Without graphing, classify the system as independent, dependent, or inconsistent.
S x – 5 = - y
| 2y - 10 = – 21

Therefore, the present value of the perpetuity that pays $1,800 per year forever, assuming a 5% interest rate, is $36,000. To find the present value of a perpetuity that pays $1,800 per year forever, we can use the formula:
Present Value = Cash Flow / Interest Rate

In this case, the cash flow is $1,800 and the interest rate is 5%. Plugging these values into the formula, we get:
Present Value = $1,800 / 0.05. Simplifying this equation, we find that:
Present Value = $36,000

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Answer:

Step-by-step explanation:

4x - 3y = 8

5x - 2y = -11

8x - 6y = 16

-15x + 6y = 33

-7x = 49

x = -7

4(-7) - 3y = 8

-28 - 3y = 8

-3y = 36

y = -12

Answer:

Pretty sure its 0.6x + 0.5= 0.75

Step-by-step explanation:

\(\boxed{\boxed{\pink{\bf \dag Value \ of \ x \ is \ \dfrac{5}{12}}}}\)

A linear equation is given to us and we need to solve the equation by converting it into a equivalent equation that does not contain fractions . So the given equation is :-

\(\bf\implies \dfrac{3}{5}x + \dfrac{1}{2}=\dfrac{3}{4}\)

Here the denominators of the fractions are 5 , 2 and 4. So LCM of 5 , 2 and 4 is , 20 .

So , Multiply whole equation by 20 .

\(\bf\implies 20 \bigg( \dfrac{3}{5}x + \dfrac{1}{2} \bigg) = 20 \times \dfrac{3}{4}\\\\\bf\implies 4\times 3x + 10 = 5\times 3 \\\\\bf\implies 12x + 10 = 15 \:\: \bigg\lgroup \blue{\bf Equivalent \ equation \ without \ fractions .}\bigg\rgroup \)

Now let's solve this equation since we successfully converted it into a equivalent equation without fractions.

\(\bf \implies 12x + 10 = 15 \\\\\bf\implies 12x = 15-10 \\\\\bf\implies 12x = 5 \\\\\bf\implies\boxed{\red{\bf x =\dfrac{5}{12}}}\)

The correct answer is C.1 raised to the power of 14 is equal to 1.so the  the simplified form of 1¹4 is 1.

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the derivative f'(x) of the function f(x) = e^(3x)/(3x) is given by:

f'(x) = (9xe^(3x) - 3e^(3x)) / (9x^2)

To find the derivative f'(x) of the function f(x) = e^(3x)/(3x), we will use the quotient rule.

The quotient rule states that if we have a function in the form of g(x)/h(x), then its derivative is given by:

(g'(x)h(x) - g(x)h'(x))/(h(x))^2

Here, g(x) = e^(3x) and h(x) = 3x.

Step 1: Find the derivatives of g(x) and h(x).
g'(x) = d(e^(3x))/dx = 3e^(3x)
h'(x) = d(3x)/dx = 3

Step 2: Apply the quotient rule.
f'(x) = (g'(x)h(x) - g(x)h'(x))/(h(x))^2
f'(x) = (3e^(3x) * 3x - e^(3x) * 3) / (3x)^2

Step 3: Simplify the expression.
f'(x) = (9xe^(3x) - 3e^(3x)) / (9x^2)

So, the derivative f'(x) of the function f(x) = e^(3x)/(3x) is given by:

f'(x) = (9xe^(3x) - 3e^(3x)) / (9x^2)

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Answer:so fresh and so clean

Step-by-step explanation:

its cheaper starting price and lower increase

The service with the cheaper initial fee is the graphed one, So Fresh & So Clean.

For both cases, we can write the costs as linear equations, so we want to see which linear equation has the smallest y-intercept.

We can see that for the graphed line, the y-intercept is b = 15.

For the data on the table, we can use the first two points to get the slope. The points are (1, 28) and (2, 36), so the slope is:

\(a = \frac{36 - 28}{2 - 1} = 8\)

Then we can write this line as:

y = 8*x + c

To find the y-intercept we can use the first point (1, 28), this means that:

28 = 8*1 + c

28 - 8 = c = 20

Then the y-intercept, in this case, 20.

This means that the service with the cheaper initial fee is the one where the line is graphed, which is So Fresh & So clean.

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Answer:

A. 20ft

Step-by-step explanation:

Answer:

d. 98.5

Step-by-step explanation:

Triangles:

5 x 4 = 20/2 = 10

Circle:

5² x 3.14 = 78.5

Add both of them 98.5

Answer:

D 100cm

Step-by-step explanation:

Answer:

\(x=-\frac{19}{2}\)

Step-by-step explanation:

hope that was the answer you were looking for :/

Answer:

x = -19/2

Step-by-step explanation:

\(-2x+5=24\)

Then subtract 5 from 24

\(-2x=19\)

Then divide -2 by 19 to get:

\(x = -\frac{19}{2}\)

Hope this helps!

The only possible degree for the polynomial p+q is 11.

Given the degree of polynomial p is 11 and the degree of polynomial q is 7, we can find all possible degrees of the polynomial p+q by considering their highest-degree terms.

When adding polynomials, the resulting polynomial will have the degree that corresponds to the highest-degree term. In this case, we have two options:

1. The highest-degree terms of both polynomials are of different degrees. In this case, the degree of p+q will be the maximum of the two given degrees, which is max(11, 7) = 11.

2. The highest-degree terms of both polynomials are of the same degree and their coefficients have opposite signs, causing them to cancel out when added. In this scenario, the degree of p+q will be less than the maximum degree, i.e., less than 11.
However, given that the degrees of p and q are different (11 and 7), it is not possible for their highest-degree terms to cancel out.

Therefore, the only possible degree for the polynomial p+q is 11.

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Answer:

9.37 divide by two = 4.685

4.685 in 2DP = 4.68

Step-by-step explanation:

i hoped this helps.

Answer:

2.98 :)

Step-by-step explanation:

the circumference is when you do pi times diameter.

do 9.37 divided by 3.14(pi) to work out the diameter.

9.37/3.14=2.984

rounded its 2.98

The vertical component of velocity can be zero at specific points in the motion of an object.

What is Velocity?

Velocity is a vector quantity that describes the rate of change of an object's position in space over time. It is defined as the displacement of an object divided by the time interval during which the displacement occurred.

The vertical component of velocity can be zero at specific points in the motion of an object. This occurs when the object reaches the highest point in its vertical motion and begins to fall back down. At this point, the vertical component of velocity changes direction from upward to downward, and its magnitude becomes zero. This moment is known as the "instant of maximum height" or "instant of maximum altitude." Beyond this point, the vertical component of velocity becomes negative, indicating that the object is moving downward.

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Answer:

100 times smaller

Step-by-step explanation

48.6 / 0.486 = 100

Answer:

15

Step-by-step explanation:

5g

g becomes 3, so 5*3

=15

Answer:

15

Step-by-step explanation:

5g g=3

5(3)

15

The sum of the measures of the exterior angles of any polygon, including a triangle, is always 360 degrees.

We have,

An exterior angle of a polygon is formed by extending one of its sides outward.

In the case of a triangle, when we extend each side, we create three exterior angles.

These exterior angles are located outside the triangle.

The key concept to understand is that the sum of the exterior angles of any polygon is always 360 degrees.

This property holds true for all polygons, regardless of their shape or size.

To visualize this, imagine starting at any vertex of a triangle and moving along its sides while measuring the exterior angles.

As you move around the triangle, the sum of the exterior angles will always add up to 360 degrees.

This is because, at each vertex, the exterior angle supplements the interior angle to form a straight angle of 180 degrees.

In a triangle, each interior angle measures less than 180 degrees.

So, when we extend each side to create the exterior angles, they collectively compensate for the deficiency of the interior angles, resulting in a sum of 360 degrees.

Therefore,

The sum of the measures of the exterior angles of a triangle is always 360 degrees.

This principle holds true for all polygons, making it a fundamental property of geometry.

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Answer:

Agency A:  y = 12x

So Agency A pays a rate of $12 per hour

Agency B:  y = 10x + 20

So Agency B pays an initial fee of $20 plus a rate of $10 per hour.

Step-by-step explanation:

Agency A

To create a straight line equation for the data in table, use  \(y = mx + b\), where m is the slope and b is the y-intercept.

To find the slope m, take 2 points from the table and use the slope formula.

Let \((x_1,y_1)\) = (3, 36)

Let \((x_2,y_2)\) = (5, 60)

Slope formula: \(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{60-36}{5-3}=12\)

Now use the point-slope formula to create the final equation:

\(y-y_1=m(x-x_1)\)

\(\implies y-36=12(x-3)\)

\(\implies y=12x\)

Therefore, Agency A pays a rate of $12 per hour.

Agency B

From inspection, the function is a straight line.

Therefore we can use the straight line equation \(y = mx + b\),

where m is the slope and b is the y-intercept.

From inspection, we can see that the line crosses the y-axis at (0,20).  Therefore, the y-intercept is 20.

\(\implies y=mx+20\)

Taking 2 points on the line and using the slope formula to find the slope m:

Let \((x_1,y_1)\) = (0, 20)

Let \((x_2,y_2)\) = (3, 50)

Slope formula: \(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{50-20}{3-0}=10\)

Therefore, the final equation is:  \(y=10x+20\)

Therefore, Agency B pays an initial fee of $20 plus a rate of $10 per hour.

Answer:

parallel because they have the same slope

Step-by-step explanation:

There are 30240  different id cards can be made if there are five digits on a card and no digit can be used more than once.

a) If repetition is allowed, then there are 10 ways to choose each of 5 digits. Hence, by the multiplication rule, we obtain that the total number of possible different ID cards is:

10⋅10⋅10⋅10⋅10 = 10⁵= 100000.

b) If repeats are not allowed, there are 10 ways to choose the first number, 9 ways to choose the second number (because we chose 1 digit as the first number), and 9 ways to choose the third number. There are 8 ways, 7 ways, and 7 ways to choose the 4th number. 6 ways to select the digit to select and the 5th digit.

So according to the multiplication rule the answer is:

10 × 9× 8×7×6 = 30240.

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Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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Answer: 120

Step-by-step explanation:

2 = 240

240 / 2 = 120

unit = per

so the answer will be 120 calories

Answer:

2:240 or 2/240, whichever you like better. If you need a single unit answer, you would just divide this rate shown by 2 in order to get 1/120 or 1:120

Step-by-step explanation:

Every single part of the chart adds the first number. 2+2=4+2=6+2=8

Same thing with the bottom, 240+240=480+240=720+240=960.

The unit rate would be 2/240 by that logic, because for every 2 servings there are 240 calories.

Answer:

here is my answer........

Step-by-step explanation:

(3-x)^2 = 9 - 3x - 3x + X2

= X2 - 6x +9

∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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Since you have basic knowledge of computer hardware, an action which you should take as an ethical employee include the following: A. Initiate help by offering to check the computer.

A computer hardware can be defined as a physical component of a computer system or an information technology (IT) that can be seen, touched and replaced.

In Computer technology, there are various examples of a computer hardware and these include the following:

Based on ethical principles, we can reasonably infer and logically conclude that an ethical employee should initiate help by offering to help check the colleague’s computer since he or she has basic knowledge of computer hardware.

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Answer:

Option B: $20x + $30 < $170 is the correct answer.

Step-by-step explanation:

Given that:

Service fee of Tina's business = $30

Per day charges = $20

Number of days =  x

Customer's budget = less than $170

According to given statement;

20x + 30 < 170

Hence,

Option B: $20x + $30 < $170 is the correct answer.

Answer:

B 16/3

Step-by-step explanation:

on edg

The volume of the pyramid shown is 16√3 cm³.

Volume of a three dimensional shape is the space occupied by the shape.

Given a solid oblique pyramid.

It has an equilateral triangle as a base with an edge length of 4√3 cm and an area of 12√3 cm².

Volume of the pyramid = 1/3 × base area × height

Base area = 12√3 cm²

Height = 4√3 × tan (30°) = 4√3 × 1/√3 = 4

Volume = 1/3 × 12√3 × 4

             = 16√3 cm³

Hence the volume is 16√3 cm³.

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The differential dy when x = 1 and dx = 0.3 is approximately 8.901.

When evaluating the differential dy of the function y = tan(5x + 3), we can use the formula dy = f'(x) * dx, where f'(x) represents the derivative of the function with respect to x. In this case, the derivative of tan(5x + 3) can be found using the chain rule, resulting in f'(x) = 5sec^2(5x + 3).

Substituting the given values into the formula, we have f'(1) = 5sec^2(5*1 + 3) = 5sec^2(8).

Evaluating sec^2(8) gives us a numerical value of approximately 9.867.

Multiplying f'(1) by the given dx of 0.3, we get dy = 5sec^2(8) * 0.3 ≈ 8.901.

To find the differential dy in this case, we applied the chain rule to differentiate the given function. The chain rule is a fundamental concept in calculus used to find the derivative of composite functions. By applying the chain rule, we were able to find the derivative of the function tan(5x + 3) and subsequently evaluate the differential dy. Understanding the chain rule is essential for solving problems involving derivatives of composite functions.

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