Find, to the nearest tenth, the area of the region that is inside the square and outside the circle. the diameter of the circle is 14 in. 10.5 in2 42.1 in2 153.9 in2 196 in2
Answers
Answer:
Option [tex]42.1\ in^{2}[/tex]
Step-by-step explanation:
we know that
The area of the region that is inside the square and outside the circle is equal to the area of the square minus the area of the circle
see the attached figure to better understand the problem
Step 1
Find the area of the square
Remember that
The area of the square is
[tex]A=b^{2}[/tex]
where
b is the length side of the square
we have
[tex]b=14\ in[/tex]
substitute
[tex]A=14^{2}=196\ in^{2}[/tex]
Step 2
Find the area of the circle
Remember that
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=14/2=7\ in[/tex]
substitute
[tex]A=\pi(7^{2})=153.9\ in^{2}[/tex]
Step 3
Find the area of the region
[tex]196\ in^{2}-153.9\ in^{2}=42.1\ in^{2}[/tex]
Related Questions
When seven times a number is decreased by 66 the result is 50. what is the number?
Answers
why does the sum of -4 and 3 complain more than the sum of -3 and 5
Answers
Final answer:
The sum of -4 and 3 is -1 because we subtract the smaller number from the larger and keep the sign of the larger absolute value number. The sum of -3 and 5 is positive 2 for the same reason.
Explanation:
The question seems to be asking about the rules for adding numbers with different signs. When adding -4 and 3, which have opposite signs, you subtract the smaller number from the larger number, and the sign of the answer is the same as the sign of the larger absolute value number.
So the sum is -1, because 4 is larger than 3, and the sign is negative. In contrast, when adding -3 and 5, you also subtract the smaller number from the larger, but since 5 is greater than 3, the sum is 2, and it has a positive sign because 5 has a positive sign.
Examples demonstrate the rules of addition:
When two positive numbers are added, like 3 + 2, the result is a positive 5.If two negative numbers are added, for example, -4 + (-2), the result is a negative -6.Mixing a negative and a positive number, such as -5 + 3, the result is -2, mirroring the sign of the larger absolute value number.These basic rules ensure clarity in arithmetic operations and provide a foundation for more complex math problems. The 'complaints' likely refer to the unexpected results when dealing with negative numbers, which can seem counterintuitive but follow consistent mathematical rules.
I need help with #22
Answers
Answer:
[tex]4 = y \\ 4 = x[/tex]
Step-by-step explanation:
The isosceles triangle containing the side of y + 12 is congruent to 3x² - 32 [base angles are congruent], and if you look closer, they are also equivalent to all three sides of the equilateral triangle adjacent to the isosceles triangle. So, we will be working with alot gadgets here, if you know what I mean. Anyway, this is how we start out:
[tex]5y - 4 = y + 12[/tex]
-5y - 5y
___________________
-4 = -4y + 12
-12 - 12
____________
-16 = -4y
___ ___
-4 -4
4 = y [Plug this back into both equations to get the value of 16.]
Next, you will set 3x² - 32 equal to 16:
[tex]16 = 3{x}^{2} - 32[/tex]
+32 + 32
_________________
48 = 3x²
__ ___
3 3
16 = x²
4 = x [In this case, we want the NON-NEGATIVE root because inputting a -4 for x will not give us identical answers.]
I am joyous to assist you anytime.
How to find the variance of a sample with only mean standard deviation size?
Answers
so if the variance is 100, then the standard deviation is sqrt 100 = 10
or, if u have the standard deviation of 10....then to find the variance, u square it....so the variance is 10^2 = 100
Why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand? Explain your reasoning.
Answers
Sample Response: A graphing calculator is more accurate than graphing by hand. If the slope and/or y-intercept is a fraction or decimal, it is more difficult to accurately graph by hand. Using a calculator might also be more time efficient because it might accept a line in any form. A calculator’s window can be adjusted quickly instead of having to redraw a graph by hand when adjusting the scale.
For time efficiency and to get a more precise solution.
Why a graphing calculator is better than graphing by hand?
There are two reasons.
1) In a graphing calculator you only need to input the functions and that's all, it will graph the functions for you, so it needs a lot less time than graphing by hand.
2) When you graph by hand, there is a limit in how much of an exact solution you can get (and there may be a mistake if the line is to thick or something like that). While in a graphing calculator you can find the exact point where the graphs intersect, so you will get a more precise solution with a graphing calculator.
These are the two reasons why using a graphing calculator may be better than graphing by hand.
If you want to learn more about systems of equations, you can read:
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How do I prove the corresponding angles theorem?
Answers
Final answer:
The corresponding angles theorem states angles in matching corners are equal when two parallel lines are intersected by a transversal. To prove this, use properties of parallel lines and transversals, and various established theorems. Euclidean postulates are employed, rather than the Pythagorean theorem or trigonometry.
Explanation:
To prove the corresponding angles theorem, one must understand that when two parallel lines are intersected by a transversal, the angles in matching corners are equal. These are called corresponding angles. For instance, suppose you have two parallel lines L1 and L2, and a transversal T that intersects them at points A and B respectively. The angle ∠PAB on line L1 would correspond to angle ∠QBA on line L2, and they would be equal.
To provide a mathematical proof, one would typically use properties of parallel lines and transversals, or other established theorems such as the alternate interior angles theorem or the exterior angle theorem. By proving all these other angles are equal due to their relationships with each other (alternate interior, consecutive interior, alternate exterior angles, etc.), one can by default establish that corresponding angles must also be equal.
Proof of this theorem often involves constructing supplementary and congruent angles and using the postulates of Euclidean geometry. The Pythagorean theorem and trigonometry need not be involved in this proof unless one is working with right triangles formed by the transversal and the parallel lines, or if dealing with more complex geometric problems.
Is 770 x 6 = 77 x 6 x 100 true or false?
Answers
because 770 x 6 = 4620
and 77 x 6 x 100 = 46200
The equation 770 x 6 = 77 x 6 x 100 is false.
To determine if the equation 770 x 6 = 77 x 6 x 100 is true or false, let's evaluate both sides of the equation.
On the left side:
770 x 6 = 4,620
On the right side:
77 x 6 x 100 = 46,200
Since 4,620 is not equal to 46,200, the equation 770 x 6 = 77 x 6 x 100 is false.
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Graph the system of constraints and find the value of x and y that maximize the objective function.
Answers
We want to maximize C, which is C= 7x - 3y. Let's explore our intuition regarding how this will look. We know that both y and x are greater than or equal to zero, which means -3y will be a negative number (or 0) and x is a positive number (or 0). We want to get x as big as possible, given the constraints, we want y to be zero, if possible
We see that, based on the constraints, y is greater than or equal to zero,
but it has no other minimum value established. We only know that y and x add up
to 5, and that y is less than or equal to (1/5)x + 2. That means y could be
0 and still satisfy the constraints.
In order to maximize C, we want to be 5 as possible
and y to be zero:
C = 7 (5) - 3(0)
C=35
Answer: Solving Systems Using Matrices Quiz Part 1
1. c) (5,0)
2. a) 20 of type A; 20 of type B
3. d) no solution
4. a) -5
5. d) 11 -12 7 5 12 -7
6. a) (-6,8)
Factor. 2xy+5x−12y−30
Answers
x(2y + 5) - 6( 2y + 5)
(2y+5) (x-6)
this is the anwser to your problem
(2y+5)(x-6)
Find height of triangle given hypotenuse and angle
Answers
then Sin(A) = h/H
so h = HSin(A)
The Statement of Theorem should be in what form?
if-then
then-if
maybe-conclusion
does not matter
Answers
Answer: If/then.
Step-by-step explanation: A theorem is a statement that has been proven on the basis of other statements, for example other theorems, which are known to be true.
We use the pattern "If A...., then B..." when we known that "A" is a statement that is true and we want to declare that since A is true, B should also be true.
Is this right? Domain and range of a function
Answers
Nice work on getting the correct answer.
Identify each sequence below as geometric, arithmetic, or neither.
(a) 1, 3, 5, 7, 9, 11, 13, 15
(b) 21, 16, 12, 9, 7, 6
(c) .3, .03. .003, .0003, .00003
(d) -4, -12, -36, -108, -324
Answers
Sequence (a) is an arithmetic sequence because the common difference is constant. Sequence (d) is a geometric sequence because the common ratio is constant. Sequences (b) and (c) do not follow the patterns of arithmetic or geometric sequences and are neither.
Explanation:The question asks to identify each sequence as arithmetic, geometric, or neither.
Arithmetic sequence: In an arithmetic sequence, the difference between successive terms is constant. This difference is also called the common difference. For example, the sequence (a) 1, 3, 5, 7, 9, 11, 13, 15 is an arithmetic sequence because the common difference between the terms is 2.Geometric sequence: In a geometric sequence, the ratio of any two successive terms is constant. This ratio is also called the common ratio. For example, the sequence (d) -4, -12, -36, -108, -324 is a geometric sequence because the common ratio between the terms is 3.Neither: If a sequence is not arithmetic or geometric, it is classified as neither. For example, the sequence (b) 21, 16, 12, 9, 7, 6 and (c) .3, .03, .003, .0003, .00003 do not follow the patterns of arithmetic or geometric sequences and therefore are classified as neither.Learn more about Sequence Identification here:https://brainly.com/question/30531377
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Factor the expression completely over the complex numbers.
x4−625
Answers
Prove: The midsegment between sides Line segment AB and Line segment BC is parallel to side Line segment AC.
Answers
have a nice day sir/maam
5 with a negative exponent of 4 over 5 with a exponent of 3 simplified
A.) 5 with an exponent of 7
B.) 5 with a negative exponent of 1
C.) 1 over 5 (fraction)
D.) 1 over 5 with an exponent of 7
Answers
Regardless, apply the exponent rule x^a/x^b = 1/x^b - a
5^-5/5^3 = 1/5^3 - (-5) = 1/5^8
Therefore the final answer is.
[tex] \frac{1}{5^8} [/tex]
Which conjunction or disjunction is equivalent to the this inequality?
5-3 |p+4| <= -10
p + 4 ≤ 5 AND p + 4 ≥ -5
p + 4 ≤ 5 OR p + 4 ≥ -5
p + 4 ≥ 5 OR p + 4 ≤ -5
p + 4 ≥ 5 AND p + 4 ≤ -5
Answers
=> (2) |p + 4| ≤ - 10
=> | p -4 | ≤ 10 / 2
=> | p - 4 | ≤ 5
=> (p + 4) ≤ - 5 and -(p+4) ≤ - 5
- (p + 4) ≤ - 5 is equivalent to p + 4 ≥ 5
So, the answer is p + 4 ≤ - 5 and p + 4 ≥ 5. That is the fourth option
p + 4 ≥ 5 AND p + 4 ≤ -5.
20! / 16! = a 24 b 11,628 c 116,280 d A number too big to compute
Answers
20! / 16! =
20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
divided by
16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
equals C. 116,280
Mattie,Joel,and Oscar each ate 325 calories at lunch each day for 18 days.About how many calories did they eat in all
Answers
[tex]325 \times 3[/tex]
which equals 975
Next, you multiply that by 18
[tex]975 \times 18[/tex]
The answer is 17559
[tex]17559[/tex]
John surveyed 30 members of a country club. He found that 9 members had signed up for tennis.
What is the experimental probability that the next member surveyed will sign up for tennis?
A.
0.3
B.
0
C.
0.7
D.
1
Answers
The experimental probability that the next member surveyed will sign up for tennis is 0.3, based on the current data where 9 out of 30 members have signed up.
The question is asking for the experimental probability that the next member surveyed at the country club will sign up for tennis based on a survey of 30 members where 9 had already signed up for tennis.
To calculate the experimental probability, you divide the number of members who have signed up for tennis by the total number of members surveyed. So, the calculation would be:
Number of members who signed up for tennis: 9Total members surveyed: 30The experimental probability is then calculated as 9/30, which simplifies to 0.3. Therefore, the correct answer is:
A. 0.3
A rectangular sandbox has a width of 5 feet. The sandbox is 5 times as long as it is wide. what is the perimeter of the sandbox?
Answers
25+25+5+5=60
Perimeter= 60ft
Hope this helps you out! Have an AWESOME rest of your day!
A triangle has two sides of length 2 and 17. what is the smallest possible whole-number length for the third side?
Answers
A bowl contains 10 quarters, 20 dimes, 15 nickels, and 5 pennies. a coin is selected at random and kept and then a second coin is selected at random. which combination would have a probability of 6/49?
Answers
In this case, the coin is taken twice, that means the denominator should be 50*49. But in this question, the probablity value is 6/49, so you need to convert it into 50*49 by multiplying the numerator with 50. The value should be:
6/49 *50/50= 300/49*50
The number 300 is multiplication of 20 and 15, that mean the answer should be: 1 dimes and 1 nickles
3(x+y)=y, if (x,y) is a solution to the equation above and y cannot equal to zero what is the ratio x/y
Answers
3(x+y)=y
y is not equal to zero
*Solution
1. The given equation is 3(x+y) = y and we are tasked to find the ratio between x and y. Distributing 3 to the terms in the parenthesis,
3(x+y) = y
3x + 3y = y
Transposing 3y to the right side OR subtracting 3y from both the left-hand side and the right-hand side of the equation would give
3x = -2y
Dividing both sides of the equation by 3,
x = (-2/3)y
Dividing both sides of the equation by y,
x/y = -2/3
Therefore, the ratio x/y has a value of -2/3 provided that y is not equal to zero.
The ratio, x/y in the equation, if y ≠ 0 is: x/y = -2/3.
What is the Solution of an Equation?Solution of an equation is the value of a variable or two variables that makes an equation true.
Given:
3(x+y)=y
We are required to find the ratio, x/y if y ≠ 0.
Thus:
3(x+y)=y
Open bracket
3x + 3y = y
Subtract 3y from both sides
3x = y - 3y
3x = -2y
Divide both sides by 3
x = -2y/3
Divide both sides by y
x/y = -2/3
Therefore, the ratio, x/y in the equation, if y ≠ 0 is: x/y = -2/3.
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Numbers mr. wahl is thinking of two numbers. the sum of the numbers is 27. the product of the numbers is 180. what two numbers is mr. wahl thinking of?
Answers
solve
5t < -15
^^^(the < sign has a line underneath along with the answers)
A. t > 3
B. t < 3
C. t > -3
D. t < -3
Answers
On each coordinate plane,the parent function f(x)=|x| is represented by a dash line translation is represented by a solid line. Which graph represents the The translation g(x)=|x+2| as a solid line?
Answers
Answer:
Refer the attached graph.
Step-by-step explanation:
Given : On each coordinate plane,the parent function [tex]f(x)=|x|[/tex] is represented by a dash line translation is represented by a solid line.
To find : Which graph represents the the translation [tex]g(x)=|x+2|[/tex] as a solid line?
Solution :
The parent function [tex]f(x)=|x|[/tex]
with the vertex (0,0)
And the graph of [tex]g(x)=|x+2|[/tex]
with the vertex (-2,0)
The graph of g(x) is the translation of f(x)
The parent function is translated towards left.
Transformation to the left,
f(x)→f(x+b) , the graph of f(x) is shifted towards left by b unit.
Same as the graph f(x) is shifted towards left by 2 unit and form graph of g(x).
We plot the graph of both the equations in which translation is shown.
Refer the attached graph below.
Michaela climbed up a mountain at an Average speed of 3 mi/h. She climbed down at an average speed of 5 mi/h. What is Michaela's average speed for the entire trip? Round to the nearest tenth
Answers
= 3.75 mi/hr
To find Michaela's average speed for the entire trip, we need to calculate the total distance traveled and the total time taken. The average speed can be calculated as (2D) / (D/3 + D/5), which is approximately 3.53 mi/h.
Explanation:To find Michaela's average speed for the entire trip, we need to calculate the total distance traveled and the total time taken.
Let's assume the distance she climbed up the mountain is D. The distance she climbed down is also D since she retraced her steps. The average speed for climbing up is 3 mi/h and the average speed for climbing down is 5 mi/h.
The total distance is 2D and the total time is D/3 + D/5. Therefore, the average speed can be calculated as (2D) / (D/3 + D/5).
Simplifying this expression gives us the average speed as 3.53 mi/h (rounded to the nearest tenth).
The number of males per 100 females in a country's population is called what?
Answers
The correct answer to your question would be: The sex ratio.
I really hope my answer benefited you! :)
The function f(x)= 70x^3/4 power can be used to estimate the BMR (Basic Metabolic Rate) of mammals. In this function, x is the mass of the animal in kilograms, and f(x) is its BMR in kilocalories (kcal) per day. Note that one kcal is equal to one food calorie. The howler monkeys at a zoo are fed a diet that contains 3.35 kcal per gram. Write a function g(x) that gives the mass of food in grams that a howler monkey must eat to obtain x kilocalories of energy. Please help!