Two square stepping stones are placed in a garden as shown below. Each stepping stone has a side length of 2 feet. The rest of the garden will have flowers in it.
How many square feet of the garden could contain flowers?
20 ft²
32 ft²
16 ft²
24 ft²

answer: more likely because its a bunch of school-aged kids so obviously they want a new park.

Find f when f"(x) = x^-2, x > 0, f(1) = 0, f(8) = 0

Integrate twice. Do not forget the constants of integration.

f'(x) = -1/x + C                    f(x) = - ln x + Cx + D

To find C and D, apply f(1) and f(2)

f(1) =  - ln (1) + C + D = 0    

C + D = 0     equation 1

f(8) = - ln 8 + 8C + D = 0  

8C + D = ln 8   equation 2

Solve for C and D from equations 1 and 2

C = ln 2/7   and D = - ln2/7

f(x) = - ln x  + (ln 2/7) x - ln 2/7

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals. Integration, along with differentiation, is a fundamental, crucial calculus operation.

It can be used to solve issues in mathematics and physics involving, among other things, the volume of a solid, the length of a curve, and the area of an arbitrary shape.

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Answer:

answers is 78 because if 6x45 that 87

The Answer is 84, because 36 x 2 =72 and then 1/3 of 36 is 12 and 12+72=84.

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The probability of needing at most 3 rolls is 1/2.The probability of needing an even number of die rolls is 1/2.

(a) The probability of needing at most 3 rolls is 1/6 + 1/6 + 1/6 = 3/6 = 1/2. This can be calculated by considering the probability of getting a 4 on the first, second and third rolls. The probability of getting a 4 on the first roll is 1/6, the probability of getting a 4 on the second roll is 1/6 and the probability of getting a 4 on the third roll is 1/6. This adds up to 3/6 which is the same as 1/2.

(b) The probability of needing an even number of die rolls is 1/2. This is because the probability of getting a 4 on an even roll is the same as the probability of getting a 4 on an odd roll. For example, the probability of getting a 4 on the first roll is 1/6, the probability of getting a 4 on the third roll is also 1/6. Therefore, the probability of needing an even number of die rolls is 1/2.

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Answer:

0.13 to 0.30 mp

Step-by-step explanation:

Triangles can be categorized as scalene triangles, acute triangles, obtuse triangles, isosceles triangles, equilateral triangles, and right angles.

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. A triangle is a polygon with three vertices and three sides. The triangle's three angles add up to 180 degrees in total. Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle.  

here ,

various triangles

Triangle of Scalene. a triangle without sides that are similar.

Sharp Triangle a triangle in which each of the three angles is less than 90 degrees.

Sharp Triangle. a triangle with one angle that is more than 90 degrees in length.

Triangles include: Right Triangle, Equilateral Triangle, and Isosceles Triangle.

Triangles can be categorized as scalene triangles, acute triangles, obtuse triangles, isosceles triangles, equilateral triangles, and right angles.

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Answer:

2 is correct answer.

Answer: y = ±√ 0.500 = ± 0.70711

Step-by-step explanation:

Solve  :    2y2-1 = 0  Add  1  to both sides of the equation :                       2y2 = 1 Divide both sides of the equation by 2:                     y2 = 1/2 = 0.500   When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:                        y  =  ± √ 1/2  

Answer:

Answer: y = ± √0.500 = ± 0.70711

Answer:

[tex]f^{-1}(x)=\sqrt{x+4}+1[/tex]

Step-by-step explanation:

[tex]f(x)=(x-1)^2-4\\y=(x-1)^2-4\\[/tex]

Swap x and y and solve for y:

[tex]x=(y-1)^2-4\\x+4=(y-1)^2\\\sqrt{x+4}=y-1\\\sqrt{x+4}+1=y\\f^{-1}(x)=\sqrt{x+4}+1[/tex]

Hence, the inverse function is [tex]f^{-1}(x)=\sqrt{x+4}+1[/tex]

The angle marked x in the regular hexagon is 120 degrees, and in the regular pentagon is 108 degrees.

The angle marked x in the regular hexagon is 120 degrees, because the sum of all the angles in a hexagon is 720 degrees (360 x 2). Each of the angles in a regular hexagon is 120 degrees, so the angle marked x must also be 120 degrees. The angle marked x in the regular pentagon is 108 degrees, because the sum of all the angles in a pentagon is 540 degrees (360 x 1.5). Each of the angles in a regular pentagon is 108 degrees, so the angle marked x must also be 108 degrees.

Regular Hexagon:

Sum of angles = 720 degrees

Number of angles = 6

Angle x = 720 ÷ 6 = 120 degrees

Regular Pentagon:

Sum of angles = 540 degrees

Number of angles = 5

Angle x = 540 ÷ 5 = 108 degrees

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We must take into account the number of options for each PIN digit in order to get the total number of 4-digit personal identification numbers (PINs) that can exist. There are nine options available because the first digit must be 0. (1, 2, 3, 4, 5, 6, 7, 8, or 9). There are a total of 10 options available for each of the remaining 3 digits, which can all be any of the digits 0 through 9. Thus, there are a total of 9 * 10 * 10 * 10 = 9000 different 4-digit PIN combinations.

  However, since we're looking for 4-digit PINs that are odd, the last digit must be one of the following: 1, 3, 5, 7, or 9. This indicates that there are 5 options available for the final digit.

  As a result, there are 4500 4-digit PINs that are odd and cannot start with 0. This is calculated as 5 * 9 * 10 * 10. This is the right response, which goes with option b.

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Answer:

Rectangle

Step-by-step explanation:

By putting the points in Desmos, it shows an image of a rectangle. It allows you to change the number of B and also A, and whatever number you change them to the image will still be a rectangle.

The solution of the polynomial ; subtracting a² - 3ab - 4b² from the sum of 3a² - ab - 2b² and 2a² + 5ab - 3b² is 4a² + 7ab - b².

Polynomials are algebraic expressions that consist of variables and coefficients. Therefore, let's perform the operation with the polynomials as follows:

Let's subtract a² - 3ab - 4b² from the sum of 3a² - ab - 2b² and 2a² + 5ab - 3b².

Hence,

3a² - ab - 2b² + 2a² + 5ab - 3b²

combine like terms

3a² + 2a² - ab + 5ab - 2b² - 3b²

5a² + 4ab - 5b²

Finally let's subtract a² - 3ab - 4b²  from 5a² + 4ab - 5b².

Therefore,

5a² + 4ab - 5b² - ( a² - 3ab - 4b²)

5a² + 4ab - 5b² - a² + 3ab + 4b²

5a² - a² + 4ab + 3ab - 5b² + 4b²

4a² + 7ab - b²

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Answer:

76.16kg

Step-by-step explanation:

68kg x (1+0.12)

the x (1+0.12) shows we are increasing by 12%

can also be written as

(68kg x 1) + (68kg x 0.12)

Non of the above Statement is true.

Standard deviation is a mathematical measure of how spread out a dataset is. It is a measure of the variation or dispersion of a set of values from the mean. It is calculated by taking the square root of the variance. Standard deviation can be used to measure the risk associated with an investment, to compare data sets, or to measure the accuracy of a data set.

The standard deviation is a measure of the dispersion of a set of data from its mean, and it is always a non-negative number. It can sometimes be zero, and it can also be larger than the variance.

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The product requested is equal to -108.8. The result found is a rational number.

The numbers can be classified as rational or irrational.  A number is classified as a rational number when this number is represented by a ratio between two integers numbers ([tex]\frac{b}{c}[/tex]), where c ≠0.  Besides, this ratio can be simplified in decimal form.

On the other hand, an irrational number represents a number that cannot be written in the form of a fraction, only in decimal form. In this case, the decimal never repeats.

The rules for the multiplication of numbers are:

The result presents a positive sign (+) because the signs are the same.

The result presents a negative sign (-) because the signs are different.

The question asks the product between [tex]\sqrt{1024}[/tex] and -3.4.

Initially, you have noted that from factoring 1024= [tex]2^{10}[/tex], consequently, your root is equal to [tex]2^5[/tex]. Here, you have that [tex]2^5=32[/tex]. After that, you should multiplicate 32 by -3.4.

Thus, you have 32 * (-3.4)= -108.8.

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one angstrom, symbolized as å, is 10-10 m, so

1 cm^3 = 10^24 angstrom^3

The angstrom, sometimes known as a ångström, is a metric length unit equal to 10^(-10)m, or one ten billionth of a metre, one hundred millionth of a centimeter, 0.1 nanometer, or one hundred picometres. The Swedish alphabet letter serves as its symbol. The Swedish physicist Anders Jonas Angström is commemorated by the unit's name.

The length of an object is measured in centimeters, which are metric units of measurement. The abbreviation is cm.

100 centimeters make up a meter.

One centimeter is equal to ten millimeters.

so one angstrom is 10^-10 m, or 10^-8 cm, so there are 10^8 angstroms in 1 cm.

1 cm^3 = 1 cm 1 cm * 1 cm

1 cm^3 = 10^8 10^8 10^8 angstrom^3

1 cm^3 = 10^24 angstrom^3

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Using simultaneous equations, Kieran and Louise's numbers are 20 and 8 respectively.

Kieran and Louise each think of a number. 4 less than Kieran's number is equal to 2 lots of Louise's number.

let's

x = Kieran's number

y = Louise's number.

x - 4 = 2y

x - 2y = 4

3 lots of Kieran's number added to Louise's number is 68.

Hence,

3x + y = 68

Hence, let's combine the system of equation.

x - 2y = 4

3x + y = 68

multiply equation(i) by 3

3x - 6y = 12

3x + y = 68

-7y = -56

y = -56 / -7

y = 8

Therefore, let's find x

x = 4 + 2y

x = 4 + 2(8)

x = 4 + 16

x = 20

Hence,

Kieran number = 20

Louise number = 8

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Answer:

[tex]\frac{2\pi}{3}\text{units}^2[/tex]

Step-by-step explanation:

[tex]\displaystyle A=\frac{r^2\theta}{2}=\frac{4^2*\frac{\pi}{12}}{2}=\frac{16\pi}{24}=\frac{2\pi}{3}\text{units}^2[/tex]

Answer:

plus or minus 11

Step-by-step explanation:

2(1)+7

=9

2(1)-4

=-2

and the difference between the 9 and -2 is -11 but the difference between -2 and 9 is 11 so that why it positive or negative 11

Realism is the faithful representation of reality in literature, and it presents life as it actually is. Option (c) is correct.

Reality is the state of things as they actually are, as opposed to how we would like them to be.

While "Naturalism is a manner and style of writing by which the author portrays 'life as it is' in accordance with the philosophic idea of determinism," "Realism is a manner and method of composition by which the author describes normal, average life, in an exact, truthful way."

Realism is a literary approach used by various schools of writing and is broadly referred to as "the faithful representation of reality" or "verisimilitude."

Therefore, Option (c) is correct. Realism is the faithful representation of reality in literature, and it presents life as it actually.

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The coordinates of the vertices after the reflection over the line y = -x is K'(-5, -4), L'(-7, -7), M'(-9, -4) and N'(-7, 1).

Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.

Given a quadrilateral KLMN.

The coordinates of the vertices are,

K(4, 5), L(7, 7), M(4, 9) and N(-1, 7)

The point (x, y) after the reflection over the line y = -x is the point (-y, -x).

K(4, 5) becomes K'(-5, -4)

L(7, 7) becomes L'(-7, -7)

M(4, 9) becomes M'(-9, -4)

N(-1, 7) becomes N'(-7, 1)

Hence the coordinates are K'(-5, -4), L'(-7, -7), M'(-9, -4) and N'(-7, 1).

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The sum of the interior angle measures of this polygon is 540 degrees

A convex polygon is simply described as closed figure having all its interior angles less than 180° and its vertices  pointing outwards.

The word 'convex' is used to described a shape that has a curve or a protruding surface.

Also, all the lines across the outline are straight and they all point outwards.

From the diagram shown, we have that;

Sum of the interior angles of a pentagon = (n - 2) 180

Substitute n as 5 in the equation

= (5 -2 ) 180

= 3(180)

= 540 degrees

Hence, the sum is 540 degrees

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For a function, f(x) = 1 + 3x , the computed value of lim h→0 [f(5 + h) − f(5)]/h is equals to the three.

In Mathematics, the limit of a function is a value of the function as the input of the function tries approaches some number. Function limits are used to define continuity, integrals, and derivatives. Mathematically, let f(x) be a function and L be limit of function, f(x) at x a exist if and only if lim f(x) = lim f(x) = L

x→a⁻ x→a⁺

We have, f(x) = 1+3x and will compute lim h→0 [f(5 + h) − f(5)]/h . Firstly, determine the value of function at x = 5 , x = 5+h.

So, f(5) = 1+ 3×5 = 16 and f(5+ h) = 1+3(5+h)

= 16+ 3h

Now, lim [ f(5 + h) − f(5)]/ h

h→0

= lim [(16 + 3h) − (16) ]/ h

h→0

= lim [ 16 + 3h - 16 ]/ h

h→0

= lim [ 3h/ h ] = lim [ 3h¹h⁻¹ ]

h→0 h→0

= lim [ 3h¹⁻¹ ] = lim [ 3h⁰ ]

h→0 h→0

= lim 3 (1) = 3 ( since, x⁰ = 1 )

h→0

Hence, the required limit value is 3.

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Part 1

[tex]m=\frac{-7-(-5)}{8-0}=\boxed{-\frac{1}{4}}[/tex]

Part 2

[tex]y=-\frac{1}{4}x-5[/tex]

the answer is 1

x = 1 is an extraneous solution for the equation 1/(x - 1) = (x - 2)/(2x² - 2).

The linear function f(x) has a slope of -5 and intersects the y-axis at the point (0, 45).  The function g(x) intersects the x-axis closer to zero than the function f(x). Option D

Generally, To find the x-intercepts of a linear function, you can set the y-value equal to zero and solve for x.

For the function f(x), we have:

f(x) = -5x + 45

0 = -5x + 45

5x = 45

x = 9

So the x-intercept of f(x) is (9, 0).

For the function g(x), we have:

g(x) = -5x - 10

0 = -5x - 10

5x = 10

x = 2

So the x-intercept of g(x) is (2, 0).

Since the x-intercept of g(x) is closer to zero than the x-intercept of f(x), the correct answer is D. The function g(x) intersects the x-axis closer to zero than the function f(x).

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The greatest number of students that can attend the party is 16.

A factor defines a number that divides another number, leaving no remainder, which is equal to zero.

And if we multiply two whole numbers to give us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

There are two methods of finding factors: multiplication and division.

Now, let us know factors 48 and 64

factors of 48 are 1,2,3,4,6,8,12,16,24,48.

factors of 64 are 1,2,4,8,16,32,64.

so the common factors of 48 and 64 are: 1,2,4,8, and 16

In the common factors of 48 and 64, 16 is the greatest number.

Therefore, the greatest number of students that can attend the party is 16.

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From the rectangle, the value of x is 4.9 or -2.4

A rectangle is a four sided polygon whose opposite sides are equal and parallel, The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.)

The parameters given for the solution are

Area = 24m

Length = x+2

width = 2x-9

Area = l*w

This implies that (x+2)(2x-9)=24

Collecting like terms we have

2x2-5x-24=0

Solving the equation we have

(5±√25+192)/4

⇒(5±√217)/4

⇒(5+14.7)/4 or( 5-14.7)/4

x=4.9 or x = 2.4

Therefore the value of x in the figure is 4.9 and -2.4 respectively

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