Jeffery Wei received a 7-year non-subsidized student loan of $32,000 at an annual interest rate of 5.2%. What are Jeffery's monthly loan payments for this loan after he graduates in 4 years?

The force applied to the other end of the lever is 100N.

The principle of a lever is based on the fact that the product of the force and the distance from the pivot point is constant.

In this case, if a force of 50N applied to the end of the lever moves that end a certain distance, then we can say that:

50N x distance = constant

Now, if the other end of the lever is moved half as far, let's call this distance "d/2". According to the principle of the lever, the product of the force and the distance from the pivot point must still be constant. Therefore, we can write:

50N x distance = F x (d/2)

where F is the force applied to the other end of the lever.

We can simplify this equation by dividing both sides by d/2:

100N = F

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the complete question is:

she applied 50 newtons of force to one end of the lever. How much force does the lever have if the other end is moved half as far?

Answer:

The mistake is the problem itself.  It should be

5x=100

x=100÷5

x=20

Step-by-step explanation:

The mistake is the problem itself.  It should be

5x=100

x=100÷5

x=20

The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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Answer: lol yes sucks

Step-by-step explanation:

Answer:

the formula to find the amount for number 7 is

A=p(1+r/n) raised to power n ,e.g

A=4000(1+4/1)raised to power 1

A=4000(1+4) raised to power 1

A=4000(5)

A=20,000.

to find interest

I=PRT/100

I=4000×4×1/100

I=#160

Answer:

The perimeter of the square is 32x + 20 inches, and the perimeter of the rectangle is (4x - 5) + (4x - 5) + (12x + 15) + (12x + 15) = 32x + 20 inches.

So, to find the value of x that makes the perimeters the same, we set 32x + 20 = 32x + 20 and solve for x.

x = 0

Step-by-step explanation:

Answer:

\(\dfrac{\sqrt{2}-\sqrt{6} }{4} }\)

Step-by-step explanation:

Find the exact value of cos(105°).

The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.    

We have,

\(\cos(105\°)\)

Using the angle sum identity for cosine.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}\)

Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.

\(105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)\)

Now applying the identity.

\(\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\)

Now utilizing the unit circle.

\(\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}\)

\(\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\)

Now simplifying...

\(\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}\)

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

Step-by-step explanation:

The rate of return for the entire portfolio, given the amount allocated to each of the four securities is

The rate of return would be the expected return of the proportion of the amounts invested into the various investment vehicles and their rates of return.

The rate of return for the portfolio is therefore :

= ∑ ( proportion invested x rate of return )

= ( 25 % x 12 % ) + ( 10 % x 7 % ) + ( 35 % x 22 % ) + ( 30 % x  - 12 % )

= 7. 8 %

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The calculated value of x in the equation (x + 1) (x - 5) = 16 is 7

From the question, we have the following parameters that can be used in our computation:

(x + 1) (x - 5) = 16

The above expression is the product of two factors

(x + 1) and (x - 5)

And the result is 16

Express 16 as 8 * 2

So, we have

(x + 1) (x - 5) = 8 * 2

By comparison, we have

x + 1 = 8 and x - 5 = 2

When evaluated, we have

x = 7 and x = 7

This means that the value of x in the equation is 7

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passive income

dividends, real estate, interest income

active income

salary, business income,  

The option 2 is correct of given question ''All the powers have a value of 1 because the exponent is zero.''

An exponent is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is written as a superscript number to the right of the quantity being multiplied.

For example, in the expression 5³, 5 is the base and 3 is the exponent. This means that 5 is being multiplied by itself three times: 5 x 5 x 5, which equals 125.

The statement "All the powers have a value of 1 because the exponent is zero" describes what these four powers have in common.

When the exponent is zero, any number (except for 0) raised to the power of 0 equals 1. Therefore, 10⁰  = 1, (-2)⁰ = 1, and any non-zero number raised to the power of 0 equals 1.

There is no fractional value involved in this case, as raising a number to the power of zero does not involve any division.

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Complete question:

Answer:

Because \(x = y\), then the solution is unique.

Step-by-step explanation:

Given

\(Ax = b\)

\(Ax=0\)

See comment for complete question

Let there be two solutions x and y.

Such that:

\(Ax = b\) and \(Ay = b\)

Since:

\(Ax = Ay = b\)

Then:

\(Ax - Ay = b - b\)

\(Ax - Ay = 0\)

This implies that:

\(Ax - Ay = A(x-y) = 0\)

The only trivial solution is:

\(Ax - Ay = A(x-y) = 0\)

Such that:

\(x -y = 0\)

Then

\(x = y\)

Because \(x = y\), then the solution is unique.

Answer:

Step-by-step explanation:

Simplify:

Answer:

\(\frac{(a+c)}{(a-x)}\)

Step-by-step explanation:

Ok, first let's factor out the numerator:

Factor: Numerator

We can use the special binomial product (a + b)² = a² + 2ab + b²

Factor: Denominator

We can factor by grouping

Simplify:

We can remove like terms.

-Chetan K

Answer:

Only did for Problem 1:

Square is: 4x^2-20x+25

Side is: 2x-5

A^2=4

2AB=-20

B^2=25

Step-by-step explanation:

The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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Answer:

67/100

Step-by-step explanation:

its the simpelist form

Answer:

2) +20

4) +14

5) -100

6) -17

7) 10

8) -9

9) -8

10) +11

Step-by-step explanation:

look at the words and it will tell you whether it's positive or negative

ex. one hundred feet below sea level- it says below which means you would be going down

The reasoning for the third step of the proof would be "Corresponding parts of congruent triangles are congruent." Let's go through the explanation:

1. Given: Quadrilateral ABCD is a rectangle.

2. Given: AB & CD (Opposite sides of a rectangle are equal).

3. To prove: AC & BD.

To prove that AC is equal to BD, we can utilize the property that opposite sides of a rectangle are equal (step 2). In a rectangle, opposite sides are parallel and congruent. Therefore, we have AB || CD and AB = CD.

Now, we need to show that the triangles ABAD and ACDA are congruent, specifically using the SAS (Side-Angle-Side) congruence theorem. The congruence of these triangles will allow us to establish the equality of their corresponding parts, including AC and BD.

4. Given: AD = AD (Reflexive Property of Equality).

5. By step 2, we know AB = CD. Additionally, AD = AD is given (Reflexive Property of Equality).

6. By step 3, ZBAD = ZCDA.

7. Using SAS triangle congruence theorem, we can conclude that triangles ABAD and ACDA are congruent.

Finally, according to the "Corresponding parts of congruent triangles are congruent" property, we can state that AC = BD. This establishes the equality of the diagonals of the rectangle.

Therefore, the correct reasoning for step 3 is "Corresponding parts of congruent triangles are congruent."

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Answer:

rational number

Step-by-step explanation:

A whole number does not have a decimal part so it cannot be a whole number

Integers are whole numbers that are positive and negative plus zero

-.23 can be written as the ratio of integers

-23/ 100 so it is a rational number

Answer:

Rational

Step-by-step explanation:

A whole number does not have a decimal part so it cannot be a whole number

Integers are whole numbers that are positive and negative plus zero

-.23 can be written as the ratio of integers

-23/ 100 so it is a rational number

Answer: 2

Step-by-step explanation:

As given, out of 30 students, 15 play guitar and 13 play piano, thats 28.

Among these, 9 play both the guitar and the piano.

That means, only 2 remaining students play neither instrument. (30-15-13)

In terms of measures of spread, Group B has a wider IQR than Group A

The comparative dot plots show the points scored in a game by two groups, Group A and Group B. Both groups have a similar spread, with most of the dots clustered around the middle of the distribution. However, there are some differences in the tails of the distribution that affect the measures of spread.

For Group A, the lowest score is 41, and the highest score is 50. The interquartile range (IQR), which is the range containing 50% of the scores, is approximately from 45 to 48. The range, which is the difference between the highest and lowest scores, is 9.

For Group B, the lowest score is 41, and the highest score is 50. The interquartile range (IQR) is approximately from 43 to 49. The range is also 9.

This indicates that Group B has a more variable distribution of scores within the middle 50% of the distribution, indicating a more variable distribution of scores within the middle.

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Answer:

￡－7

Step-by-step explanation:

15 －8 ＝7

8－15＝￡－7

This is to show that we can use a normal equation then change the digits to get an answer.

The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.

Let us assume the number of coach tickets purchased is x.

And the number of first-class tickets purchased is y.

Now,

Including Sarah, a total of 11 people took the trip.

Thus,

\(x + y = 11 \)

The cost of coach tickets and first-class tickets are $210 and $1200 respectively.

The total budget for airfare for the trip is $10,230.

Therefore,

210x + 1200y = 102309

21x + 120y = 1023

Solving both the equations, we get.

x=3

y=8

Thus, The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.

Answer:

42 squared is 1764

Step-by-step explanation:

Answer: (x + 42)(x - 42)

Step-by-step explanation:

factorise: x^2 - 42^2

. x^2 - 42^2 have ^2 in common (so you can ignore that).

. put in brackets (x - 42)(x + 42)

. +/- any order really doesn't matter :D

Answer:

please mark me brainliest

Answer:

B and D

Step-by-step explanation:

If you are dividing by 2/9, that means you are multiplying by 9/2.

This can be split into multiplying by 9 and then dividing by 2, or multiplying by 9 and multiplying by 1/2.

Therefore, B and D work