Therefore, if the borrower had paid the loan just at the end of the second year, he would have owed R 167250. The additional interest due would be R 167250 - 150000 = R 17250.
a) To calculate the amount of money that the person would have to pay at the end of the second year to clear his debt, you can use the formula for compound interest:l,
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the person took a loan of R 150000 for 2 years at an annual interest rate of 10%. He paid R 85000 at the end of the first year. So, the new principal at the beginning of the second year is P = 150000 - 85000 = 65000.
So, A = P(1 + r/n)^(nt)
A = 65000(1 + 0.1)^2
A = 65000*1.1^2
A = 73,650
So, the person should have to pay R 73650 at the end of the second year to clear his debt.
b) If the person had paid the loan only at the end of the second year, the interest would have been calculated on the original principal of R 150000 for 2 years. So,
A = P(1 + r/n)^(nt)
A = 150000(1 + 0.1)^2
A = 150000*1.1^2
A = 167250
So, the person would have had to pay R 167250 if he had paid the loan only at the end of the second year. Therefore, he would have to pay more interest of R 167250 - 150000 = R 17250.
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How do you find the measure of an angle in a triangle?.
There are several ways to find the measure of an angle in a triangle, depending on the information given about the triangle and the angles. Some common methods include:
Using the angles in a triangle sum to 180 degrees: If you know the measures of two angles in a triangle, you can use the fact that the angles in a triangle sum to 180 degrees to find the measure of the third angle.
Using the Pythagorean theorem: If you have a right triangle, you can use the Pythagorean theorem to find the measure of the right angle (90 degrees)
Using the Law of Cosines: If you know the measures of two angles and the lengths of all three sides of a triangle, you can use the law of cosines to find the measure of the third angle.
Using trigonometry: If you know the lengths of two sides of a triangle and the measure of one angle, you can use trigonometry to find the measure of the other angles.
It is important to note that in order to find the measure of an angle you need to know at least one angle and the values of the sides of the triangle or two angles.
What are the 3 arguments for the range function?.
A function argument is a value supplied to achieve the Range function's outcome. This is often alluded to as a latent variable.
This is an optional argument that determines the sequence's point of reference. The default assumption is 0.
A mathematical function includes one or much more arguments in the form of the independent variables that are specified in the definition and can also include parameters.
This is a necessary argument that determines the sequence's final chapter location.
This is an optional argument that specifies the adjustment between both sequence members. The default mode is 1.
A domain of the sum of two or multivalued argument values is considered to be the domain of a function with two or more variables.
A cyclical function's argument is angular. A hyperbolic perspective is the input of a hyper equation.
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What is the solution of the equations 8x +3y 5 and 3x 2y 5?.
The solution of the given linear equations is (x,y) = (1,-1).
The given linear equations are
8x + 3y = 5 - - - ( 1 )
3x - 2y = 5 - - - ( 2 )
As the RHS of both equations is equal, equating the LHS of both equations, we get,
8x + 3y = 3x - 2y
⇒ 8x - 3x = - 2y - 3y
⇒ 5x = - 5y
⇒ x = - 5y ÷ 5
⇒ x = - y
By substituting x = - y in equation ( 1 ), we get,
8x + 3y = 5 - - - ( 1 )
⇒ 8 ( - y ) + 3y = 5
⇒ - 8y + 3y = 5
⇒ - 5y = 5
⇒ y = - 5 ÷ 5
⇒ y = - 1
Now,
x = - y
⇒ x = - ( - 1 )
⇒ x = 1
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Question 6 of 25
f(x) = 5x + 3. Find the inverse of f(x).
O A. f-¹(x)=3-5x
OB. f-¹(x) = x-5/3
OC. f-¹(x) = 5x - 3
OD. f-¹ (x) = x-3/5
It is option D (f-¹ (x) = x-3/5
A political adviser stood at the corner of 1st Avenue and Main Street and asked every 10th person who walked past if they intended to vote in the next election. Identify the sampling method used.
Where is the vertex of the parabola y X² 2x 3?.
The vertex of the equation y = x² + 2x -3 is (-1, -4).
The term vertex in math is known as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.
Here we have the expression y = x² + 2x -3
As we all know that the given equation of parabola is written as,
=> y = ax² + bx + c
As we all know that the vertex of the parabola is given by (h, k).
Here we have calculated the value of the x coordinate of vertex as ,
=> h = -b/2a
And the value of y coordinate of vertex k by using the formula,
=> k = y(h)
Through the given equation we have identified the value of a = 1, b = 2 and c = -3
Then the value of x coordinate is calculated as,
=> h = -2/(2 × 1)
Therefore, the value of h is -1
Then the value of y coordinate is calculated as,
=> k = y (-1)
Here we have to substitute -1 in the equation, then we get
=> k = (-1)2 + 2(-1) - 3
=> k = 1 - 5 = -4
Hence the coordinate of the vertex is (-1, -4).
Complete Question:
Where is the vertex of the parabola of the equation y = x² + 2x -3?
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Find AC
A. 36
B. 60
C. 48
D. 12
Answer:
48
Step-by-step explanation:
AB+CB=AC which is 18+30 which is 48
Answer:
C. 48
Step-by-step explanation:
This distance of AC is the same as the distance between BC plus the distance between AB. In other words: AB + BC = AC
AB = 18
BC = 30
30 + 18 = AC
AC = 48
What number would you multiply the second equation by in order to eliminate the x term when adding to the first equation?.
For the given system of equations 4x – 9y = 7 , –2x + 3y = 4 answer of the following question are:
a. To eliminate x-terms we need to multiply 2 to the second equation and add it to the first equation.
b. To eliminate y-terms we need to multiply 3 to the second equation and add it to the first equation.
As given in the question,
For the given system of equation,
4x – 9y = 7 ___(1)
–2x + 3y = 4 ___(2)
a. To eliminate x-terms multiply by 2 to the (2) equation and add it to (1)
4x – 9y = 7
–4x + 6y = 8
-3y = 15
⇒ y = -5
b. To eliminate y-terms multiply by 3 to the (2) equation and add it to (1):
4x – 9y = 7
–6x + 9y = 12
-2x = 19
⇒x = -19/2
Therefore, for the given system of equations 4x – 9y = 7 , –2x + 3y = 4 :
a. To eliminate x-terms we need to multiply 2 to the second equation and add it to the first equation.
b. To eliminate y-terms we need to multiply 3 to the second equation and add it to the first equation.
The above question is incomplete , the complete question is:
Use this system of equations to answer the questions that follow.
4x – 9y = 7 , –2x + 3y = 4
a. What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?
b. What number would you multiply the second equation by in order to eliminate the y-terms when adding to the first equation?
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Solve 4.8=2.4 plsssss help
[tex]\huge\text{Hey there!}[/tex]
[tex]\frak{\text{A}ssuming. . .}[/tex]
[tex]\mathsf{4.8x = 2.4}[/tex]
[tex]\frak{\mathsf{DIVIDE}\ 4.8\ to\ both\ sides}[/tex]
[tex]\mathsf{\dfrac{4.8x}{4.8} = \dfrac{2.4}{4.8}}[/tex]
[tex]\frak{\mathsf{Simplify} \ it}[/tex]
[tex]\mathsf{x = \dfrac{2.4}{4.8}}[/tex]
[tex]\mathsf{x = 0.5}[/tex]
[tex]\huge\boxed{\frak{T}}\huge\textsf{herefore your answer should be:}}[/tex]
[tex]\huge\boxed{\mathsf{x = 0.5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
How do you solve linear and nonlinear systems?.
To see the steps of linear and non linear system of equation.
Now, According to the question:
Steps to solve non linear equation are:
Identify the graph of each equation. Sketch the possible options for intersection.Graph the first equation.Graph the second equation on the same rectangular coordinate system.Determine whether the graphs intersect.Identify the points of intersection.Check that each ordered pair is a solution to both original equations.To solve a system of linear equations using substitution:
Isolate one of the two variables in one of the equations.Substitute the expression that is equal to the isolated variable from Step 1 into the other equation. This should result in a linear equation with only one variable.Solve the linear equation for the remaining variable.Use the solution of Step 3 to calculate the value of the other variable in the system by using one of the original equations.Learn more about Linear and non linear Equation at:
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Last week, Russell bought 11 books and 12 movies for a total of
$245. Today, Russell bought 10 books and 26 movies for a total of $434. Assuming neither item has changed in price, what is the cost of a book in dollars?
The cost of a book bought by Russell is found in in dollars is $7.
What is meant by the term equation?The description of an equation in algebra is a statistical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.For the stated question-
Let the price of the each book be 'x'.
Let the price of movie be 'y'.
Then,
11x + 12y = 245 ...eq 1
10x + 26y = 434 ...eq 2
Solving both eq 1 and 2 using calculator.
x = 7 and y = 14
Thus, the cost of a book bought by Russell is found in in dollars is $7.
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Can someone please help me with this math problem? I can't use letters, the square box where I type doesn't allow it. Only numbers and infinity symbols, etc...
The math problem is in the picture, Thanks!
Answer:
Step-by-step explanation:
-4,+ infinity symbol which I can’t find
Find the angle e between vectors u and v to the nearest tenth of a degree
u = <5, 2> and v = <4, -3>
The angle e between vectors u and v to the nearest tenth of a degree is
≈ 3.14°.
What is an angle?An angle in plane geometry is a shape created by two rays or lines that have a shared termination. The name "angle" originates from the Latin word "angulus," which means "corner. "The common terminus of two rays is known as the vertex, and the two rays are known as sides of an angle.
According to the given information:When u and v's two vectors are at an angle, if, then cosθ = (u·v) / [llull llvll]
u·v = (5)(4) + (2)(-3)
= 20 - 6
= 14
llull = √[(5)2 + (2)2]
= √29
llvll = √[(4)2+(-3)2]
= √25
So, cosθ = 14 / [√725]
= 0.51
θ = cosθ-(0.51) ≈ 3.14°
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please i need help. what is the answer???
ok
0 is the smallest value or X is the smallest value
How do you plot a point?.
An x-y (or bivariate) plot is any graph or plot with two axes. The "x-axis" is typically the horizontal axis, whereas the "y-axis" is typically the vertical axis.
Your plot's axes should be identified, and the scale should be chosen (if the graph is not already labeled). Plot the first two pairs of numbers first (the top row of numbers).
Finding the number a on the horizontal, or x-, axis and tracing up or down from there while maintaining a parallel path to the vertical, or y-, axis, will allow you to draw the point at (a, b) on the Cartesian plane.
The position of the point is this area (a, b). The intersection of the two axes defines the plane's center. It is referred to as the beginning or point (0,0).
Each axis is further subdivided into equal units starting at the origin: rising, positive numbers on the x-axis and up the y-axis; falling, negative numbers on the x-axis and down the y-axis.
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What is linear inequality in two variables and linear equation in two variables?.
A linear inequality in two variables is an inequality that can be written in the form "ax + by < c" or "ax + by > c" or "ax + by = c", where a, b, and c are constants and x and y are variables. This inequality represents a boundary line and all the solutions of the inequality make up a region of the xy-plane.
For example, the inequality "2x + 3y < 6" represents the region of the xy-plane that is on one side of line 2x + 3y = 6. To graph this inequality, one can find the boundary line by setting the inequality equal to zero and then shading in the region that satisfies the inequality.
A linear equation in two variables is an equation that can be written in the form "ax + by = c", where a, b, and c are constants and x and y are variables. This equation represents a straight line in the xy-plane and all the solutions of the equation are the coordinates of the points on that line.
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the number of nickels exceeds the number of dimes by 7. the total value of the coins is $1.55. How many coins of each type are there?
Answer:
15 nickels and 8 dimes
Step-by-step explanation:
Let N = number of nickels and D = number of dimes
N - D = 7 (the number of nickels exceeds the number of dimes by 7.)
or
N = D + 7
Total value of N nickels = 5N
Total value of D nickels = 10D
Combined total value => 5N + 10D = 155
Substitute for N in terms of D
==> 5(D + 7) + 10D = 155
5D + 35 + 10D = 155
15D + 35 = 155
15D = 155 - 35
15D = 120
D = 120/15
D = 8
N = D + 7 = 8 + 7 = 15
15 nickels and 8 dimes
If Jenna Owen 15% of the stock in a business that has 50,000 shares, how many shares does she own?
Answer:
7500
Step-by-step explanation:
15/100×50000
750000/100
=7500
Cindy is 6 years older than half her
mother's age. Cindy's mom is 70 years old.
How old is Cindy?
Answer:
cindy is 51
Step-by-step explanation:
70 divided by 2 is 45
45+ 6 is 51
Tiana hare a granola bar with her brother. They each get one piece of the bar. What fraction name one part?
A fraction share that Tiana share with her brother called half part. This because the part is split into two where the first part is called first half and other called as second half.
How to name a piece that split into several part?To name a piece of an object that split into several you have to:
Determine how many part that the object splitDetermine the name the total part that created such as half for two, one third for three, quarter for four, etc. The name always following by the order of the split like the first part of quarter part called the first quarter.Learn more about fraction of a set here
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How do you find the domain and range of a square root of a quadratic function?.
Domain and range of a square root of a quadratic function is as [ 0, ∞ ) , and [ 0 ,∞ ) respectively which is find by simplification.
Let us consider a square root quadratic function y = √x.
Domain of a square root quadratic function is :
All input values of x are domain of a function.
y = √x
⇒ x = y²
⇒ x ≥ 0
All the input values representing the domain are x > 0.
This implies domain is [0 , ∞ ).
And range of a square root quadratic function is:
All output values of y are range of a function.
y = √x
As we know x = y²
√y² = y > 0 .
Range is [ 0, ∞ ).
Therefore, domain and range of square root of a quadratic function is calculated by simplifying the function.
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Write the expanded form of the expression. y(3.05x−3.75)−2.25y
Answer:
3.05yx - 6y
Step-by-step explanation:
y(3.05x−3.75)−2.25y
3.05yx -3.75y - 2.25y
3.05yx - 6y
Margo can purchase tile at a store for $0.59 per tile and rent a tile saw for $18. At another store she can borrow the tile saw for free if she buys tiles there for $1.19 per tile. How many tiles must she buy for the cost to be the same at both stores?
Answer:
30 tiles
Step-by-step explanation:
We know
First store
$0.59 per tile
Rent a tile saw for $18
Second store
1 tile = $1.19
We have the equation
0.59x + 18 = 1.19x
18 = 0.6x
x = 30 tiles
So, she must buy 30 tiles for the same cost at both stores.
Answer:
Margo must purchase 30 tiles for the cost to be the same at both stores.
Step-by-step explanation:
By analyzing the "real-world" problem, we can convert the words into two algebraic equations.
Step 1:Store 1:
"$0.59 per tile and rent a tile saw for $18."
y = 0.59x + 18
y = the price of the tiles bought
0.59 = price of one tile
x = number of tiles
18 = the fixed cost of a saw
Store 2:
"At another store, she can borrow the tile saw for free if she buys tiles there for $1.19 per tile."
In this case, the saw is free. Thus, we don't need to add a price to the equation.
y = 1.19x
y = the price of the tiles bought
1.19 = price of one tile
x = number of tiles
Step 2:Now that we have both equations, we can write down the equations that equate other. This formula will indicate that the equations would intersect at a certain point on the x and y values. Hence, this step will answer how many tiles are required for both stores to equal the same price.
[tex]0.59x+18=1.19x[/tex]
Now solve for x:
[tex]0.59x-0.59x+18=1.19x-0.59x\\\\18=0.6x\\\\\frac{18}{0.6} =\frac{0.6x}{0.6}\\\\30=x[/tex]
Margo can buy 30 tiles from both stores for the cost to be equal.
You might ask, "But what about the price?" This is where we solve for y; this variable will answer how much the tiles would cost at 30 tiles. So, we can take the answer for "x" and plug it into any of the two equations.
[tex]y=1.19x\\y=1.19(30)[/tex]
For this equation, all you have to do is multiply both numbers to get your answer.
[tex]y=35.7[/tex]
Bottom Line:Therefore, Margo can buy 30 tiles for the cost to be same at both stores at $35.70.
Please help me i am struggling only do the left side
Answer:
1. Y = -1/4x + 1
3. Y = 2/5x + 1
5. Y = 4/5x + 5
7. Y = -x + 5
9. Y = -5/2x - 16
Step-by-step explanation:
Find the slope using the formula
Use the slope and one of the points to find the y-intercept
Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
9+15/5x3 using pemdas
Answer:18
Step-by-step explanation: Using the order of operations (PEMDAS), you would first perform any calculations inside of parentheses, then exponents, then multiplication and division from left to right, and finally, addition and subtraction from left to right.
9 + 15 / 5 x 3
= 9 + 3 x 3
= 9 + 9
= 18
So the answer would be 18.
Which of the following is the quotient of the rational expressions shown below?
The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)
Which is rational expressions?The quotient of the rational expressions is
4(x+2) / 5(x-1) (x-1)
The quotient of the rational expressions shown below
Explanation in detail:
Two expressions are shown here.
Expression 1 : 2x/x-1
Expression II for 5x/2x+4.
The product of expressions I and II must be calculated.
(2x / x-1 ) ÷ (5x / 2x+4)
applying the upcoming regulation
a ÷ b = a× 1/b
(2x/x-1)×( 2x+4 / 5x)
(2x) (2x+4) / (x-1)(5x) (5x)
(2) (2) (x+2) / (x-1)(5) (5)
The solution to the previous question is 4(x+2) / 5(x-1).
The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)
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Write the prime factorization of 21. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
The prime factorization of the number 21 is:
21 = 3*7
How to write the prime factorization?We want to write the prime factorization of 21.
To do so, we just need to divide the number by prime numbers.
The first prime number we can try is 2, if we divide by 2 we get:
21/2 = 10.5
This is not an integer, so 2 is not a factor.
The next one is 3:
21/3 = 7
Now we can rewrite:
21 = 3*7
Where 3 and 7 are prime numbers, so that is the prime factorization.
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For a ride on a rental scooter, Boris paid a $8 fee to start the scooter plus $6 cents per minute of the ride. The total bill for Boris's ride was $19.58 . For how many minutes did Boris ride the scooter?
Answer:
193 minutes
Step-by-step explanation:
We know
Boris paid an $8 fee to start the scooter plus 6 cents per minute of the ride.
Let y represent the total cost and x represent the number of minutes we have the equation
y = 0.06x + 8
Now, put $19.58 in for y and solve
19.58 = 0.06x + 8
11.58 = 0.06x
x = 193 minutes
So, Boris rides the scooter for 193 minutes.
How do you find the mean and standard deviation of a discrete distribution?.
The mean and standard deviation of a discrete distribution can be found by calculating the sum of all the values in the distribution multiplied by their respective probabilities and then dividing the result by the total probability.
To calculate the standard deviation, the sum of the squares of the differences between the values and the mean has to be multiplied by the corresponding probabilities and divided by the total probability.
The square root of this outcome is then the standard deviation. The standard deviation is a measurement of the spread or dispersion of the data, whereas the mean of a discrete distribution is a measure of the central tendency of the data.
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What is the range is called?.
The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.
For e.g. the range of the function F is {1983, 1987, 1992, 1996}.
On the other hand, the whole set B is known as the codomain of the function.
It is the set that contains all the outputs of the function.
So, the set of real numbers is a codomain for every real-valued function. The codomain of the function F is set B.
How to Find the Range of a Function
Consider a function y = f(x).
The spread of all the y values from minimum to maximum is the range of the function.
In the given expression of y, substitute all the values of x to check whether it is positive, negative or equal to other values.
Find the minimum and maximum values for y.
Then draw a graph for the same.
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