Work out the circumference of this circle.
Take pi to be 3.142 and give your answer to 1 decimal place
The radius is 4cm

The length of RS is 64 units. Therefore, the correct answer is C. 64.

Since HJKL is similar to QRST, corresponding sides of the two figures are proportional.

Given that the scale factor applied to HJKL to create QRST is 8 to 7, this means that the ratio of corresponding sides of HJKL to QRST is 8:7.

Let's denote the length of RS as x.

According to the scale factor, the ratio of corresponding sides RS and HJ is 8:7. So, we can set up the following proportion:

[tex]\[\frac{RS}{HJ} = \frac{8}{7}\][/tex]

Given that HJ is 56 units (since 8 times the length of HJ), we can solve for RS:

[tex]\[x = \frac{8}{7} \times 56\][/tex]

[tex]\[x = \frac{448}{7}\][/tex]

[tex]\[x = 64\][/tex]

Therefore, RS is 64 units.

So, the correct answer is C. 64.

Say f(x) = y.

Consider option A.

[tex]y=\sqrt{x} -2[/tex]

[tex]y+2=\sqrt{x}[/tex]

Squaring, we get,

[tex](y+2)^{2} =x[/tex]

Clearly, the above equation represents a parabola (open right) with vertex at (0, -2).

We can easily notice that this function is graphed.

The original two-digit number is 86. We determined this through solving a system of equations where the sum of the digits is 14 and doubling the reversed number before adding it to the original number equals 222.

The student is given a mathematical problem involving a two-digit number. First, we are told that the sum of the digits of the number is 14. Let's assume that the number is made up of digits a and b, where a is the tens digit and b is the ones digit. Therefore, our number can be represented as 10a + b and the reversed number as 10b + a.

According to the given information:

Writing the second equation in standard form gives us 20b + 2a + 10a + b = 222, which simplifies to 21b + 12a = 222. Using the first equation, we can substitute the value of b as (14 - a) into the second equation, resulting in 21(14 - a) + 12a = 222. Solving for 'a' gives us a value of 8, and consequently, b equals 6. Therefore, the original number is 86.

The original number is 86.

To find the original number, let's assume the tens digit as 'x' and the units digit as 'y'. So, the original number can be written as 10x + y.

According to the question, we have two equations:

Equation 1: x + y = 14 (The sum of digits is 14)

Equation 2: (10y + x) + 2(10x + y) = 222 (Double the reversed number and add it to the original number is 222)

Simplifying Equation 2, we get: 12x + 21y = 222

We can now solve the system of equations by substituting the value of 'x' from Equation 1 into Equation 2:

12(14 - y) + 21y = 222

Simplifying further, we get:

168 - 12y + 21y = 222

Combining the 'y' terms, we get:

9y = 54

Dividing both sides by 9, we get:

y = 6

Substituting the value of 'y' into Equation 1, we get:

x + 6 = 14

Subtracting 6 from both sides, we get:

x = 8

Therefore, the original number is 10x + y = 10(8) + 6 = 86.

Here are a bunch of CORRECT answers, your answer is somewhere in there. For the first CORRECT answer the second point is -5,-9. Don't make the same mistake I did on question 3, but it still shows the correct answer. I love to help.

Final answer:

To find the area of the banner with a given perimeter of 72 inches and a width that is 1/3 its length, we first determine the length to be 27 inches and the width to be 9 inches, leading to an area of 243 square inches.

Explanation:

To solve the problem, let's denote the length of the rectangular banner as L inches and the width as W inches. We're given that the perimeter is 72 inches and that the width is 1/3 its length, hence W = 1/3 * L. The formula for the perimeter of a rectangle is 2L + 2W = 72.

Substituting the value of W in terms of L into the perimeter equation gives 2L + 2(1/3 * L) = 72. Simplifying this equation: 2L + 2/3L = 72, or (6/3)L + (2/3)L = 72, which simplifies to (8/3)L = 72. By solving this equation, we find that L = 27 inches. Therefore, W = 1/3 * 27 = 9 inches.

Finally, the area of the rectangle, which is Length × Width, can now be calculated as 27 inches × 9 inches = 243 square inches.

its d so i really hope this help

Using the quadratic equation f(x) = -16[tex]x^2[/tex] + 70x + 10, which models the height of the baseball, we apply the quadratic formula to find that the ball is in the air for approximately 4.438 seconds before it lands back on the ground if not caught.

The student asks how long a baseball remains in the air during practice using a quadratic equation that models the height of the baseball after a certain number of seconds. The equation provided is f(x) = -16[tex]x^2[/tex] + 70x + 10, which models the height in feet of the baseball after x seconds. To determine the time the baseball is in the air, we need to find when the ball returns to the ground level (when f(x) = 0).

We can solve this quadratic equation using the quadratic formula: x = (-b ± [tex]\sqrt{(b^2 - 4ac)) / (2a)}[/tex], where a is -16, b is 70, and c is 10. Plugging in these values, we get two solutions for t (time), and we choose the positive time value at which the height becomes zero again, indicating that the ball has landed back on the ground.

The use of the quadratic formula yields t = 4.438 seconds and t = -0.138 seconds. We discard the negative time value as it is not physically relevant to the problem, and thus the baseball is in the air for approximately 4.438 seconds before it lands back on the ground if it's not caught.