The radius of the circle is approximately 7.5 cm, and the corresponding area is approximately 56.25π cm², as calculated using the formulas for circumference and area. Here option C is correct.
1: Find the radius using the circumference formula
We know the circumference C = 157 cm.
We also know the formula for circumference of a circle: C = 2πr, where r is the radius.
Rearranging the formula to solve for r, we get: r = C / (2π).
Substituting C with 157, we get: r = 157 / (2π) ≈ 7.5 cm.
2: Calculate the area using the area formula
Now that we know the radius, we can use the formula for the area of a circle: A = πr², where A is the area.
Substituting r with 7.5, we get: A = π * (7.5)² ≈ 56.25π cm².
Therefore, the area of the circle is 56.25π cm². Here option C is correct.
Complete question:
The circumference of a circle is 157 centimeters. What is the area of the circle in terms of t?
A - 7.570 cm?
B - 157 cm
C - 56.251 cm
D - 2257 cm
Perform the indicated operation.
Answer:
your answer should be 7 1/24
Are the expressions (5+5+5+5) + (x+x+x+x) and 4(5+x) equivalent? If so, write another expression that is equivalent to both of them. If not, explain why not.
Answer:
Yes, they are equivalent. Something that is not equivalent is 5(9+10x)
Both expressions simplify to 20 + 4x. Distributing 4 in 4(5+x) yields the same result, confirming their equivalence.
Sure, let's break it down step by step:
1. **Start with the first expression**: (5+5+5+5) + (x+x+x+x)
- First, simplify the terms inside each set of parentheses:
= (20) + (4x)
- Then, add the simplified terms together:
= 20 + 4x
2. **Proceed to the second expression**: 4(5+x)
- Apply the distributive property, which states that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the results:
= 4 × 5 + 4 × x
- Multiply each term inside the parentheses by 4:
= 20 + 4x
3. **Compare the results**:
Both expressions simplify to 20 + 4x.
In both cases, we ended up with the same simplified expression, 20 + 4x. This confirms that the original expressions are equivalent.
To write another equivalent expression, we can distribute the 4 to both terms inside the parentheses in the expression 4(5+x), which results in 20 + 4x. Therefore, the expression 20 + 4x is equivalent to both (5+5+5+5) + (x+x+x+x) and 4(5+x).
PLEASE HELP
Indira created four graphs, each containing a system of equations. She drew only a part of the line for each equation. By inspection, which graph contains a system with infinitely many solutions?
Answer: THIRD OPTION.
Step-by-step explanation:
For this case it is important to know that by definition, there are three possible cases for the solution of a System of equations. These are shown below:
1. If the lines intersect each other, then the System of equations has ONE SOLUTION.
2. If the lines are parallel, then the System of equations has NO SOLUTION.
3. If the two equations are the same line, then the System of equations has INFINITELY MANY SOLUTIONS.
Observe the graphs attached in the exercise.
You can notice in the third graph that the "line a" and the "line b" are exactly the same line.
Therefore, based on the explained before, you can conclude that the third graph given in the exercise contains a System of equations with Infinitely many solutions.
Answer:
Choice 3
Step-by-step explanation:
First of all, I got 100% on EDGE. Secondly, to lines that coincide and go in the same direction have infinitely many solutions. Finally, it is correct on EDGE 2020
How do you solve 21÷1/3
Answer:
63
Step-by-step explanation:
When dividing by a fraction, it is the same a multiplying that fraction but the reciprocal of it.
21 / 1/3 is same as 21 * 3/1
63
Answer: 63
True or false the triangle was rotated 90 degrees counterclockwise?
Answer:
False
Step-by-step explanation:
if it was counter clockwise it be in the 2 and 3 quadrants
Given:
U=
[ 1 3 -57
2 14 11
L-8 05]
V=
[ 13 -1 -71
-6 1 19
[ 0 15 23
Solve:
X + U = V
X=
Answer:
answer is
[12 -4 -2]
[-8 -13 8]
[8 15 18]
Step-by-step explanation:
got it right on e2020
To solve the equation X + U = V, subtract the matrix U from both sides and simplify to find the solution for X. The solution is [12 - 4 - 14; -8 - 13 8; 8 15 18].
Explanation:To solve the equation X + U = V, we need to isolate X. Here is the step-by-step process:
First, subtract the matrix U from both sides of the equation: X = V - U.Next, subtract the corresponding elements of U from V. In this case, subtract the elements of U from the corresponding elements of V: X = [13 - 1 - 71; -6 1 19; 0 15 23] - [1 3 -57; 2 14 11; -8 0 5].Perform the subtraction and simplify: X = [12 - 4 - 14; -8 - 13 8; 8 15 18].The solution for X is the matrix [12 - 4 - 14; -8 - 13 8; 8 15 18].
What is the length and width of a rectangle given by the trinomial r squared - 6r- 55? Use factoring
Answer:
The length and width are
r-11 and r+5
Step-by-step explanation:
The given trinomial is
[tex] {r}^{2} - 6r - 55[/tex]
To factor, we need to split the middle term to get:
[tex]{r}^{2} - 11r + 5r - 55[/tex]
We now factor by grouping to obtain;
[tex]{r}(r- 11) + 5(r - 11)[/tex]
We collect common factors again to get:
[tex](r- 11)(r + 5)[/tex]
Therefore the length and width are
r-11 and r+5
Flavor of Crisps Probability of Buying
Cheese Crisps 7/25
Bacon Crisps 1/4
Ranch Crisps 3/25
Salsa Crisps 7/20
A grocery chain conducted a random survey to determine the favorite flavor of a new potato crisp. The results are shown on the table. Which flavor is MOST LIKELY to sell BEST if stocked by the grocery chain?
A) Ranch Crisps
B) Salsa Crisps
C) Cheese Crisps
D) Barbecue Crisps
Answer:
b
Step-by-step explanation:
The flavor most likely to sell best if stocked by the grocery chain is B. Salsa Crisps, as it has the highest probability of purchase at 0.35.
To determine which flavor of potato crisps is most likely to sell best if stocked by the grocery chain, we need to compare the given probabilities.
Cheese Crisps: [tex]\frac{7}{25}[/tex] = 0.28Bacon Crisps: [tex]\frac{1}{4}[/tex] = 0.25Ranch Crisps: [tex]\frac{3}{25}[/tex] = 0.12Salsa Crisps: [tex]\frac{7}{20}[/tex] = 0.35From these calculations, we can see that Salsa Crisps have the highest probability (0.35) of being bought. Therefore, Salsa Crisps are the most likely to sell best if stocked by the grocery chain.
The correct answer is Salsa Crisps.
The sum of the two positive numbers is 120. What is the maximum value of the product of these two numbers?
Please so all work, Thank you!
If its a good answer I will rate it 5 stars, thank button, and brainlist your answer!
Answer:
If one number is x, the other is (96 - x)...since if you add those two together, you will get 96..and the product is x(96 - x) = 96x - x^2
Since this is a quadratic function (x to the power of 2), it is a parabola. More specifically, it is a parabola opening downwards, because there is a negative in front of the x squared. Because it downward facing the maximum value of x is going to be where the vertex is. The x value of the vertex can be found by taking the negative of b (which is the number in front of teh x) over a squared (which is the number in front of the x squared which in this case is 1)
So x = -96 / 2(-1) = -96/-2 = 48
Since as we first stated one number is x, the first number is 48
The second number will be 48, because we stated the second number to be 96-x
Therefore 48 times 48 will give you the maximum product 2304.
Hope This Helps!!!!!!!!!!!!!!
Answer:
3,600
Step-by-step explanation:
x + y = 120
y = 120 - x
Product "P"
P = x × y = x(120-x) = 120x - x²
P = -(x² - 20x)
= -(x² - 2(x)(60) + 60² - 60²)
= -(x - 60)² + 3600
Max value is 3,600
A new car is Purchased for 16200 dollars. The value of the car depreciates at 14.25% per year. What will the value of the car be, to the nearest cent,after 6 years?
Answer:
6,440.5
Step-by-step explanation:
So the car starts at 16,200. For the first part of the equation it's 16,200 × x raised to the y. X in this equation would be 1-.1425 = 0.8575. 16,200×(.8575)^y. Y is the number of years after you purchased the car. So, 16,200×(.8575)^6 and that equals 6,440.5
Answer:
$6440.5
Step-by-step explanation:
I hope this helps!
I WILL GIVE BRAINLIEST
Answer must be simplified
4x ≤ 12
Answer: x ≤ 3
Step-by-step explanation:
4x ≤ 12
divide each side by 4
x≤3
Select from the drop-down menu to correctly complete the statement about the given figures.
Triangles ABC and DEF are (similar or not similar)
ΔABC and ΔDEF are similar by AAA similarity.
Solution:
Sum of the interior angles = 180°
In triangle ABC,
60° + 60° + m∠C = 180°
120° +m∠C = 180°
Subtract 120° from both sides, we get
m∠C = 60°
In triangle DEF,
60° + 60° + m∠F = 180°
120° +m∠F = 180°
Subtract 120° from both sides, we get
m∠F = 60°
Consider ΔABC and ΔDEF,
∠A ≅ ∠D
∠B ≅ ∠E
∠C ≅ ∠F
Therefore by AAA similarity ΔABC ≅ ΔDEF.
ΔABC and ΔDEF are similar triangles.
Answer: The answer above is correct.
Brainliest Giveaway!! Also gives all of my points.!!
Answer:
wf
axStep-by-step explanation:
Answer:
Her ride is about 15.1 miles long.
Step-by-step explanation:
40.03 = 6.75 + 3.20m
33.28 = 3.20m
ISOLATE M
m = 15.1272
m = 15.1
We love math. Please help
Answer: the answer is 907.46 in^2 so the answer is the first choice
Step-by-step explanation:
The width of a rectangle is 2m less than the length. The area is 48m squared. Find the dimensions.
Length of the rectangle is 8m and width is 6m
Step-by-step explanation:
Step 1: Given area of the rectangle = 48m². Let the length be x, then the width is x - 2. Find the dimensions using the area of the rectangle = length × breadth48 = x (x - 2)
48 = x² - 2x
x² - 2x - 48 = 0
x² - 8x + 6x - 48 = 0
x(x - 8) + 6(x - 8) = 0
(x + 6)(x - 8) = 0
x = -6, 8 (neglecting the negative value)
∴ Length of the rectangle = 8m
∴ Width of the rectangle = 8 - 2 = 6m
What is the value of x in the figure?
Enter your answer in the box.
x =
Answer:
X = 29
fyfufubivih8g8hih
Answer: X = 29
X + 61 = 90
x+61−61=90−61
x=29
Find the value of X. Please answer.
Answer:
x= 12
Step-by-step explanation:
Please see attached picture for full solution.
Find the value of x.
m∠FGH = 148°
m∠FGL = (x + 12)°
m∠LGH = (16x)°
A) 3
B) 5
C) 6
D) 8
Option D:
x = 8
Solution:
Given data:
m∠FGH = 148° , m∠FGL = (x + 12)° and m∠LGH = (16x)°
To find the value of x:
m∠FGL + m∠LGH = m∠FGH
⇒ (x + 12)° + (16x)° = 148°
⇒ x° + 12° + 16x° = 148°
⇒ 17x° + 12° = 148°
Subtract 12° from both sides of the equation.
⇒ 17x° = 136°
Divide by 17 on both sides, we get
⇒ x° = 8°
⇒ x = 8
Option D is the correct answer.
Answer:D
Step-by-step explanation:I did it on usatestprep trust me.
A cylinder-shaped container is used to store water. The container has a height of 6 feet and a diameter of 3 feet. About how much water is in the container when it is 3/4 full?
A. 127 cubic feet
B. 42 cubic feet
C. 32 cubic feet
D. 14 cubic feet
Answer:
C. 32 cubic feet
Step-by-step explanation:
The volume of a cylinder can be written in terms of diameter as ...
V = (π/4)d^2·h
If water fills the 6-foot height to only 4.5 feet, then the volume of water is ...
V = (π/4)(3 ft)^2(4.5 ft) ≈ 31.81 ft^3
The volume of water in the container is about 32 cubic feet.
If 7 oranges cost $7.56, what is the cost of 2 oranges
Answer:
$2.16
Step-by-step explanation:
7.56 ÷ 7 = 1.08
1.08 × 2 = 2.16
Answer:
$2.16
Step-by-step explanation:
7 oranges -----> costs $7.56
Find the unit rate (i.e the cost of 1 orange)
Unit rate ---> cost of 1 orange = $7.56/7 = $1.08
Cost of 2 oranges
= unit rate x 2 oranges
= $1.08 x 2
= $2.16
$800 is deposited in an account
that pays 9% annual interest,
compounded annually. Find the
balance after four years.
Answer:
The balance after four years is $1129.27
Step-by-step explanation:
The formula for compound interest, including principal sum, is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A = the future value of the investment/loan, including interestP = the principal investment amount (the initial deposit or loan amount)r = the annual interest rate (decimal)n = the number of times that interest is compounded per unit tt = the time the money is invested or borrowed for∵ $800 is deposited in an account
∴ P = 800
∵ The account pays 9% annual interest
∴ r = 9% = 9 ÷ 100 = 0.09
∵ The interest is compounded annually
∴ n = 1
∵ The time is 4 years
∴ t = 4
- Substitute the values of P, r, n, and t in the formula above
∵ [tex]A=800(1+\frac{0.09}{1})^{(1)(4)}[/tex]
∴ [tex]A=800(1.09)^{4}[/tex]
∴ A = 1129.265
∴ The balance after four years is $1129.27
can y’all help me pleasee?
Part a: Domain : [tex]\{2,5,-1,6\}[/tex]
Part b: Range : [tex]\{3,-2\}[/tex]
Part c: The relation is a function
Explanation:
Part a: The domain of the relation is the set of all input values in the relation. In other words, the domain is the set of all x - coordinates of the ordered pairs in the relation.
Hence, from the given relation, the domain is given by
[tex]\{2,5,-1,6\}[/tex]
Therefore, the domain of the given relation is [tex]\{2,5,-1,6\}[/tex]
Part b: The range of the relation is the set of all output values in the relation. In other words, the range is the set of all y - coordinates of the ordered pairs in the relation.
Hence, from the given relation, the range is given by
[tex]\{3,-2\}[/tex]
Therefore, the range of the given relation is [tex]\{3,-2\}[/tex]
Part c: A relation is said to be a function if each element in the input value of the relation is mapped to exactly one element in the output value.
Hence, from the given relation, it is obvious that the each element in the input is mapped to exactly one element in the output value.
Thus, the given relation is a function.
What is 3 to the power of 2 plus 4 to the power of 2
Answer: 25
Step-by-step explanation:
3² + 4 ² = ?
(3x3) + (4x4) = ?
9 + 16 = 25
Answer:
25
Step-by-step explanation:
3² +4² = 9 +16 = 25
_____
Your calculator can help you figure this.
_____
25 = 5², which means that the lengths 3, 4, and 5 could be the sides of a right triangle. They are the smallest integer solution to the equation ...
a² +b² = c²
Honeycrisp apples are on sale if you buy a crate, 15 pounds for $30. What is the unit price per pound
Answer:
$2
Step-by-step explanation:
$30 ÷ 15 pounds
30 ÷ 15 = 2
Answer: $2 per pound
The unit price of apple per pound is $2.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.
Given, Honeycrisp apples are on sale if you buy a crate, 15 pounds for $30.
To find the unit price,
we divide the total cost to total pound of a crate.
unit price of an apple
= $30 / 15
= $2
Therefore, the unit price of an apple per pound is $2.
To learn more about the division;
https://brainly.com/question/13263114
#SPJ2
Find the area of the shaded region. Express your answer in terms of pi
Area of the shaded region is 540 – 65.25π.
Solution:
Length of the rectangle = 12 + 9 + 6 + 3 = 30 in
Width of the rectangle = 18 in
Radius of the larger circle ([tex]r_1[/tex]) = 12 ÷ 2 = 6 in
Radius of the medium circle ([tex]r_2[/tex]) = 9 ÷ 2 = 4.5 in
Radius of the smaller circle ([tex]r_3[/tex]) = 6 ÷ 2 = 3 in
Area of the shaded region = Area of the rectangle – Area of the larger circle – Area of the medium circle – Area of the smaller circle
[tex]=l\times b-\pi r_1^2-\pi r_2^2-\pi r_3^2[/tex]
[tex]=30\times 18-\pi \times 6^2-\pi \times (4.5)^2-\pi \times 3^2[/tex]
[tex]=540-36\pi-20.25\pi-9\pi[/tex]
[tex]=540-65.25\pi[/tex]
Area of the shaded region is 540 – 65.25π.
The area of shaded region is, [tex][540-\pi(65.25)] inch^{2}[/tex]
From given figure, it is observed that unshaded region is sum of area of three circles.
Diameter of first circle = 12 inch , radius = 12/2 = 6 inch
Diameter of second circle = 9 inch , radius = 9/2 = 4.5 inch
Diameter of third circle = 6 inch , radius = 6/2 = 3 inch
Area of circle = [tex]\pi r^{2}[/tex] , where r is radius of circle.
Dimension of rectangle is,
length = 12 + 9 + 6 +3 = 30 inch
width = 18 inch
Shaded area = Area of rectangle - sum of area of three circles.
[tex]=(18*30)-\pi(6^{2} +4.5^{2} +3^{2} )[/tex]
[tex]=540-\pi(36+20.25+9)\\\\=540-\pi(65.25)[/tex]
Learn more:
https://brainly.com/question/22015185
What is the value of x, given that PQ parallel to BC
Answer:
since PQ ||BC,
Angle A is common for both triangles angle P = angle B
triangles ABC, APQ are similar,then their corresponding sides are in proportion
AP/PB =AQ/QC
4/8=x/16
x=8
Do you know basic proportionality theorem ? You can solve the problem easily by this.
In short: BPT is if a line is parallel to a side of the triangle which intersects the other sides imto two distinct points, then the line divides those sides in proportion.
In your problem, it's given that the mutual lines are parallel (PQ || BC), so it makes it divide |AP| with |AB| and |AQ| with |AC| proportionally.
|AP| / |AB| = |AQ| / |QC|
4/12 = x/16+x
4(16+x) = 12x
x=8
Hope it helps!
#MissionExam001
In circle A. MRH = 45° and mÞH =
80°. What is m&PAR?
Answer:
D
Step-by-step explanation:
∠ PAR is an angle at the centre of the circle subtended by the arc PR
The central angle is equal to the arc that subtends it, thus
∠ PAR = arc PH + arc HR = 80° + 45° = 125° → D
Denim shirts were marked down from $40.00 to $29.99. How much will be saved on 2 shirts?
Answer:
Step-by-step explanation:$40.00 is the original price of denim shirts if they are marked down to $29.99 you subtract $40.00 from $29.99 = $10.01 then you add the difference in price $10.01 x 2 to get the total savings the answer is $20.02
Elle earned $45 last month babysitting. This month she earned $35. What is the percent decrease?
Answer:
10percent
Step-by-step explanation:
I think
Elle experienced a 22.22% decrease in earnings from babysitting, from $45 to $35. This is calculated by finding the difference between the two amounts, dividing by the original amount, and then multiplying by 100 to convert to a percentage.
Explanation:Elle's decrease in earnings can be calculated using the formula for calculating the percentage decrease, which is [(Original value - New value)/(Original value)] * 100.
In Elle's case, the original value is $45 (the amount she earned last month), and the new value is $35 (the amount she earned this month). So, follow the formula:
Subtract the new value from the original value: $45 - $35 = $10Divide the decrease by the original value: $10/$45 = 0.2222Multiply the result by 100 to convert it to a percentage: 0.2222 * 100 = 22.22%So, Elle experienced a 22.22% decrease in her earnings from babysitting.
Learn more about Percentage Decrease here:https://brainly.com/question/29763752
#SPJ2
Lena draws a square with an area that is greater than the area of rectangle b what are two possible side lengths of lenas square? Explain
Suppose the square Lena draws has the following dimensions:
[tex]Side=L \\ \\ A_{s}:Area \\ \\ \\ A_{s}=L^2[/tex]
For the rectangle we have:
[tex]Base=L_{1} \\ \\ Height=L_{2} \\ \\ \\ A_{r}=L_{1}L_{2}[/tex]
Possibility 1. In order for the area of the square to be greater than the area of the rectangle, the following inequality must be true:
[tex]\boxed{\frac{L^2}{L_{1}L_{2}}>1}[/tex]
Possibility 2. If one side of the rectangle equals the side of the square, that is:
[tex]L_{1}=L[/tex]
Then, in order for the area of the square to be greater than the area of the rectangle, the following inequality must be true:
[tex]\frac{L^2}{LL_{2}}>1 \\ \\ \boxed{\frac{L}{L2}>1}[/tex]
The side lengths for Lena's square, with an area greater than rectangle B, must exceed the side lengths of rectangle B if square, or the square root of its area if not. Thus, any side length [tex]\( s \)[/tex] for Lena's square must satisfy [tex]\( s > \sqrt{A_B} \)[/tex], where [tex]\sqrt{A_B}[/tex] is area of rectangle.
Given that the area of the square is greater than the area of rectangle B, we can write the inequality:
[tex]\[ s^2 > l \times w \][/tex]
To find two possible side lengths for the square, we need to find values of [tex]\( s \)[/tex] that satisfy this inequality.
Since we do not have specific values for [tex]\( l \)[/tex] and [tex]\( w \)[/tex], we can consider a few scenarios:
1. If rectangle B is a square itself, then [tex]\( l = w \)[/tex], and the area of rectangle B would be [tex]\( l^2 \)[/tex]. For the square drawn by Lena to have a greater area, the side length [tex]\( s \)[/tex] must be greater than [tex]\( l \)[/tex]. So, any value of [tex]\( s \)[/tex] greater than [tex]\( l \)[/tex] would be a possible side length for Lena's square.
2. If rectangle B is not a square, then [tex]\( l \neq w \)[/tex]. Without loss of generality, let's assume [tex]\( l > w \)[/tex]. To ensure that [tex]\( s^2 > l \times w \)[/tex], [tex]\( s \)[/tex] must be greater than the square root of [tex]\( l \times w \)[/tex].