A married couple would like to examine the potential of using their home equity to borrow funds in order to remodel their kitchen at a cost of $17,000. The couple purchased the home 3 years ago for its market value of $135,000. The interest rate on their 30-year fixed-rate mortgage is 4.25% and they were able to put down a 5% down payment towards the purchase. The market value of the home has grown at 2.5% per year and the current balance owed on the mortgage is $121,478. If the local Credit Union is offering to lend the couple up to 80% of their home equity in the form of a home equity loan to remodel their kitchen, will they be able to borrow the money necessary to complete the project this third year?

Step-by-step explanation:

With this question ,

The length of the rectangle is 3m longer than it's width=3 +w

then the width =w

therefore perimeter= 2L +2w

34= 2(3+w) +2w

34= 6+2w +2w

34-6 = 4w

28=4w

7= w

Area= Length x breadth

Area = (7+3) x7

Area= 10 x7

Area= 70cm square

Answer:

option 1 is correct. that is the answer

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Step-by-step explanation:

As my previous answer got deleted for being wrong (in which it was right), I will answer again.

The answer is 1. Why? Just plug it into the equation. F(1) = 2(1) + 5 = 7.

This is proof that it is right, and that there are some corrupt admins on brainly.

How to get to this solution?

Well notice how we are given what f(a) is. It is 2a + 5. So plug this in for f(a).

If we do so, we get 2a + 5 = 7.

Solving this equation, we get a = 1.

Answer:

i

Step-by-step explanation:

is

coooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooool

Answer:

What tiles need to be added to both sides to remove the smaller x-coefficient?

✔ 5 negative x-tiles

What tiles need to be added to both sides to remove the constant from the right side of the equation?

✔ 4 negative unit tiles

What is the solution?

✔ x = –6

Step-by-step explanation:

Answer:

5.49

Step-by-step explanation:

3+ 51= 54                  

54 x 1/10= 5.4    + 9 x 1/100

5.4 + 0.09=

5.49    

Answer: Step-by-step explanation:

To find the average rate of change of a function over an interval, we can use the following formula:

average rate of change = (y2 - y1)/(x2 - x1)

Where x1 and x2 are the values of x at the beginning and end of the interval, and y1 and y2 are the corresponding values of the function at those points.

In this case, we are asked to compare the average rate of change of the functions g(x) and f(x) over the interval where -1≤x≤3.

For the function g(x) = x²+6x, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (g(3) - g(-1))/(3 - (-1))

= (9 + 18 - (1 - 6))/(4)

= 27/4

= 6.75

For the function f(x) = 2, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (f(3) - f(-1))/(3 - (-1))

= (2 - 2)/(4)

= 0

Since the average rate of change of the function g(x) is greater than the average rate of change of the function f(x), the function g(x) has a greater average rate of change over the interval where -1≤x≤3.

I hope this helps clarify the comparison of the average rate of change for these two functions. Do you have any other questions?

Purring. Although purring can mean a number of things, you can be sure that when your cat is curled up on your lap purring, they're expressing their love and contentment with you. ...

Answer:

The height is 15 m.

Step-by-step explanation:

V = (pi)r^2h

375(pi) = (pi)(5^2)h

Divide both sides by 25pi.

15 = h

Answer: The height is 15 m.

Answer:

137

Step-by-step explanation:

Given the following :

Margin of Error (E) = 7% = 0.07

Confidence level = 90% = 0.9

Prior study (p) = 54% = 0.54

Using the sample size formula:

([Z/E]^2) × p × (1 - p)

(1 - p) = 1 - 0.54 = 0.46

Z score at 90% confidence interval. = 1.645

[(1.645 / 0.07)^2] * 0.54 * 0.46

(23.5^2) * 0.54 * 0.46

552.25 * 0.54 * 0.46

= 137.1789

= 137

Sample size = 137

The volume of the snowball is decreasing at the rate of 502.56cm/min when the radius is 10 cm.

The volume of a sphere is given by the following equation:\(\frac{4\pi r^{3} }{3} ^{}\)

We have to do the implicit differentiation of V in function of t. The are only two variables(V and r). So

\(\frac{dv}{dt} = \frac{4\pi }{3} 3r^{2} \frac{dr}{dt}\)

\(\frac{dv}{dt} = 4\pi r^{2} \frac{dr}{dt}\)

We have to find\(\frac{dv}{dt} when\) \(\frac{dr}{dt} = - 0.4\)     r = 10

\(\frac{dv}{dt} = 4\pi (10)^{2} \times -0.4\)

\(\frac{dv}{dt} = -502cm/m\)

The negative means that the volume is decreasing.

So the answer is 502.56 cm/min.

Volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, cuboid, cone, cylinder or sphere.

Different shapes have different volume. In 3D geometry, we studied various three-dimensionally defined shapes and solids such as cubes, cubes, cylinders, cones, etc. For each of these shapes, we learn to find volume.

The volume of a solid substance is measured in cubic units. For example, if the dimensions are given in meters, the volume is in cubic meters. It is a standard unit of volume in the International System of Units (SI). Similarly, other units of volume are cubic centimetre, cubic meter, cubic meter, etc.

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The solution of the expression \(\sqrt{z^4\times z^{\frac{-3}{2}}\) will be z⁵.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The expression will be solved as:-

\(E = \sqrt{z^4\times z^{\frac{-3}{2}}\)

\(E = \sqrt{(z)^{4- {\frac{3}{2}\)

E = z⁵

Therefore, the solution of the expression is z⁵.

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The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

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Answer:

\(\$1320\)

Step-by-step explanation:

Let \(x\) be the number of units of A

\(y\) be the number of units of B

For assembling we have

\(20x+25y\leq 3000\)

For packaging we have

\(10x+5y\leq 1200\)

Let profits earned be \(Z\) so

\(Z=10x+8y\)

We have the maximize the function.

Plotting the equations we can see that the intersection points are \((0,120),(100,40),(120,0)\)

In the question it is mentioned we have to sell both the products so \(x\) or \(y\) cannot be \(0\).

So, the point of maximiztion for the function would be \((100,40)\)

The maximum profit would be

\(Z=10\times 100+8\times 40\\\Rightarrow Z=1320\)

Answer:

123fffdew2rfgg

Step-by-step explanation:

ggewrffd

Answer:

Method 1 = 8.75

method 2 = 12.16

Hope this helped gll

Step-by-step explanation:

Answer:

the answer is 12

Step-by-step explanation:

In short, a = 6 and b = 6. We can make a table of various values to help confirm that 12 is the smallest sum.

Answer: 1

Step-by-step explanation: 1 is the least possible answer because an integer is any number and 1x36 would be the least possible answer for the product.

Step-by-step explanation:

I hope this answer is helpful ):

The Amy has 42 books, Betty has 36 books, and Carol has 18 books.

Let's set up equations to represent the given information:

Let A represent the number of books Amy has.

Let B represent the number of books Betty has.

Let C represent the number of books Carol has.

Let's say Amy has x books.

Betty has 6 books less than Amy, so Betty has (x - 6) books.

Carol has half as many books as Betty, so Carol has (x - 6)/2 books.

According to the problem, the total number of books they have is 96.

So, we can write the equation:

x + (x - 6) + (x - 6)/2 = 96

To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:

2x + 2(x - 6) + (x - 6) = 192

2x + 2x - 12 + x - 6 = 192

5x - 18 = 192

5x = 210

x = 42

Amy has 42 books.

Betty has (42 - 6) = 36 books.

Carol has (36)/2 = 18 books.

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The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

This may sound wrong or confusing but I have a cousin in college and he said that it should be 3-6!

Answer:

-2x+11y+12

Step-by-step explanation:

combine like terms

Answer:

1/15

Step-by-step explanation:

1/10✖️ 2/3=1/15

Answer:

10 tenths make a one

Step-by-step explanation:

because it works like dimes making a dollar you need 10 of them to make a dollar, and they are in the tenths position.

Answer:

ten tenths

Step-by-step explanation:

10/10 = 1

Hope this helps

Answer:

12

Step-by-step explanation:

n(AUB) = n((A) + n(B) – n(AnB)

Step 1:

Identify the values for each function of the formula. n(A) = 10, n(B) = 5, n(AnB) = 3

Step 2:

Replace each function with its values

n(AUB) = n(A) + n(B) – n(AnB)

n(AUB) = 10 + 5 – 3

Step 3:

Carry on the simple arithmetic

n(AUB) = 10 + 5 – 3 (follow the BODMAS method)

= 15–3

= 12

Therefore, the n(AUB) is 12

Answer:

6xy

Step-by-step explanation:

If the table is linear the first difference will be same, if the table is quadratic the second difference will be same and if the table is exponential the ratio will be constant

If the table is a linear model

The general form of such function will be

y = mx + b

Where m is the slope of the line

b is the y intercept

So if the table is linear it will have a constant first difference

But if the table is a quadratic function then the function has constant second difference

The general form of the exponential function will be

f(x) = a^x

Where a is the constant

x is the variable

Therefore if the table is exponential it will have constant ratio

Hence, the linear table have constant first difference, the quadratic table have constant second difference and the exponential have constant ratio

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