A college student borrows $1000 for 3 months to pay for a semester of school. If the interest is $20.63, find the monthly payment. (Round to the nearest cent)

1) Subtract 4 from both sides to get 15x = 102

2) Divide by 15 on both sides to get x = 6.8

Answer:

x=6.8

Step-by-step explanation:

15x + 4 = 106

subtract 4 from both sides

15x=102

divide both sides by 15

x=6.8

We know that the sum of the internal angles is equal to 180°, then we write and solve a linear equation to see that the missing angle is 94°.

Remember that for any triangle, we know that the sum of the interior angles is equal to 180°.

In this case we know that two of the angles have a measure of 62° and 24°, and if the third angle is x, then we can write the linear equation:

62° + 24° + x = 180°

To solve this we need to isolate x, we will get:

x = 180° - 24° - 62°

x = 94°

So the measure of the third interior angle is 94 degrees.

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Answers:

1) 7.1

2) -7.1

3) -3

Plug in the numbers

Answer:

y = 19.2

Step-by-step explanation:

We know there is relationship between y and x, so according to the formula \(y = kx\)

k = 12/5

we get one function y = 2.4x

when x = 8, input it into the function,

y = 2.4×8 = 19.2

Answer:  first choice is correct

Step-by-step explanation:

\(\sqrt{10} = 3.16\\\\ \sqrt{13} = 3.6\)

22/9 = 2.44

Therefore Point A is 22/9, Point B is \(\sqrt{10}\),  Point C is \(\sqrt{13}\)

The lines with the equations y=-1/2x+1 and y=2x+1 are perpendicular lines

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The equations of the lines are given as

y=-1/2x+1 and y=2x+1

Rewrite the above equations as

y = -1/2x + 1 and y = 2x + 1

A linear equation is represented as

y = mx + c

Where the slope of the line is represented as

Slope = m

This means that the slopes of the equations of the lines given as y=-1/2x+1 and y=2x+1 are

m1 = -1/2

m2 = 2

As a general rule, the relationship between slopes are

m1 = m2 --- parallel lines

m1 * m2 = -1 ---- perpendicular lines

In the equations of the lines given as y=-1/2x+1 and y=2x+1, we have

m1 * m2 = -1/2 * 2

Evaluate

m1 * m2 = -1

The above equation is true for perpendicular lines

Hence, the lines are perpendicular lines

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The value of x is 63

To determine the value of the variable, we have that;

From the information given, we have that;

x and x - 36 are complementary angles

Now, equate the angles to 90 degrees, we have;

x + x - 36= 90

collect the like terms, we get;

2x = 90 + 36

add the terms

2x =1 26

Divide by the coefficient

x = 63

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Complete question:

The angles X,(x-36)  are complementary. What is the value of x

The true statement is now presented: If \(c > 0\) and \(|u| > c\), then \(u > c\) or \(u < -c\).

Mathematically speaking, the absolute value is defined by following expression:

\(|a| = \left \{ {{a,\,a \ge 0} \atop {-a,\,a < 0}} \right.\) (1)

If \(c > 0\) and \(|u| > c\), then \(u > c\) or \(-u > c\). Hence, \(u > c\) or \(u < -c\).

Therefore, if \(c > 0\) and \(|u| > c\), then \(u > c\) or \(u < -c\). (By tricotomy)

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Answer:

17x

Step-by-step explanation:

Answer:

8+9+x?

Step-by-step explanation:

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Answer:

The graph of the function y = 100(1.05) is shown below.

b. Calculate the cost of the hotel per night after six years.

The cost of the hotel per night after six years is $130.25. This is calculated by plugging in t = 6 into the equation y = 100(1.05)^t and solving for y.

c. What is the overall cost of 7 nights at the hotel in its sixth year of operation?

The overall cost of 7 nights at the hotel in its sixth year of operation is $910.75. This is calculated by multiplying the cost per night after six years ($130.25) by 7 nights.

2 LEARNING RESOURCES

Discuss the advantages of using online learning resources for students.

One of the main advantages of using online learning resources for students is convenience. Online learning resources can be accessed from virtually any location with an internet connection, allowing students to learn from the comfort of their own homes or from mobile devices when they are on the go. Furthermore, online learning resources reduce the need for students to commute to and from a physical school, meaning that students have more time for their studies, hobbies, and other activities.

Another advantage of online learning resources is adaptability. Online learning resources may be tailored to the needs of each individual student and can easily be adjusted should a student’s needs

Answer:

1) When r = 2, M = 20.

2) When M  = 540, r = 6.

Step-by-step explanation:

M is a directly proportional to r cubed

This means that the equation for M has the following format:

\(M = ar^3\)

In which a is a multiplier.

When r=4 M=160.

We use this to find a. So

\(M = ar^3\)

\(160 = a(4^3)\)

\(64a = 160\)

\(a = \frac{160}{64}\)

\(a = 2.5\)

So

\(M = 2.5r^3\)

1) work out the value of M when r=2

\(M = 2.5*2^3 = 2.5*8 = 20\)

When r = 2, M = 20.

2) work out the value of r when M=540

\(M = 2.5r^3\)

\(540 = 2.5r^3\)

\(r^3 = \frac{540}{2.5}\)

\(r^3 = 216\)

\(r = \sqrt[3]{216}\)

\(r = 6\)

When M  = 540, r = 6.

The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Answer:

8

Step-by-step explanation:

15 - 5 = 10

10 / 1.25 = 8

x = 12

5x + 15 = 75

5x = 75 - 15

5x = 60

x = 60 : 5

x = 12

The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

The perimeter of a triangle is the sum of the lengths of its three sides.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

In the case of triangle HGI, the perimeter is calculated by adding the three side lengths together. For example, if the three sides are labeled a, b, and c, the perimeter would be calculated as a + b + c.

The perimeter of triangle HGI can be calculated by knowing the lengths of its three sides. If the lengths of the three sides are 7, 8, and 9 units respectively, the perimeter of triangle HGI is 7 + 8 + 9 = 24 units.

The perimeter of triangle HGI can also be calculated using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. Using this theorem, the lengths of the other two sides can be calculated if the length of one side and the measure of the included angle is known.

In summary, the perimeter of triangle HGI can be calculated by adding the lengths of its three sides or by using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known.

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Answer:

I'm not doing this to steal points, but I can't see the painting. So yeah, sorry. Plese insert a image of that painting next time. Sorry.

Step-by-step explanation:

Answer:

agreed can't see the whole problem

Step-by-step explanation:

AKA the painting

-150+(-45)= -195

Negative since it’s deeper

this might be yo answer im not sure

i hope this helped u tho

Answer:

centre = (- 4, 2 ) , radius = 5

Step-by-step explanation:

the equation of a circle in standard form is

(x - h )² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

x² + 8x + y² - 4y = 5

using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides )

x² + 2(4)x + 16 + y² + 2(- 2)y + 4 = 5 + 16 + 4

(x + 4)² + (y - 2)² = 25 ← in standard form

with (h, k ) = (- 4, 2 ) and r = \(\sqrt{25}\) = 5

centre = (- 4, 2 ) and radius = 5

If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

First step:-

Right triangular prism=1⁵/₆ inches= 11/6 inches

Height of the base=8²/₃ inches = 26/3 inches

Second step:-

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

Therefore the surface area of the solid formed is about 598.33 in²

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The measure of angle Z1 is equal to 3 times the value of x, and the measure of Angle Z2 is equal to x plus 72.

The measure of angle Z1 is equal to 3 times some value x, and the measure of angle Z2 is equal to the sum of that value x and 72.

To clarify, it seems that we are dealing with two angles, Z1 and Z2, and their measures are expressed in terms of a variable x.

the given information:

- mZ1 = 3x

- mZ2 = x + 72

These equations indicate that the measure of angle Z1 is equal to 3 times the value of x, and the measure of angle Z2 is equal to x plus 72.

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La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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Answer:

Step-by-step explanation:

If you are always included to lead, that leaves 10 students to choose from.

If all that is important is being selected, then there are 10C3 = 120 ways to choose them.

If each selection has a unique duty, then there are 10P3 = 720 ways to assign them their jobs.

Answer: 10P3=720

Step-by-step explanation:

Answer:

The proportions of the graph must be accurate. If it is a box or something it should be the area.

Step-by-step explanation:

The proportions of the graph must be accurate. If it is a box or something it should be the area.

The pictograph is among the simplest ways to portray statistical data because of how simple it is to understand. We employ a key in the pictograph to indicate the symbol's value. If symbols or images are used, they should all be the same size.

The graph's proportions must be exact. If it is a box or something else, that place should be it.

A pictogram often referred to as a pictograph in mathematics is a visual representation of data that uses pictures, icons, or other symbols. Using a pictograph, we can depict the frequency of data using pertinent symbols or images. One of the simplest methods for representing data is through pictographs.

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A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.

1. The given function is f(x) = \(-2(x+4)^2\) + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.

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The five in 35.76 is 100 times bigger than the five in 26.95.

Here we want to compare the values of the 5's in two different numbers, which are 35.76 and 26.95.

To compare them we need to compare the place value in which each five is.

To compare them, just write the numbers but replacing all the other values by zeros:

35.76 = 05.00 = 5

26.95 = 00.05 = 0.05

Now take the quotient of these two, we will get:

5/0.05 = 100

Thus, the 5 in 35.76 is 100 times bigger than the 5 in 26.95.

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