Answers
Answer:
42.25π m²
Step-by-step explanation:
Let's solve!
⇒ Take the radius of the lawn to be 'r'
===========================================================
Then, area of the path equals :
⇒ Area of (lawn + path) - Area of lawn
⇒ π (r + 2)² - πr² = 30π
⇒ πr² - πr² + 4πr + 4π = 30π
⇒ 4πr = 26π
⇒ r = 6.5 m
===========================================================
Area of the lawn :
⇒ Area = πr²
⇒ Area = π × (6.5)²
⇒ Area = 42.25π m²
Related Questions
Write 320 g as a fraction of 2 kg. Give your answer in its simplest form.
Answers
Answer:
4/25
Step-by-step explanation:
320 grams over 2kj(which is 2000grams) is 320/2000, simplified is 4/25
A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than the orange
By what percent is a grapefruit heavier than an apple?
Answers
Answer:
8%+10%=180 180÷100=1.8% grapefruit is heavier than Apple
1. Create an ungrouped frequency distribution table with the data from the survey concerning the age of the people, which attend the gym. The results of a survey are presented below.
Answers
Answer:
firstly ,we need to put the set of ages into categories
Example: (Category1 = age 19 ; category2 = age 20 ; ........ )
→ The frequency of a certain value (age) is equal to the number of times that specific age appears in the data set.
Step-by-step explanation:
Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3
x = negative 1
x = 1
x = negative 1 and x = 1
x = 0, x = negative 1, and x = 1
Answers
The value of x is 1 , option B is the correct answer.
What is an Equation ?When two algebraic expressions are equated using an equal sign , the mathematical equation formed is called an Equation.
The equation is given by 3log₂(2x)=3
3log₂(2x)=3
log₂(2x) = 3/3
log₂(2x) = 1
The base of the logarithm is 2
it can also be written as
[tex]\rm 2^{log_{2}(2x)} = 2 ^1[/tex]
2x = 2
x = 1
Therefore the value of x is 1 , option B is the correct answer.
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Which of these is a correct expansion of (3x − 1)(4x² + 5)?
OA. 3x 4x2 + 3x 5+1 4x² +1.5
OB. 3x. 4x² + 3x • 5+ (−1) • 4x² + (−1) • 5
OC. 3x 4x² + (-1). 4x² + 4x².5+ (-1).5
Answers
Q varies inversely with x. if q = 12 when x = 5, find the value of q when x = 12.
Answers
q varies inversely as x: qx = k, such k is constant
Given values:
q = 12x = 5To determine the constant of variation, substitute the first two given values of q and x to the equation of variation.
qx = k(12)(5) = k60 = kTo determine the value of q, substitute the second given value of x together with the constant of variation.
x = 12, q = ?qx = 6012q = 60q = 60/12q = 5Answer:
The value of q is 5.Wxndy~~
Use DeMoivre's Theorem to find (3cis*pi/6)^3
The ANSWER is 27i ----- PLEASE EXPLAIN!!!! THANK YOU!!!
Answers
The correct value of (3cis(pi/6))³ is 27i.
What is Complex Number?Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra.
Given the complex number in polar coordinate expressed as
z = r(cos∅+isin∅)
zⁿ = {r(cos∅+isin∅)}ⁿ
According to DeMoivre’s Theorem;
zⁿ = rⁿ(cosn∅+isinn∅)
Given the complex number;
(3cis(pi/6))³
= {3(cosπ/6 + isinπ/6)}³
Using DeMoivre’s Theorem;
= 3³(cos3π/6 + isin3π/6)
= 3³(cosπ/2 + isinπ/2)
= 3³(0 + i(1))
= 27i
Thus, the correct value of (3cis(pi/6))³ is 27i.
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Write the following expression without negative exponents and without parentheses.
(5x)^−3
Answers
——-
5x^3
Bc neg exponent becomes positive if you divide one by it.
Answer:
[tex] \dfrac{1}{125x^3} [/tex]
Step-by-step explanation:
[tex] (5x)^{-3} = \dfrac{1}{(5x)^3} = \dfrac{1}{5^3x^3} = \dfrac{1}{125x^3} [/tex]
Given: MN is twice the length of
KM and KM = 8. Find the
perimeter of the total figure.
A. 24
B. 28
C. 38
D. 48
Answers
MN=2KM
2(8)16MN+KM=24
QP/KJ=MN/MK=24/16=3/2As we can see
QP is almost greater than 3/4th MN
It's atleast 10+ or even 12+
So possible perimeter excluding QJ and KJ is atleast 34 to 36 .
So it can neither be 38 nor 28 .
Only one option yields that's 48(Option D)
12. Ben says
"the difference between two consecutive square numbers is always odd."
Is Ben correct?
Answers
Answer:
Yes Ben is correct
Step-by-step explanation:
For example:
If n² is the greater of the two consecutive square numbers, then the difference will be 2n-1. So for example, if you have two consecutive squares with the values of 25, and 36, their difference will be 11. Notice though that 11=2×6–1, so it conforms to 2n-1.
How many triangles are there
Answers
Answer:
24 trianglesStep-by-step explanation:
in the picture
please help with geometry!!!! ‼️‼️‼️‼️ i will mark brainliest
Answers
Answer:
P = 156 units
Step-by-step explanation:
the perimeter (P) is the sum of the 3 sides of the triangle.
tangents from an external point to the circle are congruent , that is
HK = HJ ( substitute values )
13x - 8 = 7x + 4 ( subtract 7x from both sides )
6x - 8 = 4 ( add 8 to both sides )
6x = 12 ( divide both sides by 2 )
x = 2
Then
HK = HJ = 7x + 4 = 7(2) + 4 = 14 + 4 = 18
and
KI = IL = 21
then
GL = GJ = 60 - 21 = 39
Thus
P = HK + KI + IG + GJ + JH = 18 + 21 + 60 + 39 + 18 = 156 units
4. Reid is building a fence around a square portion of his
yard with an area of 200 square feet. Which point
below best represents the side length of one side of the
fence?
A. Point A
B. Point B
C. Point C
D. Point D
Answers
The point that best represents the length of one side of the fence of the square portion of the garden area is: B. Point B.
What is the Area of a Square?Area of a square = s², where s is the side length of the square.
Area of the square portion of his yard = 200 square feet
Side length of one side of the fence = √200 = 14.1 feet.
From the number line given, point B best represents 14.1 feet. Therefore, the side length is best represented by: B. Point B.
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Match each pair of rational numbers with their sum
Answers
The match each pair of rational numbers with their sum is:
[tex]\frac{2*(a-b)}{a^2b^2} = \frac{-2}{a^2b}+\frac{2}{ab^2}[/tex]
[tex]\frac{a-b^2}{a^2b^3} }=\frac{1}{ab^3} +\frac{-1}{a^2b}[/tex]
[tex]\frac{2ab-1}{4a^2b^2} }=\frac{1}{2ab} +\frac{-1}{4a^2b^2}[/tex]
[tex]\frac{2*(1-ab^2)}{a^2b^3} =\frac{2}{a^2b^3}+\frac{-2}{ab}[/tex]
FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
When you factor an expression using the rule a factor out a common term, it is possible simplify an expression
Then, you should factor and simplify each given algebraic expression.
[tex]\frac{2*(a-b)}{a^2b^2} =\frac{2a-2b}{a^2b^2}=\frac{2a}{a^2b^2} -\frac{2b}{a^2b^2} =\frac{2}{ab^2} +\frac{-2}{a^2b}[/tex][tex]\frac{a-b^2}{a^2b^3} }=\frac{a}{a^2b^3} -\frac{b^2}{a^2b^3} =\frac{1}{ab^3} +\frac{-1}{a^2b}[/tex][tex]\frac{2ab-1}{4a^2b^2} }=\frac{2ab}{4a^2b^2} -\frac{1}{4a^2b^2} =\frac{1}{2ab} +\frac{-1}{4a^2b^2}[/tex][tex]\frac{2*(1-ab^2)}{a^2b^3} =\frac{2-2ab^2}{a^2b^3}=\frac{2-2ab^2}{a^2b^3}=\frac{2}{a^2b^3}+\frac{-2}{ab}[/tex]
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A landscaping company has giving quotes to 2 different customers the first customer quote is $287 to install 13 bushes and 7 trees and the second customer' quote is $392 to install 8 bushes and 12 trees
Answers
The cost of installing a bush is $7 and the cost of installing a tree is $28
How to determine the cost of bushes and trees?Represent the trees with t and the bushes with b.
So, we have the following equations:
13b + 7t = 287
8b + 12t = 392
Make t the subject in 13b + 7t = 287
t = (287 - 13b)/7
Substitute t = (287 - 13b)/7 in 8b + 12t = 392
8b + 12 * (287 - 13b)/7 = 392
Multiply through by 7
56b + 12 * (287 - 13b) = 2744
Expand
56b + 3444 - 156b = 2744
Collect like terms
56b - 156b = 2744 - 3444
-100b = -700
Divide both sides by -100
b = 7
Substitute b = 7in t = (287 - 13b)/7
t = (287 - 13*7)/7
Evaluate
t = 28
Hence, the cost of installing a bush is $7 and the cost of installing a tree is $28
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3. () Triangle ABC is transformed to create Triangle A'B'C'. What type of rigid transformation is this? (1 pt)
If triangle A'B'C' is reflected over the y-ands, what are the coordinates of triangle A"B"C"? (3 pts)
-
A' (1.3)
B' (4.1)
A" (_
B (______
C' (6,5)
-
C" (
111
Answers
Answer:
see the attachment photo!
Hey i have a question i need help with this it says...
How many cups would give you 2 quarts of water
if you have an awnser for this please let me know
Answers
Answer:
8 cups = 2 quarts
Step-by-step explanation:
Answer:
Eight cups will give you 2 quarts of water
Please help me!
1. Determine whether the following table represents an exponential function. Explain why or why not.
X: 0, 1, 2, 3
Y: 12, 16, 32, 52
Does the table represent an exponential function? Why or why not?
A. No, all of the X values have a constant difference, but all of the Y values do not have a constant ratio
B. Yes, all of the X values have a constant ratio, but all of the Y values have a constant difference
C. No, all of the X values have a constant ratio, but all of the Y values do not have a constant difference.
D. Yes, all of the X values have a constant difference, and all of the Y values have a constant ratio
2. Determine whether the rule represents an exponential function. Explain why or why not.
Y=9x5^x
Choose the correct answer below
A. Since the independent variable X is the exponent, Y=9×5^x represents an exponential function
B. Since the independent variable X is not the base, Y=9×5^x does not represent an exponential function
C. Since the independent variable X is the base, Y=9×5^x does represent an exponential function
D. Since the independent variable X is not the exponent, Y=9×5^x does not represent an exponential function
3. A population of 55 foxes in a wildlife preserve quadrupled in size every 11 years. The function y=55x4^x, where X is the number of 11 year periods, models the population growth. How many foxes will there be after 22 years?
After 22 years there will be ____ foxes (type an whole number)
4. Since 2006, the amount of money spent that restaurant in a certain country has increased at a rate of 8% each year. in 2006, about $360 billion were spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2015.
About $______ billion will be spent at restaurants in 2015 if the trend continues.
5. A bird drops a stick to the ground from a height of 90 feet. The function h=-16t^2+90 gives the sticks approximate height H above the ground, in feet, after T seconds. Add about what time does the stick hit the ground?
The stick hits the ground at about _____ seconds. (Round to one decimal place as needed)
6. During halftime of a soccer game, a slingshot launches T-shirt at the crowd. A T-shirt is launch from a height of 3 feet with an initial upward velocity of 80 ft./s. Use the equation h(t) = -16t^2+80t+3, where t is time in seconds and h(t) is height. How long will it take the T-shirt to reach its maximum height? What is the maximum height?
The T-shirt takes _____ Second(s) to reach its maximum height. (type an integer or a decimal)
The T-shirts maximum height is_____ feet above the field. (type an integer or a decimal)
Please help me I really need to get this done today! I will give you everything I have!
Answers
Answer:
a
Step-by-step explanation:
Select the correct answer
The function g(x)=x²2 is transformed to obtain function h:
h(x) = g(x − 3).
Which statement describes how the graph of his different from the graph of g?
A. The graph of h is the graph of g vertically shifted down 3 units.
B. The graph of h is the graph of g horizontally shifted right 3 units.
C. The graph of h is the graph of g horizontally shifted left 3 units.
D. The graph of h is the graph of g vertically shifted up 3 units.
Answers
Answer:
B
Step-by-step explanation:
h(x) is the same as g(x), just that every y value of g(x) happens now at x instead of at x-3, so 3 units "later", and everything is therefore just moved 3 units to the right.
What is the mass of hydrogen atoms that is measured at 54 u? the relationship between atomic mass units (u) and grams (g) is 1 u = 1.66 x 10^-24 g.
Answers
The mass of hydrogen atoms that measures 54 u is 89.64 x 10^-24
Analysis:
If 1 u = 1.66 x 10^-24, then 54 u = 54 x 1.66 x 10^-24 = 89.64 x 10^-24
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3. In the expression 25-5+7x3 ÷ 1, which operation should be done first?
O division
O addition
O subtraction
O multiplication
Answers
Answer:
division
Step-by-step explanation:
please mark me as brainlest
Pls help no links or troll answers ill report them
Answers
Answer:
insufficient
Step-by-step explanation:
What is the question?
Find the sum of the interior angles of the following polygon
Answers
Answer:
540° and x = 85°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5 , then
sum = 180° × 3 = 540°
2
sum the interior angles and equate to 540°
x + 115° + 95° + 115° + 130° = 540°
x + 455° = 540° ( sum 455° from both sides )
x = 85°
You have been given data about gas prices in 15 states.
2018 Gas Price Data
Max: $2.42
Min: $2.03
Mean: $2.098
Median: $2.06
Mode: $2.04
Variance: 0.0121
Standard Deviation: $0.1098
What does the range, standard deviation, and variance say about gas prices in 2018?
Answers
The range, standard deviation, and variance say about gas prices in 2018 discussed below
What is standard deviation and variance?Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.
As the variance in 2018 is 0.0121.
A model with low variance means sampled data is close to where the model predicted it would be.
As the standard deviation in 2018 is 0.1098.
Low standard deviation means data are clustered around the mean
A small range means low variability in a distribution.
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SAmina walked nine times round a square Field. If she covered a total distance of 12 96 meters, what is the area of the field?
Answers
Explanation: You want to take 1,296 as the perimeter and divide it by 9 as she walked around it 9 times. From there plug the answer (144) into the equation to find a area and you get 1296
What is the slope of the line that passes through (-2, 7) and (4, 9)
Answers
Answer: The slope is 1/3
Step-by-step explanation:
m = y2-y1/x2-x1
m =9-7/4+2
m=2/6
m=1/3
Answer:
The slope is 1/3
Step-by-step explanation:
m=y2-y1/x2-x1
m=9-7/4-(-2)
m=2/6
m=1/3
If you bought 4 candies for a
total of $3.28, how much did it
cost you for 3 candies?
Answers
Answer:
2.46
Step-by-step explanation:
3.28/4=0.82(for one candy)
0.82×3=2.46(for 3 candies)
NEED HELP ASAP PLEASE
Answers
Answer:
y = 2x^2 + 8x + 3
Step-by-step explanation:
Step 1: use the vertex form of the quadratic equation
y = a*(x - h)^2 + k
vertex = (-2, -5) = (h, k)
y = a*(x + 2)^2 - 5
Step 2: determine a using the given point
point = (0, 3)
y = a*(x + 2)^2 - 5
3 = a*(0+2)^2 - 5
3 + 5 = a*(2)^2
8 = a*4
a = 2
vertex equation is now y = 2*(x + 2)^2 - 5
Step 3: simplify vertex equation to standard quadratic equation
quadratic equation = Ax^2 + Bx + C
y = 2*(x + 2)^2 - 5
y = 2*(x^2 + 4x + 4) - 5
y = 2x^2 + 8x + 8 - 5
y = 2x^2 + 8x + 3
Shape A can be transformed to shape B by a rotation 90° clockwise about (-1, 1) followed by a translation by vector
(a b)
Find the values of a and b
Answers
The values of a and b if the coordinate is rotated 90° clockwise is -1 and -1
Rotation of coordinatesThe rotation is a transformation technique that changes the position of an object in an xy plane. If the coordinate (x, y) is rotated 90° clockwise, the resulting coordinate will be at (-y, x)
If the coordinate (-1, 1) is therefore rotated 90° clockwise about the origin, the resulting coordinate will be (-1, -1).
Comparing
a = -1 and b = -1
Hence the values of a and b if the coordinate is rotated 90° clockwise is -1 and -1
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Please help me!! High School algebra 2 math. Big Ideas Math
Answers
Answer:
x = 8
Step-by-step explanation:
Hello!
The missing angle in the triangle can be found by subtracting 90° and 45° from 180°. The missing angle is 45°.
This means that the triangle is isosceles, as there are two congruent base angles, 45° and 45°.
The side lengths opposite these two angles are congruent.
We can see that 8 is opposite 45°, and x is opposite 45°. Therefore, x must be equal to 8.
The value of x is 8.
Answer:
x = 8
Step-by-step explanation:
The interior angles of a triangle sum to 180°.
The given triangle is a right triangle, so the missing angle is 45°
⇒ 180° - 90° - 45° = 45°
As the triangle has 2 equal angles, this means it is an isosceles triangle (with its vertex at the right angle). An isosceles triangle has legs of equal measure, therefore [tex]x=8[/tex].
Proof
This can be proven by using the tan trigonometric ratio to calculate the value of x.
Tan trig ratio
[tex]\sf tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = 45°O = 8A = xSubstituting the given values into the equation and solving for x:
[tex]\implies \tan (45^{\circ})=\dfrac{8}{x}[/tex]
[tex]\implies x=\dfrac{8}{\tan (45^{\circ})}[/tex]
[tex]\implies x=\dfrac{8}{1}[/tex]
[tex]\implies x=8[/tex]