8. charlotte is purchasing a $90,000 house with a 30-year fixed-rate mortgage
that has an interest rate of 8.9%, and she will be making a down payment of
$9000, or 10% of the purchase price, so her mortgage will be for $81,000. the
house has been assessed at $88,000, and the property tax rate in charlotte's area
is 1.35%. charlotte will make monthly pmi payments for the first two years of the
mortgage based on the following table.
charlotte wants to know how much she will pay in total per month for the first
two years of the mortgage. let's calculate the amount for charlotte by answering
the following questions.
part i: how much will charlotte owe in principal and interest each month?
part ii: how much will charlotte owe in property taxes each month?
part iii: what are charlotte's monthly pmi premiums?
part iv: how much will charlotte pay in total per month for the first two years of
the mortgage?

The rule for g is g(x) = (-2x - 10)(√(x² - 2)) for the function g(x) = -2f(x+5).

One way to think of a function is as a rule that assigns or maps each member of a set, x, to the same value, y, known as its image.

x → Function → y

Functions are frequently denoted by a letter, such as f, g, or h. F(x) = x2+ 5 is the formula for the function that squares a number and adds a 3. A function's impact on specific values can be demonstrated using the same idea.

Given that  f(x) =  √(x² - 2)

And g(x) = -2f(x+5)

Substitute the function f(x) =  √(x² - 2) in g(x) = -2f(x+5)

g(x) = -2(√(x² - 2))(x+5)

g(x) = (-2x - 10)(√(x² - 2))

Thus, the rule for g is g(x) = (-2x - 10)(√(x² - 2)) for the function g(x) = -2f(x+5).

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The third one will represent a linear relationship between x and y.

What is a linear relationship?

A linear relationship is any relationship between two variables that creates a line when graphed in the xy-plane.

Linear equations can be used to represent the relationship between two variables, most commonly x and y. To form the simplest linear relationship, we can make our two variables equal:

y=x

By plugging numbers into the equation, we can find some relative values of

x and y.

0        0

1         1

2        2

3        3

If we plot those points in the xy-plane, we create a line.

Now,

For the given graphs only the third one shows a straight line made from equations.

Hence, It represents the linear relationship between x and y.

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Answer: look it up

Step-by-step explanation:

The probability of a random variable x being greater than 43 if it is normally distributed with a mean of 50 and a standard deviation of 7 is 0.22662735237686885.

The formula for the normal distribution is:

P(x) = 1/(sqrt(2*pi*o^2)) * e^(-(x-u)^2/(2*o^2))

where u is the mean and o is the standard deviation.

For the first part, we have u = 50 and o = 7.

So, P(x>43) = 1/(sqrt(2*pi*7^2)) * e^(-(43-50)^2/(2*7^2)) = 0.22662735237686885

For the second part, we have u = 81 and o = 4.

So, P(x<76) = 1/(sqrt(2*pi*4^2)) * e^(-(76-81)^2/(2*4^2)) = 0.8413447460685429

The probability of a random variable x being greater than 43 if it is normally distributed with a mean of 50 and a standard deviation of 7 is 0.22662735237686885. Similarly, the probability of a random variable x being less than 76 if it is normally distributed with a mean of 81 and a standard deviation of 4 is 0.8413447460685429. This can be calculated using the formula for the normal distribution, which is P(x) = 1/(sqrt(2*pi*o^2)) * e^(-(x-u)^2/(2*o^2)), where u is the mean and o is the standard deviation.

the complete question is : Assume the random variable x is normally distributed with mean u = 50 and standard deviation o = 7.

Find the indicated probability. P(x >43) P(x>43)=

Assume the random variable x is normally distributed with mean u = 81 and standard deviation = 4.

Find the indicated probability. P(x <76) P(x<76)= 0.8413447460685429

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Answer:

[tex]m\angle 1=67^{\circ}[/tex]

Step-by-step explanation:

By the inscribed angle theorem, [tex]m\angle 1=21^{\circ}+46^{\circ}=67^{\circ}[/tex].

This is because the sum of the measures of a pair of supplementary angles is always 180°. Therefore, the measure of the original angle is 93.4° and the measure of its supplementary angle is 180°.

Plagiarism is the practice of taking someone else's work or ideas and passing them off as one's own. Plagiarism can take many forms, including: copying word-for-word, copying ideas or facts without providing a citation or reference, or paraphrasing someone else's words or ideas without providing a citation or reference. It can be intentional or unintentional, and it is considered a form of academic dishonesty.

The measure of the original angle is 86.6° less than the measure of its supplementary angle. This means that the measure of the original angle is 180° - 86.6° = 93.4°. The measure of the supplementary angle is 180°.

This is because the sum of the measures of a pair of supplementary angles is always 180°. Therefore, the measure of the original angle is 93.4° and the measure of its supplementary angle is 180°.

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The equation is true when putting parentheses. The equation becomes:

(5 - 3)(-1 + 6)² = 50.

What is an equation?

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

The given equation is 5 - 3 - 1 + 6² = 50.

Here we need two parentheses.

Since 50 can be written as 50 = 25 × 2 = 5² × 2

Now 2 can be written as (5-3) and 5 can be written as (-1+6).

Now put the parentheses:

(5 - 3)(- 1 + 6)²

= 50

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Answer:

1 1/2 cups of flour.

Step-by-step explanation:

You can work this as a proportion:

1/4 cup → 1/6 of a cake

x cups  → 1 cake

Cross-multiply.

(1/4 cup)(1 cake) = (x cups)(1/6 cake)

Solve for x.

x = 6(1/4) = 1 1/2 cups

The fraction of Miriam’s budget would be left for food/dining if Miriam follows these guidelines is 1/7.

The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

From the information, 2/7 of the budget will be spent on lodging.

The amount spent on sightseeing will be twice as much as the amount spent on lodging. This will be:

= 2 × 2/7

= 4/7

The fraction of Miriam’s budget would be left for food/dining if Miriam follows these guidelines will be:

= 1 - (2/7 + 4/7)

= 1/7

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Answer:

One

Step-by-step explanation: Anything that has the exponent of 0 will always be 1

The angles m∠GFH and m∠HFJ are complementary angles and the correct option for the measure of angle m∠GFH is equal to 61.9°.

In geometry, if two angles are said to be complementary, then the total of their sum is equal to 90°

From the question, we have that the complementary angle m∠HFJ = 28.1° so;

m∠GFH + m∠HFJ = 90°

m∠GFH + 28.1° = 90°

m∠GFH = 90° - 28.1°

m∠GFH = 61.9°

Therefore, the measure for the complementary angle m∠GFH is equal to 61.9°

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The rule for any number raised to the power of 1 is that the number remains unchanged.

Mathematically, this can be written as: a^1 = a where "a" is the base number. The rule for a number raised to the power of 1, is also known as the exponent.

For example, if we take the number 2, and raise it to the power of 1, we would get:

Key points:

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we can find out the domain of a given function by looking at the values of real number where the function f(x) i defined

range can be find out by putting the values of x and find out the values of y and y will be your range of a given function f(x)

let us take an example

suppose f(x)= x+1

here function is defined for all real values

therefore domain is real number

and range is also real number because if we take the value of x whatever we will take we get the value of y

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The statement best describes where she should attach each triangle is perpendicular bisectors intersect.

When perpendicular bisectors overlap, the sentence best indicates where she should join each triangle. A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Here,

When perpendicular bisectors overlap, the sentence best indicates where she should join each triangle.

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Answer:

Dimensions are 12 , 6

Step-by-step explanation:

      Let the length be 'x' miles.

                   width = (x - 6) miles

 Area of a rectangle = length * width

       x *(x -6) = 72 square miles

       x*x - x *6 = 72

     x² - 6x -72 = 0

Sum = -6

Product = -72

Factors = -12 , 6   { -12 * 6 = -72  & -12 + 6 = -6}

x² - 12x + 6x - 72 = 0       {Rewrite the middle term using the factors}

x(x - 12) +6(x - 12)=0

(x -12)(x + 6) =0

x - 12 = 0 ;

    x = 12

{x + 6= 0 is ignored, as dimensions will not have negative value}

length = 12 miles

widht = 12 - 6 = 6 miles

Que knows that the required hypotenuse of the given right triangle is 18.35 units from the Pythagorean theorem.

To determine the undiscovered side of a right-angled triangle, utilize the Pythagoras theorem.

The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c2 = a2 + b2, where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.

So, we have:

Height of 6 and bas of 9 units of the right triangle.

Pythagorean formula:

c=√a²+b²

Now, insert values and calculate as follows:

c = √a²+b²

c = √9²+16²

c = 18.35 units

Therefore, we know that the required hypotenuse of the given right triangle is 18.35 units from the Pythagorean theorem.

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Complete question:

A right triangle has a base of 9 and a height of 16. Calculate hypotenuse.

 y = 4x - 8 is linear equation .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Linear equations with two variables, and so forth, are what the equation is known as if it has two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and x + y = 2. Another example is 3x - y + z = 3.

(0,-8) and (2,0)

 m = 0 - (-8)/2 - 0

      = 8/2 = 4

y - (-8) = 4 ( x - 0)

 y + 8 = 4x

  y = 4x - 8

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The solution to the inequality is m ∈ (2, 9)

What is the Compound inequality?

A compound inequality is an inequality that contains two or more conditions that must be met simultaneously. It is formed by connecting two or more simple inequalities using the words "and" or "or". The word "and" indicates that all the conditions must be true at the same time, while the word "or" indicates that at least one of the conditions must be true.

The compound inequality "m - 3 < 6 and m + 2 > 4" can be read as "m is less than 6 and 3 less than m and m is greater than 4 and m is 2 more than 4".

To solve the inequality, we can start by isolating the variable on one side of the inequality sign.

m - 3 < 6 => m < 9

m + 2 > 4 => m > 2

The solution is the set of all m that satisfies both inequalities, which is the intersection of the solution sets of each inequality. In this case, it is the set of all real numbers m such that 2 < m < 9.

Hence, the solution to the inequality is m ∈ (2, 9)

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Answer: No, the correct answer is 125/100

Step-by-step explanation:

When adding fractions together the denominator must always be the same and stay the same when added together.

Consider that the denominator is not zero. The formula that results from simplifying will equal  -n-5/2n(1+3n).

A fraction is divided by multiplying its reciprocal:

6n²-23n+7/8n3-28n2.

2n²-10n/1-9n²

Factoring the phrase: 6n²-23n+7/4n²(2n-7). 2n(n-5)/1-9n²)

A2-b2=(a+b)(a-b) (3n-1) (2n-7)/4n² can be used to factor the expression (2n-7).

2n(n-5)/(1+3n)(1-3n)

By eliminating the most prevalent element, reduce the proportion to its lowest term. 3n-1/4n²

2n(n-5)/(1+3n)(1-3n)

Purge the expression of all except the lowest word Write 1/2n as a single fraction: -n-5/2n(1+3n)\s-n-5/2n(1+3n).

In general, a fraction with a zero denominator cannot have a single value given to it; therefore, the value is left undefined.

Any definitional attempt results in a contradiction, which is why the outcome of a division by zero is not defined. a=r*b. r*0=a. (1) However, r*0=0 for any r, hence unless a=0, there is no solution to the problem (1).

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·

Prime multiples of number 3 is number 3 itself as other multiples of three are representing composite numbers.

As given in the question,

Given number is equal to :

3

Multiples are those numbers which we get when we multiply the given number by any other integer.

Multiples of three are equal to :

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

3 × 5 = 15

............... so on.

When we multiple 'n' by three we get 3n.

All other multiples have more than two factors that is one , three , and at least number itself.

So other multiples of three are composite numbers.

Prime multiples has only two factors one and number itself.

3 represents the prime multiple.

Therefore, three is the only number which is the prime multiple of 3.

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No, These both expressions are not equal to each other.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expressions are,

⇒ 12(8y - 16k) and 16(2y - 4k)

Now, We can check both expressions as;

⇒ 12 (8y - 16k)

⇒ 12 × 8 (y - 2k)

⇒ 96 (y - 2k)

⇒ 16 (2y - 4k)

⇒ 16 × 2 (y - 2k)

⇒ 32 (y - 2k)

Thus, We get;

⇒ 96 (y - 2k) ≠ 32 (y - 2k)

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3x² is a second-degree polynomial, also known as a quadratic equation.

A polynomial is a mathematical expression that consists of constants, variables, and exponents. This polynomial can be represented as an equation in the form of ax^2 + bx + c, where a, b, and c are constants, and x is an unknown. In this case, a = 3, b = 0, and c = 0. In this case, the polynomial is 3x², which contains one constant (3) and one variable (x) with an exponent of 2. To calculate the value of this polynomial, we can substitute a value for x and then solve. For example, if x=2, then 3x² = 3x2 = 3(2)2 = 3(4) = 12.

Therefore, when x=2, 3x² = 12.

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Answer:

B. 0.25

Step-by-step explanation:

There are 8 total pieces.

2 of them are green.

that makes it a 2/8 chance it will land on green.

2/8 = 1/4

1/4 = 0.25

Answer:

B. 0.25

Step-by-step explanation:

There are 8 possible landing areas, all with equal size.

There are 2 green area.

p(event) = (number of desired outcomes)/(number of total outcomes)

The desired outcome is landing on green. There are 2 desired outcomes.

The total number of possible outcomes is 8.

p(green) = 2/8 = 1/4 = 0.25

Answer: B. 0.25

To get the simplified form of the algebraic expression x²+ y², we need to subtract -2xy from the expression x² +y²-2xy.

To subtract 2xy from the expression x² + y² - 2xy and get x² + y², you can simply remove the -2xy term. This is because subtracting 2xy is the same as adding -2xy, which is the same as negating 2xy and keeping it in the same position.

The reason for this is that subtracting a number is the same as adding its opposite. In this case, -2xy is the opposite of 2xy, so when you subtract 2xy, you are effectively adding -2xy.

Therefore, x² + y² - 2xy and x² + y² are equivalent expressions, since they both represent the same mathematical value.

In mathematical terms:

x² +y²-2xy = x²+ y² +2xy

In other words, the subtraction of 2xy is a commutative operation and the order of the terms does not matter. If you add or subtract the same value, it does not change the final result.

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The absolute value (Modulus) of a number is the distance of the number from zero.

Absolute value is always acting for in the modulus(|z|) and its value is always positive.

So, the absolute value of the complex number is Z = a + ib is |z| = √ (a2 + b2).

Now, the absolute value of the complex number is the positive square root of the sum of the square of the real part and the square of the unreal part, i.e.,

The complex number is defined as the number in the form a+ib, where a is the real part while ib is the unreal part of the complex number in which i is known as iota and b is a real number.

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In shown regular hexagon, all of the transformations that carry the hexagon onto itself are, 180° rotation counterclockwise and reflection in 'l'. So Options D,E,F are correct.

It is a type of  polygon, which has 6 equal sides and all the interior angles are 120°.

Given that,

We have one hexagon and axis of rotation l,

lets check the given options

A.  at 60° rotation clockwise it makes certain angle from the initial position, it will not onto itself

B.  at 60° rotation counter-clockwise it makes certain angle from the initial position, it will not onto itself

C.  at 90° rotation counter-clockwise and 180° rotation clockwise it makes 90° angle from initial position, it will not onto itself

D. 180° rotation counter-clockwise it will be in same plane of original position. So it will onto itself

E. Reflection in L  again it will be in same plane, So it will onto itself

F. Reflection in L and 180° rotation counter-clockwise gain it will be in same plane, So it will onto itself

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The expression of an exponential function f that has a slope of 12 of a line from the point (0, f(0)) to the point (2, f(2)) is the exponential function;

An exponential function is a function that includes the argument as an exponent, index or power of a constant.

The points on the function are; (0, f(0)), and (2, f(2))

The required slope between the points x = 0, and x = 2 is 12

Therefore;

(f(2) - f(0))/(2 - 0) = 12

f(2) - f(0) = 12 × (2 - 0) = 24

The

The exponential function can be presented in the form;  f(x) = a·bˣ

When x = 0, we get; f(0) = a·b⁰ = a

When x = 2, we get; f(2) = a·b²

f(2) - f(0) = a·b² - a = 24

a·(b² - 1) = 24

Let a = 3, and b = 3, we get;

3 × (3² - 1) = 24

Therefore, possible values of a and b are; a = 3, and b = 3

The exponential function is therefore;

The slope of the line that extends from the point (0, f(0)), to the point (2, f(2), is therefore;

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Therefore , the solution of the given problem of quadratic equation comes out to be the value of y = 12.

x2+ cx + z = 0 is a quadratic problem with one variable in quadratic algebra. a 0. According to the Underpinning Theorem of Algebra, this quadratic's second order ensures that it has at least one solution. The solutions could be simple or complex. Four variables make up a quadratic equation. This implies that at least one word should be squared. "ax2 + bx + c = 0" is one of the basic formulae for solving quadratic equations, where the numbers or integers a, b, and c stand in for the undefined variable "X".

Here,

Given :   A right angled triangle with dimension of y, y+3 and 9

To find the value of y :

We use pythagoras theorem :

So,

=> (y+3)² = y²+9²

=> y² + 9 + 6y = y²+ 81

=>  y² - y² + 6y = 81-9

=> 6y =72

=>y =72/6

=>y=12

Therefore , the solution of the given problem of quadratic equation  comes out to be the value of y = 12.

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