Find the area and circumference of the following.
(a) A circle of radius 7 cm Take π = 22/7

It is possible to construct a triangle whose sides are 3 cm 4 cm and 5 cm because the sum of two sides are greater than the third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 3 cm 4 cm and 5 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.

To check this we firstly add the 3 and 4

3 + 4 > 5

7 > 5

Now we add 3 and 5

3 + 5 > 4

8 > 4

Now we add 4 and 5

5 + 4 > 3

9 > 3

It is possible to construct a triangle whose sides are 3 cm 4 cm and 5 cm because the sum of two sides are greater than the third sides.

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No, 1234 is not an arithmetic sequence. A sequence is a list of numbers, arranged in a specific order.

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is always the same. It is also known as an arithmetic progression.

The sequence 1234 does not have a common difference between its terms. It's just a set of numbers arranged in a specific order, but the difference between the terms is not always the same.

Arithmetic sequence has the general formula of a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the number of the term. The sequence 1234 doesn't follow this formula.

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Answer:

Step-by-step explanation:

and 2.3333333333

One can use either the slope formula m = (y2 – y1)/(x2 – x1) or the standard line equation, y = mx + b to solve for the slope, m.

You can find the slope of the line by determining the rise and run of two locations on the line. The rise is the vertical change between two places, while the run is the horizontal change. The slope is calculated by dividing the climb by the run: Riserun = Slope Slope = rise and run.

Depending on the form of the equation in front of you, the procedure for calculating the slope will differ. If the equation is written as y = mx + c, the slope (or gradient) is simply m. If the equation is not in this form, attempt rearrangement. You will need to do the following to determine the gradient of additional polynomials:

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Answer:

Step-by-step explanation:

2590

To enlarge a triangle by a scale factor of 3 we divide the longer side by the short side. 6 ÷ 2 = 3 and so, the scale factor is 3.

What is a scale factor?

A scale factor is a numerical value that is used to represent an object's larger or shrunk shape. It is a number that can be used to alter the size of any geometric figure or shape in relation to its initial size. It aids in adjusting the figure's size.

Here,

We have to determine how can we enlarge a triangle by a scale factor of 3.

We concluded that

To find the scale factor of enlargement, divide the longer side by the short side. 6 ÷ 2 = 3 and so, the scale factor is 3.

This means that all of the sides on the smaller shape have been multiplied by 3. It also means that all of the sides on the larger shape can be divided by 3 to make the smaller shape.

Hence, to enlarge a triangle by a scale factor of 3 we divide the longer side by the short side. 6 ÷ 2 = 3 and so, the scale factor is 3.

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A) The standard equation of the circle, with center at (f, g) and a point on the circle at (x, y) is; (x - f)² + (y - g)² = h²

B) The domain and range of the circle are respectively;

[-5, 11] and [-9, 7]

C) Yes the point (10, –4) is inside the border of the circle

A) Using the Pythagorean theorem will generate the equation for a circle as follows;

Sum of squares of sides = square of hypotenuse

From the given image, we have;

(x - f)² + (y - g)² = h² . . . . . . circle centered on (f, g) with radius h

B) The circle is defined for values of x in the domain f ± h, and for values of y in the range g ± h.

Domain: 3 ± 8 = [-5, 11]

Range: -1 ± 8 = [-9, 7]

C) The distance from point (10, -4) to (f, g) calculated as;

h² = (10 - 3)² + (-4 - (-1))²

h² = 7² + (-3)²

h²  = 49 + 9 = 58

h = √58 < 8

Thus, the distance to the point is less than h=8 and it implies that the point is inside the circle.

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The arithmetic sequence function is c)f(n)=25 + 6(n-1).

What is arithmetic sequence?

An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.

Here the given series 25,31,37,43,...

First term [tex]a_1[/tex]= 25

Now Common difference d = [tex]a_2-a_1[/tex]=31-25 = 6.

Now using arithmetic sequence formula,

[tex]f(n)=a_1+(n-1)d[/tex]

Here putting indicated value  [tex]a_1[/tex]= 25 and d=6

=> f(n) = 25 + (n-1)6

=> f(n) = 25 + 6 (n-1)

Hence the correct option is c)f(n)=25 + 6(n-1).

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Answer:

C. f(n)=25 + 6(n-1).

Step-by-step explanation:

got it right on test

In a 45°−45°−90° triangle, the length of the hypotenuse is √2 times the length of a leg.

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The graph of the following coordinates can be graphed by plotting the points of given coordinates on the graph.

Coordinates are a pair of integers (also known as Cartesian coordinates), or occasionally a letter and a number, that identify a specific point on a grid, also known as a coordinate plane.

A point is a dot on a sheet of paper or in a plane. There are no lengths, widths, or heights in a point. It establishes a plane's position or location.

Plot the points according to the given coordinates. Connect all the points with with a smooth curve.

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Time spend on science homework is 16 minutes and time spend on math homework is 48 minutes.

Two or more expressions with an Equal sign is called as Equation

Given that,

The time spend on math homework =  3 times time spend on science homework,

Also, total time spent on math and science both homework = 64 minutes.

Let time spend by Max on science homework is t minutes,

Then by given condition, time spend on math homework = 3t

Total time = 64 minutes

t + 3t = 64 minutes

4t = 64 minutes

Divide both sides by t

t = 16 minutes

Hence, Time spend on science homework is 16 minutes and time spend on math homework is 48 minutes.

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A 3 variable graph can be graphed using a 3D scatter plot. The x, y, and z axes will represent the three variables. Each point on the graph will represent a combination of the three variables. The points can be connected to form a 3D line graph to illustrate the relationships between the variables.

1. Open a graphing software such as Microsoft Excel or a graphing calculator.

2. Choose the 3D scatter plot option.

3. Enter the values for each of the three variables.

4. The graph will appear with the x-axis, y-axis, and z-axis representing the three variables.

5. Each point on the graph will represent a combination of the three variables.

6. Optionally, you can connect the points to form a 3D line graph to illustrate the relationships between the variables.

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Therefore , the solution of the given inequality problem comes out to be

-8/5.

The equation-like form of the expression 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequality. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3. Finding the x variable values for which the inequality holds true is what we are most interested in.

Here,

Give:

=> -3(2x+2) < 10

=>2x+2>10/3

=>x+1>-10/6

=>> -10/6-1 >1

=> -8/5

Therefore , the solution of the given inequality problem comes out to be

-8/5..

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The base in the exponential function is greater than 1 because exponential growth is defined as a constant multiplication of the original value, rather than a constant addition as in linear growth. A base greater than 1 results in a growth rate that increases over time, while a base less than 1 results in a growth rate that decreases over time.

The exponential function is written as bˣ, where b is the base and x is the exponent. The base is the number that is being multiplied by itself a certain number of times, as determined by the exponent.

A base greater than 1 means that the value of the function is increasing at an increasing rate. This is because as the exponent (x) increases, the base (b) is being multiplied by itself more and more times, leading to a larger and larger result. This is known as exponential growth.

On the other hand, a base less than 1 means that the value of the function is decreasing at an decreasing rate. This is because as the exponent (x) increases, the base (b) is being multiplied by itself more and more times, leading to a smaller and smaller result. This is known as exponential decay.

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The categories are usually "felony," "misdemeanor," and "infraction." Decisions on crime classification are made by state legislators; the determination focuses on the seriousness of the crime.

8.33% probability that Michael will be chosen first and Susan will be chosen second.

Initially, there are 4 people(Susan, John, Lisa, and Michael). The probability of Michael being chosen first is 1/4.

Now, suppose Michael was chosen.

There are 3 people(Susan, John and Lisa). The probability of Susan being chosen is 1/3.

What is the probability that Michael will be chosen first and Susan will be chosen second.

Multiplying these probabilities

8.33% probability that Michael will be chosen first and Susan will be chosen second.

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Answer:

6x - 9

Step-by-step explanation:

18x -11 - (12x - 2)   Can be written

18x -11 -1(12x -2)  Distribute the -1

18x - 11 -1(12x) + (-1)(-2)

18x - 11 -12x +2  Combine like terms

6x -9

To find the coordinates of a point, you simply need to know its location in the given space and to find the midpoint of a point you need to know the coordinates of the two given points and use the formula (x₁ + x₂)/2, (y₁ + y₂)/2.

A point in geometry is a location in space that is represented by a set of coordinates, typically in the form of (x,y) or (x,y,z) for a three-dimensional space.

To find the coordinates of a point, you simply need to know its location in the given space.

The midpoint of a point is the point that is exactly halfway between two given points. To find the midpoint of a point, you need to know the coordinates of the two given points. Once you have this information, you can use the following formula to find the midpoint:

(x₁ + x₂)/2, (y₁ + y₂)/2

For example, if the coordinates of point A are (3,4) and the coordinates of point B are (7,8), the midpoint of the two points would be ( (3+7)/2 , (4+8)/2 ) = (5,6)

In conclusion, finding the point and midpoint of a point is a fundamental concept in geometry. To find the point, we need to know its location in the given space, represented by the coordinates.

To find the midpoint of a point, we need to know the coordinates of the two given points and use the formula (x₁ + x₂)/2, (y₁ + y₂)/2. These concepts are widely used in mathematics, physics, engineering and other fields that deal with spatial relationships.

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This may be computed by dividing his hitting % by the number of times he bats (20). (0.8). 20 x .8 = 16

Percentage:

a: a part of a whole expressed in hundredths a high percentage of students attended.

b: the result obtained by multiplying a number by a percent the percentage equals the rate times the base.

c: a share of winnings or profits.

If Henrie hits 80% of the time he's at bat, and he is up to bat 20 times this weekend, he is expected to hit 16 times. This can be calculated by multiplying the number of times he is up to bat (20) by his hitting percentage (0.8). 20 x .8 = 16

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Standard form is ax^2 + bx + c. Vertex form is a(x-h)^2 + k, which reveals the vertex and axis of symmetry. Factored form is a(x-r)(x-s), which reveals the roots.

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Answer:

a. $2908.93

Step-by-step explanation:

We use the formula:

A = P( 1 + r)^t

P = $1986

r = 4% = 0.04

t = 23 years

Let's solve

A = 1986(1 + 0.04)^23

A = 1986( 1 + 0.04)

A = 1986( 1.04)^23

A = $4894.925

Now we take

$4894.925 - $1986 = $2908.925

$2908.925 round-up =  $2908.93

So, the answer is A

Answer:

216.7 m/min

Step-by-step explanation:

1 km = 1000 m

1 hour = 60 min

13km/h = 13 (1000 m) / (60 min) = 216.7 m/min

Answer:216.6667

Step-by-step explanation:

kph × 16.66667

m/min =13 × 16.66667

m/min =216.6667

The rate of change of f on the interval [2, 4] is 6.

The rate of change of a function f on the interval [a,x] is the slope of the corresponding secant line m(sec), which is given by the following formula:

m(sec)=(f(x)-f(a))/(x-a)

To calculate the rate of change, we can take an example function f(x) = x^2. Let's say we want to find the rate of change of f on the interval [2, 4]. Using the formula from above, we get:

m(sec)=(f(4)-f(2))/(4-2)

= (4^2 - 2^2)/(4-2)

= (16 - 4)/2

= 12/2

= 6

Therefore, the rate of change of f on the interval [2, 4] is 6.

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The 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions.

Linear equations are equations that have constant average rates of change, slope or gradient.

A system of linear equations is a collection of at least two linear equations.

here, we have,

In this case, the system of equations is given as

6x - 5y = -8

6x - 5y = -8

Subtract the equation 6x - 5y = -8 from the equation 6x - 5y = -8

6x - 5y = -8

(-) 6x - 5y = -8

----------------------

0 = 0

This in other words means that the difference between both equations is 0.

When the solution to a system of equation is 0 = 0, it means that the system of equations have infinitely many solutions.

Hence, the 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions.

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As per the given volume, it take 223 minutes to fill the pool.

The term volume in math is defined as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface and it measured as cubic units.

Here we have given that a 9,000-gallon pool is being filled at a rate of 40 gallon per minute.

Here we need to find the time taken to fill the pool.

While we looking into the given question, we have identified the following values,

Total volume of pool = 9000 gallon.

Amount of water filled in one minute = 40 gallon,

then the time take by the pool to fill is calculated by dividing the total amount by the amount of water per minute then we get,

=> 9000/40

When we simplify this one then we get,

=> 225

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The thermometer functions because of temperature-related expansion and contraction. Conduction is the process by which heat moves from one item to another.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

given

The thermometer will display a greater temperature as the liquid expands and rises as it gets hotter.

The thermometer functions because of temperature-related expansion and contraction.

Conduction is the process by which heat moves from one item to another.

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Similar to when a woman is 1 cm dilated, 2 cm dilation does not indicate that labor will start soon. If a woman is 2 cm dilated, some of them may give birth in a few of hours. For a few days or weeks until labor advances, some women will stay 2 cm dilated.

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To find the equation of a graphed line, find the y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. Slope is the change in y over the change in x.

Linear equations with two variables have straight line graphs. There are numerous ways to express linear equations:

Slope-Intercept Formula: y=mx+b

The slope is m and the y-intercept is the point in an equation of the type y = mx + b, such as y = 2x 3. (0, b). Create a table of values (Method 1) or use the slope and y-intercept (Method 3) to graph equations of this kind (see Examples 1 and 6).

Basic Formula: axe + by = c

Find the x- and y-intercepts (Method 2) to graph equations of this type, such as 3x 2y = 6, or solve the equation for y to form y = mx + b and create a table of numbers (see Example 2).

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Our Pythagorean triplets will be (6,8,10), (5,12,13), and (3,4,5).

So what is the Pythagorean triplet?

The square of the greatest number in a Pythagorean triplet equals the sum of the squares of the other two numbers.

The greatest side in a right-angled triangle is called the hypotenuse.

So, in our first triplet A(6,8,10) the greatest side is 10. So, hypotenuse = 10.

= [tex]hypotenuse^{2}[/tex] = [tex]10^{2}[/tex] = 100.

Now, [tex]6^{2}[/tex] + [tex]8^{2}[/tex] = 36 + 64 = 100.

[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]8^{2}[/tex]

Thus A(6,8,10) is a Pythagorean triplet.

In the second case B(5,12,13) hypotenuse = 13.

= [tex]hypotenuse^{2}[/tex] = [tex]13^{2}[/tex] = 169.

Now, [tex]12^{2}[/tex] + [tex]5^{2}[/tex] = 144 + 25 = 169.

[tex]13^{2}[/tex] = [tex]12^{2}[/tex] + [tex]5^{2}[/tex]

Thus B(5,12,13) is a Pythagorean triplet.

In the Third case C(7,13,15) Hypotenuse = 15.

= [tex]hypotenuse^{2}[/tex] = [tex]15^{2}[/tex] = 225.

Now, [tex]7^{2}[/tex] + [tex]13^{2}[/tex] = 49 + 169 = 218.

[tex]15^{2}[/tex] [tex]\neq[/tex] [tex]7^{2}[/tex] + [tex]13^{2}[/tex]

Thus C(7,13,15) is not a Pythagorean Triplet.

In the last case D(3,4,5) Hypotenuse = 5.

= [tex]hypotenuse^{2}[/tex] = [tex]5^{2}[/tex] = 25.

Now, [tex]3^{2}[/tex] + [tex]4^{2}[/tex] = 9 + 16 = 25.

[tex]5^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex]

Thus D(3,4,5) is a Pythagorean triplet.

Therefore our three results A(6,8,10) B(5,12,13) and D(3,4,5) are Pythagorean triplets.

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