One dimension of a rectangle is 3 more than twice the other dimension. Let x be the
shortest dimension. Write an equation for the area of the rectangle.
A= x + 2x + 3
A = x(2x + 3)
A= 3x +2
A= 2x +3

With deceleration of 6 ft/s² and initial speed of 66 ft/s, the airplane will stop after travelling 363 ft.

Use the equation of motion:

v² = u² + 2 · a · s

Where:

v = final velocity

a = acceleration

u = initial velocity

s = distance

Deceleration is a negative acceleration.

Parameters given from the problem:

u = 66 ft/s

a = - 6 ft/s²

v = 0  since the airplane stops.

Plug these parameters into the formula:

v² = u² + 2 · a · s

0 = 66² + 2 · (-6)· s

s = 66² / 12

s = 363 ft.

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The graph of the system of inequalities can be seen in the image at the end.

Here we have the following system of inequalities:

y < 2x - 5

y > -3x + 1

So first we need to graph the two lines:

y = 2x - 5

y = -3x + 1

With dashed lines (because the symbols < and > are used).

And then we shade all the region below the line:

y = 2x - 5

And we shade the region above the line:

y = -3x + 1

So we will get the graph below:

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Answer:

(-5,-4)

as 90 degree rotation counter clockwise would land in the third quaderant where both x and y are negative

The function f(x) = -[tex]5x^5 -5760-2880x+520x^2+260x^3-10x^4[/tex] end behavior is As, x → infinity , f(x) → - infinity ; as x → - infinity , f(x) → infinity .

Given,

The function is given as:

f(x) = -[tex]5x^5 -5760-2880x+520x^2+260x^3-10x^4[/tex]

To find the bend behavior of f(x)

Now, According to the question:

Based on the given condition:

Analyze the end behavior of

f(x) = -[tex]5x^5 -5760-2880x+520x^2+260x^3-10x^4[/tex]

As, x → infinity , f(x) → - infinity ;

as x → - infinity , f(x) → infinity .

Hence, The function f(x) = -[tex]5x^5 -5760-2880x+520x^2+260x^3-10x^4[/tex] end behavior is As, x → infinity , f(x) → - infinity ; as x → - infinity , f(x) → infinity .

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Answer:

0.65

Step-by-step explanation:

1.65 is 0.65 greater than 1

Answer:

No real zeros.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Discriminant of the Quadratic Formula}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\When $b^2-4ac > 0 \implies$ two real zeros.\\When $b^2-4ac=0 \implies$ one real zero.\\When $b^2-4ac < 0 \implies$ no real zeros.\\\end{minipage}}[/tex]

The value of the discriminant shows how many zeros the function has.

Given quadratic function:

[tex]f(x)=5x^2+5x+21[/tex]

Therefore:

Substitute the values into the discriminant and solve:

[tex]\begin{aligned}\implies b^2-4ac&=(5)^2-4(5)(21)\\& = 25 - 20(21)\\&=25-420\\&=-395\end{aligned}[/tex]

Therefore, as -395 < 0, there are no real zeros.

The average speed of the train is 18m/sec and the length of the train is 72 m.

let  x represent the length of the train.

and 'S' be the speed of the train.

Given, that the train passes through 360 m long tunnel  completely in 24 sec.

⇒ 360+x/24 = s

⇒ 24s = 360+x ...eq(1)

And also given that it passes through another tunnel 216 m long completely in 16 sec.

⇒ 216+x/24 = s

⇒ 16s = 216 + x .... eq(2)

⇒ subtract eq(1) from eq(2)

⇒ 24s = 360 + x

   16s = 216 + x

8s = 144

s = 18 m/sec

length of the train: 24s = 360+x

24(18) = 360+x

432 = 360+x

x = 432-360

x = 72m

Hence the length of the train is 72 m.

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Answer:

129 degrees.

Step-by-step explanation:

The Sum of all the interior angles of an a-sided polygon is always (n−2) × 180 degrees.

As this is a seven-sided polygon, the sum of its interior angles is (7−2) × 180 degrees = 5 × 180 degrees = 900 degrees.

Step 1: Find the sum of six of the angles is 130 degrees, 118 degrees, 135 degrees, 128 degrees, 126 degrees, and 134 = 771 degrees

Hence the seventh angle is x = 900 degrees − 771 degrees= 129 degrees.

The expression of 3D-3C is 6x²-12x+6 in the standard form when the D=1-x² and C = -1-3x²+4x.

Given that,

The equations,

D=1-x² and C = -1-3x²+4x

We have to find the expression 3D-3C in standard form.

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

We get,

3D-3C

3(1-x²)-3(-1-3x²+4x)

3-3x²+3+9x²-12x

6+6x²-12x

6x²-12x+6

Therefore, The expression of 3D-3C is 6x²-12x+6 in the standard form when the D=1-x² and C = -1-3x²+4x.

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The numbers are inserted into the tree and shown in the below diagrams.

Given that,

Put these numbers into a 2-3-4 tree: 10, 15, 20, 40, 60, 80, 90, 100, 30, 70, and 50.

Binary Tree Data Structure: What is it?

A Binary Tree is a Tree data structure with two children or less. We typically refer to them as the left and right child since each element in a binary tree can only have two children.

Representation of a Binary Tree

A pointer to the topmost node of a binary tree serves as its representation. The root's value is NULL if the tree is empty.

The following components are found in a binary tree node:

Data

Pointer to left child in data

Pointer to the right-hand child

Thereforer, The numbers are inserted into the tree

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The question was incomplete. Check below the complete question.

insert 10, 15, 20, 40, 60, 80, 90, 100, 30, 70, and 50 into a 2-3-4 tree and select the correct answer

Answer:

x y

-2 -9

0 1

2 -9

4 -19

explanation:

you simply replace the x with the figure given in the x table or columns or rows

Answer:

so -2024y0000 division is s

One-half of the number is 18.

Given that

One-third of a number is 12.

Let "x" be the number

Given that,

One-third of a number is 12

Which means,

[tex]\frac{1}{3} *x = 12[/tex]

x = 3*12

x = 36

Thus the number is 36

Work out one-half of the number

one half of the number = [tex]\frac{x}{2}[/tex]

one half of the number = [tex]\frac{36}{2}[/tex]

one half of the number = 18

Hence the answer is, one-half of the number is 18.

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Answer:

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

Slope-intercept form is:

Given line in standard form:

Convert this to slope-intercept form:

Answer:

[tex]\boxed{y=\dfrac{3}{4}x-\dfrac{3}{4}}[/tex]

[tex]\implies \textsf{Slope}=\dfrac{3}{4}[/tex]

[tex]\implies \textsf{$y$-intercept}=-\dfrac{3}{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]-3x+4y+3=0[/tex]

To write the given equation in slope-intercept form, rearrange the equation to isolate y.

Add 3x to both sides of the equation:

[tex]\implies -3x+4y+3+3x=0+3x[/tex]

[tex]\implies 4y+3=3x[/tex]

Subtract 3 from both sides of the equation:

[tex]\implies 4y+3-3=3x-3[/tex]

[tex]\implies 4y=3x-3[/tex]

Divide both sides of the equation by 4:

[tex]\implies \dfrac{4y}{4}=\dfrac{3x-3}{4}[/tex]

[tex]\implies y=\dfrac{3}{4}x-\dfrac{3}{4}[/tex]

Compare the rearranged equation with the slope-intercept formula:

[tex]\implies \textsf{Slope}=\dfrac{3}{4}[/tex]

[tex]\implies \textsf{$y$-intercept}=-\dfrac{3}{4}[/tex]

Kirk will drive 15 kilometer east  to get back to his home

The problem will be solved using basic addition operator and subtraction

Let the given information be represented as follows

he drives 15 kilometers west = 15 W

45 kilometers east = 45 E

75 kilometers west = 75 W

Kirk will drive East to get home = ?

since the distances are all in the horizontal direction we add up the west directions and subtract the east direction

15 W + 75 W = 45 E + ?

90 W = 45 E + ?

? = 90 - 45

? = 45 E

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Answer:

below

Step-by-step explanation:

Rate =  4/5 mi / 2/5 hr =  2 mi /hr

3/4 hr for lunch

20 miles / 2 miles/hr   + 3/4 hr =  10 3/4 hr to hike 20 miles with a lunch

The answer of the question is A. Cluster Analysis

Data reduction is a stage of qualitative data analysis techniques. Data reduction is simplification, classification, and unnecessary hoarding of data in such a way that the data can produce meaningful information and facilitate drawing conclusions.

Data reduction is done to provide more specific representation and make it easier for researchers to collect data then look for additional data if needed.

Various dimension reduction methods are used to reduce the complexity of data before further processing. One of data reduction techniques is Cluster Analysis. Cluster analysis is used to group or classify data with various types, for example in types according to the concept, and certain categories according to the research being conducted.

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The equation of line passing through the point (-3, -1) and is perpendicular to the line y = -x/2 - 5 is y = 2x + 5

perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°).

In such lines the product of their gradients is -1.

if y = -x/2 - 5

then comparing the equation with y = mx + c

it means slope(m) = -1/2

so the slope(p) of the second line perpendicular to the above line will be

p x m = -1

p = -1/m

p = -1 ÷ -1/2

p = 2

so if x = -3, y = -1 and substituting these values into the equation of line , y = mx + c becomes

-1 = 2 x (-3) + c

-1 = -6 + c

collect like terms

c= 6 - 1

c = 5

Equation of the second line becomes,

y = 2x + 5

In conclusion, the equation of the lines passing through point(-3, -1) is y = 2x + 5

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Answer and Explanation:

m∠1 = 43° because opposite angles are congruent

m∠2 = 137° because ∠2 and 43° are supplementary, so m∠2 + 43° = 180°

m∠3 = 137° because opposite angles are congruent, so m∠3 = m∠2

m∠5 = 43° because alternate angles are congruent

m∠6 = 137° because ∠5 and ∠6 are supplementary, so 43° + m∠6 = 180°

m∠7 = 137° because alternate exterior angles are congruent, so m∠7 = m∠2

m∠8 = 43° because alternate exterior angles are congruent, so m∠8 = m∠1

Answer:

angle 1: 43

angle 2: 137

Step-by-step explanation:

Lets find angle 1 first :)

Since oposite diagonal angles are the same, this will make angle 1 43 degrees :)

Now lets find angle 2!

Since 1 was 43 degrees, and a flat line is 180 degrees we must subtract!

Lets do that now!

180 - 43 = 137

Angle 2 will be 137 degrees!

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The equation of the required perpendicular line is y = (-5/4)x - 30.

We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation of the given straight line is y = (4/5)x + 23. We need to find the equation of the straight line that is perpendicular to the given line and passes through the point that has coordinates (-40, 20).

The slope of the given line is 45. Let the slope of the required perpendicular line be represented by the variable "m". The slope of the perpendicular line must be the negative reciprocal of the slope of the given line.

m = -1/(4/5)

m = -5/4

The equation of the required line is of the form y = mx + c.

y = (-5/4)x + c

We know that this line passes the point (-40, 20).

20 = (-5/4)(-40) + c

20 = 50 + c

c = -30

Hence, the equation of the required line is y = (-5/4)x - 30.

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The tip is 18%

From the question, we have

food and beverages cost = $25.30

meals tax = 8%

Tax = (8/100)* 25.3 =  $2.02

Bill = $25.30 + $2.02

= $27.32

After adding a tip, the total lunch cost was $32.24.

Tip = $32.24. -  $27.32  = $4.92

% of Tip  = (4.92 /  27.32) * 100 =  18 %

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Hey there! I explained and wrote everything on paper since it's hard to type so you can view the pic uploaded! Hope it helps, if you have any doubts, please feel free to ask :)

Correlation is a bi-variate analysis that measures the strength of association between two variables and the direction of the relationship.

What is bi-variate analysis?

Bivariate analysis is one in every of the only kinds of quantitative (statistical) analysis. It involves the analysis of 2 variables (often denoted as X, Y), for the aim of deciding the empirical relationship between them.

Main Body:

The correlation coefficient's value ranges from +1 to -1. the entire degree of correlation between the 2 variables is indicated by a worth of one. The association between the 2 variables are weaker because the parametric statistic price approaches zero.

Hence correlation investigate linear association between two variables.

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The probability that at least one number is odd and the sum of the two numbers is even is 1/4

The probability that exactly one number is 6 and the product of the two numbers is at most 15 is 1/9

The easiest way to figure out probability problems with small data sets is to write out your entire sample space and then divide by the total:

Sample size = 6 * 6 = 36

S = {[1,1],[1,2],[1,3],[1,4],[1,5],[1,6],[2,1],[2,2],[2,3],[2,4],[2,5],[2,6],[3,1],[3,2],[3,3],[3,4],[3,5],[3,6],[4,1],[4,2],[4,3],[4,4],[4,5],[4,6],[5,1],[5,2],[5,3],[5,4],[5,5],[5,6],[6,1],[6,2],[6,3],[6,4],[6,5],[6,6]}

The only way to make a number combination that's even while 1 die is odd is to have 2 odd numbers.

{[1,1],[1,3],[1,5],[3,1],[3,3],[3,5],[5,1],[5,3],[5,5]}

This gives us 9 results.

The probability of this happening is 9/36 = 1/4 = 0.25

Now if we have to get a 6 with the product being at most 15 we know that the biggest number that 6 can be multiplied by is 2 which gives us 12.

We are left with 4 options:

{[1,6],[2,6],[6,1],[6,2]}

The probability of this happening is 4/36 = 1/9 = 0.1111...

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Answer:

Step-by-step explanation:

3y+6-4x=0

3y-4x=0-6

3y-4x=-6

y-4x=6/3

y-4x=2

y-x=2/4

y-x=0.5

Answer:it depends on how many sides their are

Step-by-step explanation:

just factual

The proof of Δ SUE is not an isosceles triangle. is shown below.

If there are two points A(a, b) and B( c, d) then the distance between these two points are

AB= √( c-a )² + ( d-b )²

Given:

S(-2, -4), U(2, -1) and E(8, -9)

Using Distance formula

SU= √( 2 -(-2))² + ( -1-(-4))²

SU = √4²+ 3²

SU = √16+9

SU =5

and, UE = √( 8 -(2))² + ( -9-(-1))²

UE = √6²+ 8²

UE = √36+64

UE =10

and, ES= ( 8 +2 ))² + ( -9+4)²

ES = √10²+ 5²

ES = √100+25

ES = 5√5

As, none of the two sides are equal.

So, Δ SUE is not an isosceles triangle.

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Answer: 6x(-x+3)

Step-by-step explanation:

You can factor out the 6 and x. -6x^2 divided by 6x = -x, and 18x divided by 6x = 3. So the answer is 1. 6x(-x+3)

Answer:

-6x^2+18x

-6x^2-18x

6x^2+18x

-6x^2+108x

Step-by-step explanation:

1.

6x(-x+3)

6x(-x)+6x(3)

-6x^2+18x

2.

-6x(X+3)

-6x(X)+-6x(3)

-6x^2-18x

3.

x(6x+18)

x(6x)+x(18)

6x^2+18x

4.

6(-x^2+18x)

6(-x^2)+6(18x)

-6x^2+108x

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