
◘ (2, 3)
◘ 3
◘ is
◘ each value of Day corresponds to exactly one value of Number of birds
Explanation:
◘◘ In the graph, Days represents the x-axis, and Number of birds represents the y-axis. Therefore each marked point on the graph can be thought of as a Cartesian coordinate. This means that the answers for the first and second question could be any of (1, 2), (2, 3), (3, 9), (4, 8), or (5, 1).
◘ In the graph, we can see that the point above Day 2 corresponds to 3 on the Number of birds axis, which means on day 2, 3 birds visited the feeder.
◘ The relation shown is a function because each value of Day corresponds to exactly one value of Number of birds. A function is a relationship that provides one output for each input, and this graph follows that.
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer: [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.
Step-by-step explanation:
Finding the third angle in triangle XYZ,
[tex]m\angle YXZ=180^{\circ}-77^{\circ}-48^{\circ}=55^{\circ}[/tex],
Thus, [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Find the factors of function f, and use them to complete this statement. From left to right, function f has zeros at , , , and .
The factorized form of the given function, f(x) = 2x⁴ - x³ - 18x² + 9x, is, f(x) = x(2x - 1)(x + 3)(x - 3), and the complete statement is, From left to right, function f has zeros at x = -3, x = 0, x = 1/2, and x = 3.
In the question, we are asked to find the factors of the function f, and complete the given statement.
The function f, given to us is:
f(x) = 2x⁴ - x³ - 18x² + 9x.
To factor the function, we first group the terms as follows:
f(x) = (2x⁴ - 18x²) - (x³ - 9x).
Now, we take common terms out of the group as follows:
f(x) = 2x²(x² - 9) - x(x² - 9).
Now, we again take common terms, as follows:
f(x) = (2x² - x)(x² - 9),
or, f(x) = x(2x - 1)(x + 3)(x - 3).
This is the factored form of the given function, f.
The statement given to us is:
From left to right, function f has zeros at x = _, x = _, x = _, and x = _.
To find the zeroes of the function, we equate the factorized form to 0.
x(2x - 1)(x + 3)(x - 3) = 0.
By zero-product rule, the zeroes are at:
x = 0,
2x - 1 = 0, or, x = 1/2,
x + 3 = 0, or, x = -3,
x - 3 = , or, x = 3.
Arranging these in ascending order, the zeroes are at: -3, 0, 1/2, and 3.
Thus, the factorized form of the given function, f(x) = 2x⁴ - x³ - 18x² + 9x, is, f(x) = x(2x - 1)(x + 3)(x - 3), and the complete statement is, From left to right, function f has zeros at x = -3, x = 0, x = 1/2, and x = 3.
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For the complete question, refer to the attachment.
Answer: Edmentum/plato
Step-by-step explanation:
Trigonometry. What's x? Dont know how to do it
Answer:
12.11069457
Step-by-step explanation:
You start by using sin(48) = 9/x
You then multiply both sides by x to give you
xsin(48) = 9
you then divide both sides by sin(48) to get x by itself
x = 9/sin(48)
this gets you
x=12.11069457
What is the term for breaking a larger number apart into smaller numbers that can be multiplied together to get a specific result?.
Answer:
factoring
Step-by-step explanation:
As a construction estimator you estimate the cost of bathroom remodels for a general contractor one client asks for an estimate for two bathroom remodels. you estimate it will cost $20,000 for both remodels when the project is finished all the supplies came in at the estimated budget except for two vanities which were each $100 less than the budgeted amount what was the difference between the actual cost and estimated cost for the two bathroom remodels
For two bathroom remodel estimate budget is $[tex]20000[/tex] for both remodels. when the project is finished all the supplies came in at the estimated budget except for two vanities which were each $[tex]100[/tex] less than the budgeted .So the actual cost of two bathroom remodel is $ [tex]19800[/tex] and the different of actual and expected budgets is $[tex]200[/tex]
How can we find the actual costing of the bathroom remodel ?
Expected estimate budget of two bathroom's remodel is $[tex]20000[/tex]
So budget of one bathroom remodel is
[tex]20000/2\\=10000[/tex]
All supplies are come except for two vanities which were each $[tex]100[/tex]
So for two bathroom remodels
[tex]=2*100\\=200[/tex]
So the actual cost of remodel of both bathroom is
[tex]=20000-200\\=19800[/tex]
And difference between actual and estimated cost is
[tex]=20000-19800\\=200[/tex]
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A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented by the x-axis and the base of the house is at the origin. There are two trees on the property. One tree is 8 feet from the base of the house and is 16 feet tall. The other tree is 11 feet from the base of the house and is 9 feet tall. What is the distance from the base of the house to the closest treetop? Round your answer to the nearest tenth. Need answer ASAP.
The distance from the base of the tree to the tallest would be 14.21 cm
We have the following data points in this questionX1 = 8 feet
y1 = 16 feet
x2 = 11 feet
y2 = 9 feet
To proceed with the solution we have to
We have to solve for the shorter tree
[tex]\sqrt{(y2 -y1)^2 + (x2-x1)^2} \\\\= \sqrt{9-0^2 + 11-0^2}[/tex]
= 9² + 11²
= √81 +121
= 14.21
For the taller tree we would have√8² + 16²
= √64 +256
= 17.89
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If a car travels 368.5 miles on 50 liters of gas, how many liters of gas will it take to go 691 miles if the car travels at the same rate? (Round to the nearest tenth)
A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
Answer Options:
A.11.65
B.50.00
C.171.65
D.210.00
The time it took the rider to reach the ground level is 171.651seconds
Quadratic functionsQuadratic functions are functions that has a leading degree of 2.
Given the equation that represents roller coaster’s height as shown
h = –0.025t^2 + 4t + 50
The coaster will reach the ground when h = 0
Substitute
0 = –0.025t^2 + 4t + 50
Factorize
On factorizing, the time it took the rider to reach the ground level is 171.651seconds
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Answer:
171.65 seconds
Step-by-step explanation:
did the test and got it right
what is the volume of the truck bed which is
10 feet long, 4 feet wide, and has a height of 3
feet?
Answer:
120 ft cubed
Step-by-step explanation:
V=lwh
V=10(4)(3)
V=120 ft cubed
Find the measures of the numbered angles in each rhombus.
Answer:
Step-by-step explanation:
2=27
3=27
5=27
1=126
4=126
I don't understand any recursive sequences please help explain so
The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 units. Which statement about the domain and range of each function is correct?
A).Both the domain and range of the transformed function are the same as those of the parent function.
B).Neither the domain nor the range of the transformed function are the same as those of the parent function.
c).The range of the transformed function is the same as the parent function, but the domains of the functions are different.
D).The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.
The statement that is true about the domain and range of each function is; A) Both the domain and range of the transformed function are the same as those of the parent function.
How to interpret reflection of a function?We are told that the graph of f(x) = |x| is reflected across the y-axis. Thus;
|-x| = x
Now, the function is translated to the left by 5 units and so the transformed function is; g(x) = |x + 5|
Thus, from the graph, we get;
Domain of both functions is the set of all real numbers.
Range of both functions is the set {y|y ≥ 0}
Thus, we conclude that Both the domain and range of the transformed function are the same as those of the parent function.
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The marks obtained by 10 student in a test are as follows: 3,7,6,2,8,5,9,1,4 and 10. find the mean mark
Answer:
[tex]5.5[/tex]
Step-by-step explanation:
Mean:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is
[tex]\mu = \frac{{\sum}x}{N}[/tex]
The formula for the mean of a sample is
[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:
[tex]\frac{55}{10} = 5.5[/tex]
The volume of a rectangular box is 1.0 ft3. what is the length if the width is 1.0 ft and the height is 1.5 ft?
The length of the rectangular box is 0.67 feet
How to determine the length of the box?The given parameters are:
Length = ??
Width = 1.0 ft
Height = 1.5 ft
Volume = 1.0 ft^3
The volume is calculated as:
Volume = Length * Width * Height
Substitute the known values in the above equation
1 = Length * 1 * 1.5
Evaluate the product
1 = Length * 1.5
Divide both sides by 1.5
Length = 0.67
Hence, the length of the rectangular box is 0.67 feet
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
A, B, F
- The radius of the circle is 3 units
- The center of the circle lies on the x-axis
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9
Step-by-step explanation:
The first option is correct because the standard equation of the circle is:
[tex](x - 1)^{2} + {y}^{2} = 9[/tex]
making the radius equal to 3.
The center is at (-1,0), therefore it lies on the x-axis.
And lastly, the last option is correct because both options have the radius of 3.
which of the answer choices could be the one missing data item for the following set, if the mode is 12? 7, 12, 9, 15, 12, 7, 9, 7, 12, 15 a. 15 b. 9 c. 7 d. 12
Answer: D. 12
Step-by-step explanation: The mode is the most popular number in a set of numbers. In this set, there are 3 sevens, 3 twelves, 2 nines, and 2 fifteens. If the mode is twelve, you need one more 12 because there are the same amounts of twelves and sevens. So that means the answer is 12!
2. The prices of several different cereals are given below. Find the mean, median, mode, MAD, and IQR of these values. Which measure of center and which measure of variability best describe the data? $3.50, $4.25, $6, $4.75, $5.80, $4
I need this with explanation please:(
Mean = $ 4. 72
Median = $ 4. 5
Mode = No mode
MAD = $ 4. 8
IQR = $ 0. 5
Measure of center = $ 4. 5
Measure of variability = $ 2. 50
How to determine the valuesGiven the data;
$3.50, $4.25, $6, $4.75, $5.80, $4
Mean = sum of data/ number of data values
Mean = [tex]\frac{3. 50 + 4. 25 + 6 + 4. 75 + 5. 80 + 4}{6}[/tex]
Mean = $ 4. 72
Median is the number in the center when the data is arranged in an ascending order
$3. 50, $4, $4. 25, $4. 75, $5. 80, $6
Median = [tex]\frac{4. 25 + 4. 75}{2}[/tex]
Median = $ 4. 5
Mode is the number with the highest repeats.
From the given data, none of the numbers was repeated.
Thus, there is no mode.
MAD, mean absolute deviation = |data value - mean|
MAD = [tex]|(3. 50 - 4. 72) + (4. 25 - 4. 72) + (6 - 4. 72) + (4. 75 - 4. 72) + (5. 80 - 4.72) + (4- 4. 72) |[/tex]
MAD = [tex]1. 22 + 0. 47 + 1. 28 + 0. 03 + 1. 08 + 0. 72[/tex]
MAD = $ 4. 8
IQR, interquartile range = Quartile 3 - quartile 1
IQR = 4. 75 - 4. 25
IQR = $0. 5
Note that the mean and median are the most common measures of center.
A measure of variability is a single number that is used to describe the spread of a data set
The measure of the center best for the data is the median = $4. 5
Measure of variability = range = highest value - lowest value = $6 - $3. 50 = $2. 50
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How does the figure help verify the triangle inequality theorem?
The line is drawn from a length of 15, two lines constructing a triangle and intersecting the arc from a length of the lines 7, 4
A.
by showing that only one triangle can be formed when the sum of the lengths of two sides equals the length of the third
B.
by showing that a triangle cannot be formed when the sum of the lengths of two sides equals the length of the third
C.
by showing that only one triangle can be formed when the sum of the lengths of two sides is less than the length of the third
D.
by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side
Option D. The triangle inequality theorem is verified by by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side.
How to make this proofFrom the given picture we can see the length of the sides. These are 7, 4 and 15.
The length of the two sides cannot join due to the fact that they are less than 15.
4 + 7 < 15
11< 15
Hence the answer is D.
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by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side
g(x) = (x ^ 3 - 9x)/(x ^ 2 - 6x + 9)
The expression is simplified to x
How to simplify the expressiong(x) = (x ^ 3 - 9x)/(x ^ 2 - 6x + 9)
First, we simplify the numerator
= [tex]\frac{x (x^2 - 3^2)}{x^2 - 6x + 9}[/tex]
Now, let's solve the quadratic equation in the denominator
= [tex]\frac{x(x^2 - 3^2)}{x^2 - 3x - 3x + 9}[/tex]
= [tex]\frac{x(x^2 - 3^2)}{x(x-3) - 3(x - 3)}[/tex]
= [tex]\frac{x(x - 3) (x -3)}{(x -3) ( x-3)}[/tex]
Divide the like factors
= x
The answer is x
Thus, the expression is simplified to x
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#12Writethe converse, inverse, and contrapositive of the following statement. Find the truth value of each.“If Brielle drives at exactly 0 mi/h, then she travels 10 mi in 0 mins
See below for the converse, inverse, and contrapositive of the statement
How to write the conditional statements?The statement is given as:
If Brielle drives at exactly 30 mi/h, then she travels 10 mi in 20 mins
The speed is calculated as:
Speed = Distance/Time
So, we have:
Speed = 10 mi/20 mins
This gives
Speed = 10 mi/1/3 h
Speed = 30 mi/h
The converse
To do this, we simply switch the hypothesis and the conclusion
So, the converse is:
If Brielle travels 10 mi in 20 mins, then she drives at exactly 30 mi/h
The above statement is true
The inverse
To do this, we simply negate the hypothesis and the conclusion
So, the inverse is:
If Brielle did not drive at exactly 30 mi/h, then she did not travel 10 mi in 20 mins
The above statement is false
The contrapositive
To do this, we simply negate the hypothesis and the conclusion, and then switch them
So, the contrapositive is:
If Brielle did not travel 10 mi in 20 mins, then she did not drive at exactly 30 mi/h
The above statement is false
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A machine fills bags with sweets there are 4275 sweets there are 28 sweets in each full bag the machine fills as many bags as possible how many sweets are left must show your working
19 sweets are lefted.
Lets simplify the problem,
Maximum no. of bag filled by 4275 sweets
Through Simple Division we get,
4275/28 ~=152
Therefore , there is 4256 sweets in 152 bags
Therefore, 4275-4256=19 sweets are left
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please i seriously need step-by-step on this tyty
Answer: G=4
Step-by-step explanation:
The following table shows Kamal’s bank account balance after 7 months.
*TABLE IN THE FILE ATACHED BELOW*
a) What is the rate of change? Show your work.
b) What does the rate of change mean in Kamal’s scenario?
c) What is the initial value?
d) What does the initial value represent in Kamal’s scenario?
e) Determine the equation of the linear relation which represents his bank account balance.
PLEASE HELP I DON'T HAVE ANY TIME
a. The rate of change = -25/month
b. Kamal's account balance reduces by 25$ per month.
c. To find the $725.
d. Kamal's opening balance or initial deposit.
e. The linear equation is: A = -25n + 725.
How to Find the Rate of Change and Initial Value of a Linear Relation?The rate of change (m) = change in y/change in x.
a. The rate of change (m) = change in A / change in n = (700 - 650)/(1 - 3) = -25/month.
b. -25 dollar per month means every month, Kamal's account balance reduces by 25$
c. To find the initial value (b), substitute m = -25 and (7, 550) = (n, A) into A = nm + b:
550 = 7(-25) + b
550 = -175 + b
550 + 175 = b
b = 725.
Initial value is: 725.
d. The initial value, $725, is Kamal's opening balance or initial deposit.
e. To write the linear equation, Substitute m = -25 and b = 725 into A = nm + b:
A = -25n + 725
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Simplify the following expression. (2x-3)(5x^4-7x^3+6c^2-9)
The simplification of the expression (2x - 3)(5x⁴ - 7x³ + 6x² - 9) is 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27
Simplification(2x - 3)(5x⁴ - 7x³ + 6x² - 9)
= 10x^5 - 14x⁴ + 12x³ - 18x - 15x⁴ + 21x³ - 18x² + 27
= 10x^5 - 14x⁴ - 15x⁴ + 12x³ + 21x³ - 18x² - 18x + 27
= 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27
The simplified expression is 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27
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