The question requires understanding of real estate value, equity, and mortgage calculations related to buying a house. Freda's equity is the entire value of her house at $250,000. Ben has paid off a portion of his loan and has an equity of $100,000 in his home.
Explanation:The question provided deals with the financial aspects of purchasing a house and understanding real estate value, equity, and mortgage calculations. Helena purchasing a house for $210,000 would fall under the mathematics or business subject area as it involves financial calculations.
Freda's house situation, where she bought a house for $150,000 in cash and its current value is $250,000, tells us that her equity in the property would be the entire value of the house, which is $250,000, since she owes nothing to the bank.
As for Ben, he initially purchased his house for $100,000 and made a 20% down payment. He took a loan from the bank to cover the remaining 80%, later paid off $20,000 of it, and his house value has increased to $160,000. Ben's remaining loan balance would be the original borrowed amount minus what he has already paid back. Since he had taken 80% of $100,000, that would have been $80,000 initially, minus the $20,000 paid, leaves him with a $60,000 debt. The equity that Ben has in his house is the current market value minus the debt, which is $160,000 - $60,000, giving him an equity of $100,000.
In another scenario provided, Joanna is looking to determine how much she can afford in terms of a house loan with yearly payments of $12,000 at an interest rate of 4.2% over a 30-year period. She would need to apply the formula for calculating a mortgage payment and the total amount paid over the course of the loan.
Helena's total monthly payments are approximately $2,361.17. The closest answer choice is C. $2330.20.
Principal and Interest:
Down payment = 5% of $210,000 = $10,500
Loan amount = $210,000 - $10,500 = $199,500
Using a mortgage calculator, the monthly principal and interest payment for a 15-year loan at 4.5% interest on $199,500 is $1595.54.
PMI (Private Mortgage Insurance):
Loan-to-value ratio (LTV) = $199,500 / $200,000 = 99.75%
Based on the table, the PMI premium for a 15-year fixed-rate loan with an LTV of 95.01% to 97% is 0.79%.
Annual PMI premium = 0.79% of $199,500 = $1575.05
Monthly PMI premium = $1575.05 / 12 = $131.25
Property Taxes:
Annual property taxes = 3.5% of $200,000 = $7000
Monthly property taxes = $7000 / 12 = $583.33
Homeowners Insurance:
Monthly homeowners insurance = $600 / 12 = $50
Total Monthly Payments:
Principal and Interest: $1595.54
PMI: $131.25
Property Taxes: $583.33
Homeowners Insurance: $50 Total: $2350.12
Complete Question:
Helena is purchasing a house for $210,000, with a 15 -year fixed-rate mortgage at 4.5% interest. She has made a 5% down payment. The house is valued at $200,000, and the local tax rate is 3.5%. Her homeowners insurance is $600 per year. What are her total monthly payments? (Use the table below to calculate PMI premiums.)
[tex]\begin{tabular}{lcccl} Base-To-Loan\% & \multicolumn{2}{c}{ Fixed Rate Loan } & \multicolumn{2}{c}{ ARM 2\%+1 Year Cap } \\& $30 {yrs}$ & $15 {yrs}$ & $30 {yrs}$ & $15 {yrs}$ \\$95.01 \%$ to $97 \%$ & $0.90 \%$ & $0.79 \%$ & ${n} / {a}$ & ${n} / {a}$ \\$90.01 \%$ to $95 \%$ & $0.78 \%$ & $0.26 \%$ & $0.92 \%$ & $0.81 \%$ \\$85.01 \%$ to $90 \%$ & $0.52 \%$ & $0.23 \%$ & $0.65 \%$ & $0.54 \%$ \\$85 \%$ and Under & $0.32 \%$ & $0.19 \%$ & $0.37 \%$ & $0.26 \%$\end{tabular}[/tex]
A. 2654.23
B. 2894.71
C. 2330.20
D. 2202.72
Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y-3=-1/5(x+2);(-2,7)
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the line
[tex]y-3=-\dfrac{1}{5}(x+2)\to m=-\dfrac{1}{5}[/tex]
If m₁ and m₂ are the slopes of the perpendicular lines, then
[tex]m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
Therefore the slope of ouer line is
[tex]m=-\dfrac{1}{-\frac{1}{5}}=5[/tex]
We have the point (-2, 7). Put the coordinates to the equation of a line in the point-slope form:
[tex]y-7=5(x-(-2))[/tex]
[tex]y-7=5(x+2)[/tex] use the distributive property
[tex]y-7=(5)(x)+(5)(2)[/tex]
[tex]y-7=5x+10[/tex] add 7 to both sides
[tex]\boxed{y=5x+17}[/tex]
PRE CALC PLEASE HELP!!!
Topic: Rational Functions
If f(x)=2x^3-bx^2+cx+12, Were b and c integers, list all possible rational roots of f(x)
Answer: [tex]\bold{\pm \{1, 2, 3, 4, 6, 12, \dfrac{1}{2}, \dfrac{3}{2}\}}[/tex]
Step-by-step explanation:
Q P
f(x) = 2x³ - bx² + cx + 12
Possible rational roots are all of the factors of P divided by all of the factors of Q, including both positive and negative signs.
[tex]\quad \pm \dfrac{\text{factors of P}}{\text{factors of Q}}\\\\=\pm \dfrac{\text{factors of 12}}{\text{factors of 2}}\\\\=\pm \dfrac{1,2,3,4,6,12}{1,2}\\\\=\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \dfrac{1}{2}, \pm \dfrac{3}{2}\\[/tex]
a student phototcopies a drawing without realizing tht the copier is set to enlarge the image by 15%. if the height of the actual drawing is 4.25 inches, approximately how tall is the phototcopied drawing?
If an image is being enlarged by 15% you would take the base number multiply it by the percent in decimal form and add the result to the base number.
4.25*0.15=0.6275
0.6375+4.25=4.8875
Answer: 4.8875
To find out the height of the photocopied drawing, we first calculate 15% of the original height (4.25 inches) and add this to the original height. The photocopied drawing is approximately 4.89 inches tall.
Explanation:The student photocopied a drawing with the copier set to enlarge the image by 15%. If the original drawing is 4.25 inches tall, the enlarged photocopied drawing would be larger by 15% of 4.25 inches.
Firstly, to find 15% of 4.25 inches, you multiply 4.25 by 0.15 (the decimal equivalent of 15%), which equals 0.6375 inches.
Adding this to the original height of the drawing, we get 4.25 inches + 0.6375 inches = 4.8875 inches, which is approximately 4.89 inches when rounded to two decimal places.
So, the photocopied drawing is approximately 4.89 inches tall.
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show that the points p(7,12) and q(-3,-12) and r (14,5) lie on a circle with center c(2,0)
If the points P (7, 12), Q (-3, -12) and R (14, 5) lie on a circle with the center C (0, 2), then the distance OP, OQ and OR are the same.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute:
[tex]OP=\sqrt{(2-7)^2+(0-12)^2}=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OP=13}\\\\OQ=\sqrt{(2-(-3))^2+(0-(-12))^2}=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OQ=13}\\\\OR=\sqrt{(2-14)^2+(0-5)^2}=\sqrt{(-12)^2+(-5)^2}=\sqrt{144+25}=\sqrt{169}\\\\\boxed{OR=13}[/tex]
OP = OQ = OR, therefore the points P, Q and R lie on one circle.
pleasee answer the question in the picture
Answer:
a (5,2)
Step-by-step explanation:
To get to the smiley face, we move 5 units in the x direction from the origin, then we move 2 units up in the y direction (x,y) so the point is at (5,
Solve 100 divided by 5 x 4 + 4³
Answer:
144
Step-by-step explanation:
4 x 4 x 4 = 64
100/5 = 20
20 x 4= 80
80 + 64 =144
Answer:
100 /( 5 x 4 + 4³) = 1 4/21
100 / 5 x 4 + 4³ = 144
Step-by-step explanation:
100 /( 5 x 4 + 4³)
PEMDAS tells us to do what is inside the parenthses
We will do the power in side the parentheses first 4^3 = 64
100 /( 5 x 4 + 64)
Now we will multiply
100/(20+64)
Now we add inside the parentheses
100/84
Divide the top and bottom by 4
25/21
Changing from an improper fraction to a mixed number
1 4/21
OR
100 / 5 x 4 + 4³
If the quantity is not in parentheses
We will do the power first 4^3 = 64
100 / 5 x 4 + 64
Then we do the multiplication and division from left to right
20 *4+64
80+64
144
PLS HELP ASAP
Which equation represents a proportional relationship?
y=32x
y=−2x
y = 4x + 3
y=2(x+1)
The proportional relationship:
y = ax for a > 0.
Therefore your answer is:
y = 32xDianna earns $8.50 an hour working as a lifeguard write an equation to find Dianna’s money earned?
y=8.5x
y= money earned
x= hours worked
The equation to find Dianna's money earned as a lifeguard is e = 8.50h.
To find Dianna's money earned, we can write an equation using the formula for calculating earnings:
Earnings=Hourly Rate × Number of Hours Worked
In this case, Dianna's hourly rate is $8.50, and let's denote the number of hours she worked as ℎ.
So, the equation to find Dianna's money earned
E=8.50×h
Where:
E represents the total earnings
8.50 represents Dianna's hourly rate
h represents the number of hours worked
This equation will give us the total amount of money Dianna earned based on the number of hours she worked.
If a person draws 2 cards at random from a standard deck of 52 cards, what is the probability that they get 2 aces?
Answer:4/52=1/13
Step-by-step explanation:
The deck has 52 cards and contains 4 aces. When you draw a card, the probability of drawing an ace is 4/52=1/13
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.
Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
Let x = the number of packages of pasta and y = the number of jars of pasta sauce.
Identify each point as either a solution to the system or not a solution to the system of inequalities.
(1, 12) Solution or Not a Solution
(2, 10) Solution or Not a Solution
(4, 5) Solution or Not a Solution
(6, 10) Solution or Not a Solution
(12, 8) Solution or Not a Solution
(18, 6) Solution or Not a Solution
Answer:
1,12/ Not a solution
2,10/ solution
4,5/ solution
6,10/ not a solution
12,8/ not a solution
18,6/ not a solution
Step-by-step explanation:
all you have to do is put it into the equation.
for example:
1,12
1x1+12x3= $37
1x1+12x1.5= 19lbs
This is not a solution because he can carry it but doesn't have the money to buy it.
Answer:
(1,12)=no solution
(2,10)=Solution
(4,5)=Solution
(6,10)=no solution
(12,8)=no solution
(18,6)=no solution
Step-by-step explanation:
You have to add the money and pounds each together. For example, the equation you would set up would be, for money: 1(1)=1 and the jars 3(12)=36. Together, it equals 37, which would be over the total amount that Tyler may buy. If you do all of these to show your work, then the answers are the ones shown above.
What is 4:2 the same as
Answer:
4:2 is the same as:
2:1
8:4
or anything that is proportional to 4:2
Step-by-step explanation:
A proportion is anything that corresponds in size or amount to something else.
Answer:
2:1
Step-by-step explanation:
just reduce the ratio b and divivd bith sides by 2
Sneakers normally cost $89.99, but on sale, they are marked down to $56.49. What percent off is the sale price?
Answer:
60%
Step-by-step explanation:
Use the equation a=pw. A= Part P= Percent. W= Whole
A= $56.49
P = x (unknown)
W= $ 89.99
Equation = 56.49=89.99x
You divide 89.99 on both sides to be equal and isolate the variable x. You would divide 56.49 by 89.99 and will get 0.627736415. You would round it to the nearest tenth , 0.6 so the percent is 60%
The percent off is 37.2263 % of the sale price.
What Is Percentage Change?In finance, percentage change is frequently used to denote the percentage-based price change of a stock over time. Depending on whether the change is an increase or a reduction, a simple mathematical formula is employed to quantify this change as a percentage.The most common use of percentage change in finance is to monitor changes in stock and market index prices.Comparing the values of several currencies also involves using change expressed as a percentage.Additionally, balance sheets with comparative financial statements contain percentage change.Depending on whether there is an increase or decrease, there are slight differences in how to calculate percentage change.Calculations :
According to the given conditions, state = 33.5/89.99 Multiply the numerator and denominatorwith the same whole number = 3350/8999
Rewrite a fraction as a decimal = 0.372263Multiply a number for both thenumerator and the denominator = 0.372263 x [tex]\frac{100}{100}[/tex]
Write as a simple fraction = 0.372263 x 100 / 100Calculate the product or coefficient = 37.2263 / 100Rewrite a fraction with the denominatorequal to 100 as a percent = 37.2263 %
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The percent change of 40;50
Answer:
25%
Step-by-step explanation:
Change = Final - initial
% Change =(Final - Initial)/Initial × 100%
% Change = (50 - 40)/40 × 100%
% Change = 10/40 × 100%
% Change = 25%
Answer:
25%
Step-by-step explanation:
1) Find the difference of the two numbers, do (Largest Number)-(Smallest Number).
2) Use your difference as a fraction. Use the difference over the initial value.
3) Create a proportion
10/40 = x/100
4) Cross multiply, 10*100 = 200, 40*p = 40p
5) Simplify expression 1,000=40p
6) Solve, 1,000/40 = 25
7) Put it as a fraction, 25/100
8) Make it a percent 25%
If sinx is approximately 0.2588, what is the measurement of x to the nearest degree? Approximately, what is the cosine of the angle that is complementary to x? A) 15°; 0.2588 B) 15°; 0.9659 C) 75°; 0.2588 D) 75°; 0.9659
Answer:
A
Step-by-step explanation:
given sin x ≈ 0.2588, then
x = [tex]sin^{-1}[/tex](0.2588) ≈ 15°
using the cofunction identity
cos x = sin(90 - x)
the complement of 15° is 90° - 15° = 75°, hence
cos 75° = sin(90 - 75)° = sin15° ≈ 0.2588
What is the eighth term in the arithmetic sequence defined by the explicit formula an=2n+7? Enter your answer in the box.
Answer:
The 8th term is 23
Step-by-step explanation:
If we are given the formula for the sequence
an=2n+7,
then to find the 8th term we substitute n=8 into the formula.
a8 = 2(8) +7
a8 = 16+7
a8 = 23
The 8th term is 23
Find the x-intercepts (solve for x) for the following AND PLEASE SHOW YOUR WORK! y=−2x^2−9x+5
Answer:
see explanation
Step-by-step explanation:
To find the x- intercepts set y = 0, that is
- 2x² - 9x + 5 = 0
To factorise the quadratic consider the factors of the product of the coefficient of the x² term and the constant term that sum to give the coefficient of the x- term.
product = - 2 × 5 = - 10 and sum = - 9
The factors are - 10 and + 1
Use these factors to split the middle term
- 2x² - 10x + x + 5 = 0 ( factor the first/second and third/fourth terms )
- 2x(x + 5) + 1(x + 5) ( factor out (x + 5) )
(x + 5)(- 2x + 1) = 0
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
- 2x + 1 = 0 ⇒ x = [tex]\frac{1}{2}[/tex]
x-intercepts are x = - 5 and x = [tex]\frac{1}{2}[/tex]
write an equation of a line that passes through (3,0) and (6,-3) in slope intercept and point slope form
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (3, 0) and (6, -3). Substitute:
[tex]m=\dfrac{-3-0}{6-3}=\dfrac{-3}{3}=-1[/tex]
The point-slope form:
[tex]y-(-3)=-1(x-6)\\\\\boxed{y+3=-(x-6)}[/tex]
or
[tex]y-0=-1(x-3)\\\\\boxed{y=-(x-3)}[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
From the second point-slope form we have slope-intercept form:
[tex]y=-(x-3)\\\\y=-x-(-3)\\\\\boxed{y=-x+3}[/tex]
What is the decimal equivalent of four over nine ?
Answer: 0.44444444444....
Step-by-step explanation: 4/9 is the same as 4 ÷ 9. 9 does not divide into 4, so we add a 0 and bring down a 0 to get 9 divided by 40. 9 can be multiplied by 4 to get 36, 40 - 36 = 4, bring down another 0, 9 can be multiplied by 4 to get 36, 40 - 36 = 4.... this is a never ending decimal.
What is the equation of the line, in standard form, that passes through (4, -3) and is parallel to the line whose equation is 4x + y - 2 = 0?
answers:
4x - y = 13
4x + y = 13
4x + y = -13
Answer:
The equation of this line would be 4x + y = 13
Step-by-step explanation:
In order to find this equation we must first find the slope of the original line. To do this, we solve the original equation for y.
4x + y - 2 = 0
4x + y = 2
y = -4x + 2
The original slope (the coefficient of x) is -4, which means the new slope will also be -4 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line. Just plug in the numbers and solve for the coefficient.
y - y1 = m(x - x1)
y + 3 = -4(x - 4)
y + 3 = -4x + 16
4x + y + 3 = 16
4x + y = 13
Which steps should be used to compare the fractions 2/9 and 5/6
Answer: you need to get a common denominator.. once you have a common denominator, you can compare numerators to see what is larger..
Step-by-step explanation:
to get the common denominator, you would first see what this would be.. in this case 18, as that's the lowest. then, you would multiply each fraction by 2/2 for first and 3/3 for second, which are just funky looking ones. therefore, D is the correct answer.
Answer:It is C
Step-by-step explanation:In the question it says to COMPARE the fraction.
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a used automobile dealership recently reduced the price of a used compact car by 10 % if the price of the car before discount was $33500 find the discount and the new price
Answer: The new price is $3350.
Answer:
$3350; $30 150
Step-by-step explanation:
Original price = $33 500
Discount = 33 500 × 10 %
Discount = 33 500 × 0.10
Discount = $3350
New price = Original price - Discount
New price = 33 500 - 3350
New price = $30 150
Find the area of this trapezoid. Be sure to include the correct unit in your answer.
Answer:
the area of this trapezoid= 81 square inches
Step-by-step explanation:
To find area of trapezoid , we use formula
[tex]Area = \frac{a+b}{2} * h[/tex]
Where a,b are the base of the trapezoid
h is the height of the trapezoid
Here a= 3 in
b = 15 in
h = 9 in
Plug in all the values in the formula
[tex]Area = \frac{a+b}{2} * h[/tex]
[tex]Area = \frac{3+15}{2} * 9[/tex]
[tex]Area = \frac{18}{2} * 9[/tex]
Area = 9 * 9 = 81
the area of this trapezoid= 81 square inches
Question 1(Multiple Choice Worth 1 points) (02.06 MC) Charles wants to determine which car is the fastest. The actual speed of four cars is shown below: Car A B C D Speed (in km/h) 60.34 60.32 60.33 60.35 If the speedometer can only measure to the nearest tenth of a second, which car will have a different measurement?
Answer:
Car D will have a different measurement because the 60.35 would round up to be 60.31 where all the other would round down and remain at 60.30
Step-by-step explanation:
David sells two calculators for ₹1500 each .He earns a profit of 25% on
one and suffers a loss of 25% on the other. Find his total profit or loss on
the whole deal. Also calculate it as a percentage
Answer:
100% profit of 1500
Step-by-step explanation:
One the first calculator David earns 25% profit:
25% + 1500 = 1,875
He gets a 25% on the second calculator:
1500 - 25% = 1,125
In total he receives 1125 + 1875 = 3000
Therefore he has 100% profit
the first five terms of a sequence are 7,10, 13 , 16 and 19. which of the following functions define this sequence for all integers n>or equal to 1?
A. f[n]= 3n=7
B.f[n]= 4+3n
C. f[n]= 4[3]^n-1
D.f[n]=7[3]^n-1
Answer:
Option B is correct
For [tex]n\geq 1[/tex] , the function for the given sequence is defined as; [tex]f[n] = 4 +3n[/tex]
Step-by-step explanation:
An arithmetic sequence is a sequence in which the difference between each consecutive term is constant.
An explicit formula for this arithmetic sequence given by;
[tex]a_n = a+(n-1)d[/tex] where a represents first term
Since, the given sequences; 7 , 10 , 13 , 16 and 19
⇒ common difference(d) = 3 and a = 7
Since.
10 -7 = 3
13- 10 = 3 ....
The function which defined this sequence is;
[tex]f[n]=a_n = 7 +(n-1)(3)[/tex]
using distributive property:
[tex]f[n] = 7 + 3n -3[/tex]
[tex]f[n] = 4 +3n[/tex]
therefore, the function for the given sequence for all integers [tex]n\geq 1[/tex] is; [tex]f[n] = 4 +3n[/tex]
The correct option is D) f(n) = 4 + 3n.
Step-by-step explanation:
Given :
Arithmetic Sequence -- 7,10,13,16,19
Solution :
The explicit formula of arithmetic sequence is given by,
[tex]T_n = a+(n-1)d[/tex] ------- (1)
where, common difference (d) = 10 - 7 = 3
first term (a) = 7
So from equation (1),
[tex]T_n = 7+(n-1)3 = 7+3n-3[/tex]
[tex]T_n = 4 + 3n[/tex]
Therefore, the correct option is D) f(n) = 4 + 3n.
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Joshua has $34 in his bank account. With his new job, he deposits the same amount each week into the account. After 35 weeks, Joshua has $909. What function can find the amount in Joshua's account after w weeks?
Answer:
f(x) = 34 + 25w
Step-by-step explanation:
First, we need to find the amount he was paid over the 35 weeks:
909 - 34 = 875
35w = 875
w = 875 / 35 = 25
So every week he is paid $25
The function has to start with 34, as that is the amount already in there, and as w is multiplying by 25, this can be written as 25w
So put these two together:
f(x) = 34 + 25w
What is the 33rd term of this arithmetic sequence? 7, 17, 27, 37,47
Answer:
327 FOR A FACTTTTT
Step-by-step explanation:
Answer:
the answer would be 327
Step-by-step explanation:
hope this helps :)
Choose all of the equations that graph as an increasing function.
2
A. y = -- x + 7
3
B. y = -3x - 4
C. y = -5x
D. = 0.05x + 10
Answer:
A. y = -(-x) +7 = x + 7
D. y = 0.05x + 10
five more then -8 times a number is 29. What is the number? Let the mystery number be represented by n.
Answer:
The mystery number is -3
Step-by-step explanation:
five more then -8 times a number is 29.
-8n +5 = 29
Subtract 5 from both sides
-8n +5-5 = 29-5
-8n = 24
Divide by -8 on each side
-8n/-8 = 24/-8
n= -3
The mystery number is -3
The mystery number in the equation is -3, determined by solving the algebraic equation 5 + (-8 × n) = 29.
The equation given in the problem statement translates to the mathematical expression 5 + (-8 × n) = 29, where n is the mystery number. To find the value of n, we can perform the following steps:
Subtract 5 from both sides to get -8n = 24.
Divide both sides by -8 to isolate n, giving us n = 24 / -8.
Calculate the result to find that n = -3.
Therefore, the mystery number is -3.
the sum of two numbers is 53. their difference is 17. Find the numbers.
Answer: the two numbers is 35 and 18
Step-by-step explanation: 35+18=53 35-18=17
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Final answer:
The two numbers are 35 and 18. We found these by solving the simultaneous equations x + y = 53 and x - y = 17, representing their sum and difference.
Explanation:
Finding Two Numbers Given Their Sum and Difference
Let's denote the two unknown numbers as x and y. According to the conditions given:
x + y = 53 (Equation 1: The sum of the two numbers)
x - y = 17 (Equation 2: The difference of the two numbers)
We can solve these two simultaneous equations to find the values of x and y.
Add the two equations:
(x + y) + (x - y) = 53 + 17
2x = 70
x = 35
Substitute x in Equation 1:
35 + y = 53
y = 53 - 35
y = 18
Therefore, the two numbers are 35 and 18.