The endpoints of AB are A (-8, 5) and B (0,7). Find the coordinates of the midpoint M.
The coordinates of the midpoint M are

Just like polynomials and other expressions, you can perform basic arithmetic operations on rational expressions: addition, subtraction, multiplication, and division. A rational expression is a fraction whose numerator and the denominator is a polynomial. If f is a logical expression, then we can write f in the form of p/q, where p and q are polynomials.

Solution:

To find the restriction on a variable in the denominator, we Set the denominator equal to zero. Then we solve for X

So,

X+1 = 0

X = -1

X-4 = 0

X = 4

When we put the X= -1 or X= 4, we get 0 in the denominator, so these are restrictions variables

= (x2+4x+3)/(x2-3x-4)

= (x+1) (x+3)/(x+1) (x-4)

Now cancel the common factor (x+1)

= x+3x-4

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Answer:

Step-by-step explanation:

t = number of trees per 3 oranges

3t = 15

3t/3 = 15/3

    t = 5 trees

An equation that could be used to represent the context if a represents the number of miles in the taxi ride is ​1.70 + 1.75a = 17.45

We are given;

Base pick up fee = $1.70

Additional taxi fee per mile covered = $1.75

Total taxi fare = $17.45

Now, if we assume that a represents the number of miles in the taxi ride, then we can form the equation to represent the given scenario above as;

1.70 + 1.75a = 17.45

We conclude that an equation that could be used to represent the context if a represents the number of miles in the taxi ride is ​1.70 + 1.75a = 17.45

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Answer: #11? y^2-14 #12 m^2-64

Step-by-step explanation:

- For the second question you apply the same steps to #12 to get m^2-64

Th given sequence is geometric with the common ratio being [tex]\frac{-1}{3}[/tex].

Given: 18, -6, 2, -2/3, ....

Here, [tex]\frac{-6}{18}=\frac{2}{-6}=\frac{\frac{-2}{3}}{2}=\frac{-1}{3}[/tex]

Since, it follows the definition of a geometric progression, the sequence is geometric.

Thus, the given sequence is geometric, having common ratio = [tex]\frac{-1}{3}[/tex].

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The formula for finding any term of the given sequence is [tex]a_{n}[/tex] = [tex]n^3[/tex].

According to the given question.

We have a sequence

-1,1,-1,1,-1,1....

As we know that, a sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.

The above of given sequence -1,1,-1,1,-1,1,.....  is following a rule i.e. each term is the cube of its number of term.

Here,

The first term is -1, so the cube of -1 is -1.

The second term is 1, so the cube of 1 is 1.

So, the nth term of the given sequence is [tex]n^{3}[/tex].

Therefore, the formula for finding any term of the given sequence is given by

= [tex]n^3[/tex]

Where, n = Therefore, the formula for finding any term of the given sequence is given by

 = [tex]n^3[/tex]

Where, n =  -1,1,-1,1,-1,1, .......

So, for n = -1

The first term will be -1.

for n =1

The second term will be 1

for n= 1

The fourth term will be 1 and so on .

Hence, the formula for finding any term of the given sequence is [tex]n^3[/tex].

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Work Shown:

3b+2 ≤ 8

3b+2-2 ≤ 8-2

3b ≤ 6

3b/3 ≤ 6/3

b ≤ 2

Explanation: In the 2nd step, I subtracted 2 from both sides. In step 4, I divided both sides by 3. The inequality sign stays the same. It would flip if we multiplied or divided both sides by a negative number.

If you want to graph this on a number line, then plot a closed filled in circle at 2. Then shade to the left. This visually represents numbers that are 2 or smaller.

The number of problems which Darren must correct each week according to the task content is; 900 corrections.

Since it follows from the task content that; the class contains 25 students, each who are each given 3 assignments per week consistent of 12 problems.

On this note, the number of problems he must correct since the homework is assigned distinctly to each student, the number of problems which he must correct is;

= 25 × 12 × 3

= 900 corrections.

However, if the assignment is same for all students; the number of corrections is;

= 12 × 3 = 36 corrections.

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Answer:

-3, -1, 1

Step-by-step explanation:

Answer: -3,-1, and 1.

Step-by-step explanation: You are given the relation R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} The domain of the relation are all possible inputs and the range of the relation are all possible outputs. So, the inputs are : -3,-1,1; and the outputs are : -2,0,2. As a result, the domain is : -3,-1,1; and the range is : -2,0,2.

The probability. In a bag of 3 green and 4 blue marbles, a blue marble is drawn and not replaced. Then, a second blue marble is drawn is 3/7.

Total number of marbles is 7.

Number of blue marbles are 4.

the probability  that a second blue marble is drawn is 3/7.

Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.

Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated. To forecast the likelihood of events, probability has been introduced in mathematics.

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The answer is 4. The generalized equation is y = f(x). So when the coordinate of x is 4, value of y is 2

Graph of the equation y= f(x) passes through the points (0,2), (2,4), (4,6), and (7,9).

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.

The coordinate plane comprises a horizontal line (x-axis) and a vertical line (y-axis), and it is divided into four quadrants named using roman numbers (I, II, III and IV).

The different points in a graph have coordinates written as ordered pairs (pairs of numbers within parentheses separated by a comma). The first number in an ordered pair (x, y) represents the value of x, and the second one represents the value of y for a given point.

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Answer:

Step-by-step explanation:

Using algebraic expression, For the given expression, the height of the scarf will be 2h - 7

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given the height = h

length of the base = 2h - 7

The area will be - 1/2 . B . H

= 1/2 . (2h - 7) . (h)

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Step-by-step explanation:

let's just write it down in mathematical notation :

length = 2×width - 1

the perimeter is the way all around an object.

so, for a rectangle that is

2×length + 2×width

for our rectangle here

2×length + 2×width = 70

now we use the original identity of length via width and get

2×(2×width - 1) + 2×width = 70

4×width - 2 + 2×width = 70

6×width - 2 = 70

6×width = 72

width = 12

FYI

length = 2×width - 1 = 2×12 - 1 = 24 - 1 = 23

Answer:

A shipping box is in the shape of a cube. What is the volume of the shipping box if the length of one side of the box is 4m24n4

The future value and interest earned when compounded semiannually are $13,576.14 and $4,871.58 respectively.

The future value and interest earned when compounded continuously are $13,651.47 and $4,946.91 respectively.

Compound interest is mathematically expressed as;

A = P(1 + r/n)^nt

Given the data in the question;

a) Determine the accrued amount and interest when compounded semiannually ( n = 2 )

A = P(1 + r/n)^nt

A = 8704.56(1 + 0.05/2)^( 2× 9 )

A = 8704.56(1 + 0.025)¹⁸

A = 8704.56(1.025)¹⁸

A = 8704.56(1.025)¹⁸

A = $13,576.14

Note that; A = Principal + Interest.

Interest = $13,576.14 - $8704.56 = $4,871.58

b) Determine the accrued amount and interest when compounded continuously.

A = P × e^(r × t)

A = 8704.56 × e^(0.05 × 9)

A = 8704.56 × e^0.45

A = $13,651.47

Note that; A = Principal + Interest.

Interest = $13,651.47 - $8704.56 = $4,946.91

The future value and interest earned when compounded semiannually are $13,576.14 and $4,871.58 respectively.

The future value and interest earned when compounded continuously are $13,651.47 and $4,946.91 respectively.

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Answer: 5:12

Step-by-step explanation:

25:60

But we can simplify this down too.

25:60

5:12

When someone cries guiltily, but the person is angry and sad with him/herself is reflex crying.

Verb, adjective, another adverb, determiner, clause, preposition, or sentence is typically modified by an adverb. Adverbs often answer questions like "how," "in what way," "when," "where," and "to what extent" by expressing things like method, place, time, frequency, degree, level of certainty, etc.

Many adverbs have -ly endings, and they frequently follow the word they modify. Adverbs typically give information about an action's when, where, how, and how much it happened.

It should be noted that in literature, an adverb simply means the part of speech that can be used to qualify a verb.

It should be noted that when someone cries guiltily, but the person is angry and sad with him or herself is reflex crying.

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The coordinate of another point will be (a/2,y) where y can be any value.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

An isosceles triangle is a triangle whose two sides are equal.

Let's say AB = AC

So,

Distance associate to AB = Distance associate to AC

(x- 0)² + (y - 0)² = (x - a)² + (y - 0)²

x² + y² = (x - a)² + y²

x = a/2

So the coordinate of the third vertex is (a/2,y)

Hence "The coordinate of another point will be (a/2,y) where y can be any value".

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Answer:

257757

Step-by-step explanation:

Answer:

300 minutes 0.23c1=44.95+0.08c2

Step-by-step explanation:

Answer:

40 psi

Step-by-step explanation:

We can see that the relationship is linear with pressure increasing by 5 psi for every extra 15 feet depth

The data is given from depth of 40 feet

At 40 feet, pressure = 10 psi  

At 55 feet, pressure = 15 psi

At 70 feet pressure = 20 psi

We have to use 40 as the base depth since there are no measurements less than that value. So relative depth is d - 40 and since for every 15', there is an increase of 5psi, the relative increase in pressure  per 15' is [tex]= \dfrac{d-40}{15}\cdot 5[/tex]

But the base pressure is 10psi not 0 so we have to add 10 to this equation to get the absolute psi

So the equation that connects depth (d) and pressure (p) is:

[tex]p = \dfrac{d - 40}{15}\cdot 5 + 10\\\\\textrm{At 130' depth},\\p = \dfrac{130-40}{15}\cdot 5 + 10\\= \dfrac{90}{15}\cdot 5 + 10\\\\= 30 + 10 = 40 psi\\[/tex]

If we plot these values, we can see they fit a straight line with slope = 1/3 and y-intercept = -10/3

Hope that helps

Step-by-step explanation:(4/100x)+(6/100y)=178---------(i)

2х+3y=8900-----------(i)

x+y=3600---------(ii)

where x is phone

y is pen

The system of equations that describes the situation are 4x + 6y = 17800 and x + y = 3600.

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Let the cost of 1 phone is x dollars and cost of 1 computer is y dollars.

Cameron earns a 4% commission on the total dollar amount of all phone sales he makes and earns a 6% commission on all computer sales.

∴ (4/100)x + (6/100)y = 178

4x + 6y = 17800...(i)

Cameron made a total of $3600 in sales.

∴ x + y = 3600...(ii)

Now to solve the equations we'll multiply eqn(ii) by 4 or 6 to cancel out x or y, and then we'll substitute the numerical value of x or y in any of these equations.

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Answer: x=2/3

Step-by-step explanation:

The smallest integer is 1 and solution is (₋1)

Given, the inequality is 2x ₋ 8 ≥ ₋11

The mathematical expressions with inequalities are those with unequal sides on both sides. Unlike equations, we compare two values when we work with inequality. A statement that two things are not equal is what is meant by the word "inequality." It's possible for one of the items to be more than, smaller than, equal to, or equal to the other things.

now add 8 on both sides.

2x ₋ 8 ₊ 8 ≥ ₋11 ₊ 8

2x ≥ ₋3

dividing both sides by 2.

2x/2 ≥ ₋3/2

⇒ x ≥ ₋3/2

₋3/2 is not an integer.

hence the smallest integer value of x is 1, and solution is (₋1)

Hence we get the integer value as 1.

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The quotient of 117 divided by 9 is 13.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

The answer thus got is called the quotient.

We have to divide 117 by 9.

Division algorithm states that,

Dividend = (Divisor × quotient) + Remainder

Remainder will be 0 if divisor is a factor of dividend.

Here dividend = 117 and divisor = 9

We know that 90 is a multiple of 9, where 90 = 9 × 10.

Remainder is 117 - 90 = 27

27 = 9 × 3

Hence 117 = 90 + 27 = (9 × 10 ) + (9 × 3) = 9 (10 + 3) = 9 × 13

So 117 / 9 = 13

Hence the quotient is 13.

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Answer:

14ft 8in by 12ft 10in

Answer:

2

Since the numbers after the decimal are above 500 , thereby rounding it to nearest whole number is 2.

The given statement is False. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.

Euclidean geometry a mathematical system in which we study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid.

Parallel Postulate is one of the five postulates of Euclidean geometry. It is Euclid's fifth postulate which states that through any given point not on a line there passes exactly one line parallel to that line in the same plane. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.

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Answer:

49π in²

Step-by-step explanation:

Formula for Area of a Circle: A = πr²

The image shows the radius (r) = 7in

A = πr² → A = π(7)²→ A = π(49)

A = 153.94 in²

Step-by-step explanation:

Area of circle with radius of r is given by:

[tex] a = \pi {r}^{2} \\ a = 49\pi {(in)}^{2} \\ or \: \: a = 153.9 \: {(in)}^{2} [/tex]

to get the equation of any straight line, we simply need two points off of it, let's use the points from the table in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 3 }\implies -1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-x+2\implies {\LARGE \begin{array}{llll} y=-x+6 \end{array}}[/tex]