Answer:
[tex]radius=5\ cm[/tex]
Step-by-step explanation:
Let r be the radius of the circle and A be the area of the circle.
Given:
[tex]r_{1} = 2\ cm, A_{1}=12.566\ cm^{2}[/tex]
And [tex]r_{2} = ?, A_{2}=78.54\ cm^{2}[/tex]
The area of a circle is directly proportional to the square of its radius.
A ∝ [tex]r^{2}[/tex]
[tex]A = kr^{2}[/tex]-----------(1)
Where k is the constant of proportionality
Find constant value by substituting [tex]r_{1} = 2\ cm, A_{1}=12.566\ cm^{2}[/tex]
in equation 1.
[tex]A = kr^{2}[/tex]
[tex]A_{1}=k(r_{1})^{2}[/tex]
[tex]12.566=k\times 2^{2}[/tex]
[tex]12.566=k\times 4[/tex]
[tex]k=\frac{12.566}{4}[/tex]
[tex]k=3.141[/tex]
Find [tex]r_{2}[/tex] by substituting k and [tex]A_{2}[/tex] value in equation 1.
[tex]A = kr^{2}[/tex]
[tex]A_{2}=k(r_{2})^{2}[/tex]
[tex]12.566=3.141\times (r_{2})^{2}[/tex]
[tex](r_{2})^{2}=\frac{78.54}{3.141}[/tex]
[tex](r_{2})^{2}=25.004[/tex]
where: 25.004 ≅ 25
[tex](r_{2})^{2}=25[/tex]
[tex]r_{2}=\sqrt{25}[/tex]
[tex]r_{2}=5\ cm[/tex]
Therefore; the radius of the circle is 5 cm.
Final answer:
The radius of a circle with an area of 78.54 cm² is approximately 4 cm, after setting up a proportion with a known circle area and solving for the unknown radius.
Explanation:
The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle. Given that a circle with a radius of 2 cm has an area of 12.566 cm², we set up a proportion to find the radius of a circle with an area of 78.54 cm²:
(12.566 cm²) / (2 cm)² = (78.54 cm²) / r².
Solving for r, we find r² = (78.54 cm²) × (2 cm)² / (12.566 cm²).
After calculation, we get r approximately equal to 4 cm, rounding to the nearest whole number.
At 1:00pm, ship A is 30 miles due south of ship B and is sailing north at a rate of 15 mi/hr. If ship B is sailing
west at a rate of 10 mi/hr, find the time at which the distance d between the ships is minimal.
Answer:
2:23 pm
Step-by-step explanation:
We can solve this considering a a right triangle
let t = travel time of both ships
therefore,
15t = distance traveled by ship A
however, it is traveling toward the point of reference, therefore we write it
(30-15t)
and
10t = distance traveled by ship B, away from the point of reference
Let d = distance between the ships at t time, (the hypotenuse of the right triangle)
[tex]d= \sqrt{(30-15t)^2+10t^2}[/tex]
and combine like terms
[tex]d= \sqrt{(900-900t+225t^2)+100t^2}[/tex]
[tex]d= \sqrt{3325t^2-900t+900}[/tex]
from this d to minimum we can find the axis of symmetry, where in
a=325 and b= -900
the t=-b/2a
[tex]t= -\frac{-900}{2\times325}[/tex]
t= 1.384 hours
now putting the value we get
[tex]d= \sqrt{3325(1.384)^2-900(1.384)+900}[/tex]
solving this we get
d= 16.64 miles
therefore,
16.64 mi apart after 1.3846 hrs, minimum distance between the ships
now, 1.384 hours = 1+60(0.348) hour
= 1 hour and 23 minutes
so, the time at which the distance d between the ships is minimal = 1:00 pm + 1 hour and 23 minutes = 2:23 pm
A bird at the top of a tree looks down on a field mouse at an angle of depression of 65°. If the field mouse is 30 meters from
the base of the tree, find the vertical distance from the ground to the bird's eyes. Round the answer to the nearest tenth
a 14 m
b. 28.6 m
C. 58.3 m
d. 64.3 m
Answer:
14m
Step-by-step explanation:
Answer:
d. 64.3 m
Step-by-step explanation:
please help me ill appreciate it
Answer:
D
Step-by-step explanation:
Two figures are similar.
It means that the corresponding sides are proportional.
TM corresponds to SC
MV corresponds to CI
Lets write the ratios and equate:
[tex]\frac{3}{2}=\frac{MV}{6}[/tex]
Now, we can cross multiply and use algebra to solve for MV. Process shown below:
[tex]\frac{3}{2}=\frac{MV}{6}\\2MV=3*6\\2MV=18\\MV=\frac{18}{2}\\MV=9[/tex]
Correct answer is D
And Another Question 35 points
Answer:
50
Step-by-step explanation:
The x-axis represents the number of broken light bulbs, as labelled on the histogram. The highest range is 41 to 50, therefore the greatest possible number of broken light bulbs is 50.
Answer:
50
Step-by-step explanation:
The last bar on the number of broken light bulbs (x) axis covers the range 41-50. Thus, 50 is the maximum number of broken light bulbs that can be and is represented in this histogram.
The Read and Feed restaurant wants to know how satisfied their customers are with their service. They printed an internet link to a survey on every receipt, and 150150150 of their customers chose to answer the survey. The data showed that 60\%60%60, percent of the customers were satisfied with their service.
Based on this data, which of the following conclusions are valid?
Answer: The answer is A my bro trust me *Fist Bump*
Answer:
A
Step-by-step explanation:
I did it and got it right.
Hope this helps:)
At a local food store a child stole $500 from the shopkeeper's cash register to purchase goods in the store. The items the child purchased total $350 which he paid using the money he stole and received change of $150. How much money in total did the shopkeeper lose
Answer:
The shopkeeper lost $500
Select the correct answer. If f(x)=x/1+x , what is the value of f(x+h)?
Answer:
Step-by-step explanation:
f(x)=2x+3 and g(x)=x^2-8, find (f+g)(x)
Answer:
[tex](f+g)(x)=x^2+2x-5[/tex]
Step-by-step explanation:
Given:
The functions given are:
[tex]f(x)=2x+3\\g(x)=x^2-8[/tex]
To find: [tex](f+g)(x)[/tex]
[tex](f+g)(x)[/tex] is equal to the addition of both the functions. So, we need to add the values of both the functions and then simplify to arrive the final answer.
Therefore, [tex](f+g)(x)[/tex] is given as:
[tex](f+g)(x)=f(x)+g(x)[/tex]
Plug in the values of [tex]f(x)\ and\ g(x)[/tex] and simplify. This gives,
[tex](f+g)(x)=2x+3+x^2-8[/tex]
Combining like terms using commutative property of addition, we get
[tex](f+g)(x)=x^2+2x+3-8\\(f+g)(x)=x^2+2x-5[/tex]
Therefore, the addition of the two functions is simplified to:
[tex](f+g)(x)=x^2+2x-5[/tex]
After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has
7 eggs left over. Each carton holds 12 eggs.
How many eggs did Dale collect?
What is the initial value of the function represented by this table? (5 points)
Answer:
0
4
5
9
Step-by-step explanation:
what is 14.79 as a rounded number
Answer:
15
Step-by-step explanation:
Answer:
15 or 14.8, depending on whether it is a ehole number on on decimal place
Step-by-step explanation:
if you vertically stretch the quadratic parent function, f (x) = x^2 by multiplying by 7 what is the equation of the new function
Answer:
F(x)=7x^2 or G(x)=7x^2
Step-by-step explanation:
how do i find the perimeter of a rectangle that is 15 in. x 24 in.
You can apply the formula of perimeter of rectangle and that is 2(l+b)....
two consecutive even integers have a sum of 254. write the equation that will solve for the two integers.
Answer: 126 and 128
Step-by-step explanation: In this problem have two consecutive even integers whose sum is 254.
Consecutive even integers can be represented as followed.
X ⇒ first even integer
X + 2 ⇒ second even integer
Since the sum of these is 254, our equation reads X + X + 2 = 254.
We can simplify on the left side of the equation to get 2x + 2 = 254.
Now, we subtract 2 from both sides of the equation to get 2x = 252.
Lastly, we will divide both sides of the equation by 2 in order to isolate x. On the left side, the 2's cancel out and on the right, 252 divided by 2 is 126.
If our first integer is 126, our next consecutive even integer will be 126 + 128 which simplifies to 254.
Therefore, our two consecutive even integers are 126 and 128.
Find the exact volume of the cylinder.
A) 65π m3
B) 130π m3
C) 260π m3
D) 325π m3
Answer:
d
Step-by-step explanation:
What is the algerbraic expression for the following word phrase: the product of 5 more than p and 7?
Answer:
Step-by-step explanation:
7(p+5)
What’s this answer y=10 4x-5y=3
Answer:
x = 13.25 or 13 1/4
Step-by-step explanation:
4x - 50 = 3
4x = 53
x = 13.25 or 13 1/4
Answer:
53 / 4
13 whole number, 1/4
Step-by-step explanation:
Solve system of equation
2x+3y=4
2x=7y+24
Answer:
X= 5 Y= -2
Step-by-step explanation:
Which pair of number has the same greatest common factor as 48 and 78
Answer:
48
Step-by-step explanation:
48=2×2×2×2×3
78=13×2×3
48 has 5 factors.
What is the quote that of 2^4/2^-4
Answer:
[tex]2^8[/tex]
Step-by-step explanation:
To find the quotient of:
[tex]\frac{2^4}{2^{-4}}[/tex]
Solution:
We will apply quotient rule of exponents to find the quotient of the given expression.
By Quotient rule: [tex]\frac{a^x}{a^y}=a^{(x-y)}[/tex]
Thus the quotient for the expression can be given as:
[tex]\frac{2^4}{2^{-4}}[/tex]
⇒ [tex]2^{(4-(-4))}[/tex]
⇒ [tex]2^{(4+4)}[/tex]
⇒ [tex]2^8[/tex] (Answer)
The expression [tex]\frac{2^4}{2^-4}[/tex] can be simplified to 256.
To solve the expression [tex]\frac{2^4}{2^-4}[/tex], we can use the properties of exponents :
Recall that when you divide powers with the same base, you subtract the exponents: [tex]\frac{2^a}{2^b}[/tex] [tex]=[/tex] [tex]2^(a-b)[/tex].So, for our expression : [tex]\frac{2^4}{2^-4}[/tex] = [tex]2^(4-(_4))[/tex] = [tex]2^(4+4)[/tex] = [tex]2^8[/tex].Next, calculate [tex]2^8[/tex] : [tex]2^8[/tex] = 256.Therefore, the value of the expression [tex]\frac{2^4}{2^-4}[/tex] is 256.
Tara paid $3.52 for 4 boxes of macaroni and cheese. Jarrett paid $5.40 for 6 boxes of macaroni and cheese. Which of
the following statements is true?
Tara paid more per box
Jarrett paid more per box.
Tara and Jarrett paid the same per box
Answer: Tara paid more per box
Step-by-step explanation:
Which system of equations has no solutions
A. 3x + 4y = 5
6x + 8y = 10
B. 7x - 2y = 9
7x - 2y = 13
C. 2x - y = -11
-2x + y = 11
D. 3x + 6y = 1
x + y = 0
A. 90 degrees
B. 180 degrees
C. 270 degrees
D. 360 degrees
Answer:
What was the question (I can't see the picture)
Step-by-step explanation:
Answer:
B. 180 degrees
Step-by-step explanation:
∠A, ∠B and ∠C are collective the internal angles of a triangle.
By definition, the internal angles of a triangle sum to 180degrees
hence ∠A + ∠B + ∠C = 180 degrees
(see also attached graphic for reference)
The temperature at sunrise was -2 degrees Fahrenheit. The temperature at sunset was 18 degrees warmer than it was at sunrise. What was the temperature at sunset?
a) -20 degrees Fahrenheit
b) -16 degrees Fahrenheit
c) 20 degrees Fahrenheit
d) 16 degrees Fahrenheit
Answer:
d) 16 degrees Fahrenheit
Step-by-step explanation:
What do we know? Initial temperature: -2. Then the temperature rose by 18 degrees. We can express this mathematically:
[tex]-2+18[/tex]
If you are not particularly comfortable with negatives, you can rewrite this expression as such:
[tex]18-2[/tex]
[tex]16[/tex]
Thus the temperature at sunset was 16 degrees Fahrenheit.
Answer:
16 degrees
-2 + 18 is 16
Step-by-step explanation:
If this is wrong EXPLAIN HOW ITS WRONG
If sin theta +cos theta=root2cos theta then the value of tan theta is
Answer:
√2 - 1
Step-by-step explanation:
Please see attached picture for full solution.
Sam and Odel have been selling frozen pizzas for a class fundraiser. Sam has sold half as many pizzas as Odel. Together they have sold a total of 126 pizzas. How many pizzas did Sam sell
Answer:
63 pizzas
Step-by-step explanation:
In the problem it states that Sam sold half as many pizzas as Odel and sold 126 together in total. If you divide 126 pizzas by 2 or 1/2, you should get 63 pizzas for both people. Hope this helps.
The total number of frozen pizzas which Sam sell for a class fundraiser is 42 which is half as many pizzas sell by Odel.
What is system of equation?A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
Sam and Odel have been selling frozen pizzas for a class fundraiser. Let the Sam has sold x number of pizzas and Odel is sold y number of pizzas.
Now it is given in the problem that, Sam has sold half as many pizzas as Odel. Thus,
[tex]x=\dfrac{y}{2}\\y=2x[/tex] ......1
Together Sam and Odel have sold a total of 126 pizzas. Thus,
[tex]x+y=126\\[/tex]
Put the value of y from the equaiton 1 in the above equation,
[tex]x+2x=126\\3x=126\\x=\dfrac{126}{3}\\x=42[/tex]
Hence, the total number of frozen pizzas which Sam sell for a class fundraiser is 42 which is half as many pizzas sell by Odel.
Learn more about the system of equations here;
https://brainly.com/question/13729904
I need to buy a carpet-for a-room the measures 3m by 2m.how many square meters do I need?
Final answer:
To carpet a room measuring 3 meters by 2 meters, you need 6 square meters of carpet.
Explanation:
To calculate the area of a rectangular room that measures 3 meters in length and 2 meters in width, you multiply the length by the width.
Using the formula Area = length × width,
As we can see that the room is a rectangle with width 2 and length 3
So,
Length = 3 m
Width = 2 m
We find that the room's area is 6 square meters (3m × 2m = 6m²).
Therefore, to carpet a room of this size, you would need to buy 6 square meters of carpet.
easy + brainliest
2x(^3) + 10x(^2) − 4x(^2)y − 20xy
factor this pls, (show all work)
Answer:
Answer:
2x • (x2 - 2xy + 5x - 10y)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(((2•(x3))+(10•(x2)))-(22x2•y))-20xy
Step 2 :
Equation at the end of step 2 :
(((2 • (x3)) + (2•5x2)) - 22x2y) - 20xy
Step 3 :
Equation at the end of step 3 :
((2x3 + (2•5x2)) - 22x2y) - 20xy
Step 4 :
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
2x3 - 4x2y + 10x2 - 20xy =
2x • (x2 - 2xy + 5x - 10y)
Final result :
2x • (x2 - 2xy + 5x - 10y)
Step-by-step explanation:
Answer:
2x • (x2 - 2xy + 5x - 10y)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(((2•(x3))+(10•(x2)))-(22x2•y))-20xy
Step 2 :
Equation at the end of step 2 :
(((2 • (x3)) + (2•5x2)) - 22x2y) - 20xy
Step 3 :
Equation at the end of step 3 :
((2x3 + (2•5x2)) - 22x2y) - 20xy
Step 4 :
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
2x3 - 4x2y + 10x2 - 20xy =
2x • (x2 - 2xy + 5x - 10y)
Final result :
2x • (x2 - 2xy + 5x - 10y)
An engineering student answered 81 questons correctly ona 90 question test. What percent of the question did she answer correctly? questions correctly on a 90 question test. What percent of the questions she answered correctly?
Answer:
correct answer = 90%
Step-by-step explanation:
Let x be the percent of the question did she answer correctly.
Given:
An engineering student answered 81 questions correctly on a 90 question test.
Find the percent of the question did she answer correctly.
Solution:
Percentage formula is given below
% answer [tex]=\frac{correct\ answer}{total\ questions}\times 100[/tex]
% answer [tex]=\frac{81}{90}\times 100[/tex]
% answer [tex]=\frac{81\times 100}{90}[/tex]
% answer [tex]=\frac{81\times 10}{9}[/tex]
% answer [tex]=9\times 10[/tex]
% answer [tex]=90[/tex]
correct answer = 90%
Therefore, she answered 90% correctly.
Answer:
90%
Step-by-step explanation:
For the function f(x)=8(x−3)+13, find the value of f(5) please help
Answer:
29
Step-by-step explanation:
f(x)=8(x−3)+13
f(5)= 8(5-3)+13
f(5) = 8(2) +13
f(5) = 16 +13
f(5)= 29
Hope this helps!
Please mark brainliest if you think I helped! Would really appreciate!
Answer:
Your correct answer is 29! Here is the step by step explanation!
Step-by-step explanation:
f(x)=8(x−3)+13
f(5)= 8(5-3)+13
f(5) = 8(2) +13
f(5) = 16 +13, wich means when you do this,
f(5)= 29
you get your answer of 29! Please mark brainliest! Hope it helped! Have a nice day!