Answers
The numeric value for the logarithmic expressions is given as follows:
1. [tex]\log_{6}{\left(\frac{5}{8}\right)} = -0.263[/tex]
2. [tex]\log_6{40} = 2.059[/tex]
3. [tex]\log_6{64} = 2[/tex]
4. [tex]\log_6{125} = 2.694[/tex]
a. [tex]\log_{5}{\left(\frac{11}{30}\right)} = -0.623[/tex]
b. [tex]\log_5{330} = 3.603[/tex]
c. [tex]\log_5{121} = 2.98[/tex]
How to obtain the numeric value for the logarithmic expressions?For the first expression, we have that the logarithm of the quotient is the subtraction of the logarithms, hence:
[tex]\log_{6}{\left(\frac{5}{8}\right)} = \log_6{5} - \log_6{8} = 0.898 - 1.161 = -0.263[/tex]
The same rule is applied for item a, hence:
[tex]\log_{5}{\left(\frac{11}{30}\right)} = \log_5{11} - \log_5{30} = 1.49 - 2.113 = -0.623[/tex]
For the second expression, we apply the logarithm of the product, which is the sum of the logarithms, hence:
[tex]\log_6{40} = \log_6{5 \times 8} = \log_6{5} + \log_6{8} = 0.898 + 1.161 = 2.059[/tex]
For item b, we have that:
[tex]\log_5{330} = \log_5{11 \times 30} = \log_5{11} + \log_5{30} = 1.49 + 2.113 = 3.603[/tex]
For the third expression, we have that the exponent is equals to the base, hence we just take the lower term, as follows:
[tex]\log_6{64} = \log_6{2^6} = 2[/tex]
For the fourth term, we have the rule for the logarithm of an exponent, hence:
[tex]\log_6{125} = \log_6{5^3} = 3\log_6{5} = 3 \times 0.898 = 2.694[/tex]
The same rule is applied for item c, as follows:
[tex]\log_5{121} = \log_5{11^2} = 2\log_5{11} = 2 \times 1.49 = 2.98[/tex]
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Related Questions
HELP PLEASE
Solve the right triangle if the hypotenuse is 5 and one acute angle is 34°. Round answers to two decimal places.
Answers
Given that the hypotenuse of the right triangle is as given then;
i. α = 56^o
ii. Adjacent = 2.80
iii. Opposite = 4.15
Properties of a right angled triangle.A right triangle is a type of triangle which has only one of its internal angles equal to 90^o. Thus the hypotenuse is opposite to the greatest angle, while the second long side is opposite to the greater angle, and the shortest side opposite to the measure of the least angle.
Applying the Pythagorean theorem to the triangle, we have;
i. The sum of angles in a triangle is 180^o. So that;
α + 34 + 90 = 180
α + 124 = 180
α = 56^o
ii. Let the length of the opposite side be represented by y;
Sin θ = opposite/ hypotenuse
Sin 34 = y/ 5
y = 5 * Sin 34
= 2.796
The length of its opposite side is 2.80.
iii. Let the length of the adjacent side be represented by x;
Cos θ = adjacent/ hypotenuse
Cos 34 = x/ hypotenuse
= x/ 5
x = 5 * Cos 34
= 4.145
The length of its adjacent side is 4.15.
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Given: m∥n , m∠1=65∘ , m∠2=60∘ , and BD−→− bisects ∠ABC . Prove: m∠6=70∘ Line m parallel to line n. Line t passing through both lines. There are four angles formed by lines m and t intersecting at point B. The lower left angle is labeled 5. The upper right angle is angle A B C with point A on line t and point C on line m. Angle A B C is separated by ray B D. The angle on the right side of the ray is labeled 4. The angle on the left side is labeled 3. A segment joins points A and D forming a triangle with angle 3 as one of its interior angles. The other two interior angles are labeled 1 and 2. There are four angles formed by lines n and t intersecting. The upper left angle is labeled 6. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. It is given that m∥n , m∠1=65∘ , m∠2=60∘ , and BD−→− bisects ∠ABC . Because of the triangle sum theorem, m∠3=55∘ . By the Response area, ∠3≅∠4 , so m∠4=55∘ . Using the Response area, m∠ABC=110∘ . m∠5=110∘ because vertical angles are congruent. Because of the Response area, m∠5+m∠6=180∘ . Substituting gives 110∘+m∠6=180∘ . So, by the Response area, m∠6=70∘ .
Answers
The answers are as follows:
1 Angle Bisector Theorem
2 Sum of Adjacent Angles
3 Co-interior angle property
4 Additive law
What is parallel line?Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
Note: Diagram for Question is attached
1. Angle Bisector Theorem
The angle bisector is BD. Bisection entails splitting into two equal pieces. Angles 3 and 4 are therefore equal.
2. Sum of Adjacent Angles
To determine the greater angle that is created by the two adjacent angles, add the two angles together.
3. Co-interior angle property
According to the co-interior property, the sum of interior angles (on the same side) formed when a single line crosses two parallel lines is equal to 180.
4. Additive law
By applying the additive law, we can take a value away from both sides of the equation without throwing the equation out of balance. Therefore, we may take 110 out of both sides of the equation to get the final result of 70.
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Need help on this one
Answers
If I remember correctly. You multiply the coefficients and add the exponents.
Therefore getting you 8x^5y^7
Does 5 7 11 make triangles?
Answers
It is possible to construct a triangle whose sides are 5 cm 7 cm and 11 cm because the sum of two sides are greater than three sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 5 cm 7 cm and 11 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 5 and 7
5 + 7 > 11
12 > 11
Now we add 7 and 11
7 + 11 > 5
18 > 5
Now we add 5 and 11
5 + 11 > 7
16 > 7
It is possible to construct a triangle whose sides are 5 cm 6 cm and 11cm because the sum of two sides are greater than third sides.
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Please help me with this problem
Answers
The variable for the number of wraps and the number of gift bags are x and y.
What are linear and non-linear functions?A linear function can be used to depict a straight line on the coordinate plane. The equation y = 3x - 2 serves as an illustration of a linear function since it represents a straight line in the coordinate plane.
Nonlinear functions are those whose graphs do not follow a straight line. A graph of it can be any curve other than a straight line.
A quadratic function is an illustration of a non-linear function.
Let, The number of wraps be 'x' and the number of gift bags be 'y'.
Therefore, From the given information x + y = 25 and 6x + 2y = 110.
Solving this linear system graphically we have an intersection (x, y)
at (15, 10).
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15.
Marco is making blueberry muffins. The ratio between flour and blueberries for the recipe being used is shown in the table below.
Cups of Cups of
Flour Blueberries
1-2
24
A.Ocup
2
8
How many cups of blueberries will Marco need if he has 2 cups of flour to use?
B.
cup
D
1
2
3
4
1
c. 11 cups
6 cups
Answers
Therefore , the magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.
What is a ratio?An ordered combination of numbers “ a ” and “ b that is stated as just a / b, where b not greater than zero, is referred to as a ratio. A ratio is the result of equating two ratios. If there were one boy and three girls, the ratio could be shown as 1:3. 1/4 are boys, and 3/4 are girls. A part is a number, a proportion of size, or a difference among two or more things.
Here,
Since: Marco To avoid your batter and bakery items acquiring a purple-blue tinge, wash freeze blueberries multiple times in water it until water becomes lighter in color.
The magic muffin ratio is 2:2:1:1, which equals 1-two cups and 2,8 cups.
With a paper towel, dry them off, and then delicately fold it into the batter. Maintaining the lightness of rapid breads is the aim of this process.
The magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.
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Which of the diagrams A-D shows the locus of points inside the rectangle PQRS that are 5 m away from the edge QR? A с S P₁ S 5m 5m E 1Q R 7Q R B P S P₁ S 5m 5m 1Q R 1Q R
Answers
The correct answer is B.
What are the 5 steps to solving inequalities?
Answers
The five steps to solving inequalities are:
Isolate the inequality symbol by using inverse operations. Simplify the inequality by combining like terms on either side of the inequality. Graph the inequality on a number line. Make a sign analysis of the inequality by determining the sign of the expression on either side of the inequality. Find the solution set of the inequality by identifying the values that make the inequality true.To solve an inequality, one must isolate the inequality symbol, simplify the inequality, graph the inequality on a number line, make a sign analysis of the inequality, and find the solution set of the inequality.
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The division property of equality could be used to solve which of the following equations?
X/4= 16
(x+2)(x-2) = 0
5 x=30
x+3=7
Answers
Please help with this
Answers
Consequently, x = 1, 2, 3, 4, 5, 6,..., and no matter what x number we enter, 7 + x is always more than 2x.
what is expressions ?A statement that contains at least two numbers or variables, along with at least one mathematical operation, is referred to as a mathematical expression. Any one of the following mathematical operations could be used: addition, subtraction, multiplication, or division. The following are an expression's fundamental parts: : (Number/Variable, Math Operator, Number/Variable). A statement that includes at least two numbers or variables, at least one mathematical operation, and the word "expression" is referred to as a mathematical expression. Let's review expressive writing. The alternative number, which is known as x, is 6 more than half of the given number. This sentence is denoted by the phrase x/2 + 6 in mathematics.
given
substituting the value of x
7+x > 2x
so x = 1
x = 2
x = 3
x= 4
x= 5
Consequently, x = 1, 2, 3, 4, 5, 6,..., and no matter what x number we enter, 7 + x is always more than 2x.
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What are the two types of longitude?
Answers
The two types of longitude are the Prime Meridian and the International Date Line.
The Prime Meridian is the imaginary line of 0° longitude that divides the earth into the Eastern and Western hemispheres. It passes through Greenwich, England and is the reference point for all other longitudes on the Earth’s surface.
The International Date Line is an imaginary line located on the opposite side of the Earth from the Prime Meridian at 180° longitude. It is the reference point from which we measure the date change when traveling from one side of the world to the other.
The calculation for longitude is fairly simple. Longitude is measured in degrees, with a full circle being 360°. Each degree can be divided into 60 minutes and each minute into 60 seconds. To calculate the longitude, the degree and minutes are added together and converted into decimal form. For example, if a point has a longitude of 15° 22’ 30”, the calculation would be 15 + (22/60) + (30/3600) = 15.375°.
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30 points for this simple question
How many prime numbers are there between 1 - 2020??
Answers
Answer:
How many prime numbers are there in 2020?
There are 12 factors of 2020, of which the following are its prime factors 2, 5, and 101. The Prime Factorization of 2020 is 2^2 × 5^1 × 101^1.
...
Sum of Factors of 2020: 4284.
Step-by-step explanation:
5. Waimarama goe on a flight from Bueno Aire to Auckland and mie all
24 hour of her birthday. How could thi happen? Decribe a flight where
that would happen
Answers
According to the concept of time difference, the resulting situation is explained below.
The term time difference refers the difference between one measurement of time and another; the length of a time interval and the difference in clock time between two or more different time zones.
Here we have given that Waimarama goes on a flight from Buenos Aires to Auckland and misses all 24 hours of her birthday.
Here we want to know that we need to consider that the cities are in different time zones is Buenos Aires is 16 hours behind of Auckland.
Here we also know that Airlines require travelers to check in 2 or three hours before the flight. Check with the Airlines for their regulations. Accordingly ensure you reach the Airport at least 2 or 3 hours before the scheduled departure of the Aeroplan.
Through the given details, we have identified that following values,
Aeroplan Travelling time = 16
Check in time = 3
Departure time = 3
Home town travel time = 2
when we sum up all these we can get the total time as,
=> 16 + 3 + 3 + 2
=> 24 hours.
Based on these we have concluded that she misses her whole birthday for travelling.
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can you please help me i really need it
Answers
Maximum number of bracelets Tara can make is 6.
What is Number line?
Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
Given that;
Tara has a plastic string that is 3 3/4 feet.
And, She will cut the string to make bracelets that are each 5/8 feet long.
Now,
To find maximum number of bracelets Tara can make, we can draw the point at equal distance 5/8 feet to reach 15/4 feet.
Then, Calculate the number of points to draw which is equal to the maximum number of bracelets Tara can make.
That is,
Maximum number of bracelets Tara can make = 15/4 ÷ 5/8
= 15/4 × 8/5
= 6
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10. Last year students were offered pictures for purchase as a basic package plus sheets of portraits.
The table below shows the relationship between p, the number of sheets of portraits purchased, and c,
the total cost of all the pictures ordered.
Number of Portrait
Sheets, p
1
3
6
8
Total Cost ($), C
33
49
73
89
11.3=33
10
+23
This year the price of the basic package increased by $3. What is the new cost of 4 sheets of portraits?
Answers
On solving the provided question, we can say that by addition new total cost = 36 52 76 92
what is addition?The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.
here,
Number of portrait sheet = 1 3 6 8
Total cost = 33 49 73 89
A, This year the price of the basic package increased by $3.
so new total cost = 36 52 76 92
here,
we use addition
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How do you find the exterior angle of a triangle Class 7?
Answers
A triangle's exterior angle is the product of its interior opposing angles.
Exterior angles are those that run parallel to a polygon's exterior angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle.
At each vertex, there are two equivalent exterior angles.
Each vertex often only shows one external angle, though.
A triangle's exterior angles have these three essential qualities:
(1) A triangle's corresponding and exterior angles pair together to form a linear pair of angles. The inner and exterior angles therefore total up to 180 degrees.
(2) The size of a triangle's external angle is equal to the sum of its two diametrically opposed internal angles. The exterior angle theorem is another name for this property.
(3) A triangle's outside angles add up to a total of 360.
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Can you insert a formula in a table?
Answers
In a table cell, enter a formula. Choose the table cell in which you wish the result to appear.
what is sequence ?A sequence is a list of objects that is in order in mathematics (or events). Similar to a set, it has members (also called elements, or terms). You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences. A set of numbers connected by a rule is referred to as a number sequence. You can determine the following numbers in the sequence if you figure out the rule. Therefore, adding 6 each time is the rule for this sequence.
given
In a table cell, enter a formula. Choose the table cell in which you wish the result to appear.
Delete the contents of the cell if it is not empty. Click Formula under the Data group on the Layout tab of the Table Tools.
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What are the first five multiples 8?
Answers
Answer:
Step-by-step explanation:
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80… and so on.
What are exponent examples?
Answers
Answer:
An exponent refers to how many times a number is multiplied by itself.
Step-by-step explanation:
For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
100 points
solve each system by graphing
y=5/4x + 1
y=1/4x-3
Answers
slope: 5/4
y-intercept: (0, 1)
x - 0, 4
y - 1, 6
y=1/4x-3
slope: 1/4
y-intercept: (0, -3)
x - 0, 4
y - -3, -2
Answer:
(- 4, - 4)------------------------
Given system:
y = 5/4x + 1y = 1/4x - 3Plot each line and find the intersection, this is the solution.
The solution is (-4, - 4) as per attached graph.
A factory makes 718 toy trains in one day. The toy trains are placed in boxes of 30
Answers
Answer:
23.9
Step-by-step explanation:
Determine the equation of a straight line passing through (-1,3) and parallel to the line whose equation is 3x-5y=10.
Answers
Answer:
3x - 5y = - 18
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x - 5y = 10 ( subtract 3x from both sides )
- 5y = - 3x + 10 ( divide through by - 5 )
y = [tex]\frac{3}{5}[/tex] x - 2 ← in slope- intercept form
with slope m = [tex]\frac{3}{5}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{3}{5}[/tex] x + c ← is the partial equation of the parallel line
to find c substitute (- 1, 3 ) into the partial equation
3 = - [tex]\frac{3}{5}[/tex] + c ⇒ c = 3 + [tex]\frac{3}{5}[/tex] = [tex]\frac{18}{5}[/tex]
y = [tex]\frac{3}{5}[/tex] x + [tex]\frac{18}{5}[/tex] ← equation of parallel line in slope- intercept form
multiply through by 5 to clear the fractions
5y = 3x + 18 ( subtract 5y from both sides )
0 = 3x - 5y + 18 ( subtract 18 from both sides )
- 18 = 3x - 5y , that is
3x - 5y = - 18 ← in standard form
Evaluate the expression when a=−15
and b=−5
a/b
Answers
Answer: 3
Step-by-step explanation:
what is the value of this equation
[tex](15 ^{ \frac{1}{5} } ) {}^{5} [/tex]
Answers
The value of the given equation with a fractional index is 15.
What are fractional indices?
We can determine how many times a term has been multiplied by itself using an index, which is a small number. Powers of a term that are fractions are known as fractional indices.
The fractional power's two components both have significance. The number's or letter's root serves as the fraction's denominator. The power to raise the answer is contained in the fraction's numerator.
For example,
A value raised to the power of ½ means we have to find the square root.
A value raised to the power of ⅓ means we have to find the cube root
Some of the rules of fractional indices are
[tex]a^{1/m} * a^{1/n} = a^{1/m + 1/n} \\\a^{1/m} / a^{1/n} = a^{1/m - 1/n} \\\a^{1/m} * b^{1/m} =( ab)^{1/m}\\\a^{1/m} / b^{1/m} =( a/b)^{1/m}[/tex]
[tex](a^\frac{1}{m}) ^\frac{1}{n} = a^\frac{1}{mn}[/tex]
For the given question,
[tex](15^\frac{1}{5} )^5[/tex] = [tex]15^\frac{5}{5} =15^1 =15[/tex]
Therefore the value of the given equation with a fractional index is 15.
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How many pairs in a set?
Answers
If the Set A is denoted by the set of elements {1,2,3} , then the number of ordered pairs that it can have is 9 .
The Ordered Pair is defined as a pair formed by two elements which are separated by comma and written inside the parentheses .
For Example : the (x,y) represents a ordered pair .
The Ordered Pairs can be obtained by developing a function or by performing the operation which is called as Cartesian product.
The set A is given as : {1,2,3} ;
the ordered pair can be written as : [tex](1,1) , (2,2), (3,3) , (1,2) , (1,3) , (2,1) , (2,3) , (3,1) , (3,2) .[/tex]
Therefore , The number of ordered pairs formed of Set A are 9 .
The given question is incomplete , the complete question is
How many ordered pairs can be formed from the set A = {1,2,3} ?
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Find the coordinate of the point where the line through (-1, 1, - 8) and
(5,-2, 10) croe the ZX plane.
Answers
The point of intersection is (1, 0, -2)
To find the point where the line through (-1, 1, -8) and (5, -2, 10) crosses the ZX plane, we need to find the point on the line that has a y-coordinate of 0.
We know that the equation of a line in 3D space is given by:
P = P0 + t(P1 - P0)
where P0 is a point on the line, P1 is another point on the line, t is a scalar parameter, and P is a variable point on the line.
We can substitute in the coordinates of the two given points for P0 and P1:
P = (-1, 1, -8) + t((5, -2, 10) - (-1, 1, -8))
and set the y-coordinate to 0:
1 + t(-3) = 0
t = 1/3
so the point of intersection is:
P = (-1, 1, -8) + (1/3)((5, -2, 10) - (-1, 1, -8))
P = (-1, 1, -8) + (1/3)((6, -3, 18))
P = (-1, 1, -8) + (2, -1, 6)
P = (1, 0, -2)
So the point of intersection is (1, 0, -2)
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Start at 10. Create a pattern that multiplie each number by 10 top when you have 5 number
Answers
So, the sequence is 10, 100, 1000, 10000, 100000
A pattern that multiplies each number by 10 to get the next number in the sequence would be as follows:
Start with 10.
Multiply 10 by 10 to get 100.
Multiply 100 by 10 to get 1000.
Multiply 1000 by 10 to get 10000.
Multiply 10000 by 10 to get 100000.
This pattern creates a sequence of numbers that increases exponentially, with each number being 10 times larger than the previous one. The pattern can be represented by the following rule: "Each number in the sequence is the previous number multiplied by 10."
So, the sequence is:
10, 1010 = 100, 10010 = 1000, 100010 = 10000, 1000010 = 100000
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Find the measure of each unknown angle. (all question) please explain how to solve these questions!
Answers
Therefore , the solution of the given problem of triangle comes out to be angle is 58° is third angle.
What precisely is a triangle?Since a triangle has four or even more sections, it is a polygon. It has an easy geometric form. Triangle ABC refers to a square with edges A, B, and C. A single plane or square are produced by Euclidean geometry when the edges are not collinear. A triangle is a polygon if it has three sides & three corners. Where a triangle's three sides come together are known as the corners. A triangle's angles add up to 180 degrees.
Here,
Given :
A triangle has given angles ,
To find the angle :
=> x + 98° + 24° = 180°
=> x = 180° - 122°
=> x = 58°
Thus , angle is 58° .
Therefore , the solution of the given problem of triangle comes out to be angle is 58° is third angle.
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The Vincent family uses up a
1
2
-gallon jug of milk every 3 days. At what rate do they drink milk?
Answers
Answer:
4 gal / day
Step-by-step explanation:
12 gallons / 3 days
12/3 = 4
4 gallons / 1 day
to fact check we can take the 3 gallons a day, and multiply it by 4 days and you have 12 gallons
Ian is looking to take out a mortgage for $420, 000 from a bank offering an annual interest rate of 3%, compounded monthly. Using the formula below, determine his monthly payment, to the nearest dollar, if the loan is taken over 25 years.
Answers
His monthly payment, to the nearest dollar, if the loan is taken over 25 years is $1,978.54
What is mortgage? How to calculate fixed monthly payment using mortgage formula?Mortgage is a loan taken out to purchase a property. It is usually secured against the value of the property with the lender having the right to repossess the property if the loan is not repaid.
The fixed monthly payment for a mortgage can be calculated using the following formula:
Monthly Payment = [P x R(1+R)^N]/[(1+R)^N-1]
P = Principal Amount
R = Monthly Interest Rate
N = Total Number of Payments
Where Interest Rate is the interest rate per annum, Principal Loan Amount is the amount of money borrowed, and Term in Months is the duration of the mortgage loan in months.
Solution:
Monthly Payment = [$420,000 x (0.03/12)(1 + 0.03/12)^300]/[(1 + 0.03/12)^300 - 1]
Monthly Payment = $1,978.54
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