Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.

Several years ago Bill got a home mortgage of $116,000 with a term of 30 years at an APR of 9%. Use the Monthly Payments for Long-Term Loans Rule of Thumb to estimate his monthly payment.
$


Compare this estimate with what the monthly payment formula gives. (Round your answer to the nearest integer.)
The actual monthly payment is about $
greater than the estimated payment.

The value of f(1/2) for the given function f(x) = -3(4x² + 12) + 3/4(8x) - 2x is:  -37. (None of the options are correct).

If given a function, to evaluate the function for a given value of x, input the value of x in the equation and solve to evaluate the function.

Given the function, f(x) = -3(4x² + 12) + 3/4(8x) - 2x, to find the value of f(1/2), substitute x = 1/2 into the equation:

f(1/2) = -3(4(1/2)² + 12) + 3/4(8(1/2)) - 2(1/2)

Evaluate

f(1/2) = -3(4(1/4) + 12) + 3/4(4) - 1

f(1/2) = -3(1 + 12) + 3 - 1

f(1/2) = -3(13) + 2

f(1/2) = -39 + 2

f(1/2) = -37

The value of the function f(1/2) is: -37. (none of the given options are correct).

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g(x) is a dilation of scale factor 1/2 of f(x), and the rule is:

g(x) = 2x + 3

Here we have the function f(x) = 4x + 6 and the function g(x) that is defined as:

g(x) = (1/2)*f(x)

So g(x) is a vertical dilation of scale factor k = 1/2 of f(x).

Replacing f(x) in there we get:

g(x) = (1/2)*(4x + 6) = (4/2)*x + 6/2 = 2x + 3

The rule for g is:

g(x) = 2x + 3

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Using proportions, the amounts are given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.

One example of application is for percentage problems, as the equivalent amount can be found multiplying the equivalent decimal by the total amount.

The amount of Federal Income Tax Withholding each month is given by:

0.2 x 3500 = $700.

The amount of State Income Tax Withholding each month is given by:

0.12 x 3500 = $420.

The amount of Social Security Tax Withholding each month is given by:

0.0825 x 3500 = $288.75.

The amount contributed to the 401k each month is:

0.04 x 3500 = $140.

The take-home pay for the month is the $3,5500 subtracted by all the with holdings, hence:

3500 - (700 + 420 + 288.75 + 140) = $1,951.25.

A year has 12 months, hence the take-home pay for the year is given by:

12 x 1951.25 = $23,415.

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Answer: the property needed to find this is negative exponents

Step-by-step explanation: find the reciprocal of g to the -7th power which would be 1 over g to the 7th power

Check the picture below.

Therefore Option B is correct

Answer:

7-x

Step-by-step explanation:

If one piece is x, and the whole is 7, the missing piece would be 7-x

Hope this helps :)

The equation to determine the number of players the team can bring is $842.50 + $21.50y = $1,186.50

The team can bring 16 players to the tournament.

To go to a tournament, softball team members raised $1186.50 and rented a bus for $842.50, and the cost of meals of each player is $21.50.

Let y represent the number of players.

$842.50 + $21.50 × y = $1,186.50

$842.50 + $21.50 × y = $1,186.50

$842.50 + $21.50y = $1,186.50

Subtracting $842.50 from each side.

$21.50y =  $1,186.50 - $842.50

$21.50y =  $344

Divide both side of the equation by $21.50.

x = $344 / $21.50

x = 16 players

As a result, the team is allowed to enter 16 players into the competition.

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Answer:

I hope the deadline hasn't passed!

Your last question got deleted

Answer is;

Using a system of equations, a possible set of values for a, b and c such that it results in an integer number is given by:

a = 6, b = 3, c = 2.

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.

In the context of this problem, the variables are the given ones of:

a, b and c.

An integer number is a number that has no decimal part, hence the easiest way to solve this is making the sum of 1.

Attributing a = 6, we have that:

[tex]\frac{1}{6} + \frac{1}{b} + \frac{1}{c} = 1[/tex]

[tex]\frac{1}{b} + \frac{1}{c} = \frac{5}{6}[/tex]

This is possible with these two fractions:

[tex]\frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6} = \frac{5}{6}[/tex]

Hence the other possible values are given by:

b = 2, c = 3.

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Given: The system of equations below...

To Determine: The value of x and y

Using substitution method, Substitute for y in the second equation

Substitute for x in the first equation to solve for y

ence,

x = -4; y = -10

G

The given quadrilateral RSTV is a kite.

The following characteristics apply to quadrilaterals, which are polygons.

To classify the quadrilateral calculate the length of its sides using the distance formula given as follows:

[tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }[/tex]

In the given quadrilateral RSTV,

RS = [tex]\sqrt{(2 - (-5))^{2} + (6 - 7)^{2} }[/tex] = [tex]\sqrt{50 }[/tex]

RV = [tex]\sqrt{(-4 - (-5))^{2} + (0- 7)^{2} }[/tex] = [tex]\sqrt{50}[/tex]

ST = [tex]\sqrt{(5 - 2)^{2} + (-3- 6)^{2} } = \sqrt{90}[/tex]

VT = [tex]\sqrt{(-3 - 0)^{2} + (5- (-4))^{2} } = \sqrt{90}[/tex]

The two adjacent sides of the quadrilateral are equal i.e. RS = RV and ST = VT.

A kite is a quadrilateral with two pairs of sides that are both the same length and are next to one another.

Therefore, the quadrilateral is a kite.

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Answer:

option 3

It has a zero a set of whole no has 0 in it and it start after the no 3 as it says GREATER then 3.

Answer:

they filter the air coming into the body

Step 1. Find the volume of just one box.

To find the volume V of one box, we multiply all of the dimensions of the box:

In this case, the volume of one box is:

The result is:

Step 2. We are told that Ying bought 12 boxes, so the total volume that the boxes occupy will be the volume of one box multiplied by 12:

Answer:

An estimated answer is 237.44 and the exact answer is 237.475.

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Answer:

[tex]y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]

Step-by-step explanation:

The genera slope-intercept equation of a line is

y = mx + 8 where m is the slope and b the y-interecept

A perpendicular line will have a slope = -1/m ie the negative of reciprocal of the first line such that m x (-1/m ) = -1

The equation of the tangent line is

3x + 2y = 28.

1. Convert to slope-intercept form:

So slope = -3/2

Reciprocal of -3/2 = -2/3
Negative of reciprocal = +2/3

Slope of a perpendicular line should be -1/3 and the resultant equation of the line(the support arm) should be:

y = (2/3)x + b

To calculate b for the complete line equation plug in the point B(4, 8) and solve for B

y = 8 when x = 4

=> 8 = (2/3)(4) + b

Switch sides: (does not change any signs)
8/3 + b = 8

Subtract  8/3 on both sides
b =  8 - 8/3

b = 24/3 -  8/3

b = 16/3

So equation of the support arm is

[tex]\boxed{y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]

1) [tex]m\angle A=76^{\circ}[/tex] (given)

2) [tex]m\angle B=76^{\circ}[/tex] (base angles theorem)

3) [tex]m\angle BCA=28^{\circ}[/tex] (sum of angles in a triangle)

4) [tex]m\angle ECD=28^{\circ}[/tex] (vertical angles)

5) [tex]m\angle DEC=90^{\circ}[/tex] (perpendicular lines)

6) [tex]m\angle D=62^{\circ}[/tex] (sum of angles in a triangle)

Answer:

d 144

Step-by-step explanation:

Each number is the square starting with 10

10² = 100

11² = 121

12² = __?
13²=169

The real zeros of the following function [tex]$\quad f(x)=\left(x^4-16\right)\left(x^2+3 x-18\right)$[/tex] are

2,-2,3,-6, and the graph is attached below

This is further explained below.

[tex]$\quad f(x)=\left(x^4-16\right)\left(x^2+3 x-18\right)$[/tex]

as we know the formula a^2-b^2=(a-b)(a+b)

[tex]\begin{aligned}x^4-16 &=\left[\left(x^2\right)^2-(4)^4\right]=\left(x^2-4\right)\left(x^2+4\right) \\&=\left((x)^2-(2)^2\right)\left(x^2+4\right) \\x^4-16 &=(x-2)(x+2)\left(x^2+4\right)\end{aligned}[/tex]

substituting it in equation (1) we get.

[tex]\begin{gathered}f(x)=(x-2)(x+2)\left(x^2+4\right)\left(x^2+3 x-18\right) \\\\\left(x^2+3 x-18\right)=x^2+6 x-3 x-18=x(x+6)-3(x+6) \\\\f(x)=(x-2)(x+2)(x-3)(x+6)\left(x^2+4\right) \\\\x^2+4=(x+2 i)(x-2 i)=\left[(x)^2-(2 i)^2\right] \\\\f(x)=(x-2)(x+2)(x-3)(x+6)(x+2 i)(x-2 i)\end{gathered}[/tex]

Real zuoes =2,-2,3,-6

imaginary zuroes =2 i,-2 i

In conclusion, In the question, we have to answer the real zeroes of the function f(x)

which is 2,-2,3,-6

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From the figure of triangles, scale factor of A and B, the value of x = 3

According to the question, given that

when two triangle are same, then we easily get missing value x

From the figure, two triangle are similar in it thus,

[tex]\frac{x}{1}[/tex] = [tex]\frac{9}{3}[/tex]       {property of triangles which are similar}

x = [tex]\frac{9}{3}[/tex] .

x = 3

Therefore, we get scale factor of triangle A and B, the missing value of missing x = 3.

Scale factor is the proportion of an original object's scale to a new one that is a representation of it but is a different size (bigger or smaller).

For example, if we have a rectangle of sides 4 cm and 6 cm, we can enlarge it by multiplying each side by a number, say 4. The new figure we get will be similar to the original figure, but all its dimensions will be twice that of the original rectangle.

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We can conclude that the position of the number -7 in the provided Venn diagram is incorrect as -7 is an integer but, not a whole number.

Integers:

As we can read the definitions whole numbers do not include negative numbers and integers do include negative numbers, so we can conclude that the number -7 in the given Venn diagram is not in the correct location.

Therefore, we can infer that the position of the number -7 in the provided Venn diagram is incorrect as -7 is an integer but, not a whole number.

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The image of the point is (0, -5) after applying the geometric transformation, the answer is (0, -5).

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that:

The point is (0, 5)

As we know, the

The rule for the above transformation:

(x, y) → (-x, -y)

(0, 5) → (0, -5)

Thus, the image of the point is (0, -5) after applying the geometric transformation, the answer is (0, -5).

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When two lines are perpendicular, their slopes have the following relation:

If we rewrite this expression, we have:

The product of each slope is equal to -1.

Therefore the correct option is the fourth one.

The most appropriate choice for percentage will be given by- Percentage change in cost = 37.09 %

What is percentage?

A number or ratio which can be expressed as just a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a portion per hundred. Per 100 is what the word percent means. The letter "%" stands for it. As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any subject have been calculated in terms of percentages in academics. Ram, for instance, scored 78% on his final exam. This rate is computed based on Ram's overall grade point average (GPA) across all subjects.

For example 2% means [tex]\frac{2}{100}[/tex].

Here,

Cost last year = 24500

Cost today = 14300

Change in cost = 24500 - 14300

                         = 10200

Percentage change in cost = [tex]\frac{10200}{24500} \times 100[/tex]

                                              = 37.09 %

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Given the function f(x):

We will find the point on the given parabola where the slope of the tangent is horizontal

The horizontal line has a slope = zero

The slope of the line is the first derivative of the function

So, we will find the first derivative and equate it to zero

solve the equation to find (x):

substitute with the value of (x) into the given function to find the y-coordinate

So, the answer will be the point will be as follows:

See the following figure:

Value of p for given inequality of three fourths times p plus 8 is greater than or equal to 3 is p is greater than or equal to negative twenty over three.

As given in the question,

Given inequality:

Three fourths times p plus 8 is greater than or equal to 3 is written as

(3/4)p + 8 ≥ 3

Simplify inequality to get the value of p

  (3p + 32)/4 ≥ 3

⇒ 3p + 32 ≥ 12

⇒ 3p ≥ 12 -32

⇒ 3p ≥ -20

⇒ p ≥ -20 /3

Therefore, value of p for given inequality of three fourths times p plus 8 is greater than or equal to 3 is p is greater than or equal to negative twenty over three.

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In order to find what factors could represent the length and the width, we need to factor the polynomial that represents the area.

To do so, first let's find the zeros a1 and a2, then we can factor as follows:

Where k is the coefficient of the quadratic term (so k = 12).

Using the quadratic formula, we have:

Then, we have:

Therefore the factors are 2a-1 and 6a+5.