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If a circle has a circumference of 10 pi inches, then what is the area of the same circle in square inches?
To find the area of the circle, use the formula A = πr² and solve for the radius with the equation C = 2πr. Then, substitute the radius value into the area formula to find the area.
Explanation:In order to find the area of the circle, we need to use the formula A = πr², where A is the area and r is the radius of the circle. In this case, we are given that the circumference of the circle is 10π inches.
We know that the formula for circumference of a circle is C = 2πr, where C is the circumference and r is the radius. We can set up an equation to solve for the radius:
10π = 2πrr = 10/2r = 5 inchesNow that we know the radius is 5 inches, we can use the formula A = πr² to find the area:
A = π(5)²A = 25π square inchesSo, the area of the circle is 25π square inches.
The area of the circle is [tex]\( 25\pi \)[/tex] square inches.
To find the area of the circle, we first need to determine the radius of the circle. The circumference [tex]C[/tex] of a circle is given by the formula [tex]\( C = 2\pi r \),[/tex] where [tex]r[/tex] is the radius. Given that the circumference is [tex]\( 10\pi \)[/tex] inches, we can solve for the radius:
[tex]\[ 10\pi = 2\pi r \][/tex]
[tex]\[ r = \frac{10\pi}{2\pi} \][/tex]
[tex]\[ r = 5 \][/tex]
Now that we have the radius, we can find the area [tex]\( A \)[/tex] of the circle using the formula [tex]\( A = \pi r^2 \):[/tex]
[tex]\[ A = \pi (5)^2 \][/tex]
[tex]\[ A = 25\pi \][/tex]
Therefore, the area of the circle is [tex]\( 25\pi \)[/tex] square inches.
When ordering a student desk priced at $69.00, the shipping charges are 6%. What is the total cost of the desk?
What is the simplified form of 1 over x minus 2 over x squared plus x ?
Step-by-step explanation:
Given expression [tex]\frac{1}{x} -\frac{2}{x^2+x}[/tex].
Let is factor second denominator [tex]x^2+x[/tex] first.
Factoring out GCF x we get
[tex]x^2+x= x(x+1)[/tex]
Rewriting the equation
[tex]\frac{1}{x} -\frac{2}{x^2+x} = \frac{1}{x} - \frac{2}{x(x+1)}[/tex]
Now, we need to find the lowest common denominator of x and x(x+1).
The lowest common denominator of x and x(x+1) is x(x+1).
So, we need to multiply first fraction by (x+1) in top and bottom to get lowest common denominator x(x+1) under first fraction.
[tex]\frac{1}{x} - \frac{2}{x(x+1)} = \frac{1(x+1)}{x(x+1)} - \frac{2}{x(x+1)}[/tex]
[tex]= \frac{x+1}{x(x+1)} - \frac{2}{x(x+1)}[/tex]
We got denominators same.
Therefore, subtracting numerators, we get
[tex]=\frac{x+1-2}{x(x+1)}[/tex]
[tex]\frac{x-1}{x(x+1)}[/tex].
Therefore, simplified form is [tex]\frac{x-1}{x(x+1)}[/tex].
The base of a triangular prism is an equilateral triangle with a perimeter of 15in. If the height of the prism is 4in, find the surface area.
Find the area of a rectangle with a length of (4x^2) and a width of (x+6)
An open box with a square base should be constructed. the bottom, should be constructed from a heavy duty cardboard that cost $3 per square inches and the sides from a medium duty cardboard that cost $2 per square inches. if the volume of the box must be 120 cubic inches, what should be the dimensions of the box in order to minimize the cost for the material?
Please help with the question,
To form a quadratic equation, let α and β be the two roots.
Let us assume that the required equation be ax22 + bx + c = 0 (a ≠ 0).
According to the problem, roots of this equation are α and β.
Therefore,
α + β = - baba and αβ = caca.
Now, ax22 + bx + c = 0
⇒ x22 + babax + caca = 0 (Since, a ≠ 0)
⇒ x22 - (α + β)x + αβ = 0, [Since, α + β = -baba and αβ = caca]
⇒ x22 - (sum of the roots)x + product of the roots = 0
⇒ x22 - Sx + P = 0, where S = sum of the roots and P = product of the roots ............... (i)
Formula (i) is used for the formation of a quadratic equation when its roots are given.
Given the roots: (-1+-i)
where; i=sqrt(-1)
Thus, the answer is (2x)
You can also do checking to verify if x^2+2x+2 will have roots equal to (-1+-i)
when Derek planted a tree it was 36 inches tall the tree grew one and one fourth inches per year the tree is now forty four and three fourths how many years ago did Derek plant the tree
Answer:
7
Step-by-step explanation:
Figure out all the fractions in decimal form
44 3/4= 44.75
1 1/4= 1.25
Subtract:
44.75- 36= 8.75
Divide:
8.75/1.25= 7
The answer therefore is 7!
Hope this helps!!!
The equation sin(40o) = can be used to determine the length of line segment AC. What is the length of ? Round to the nearest tenth._____cm
Answer:
12.9 centimetersStep-by-step explanation:
The given equation is
[tex]sin(40\°)=\frac{b}{20}[/tex]
Where [tex]b[/tex] represents the length of the segment AC, according to the given graph.
To find [tex]b[/tex] we just need to isolate it in the given equation,
[tex]b=20sin(40\°)[/tex]
Then, we know that [tex]sin(40\°) \approx 0.64[/tex], so
[tex]b=20(0.64)=12.9cm[/tex]
Therefore, the length of segment AC is 12.9 centimeters, rounded to the nearest tenth.
Answer:
B
Step-by-step explanation:
edge 2021
for every 5 serves Gabby makes tanning makes 3 at volleyball practice Tammy makes 21 serves how many serves did Gabby make show your answer will mark brainiest
Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once.
Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?
Answer:
To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.
Step-by-step explanation:
write (-5,2) and (-5,6) in standard form [if you can describe how to do this for the future]
The price of a dozen roses in the united states is $30. if $0.3472 can purchase 1.00 turkish lira, how much does the same dozen roses cost in turkey if purchasing power parity holds
well $30 is 185.02 in turkish lira.
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- Use your calculator and hit the "2nd" button and then the log button which should be the 10x function. Your answer should be 0.00355.
The concentration of hydrogen ions ([H+]) in the solution with a pH of 2.45 is approximately 0.00355 moles per liter (M).
The process you described is correct for finding the concentration of hydrogen ions ([H+]) from a given pH value using the formula [H+] = 10^(-pH).
Here's how you would calculate the [H+] concentration for a solution with a pH of 2.45:
a) Take the negative of the pH value:
-log(2.45) = -0.389
b) Now, use your calculator and calculate 10 raised to the power of the negative pH value:
10^(-0.389) ≈ 0.00355
So, the concentration of hydrogen ions ([H+]) in the solution with a pH of 2.45 is approximately 0.00355 moles per liter (M).
for such more question on hydrogen ions
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Simplify (x − 4)(x2 − 2x − 3).
a disk jockey wants to select five songs from a new CD that contains 12 songs. How many ways can a disc jockey choose 5 songs
The height of a free falling object at time t can be found using the function, h(t) = - 12t2 + 36t. Where h(t) is the height in feet and t is the in seconds. Find the time when the object hits the ground
An oil company is considering 2 sites on which to drill, described as follows:
Site A: profit of oil is found: $60 million
Loss if no oil is found: $5 million
Probability of finding oil: 0.2
Site B: profit of oil is found: $90 million
Loss of no oil is found: 0.1
A: Which site has the larger expected profit?
B: if the expected profit for both sites is not the same, by how much is the expected profit larger?
When a number is decreased by 24% of itself the result is 171. What is the number?
Graph the quadratic function
F(x)=3x^2+6x-24
Use technology to determine an appropriate model of the data. (0,0), (1,3), (2,4), (3,3), (4,0)
f(x) = – x2 + 4x
f(x) = x2 - 4x
f(x) = - x2 + 4x - 1
f(x) = x2 - 4x + 1
Answer:
Option A.
Step-by-step explanation:
To determine an appropriate model of the data each data should satisfy the expression.
For function 1. f(x) = -x² + 4x
Now for each point
f(0) = 0 , f(1) = 3, f(3) = 3 and f(4) = 0
therefore the given points lie on the function.
For option 2
f(0) = 0, f(1) = -3, f(2) = -4, f(3) = -3 and f(4) = 0
Therefore points do not lie on the function.
For Option 3.
f(0) = -1, f(1) = 2, f(2) = 3, f(3) = 2 and f(4) = -1
Therefore the points do not satisfy the expression.
For option 4.
f(0) = 1, f(1) = -2, f(2) = -3, f(3) = -2 and f(4) = 1
Therefore, the points do not satisfy the expression.
Option A. is the correct option.
In a right triangle, if the measures of the other two angles are 2x – 5 and 3x + 10, what are the measures of these two angles?
A. 30° & 60°
B. 29° & 61°
C. 50° & 40°
D. 51° & 39°
Answer: B. 29° & 61°
Step-by-step explanation:
Peter makes $7,000 a month plus some extra commission he makes 6% of everything he sells if Peter sold $55,000 of jewelry this month what his salary this month
Using the graph below, what are the common ratio and the general term equation, an, of the geometric sequence?
Hint: an = a1(r)n − 1, where a1 is the first term and r is the common ratio.
A jogger goes 1.2 mi west then turns south. If the jogger finishes 1.3 mi from the starting point, how far south did the jogger go?
0.5 miles
The jogger's movement can be represented as a right-angled triangle, where the legs of the triangle represent the distances traveled west and south, and the hypotenuse is the direct distance from the starting point to the finishing point. To solve for the distance the jogger traveled south, we need to use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as c2 = a2 + b2.
Using the Pythagorean theorem:
1.32 = 1.22 + b2
Therefore:
b2 = 1.32 - 1.22
b2 = 1.69 - 1.44
b2 = 0.25
b = [tex]\sqrt{0.25}[/tex]
b = 0.5 mi
So, the jogger traveled 0.5 miles south.
QM Q6.) Write the slope-intercept equation of the function f whose graph satisifies the given conditions.
Mr zucco baked a total of 270 cupcakes and muffins. After ue sold 1/3 of the cupcakes and baked 18 more miffins, he had twice as many cupcakes as muffins. How many cupcakes and muffins did mr. Zucco bake to begin with?
Find the sum: (x5 - 3x4 + x2 - 4) + (5x4 + 3x2 + 2x + 1). Enter your answer as a polynomial in descending order below, and use the caret (^) for exponents. For example, you would write as 4x^2.
Gabriel determined that his total cost would be represented by 2.5x + 2y – 2. His sister states that the expression should be x + x + 0.5x + y + y – 2. Who is correct? Explain.
Gabriel and his sister's expression mean the same; However, the information available is not sufficient to determine if they are correct or not.
According to the question;
Gabriel representation is; 2.5x + 2y – 2.His sister's expression is; x + x + 0.5x + y + y – 2.Upon computation; we find out that the expressions supplied by Gabriel and his sister are the same.
However, we must note that the information available is not sufficient to determine if both parties are correct or not.
Ultimately, if Gabriel is correct, then his sister is too and if otherwise, she is not correct too.
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