Find correct two decimal places, the radius of the circle with the given circumference: 35cm

Answers

Answer 1

Answer: $C=2 \pi r$
C - circumference, r - radius

$C=35 \ [cm] \n \n35=2 \pi r \nr=(35)/(2 \pi) \nr=(17.5)/(\pi) \n\boxed{r \approx 5.57 \ [cm]}$

Answer 2

Answer: $C=2\pi r=35\n2\pi r=35\nr=(35)/(2\pi)\approx5.57\text{ cm}$

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An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for eachdog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday.
Write an equation to represent the possible numbers of cats and dogs that could have been at the
shelter on Wednesday.
Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s
numbers possible? Use your equation to justify your answer.
Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on
Wednesday. How many cats were at the shelter on Wednesday?

Answers

Equation:
89.50=2.35c+5.50d

If theres 22 dogs and cats in total you can plug in number less than 22 for c(# of cats) and d(# of dogs).

So we try pats numbers 8 cats and 14 dogs so

89.50=2.35(8)+5.50(14)

89.50=18.8+77

89.50=95.8

So pats numbers were wrong so we try different numbers

So i started pluging in numbers from under 22 so i got c is 10 and d is 12 lets try it with the equation

89.50=2.35(10)+5.50(12)

89.50=23.5+66

89.50=89.50 so it works the answer to how many number of dogs and cats is 12 dogs and 10 cats

Final answer:

The equation representing the costs to care for the animals is 2.35c + 5.5d = $89.50. Pat's proposal of 8 cats and 14 dogs does not match the costs. Upon using additional information of the total number of animals being 22, we can solve the system of equations to find that there were 16 cats and 6 dogs at the shelter on Wednesday.

Explanation:

Let's denote the number of cats as c and the number of dogs as d. We know from the cost of care per day per animal that 2.35c + 5.5d = $89.50. This is the equation representing the possible number of cats and dogs at the shelter in terms of costs. For Pat's numbers, we can substitute c=8 and d=14 into the equation and check if they are possible. That is, substitute and check if 2.35(8) + 5.5(14) equals to 89.5. In this case, it does not since the total here comes to more than $89.50. So, Pat's numbers were not possible.

Regarding the total number of animals, we know that c + d = 22. With this equation, we can solve the system of equations to find out the actual number of cats and dogs at the shelter on Wednesday. Solving these two equations, we will find that 16 cats and 6 dogs were present at the shelter on Wednesday.

Learn more about System of Equations here:

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If the domain of the square root function f(x) is x<=7, which statement must be true?7 is subtracted from the x-term inside the radical.
The radical is multiplied by a negative number.
7 is added to the radical term.
The x-term inside the radical has a negative coefficient.

Answers

Consider the funcion $y=√(x)$ . The dmain of this function is $\ge 0$ and the range is $y\ge 0$ .

Now if $x\le 7$ you can calculate that

$x-7\le 0,\n 7-x\ge 0$

and the function $y=√(7-x)$ will have the domain $x\le 7$ (state this using that expression under the root is $\ge 0$ ).

As you can see the x-term inside the radical has a negative coefficient.

Answer: correct choice is D.

Correct answer is D.

The expression inside the radical must be greater than or equal to zero.

$x \leq 7\n0 \leq 7-x\n7-x \geq 0$

Therefore, the x-term inside the radical has a negative coefficient.

Functions f(x) and g(x) are both increasing. In addition, the range of g is in domain of f. Prove that composite function f(g(x)) is increasing

Answers

f: D -> E;
g: F -> G, where, g(F) is in D;

Let be x1, x2 ∈ F, with x1 < x2;
But, g(x1) < g(x2), because g is increasing; => f(g(x1) < f(g(x2) , because f is increasing =>
f(g(x) is increasing.

The division property of equality could be used to solve which of the following equations?a. 5x= 30
b. x+ 3 = 7
c. (x+ 2) (x- 2) = 0
d. = 16

Answers

If you would like to know which of the above equations could be solved by the division property of equality, you can find this using the following steps:

a. 5 * x = 30 /5
x = 30 / 5
x = 6
b. x + 3 = 7 /-3
x = 7 - 3 = 4
c. (x + 2) * (x - 2) = 0
1. x = -2
2. x = 2
d. = 16

The correct result would be a. 5 * x = 30 can be solved by the division property of equality.

Answer:

Option a is correct that is 5x=30 will use division property of equality.

Step-by-step explanation:

We have been given four different equations we need to tell which one could be used to solve by division property:

In Option a:

x can will be solved by division property

$5x=30$

5 will divide 30 on right hand side by the transformation rule which is

when multiplication is shifted to the other side of the equation it will be in division on the other side.

$x=6$

Therefore, option a is correct.

What expression is factor of 6x^3-13x^2-28x

Answers

The answer is $x(2x-7)(3x+4)$

Hope this helps!

This is the expression that is a factor of the equation above: x(2x-7)(3x+4)

If x / y is an integer, which of the following statements must be true?A. both x and y are integers
B. x is an integer
C. either x or y is negative
D. y / x is an integer
E. x = ny where n is an integer

Answers

Only E) is true. If I were to arbitrarily pick x = 2.2 and y =1.1, then I could show that A), B), C), and D) to be false, given x/y = 2.2/1.1 = 2 (which is an integer). However for E), if we define x/y = n where n is an integer, then by rearranging terms, we can show x = n*y where n still equals an integer and our original equation is still valid.

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