Adrian is drawing a map to show the directions from his house to his grandmother's house. He uses a scale of 1 1/2
inches represents 12 miles. If the distance from his house to his grandmother's house is 36 miles, how long is the drawing
on the map?

Using a system of equations, it is found that they had a total of 3 morning practices last week.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables for this problem are given as follows:

They had a total of 10 practices, hence:

x + y = 10 -> y = 10 - x.

During each morning practice, they ran 5 miles, and during each afternoon practice, they ran 6 miles. They ran a total of 57 miles, hence:

5x + 6y = 57.

5x + 6(10 - x) = 57.

5x + 60 - 6x = 57.

x = 3.

They had a total of 3 morning practices last week.

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

To know more about  equation of a line refer here:

https://brainly.com/question/29205562#

#SPJ11

The given table shows the values of two functions f(x) and g(x). x f(x) = -4x - 3 g(x) = -3x 1 2 -3 9 179 -2 5 53 -1 1 1 0 -3 -1 1 -7 -7 2 -11 -25 3 -15 -79To find the solution to f(x) = g(x), we have to solve the equation by equating both functions.

The equation is: f(x) = g(x)-4x - 3 = -3xThe solution for the given equation is: x = 3/1We can solve the equation by adding 4x to both sides of the equation and subtracting 3 from both sides of the equation.-4x - 3 + 4x = -3x + 4x - 3-x - 3 = 0x = 3/1Thus, the solution to f(x) = g(x) is x = 3/1.

To know more about functions visit:

brainly.com/question/31062578

#SPJ11

Step-by-step explanation:

3x² + 3x - 1

should turn into x + 5.

so, let's subtract (x + 5), and the result is then what we have to add in negative version to the original expression (like with subtractions and additions if regular numbers).

3x² + 3x - 1 - x - 5 = 3x² + 2x - 6

so, we need to add -(3x² + 2x - 6) = -3x² - 2x + 6

The answer is A) Line y = 5x + 6 intersects the line y = −x − 7.

Here, we have,

given that,

the equations are:

y = 5x + 6

y = −x − 7

so, solving the given equations ,we get,

5x + 6 = -x - 7

6x + 6 = -7

6x = -13

x = -13/6

y = 5(-13/6) + 6

y = -29/6

The solution is (-13/6, -29/6) and that tells us that the two lines do not intersect at the origin or any of the two axis.

If they intersected at the origin, then the solution should have been (0, 0).

If they intersected at the x-axis, the solution should have been (x, 0).

If the two lines intersected at the y-axis, the solution would have been (0, y).

The answer is A) Line y = 5x + 6 intersects the line y = −x − 7.

To learn more on equation click:

brainly.com/question/24169758

#SPJ1

complete question:

Consider the following system of equations: y = 5x + 6 y = −x − 7 Which description best describes the solution to the system of equations?

Line y = 5x + 6 intersects line y = −x − 7.

Lines y = 5x + 6 and y = −x − 7 intersect the x-axis.

Lines y = 5x + 6 and y = −x − 7 intersect the y-axis.

Line y = 5x + 6 intersects the origin.

Each side of cube is 100 cm.

In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.

Given that,

Volume of cube = 1 cubic meter

We know that,

1 m = 100 cm

Also  volume of cube = \(a^{3}\)

Then,

Volume of cube = 1000000 cm

                   \(a^{3}\)  = \(100^{3}\)

                   a = 100 cm

Hence, Each side of cube is 100 cm.

To learn more about cube from the given link:

https://brainly.com/question/1972490

#SPJ4

Answer: 7*\(\sqrt{3}\)

Step-by-step explanation:

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

To learn more about annual interest rate click here: brainly.com/question/20631001

#SPJ11

Step-by-step explanation:

To help solve this question we will put it into a ratio:

MILES:KM

5        :8              This ratio shows that 5 miles equals 8km.

47.5         :76       We can put 76 on the km side because we are told that in                                    

                            in the question. Lets find out how many times 8 was

                            multiplied to equal 76. 76 divided by 8=9.5 Because 8 was

                            multiplied by 9.5 we shall multiply 5km by 9.5  5x9.5=47.5

Therefore 76km is equal to 47.5miles.

Answer:

2.80$

Step-by-step explanation:

56 times 5

Answer:

32=x+2x+4x

32=7x

x=4.571428571428571428

and,2x=9.142857142857142857

and,4x=18.28571428571428571

Step-by-step explanation:

hope it helps

mark me as brainliest

Answer:

Lengths are 32/7, 64/7, and 128/7

I recommend seeing the explanation. I included the answers in decimal, how I got each answer, and which sides is for which expression

Step-by-step explanation:

A perimeter is the length of all sides and we know the perimeter of this triangle is 32 meters. It's given that the three sides of the triangle are x, 2x, and 4x, so if we add these sides together, we get 32

x + 2x + 4x = 32

We have to solve for x before we proceed to anything else

x + 2x + 4x = 32

Add like terms

7x = 32

Divide both sides by 7

x = 32/7 or 4.5714

Now that we have solved for x, we can now move on to find the sides. One of the sides is x meters and we already know x is equal to 32/7, so that is our answer.

To find 2x meters, we will have to multiply 2 by 32/7

2 * 32/7

We have to find a denominator for 2 that will both terms like fractions. 14/7 is the same as 2 so we will replace 2 with that (or you could find the LCM)

14/7 * 32/7 = 448/49

448 and 49 has a common factor of 7, so we will divide the numerator and denominator by 7

448 ÷ 7/49 ÷ 7 = 64/7

2x = 64/7 or 9.1428

To find 4x meters, we wil lhave to multiply 4 by 32/7

4 * 32/7

We will use the same method of making 4 into a fraction that is like terms with 32/7 (or find the LCM again)

28/7 * 32/7 = 896/49

896 and 49 has a common factor of 7, so we will divide the numerator and denominator by 7

896 ÷ 7/49 ÷ 7 = 128/7

4x = 128/7 or 18.2857

Answer:

h-4^10

Step-by-step explanation:

The difference of h and 4 is h-4

to the 10th power, is putting 10 as the exponent.

The net return, in this case, is -$3,650, indicating a negative return. A negative net return suggests that the investment is not profitable and results in a loss of $3,650.

The net return can be calculated by multiplying the price and yield, and then subtracting the cost. In this scenario, with a price of $350, yield of 11 tons, and a cost of $7,500, the net return is calculated as follows:

Net Return = (Price * Yield) - Cost

= ($350 * 11) - $7,500

= $3,850 - $7,500

= -$3,650

The net return in this case is -$3,650, indicating a negative return. This means that the cost of $7,500 exceeds the revenue generated from the given price and yield values of $3,850. A negative net return suggests that the investment is not profitable and results in a loss of $3,650. It is important to consider these financial aspects when making decisions related to pricing, yield, and cost in order to achieve positive net returns and profitability.

Learn more about cost here:

https://brainly.com/question/10673310

#SPJ11

Answer:

If I know I will defiantly answer .but where is the question

In the situation, the number of bacterias are doubling for each sheet of paper cut, thus, the exponential equation for the puber is:

\(f(n) = 2^n\)

Initially, there was only one sheet of paper. Then, each sheet is cut in half, so we will have 2 sheets, then 4 sheets, then 8 sheets, and so on. That is, the number of sheets is continuously doubling, thus, the population after n cuts can be modeled by the following exponential equation:

\(f(n) = 2^n\)

A similar problem is given at https://brainly.com/question/15563161

The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.

To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.

Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.

Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.

Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.

Therefore, the correct answer is option c. π/4.

To know more about circle refer here:

https://brainly.com/question/11987349

#SPJ11

2. alternate angles I think

3. vertically opposite angles

4. Interior angles

Answer:

expanded form : 4000+ 600+ 50+ 1.

The correct answer is y=1/2+2

The result of the addition of fractions is given by:

D. \(-\frac{19}{x - 5}\)

The original expression is given by:

\(\frac{x^2 + 10x + 25}{x + 5} - \frac{x^2 - 6}{x - 5}\)

We consider the square of the sum notable product, given as follows:

(a + b)² = a² + 2ab + b².

Hence the following simplification can be applied:

Thus, we can simplify the expression as follows:

\(\frac{x^2 + 10x + 25}{x + 5} - \frac{x^2 - 6}{x - 5} = x + 5 - \frac{x^2 - 6}{x - 5}\)

Then, applying the least common factor of the denominator for the sum of the fractions, we have that:

\(x + 5 - \frac{x^2 - 6}{x - 5} = \frac{(x + 5)(x - 5) - x^2 + 6}{x - 5} = \frac{x^2 - 25 - x^2  + 6}{x - 5} = -\frac{19}{x - 5}\)

Hence the equivalent expression is:

D. \(-\frac{19}{x - 5}\)

More can be learned about addition of fractions at https://brainly.com/question/78672
#SPJ1

Answer:

\(x=-2\)

Step-by-step explanation:

This is a vertical line, so the equation is of the form \(x=c\). Since the line passes through \((-2,2)\), it follows that \(c=-2\).

Answer:

See below

Step-by-step explanation:

A binomial distribution has the value of x representing the number of successes in n​ trials, while a geometric distribution has the value of x representing the first trial that results in a success.

The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

Learn more about Graphical method

brainly.com/question/29193266

#SPJ11

With all of the edges 6 feet long, the total surface area of the greenhouse including the floor is approximately 98.39 ft².

To find the total surface area of Reina's greenhouse, we'll need to calculate the area of the equilateral triangular sides and the square base.

1. Equilateral triangular sides:
There are four congruent equilateral triangles with edges of 6 feet each. To find the area of one triangle, we can use the formula A = (s² * √3) / 4, where A is the area and s is the side length.

A = (6² * √3) / 4 = (36 * √3) / 4 = 9√3 square feet

Since there are four triangles, the total area of the triangular sides is 4 * 9√3 = 36√3 square feet.

2. Square base:
The base is a square with side lengths of 6 feet. To find the area, we can use the formula A = s².

A = 6² = 36 square feet

Now, let's add the area of the triangular sides and the square base

Total surface area = 36√3 + 36 ≈ 98.39 ft² (rounded to the nearest hundredth)

So, the total surface area of the greenhouse including the floor is approximately 98.39 ft².

More on area: https://brainly.com/question/14849668

#SPJ11

The equation that represents the situation is:

d = 525h

In this equation, d represents the distance traveled and h represents the number of hours spent flying. The equation states that the distance traveled (d) is equal to the product of the speed (525 miles per hour) and the number of hours spent flying (h). This equation shows the relationship between the distance and time for the airplane flying at a constant speed of 525 miles per hour.

       The Equation Representing The Situation is:

       d  =  525 *  h

Make A Plan:

We need to find the Equation representing the relationship between the distance traveled (D) and the number of hours spent flying (H).

The Airplane is flying at a Constant Speed of 525 Miles Per Hour (mph). However, The Distance Traveled is Equal to the speed Multiplied by the Time Spent Flying.  

        d   =   525  *   h

        The Equation Representing The Situation is:

        d  =  525 *  h

I hope this helps you!

Answer:

Step-by-step explanation:

The way I see it is that since it has no thousandths place then the answer should be 197.82.

The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

The given equation represents the motion of a mass connected to a spring with viscous friction. To plot the displacement, y(t), we need to solve the differential equation. With initial conditions y(0) = 0, we can find the solution using the Laplace transform. After solving the equation, we can plot y(t) for t < 0 and t ≥ 0 separately. For t < 0, the applied force, f(t), is zero, so the mass will not experience any external force and will remain at rest. For t ≥ 0, the applied force is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position.

To solve the given differential equation, we can start by finding the characteristic equation by setting the coefficients of y, its derivative, and its second derivative to zero:

s^2 + 18s + 102 = 0.

Solving this quadratic equation gives us the roots s1 = -3 + 3i and s2 = -3 - 3i. These complex roots indicate that the mass will undergo damped oscillations.

Using the Laplace transform, we can solve the differential equation and obtain the expression for Y(s), the Laplace transform of y(t):

(s^2 + 18s + 102)Y(s) = F(s),

where F(s) is the Laplace transform of f(t). Since f(t) = 10 for t ≥ 0, its Laplace transform is F(s) = 10/s.

Solving for Y(s) gives us:

Y(s) = 10 / [(s^2 + 18s + 102)].

To find y(t), we need to inverse Laplace transform Y(s). Using partial fraction decomposition, we can express Y(s) as:

Y(s) = A / (s - s1) + B / (s - s2),

where A and B are constants to be determined. After finding A and B, we can inverse Laplace transform Y(s) to obtain y(t).

With the given initial condition y(0) = 0, we can solve for A and B by setting up equations using the initial value theorem:

A / (s1 - s1) + B / (s1 - s2) = 0,

A / (s2 - s1) + B / (s2 - s2) = 0.

Solving these equations will give us the values of A and B. Finally, we can substitute these values back into the inverse Laplace transform of Y(s) to obtain y(t).

For t < 0, since the applied force f(t) is zero, the mass will not experience any external force. Therefore, y(t) will remain at its initial position, y(0) = 0.

For t ≥ 0, the applied force f(t) is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position. The displacement, y(t), will depend on the properties of the mass, the spring, and the viscous friction. The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

Learn more about equation here: brainly.com/question/29657983

#SPJ11

In 0.75lb (340g) of 85% lean ground beef, there are approximately 72 grams of fat.

To calculate the grams of fat in 0.75lb of 85% lean ground beef, we need to determine the fat content based on the percentage given. The term "85% lean" indicates that 85% of the weight of the ground beef is lean meat, while the remaining 15% is fat.

First, we convert 0.75lb to grams. Since 1lb is equal to 454g, multiplying 0.75lb by 454g/lb gives us 340g.

Next, we calculate the fat content by multiplying the weight of the ground beef (340g) by the percentage of fat (15%).

340g * 0.15 = 51g

Therefore, in 0.75lb (340g) of 85% lean ground beef, there are approximately 51 grams of fat.

However, the question asks for the fat content, so we subtract this value from the total weight to find the grams of fat:

340g - 51g = 289g

Therefore, there are approximately 72 grams of fat in 0.75lb (340g) of 85% lean ground beef.

Learn more about: Approximately

brainly.com/question/30707441

#SPJ11