Find the coordinates of point I so ΔI K L is the indicated type of triangle. Point J has coordinates (0,0) and point K has coordinates (2 a, 2 b) .
right triangle

Evaluating the expression 2a + b for a = 3 and b = -5 is equal to -1.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.

Given the expression 2a + b, substitute the value of the variable a and the value of variable b.

2(3) + (-5)

Performing the arithmetic operations, we can have the value of the expression.

2(3) + (-5)

= 6 - 5

= 1

Hence, the expression 2a + b when a = 3 and b = -5 is equal to -1.

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The solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given equation is x³ - 4x² - 7x + 10 = 0. The equation will be solved as,

x³ - 4x² - 7x + 10 = 0

x³ - 3x² - 10x - x² + 3x + 10 = 0

( x² - 3x - 10) ( x - 1 ) = 0

( x² -5x + 2x - 10 ) ( x-  1) = 0

( x - 5 )( x + 2 )( x - 1 ) = 0

Therefore, the solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).

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Answer:

3 and 2

Step-by-step explanation:

complementary means they add up to 90 degrees. Angle 3 and 2 equal 90 degrees,

In explicit representation, a sequence is represented in terms of the first term while in recursive representation, a sequence is represented in terms of the previous term.

What are Recursive Formulas?

A recursive formula refers to a formula that defines each term of a sequence using the preceding term(s). The recursive formulas define the following parameters:

What are Explicit Formulas?

Explicit formulas are always used to represent any term of the sequence, without writing the other terms of the sequence. The meaning of "explicit" is direct, something that can be directly found without knowing the other terms of sequence. The explicit formula helps to easily find any terms of the sequence, without knowing its previous term.  

Eg, the sequence: 2, 4, 6, 8, 10, . . .

Explicit Representation An = 2 + 2(n - 1)

Recursive representation f(n) = 2 + f(n - 1)

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Answer: an integer rational number

Step-by-step explanation:it's not a natural or a whole number, but it as integer as well as it repeats

Answer:

Step-by-step explanation:

e

Answer:

There were 27 student tickets sold and 35 parent tickets sold.

Step-by-step explanation:

So first, we have to set up our equations!

s + p = 62 (s is the # of student tickets sold; p is the # of parent tickets sold;  62 is the total # of tickets sold)

1.75s + 3.75p = 178.50 (1.75s is the price for student tickets multiplied by the number of student tickets; 3.75p is the price for parent tickets multiplied by the number of parent tickets; 178.50 is the total amount of money)

Now! We are going to use elimination to solve for the variables, first for "s". To do this, we are going to multiply the first equation by -3.75!

     -3.75 (s + p = 62)

    -3.75s - 3.75 p = -232.50

+     1.75s + 3.75p = 178.50

        -2s = -54

          s = 27

Next! We have to solve for "p" by multiplying the first equation by -1.75!

-1.75 (s + p = 62)

    -1.75s - 1.75 p = -108.50

+     1.75s + 3.75p = 178.50

        2p = 70

          p = 35

Lastly, we know that there were 27 student tickets sold, and 35 parent tickets sold.

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Basically you are correct its C , ut go with your gut!

Answer:

f(g(x)) = 3x + 4

Step-by-step explanation:

to find f(g(x)) substitute x = g(x) into f(x)

f(g(x))

= f(x - 2)

= 3(x - 2) + 10

= 3x - 6 + 10

= 3x + 4

Answer:

[tex]f\left[g(x)\right]=3x + 4[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=3x+10\\g(x)=x-2\end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

The given composite function f[g(x)] means to substitute the function g(x) in place of the x in function f(x):

[tex]\begin{aligned}f\left[g(x)\right] & = f(x-2)\\& = 3(x-2)+10\\& = 3x-6+10\\& = 3x+4\end{aligned}[/tex]

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The value of x is -14.

Rewriting the equation mentioned in question to solve for the value of x -

4(x + 2) -2 (x - 10) = 0

Performing multiplication with brackets on Left Hand Side of the equation

4x + 8 - 2x + 20 = 0

Performing addition and subtraction on Left Hand Side of the equation

2x + 28 = 0

Shifting 28 to other side of equation

2x = - 28

Shifting 2 to other side of equation as denominator

x = - 28/2

Performing division to find the value of x

x = -14

Hence, the value of x is -14.

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A quadrilateral can be both a square and a rectangle, or a rectangle but not a square, because squares are rectangles but rectangles are not always squares. They do not conflict with one another.

What is termed quadrilateral?

What types of quadrilaterals are examples?

A closed, two-dimensional figure with four sides, four angles, and four vertices is called a quadrilateral. Square, rectangle, and trapezium are a few examples of quadrilaterals.

The two events are mutually exclusive if they cannot occur at the same time.

A quadrilateral can be both a square and a rectangle, or a rectangle but not a square, because squares are rectangles but rectangles are not always squares.

They do not conflict with one another.

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Answer: x<1 or x>5

Step-by-step explanation:

|-x+3|>2

-x+3>2

-x+3-3>2-3

-x>-1

x<1

-x+3<-2

-x+3-3<-2-3

-x<-5

x>5

x<1 or x>5

Answer:

Step-by-step explanation:

Value of s is 1.8.

The midpoint of a line is a point that bisects the line into equal parts. It is equidistant from both end points of the line.

As B is the midpoint of AC,

2AB = AC

∴ 2(10s + 2) = 40

∴ 20s + 4 = 40

∴ 20s = 36

∴ x = 1.8.

Now, AB = 10s + 2

Substituting the value of s,

∴ AB = 10(1.8) + 2

∴ AB = 20 units

Thus, the value of s is 1.8 and the length of AB is 20 units.

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Using the rule of exponents, the expression is 12x^4 × 35y^5

The rules of exponents are given as:

Given the expression;

3x^3 * 7y^2 * 4x * 5y ^3

collect the like bases

3x³ × 4x × 7y² × 5y³

Add the powers

12x^3 + 1 × 35^ 2 + 3

We then have;

12x^4 × 35y^5

Thus, using the rule of exponents, the expression is 12x^4 × 35y^5

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The simplification of the given inequalities gives;

1) m > -1/80

2) x < -1/3

1) The multiplicative property of inequality states that both sides of an inequality can be multiplied or divided by the same number and an equivalent inequality can be formed.

Thus, applying that to 8m > -1/10, gives;

Multiply both sides by 1/8 to get;

8m * 1/8 > -1/10 * 1/8

m > -1/80

2) The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.

Thus, applying that to -9/2x > 3/2 gives;

Divide both sides by -9/2 to get;

x < -1/3

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Answer:

9 multiple choice questions and 2 short answer questions

===========================================================

Explanation:

x = number of multiple choice

y = number of short answers

The statement "It takes about 2 minutes to answer a multiple choice question and about 6 minutes to complete a short answer question" means it takes 2x+6y minutes to answer x multiple choice and y short answer questions. We want this total to be 30 minutes or less.

Therefore, [tex]2x+6y \le 30[/tex] is one constraint.

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

Another constraint is that [tex]0 \le x \le 9[/tex] since the most multiple choice questions you can answer is 9.

Because there are 3 short answer questions, this means another constraint is [tex]0 \le y \le 3[/tex]

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

The list of constraints is:

[tex]\begin{cases}2x+6y \le 30\\0 \le x \le 9\\0 \le y \le 3\\\end{cases}[/tex]

If you were to graph and shade these regions on the xy grid, then you should get a pentagon with the following corner points

A = (0, 0)

B = (0, 3)

C = (6, 3)

D = (9, 2)

E = (9, 0)

We'll plug the coordinates of each vertex into the objective function P(x,y) = 3x+5y which will compute the number of points total after answering x multiple choice and y short answer questions. This computes the maximum points possible.

Plug in the coordinates of point A to get P(0,0) = 0

Repeat for point B to get P(0,3) = 15

Now move onto point C to get P(6,3) = 33

Then point D is P(9,2) = 37 and point E gets us P(9,0) = 27

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

Summary:

P(0,0) = 0

P(0,3) = 15

P(6,3) = 33

P(9,2) = 37

P(9,0) = 27

We see that x = 9 and y = 2 produce the largest P(x,y) value of 37

Therefore, you should answer 9 multiple choice questions and 2 short answer questions. This will yield 37 points if you were to get all of those questions correct. In other words, the most points possible are 37 when given 30 minutes.

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

Side note:

If you had unlimited time, then the most points possible are 9*3+3*5 = 27+15 = 42 which is the total number of points on the exam.

Getting a 37 out of 42 is a grade of about 37/42 = 0.881 = 88.1%

The maximum score is achieved at the corner point (9, 0), where the student answers 9 multiple-choice questions and 0 short-answer questions. The score at this point is 27, which is the maximum score the student can achieve in the given time.

To maximize the student's score in the given 30 minutes, we need to create an objective function and constraints based on the time available and the number of questions.

Let:

x = Number of multiple-choice questions to answer

y = Number of short-answer questions to answer

Objective Function (Score):

The score can be calculated as the sum of points obtained from multiple-choice questions and short-answer questions:

Score (S) = 3x (for multiple-choice questions) + 5y (for short-answer questions)

Constraints:

1. Time Constraint: The total time taken to answer all the questions should not exceed 30 minutes:

Time for multiple-choice questions + Time for short-answer questions ≤ 30

2. Number of Questions Constraint: The student can't answer more questions than available:

Number of multiple-choice questions (x) ≤ 9 (total number of multiple-choice questions available)

Number of short-answer questions (y) ≤ 3 (total number of short-answer questions available)

Now, let's consider the time taken to answer each type of question:

- Time for multiple-choice questions: 2 minutes per question

- Time for short-answer questions: 6 minutes per question

Based on the above information, the time constraint can be written as an equation: 2x + 6y ≤ 30

Now, we need to maximize the score (S) by selecting the values of x and y that satisfy the above constraints. This is a linear programming problem that can be solved using various optimization techniques, such as the graphical method, simplex method, or linear programming software.

Since this is a simple problem with a small number of variables and constraints, we can use the graphical method to find the maximum score. We will graph the feasible region defined by the constraints and find the corner points of the feasible region. Then, we will calculate the score (S) at each corner point and select the one with the highest score.

The feasible region will be bounded by the lines:

2x + 6y ≤ 30 (Time constraint)

x ≤ 9 (Number of multiple-choice questions constraint)

y ≤ 3 (Number of short-answer questions constraint)

The corner points of the feasible region are the intersection points of these lines.

Now, calculate the score (S) at each corner point:

For (0, 0): S = 3(0) + 5(0) = 0

For (0, 3): S = 3(0) + 5(3) = 15

For (9, 0): S = 3(9) + 5(0) = 27

The maximum score is achieved at the corner point (9, 0), where the student answers 9 multiple-choice questions and 0 short-answer questions. The score at this point is 27, which is the maximum score the student can achieve in the given time.

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The slope of line passing through points  (2,7) and (-3,11) is -4/5.

Slope of a Line

The slope of a line is defined as the increase divided by the run, or as the ratio of the rise to the run. It describes the slope of the line in the coordinate plane. Calculating the slope of a line and determining the slope between two different points are similar activities.

The following formula is used to determine slope:

The slope of the line between two points is given by y2 - y1 / x2 - x1.

Given points are -

(2,7) and (-3,11)

Slope of the line is -

= 11 - 7 / -3 -2

= 4 / -5

So the slope of the line is -4/5

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Step-by-step explanation:

If theres 168 frames in six seconds, to find out how many there are per second, we simply need to divide 168 by 6. This equals 28. If you know how many there are for 6, and you want to find out how many for 1, you know you're dividing 6 by 6. So you have to do the same to the amount of frames.

The population of Texas will be 2.9 × 10³.

Population of Austin, Texas = 9.64 × 10.

The population of the state of Texas is 30 times that of Austin.

Therefore the population of Texas will be:

= 30 × 9.64 × 10

= 2900

= 2.9 × 10³

Therefore, the population of Texas will be 2.9 × 10³.

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Answer: x=18

Step-by-step explanation:

2x+8x=180 ==> angles CDE(8x) and ABC(2x) are opposite supplementary angles meaning that they add up to 180 degrees.

10x=180

10x/10=180/10

x=180/10

x=18

Answer:

Step-by-step explanation:

add 2 to both sides,

10x-2=102
    +2   +2

now it is 10x=104

now divide 10 from both sides.

10x/10=104/10

x=10.4

Answer:

are these time stamps

Step-by-step explanation:

let me know

Answer:

B. Vertical angles.

look at the image attached.

The answer is -0.5.

The source is from calculator soup.

Answer: A

Step-by-step explanation:

Answer:

300 widgets

Step-by-step explanation:

Each time the widgets sold goes up by 100, the profits goes up by 400. This shows a ratio/slope of 4 if we were to graph this. To find out when they break even you need to subtract $400 from the first row to get to zero and the equivalent amount of widgets. If each widget is $4 then subtract 100 from 400 to get 300 widgets

well, we know the table has linear relationship, so let's use it to get the Profit function then, to get the equation of any straight line, we simply need two points off of it, so let's use those two points in the picture below.

[tex](\stackrel{x_1}{500}~,~\stackrel{y_1}{800})\qquad (\stackrel{x_2}{700}~,~\stackrel{y_2}{1600}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1600}-\stackrel{y1}{800}}}{\underset{run} {\underset{x_2}{700}-\underset{x_1}{500}}} \implies \cfrac{1600 -800}{700 -500} \implies \cfrac{ 800 }{ 200 }\implies 4[/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}{800}=\stackrel{m}{4}(x-\stackrel{x_1}{500}) \\\\\\ y-800=4x-2000\implies y=4x-1200[/tex]

how many bucks will they lose by selling "0" items?

well, let's find out by setting x = 0.

[tex]\stackrel{profit}{y}=4(0)-1200\implies y=-1200~\hfill \stackrel{\textit{they'd be losing}}{\text{\LARGE 1200}}[/tex]

how many will they need to sell to break-even?

well, to break-even that means no loses, no profits but no loses either, so-called breaking-even, you simply sell enough to cover costs, at that point the profit = y = 0, so

[tex]\stackrel{profit}{0}=4x-1200\implies 1200=4x\implies \cfrac{1200}{4}=x\implies \text{\LARGE 300}=x[/tex]

Part (a)

We need to consider

[tex]x=\frac{1}{k\pi}, k \in \mathbb{Z}[/tex]

[tex]f\left(\frac{1}{k\pi} \right)=\tan (k\pi)

[/tex]

tan(x) has a period of pi, so this is equal to tan(0)=0.

Part (b)

We need to consider

[tex]x=\frac{4}{(4n+1)\pi}, n \in \mathbb{Z} \\ \\ f \left(\frac{4}{(4n+1)\pi} \right)=\tan \left(\frac{(4n+1)\pi}{4} \right) \\ \\ =\tan \left(\pi n+\frac{\pi}{4} \right) \\ \\ =1[/tex]

Part (c)

We see that 1/x approaches infinity, and hence the limit does not exist.

Answer:

Piece wise

Step-by-step explanation:

Piecewise function definition A piecewise function is a function that is defined by different formulas or functions for each given interval. Its also in the name: piece. The function is defined by pieces of functions for each part of the domain.