Factorise the following:
2x²-6x

To find the length of the third side of the triangular birthday card, Sarah can use the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

In other words, 4 + 9 > x, so 4 + 9 > x is the inequality that is true.

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the third side. This means that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This theorem is useful for determining the possible lengths of the sides of a triangle, as well as for proving that a set of three lengths cannot form a triangle.

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If Vector A = [15, 80 degrees] and Vector B = 12i - 16j, the magnitude of Vector A - Vector B is 32.17

We are given Vector A = ( 15, 80° )

It can be written as: Vector A = 15 cos 80° i + 15 sin 80° j

                   Vector A = 2.6 i + 14.77 j

Also, Vector B = 12 i - 16 j

Now, Vector A - Vector B = 2.6 i + 14.77 j - ( 12 i - 16 j )

                                          = -9.4 i + 30.77 j

We are asked to calculate the Magnitude of Vector A - Vector B = | A - B|

                                                        = ((-9.4)² + (30.77)²)^0.5

                                                        = (88.36 + 946.79)^0.5

                                                        = 32.17

Therefore, the magnitude of Vector A - Vector B is 32.17

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Step-by-step explanation:

So what you should do is open up the brackets of the top row, and to open up brackets with addition inside simply multiply the outside number with the two inside numbers. This would result in:

First Column: 5(5+7) = 5*5 + 5*7 = 25 + 35

Second Column: 5(5+8) = 5*5 + 5*8 = 25 + 40

Third Column: 7(4+5) = 7*4 + 7*5 = 28 + 35

Fourth Column: 14(2+3) = 14*2 + 14*4 = 28 + 42

Fifth Column: 15(2+3) = 15*2 + 15*3 = 30 + 45

An essay on the real - life application of lines would include different fields where lines are used in real life.

Line drawings are used in the design and construction of buildings and infrastructure to represent their structure and layout.  Lines are a fundamental element in graphic design, used to create contrast, texture, and visual interest in illustrations, logos, and other design elements.

Line drawings are used in medical illustrations to represent anatomy and in graphs to represent medical data and trends. Line production and assembly lines are used in the production of goods in many industries such as automotive, electronics, and food processing.

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Answer:

The function H(x) that represents how much you would pay if you use the mall coupon followed by applying the store discount of 25% would be: H(x) = (x-5)*0.25. This function takes the original cost of the jeans (x) and subtracts $5 from it (x-5) to account for the coupon, and then multiplies the result by 0.25 to account for the store discount.

Answer: [tex]1.32*10^5[/tex]

For given function h(x), Value of h(7) will be 59.

A function is described as a relationship between a set of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output. Every function has a domain and a co-domain, or range.

In mathematics, various function types exist. Important types include the following:

When there is a mapping for a range for each domain between two sets, this is known as an injective function or one-to-one function.

Surjective functions or Onto functions: When more than one element is mapped from domain to range.

A polynomial function is a function made up of polynomials.

Functions that can invert other functions are known as inverse functions.

Now,

Given that  f(x) = -4x,

g(x)= x − 5 and

h(x) = −3ƒ(x − 2) + g(x − 3),

So, the function h(x) will be

h(x)=-3*(-4*(x-2))+x-3-5

h(x)=-3*-4x-3*8+x-8

h(x)=12x+x-32

h(x)=13x-32

h(7)=13*7-32

=91-32

h(7)=59

Hence,

         Value of h(7) will be 59.

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Metrics and data are intimately connected in the sense that metrics rely on data to function. Metrics are used to measure the performance of an organization Data is the source of information that is used to calculate metrics.

It is the raw numbers and facts that are collected, analyzed, and turned into metrics that can be used to measure performance. Data is the foundation of metrics because metrics are just a way of interpreting and organizing the data to gain insight into performance.

Without data, metrics would not exist. It is through data that metrics are able to provide an understanding of what is working and what is not. Metrics are the tool used to interpret data and make decisions that can help guide an organization or individual to success.

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while statistics is a valuable tool for understanding and making decisions based on data, it is important to remember that mathematics cannot evaluate non-numerical priorities.

Therefore, correct answer will be:- a. Non-numerical priorities

Statistics is a field of mathematics that deals with collecting, analyzing, and interpreting data. It involves the use of mathematical techniques and methods to extract insights and make decisions based on data.

Non-numerical priorities refer to values, beliefs, and preferences that cannot be quantified or measured using numbers. For example, considerations such as morality, ethics, cultural norms, personal opinions, and emotions cannot be expressed or evaluated using mathematical models or statistical techniques.

When making decisions, it is often necessary to take into account these non-numerical priorities, in addition to the quantitative data and analysis.

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On solving the provided question, we can say that the coordinates are (-2,0) and (0,2) slope is = m = 2-0/0+2= 1 and slope intercept equation is y-2 = x+2 => x-y = 0

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

the coordinates are (-2,0) and (0,2)

slope is = m = 2-0/0+2= 1

slope intercept equation is y-2 = x+2

x-y = 0

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The value of the fraction is given by the equation A = (x - 6) / (x + 2) (3x - 2)

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction be represented as A

Now , the equation will be

A = [ 1 / ( x + 2 ) ] - [ 2/ ( 3x - 2 ) ]

On simplifying the equation , we get

Finding the common denominator and LCM , we get

A = [ ( 3x - 2 ) - 2 ( x + 2 ) ] / (x + 2) (3x - 2)

On further simplification , we get

A = ( 3x - 2 - 2x - 4 ) / (x + 2) (3x - 2)

A = ( x - 6 ) / (x + 2) (3x - 2)

Hence , the fraction is A = ( x - 6 ) / (x + 2) (3x - 2)

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Answer:

Yes it can!

Step-by-step explanation:

In the given triangles,
∠B = ∠F
Also, ratio of sides given are
2.3/13.8 ≈ 1.67 -> (i)
And 1.9/11.4 ≈ 1.67 -> (ii)
Thus, (i) = (ii)
∴ AB/BF = BC/DF

So we can prove both triangles are similar as the two sides are proportional and the angle between the corresponding sides are equal, so we can use the SAS similarity postulate as the two sets of corresponding sides are proportional and the included angles are congruent .

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

[tex]\frac{1}{6}[/tex] - [tex]\frac{1}{12}[/tex]

[tex]\frac{1}{6}[/tex] x [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{12}[/tex]   ([tex]\frac{2}{2}[/tex] is another name for 1, so we are just multiplying [tex]\frac{1}{6}[/tex] x 1)

[tex]\frac{1}{6}[/tex] is equivalent to [tex]\frac{2}{12}[/tex]

[tex]\frac{2}{12}[/tex] - [tex]\frac{1}{12}[/tex] = [tex]\frac{1}{12}[/tex]

Answer:

Line segment DK is the median

Step-by-step explanation:

The median is the line segment that joins the vertex to the midpoint of the opposite side.

Answer:

20

Step-by-step explanation:

The hypotenuse is 24 + 6 of the biggest right triangle.

= 30

If it's a 45-45-90 triangle, you know you can use Pythagorean theorem to solve for missing sides.

But, the 45-45-90 triangle is a special triangle. The two legs are equal.

So, assume the two legs = x.

x^2 + x^2 = 30^2

2x^2 = 900

x^2 = 450

Square root both sides to get rid of the power of 2.

x = 21.2

A shortcut to this without pythagorean theorem is dividing the hypotenuse by rad 2. If you do 30 / (rad2) on your calculator, you'll get 21.2

Now that we know x = 21.2, we can find y for the other right triangle.

X is the hypotenuse, since it is opposite to the right angle.

x^2 = y^2 + 6^2

We know x to the power of 2 is 450 (highlighted)

450 = y^2 + 36

Subtract 36 on both sides

y^2 = 414

Square root both sides

y = 20.347

approx. 20

A variety of healthful sizes are available for newborns. The average baby weighs between 5 pounds, 8 ounces (2,500 grammes) and 8 pounds, 13 ounces when they are born between 37 and 40 weeks (4,000 grams). It's usually ok for newborns who weigh more or less than the typical infant.

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There are 4 possible answers for each question, so there are 4^10 = 10,048 different ways to answer the quiz.

This is because for each question, there are 4 choices, and since there are 10 questions, the total number of choices is 444444444*4 = 4^10, which equals 10,048.

Answer:

=2x-3<7

=2x=7+3

=2x<10/2

=x=5

therfore x=5

range=1,2,3,4 5

Step-by-step explanation:

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Therefore, the state with the highest improvement in SAT score from 2011 to 2014 is Wyoming


EXPLANATION:

Step-1:
a.

Obtain the two SAT score distributions by using graph, using MINITAB.

For SAT 2011.

MINITAB procedure:

1: Choose Graph > Histogram.

2: Choose Simple, and then click OK.

3: In Graph variables, enter the corresponding column of SAT2011.

4: Click OK.

Step-2:
For SAT 2014

MINITAB procedure:

1: Choose Graph > Histogram.

2: Choose Simple, and then click OK.

3: In Graph variables, enter the corresponding column of SAT2014.

4: Click OK.

Conclusion:

The frequency of SAT score in 2014 is comparatively higher than that of SAT score of 2011.There is an increase in frequency of SAT score in between 1500 and 1600, from 2011 to 2014.However there is a sudden decrease in SAT score of 1600, from 2011 to 2014, and again rise of the score between 1700 to 1800.


step-3
b.

Summarization:

Obtain a graph for the difference in the SAT scores of 2014 and 2011, using MINITAB.

MINITAB procedure:

1: Choose Graph > Histogram.

2: Choose Simple, and then click OK.

3: In Graph variables, enter the corresponding column of SAT2014.

4: Click OK.

step-4:
c.

Interpretation:

In part (b), maximum of the times, there is no difference in SAT score from 2011 to 2014. However in some cases, there is an increase in SAT score in 2014, than in 2011.

In part (a), individual SAT score was found, and hence no conclusion was drawn on whether the SAT score increases or decreases form 2011 and 2014. The difference and the comparison of the score is observed in part (b) of the exercise.

d.
Observe the state with the highest improvement in SAT score from 2011 to 2014.

The state with the highest improvement in SAT score from 2011 to 2014 is Wyoming, with a difference of 65 scores from 2011 to 2014.

Therefore, the state with the highest improvement in SAT score from 2011 to 2014 is Wyoming.

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The slope-intercept format of the linear function in this problem is given as follows:

y = x - 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

Two points on the graph of the function are given as follows:

(-8, -10) and (12,10).

When x increases by 20, y increases by 20, hence the slope m is given as follows:

m = 20/20 = 1.

Hence:

y = x + b.

When x = 12, y = 10, hence the intercept b is given as follows:

10 = 12 + b

b = -2.

Hence the function is:

y = x - 2.

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To create this graph, the best option for the information in two axes is "Horizontal axis: sales, in hundreds; vertical axis: dollars, in thousands " (option B)

To facilitate data analysis and observation it is recommended to have the sales on the horizontal axis (number of units sold), also known as the x-axis, and the money obtained or profit on the vertical axis or y-axis (dollars).

Considering the current data is $32,000 for 2200 lawnmowers, the best is to use thousands of dollars in the sales while using hundreds in the number of units (2200/ 100 = 22)

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Answer:

d.70

Step-by-step explanation:

Answer:

d.70. Angles of a triangle add up to 180°.Therefore 180-(50+60)=70.Exterior angle is equal to interior opposite angle

At the bicycle manufacturer, the average cost per bicycle is $77.

Now, According to the question:

"Information available from the question"

It costs $72 to make the first bicycle,

$83 to make the second,

and $77 to make the third.

To find the average cost per bicycle

We need to find the total cost of making all three bicycles and divide that by the number of bicycles.

The total cost is of the bicycles is given by -

$72 (cost of first bicycle) + $83 (cost of second bicycle) + $77 (cost of third bicycle) = $232

Now to find the average cost per bicycle, we will divide the total cost by the number of bicycles.

Hence, $232 ÷ 3 = $77

Therefore, the average cost per bicycle is $77.

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Answer:

Step-by-step explanation:

Lets assume the following binary numbers:

a=101,b=10

1)a-b=101-10=91

2)a*b=1010

3)a/ba= ie=b*a=1010

a/ba=101/1010=0.1

4)a-b=101-10=91

5)a/b=101/10=10.1

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Solving the assumed pairs of binary numbers for the operations such as addition, subtraction , multiplication and divisions give 9,090 , 10,212,111 and 9.99

What is binary number?

A binary number system is one of the four types of number system. In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one). The binary numbers here are expressed in the base-2 numeral system. For example, (101)2 is a binary number

Lets assume the following binary numbers:

a=10101, b=1011

1) a-b=10101-1011=9,090

2) axb=10,212,111

3) a/b= 10101 / 1011 = 9.99

4) a + b = 10101 +1011 = 11,112

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The complete question is :

calculate  a−b, a×b , and a÷b, a+b,  for the following pairs of binary numbers : for a=10101 and b=1011.

The top right line has a slop of 3/2

It goes up 3 and goes to the left 2

Answer:

B

Step-by-step explanation:

Points on graph B (2,3) (4,6)

We see the y increase by 3 and the x increase by 2, which matches the slope of 3/2

So, the answer is B

Answer: it depends how many points but if its a higher number of points like a 100 point test or so then it easily could

Step-by-step explanation:

The equation for the plane through p0(−1,1,9) perpendicular to the following line vector is, ( x , y , z ) = ( 0 , 0 , 10)

A quantity that has both magnitude and direction but not position. Examples of such quantities are velocity and acceleration.

Given that,

The equation for the plane through p0(−1,1,9)

The xy-plane has a normal vector of 〈0, 0, 1〉, and any plane parallel to it will have the same normal vector.

Then the equation of the plane through (-1, 1, 9) that is parallel to the xy-plane has equation

〈x - (-1), y - 1, z - 9〉 • 〈0, 0, 1〉 = 0

x + 1 = 0

y - 1 = 0

z - 9 = 1

z = 1 + 9

z = 10

Therefore,

The equation for the plane through p0(−1,1,9) perpendicular to the following line vector is, ( x , y , z ) = ( 0 , 0 , 10)

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Given P(-4,17), Q (1,-3), R(-9,3), S(-5,4), slope of line PQ m(PQ) = -4 and slope of line RS m(RS) = 1/4 and Both lines are perpendicular.

If two non-vertical lines in the same plane intersect at a right angle then they are said to be perpendicular. Horizontal and vertical lines are perpendicular to each other i.e. the axes of the coordinate plane.

To calculate the slope of the two lines;

Mathematically;

Slope = y2-y1/x2-x1

For PQ; slope will be;

Slope of line PQ m(PQ) = (-3-17)/(1-(-4)

Slope of line PQ m(PQ) = -20/5

Slope of line PQ m(PQ) = -4

For RS; slope will be;

Slope of line RS m(RS) = (4-3)/(-5-(-9))

Slope of line RS m(RS) = 1/4

We want to determine the relationship between the two lines.

The product of both is 1/4 * -4 = -1

When two lines are perpendicular, the product of their slopes is -1

We can conclude that both lines are perpendicular to one another.

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The height of the person is 6.27 feet.

you are having a staring contest with your cat. You are looking down at 37° while standing 7 feet away from it. Your cats eye line is 1 foot off the ground. Let's find your height.

Therefore, the situation forms a right angle triangle.

Using trigonometric ratio,

tan 37 = opposite / adjacent

tan 37° = x / 7

where

cross multiply

x = 7 tan 37°

x = 7 × 0.7535540501

x = 5.27487835072

Therefore,

height of the person = 1 + 5.27487835072

height of the person = 6.27 ft

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The random variable can only take on values greater than or equal to 2.83

A random variable is a variable that can take on different values depending on the outcome of a random process.

In this problem, we are given a probability density function (pdf) for a random variable and asked to find the value of the constant "a". The pdf, f(x), represents the probability of the random variable taking on a particular value, x.

Here we have the constant "a" in the equation

=> f(x)=12/X³, x>=a,

is the minimum value that the random variable can take on.

This means that the total probability of the random variable taking on any value between "a" and infinity must equal 1.

Now by using calculus, we can find the value of "a" by solving the equation

=> ∫(a,∞) (12/X³) = 1.

This equation tells us that the total probability of the random variable taking on any value greater than "a" must equal 1.

By solving for "a", we find that it is approximately equal to 2.83.

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