Match the reasons with the statements in the proof.
1. j||k, m∠3 = m∠1
If alternate interior angles are =, then lines are ||.
2. m∠1 = m∠2
Substitution
3. m∠2 = m∠3
Given
4. l||m
If lines are ||, then corresponding angles are =.
Answers
Given
2. m∠1 = m∠2
If lines are ||, then corresponding angles are =.
3. m∠2 = m∠3
Substitution
4. l||m
If alternate interior angles are =, then lines are ||.
Answer:
1-given
2-if lines are parallel, then corresponding angles are equal
3-Substitution
4-if alternate interior angles are equal then lines are parallel.
Step-by-step explanation:
Given j is parallel to k,[tex]m\angle3 =m\angle 1[/tex]
We have to prove that line l is parallel to m
We have to match reason with its correct statement in given proof.
1.j is parallel to k,[tex] m\angle 3=m\angle 1[/tex]
Reason:given
2.[tex]m\angle 1=m\angle 2[/tex]
Reason:if the lines are parallel , then corresponding angles are equal.
3.[tex]m\angle 2=m\angle 3[/tex]
Reason: substitution
4.line l is parallel to m
Reason: If alternate interior angles are equal ,then lines are parallel.
Related Questions
in a given circuit, the supplied voltage is 1.5 volts, and the resistor value is 3 ohms. use ohm's law to determine the current in the circuit
Answers
Final answer:
The current in a circuit with a supplied voltage of 1.5 volts and a resistance of 3 ohms is calculated using Ohm's Law (I = V/R), resulting in a current of 0.5 amperes.
Explanation:
Using Ohm's Law to Calculate Current
To determine the current in a circuit with a supplied voltage of 1.5 volts and a resistor value of 3 ohms, we can use Ohm's Law, which is stated as I = V/R, where I is the current, V is the voltage, and R is the resistance. Plugging in the values, we have I = 1.5 volts / 3 ohms. Therefore, I = 0.5 amperes or 500 milliamperes. This is the current flowing through the circuit.
Ohm's Law is a fundamental principle in physics used for analyzing simple circuits where the relationship between voltage, current, and resistance is linear. Remember that this law holds true for ohmic materials where the resistance remains constant over a range of voltages and temperatures.
Which linear inequality is represented by the graph? y > 2/3x – 1/5 y ≥ 3/2x + 1/5 y ≤ 2/3x + 1/5 y < 3/2x – 1/5
Answers
We have then that by substituting the values of x = 0 and x = 3 we obtain:
y = 0.2
y = 2.2
Respectively.
So, the line is:
y = 2 / 3x + 1/5
Then, the points that satisfy the inequality are all those of the shaded region.
Answer:
The inequality is:
y ≤ 2 / 3x + 1/5
Answer: The correct option is third, i.e., [tex]y\geq \frac{3}{2} x+\frac{1}{5}[/tex].
Explanation:
From the figure it is noticed that the line passing through the points (0,0.2) and (3,2.2).
The equation of line passing through two points is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
[tex]y-0.2=\frac{2.2-0.2}{3-0}(x-0)[/tex]
[tex]y-\frac{1}{5} =\frac{2}{3} x[/tex]
[tex]y =\frac{2}{3} x+\frac{1}{5}[/tex]
The equation of the line is [tex]y =\frac{2}{3} x+\frac{1}{5}[/tex].
From the figure it is noticed that as the value of x increases the value of y is less.
he point (1,0) lies on the shaded reason it means this point must satisfy the equation.
[tex](0)=\frac{2}{3} (1)+\frac{1}{5}[/tex]
[tex](0)=\frac{2}{3} +\frac{1}{5}[/tex]
[tex](0)=\frac{10+3}{15}[/tex]
[tex](0)=\frac{13}{15}[/tex]
It is true of the sign is less than or equal to instead of equal.
[tex]y \leq \frac{2}{3} x+\frac{1}{5}[/tex]
Therefore, option third is correct.
In a Quadratic Regression problem, a graph is a perfect fit for the data when r = ? a. 1 c. 2 b. 0 d. 100 Please select the best answer from the choices provided A B C D
Answers
Answer:
the answer is A on edge :)
Step-by-step explanation:
The graph that is a perfect fit for the given data in a quadratic regression problem is when r is; A: 1
What is a quadratic regression?Quadratic regression is defined as a statistical technique that is used to find the equation of the parabola that best fits a set of data.
Now, this type of regression is an extension of simple linear regression that is used to find the equation of the straight line that best fits a set of data.
Thus, in this type of regression, we say a graph is a perfect fit when r = 1.
Read more about Quadratic Regression at; https://brainly.com/question/26174369
#SPJ5
Instructions:Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
is parallel to . and are perpendicular to and .
The ratio of the lengths of and is
:
.
Answers
Answer:
The ratio of the lengths of PR and QS is 1 : 1
Step-by-step explanation:
If your question is based on this exercise:
PQ Is parallel to RS. PR and QS are perpendicular to PQ and RS
Here is why
Use the Remainder Theorem to find the remainder: (–6x3 + 3x2 – 4) ÷ (2x – 3).
23
-17.5
-4.4444444...
-0.8888888...
Answers
(–6x³ + 3x² – 4) ÷ (2x – 3)
----------------------║--------------------------
+6x³+9x² -3x²+6x+9
---------------------
12x²-4
-------------------
-12x²+18x
-------------------
18x-4
-----------------
-18x+27
----------------
23-----------------> the remainder
the answer is 23
The remainder obtained when we carry out the operation (-6x³ + 3x² - 4) ÷ (2x - 3) is -17.5 (2nd option)
How do i determine the remainder?The following data were obtained from the question:
Expression = (-6x³ + 3x² - 4) ÷ (2x - 3)Remainder =?Using the remainder theorem, we can obtain the remainder as illustrated below:
Let
f(x) = -6x³ + 3x² - 4
2x - 3 = 0
From 2x - 3 = 0, make x the subject as shown below:
2x - 3 = 0
x = 3/2
Substitute the value of x into f(x). We have:
f(x) = -6x³ + 3x² - 4
f(3/2) = -6(3/2)³ + 3(3/2)² - 4
= -6(27/8) + 3(9/4) - 4
= -20.25 + 6.75 - 4
= -17.5
Thus, we can conclude that the remainder obtained when (-6x³ + 3x² - 4) is divided by (2x - 3) is -17.5 (2nd option)
Learn more about remainder theorem:
https://brainly.com/question/29127375
#SPJ6
Which expression represents the number of sides in the polygon for the nth member of the pattern? A) n + 3 B) n3 C) n + 2 D) 3n
Answers
2nd member has 6 sides (3x2)
3rd member has 9 sides' (3x3)
Therefore, i think for nth member
the appropriate expression for n th member will be 3n
if you received an annual salary of 33500 paid monthly what would your gross pay be each pay period
Answers
Joan has 45 marbles . MARY HAS m marbles if Joan has 15 times as many marbles , write an equation that shows how many marbles mary has
Answers
Mary has 3 marbles.
Explanation:To find out how many marbles Mary has, we can use the information that Joan has 45 marbles and Joan has 15 times as many marbles as Mary. So, we can set up an equation:
45 = 15m
To solve for m, we divide both sides of the equation by 15:
m = 45/15
Simplifying the expression, we get:
m = 3
Therefore, Mary has 3 marbles.
A rectangle is 2 times as long as it is wide. if the area is 18 square feet, find its perimeter.
Answers
Danielle poured 3/4 gallon of water from a 7/8 gallon bucket. How much water is left in the bucket?
Answers
Subtract 3/4 from 7/8 and we get
7/8 - 3/4 = 7/8 - 6/8 = (7-6)/8 = 1/8
There is 1/8 of a gallon left
PLEASE HELP
Is this A, B, or C?
Answers
The sum can be written like this:
[tex]-4\frac{1-\left(\frac{1}{2}\right)^6}{1-\frac{1}{2}}=-8\left(1-\dfrac{1}{2^6}\right)\\ =-8\dfrac{63}{64}\\=-\dfrac{63}{8}[/tex]
The correct answer is the second one.
The formula used to find the length of a line segment in space.
Answers
length = √((∆x)^2 +(∆y)^2 +(∆z)^2)
.. where ∆x, ∆y, ∆z are the differences between the end-point coordinates in the x-, y-, and z-directions, respectively.
if youre doing the vocab thing -- Distance
PLEASE HELP ME ASAP 40 POINTS AND BRAINLIEST SHOW WORK
Find the variables and the lengths of the sides of this kite
Answers
Y = 16
Since we know that the bottom two sides are congruent we can make an equation to solve for that X first [2x + 5 = x + 12] . (since we cannot make an equation with the two congruent sides at the top because there are different variables).
Now that we've solved for X which is 7, we can plug it into the top equation [y - 4 = x + 5] which would simplify to [ y - 4 = 12] which would give us 16 for Y
Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.
Answers
Answer: The answer is 5, 10, 20, 40 and 80.
Step-by-step explanation: We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.
Let the first five terms of a sequence be 5, 10, 20, 40 and 80. These terms are taken from a geometric sequence with first term [tex]a_1 5[/tex] and common ratio [tex]r=2.[/tex]
Therefore, we have
[tex]a_2=a_1\times r,\\\\a_3=a_2\times r,\ldots[/tex]
Therefore, the recursive formula is
[tex]a_{n+1}=2a_n,~~a_1=5.[/tex]
And explicit formula is
[tex]a_n=a_1r^{n-1}.[/tex]
Answer:
Let the first five terms of a sequence be, 4,8,12,20,24
Ok, let me explain the meaning of term explicit and Recursive formula.
Explicit formula ,is the general formula to find any term of the sequence.
And, Recursive formula, is the method by which, we can find the nth term of the sequence if (n-1)th term of the sequence is known.
So,the explicit formula for the sequence is,
y = 4 n, where , n is any natural number.
And the recursive formula is .
y = 4 (n-1), with the help of (n-1)th term we can find nth term.
First term =4=4 × 1
Second term =8 =4 × 2
Third term =12=4×3
Fourth term =16 =4 × 4
.....................
...........................
.................................
(n-1) th term =4 × (n-1)
nth term =4 × n
Applying the simple procedure by looking at the first , second and the way the next term goes , the general and recursive formula is obtained.
As, you said you don't want simpler sequence
Consider the first five terms of the sequence, 0, 3,8,15, 24.
Explicit formula =n² + 2 n
Recursive formula=(n-1)²+2(n-1)
If,you will look at the sequence, it is neither Arithmetic nor geometric .
First term =0=0²+0×0
Second term =3=1+2=1²+2 × 1
Third term =8=4+4=2²+2×2
Fourth term =15=9+6=3²+2×3
Fifth term =24=16 +8=4²+2×4
So, Explicit formula= n²+ 2 n, where n is a whole number.
Tickets for the school play cost $17 each. Gary wrote the expression n X 17 to find the cost of n tickets to the play. He used the Distributive Property to find the product. Use the Distributive Property to write Gary's expression another way.
Answers
We have then that the expression used by Gary:
n = X * 17
Using the distributive property we have another way to rewrite the expression is:
n = 17 * X
Where,
x: is the sum of all tickets sold.
Answer:
n = 17 * X
Which graph represents the function over the interval [−3, 3]?
Answers
Function floor (or ground), that to each real number assigns the nearest whole number by defect, that is to say, the greater whole number equal or smaller than that real number.
Let's evaluate the extremes of the interval
x = -3
g (-3) = floor (-3) -2 = -5
x = 3
g (3) = floor (3) -2 = 1
Therefore, the graph that best corresponds to the function in the given interval is the attached graph.
Third graphrepresents the function [tex]f\left( x \right) = \left\lfloor x \right\rfloor-2[/tex] over the interval [tex]\left[ { - 3,3} \right].[/tex]
Further explanation:
Given:
The function is [tex]f\left( x \right) = \left\lfloor x \right\rfloor- 2.[/tex]
The function is defined in the interval [tex]\left[ {-3,3}\right].[/tex]
Explanation:
The greatest integer function is represented [tex]y = \left\lfloor x \right\rfloor.[/tex]
The greatest integer can also be known as floor function. The function is integral part of real numbers.
The values of greatest function [tex]f\left( x \right)= \left\lfloorx \right\rfloor- 2[/tex] in interval [tex]\left[{ - 3,3}\right][/tex] can be obtained as follows,
Substitute [tex]-3[/tex] for [tex]x[/tex] in the function [tex]f\left( x \right)= \left\lfloor x \right\rfloor- 2.[/tex]
[tex]\begin{aligned}f\left({- 3} \right)&=\left\lfloor{ - 3} \right\rfloor- 2\\&=- 3- 2\\&=- 5\\\end{aligned}[/tex]
Substitute [tex]3[/tex] for [tex]x[/tex] in the function [tex]f\left( x \right)=\left\lfloor x \right\rfloor- 2.[/tex]
[tex]\begin{aligned}f\left( 3 \right)&= \left\lfloor3\right\rfloor- 2\\&=3- 2\\&=1\\\end{aligned}[/tex]
The minimum value of the function in [tex]\left[ { - 3,3} \right] {\text{is}\: \boxed{ - 5}.[/tex]
The maximum value of the function in [tex]\left[ { - 3,3} \right] {\text{is}\: \boxed{1}.[/tex]
Third graphrepresents the function [tex]f\left( x \right)=\left\lfloor x\right\rfloor- 2[/tex] over the interval [tex]\left[{ - 3,3}\right].[/tex]
Kindly refer to the image attached.
Learn more
1. Learn more about the polynomial https://brainly.com/question/12996944
2. Learn more about logarithm model https://brainly.com/question/13005829
3. Learn more about the product of binomial and trinomial https://brainly.com/question/1394854
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.
An inscribed angle has a measure of 48°. Determine the measure of the intercepted arc.
24° 48° 72° 96°
Answers
[tex]\frac{48}{\frac{1}{2}}=\frac{\frac{1}{2}x}{\frac{1}{2}} \\ 48 \div \frac{1}{2} = x \\ \frac{48}{1} \div \frac{1}{2} = x \\ \frac{48}{1}*\frac{2}{1} = x \\ \frac{96}{1}=x \\ 96=x[/tex]
The measure of the intercepted arc is 96°.
helppppppppppppppppppppp
Answers
f (a) = 5 + a ^ 2
g (a) = root (a-5) -2
By making the composition we have:
g (f (a)) = root ((5 + a ^ 2) -5) -2
Rewriting the function:
g (f (a)) = root (5 + a ^ 2-5) -2
g (f (a)) = root (a ^ 2) -2
g (f (a)) = lal-2
Answer:
The functions are:
f (a) = 5 + a ^ 2
g (a) = root (a-5) -2
option 3
Is .8/100 equal to .8%
Answers
but is also equal to 2/25, the simplest form of .8/100
The city of Beijing has a population of more than 10 to the 7th power people. Write 10 to the 7th power without using an exponent
Answers
Answer:
[tex]10\times 10\times 10\times 10\times 10\times 10 \times 10[/tex]
Step-by-step explanation:
Exponentiation is the operation used to write the product of two or more equal factors. This expression can written as follows:
[tex]a^n\\\\Where:\\\\a=Base\\n=Exponent[/tex]
That is, [tex]a^n[/tex] is the product of multiplying n bases:
[tex]a^n=a\times...\times...\times a[/tex]
In this sense:
[tex]10^7=10\times 10\times 10\times 10\times 10\times 10 \times 10[/tex]
if the remainder on division of x^3+2x^2+kx+3 by x-3 is 21,find the quotient and the value of k. Hence,find the zeroes of the cubic polynomial x^3+2x^2+kx-18.
Answers
On dividing p(x) by x-3, the remainder is 21. Therefore,
P(3)=21
Substituting x=3 in p(x)
P(3)=3^3 +2*(3)^2+k*3+3
=27+18+3k+3
=48+3k
We know that, p(3)=21.
So, 48+3k=21
3k=21-48
3k=-27
k=-27/3 =-9
now, p(x) =x^3+2x^2-9x-18
-2 is a factor of p(x) on inspection. Therefore, divide p(x) by x+2 to find the
zeroes of the polynomial.
On dividing, we get the factors to be, (x^2-9)(x+2)
(x^2-3^2)(x+2)
Factorizing using the identity a^2-b^2=(a+b)(a-b) we get,
(x+3)(x-3)(x+2)
Therefore, the zeroes of the polynomials are -3,+3 and -2.
If a < 0 and b > 0, then the point (a, b) is in Quadrant A) I. B) II. C) III. D) IV.
Answers
Answer:
The actual answer is D
The point (a, b) lies in the second quadrant. Then the correct option is B.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
If a < 0 and b > 0.
Then the point (a, b) is in Quadrant will be given as,
If a > 0 and b > 0, then the points is in first quadrant.If a < 0 and b > 0, then the points is in second quadrant.If a < 0 and b < 0, then the points is in third quadrant.If a > 0 and b < 0, then the points is in fourth quadrant.Thus, the point (a, b) lies in the second quadrant.
Then the correct option is B.
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
#SPJ2
What is the circumference of a circle with a radius of 6.1 centimeters? Enter your answer as a decimal in the box. Use 3.14 for pi. Round your answer to the nearest tenth. cm
Answers
C = 2 * pi × r
Substitute:
C = 3.14 × 6.1 × 2
C = 38.303
Round to the nearest tenth:
38.3.
ANSWER:
The circumference of the circle is about 38.3 centimetres.
:D
A small plane leaves an airport at a speed of 252 miles per hour. A jet leaves the airport 2 hours later traveling at 672 miles per hour. How long will the small plane be flying before the jet catches up to it? What unit will you use for your answer?
Answers
the small plane runs at a rate of 252 mph, the jet runs at 672 mph, but the jet takes off 2 hours later.
if the jet plane say has been traveling for "t" hours by the time they meet, the small plane was already rolling before the jet, actually 2 hours earlier, so if the jet has gone for "t" hours, the small plane has been going for "t+2" hours.
now, by the time they both meet, the distance covered by say the small plane is "d" miles, but the distance covered by the jet is also the same "d" miles, since they're meeting.
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{small plane}&d&252&t+2\\ \textit{jet plane}&d&672&t \end{array} \\\\\\ \begin{cases} d=252(t+2)\\ d=672t\\ --------\\ 252(t+2)=672t \end{cases} \\\\\\ 252t+504=672t\implies 504=420t\implies \cfrac{504}{420}=t\implies \cfrac{6}{5}=t \\\\\\ \textit{an hour and 12 minutes}=t[/tex]
No, thanks to you, I got the question wrong it was hours.
What is the area of the composite figure whose vertices have the following coordinates? (−1, 5) , (3, 5) , (7, 3) , (3, 0) , (−1, 1)
Answers
Answer:
28
Step-by-step explanation:
Square: 4 * 4 = 16
Small Triangle: 1 * 4 = 4 / 2 = 2
Large Triangle: 5 * 4 = 20 / 2 = 10
16 + 2 + 10 = 28
A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area of the remaining portion of the circle in square feet?
Answers
we know that
the side of square=2*[r*√2/2]=r*√2
r=14 ft
the side of square=14*√2=19.80 ft
[area of the remaining portion of the circle]=[ area of a circle]-[area of a square]
[area of a square]=(14√2)²=392 ft²
[ area of a circle]=pi*14²=615.75 ft²
therefore
[area of the remaining portion of the circle]=615.75-392=223.75 ft²
the answer is 223.75 ft²
A square is cut from a circle with a 14-foot diameter. Remaining circle area ≈ 53.86 sq ft here nearest round off option is c. 50 square feet.
To find the area of the remaining portion of the circle after a square with a side of 10 feet is cut out,
Find the area of the square:
Area of square
= side × side
= 10 feet × 10 feet
= 100 square feet
Find the radius of the circle:
The diameter is approximately 14 feet, so the radius is half of that:
Radius = 14 feet / 2 = 7 feet
Find the area of the entire circle:
Area of circle = π × radius²
Area of circle
= π × (7 feet)²
≈ 153.86 square feet (using π ≈ 3.14)
Subtract the area of the square from the area of the circle to find the remaining portion:
Remaining area = Area of circle - Area of square
Remaining area
≈ 153.86 square feet - 100 square feet
≈ 53.86 square feet
Therefore, the approximate area of the remaining portion of the circle is approximately 53.86 square feet nearest option is c. 50 square feet.
learn more about area here
brainly.com/question/13875505
#SPJ3
The above question is incomplete , the complete question is:
A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area of the remaining portion of the circle in square feet?
Attached figure
Can someone help me please!!!
Answers
3x + 2(5x - 1) = 11
3x + 10x - 2 = 11
13x = 13
x = 1
y = 11 - 3x
y = 11 - 3
y = 8
y = 5x -1
Using substitution
3x + 2(5x-1) = 11
3x + 10 x -2 = 11
13x = 13
x = 1
but, y= 5x -1
y = 5 (1)- 1
= 4
Therefore, y =4 and x = 1
Question 2
Using linear combination method
2x -3y = 13
x+2y = -4 multiplying the second equation by 2 to eliminate x
we get
2x - 3y = 13
2x + 4y = -8 ( subtracting the two equations)
-7y = 21
y = -3
To get x we substitute y with -3 in one of the equation
x = -4 -2y
x = -4 - 2(-3)
x = 2
Therefore, the value of x = 2 and y =-3
Question 3
The first thing is to get a table of values for each of the equation using at least three values of x, this gives you at least three coordinates that can be used to plot the lines on the Cartesian plane.
That is;
For; y = (1/2)x + 3
x y
(2 , 4)
(4, 5)
(6, 6)
And for -3x +y = -2 which is the same as y =-2 +3x
x y
(0, -2)
(1, 1)
(2, 4)
Then, plot the two lines on the plane using the above coordinates,
The solution will be the point of intersection of the two lines (where the two lines plotted meet)
An ellipse has vertices along the major axis at (0, 1) and (0, −9). The foci of the ellipse are located at (0, −1) and (0, −7). The equation of the ellipse is in the form below.
Answers
now, the center is half-way between the vertices, therefore it'd be at 0, -4, like in the picture in red.
the distance from the center to either foci, is "c", and that's c = 3.
the "a" component of the major axis is 5 units, now let's find the "b" component,
[tex]\bf \textit{ellipse, vertical major axis} \\\\ \cfrac{(x- h)^2}{ b^2}+\cfrac{(y- k)^2}{ a^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases}\\\\ -------------------------------[/tex]
[tex]\bf \begin{cases} a=5\\ c=3 \end{cases}\implies c=\sqrt{a^2-b^2}\implies c^2=a^2-b^2\implies b^2=a^2-c^2 \\\\\\ b=\sqrt{a^2-c^2}\implies b=\sqrt{5^2-3^2}\implies b=4\\\\ -------------------------------\\\\ \begin{cases} h=0\\ k=-4\\ a=5\\ b=4 \end{cases}\implies \cfrac{(x- 0)^2}{ 4^2}+\cfrac{[y-(-4)]^2}{ 5^2}=1 \\\\\\ \cfrac{(x- 0)^2}{ 16}+\cfrac{(y+4)^2}{25}=1[/tex]
The equation of the ellipse is required.
The required equation is [tex]\dfrac{x^2}{16}+\dfrac{(y+4)^2}{25}=1[/tex]
It can be see that the major axis is parallel to the y axis.
The major axis points are
[tex](h,k+a)=(0,1)[/tex]
[tex](h,k-a)=(0,-9)[/tex]
[tex]k+a=1[/tex]
[tex]k-a=-9[/tex]
Subtracting the equations
[tex]2a=10\\\Rightarrow a=5[/tex]
The foci are
[tex](h,k+c)=(0,-1)[/tex]
[tex](h,k-c)=(0,-7)[/tex]
[tex]k+c=-1[/tex]
[tex]k-c=-7[/tex]
Subtracting the equations
[tex]2c=6\\\Rightarrow c=3[/tex]
[tex]k+c=-1\\\Rightarrow k=-1-c\\\Rightarrow k=-1-3\\\Rightarrow k=-4[/tex]
Foci is given by
[tex]c^2=a^2-b^2\\\Rightarrow b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{5^2-3^2}=4[/tex]
The equation is
[tex]\dfrac{(x-h)^2}{b^2}+\dfrac{(x-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-0)^2}{4^2}+\dfrac{(y+4)^2}{5^2}=1\\\Rightarrow \dfrac{x^2}{16}+\dfrac{(y+4)^2}{25}=1[/tex]
Learn more:
https://brainly.com/question/12812293?referrer=searchResults
Ben and Marge are purchasing a house with a 20-year, 5/1 ARM for $265,000 at 5.25% with a 3/12 cap structure. What will the difference in payments be from year 5 to year 6?
A. $925.81
B. $880.29
C. $369.32
D. $234.39
Answers
The difference in payments from year 5 to year 6 is approximately $369.32 for the 5/1 ARM mortgage.
To calculate the payment difference from year 5 to year 6 for a 5/1 ARM (Adjustable Rate Mortgage) with a 3/12 cap structure, we need to understand how the ARM works and how the caps affect the adjustment.
1. Initial Mortgage Parameters :
- Loan Amount: $265,000
- Interest Rate: 5.25%
- Term: 20 years
2. Adjustment Frequency : The 5/1 ARM adjusts after the initial 5-year fixed period, then annually.
3. Cap Structure :
- Initial Adjustment Cap: 3%
- Subsequent Adjustment Cap: Each year after the initial adjustment, the rate can adjust up to 3% from the previous rate.
4. Calculation Steps :
a. Calculate the initial monthly payment using the loan amount, interest rate, and term.
b. Determine the new interest rate for year 6 based on the cap structure.
c. Calculate the monthly payment for year 6 with the new interest rate.
d. Find the difference between the payments from year 5 to year 6.
Let's start the calculations:
a. Calculate the initial monthly payment using the loan amount, interest rate, and term. We'll use the formula for a fixed-rate mortgage:
[tex]\[ P = \frac{P_r \cdot A}{1 - (1 + r)^{-n}} \][/tex]
Where:
- [tex]\( P \)[/tex] = Monthly Payment
- [tex]\( P_r \)[/tex] = Periodic Interest Rate (annual rate divided by 12)
- [tex]\( A \)[/tex] = Loan Amount
- [tex]\( r \)[/tex] = Periodic Interest Rate
- [tex]\( n \)[/tex] = Total number of payments (loan term in years multiplied by 12)
For the initial fixed period of 5 years:
[tex]\[ P_r = \frac{5.25\%}{12} = 0.004375 \][/tex]
[tex]\[ n = 20 \times 12 = 240 \][/tex]
Plugging these values into the formula:
[tex]\[ P = \frac{0.004375 \cdot 265000}{1 - (1 + 0.004375)^{-240}} \][/tex]
[tex]\[ P \approx 1645.80 \][/tex]
So, the initial monthly payment is approximately $1,645.80.
b. Determine the new interest rate for year 6 :
- The initial rate can adjust up to 3% in year 6.
- So, the new interest rate could be up to \( 5.25\% + 3\% = 8.25\% \).
c. Calculate the monthly payment for year 6 :
- Use the formula for the monthly payment again with the new interest rate:
[tex]\[ P_r = \frac{8.25\%}{12} = 0.006875 \][/tex]
Plugging into the formula:
[tex]\[ P = \frac{0.006875 \cdot 265000}{1 - (1 + 0.006875)^{-240}} \][/tex]
[tex]\[ P \approx 1985.09 \][/tex]
So, the monthly payment for year 6 is approximately $1,985.09.
d. Find the difference in payments from year 5 to year 6:
[tex]\[ Difference = Payment_{Year6} - Payment_{Year5} \][/tex]
[tex]\[ Difference = 1985.09 - 1645.80 \][/tex]
[tex]\[ Difference \approx 339.29 \][/tex]
So, the difference in payments from year 5 to year 6 is approximately $339.29.
Therefore, the closest answer is C. $369.32 .
Which is the ratio for sin a written as a fraction in simplest form
Answers
your Answer issss:
√3/2