Bill Gates wants to construct an in ground swimming pool for his dog. he wants it's length to be 8 yards shorter than twice it's width. he then wants to surround it with a concrete walkway 6 yards wide. he can only afford 570 square yards of concrete. what should the dimensions be of the pool ?

Mary is 15 years old and Jose is 3 years old. This is determined by setting up a system of linear equations based on the relationship of their ages and solving for their individual ages.

The question involves solving a system of linear equations to find the ages of Mary and Jose. Let's denote Mary's age as M and Jose's age as J. According to the problem, Mary is five times older than Jose, so we have M = 5J. Additionally, the sum of their ages is 18, which gives us a second equation: M + J = 18.

To solve for both ages, substitute the first equation into the second to get: 5J + J = 18. Combining like terms, we get 6J = 18. Dividing both sides by 6 gives us J = 3. This means Jose is 3 years old. To find Mary's age, we substitute J back into the first equation: M = 5(3), resulting in M = 15, so Mary is 15 years old.

To solve this problem, set up a system of equations where Mary's age is M and Jose's age is J. Use substitution method to solve the system. Mary is 15 years old and Jose is 3 years old.

To solve this problem, we can set up a system of equations. Let's assume that Mary's age is M and Jose's age is J. We are given two pieces of information: 1) Mary's age is 5 times Jose's age, so we can write the equation M = 5J, and 2) the sum of their ages is 18, so we can write the equation M + J = 18.

Now we have a system of two equations with two variables:

We can solve this system by substitution or elimination. Let's use the substitution method. From equation 1, we know that M = 5J. We can substitute this value of M into equation 2 and solve for J:

5J + J = 18

6J = 18

J = 3

Now that we know J, we can substitute this value into equation 1 to find M:

M = 5(3) = 15

Therefore, Mary is 15 years old and Jose is 3 years old.

The following are the value of the unknown length x to the nearest tenth;

9. x = 9.0

10. x = 16.3

11. x = 54.1

12. x = 46.7

What is the value of the unknown length?

9.

cos θ = Adjacent / Hypotenuse

cos θ = 90° - 37° = 53°

cos 53° = x/15

cross product

15 × cos 53° = x

15 × 0.601815023152048 = x

x = 9.0272

Approximately, 9.0

10.

cos θ = Adjacent / Hypotenuse

cos 53° = x/27

cross product

27 × cos 53° = x

27 × 0.601815023152048 = x

x = 16.25

Approximately, 16.3

11.

cos θ = Adjacent / Hypotenuse

cos 75° = 14/x

cross product

x × cos 75° = 14

x = 14/cos 75°

x = 14/0.258819045102520

x = 54.1

12.

cos θ = Adjacent / Hypotenuse

cos θ = 90° - 24° = 66°

cos 66° = 19/x

cross product

x × cos 66° = 19

x = 19/cos 66°

x = 19/0.406736643075800

x = 46.7132

Approximately,

x = 46.7

Answer:

old quetstion xd

Step-by-step explanation:

Answer:

5 nights

Step-by-step explanation:

Let x represent the number of nights.  She can spend up to and including 500; this gives us the inequality

60x+150 ≤ 500

Subtract 150 from each side:

60x+150-150 ≤ 500-150

60x ≤ 350

Divide both sides by 60:

60x/60 ≤ 350/60

x ≤ 5.83

Since she cannot stay just a portion of a night, she can stay up to 5 nights.

Jennifer can afford to stay in the hotel for up to 10 nights.

To determine the number of nights Jennifer can afford in the hotel, we need to subtract the cost of the flights from her budget and divide the remaining amount by the cost per night.

First, convert Jennifer's budget from pounds to dollars. Assuming an exchange rate of 1 pound = 1.5 dollars, £500 is equal to $750.

Next, subtract the cost of the flights from Jennifer's budget to find her remaining budget for the hotel. $750 - $150 = $600

Finally, divide the remaining budget by the cost per night to find the number of nights she can afford. $600 / $60 = 10 nights.

Therefore, Jennifer can afford to stay in the hotel for up to 10 nights.

Answer:

To decompose this shape I would draw a vertical line from the vertex that is pointing outside to the vertex that is pointing inside. By doing this the vertical line will give me 2 congruent parallelograms. Yes it's that simple

Step-by-step explanation:

Answer:

Area of circle is 1145.50 cm²

Step-by-step explanation:

Given : Circumference of circle = 120 cm

We have to find the area of the given circle.

Consider the given circle

We know circumference of circle = [tex]2\pi r[/tex]

Thus,  [tex]120=2\pi r[/tex]

Put π = 3.14

We have,

[tex]120 =2\times 3.14\times r[/tex]

Divide both sides by 6.28, we have,

r = 19.1 cm

Now, area of circle = [tex]\pi r^2[/tex]

Put r = 19.1

We have

Area of circle  = 1145.50 cm²

Thus, Area of circle is 1145.50 cm²

Given:

[tex] \angle A=(12x-5)^{\circ}\\ \\ x=9 [/tex]

Solution:

Substitute 9 for x in the expression for angle A.

[tex] \angle A=12(9) -5=108-5=103^{\circ}\\ \\ [/tex]

An obtuse angle is an angle of greater than 90° and less than 180°, so..

[tex] \angle A \; is \; equal \; to \; 103^{\circ} \; and \; it \; is \; an \; Obtuse \; Angle! [/tex]

Answer:

The answer is 1/6 yard

Step-by-step explanation:

The length, width, and height of a cube are equal. Each cubic block must have the same length, width, and height:

Length of tank= 1/6 yard = 1/6 yard = 3 x 1/6 yard

Height of tank: 2/6 yard = 2 x 1/6 yard

width of tank= 1/6 yard

Because the length and height of the tank are multiples of the width, the length of each cubic block should be equal to the width of the tank:

= 1.6 yard

Here is your answer, my good sir, or maiden.

Final answer:

To find the volume of a sphere with a diameter of 6 cm, first determine the radius, which is 3 cm, and then use the formula V = (4/3)πr³ to calculate the volume, resulting in approximately 113.097 cm³.

Explanation:

The volume of a sphere is calculated using the formula V = (4/3)πr³, where V represents the volume and r is the radius of the sphere. When the diameter of the sphere is given as 6 cm, the radius is half of that, which is 3 cm. Therefore, substituting the radius into the formula yields:

V = (4/3)π(3 cm)³ = (4/3)π(27 cm³) = 36π cm³

This results in a volume of approximately 113.097 cm³ (since π is approximately 3.14159).

Answer:

21.5

Step-by-step explanation:

took test 100% 4.08 Quiz: Finding the Volume of Rectangular Prisms and Problem Solving

The logarithmic graph for the function loga(x) represents relationships similar to that of a log-log plot such as exponential relationships. Understanding properties of logarithms and principles of graphing can help interpret this function. Unlike linear equations, these graphs have a unique shape that are not straight lines.

The graph of the logarithmic function f(x) = loga(x) can be understood using logarithmic properties and graph principles. The log-log plot reveals that logarithmic graphs represent exponential relationships such as the decay of radioactivity or the relationship between light's frequency and wavelength. The logarithmic scale is advantageous in graphing large ranges of values.

There are a few principles to note about logarithms for this. For instance, the logarithm of a number with an exponent is equal to the exponent multiplied by the logarithm of the number. Similarly, the logarithm resulting from dividing two numbers is the difference between the logarithms of the two numbers. These properties can be helpful in interpreting the logarithmic graph.

Our graph, however, is not a straight line as in the case of linear equations which have a uniform slope, a y-intercept and x as the horizontal axis. Logarithmic graphs have unique characteristics determined by the base and the values of x.

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