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The equations of the line are listed according to slope and intercept below:

According to Euclidean geometry, a line can be constructed by knowing the location of two different points set on Cartesian plane. From analytical geometry we find that lines are represented by an equation of the form:

y = m · x + b

Where:

The slope can be found by secant line formula:

m = Δy / Δx

Now we proceed to find the equation of the line for each case:

Case 1 - (x₁, y₁) = (3, 2), (x₂, y₂) = (5, 7)

m = (7 - 2) / (5 - 3)

m = 5 / 2

b = y - m · x

b = 2 - (5 / 2) · 3

b = 2 - 15 / 2

b = - 11 / 2

y = - (5 / 2) · x - 11 / 2

Case 2 - (x, y) = (- 3, 4), m = 2

b = y - m · x

b = 4 - 2 · (- 3)

b = 4 + 6

b = 10

y = 2 · x + 10

Case 3 - m = - 3, b = 5

y = - 3 · x + 5

Case 4 - x-intercept: 3, y-intercept: 0

m · 3 + b = 0

3 · m = - b

m · 0 + b = 0

b = 0

m = 0

y = 0

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The measure of the base BC in the given triangle is (C) 25 units.

A polygon with three edges and three vertices is called a triangle.

It is one of the fundamental geometric shapes.

The letter ABC stands for a triangle having the vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

If all of the geometry is in the Euclidean plane, then all triangles are encompassed in a single plane, however, in higher-dimensional Euclidean spaces, this is no longer the case.

This article concerns triangles in Euclidean geometry, specifically the Euclidean plane unless otherwise stated.

So, the given triangle is an isosceles triangle with AB = AC.

Then get the value of x as follows:

AB = AC

4x + 1 = 2x + 23

4x - 2x = 23 - 1

2x = 22

x = 22/2

x = 11

Now, substitute x = 11 in 3x - 8 that is BC.

3x - 8

3(11) - 8

33 - 8

25

Therefore, the measure of the base BC in the given triangle is (C) 25 units.

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Correct question:
What is the measure of the base in the triangle below?

a. 11

b. 45

c. 25

d. 30

The solution to this system of linear equations is x = 3 & y = -1.

Given linear equations are

2x + 3y = 3   ---- 1

7x - 3y = 24  ---- 2

By dividing both the equations, we get

9x = 27

x = 27/9

x = 3

Now substituting x = 3 in the equation 1, we get

2(3) + 3y = 3

6 + 3y = 3

3y = 3 - 6

y = -3/3

y = -1

Hence the answer is the solution to this system of linear equations is x = 3 & y = -1.

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Answer:

240 cm³

Step-by-step explanation:

Volume = [ 2(3) - 3]( 3 + 5)[ 3(3) + 1 ]

Volume = ( 6 - 3 )( 8 )( 9 + 1)

Volume = ( 3 )( 8 )( 10 )

Volume = 24(10)

Volume = 240 cm³

The I quadrant will contain the point (6, 8). The number is in the I quadrant as a result.

What is Quadrant?

A quadrant is any one of the four divisions of the coordinate plane. Additionally, we refer to the sections as they are divided by the coordinate axes when we talk about the sections. The y-axis is situated on this up-down axis, and the x-axis is situated here. As you can see, it divides the coordinate space into four parts.

A point can be mathematically expressed as:

A(x, y )

The intersection of the coordinate axes divides the cartesian plane into four quadrants (x and y-axis).

                        (x, y )

In the first quadrant, the x and y coordinates are both positive.

              (x, y)

Y is positive while x is negative in the second quadrant.

                      (-x, y)

The point will be located in the third quadrant if both x and y are equally negative.

                      (-x, -y)

The point will be located in the fourth quadrant if both x and y are positive.

                       (x, -y)

pointed out; A(6, 8)

The y-coordinate in the highlighted position is positive at (8), while the x-coordinate is negative at (6).

Remember that if the x-coordinate is negative and the y-coordinate is positive, the point is in the I quadrant.

As a result, the provided point (6, 8) is said to be in the I quadrant.

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Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

Given that,

We have to find what are the 2 characteristics of a regular polygon.

We know that,

Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

Regular triangles and quadrilaterals are given unique names, such as squares and equilateral triangles.

Therefore, Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

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The equivalent rational expression of the given expression, 9/5u² - 40u - 45, is 9/(5u + 5)(u - 9)

The equivalent rational expression of the given expression, 2u/5u² + 30u + 25 , is 2u/(5u + 5)(u + 5)

From the question, we are to rewrite the given expressions as equivalent rational expressions.

The given expressions are:

9/5u² - 40u - 45 and 2u/5u² + 30u + 25

Writing an equivalent expression for 9/5u² - 40u - 45

Factorize the denominator

5u² - 40u - 45

5u² - 45u + 5u - 45

5u(u - 9) + 5(u - 9)

(5u + 5)(u - 9)

Thus,

The equivalent expression is 9/(5u + 5)(u - 9)

Writing an equivalent expression for 2u/5u² +30u + 25

Factorize the denominator

5u² +30u + 25

5u² +25u + 5u + 25

5u(u + 5) + 5(u + 5)

(5u + 5)(u + 5)

Thus,

The equivalent expression is 2u/(5u + 5)(u + 5)

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The statement "I have anywhere from $5 to $8 in my pocket." has been represented on the number line shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Translating the statement, we have the following inequality:

Let the variable x represent the amount of money in pocket.

From $5 to $8 in my pocket = 5 ≤ x ≤ 8.

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The five inequality symbols are greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol ().

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The volume of the cone is 91.05[tex]m^{3}[/tex]

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex. We can also define the cone as a pyramid which has a circular cross-section, unlike pyramid which has a triangular cross-section.

circumference of the base of a cone is same as circumference of a circle which is 2[tex]\pi[/tex]r

15.8 = 2[tex]\pi[/tex]r

make r subject of equation

r = [tex]\frac{15.8}{2\pi }[/tex]

r = 2.51m

Volume of a cone = 1/3 x [tex]\pi[/tex][tex]r^{2}h[/tex], but h =13.8m

volume = 1/3 x 3.142 x [tex](2.51)^{2}[/tex] x 13.8 which is 91.05[tex]m^{3}[/tex]

In conclusion the volume of the cone is 91.05[tex]m^{3}[/tex]

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If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.

There are three additional names for a rhombus:

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Answer:

$13.50

Step-by-step explanation:

If the shirt is 10% off, that means the shirt is 90% of the original cost, which is $15.

If the shirt is 90% of the original cost which is 15, that means that we must turn the percentage into a decimal (0.9) and multiply it by 15.

0.9*15 = 13.5

The sale price of the shirt is $13.50

The volume of the rectangular prism with length of 5 units, width of 4 units and height of 3 units is 60 unit³

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Volume is the amount of space occupied by a three dimensional side or object.

Let us assume that the rectangle prism have length of 5 units, width of 4 units and height of 3 units. Hence:

Volume of prism = length * width * height

Volume = 5 units * 4 units * 3 units = 60 unit³

The volume is 60 unit³

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We know that  △ ABC ≅ △ DEF are congruent because AB corresponds to DE of another triangle, BC corresponds to EF and AC corresponds to DF.

According to the question,

We have the following information:

△ ABC ≅ △ DEF

Now, we know that this sign is used to show that the two triangles are congruent.

Now, we also know that in these two triangles, their corresponding sides will be equal. So, all the three sides of one triangle will be corresponding to the same sides in another triangle.

Hence, we know that  △ ABC ≅ △ DEF are congruent because AB corresponds to DE of another triangle, BC corresponds to EF and AC corresponds to DF.

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The function of the graph is g(x) = [x]+2

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of terms

y = output variable

x = input variable

m = slope

c = y intercept

The c from the graph is +2

m for points (1, 3) and (-3, -1)

= (-1 - 3) / (-3 - 1)

= -4/-4

= 1

substituting to the equation  y = mx + c

y = x + 2

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It is not a function because it has one-to-many function when it also has one-to-one and many-to-one.

Given that,

In the picture we have a diagram

We have to find if the diagram is a function or not.

We know that,

Mathematical calculus' core component is functions. The unique types of relationships are the functions. When it comes to math, a function is represented as a rule that produces a different result for each input x.

Function is satisfy one-to-one and many-to-one.

So,

In the picture we can see

Input -2 to output 7 it is one-to-one

Input 7 to output 8 and 2 it is one-to-many

Input 11 and 2 1/3  to output 5 it is many-to-one

Therefore, It is not a function because it has one-to-many function when it also has one-to-one and many-to-one.

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The binary number (100[tex])_2[/tex] in decimal system is written as [tex]4_{10}[/tex].

Given:

Binary number = [tex](100)_2[/tex]

Converting Binary to decimal system:

Binary:

In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one).

Decimal:

Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

[tex]100_2 = 1*2^2 + 0*2^1+0*2^0[/tex]

we know that,

[tex]2^0 = 1[/tex]

[tex]2^1 = 2\\2^2 =4[/tex]

substitute these values

[tex]100_2 = 1*4 + 0*2 + 0*1[/tex]

= 4 + 0 + 0

= 4 + 0

= [tex]4_{10}[/tex]

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Answer:

[tex]\textsf{(d)} \quad \sf \dfrac{1}{5} < c < \dfrac{1}{3}[/tex]

(e)    p ≤ -5

(f)     -m ≥ -9

Step-by-step explanation:

Symbol notation

A negative real number is any real number that is less than zero.

A positive real number is any real number that is greater than zero.

Zero is neither positive nor negative.

[tex]\textsf{c is between $\dfrac{1}{5}$ and $\dfrac{1}{3}$}.[/tex]

If c is between 1/5 and 1/3, it is greater than 1/5 and less than 1/3 (as 1/5 < 1/3), but not equal to either number:

If p is not greater than -5, then it is less than or equal to -5:

If the negative of m is not less than -9, then it is greater than or equal to -9:

Mixed Fractions A mixed fraction is a type of fraction in which there is a whole number part and a fractional part. For example, 31, 7, 3, 1, and 7 are all mixed fractions. It is also referred to as a mixed number.

Answer:

Fraction 7/2

Mixed fraction of the above 3 1/2

Step-by-step explanation:

a mixed number is a whole number and.  Fraction for an answer

So 3 1/2 is a mixed number 7/2 is the fraction befor reduced to a mixed number

The steam-leaf display is shown as follows

A stem and leaf plot resembles a bar graph in appearance. The term stems from the fact that each number in the data is divided into a stem and a leaf. The number's final digit is not part of the stem. The number's leaf will always be one digit.

Pencil and paper can be used to quickly create the plot. The plot can be used to determine the values of each individual data point. Since the stem is not repeated across multiple data points, the data is organized compactly.

The stem-and-leaf display for the given data is shown below followed by a detailed explanation.

0|358

1|25179476

2|73823

3|44

4|0

Note that it is often customary to organize the "leaf" values from lowest to highest as follows:

0|3578

1|12456779

2|23378

3|44

4|0

Each row's initial number is referred to as the stem, and the group of numbers that come after it as the leaves. The tenth position of the numerals is indicated by the stem. Therefore, a stem of 0 indicates a single-digit number, a stem of 1 indicates a number between 10 and 19, and so on. The leaves identify the numerals' unit position. If the number is 28, for instance, the stem and leaf are each two.

The data for stem 0 contains four one-digit numbers, which are 3, 5, 8 and 7 in appearance order. Therefore, the stem 0's leaves are 3, 5, 8, and 7.

Eight values between 10 and 19 may be found in the data for stem 1, and they are 12, 15, 11, 17, 19, 14, and 16 in that sequence. Therefore, 2, 5, 1, 7, 9, 4, and 6 make up the stem 1's leaves.

Five values between 20 and 29 may be found in the data for stem 2, and they are 27, 23, 28, 22, and 23 in that sequence. As a result, the stem 2's leaves are 7, 3, 8, and 3.

For stem 3, the data contain two integers between 30 and 39 that, in the order of appearance, are 34 and 34. The leaves for the stem 3 are therefore formed by 4 and 4.

For stem 4, the data only contains the number 40, which falls within the range of 40 to 49. Consequently, 4 creates the leaf for stem 2.

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Answer:

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

                                   Hope this helps!

The mean, median and mode of the distance from home plate to the left-field fence  is 302.57 ft, 303 ft, 310 ftrespectively.

Mean is the sum of all values divided by the total number of values

To calculate the mean of the data given, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Also, to calculate the median of the distribution, we arrage the data into ascending or decending order.

Ascending order ⇒ 279, 297, 301, 303, 310, 310, 321

Then, the median is the middle term in the distribution

Finally to get the mode, we look for the term in the distribution that has the higest frequency.

Hence, the mean, median and mode is 302.57ft, 303 ft, 310 ft respectively

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The answer to this question is after solving definite integration 0,1,-4,-10

What is Definite integration?

It is just basically Simple Integration with limits. In other words it is completely same as area under curve

Solution:

We will proceed by finding area under curve

Here we have to consider the area above x axis as positive and area under x axis as negative area

In First part +ve area and -ve area cancels each other hence answer is 0

In second part after cancellation only 1 square block above x axis remains whose area is 1  hence answer is 1

remaining 2 parts graph is completely below x axis hene area is negative therefore definite integeration will be negative

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Solving M2 in terms of Fg, G, M1 and r yields,

[tex]M2 = F {r}^{2} /GM1[/tex]

What does gravitational force between two objects mean?

An object with mass attracts another object with mass this attractive force that exists between all objects is known as gravitational force. It is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects.

Given,

The formula to calculate the gravitational force between two objects is F,

[tex]F=G M1 M2/ {r}^{2} [/tex]

where M₁ and M2 are the masses of the objects, G is the gravitational constant and

r is the distance between the objects.

Solving the equation for G2 we get,

[tex]F {r}^{2} =G M1 M2[/tex]

[tex]F {r}^{2}/G M1=M2[/tex]

[tex]M2 = F {r}^{2} /GM1[/tex]

This means, if there are two objects having mass M1 and M2 then M2 is directly proportional to the gravitational force between the two objects and the square of the distance between them, and it is indirectly proportional to M1.

Hence,

Solving M2 in terms of Fg, G, M1 and r yields,

[tex]M2 = F {r}^{2} /GM1[/tex]

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Answer:

Step-by-step explanation:

27.5 percent of what is 13.75

13.75 : 27.5 * 100 =

(13.75 * 100) : 27.5 =

1375 : 27.5 = 50

Answer: B

Step-by-step explanation:

     First, we will turn this equation into slope-intercept form as it is easier to view in terms of a graph.

     Given:

x - y = 2

     Add y and subtract 2 from both sides of the equation:

y = x - 2

     We can see that this equation has a y-intercept of -2, so it must intercept the graph at (0, -2). The answer option that meets these requirements is B.

Answer: it is graph A

Step-by-step explanation:

It is pretty easy to tell when x-y= -2

Let's say x is 0 then we have left is -y=-2

So y= 2

And we have [0,2] so graph A is correct

The value of s in the formula

[tex]s = ut + \frac{1}{2}at^2[/tex] is [tex]\frac{19}{4}[/tex]

What is subject of a formula?

At first, it is important to know about formula

Formula is an equation which consists of variables and numbers and they are connected by mathematical operations.

In a formula, there are many variables present.

Subject of a formula is that variable which can be expressed in terms of other variables present in the formula.

Here, s is the subject of the formula

[tex]s = ut + \frac{1}{2}at^2[/tex]

u = 10, a = -2, t = [tex]\frac{1}{2}[/tex]

s = [tex]10 \times \frac{1}{2} + \frac{1}{2}\times (-2) \times (-\frac{1}{2})^2\\[/tex]

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

s = [tex]\frac{20 - 1}{4}\\[/tex]

s = [tex]\frac{19}{4}[/tex]

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Answer:

6.3[tex]\pi[/tex]

Step-by-step explanation:

6.3[tex]\pi[/tex] is the exact answer.

C= circumference

d = diameter

C = [tex]\pi[/tex]d

C = 6.3[tex]\pi[/tex]

Pi is an irrational number.  It never ends or terminates.  We will often use 3.14 for an estimate of Pi, but you were asked for an exact answer.

Function composition is only one way to combine existing functions. Another way is to carry out the usual algebraic operations on functions, such as addition, subtraction, multiplication and division.

Find the attachment of answer

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Functions of the form  f(x)=kx represents direct variation.

The table of values that appears a constant proportion between two variables speaks to a direct variation function. In the event that there's at slightest one pair of values that features a different proportion, at that point the function isn't a direct proportion.  the equation applies to each corresponding value between the two variables. Functions of form f(x)=kx, where k is the constant, are as they were functions that can speak to a direct variation. Typically since direct proportion is spoken to by the direct variation formula that's given by. Functions of the form, there may be a constant, are the as it were functions that can speak to a direct variety. Typically since coordinate proportion is spoken to by the coordinate variation formula that's given by y=kx.

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