1. The loan balance after 2 years is $45,262.
2. The loan balance after 3 years is $42,678.
3. The loan balance after 1 year is $47,700.
What is the loan balance?The loan balance is the amount remaining from the principal amount after the deduction of repayment and the addition of interest for the period.
The loan balance can be computed manually as below:
Data and Calculations:Loan amount = $50,000
Interest rate = 6%
Annual repayments = $5,000
1st year:
Loan amount = $50,000
Repayment = ($5,000)
Interest = $2,700 ($50,000 - $5,000) x 6%
Loan balance = $47,700 ($50,000 - $5,000 + $2,700)
2nd year:
Loan balance = $47,700
Repayment = ($5,000)
Interest = $2,562 ($47,700 - $5,000) x 6%
Loan balance = $45,262 ($47,700 - $5,000 + $2,562)
3rd year:
Loan balance = $45,262
Repayment = ($5,000)
Interest = $2,416 ($45,262 - $5,000) x 6%
Loan balance = $42,678 ($45,262 - $5,000 + $2,416)
Thus, the loan balance after 3 years is $42,678.
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Consider the linear system:
[tex]\overrightarrow y'=\begin{bmatrix}-6 & -4 \\12 & 8\end{bmatrix}\overrightarrow y[/tex]
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
b. For each eigenpair in the previous part, form a solution of [tex]\overrightarrow y' = A\overrightarrow y[/tex]. Use [tex]t[/tex] as the independent variable in your answers.
c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions?
a. If A is the coefficient matrix, solve det(A - λI) = 0 for the eigenvalues λ :
[tex]\det\begin{bmatrix}-6-\lambda & -4 \\ 12 & 8-\lambda\end{bmatrix} = (-6-\lambda)(8-\lambda)+48 = 0 \implies \lambda(\lambda-2)=0[/tex]
[tex]\implies \lambda = 0, \lambda = 2[/tex]
Let v = [v₁, v₂]ᵀ be the eigenvector corresponding to λ. Solve Av = λv for v :
[tex]\lambda=0 \implies \begin{bmatrix}-6&-4\\12&8\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix} = \begin{bmatrix}0\\0\end{bmatrix} \implies 3v_1 + 2v_2 = 0[/tex]
If we pick v₂ = -3, then v₁ = 2, so [2, -3]ᵀ is the eigenvector for λ = 0.
[tex]\lambda = 2 \implies \begin{bmatrix}-8&-4\\12&6\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix} = \begin{bmatrix}0\\0\end{bmatrix} \implies 2v_1 + v_2 = 0[/tex]
Let v₁ = 1, so v₂ = -2.
b. λ = 0 and v = [2, -3]ᵀ contributes a constant solution,
[tex]\vec y_1 = e^{\lambda t} v = \begin{bmatrix}2\\-3\end{bmatrix}[/tex]
while λ = 2 and v = [1, -2]ᵀ contribute a solution of the form
[tex]\vec y_2 = e^{\lambda t} v = e^{2t} \begin{bmatrix}1\\-2\end{bmatrix}[/tex]
c. Yes; compute the Wronskian of the two fundamental solutions:
[tex]W(1, e^{2t}) = \det\begin{bmatrix}1 & e^{2t} \\ 0 & 2e^{2t}\end{bmatrix} = 2e^{2t} \neq 0[/tex]
The Wronskian is non-zero, so the solutions are independent.
The scatter plot below represents the weight of a bunch of
bananas based on the number of bananas in the bunch. A
trend line shows the relationship.
About how many pounds does the trend line predict that a bunch with 9 bananas will weight?
A. 3.0
B 4.0
C 3.5
D 4.5
Answer: B 3.0
Step-by-step explanation:
solve for y :
[tex]\longrightarrow \: \bold{3 + y = 18}[/tex]
ty! ~
Answer:
y = 15
Step-by-step explanation:
Given :
3 + y = 18
This a simple algebraic equation.
Subtract 3 from both sides :
⇒ 3 + y - 3 = 18 - 3
⇒ y = 15
Answer:
y = 15
Step-by-step explanation:
Given equation:
3+y=18To Find:
Value of ySolution:
We can rewrite this equation as:
y+3 = 8[This'll ain't change the answer]
Now we could solve on a easy way.
STEPS:
Transpose +3 to the RHS, make sure to change it's sign from “+” to “-”.
=> y = 18-3
Subtract the integers which's on the RHS:
=> y = 15
Hence,the value of y will be 15.
[tex] \rule{225pt}{2pt}[/tex]
Which quadrilateral is not a parallelogram?
Rhombus
O Rectangle
Kite
Square
Answer:
Kite is not a parallelogram
Step-by-step explanation:
The sides aren't evenly lined up properly to be a parallelogram
ANSWER:
kite
STEP BY STEP EXPLANATION
A kite isnerally not a parallogram because it is a quadrilateral whose four sided can be grouped into two pairs of sideame length that arch other
Andrew's number is 4 less than Sophia's number. The
sum of their numbers is 46. Find the numbers
If an emitter current is changed by 4 mA, the collector current changes by 3.5 mA. The value of beta will be :
change in emitter current, ∆l(E) = 4 mA
change in collector current,∆I(C) = 3.5 mA
To find -:value of B
Solution :-∆I(E) = ∆I(C) + ∆l(B), here ∆l(B) is the change in base current.
4 = 3.5 + ∆l(B)
∆I(B) = 0.5 mA
Now, B = ∆l (C) ÷ ∆l (B)B = 3.5 ÷ 0.5
B = 7.0
so, the value of A = 7.0[tex]\frac{1}{2} (5x - 9 ) = 2 (\frac{1}{3} + 6 )[/tex]
Answer: 103/15
Step-by-step explanation:
We can simplify the right-hand side to be [tex]2 \left(\frac{1}{3}+6 \right)=2 \left(\frac{19}{3} \right)=\frac{38}{3}[/tex].
This means we need to solve:
[tex]\frac{1}{2}(5x-9)=\frac{38}{3}\\5x-9=\frac{76}{3}\\5x=\frac{103}{3}\\x=\boxed{\frac{103}{15}}[/tex]
6 children were jumping rope.
5 children joined them.
2 children left because the line was too long.
How many children were jumping rope then
Answer:
9 children were jumping then.
Step-by-step explanation:
6+5 equals to 11 - 2 of the children left would equal 9 children left.
The sum of the three interior angles of a triangle is 180°. Suppose one angle is 68° and the remaining two angles are the same measure. Reason numerically to find the measures of the remaining angles.
Answer:
56°Step-by-step explanation:
Let ∠A and ∠B and ∠C.
be the three interior angles of the triangle.
∠A + ∠B + ∠C = 180
If ∠A = 68 and ∠B = ∠C .
Then
∠B + ∠C = 180 - 68 = 112
Then
2∠B = 112
Then
∠B = 112 ÷ 2 = 56°
Work out, giving your answer in its simplest form: 3 3/4 × 2 4/5
Answer:
⇒ [tex]\frac{21}{2}[/tex]
or
⇒ [tex]10 \frac{1}{2}[/tex]
Step-by-step explanation:
3 3/4 = 15/4
2 4/5 = 14/5
⇒[tex](\frac{15}{4} *\frac{5}{5} )(\frac{14}{5} *\frac{4}{4} )[/tex]
⇒[tex]\frac{75}{20} *\frac{56}{20}[/tex]
⇒[tex]\frac{4200}{400}[/tex]
⇒ [tex]\frac{21}{2}[/tex]
or
⇒ [tex]10 \frac{1}{2}[/tex]
Find the quartiles for these data values:
5,7,7,8,10,11,12,15,17
A. Q1=7, Q2=11, Q3=15
B. Q1=7, Q2=10, Q3=13.5
C. Q1=6, Q2=9, Q3=12
D. Q1=7.5, Q2=10.5, Q3=13.5
Q1 = 7, Q2 = 10, Q3 = 13.5
=============================================================
Explanation:
Start with {5,7,7,8,10,11,12,15,17}
Notice how this data set is already sorted for us from smallest to largest.
Cross off the first and last items to get {7,7,8,10,11,12,15}
Repeat the last step to get this smaller set {7,8,10,11,12}
Repeat again: {8,10,11}
Repeat one more time: {10}
The 10 is at the very center, so it is the median aka the value of Q2.
-------------
An alternative way to get the median is to follow these steps:
There are n = 9 numbers in the original set before we crossed off any items. The middle number is in slot 5 because n/2 = 9/2 = 4.5 rounds up to 5. The value in the fifth slot is 10, so 10 is the median.
There are 4 items below the median and 4 items above it, giving n = 4+1+4 = 9 items total.
-------------
Next, break the data set into two smaller groups
L = lower set = every value below the median
L = {5, 7, 7, 8}
U = upper set = every value above the median
U = {11, 12, 15, 17}
The median itself is in neither set L nor set U.
The median of set L is (7+7)/2 = 7, so this is the value of Q1
The median of set U is (12+15)/2 = 13.5 which is the value of Q3
-------------
Summary:
Q1 = 7
Q2 = 10 (aka the median of the original set)
Q3 = 13.5
Answer:
B. Q1=7, Q2=10, Q3=13.5
Step-by-step explanation:
First Solution:
The first quartile of the data set is 7.
The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.
5 7 7 8 10 11 12 15 17
So, the bottom half is
5 7 7 8
The median of these numbers is 7.
Second Solution:
The median of the data set is 10.
Quartile 2, also known as the median, is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
5 7 7 8 10 11 12 15 17
So, the median is 10 .
Third Solution:
The third quartile of the data set is 13.5.
The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.
5 7 7 8 10 11 12 15 17
So, the upper half is
11 12 15 17
The median of these numbers is 13.5.
Determinar cuales de las siguientes frases son proposiciones
a) 3+2 = 0 c) ¡Hola!
b) x + 1 = 4 d) Yo estudio
The exercise is designed to test the students knowledge of prepositions. The correct answer thus is (Option D) Yo estudio (which translates) "I study".
What is the explanation for the answer above?To understand the answer, you need to know what a preposition is. A preposition, in simple terms, is a word or group of words that comes before a noun.
The function of a preposition (much like an adjective) is to give clarity to the noun that it precedes.
Let us complete the Preposition phrase to give meaning to it:
"I study Mathematics". Where;
"Mathematics" is the noun;
"I Study" is the prepositional phrase. Hence the correction answer to the question above is Option D.
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with full explanation from the internet like before
1/(x-5)+3/(x+2)=4
Solution :
[tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]
Step-by-step explanation:[tex] \frac{1}{(x - 5)} + \frac{3}{(x - 2)} - 4[/tex]
1. Multiply by LCM[tex]x = 2 + 3( x - 5) = 4 - (x - 5)(x + 2)[/tex]
2. Solve[tex]x = 2 + 3(x - 5) = 4 (x - 5)(x + 2)[/tex][tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]3.Verify SolutionsFind undefined (singularity) points : x=5,x=–2[tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{x-5}+\dfrac{3}{x+2}=4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+2+3x-15}{(x-5)(x+2)}=4[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x-5)(x+2)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x(x+2)-5(x+2))[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x^2+2x-5x-10)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x^2-3x-10)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4x^2-12x-40[/tex]
[tex]\\ \rm\Rrightarrow 4x^2-16x-53=0[/tex]
On solving we get
[tex]\\ \rm\Rrightarrow x=2\pm\dfrac{69}{2}[/tex]
If f(x) = 2x + 3, what is f(–2)?
Substitute -2 for x
[tex]f( - 2) = 2( - 2) + 3 \\ y = - 4 + 3 \\ y = - 1[/tex]
Hope it helps
Please give brainliest
Answer:
-1
Step-by-step explanation:
Hi student! Let me help you out on this question.
_____________________
To find the value of f(-2), we need to stick in -2 for x.
[tex]\mathsf{f(-2)=2\cdot(-2)+3}[/tex]. Multiply first.
[tex]\mathrm{f(-2)=-4+3}[/tex]. Now simplify completely.
[tex]\mathsf{f(-2)=-1}[/tex]. Which is our final answer.
Hope that this helped you out! have a good day ahead.
Best Wishes!
[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
◆◈-Greetings!-◆◈
__________________
a man is carrying load attached at the end of a stick load placed over his shoulder . show that the pressure at his shoulder is directly proportional to the distance between the shoulder and the load?
According to the above information, it can be stated that the pressure on the man's shoulders is directly proportional to the distance between the shoulder and the load, since the greater the distance he will feel the more weight due to instability.
What is a directly proportional relationship?A directly proportional relationship is a term that refers to the relationship between two variables in which if one of the variables increases, the other also increases.
How is the directly proportional relationship demonstrated in the situation presented?According to the information, it can be inferred that the man will feel more weight on his shoulders if the load is more distant because this causes greater instability on his shoulders, so he will have to make a greater effort to move the load.
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Which of the following functions is graphed below?
Answer:
A.
Step-by-step explanation:
the correct answer is A. y=|x-2|+3.
For more details see the attachment.
El número equivalente de 25/50 por favor
Answer:
El número equivalente de 25/50 es 1/2
Step-by-step explanation:
HELP NEEDED ASAP
answer this question for me, image below
Answer: Heyaa! ~
Your Answer Is... 13
Step-by-step explanation:
385 divided by 28 = 13. 75Reduce the expression, if possible, by cancelling the common factors.Hopefully this helps you! ~
a bicycle wheel has a diameter of 65cm what is the length of 1000 revolutions of the wheel in metres
Answer: 2041 meters
A bicycle wheel is a circular object.
The circumference of a circle is 2π(radius)
Here given:
diameter: 65 cmradius = diameter/2 = 65/2 = 32.5 cmHence find the length for each revolution:
2π(32.5) = 204.1 cm per revolutionThen for 1000 revolutions:
204.1 × 1000 = 204100 cm ≈ 2041 meterThe large rectangle shown here is 3cm by 5 cm. What is a direct way to determine the area of the rectangle in square centimeters that relies on the meaning of area?
Answer:
Place the squares on the rectangle.
Step-by-step explanation:
Hello!
The area of the 1cm by 1cm square is 1 square cm.
We can solve for the area by placing multiple of those squares in the larger rectangle.
If we place it, we get 15 placed squares, with a total area of 15 square cm. This relies on the meaning of area, as we are simply measuring the number of square cm taken up by the object.
We would place 3 rows of 5 squares, representing a height of 3 cm (side length of 3 squares), and a length of 5 cm (side length go 4 squares).
This also proves the area formula A = L * W, as we multiple the side lengths to find the number of square units.
The point −20, 21 is on the terminal arm of an angle = in standard position. Find sin = and cos =.
The point −20, 21 is on the terminal arm of an angle = in standard position. Hence, sinФ = 21/29 and cos Ф = -20/29
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
Given Data
A (-20 , 21)
We have to find sin = ? and cos = ?
The point is in the fourth quadrant
We have the Opposite side and the Adjacent side
Calculate the hypotenuse
c² = (-20)² + (21)²
c² = 400 + 441
c² = 841
c = 29
Hence,
sinФ = 21/29
cos Ф = -20/29
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The linear equation y = 25x describes how far from home Gary is as he drives from Montreal to Miami. Let x represent the number of hours and y represent the number of miles. How far from home is Gary in 12 hours? Graph the equation and tell whether it is linear.The linear equation y = 25x describes how far from home Gary is as he drives from Montreal to Miami. Let × represent the number of hours and y represent the number of miles. How far from home is Gary in 12 hours? Graph the equation and tell whether it is linear.
The distance that Greg is from home after 12 hours is given as follows:
300 miles.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is given as follows:
y = 25x.
Hence the distance after 12 hours is given as follows:
y = 25 x 12
y = 300 miles.
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What is the output of this program?
numA = 2
numB = 3
if numA == 2 or numB == 2:
print("yes")
elif numA == 2 and numB == 3:
print("no")
Output:
PLEASE HELP ME PLEASE
Help! I need the explanation if the answer is 72!!!
∠72
Step-by-step explanation:
It is isosceles Triangle.Therefore Two sides will be equal
∠b = ∠c ------ ☆
Given in the question - Angle b is twice the angle a.=> ∠b = 2∠a
=> ∠a = ∠b/2 -------(1)
sum of two sides on isosceles Triangle is 180°=> ∠a + ∠b + ∠c = 180
Put value of ∠a from equation (1)
=> ∠b/2 + ∠b + ∠b =180
[ look equation marked - ☆ ]
with LCM=> 5∠b/2 = 180
=> 5∠b = 180 × 2
=> 5∠b = 360
=> ∠b = 360 / 5
=> 72
_______________Some properties of Triangle-
two sides are equal. two internal angles are equal. two angles are opposite to equal side are equal. sum of two angles 180°_______________Findthe domain of the function f(x) = √19-x
Answer:
(-∞,19)
Definition: The domain of a function is the set of input or argument values for which the function is real and defined
Answer:
(-∞, 19]
Step-by-step explanation:
The domain of this function is only true for all real values of f(x).
That means the lower limit of the function is -∞ as the values are positive, and the upper limit is 19, because that is the greatest value it can become before becoming negative.
The domain is : (-∞, 19]
Solve 24x ⋅ 321-x = 8x+2
Answer:
[tex]x=2/7695[/tex]
≡ Small number, yes, but the steps explain why x is equal to this.
Step-by-step explanation:
simplify
[tex]24x\cdot 321-x=8x+2\\\left(24\cdot 321\right)x-x=8x+2\\7703x=8x+2[/tex]
group
[tex]7703x=8x+2\\7703x-8x=8~x+2-8x\\7695x=8x+2-8x\\7695x=8x-8x+2\\7695x=2[/tex]
isolate
[tex]7695x=2\\\frac{7695x}{7695}=\frac{2}{7695}\\x=\frac{2}{7695}[/tex]
The fraction is in its simplest form, so that is the final answer.
I don’t quite understand this problem could someone help me please
Answer:
[tex]\frac{7\sqrt{65}}{65}[/tex]
Step-by-step explanation:
Cosine is the ratio of the side adjacent to the angle and the right triangle hypotenuse.
[tex]cos[/tex] B = [tex]\frac{7}{\sqrt{65}}[/tex] = [tex]\frac{7\sqrt{65}}{65}[/tex]
please help i dont know
x²-12x+36
A. (x-6)(x+6)
B. (x+9)(x-4)
C. (x+6)(x+6)
D. (x-6)(x-6)
SUBMIT
Answer:
x²-12x+36
x²-6x-6x+36
x(x-6)-6(x-6)
(x-6)(x-6)
=(x-6)²
how to solve for x:
Answer:
x = 2
Step-by-step explanation: