Creating parallel and perpendicular lines involves understanding that parallel lines share the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. A line that is neither parallel nor perpendicular to a given line simply has a slope that does not meet these conditions.
Explanation:Given the lines in your question, you're asked to create a parallel, perpendicular, and neither parallel nor perpendicular line. Let's consider the first line: y = 3x.
1) A line parallel to y = 3x will have the same slope, so the equation of such a line can be y = 3x + b. You can choose any value for b, as it shifts the line up or down but doesn't change its slope.
2) A line perpendicular to y = 3x would have a slope that is the negative reciprocal of 3, which is -1/3. So, such a line can be represented by the equation y = -1/3x + b. Again, any value of b will work.
3) A line that is neither parallel nor perpendicular to y = 3x could have any slope that's not equal to 3 or -1/3. For instance, the line y = 2x + b is neither parallel nor perpendicular to y = 3x.
Do the same for all the remaining lines by understanding these principles.
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At present Asha's age (in years) is two more than the square of her daughter Nisha's age (in years). When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present age of Asha and Nisha
Answer:
Asha's present age is 27 years and Nisha's present age is 5 years.
Step-by-step explanation:
Let the present age of Nisha be [tex]x[/tex] years.
As per question, Asha's present age is 2 more than the square of Nisha's age.
[tex]\therefore[/tex] Asha's present age = [tex]x^2+2[/tex]
Now, Nisha will reach her mother's age after [tex]x^2+2-x[/tex] years.
Therefore, age of Asha after [tex]x^2+2-x[/tex] years will be = [tex]x^2+2+x^2+2-x=2x^2-x+4[/tex]
Now, as per question,
[tex]2x^2-x+4=10x-1\\2x^2-x-10x+4+1=0\\2x^2-11x+5=0\\2x^2-x-10x+5=0\\x(2x-1)-5(2x-1)=0\\(2x-1)(x-5)=0\\x=\frac{1}{2}\ or\ x=5[/tex]
As age can't be in fraction, we consider the present age of Nisha as 5 years. So, Asha's present age is [tex]x^2+2=5^2+2=25+2=27[/tex] years.
Therefore, Asha's present age is 27 years and Nisha's present age is 5 years.
megan has a rope that is 15 feet in length she cuts the rope into 4 pieces how long is each section of to
Answer:
3.75
Step-by-step explanation:
You take your 15 feed and divide it by 4 for the four pieces she cuts the rope into giving you with each section of the cut rope being 3.75 in.
The length of each piece is 3.75 feet long.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Megan who has a rope that is 15 feet in length and she cuts the rope into 4 pieces.
Assume that the length of each piece is x ft. Then -
4x = 15
x = 15/4
x = 3.75 ft
Therefore, the length of each piece is 3.75 feet long.
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HELP ASAP!!! 100 POINTS!!!
1. It takes the earth 24 h to complete a full rotation. It takes Mercury approximately 58 days, 15 h, and 30 min to complete a full rotation. How many hours does it take Mercury to complete a full rotation? Show your work using the correct conversion factors.
Answer:
HERE IS THE ANSWER 1407.5 hours
Step-by-step explanation:
complete the linear equation
Answer:
[tex]y=-30x[/tex]
Step-by-step explanation:
The intercept of the function is the value of y when x=0. In this particular case, when x=0, y=0, then the intercept is y=0.The slope of the function must tell us what is the change in y when x changes. When x changes in one unit (from x=0 to x=1), y takes the value of y=-30, y=1x(-30). When x takes the value of x=2, y takes the value of y=-60, then y=2x(-30), and when x=3, y=3x(-30)=-90.This means that y always takes the value of -30x. Then the slope is -30, which is the rate of change of y as x changes.Jiang purchased a moving truck for the business. He paid $40,000 for the truck. Its salvage value is $8,500. Select the correct answer from the drop-down menu.
The depreciation expense of the moving truck for a useful life of 10 years is (blank space). If the truck’s useful life where 15 years, the depreciation expense would come to(blank space).
Answer:
A. $3,150
B. $2,100
Step-by-step explanation:
A. Given,
Trucks cost price = $40,000
Salvage Value = $8,500
Useful life = 10 years
Since there is no requirement, I am using straight-line depreciation method to calculate the depreciation expense.
We Know,
Depreciation Expenses = (Cost price - Salvage Value) / Useful Life
Therefore,
Depreciation expense = ($40,000 - $8,500)/10
Depreciation Expense = $31,500/10
Depreciation Expense = $3,150
Therefore, under the straight-line method, the depreciation expense will be = $3,150.
B. Given, (When the useful year is 15)
Trucks cost price = $40,000
Salvage Value = $8,500
Useful life = 15 years
Since there is no requirement, I am using straight-line depreciation method to calculate the depreciation expense.
We Know,
Depreciation Expenses = (Cost price - Salvage Value) / Useful Life
Therefore,
Depreciation expense = ($40,000 - $8,500)/15
Depreciation Expense = $31,500/15
Depreciation Expense = $2,100
Therefore, under the straight-line method, the depreciation expense will be = $2,100
The sum of two numbers, x and y, is 142. Their
could be used to find the numbers?
nbers,
and y, is 142. Their difference is 14. Which system of equations
x + 142 = y
+
18.64
x + y = 142
y = 14
B.
- 14 = y
c
x - y = 142
x + y = 14
D.
14
x=142 + y
y = 14- X
+
The system that will be used to find the numbers
x+y=142
x-y = 14
Step-by-step explanation:
The linear equations are used for representing real life situations
Let x be the first number
and
y be the second number
Then
According to given statement,
"The sum of two numbers, x and y, is 142."
[tex]x+y=142[/tex]
And
"Their difference is 14."
[tex]x-y=14[/tex]
Hence
The system that will be used to find the numbers
x+y=142
x-y = 14
Keywords: Linear Equations
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What is 3 ÷ 2/5? The quotient is 7 and _____
HELP PLEASE
Answer:
Your answer is 15/2 i hoped i helped
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
3×5/2
15/2
The remainder is 1
Factor each expression 12x + 24
Answer:
12(x+2)
Step-by-step explanation:
Factor a 12 out of
12x + 24
12 goes into 12 once
12 goes into 24 twice
= 12(x+2)
Beth read a total of 12 books over 7 months.
If Beth has read 84 books so far, how many months has she been with her book club?
Solve using unit rates.
She has been with her book club for 49 months.
Step-by-step explanation:
Books read = 12 books
Time period = 7 months
Therefore,
12 books = 7 months
1 book = [tex]\frac{7}{12}\ months[/tex]
Books read so far = 84 books
Total time period = x
84 books = x months
1 book = [tex]\frac{x}{84}\ months[/tex]
Using both unit rates;
[tex]\frac{x}{84}=\frac{7}{12}\\x=\frac{7}{12}*84\\x=\frac{588}{12}\\x=49\ months[/tex]
She has been with her book club for 49 months.
Keywords: Unit rates, multiplication
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passes through (-5,9) and (1,3)
Answer:
m=-1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-9)/(1-(-5))
m=-6/(1+5)
m=-6/6
m=-1
Find values of a and b that make the following equality into identity:
Answer:
1. [tex]a=b=\dfrac{3}{4}[/tex]
2. [tex]a=-3,\ b=3[/tex]
Step-by-step explanation:
1. Given:
[tex]\dfrac{3x}{(x-2)(3x+2)}=\dfrac{a}{x-2}+\dfrac{b}{3x+2}[/tex]
To find a and b, add two fractions in right side:
[tex]\dfrac{a}{x-2}+\dfrac{b}{3x+2}\\ \\=\dfrac{a(3x+2)+b(x-2)}{(x-2)(3x+2)}\\ \\=\dfrac{3ax+2a+bx-2b}{(x-2)(3x+2)}\\ \\=\dfrac{(3a+b)x+(2a-2b)}{(x-2)(3x+2)}[/tex]
So,
[tex]\dfrac{3x}{(x-2)(3x+2)}=\dfrac{(3a+b)x+(2a-2b)}{(x-2)(3x+2)}[/tex]
Two fractions with same denominators are equal when they have equal numerators, so
[tex]3x=(3a+b)x+(2a-2b)[/tex]
Equate coefficients:
[tex]At\ x:\ \ 3=3a+b\\ \\At \ 1: 0=2a-2b[/tex]
From the second equation:
[tex]a=b[/tex]
Substitute it into the first equation:
[tex]3b+b=3\\ \\4b=3\\ \\b=\dfrac{3}{4}[/tex]
Hence,
[tex]\dfrac{3x}{(x-2)(3x+2)}=\dfrac{\frac{3}{4}}{x-2}+\dfrac{\frac{3}{4}}{3x+2}[/tex]
2. Given:
[tex]\dfrac{3}{x^2-5x+6}=\dfrac{a}{x-2}+\dfrac{b}{x-3}[/tex]
Note that [tex](x-2)(x-3)=x^2-3x-2x+6=x^2-5x+6[/tex]
To find a and b, add two fractions in right side:
[tex]\dfrac{a}{x-2}+\dfrac{b}{x-3}\\ \\=\dfrac{a(x-3)+b(x-2)}{(x-2)(x-3)}\\ \\=\dfrac{ax-3a+bx-2b}{(x-2)(x-3)}\\ \\=\dfrac{(a+b)x+(-3a-2b)}{(x-2)(x-3)}[/tex]
So,
[tex]\dfrac{3}{(x-2)(x-3)}=\dfrac{(a+b)x+(-3a-2b)}{(x-2)(x-3)}[/tex]
Two fractions with same denominators are equal when they have equal numerators, so
[tex]3=(a+b)x+(-3a-2b)[/tex]
Equate coefficients:
[tex]At\ x:\ \ 0=a+b\\ \\At \ 1: 3=-3a-2b[/tex]
From the first equation:
[tex]a=-b[/tex]
Substitute it into the second equation:
[tex]-3(-b)-2b=3\\ \\3b-2b=3\\ \\b=3\\ \\a=-3[/tex]
Hence,
[tex]\dfrac{3}{x^2-5x+6}=\dfrac{-3}{x-2}+\dfrac{3}{x-3}[/tex]
To turn an equality into an identity, you would find values for 'a' and 'b' that work for all values of 'x'. The process involves equating coefficients and solving the resulting equations. Without specific equations, we must rely on general methods, such as using the quadratic formula when 'c' is known.
Explanation:Finding Values of a and b
To make the equality into an identity, you'll typically want to find values of 'a' and 'b' that satisfy the given equations for all values of 'x'. It seems like part of your question is missing, as we would need the specific equations to give a precise answer. However, the process involves equating coefficients of the same powers of 'x' from both sides of the equation and solving the resulting system of equations.
For example, if you have an equation of the form ax2 + bx + c = 0 and you want to make it an identity, you can find 'a' and 'b' by applying the quadratic formula when 'c' is given.
In the case of a quadratic equation ax2 + bx + c = 0, you can determine 'a' and 'b' by solving:
-b ± √(b2 - 4ac) / (2a)
Which simplifies down when given specific constants, as shown by the example where a = 3, b = 13, and c = -10. This yields two possible solutions for 'x' which can verify the values of 'a' and 'b'.
If an equation already has set constants like a = 1.00, b = 10.0, and c = -200, then the equation is already defined, and the values are given.
Find the distance between the points (7, 6) and (7, -4).
Answer:
If I'm correct it is 10.
Step-by-step explanation:
The distance was 10 ;-;.
Tip: use desmos for this
write an equation in slope for a line that passes through (3,4) (and has a y intercept of -8)
Answer:
Part 1) The equation in slope intercept form is [tex]y=4x-8[/tex]
Step-by-step explanation:
Part 1) Write an equation in slope-intercept form for a line that passes through (3,4) (and has a y intercept of -8)
we know that
The equation of a line in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]b=-8[/tex]
[tex]point\ (3,4)[/tex]
substitute
[tex]4=m(3)-8[/tex]
solve for m
[tex]4+8=3m[/tex]
[tex]3m=12[/tex]
[tex]m=4[/tex]
therefore
[tex]y=4x-8[/tex]
Please help! :) Need answer fast!
Answer:
x = 3
y = 2
Step-by-step explanation:
When 2 triangles are congruent, they will have exact same 3 sides length and exact same 3 angles measure.
So we can say:
-2x + 6y = 6
and
-7x + 8y = -5
Let's multiply first equation by 7 and 2nd equation by -2, to get:
7 [-2x + 6y = 6] = -14x +42y = 42
and
-2 [-7x + 8y = -5] = 14x - 16y = 10
Now adding these 2 new equations and solving for y:
-14x +42y = 42
14x - 16y = 10
----------------------
26y = 52
y = 52/26
y = 2
Now we put y = 2 into 1st equation (or any other) and solve for x:
-2x + 6y = 6
-2x + 6(2) = 6
-2x + 12 = 6
6 = 2x
x = 6/2
x = 3
what is the Y intercept of Y equals 4x +15 ?
Answer: 15
Step-by-step explanation: Linear equations can be written in the form
y = mx + b where the base "b" represents the y-intercept of the line.
So in this case, the y-intercept of the line would positive 15.
The equation can written as y = 4x + 15.
This equation is written in slope-intercept. y = mx + b
m = slope
b = y-intercept
In this equation the y-intercept (b) is 15.
_______
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write the following quadratic equation to standard form and find a,b,c
1) 2x²=3x
2)4x²-10=5
3)3(x²-4x)=2(x+2)
4)3x(x+2x)=11
5)6x(x-8)=2x²+4
1) The standard form of the equation is 2x² - 3x = 0, a = 2 , b = -3 ,
c = 0
2) The standard form of the equation is 4x² - 15 = 0, a = 4 , b = 0 ,
c = -15
3) The standard form of the equation is 3x² - 14x - 4 = 0, a = 3 , b = -14 ,
c = -4
4) The standard form of the equation is 9x² - 11 = 0, a = 9 , b = 0 ,
c = -11
5) The standard form of the equation is 4x² - 48x - 4 = 0, a = 4 , b = -48 ,
c = -4
Step-by-step explanation:
The standard form of a quadratic equation is ax² + bx + c = 0, where
a is the coefficient of x²b is the coefficient of xc is the numerical term1)
∵ 2x² = 3x
- Subtract 3x from both sides
∴ 2x² - 3x = 0
∵ The coefficient of x² = 2
∴ a = 2
∵ The coefficient of x = -3
∴ b = -3
∵ There is no numerical term
∴ c = 0
The standard form of the equation is 2x² - 3x = 0, a = 2 , b = -3 , c = 0
2)
∵ 4x² - 10 = 5
- Subtract 5 from both sides
∴ 4x² - 10 - 5 = 0
- Add like terms
∴ 4x² - 15 = 0
∵ The coefficient of x² = 4
∴ a = 4
∵ There is no x term
∴ b = 0
∵ The numerical term = -15
∴ c = -15
The standard form of the equation is 4x² - 15 = 0, a = 4 , b = 0 , c = -15
3)
∵ 3(x² - 4x) = 2(x + 2)
- Simplify each side
∴ 3x² - 12x = 2x + 4
- Subtract 2x from both sides
∴ 3x² - 12x - 2x = 4
- Subtract 4 from both sides
∴ 3x² - 12x - 2x - 4 = 0
- Add like terms
∴ 3x² - 14x - 4 = 0
∵ The coefficient of x² = 3
∴ a = 3
∵ The coefficient of x = -14
∴ b = -14
∵ The numerical term = -4
∴ c = -4
The standard form of the equation is 3x² - 14x - 4 = 0, a = 3 , b = -14 ,
c = -4
4)
∵ 3x(x + 2x) = 11
- Add the terms in the bracket
∴ 3x(3x) = 11
- Simplify the left hand side
∴ 9x² = 11
- Subtract 11 from both sides
∴ 9x² - 11 = 0
∵ The coefficient of x² = 9
∴ a = 9
∵ There is no x term
∴ b = 0
∵ The numerical term = -11
∴ c = -11
The standard form of the equation is 9x² - 11 = 0, a = 9 , b = 0 ,
c = -11
5)
∵ 6x(x - 8) = 2x² + 4
- Simplify the left hand side
∴ 6x² - 48x = 2x² + 4
- Subtract 2x² from both sides
∴ 4x² - 48x = 4
- Subtract 4 from both sides
∴ 4x² - 48x - 4 = 0
∵ The coefficient of x² = 4
∴ a = 4
∵ The coefficient of x = -48
∴ b = -48
∵ The numerical term = -4
∴ c = -4
The standard form of the equation is 4x² - 48x - 4 = 0, a = 4 , b = -48 ,
c = -4
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What is the value for x?
Answer: X = 4.33
Step-by-step explanation:
cos angle = hypotenuse / opposite side
cos 30° = X/5
0.866 = X/5
X = 4.33
Simplify x² + 3x + 2/X +1
To simplify the expression x² + 3x + 2 / X + 1, factor the numerator and denominator expressions separately. The simplified form of the expression is (x + 2) / 1.
Explanation:To simplify the expression, x² + 3x + 2 / X + 1, we can use the factoring method. First, we factor the numerator expression. The expression x² + 3x + 2 can be factored as (x + 2)(x + 1). Then, we factor the denominator expression X + 1. So, the simplified form of the expression is (x + 2) / 1.
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The length of a rectangle is 9 cm more than its
width. If the area of the rectangle is 36 cm2,
what are the dimensions? Justify your answer.
= 4 = x²
x = Answer: Length= 11 , Brteadth = 2
Step-by-step explanation: Let the breadth of the rectangle be x
length = 9 + x
area = 36 cm²
A.T.Q
36cm² = 9x*x
36 = 9x²
36/9 = 4 = x²
x = root of 4
x= 2
Therefore , breadth of rectangle is 3cm and length is 12 cm
verification:
l*b = 12*3 = 36cm²
if 3 miles is equal to 4828.05 miles, how many meters are in 5 miles
There are 8046.75 meters in 5 miles
Step-by-step explanation:
Method 1:
First of all we have to calculate the unit conversion.
Assuming that 3 miles is equal to 4828.05 meters
We have to find that how many meters make one mile
So,
3 miles = 4828.05 meters
[tex]1\ mile=\frac{4828.05}{3}\\=1609.35\ meters[/tex]
Now we know that:
[tex]1\ mile=1609.35\ meters\\5\ miles=1609.35*5 = 8046.74\ meters[/tex]
Method 2:
We can also use ratios to find the number of meters in 5 miles as:
3:4828.05::5:x
where x is the number of meters in 5 miles
[tex]\frac{3}{4828.05}=\frac{5}{x}\\x=\fac{5*4828.05}{3}\\=8046.75\ meters[/tex]
Hence,
There are 8046.75 meters in 5 miles
Keywords: Conversions, Units
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Write an equation in point slope form (12,7) m=-2
Answer:
y= -2x+31
Step-by-step explanation:
Y=-2x+B
7=-2(12)+B
7=-24+B
7+24= (-24+24)+B
31=B
Y=-2x+31
Hope it helps!!
13m-7-10m=2? I need help
Answer:
[tex]\displaystyle 3 = m[/tex]
Step-by-step explanation:
2 = −7 + 3m
+ 7 + 7
__________
[tex]\displaystyle \frac{9}{3} = \frac{3m}{3} \\ \\ 3 = m[/tex]
I am joyous to assist you anytime.
A bag contains 8 blue marbles 6 red marbles and 4 green marbles what is the probability of selecting a blue marble replaced it in the bag and then selecting a red marble
Answer:
[tex]\dfrac{4}{27}[/tex]
Step-by-step explanation:
A bag contains 8 blue marbles 6 red marbles and 4 green marbles, 8 + 6 + 4 = 18 marbles in total.
The probability of selecting a blue marble is
[tex]P(\text{blue marble})=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}=\dfrac{8}{18}=\dfrac{4}{9}[/tex]
Then the blue marble was replaced in the bag.
The probability of selecting a red marble is
[tex]P(\text{red marble})=\dfrac{\text{Number of red marbles}}{\text{Total number of marbles}}=\dfrac{6}{18}=\dfrac{1}{3}[/tex]
The probability of selecting a blue marble replaced it in the bag and then selecting a red marble is
[tex]P=\dfrac{4}{9}\cdot \dfrac{1}{3}=\dfrac{4}{27}[/tex]
Please answer this correctly
28 to nine means it is 8:32 ( to get this you subtract 28 from 9.) ( its saying there are 28 minutes left until it is 9)
add 8 hours
= 8+ 8 = 16
well we arent talking about military time sooo 16-12 = 4
4 : 32 and you need to add the 59 so
32+ 59 = 91
91 - 60 = 31 (dont forget to add the extra 1 hour because we subtracted 60 minutes :). )
so the correct time will be 5: 31
Answer: 5:31
Step-by-step explanation:
28 minutes to 9 is 8:32
8 hours and 59 minutes later it would be 5:31
How many solutions does this system have?
Answer:
x=0, exactly one solution.
Step-by-step explanation:
y=3x+3
y=-2x+3
-----------
3x+3=-2x+3
3x-(-2x)+3=3
3x+2x+3=3
5x+3=3
5x=3-3
5x=0
x=0/5
x=0
2x - 2(4x-3) = 6 - 6x
Answer:
x=
Step-by-step explanation:
Open parenthesis first:
2x-8x+6=6-6x
Combine like terms:
-6x+6=6-6x
Then move all like terms to one side:
6-6=-6x+6x
Simplify:
0=0
0=0 is true, so x can equal any number and the result will be true. (Like the number 4, for example. If x was 4, you would get 4=4.)
~Stay golden~ :)
Solve: In 2x + In 2 = 0
DONE
Answer:
[tex]x=\frac{1}{4}[/tex]
Step-by-step explanation:
We can use some logarithmic rules to solve this easily.
Note: Ln means [tex]Log_e[/tex]
Now, lets start with the equation:
[tex]ln(2x) + ln(2) = 0\\ln(2x) = -ln(2)[/tex]
Writing left side with logarithmic base e, we have:
[tex]Log_{e}(2x) = -ln(2)[/tex]
We can now use the property shown below to make this into exponential form:
[tex]Log_{a}b=x\\means\\a^x=b[/tex]
So, we write:
[tex]Log_{e}(2x) = -ln(2)\\e^{-ln(2)}=2x[/tex]
We recognize another property of exponentials:
[tex]a^{bc}=(a^{b})^{c}[/tex]
So, we write:
[tex]e^{-ln(2)}=2x\\(e^{ln(2)})^{-1}=2x[/tex]
Also, another property of natural logarithms is:
[tex]e^{(ln(a))}=a[/tex]
Now, we simplify:
[tex](e^{ln(2)})^{-1}=2x\\(2)^{-1}=2x\\\frac{1}{2}=2x\\x=\frac{\frac{1}{2}}{2}\\x=\frac{1}{4}[/tex]
This is the answer.
how do I solve for w
Answer:
w ≥ 141/2
Step-by-step explanation:
12 − 4/6 w ≤ 2/8 − 3/6 w
First, combine like terms. Add 4/6 w to both sides, and subtract 2/8 from both sides.
12 − 2/8 ≤ 4/6 w − 3/6 w
12 − 2/8 ≤ 1/6 w
Reduce 2/8 to 1/4:
12 − 1/4 ≤ 1/6 w
To get rid of the fractions, multiply both sides by 12 (the LCM of 4 and 6):
12 (12 − 1/4) ≤ 12 (1/6 w)
144 − 3 ≤ 2w
141 ≤ 2w
Divide by 2:
141/2 ≤ w
If you'd like, flip the equation:
w ≥ 141/2
Score: 0 of 1 pt
3 of 21 (14 complete)
6.5.25
A family paid $25,900 as a down payment for a home. If this represents 14% of the price of the home, find the price of the home.
The price of the home is $
the answer box and then click Check Answer
The price of house is $185000.
Step-by-step explanation:
The percentage formula will be used for finding the price of the house
Given
Down payment = $25900
Percentage = 14%
Let x be the price of the home
Then
[tex]Down\ payment=14\%\ of\ x\\\\25900=0.14 * x\\\\x = \frac{25900}{0.14}\\\\x =185000[/tex]
Hence,
The price of house is $185000.
Keywords: Down payment, percentage
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Noreen is considering a purchase of a $170,000 home and her bank is
offering her a 5.15% interest rate on a 30-year mortgage with an option of
purchasing points. The bank is requiring a 20% down payment. If she decides
to apply the price of 2 points to her down payment instead, what will her
monthly mortgage payment be? Round your answer to the nearest dollar.
Answer:$728
Step-by-step explanation:
Final answer:
To provide Noreen with her new monthly mortgage payment, the cost of 2 mortgage points is added to the original 20% down payment, resulting in a decreased loan amount. A mortgage calculator or formula is then used to determine the monthly payment at a 5.15% interest rate for the new loan amount over 30 years, which would be higher than with the points purchased. Answer : 725$
Explanation:
To calculate Noreen's monthly mortgage payment, we need to first understand the impact of her decision to apply the price of 2 points to her down payment instead of purchasing points. Points are upfront fees paid to the lender at closing in exchange for a reduced interest rate. One point is equal to 1% of the loan amount. However, since Noreen is opting to add the cost of these points to her down payment, we'll calculate her down payment and loan amount without considering a reduction in interest rate.
1. Calculate the down payment:
Noreen's home costs $170,000, and she is required to make a 20% down payment.
Down payment = 20% of $170,000 = 0.20 * $170,000 = $34,000
2. Calculate the cost of 2 points:
Since Noreen is not buying points and instead adding this cost to her down payment, we calculate the initial loan amount to find out how much 2 points would cost.
Initial loan amount without points = $170,000 - $34,000 = $136,000
Cost of 2 points = 2% of $136,000 = 0.02 * $136,000 = $2,720
3. Adjust the down payment:
Noreen decides to add the $2,720 (cost of 2 points) to her down payment.
New down payment = $34,000 + $2,720 = $36,720
4. Calculate the new loan amount:
New loan amount = Home price - New down payment = $170,000 - $36,720 = $133,280
Now, we use the loan amount of $133,280 and the original interest rate of 5.15% to calculate the monthly mortgage payment over a 30-year term.
The formula for monthly mortgage payments is:
[tex]\[M = P\frac{r(1+r)^n}{(1+r)^n - 1}\][/tex]
First, calculate the monthly interest rate:
[tex]\[r = \frac{0.0515}{12} = 0.00429167\][/tex]
Then, plug in the values into the formula:
[tex]\[M = 133,280\frac{0.00429167(1+0.00429167)^{360}}{(1+0.00429167)^{360} - 1}\][/tex]
This calculation can be complex, so it's often easiest to use a mortgage calculator or financial calculator to compute \(M\).
When you perform this calculation, you should get:
[tex]\[M \approx 725\][/tex]
Thus, Noreen's monthly mortgage payment would be approximately $725 when rounded to the nearest dollar. Please note, the exact payment can slightly vary based on the precision of the interest rate conversion and the calculation method.