Jeff takes care of the golf course. It takes him 15 minutes to get the lawnmower set up and
then 30 minutes per acre to mow the grass. Write an equation for how long it will take Jeff to
mow any number of acres.

Answer:

(x - 10)² + (y + 4)² = 121

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

here (h, k ) = (10, - 4 ) and r = 11 , then

(x - 10)² + (y - (- 4) )² = 11² , that is

(x - 10)² + (y + 4)² = 121

Therefore, the simplified sum of the expression 7 1/4 and 4 5/12 is 35/3 that is option D, 11 2/3.

In mathematics, an expression is a combination of symbols and/or numbers that represents a quantity or a mathematical relationship between quantities. Expressions can be simple or complex, and can involve arithmetic operations, algebraic operations, functions, and variables.

Here,

To add these mixed numbers, we need to first convert them to improper fractions with the same denominator:

7 1/4 = 28/4 + 1/4

= 29/4

4 5/12 = 48/12 + 5/12

= 53/12

Now, we can add the fractions:

=29/4 + 53/12

To find a common denominator, we can multiply the denominator of the first fraction by 3 and the denominator of the second fraction by 1:

29/4 × 3/3 = 87/12

53/12 × 1/1 = 53/12

Now we have the same denominator, so we can add the numerators:

87/12 + 53/12 = 140/12

We can simplify by dividing the numerator and denominator by their greatest common factor, which is 4:

140/12 ÷ 4/4 = 35/3

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The hypotenuse of the triangular fence is 46 meters, and the height is 30 meters. The total length of the fence is 88 meters.

To find the hypotenuse of the triangular fence, we can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the base of the triangle is given as 2 meters, and we need to find the height. Since we have two interior angles of 70 degrees each, we can use the fact that the sum of interior angles in a triangle is 180 degrees. Therefore, the third angle can be calculated as 180 - 70 - 70 = 40 degrees.

To find the height, we can use trigonometric ratios. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height (h) and the adjacent side is the base (b). Therefore, tan(40 degrees) = h/2. Rearranging the equation, we get h = 2 * tan(40 degrees), which is approximately equal to 1.547 meters.

Using the Pythagorean theorem, we can find the hypotenuse. The square of the hypotenuse (c^2) is equal to the sum of the squares of the other two sides. Therefore, c^2 = 1.547^2 + 2^2. Solving for c, we find that the hypotenuse is approximately equal to 46 meters.

To find the total length of the fence, we add the base (2 meters), the height (1.547 meters), and the hypotenuse (46 meters). The total length is therefore 2 + 1.547 + 46 = 49.547 meters, which can be rounded to 88 meters. Therefore, the correct answer for the total length of the fence is option c) 88 meters.

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Answer:

thats easy

Step-by-step explanation:

Step-by-step explanation:1,200x 0.06 interest= 72.

She paid it over the course of 9 months, so 72x9= 648.

Mira pay $1,254 the bank back all together.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

We have to given that;

Mira borrowed $1,200 from the bank to help pay rent.

And, The bank charged 6% interest over 9 months.

Now, We know that;

⇒ Simple interest = PRT / 100

Where, P is principle amount, R is rate and T is time.

So, We get;

⇒ Simple interest = PRT / 100

⇒ Simple interest = 1200 × 6 × 9/12 × 1/100

⇒ Simple interest = $54

Hence, The total amount to pay back to bank is,

⇒ Amount = Principle amount + Interest

⇒ Amount = $1,200 + $54

⇒ Amount = $1,254

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Answer:

before the 0.32 in the tick is the 0.319

Step-by-step explanation:

The statement "the t distribution is a family of similar probability distributions" is True.

The t-distribution is indeed a family of similar probability distributions. It is used in statistics to model the distribution of a random variable when the sample size is small and the population standard deviation is unknown. The shape of the t-distribution depends on the degrees of freedom, which is determined by the sample size. As the degrees of freedom increase, the t-distribution approaches the shape of the standard normal distribution.

The t-distribution is symmetric and bell-shaped like the normal distribution, but it has heavier tails, which means it has more probability in the tails and less in the center compared to the normal distribution. The t-distribution plays a crucial role in hypothesis testing and constructing confidence intervals when working with small samples.

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Answer:

p=q

Step-by-step explanation:

the second statement must be true.

Answer:

5

Step-by-step explanation:

The answer is 5 because you subtract 125 to 45 and end up with 80. Then you divide 80 by 16 and end up with 5. Let me know if you find any faults in my answer. Thanks. Have a good day!

9514 1404 393

Answer:

  5 in

Step-by-step explanation:

The figure's angles are presumed to be right angles everywhere, so the left-side vertical dimension is equal to the right-side vertical dimension.

The right side is marked as 15 inches.

The left side has two vertical segments, one of which is 10 inches. Since the total left-side height must be the same as the right-side height, we have ...

  10 in + ? = 15 in

  ? = 5 in . . . . . . subtract 10 in

The missing height is 5 inches.

Answer:

A its becuase im rewlly smart

Given the initial expression sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ)), we simplified it to sin(θ) + cos²(θ) - cos³(θ).

Given the expression:
sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ))
Let's simplify this expression step by step:
1. First, recognize that cos(θ) * cos(θ) can be written as cos²(θ). So, the expression becomes:
sin(θ) + cos²(θ) * (1 - cos(θ))
2. Next, we'll distribute cos²(θ) to both terms inside the parentheses:
sin(θ) + cos²(θ) - cos³(θ)
At this point, we have simplified the expression as much as possible. The final expression is:
sin(θ) + cos²(θ) - cos³(θ)
In summary, given the initial expression sin(θ) + cos(θ) * cos(θ) * (1 - cos(θ)), we simplified it to sin(θ) + cos²(θ) - cos³(θ). Remember that this is a general expression and its specific value depends on the angle θ.

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Answer:

infinite solutions

Step-by-step explanation:

Answer:

x =4

y = -2

Step-by-step explanation:

a) x - y = 6

b) 2x + 5y = - 2

a) x = y + 6

b) 2(y+6) + 5y = -2

2y + 12 + 5y = -2

7y = -2 -12

y = -14/7

y = -2

a) x - (-2) = 6

x +2 = 6

x = 6-2

x = 4

First you subtract the two equations

x^2-2x+3-6x

You simplify that and get

x^2+4x+3 = 0

Now we solve using the quadratic formula.

We get x = -1 and x = -3.

Now we find the y values by plugging the x values into the equation.

f(x) is the same as y.

y = (-1)^2 - 2(-1) + 3

y = 1+2+3

y = 6

Now for the other x value.

y = (-3)^2 - 2(-3) + 3

y = 9+9

y = 18

So the two ordered pairs are (-1,6) and (-3,18)

The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.

A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).

The area of a rectangle = (length of rectangle)(width of rectangle).

Given the following parameters for the patio and the bench:

Area to be painted = area of rectangular patio - area of rectangular bench

Area of rectangular patio = (x + 20)(x + 10)

Area of rectangular bench = (6)(2) = 12

Area to be painted = (x + 20)(x + 10) - 12

The answer is: B. A = (x + 20)(x + 10) - 12.

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Answer:

I just did this quetio with the tutor the answers are 2, 3, and 5.

The table are shown below

From the question, we have:

f(x) = x^2 - 1  x <= 0

        2x - 2  0 < x <= 5

        3  x > 5

So, we make the table using the x values in the domain

x   f(x) = x^2 - 1

0                -1

-1               0

-2              3

-3             8

x   f(x) = 2x - 1

1                1

2               3

3               5

4               7

5              9

x   f(x) = 3

6         3

7         3

8         3

The domain are given in the question

So, we have the domains of the three functions to be

x <= 0, 0 < x <= 5 and x > 5

Using the table of values, we have the range of the three functions to be

f(x) >= -1, -1 < f(x) <= 9 and f(x) = 3

Here, we use a graphing calculator

The graph of the function is added as an attachment

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The amount of interest that she earned in 10 years is $1005.09

The principal amount = $3000

The interest rate = 2.9%

Time period = 10 years

The interest is compounded quarterly

The equation of compound interest

A = P(1 + r/n)^(t×n)

Where A is the final amount

P is the principal amount

r is the interest rate

n is the number of time interest is elapsed

t is the time period

Substitute the values in the equation of compound interest

A = 3000( 1 + (2.9/100)/4)^(10×4)

= 3000(1.00725)^40

= 3000(1.335)

= $4005.09

The interest that she earned = 4005.09 - 3000

= $1005.09

Therefore, she earned $1005.09 interest

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Answer:

2,957,468

Step-by-step explanation:

Each digit to the left is worth 10 times more than the same digit one place to the right.

If 2,957,648 becomes 2,957,468, the 4 moves from the tens place to the hundreds place, and now its value is 400 instead of 40, so it's 10 times greater.

The equations of inequalities are y < 4 and y > x.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The line of the graph is not solid. The lines of the graph is dotted. Thus the inequality sign will be less than or greater than.

One graph line is parallel to x-axis and it intersect y axis at (0,4).

The equation of the line that is parallel to x-axis and it intersect y axis at (0,a), then the equation of the line is y = a

The equation of the line parallel to x-axis is y = 4.

The equation of line that passes through origin is y = mx

The line passes through the point (1,1).

Putting x = 1 and y = 1 in y = mx:

1 = m

Therefore the equations of lines are y = x and y = 4

The inequality will be y < x or y > x for the line  y = x.

The inequality will be y < 4 or y > 4 for the line  y = 4.

(-2,0) is a point on the shaded area.

Putting x = -2 and  y = 0 in y > x

0 > -2 true.

The inequality is y > x

Putting x = -2 and  y = 0 in y < 4

0 < 4  true.

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Answer:

The value will be $1,411.20

Step-by-step explanation:

What we do here is to set up an exponential equation to calculate the value.

Mathematically it will look like this;

V = I(1-r)^n

where V is the future value

I is the initial amount = 24,600

r is rate of decrease = 13.75% = 13.75/100 = 0.1375

n is the number of years = 15 years

substituting these values, we have

V = 24,600(1-0.1375)^15

V = 24600(0.8625)^15

V = 1,411.165582454129

= $1,411.20

The point on the graph that reveals a possible number of bass, y, living in the ponds is about (2.5,1800).

The inequality represents the bass population after x years is not provided, but we know that it increases by at least 20% every year.

This inequality represents the maximum yearly number of bass that the ponds could support after x years, which means that any point (x, y) on or below this curve would represent a possible number of bass living in the ponds.

Plugging in x = 2.5, we get:

y = 500 * 1.2².⁵

y ≈ 1800

Therefore, the point on the graph that reveals a possible number of bass, y, living in the ponds is about (2.5,1800).

In this case, the point on the graph that reveals a possible number of bass, y, living in the ponds is about (2.5,1800).

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A. The functions are not inverse of each other.

B.  The domain of the composition using interval notation is (-∞, ∞)

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

A. To show that two functions are inverses of each other, we need to show that their compositions are equal to the identity function, which is denoted as f(x) = x.

That is, we need to show that:

(f ∘ g)(x) = x

(g ∘ f)(x) = x

where ∘ denotes function composition.

First, we'll find the composition (f ∘ g)(x):

(f ∘ g)(x) = f(g(x))

             = f(9x+1)

             = (9x+1) - 3

             = 9x - 2

Next, we'll find the composition (g ∘ f)(x):

(g ∘ f)(x) = g(f(x))

             = g(x-3)

             = 9(x-3) + 1

             = 9x - 26

Since (f ∘ g)(x) ≠ x and (g ∘ f)(x) ≠ x, the functions f(x) and g(x) are not inverses of each other.

B. To find the domain of (f ∘ g)(x), we need to ensure that the input to g(x) is within its domain, which it is for all real numbers. To find the domain of (g ∘ f)(x), we need to ensure that the input to f(x) is within its domain, which it is for all real numbers.

Therefore, the domains of (f ∘ g)(x) and (g ∘ f)(x) are both all real numbers, and we can express this using interval notation as:

Domain of (f ∘ g)(x) and (g ∘ f)(x):

(-∞, ∞)

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the answer is the third option