The width of a rectangle is 8 units less than the length. The area of a rectangle is 9 units. What is the length, in units of the rectangle?

Pseudocode algorithms are used as prototypes of an actual program.

The required pseudocode algorithm is as follows:

1. Start

2. Input n

3. Odd = 1

4. For i in range(n):

    4.1 Print Odd     4.2 Odd = Odd + 2

The pseudocode that prints the first n odd numbers starting from 1 is as follows:

1. Start

2. Input n

3. Odd = 1

4. For i in range(n):

    4.1 Print Odd     4.2 Odd = Odd + 2

The above pseudocodes would print the first n odd numbers starting from 1, given that n is the input

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f (4) = 61

g (4) = 2

Step-by-step explanation:

f(4) = 2(4)² - 3

f(4) = 8² - 3

f(4) = 64 - 3

f(4) = 61

g (4) = -4 + 6

g (x) = 2

Using integer numbers, we have that:

1. The integer -5 would represent traveling west at -5 miles per hour, while the integer 5 would represent traveling east at 5 miles per hour.

2. The positions are given as follows:

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

For the number line, we have that:

Hence, for item 1, we have that:

The integer -5 would represent traveling west at -5 miles per hour, while the integer 5 would represent traveling east at 5 miles per hour.

A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

For item b, to find the distance, we apply the proportion, multiplying the velocity by 5, hence the positions would be given by:

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The slope is (-1/2) an  y -intercept is (-5/2) in the line  -(1/3)x - (2/3)y = 5/3

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope.

We know that the equation for slope(m) and y - intercept(c) of a line is given by :

y = mx + c

Here the equation is -(1/3)x - (2/3)y = 5/3

⇒ -(1/3)x - (2/3)y = 5/3

⇒  - (2/3)y = (1/3)x +  5/3

⇒ [tex]\frac{-2y}{3}[/tex] = [tex]\frac{x + 5}{3}[/tex]

⇒ -2y = x + 5

⇒  y = [tex]\frac{x + 5}{-2}[/tex]

⇒  y = [tex]\frac{-1}{2}x -\frac{5}{2}[/tex]

Hence, slope is (-1/2) and  y - intercept is (-5/2)

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The found value are-

A straight line's general equation is y = mx + c, in which m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.

Now, as per the given question;

The general equation of the line is given as;

y = mx + b

Each point (x,y) of the line is moved to the point (x+a, y+b) by the translation:

(x,y) ---> (x+a, y+b)

We find the original line's x and y intercepts:

Put y=0 in general equation of the line

⇒mx+b = 0

⇒x = −b/m

When, x=0

⇒y = m⋅0 + b

⇒ y = b

A, (0,b) and B( -b/m, 0)

We find the translational coordinates of the points A,B:

A(0,b) ---> A′ (0+a,b+b)

A(0,b) ---> A′ (a,2b)

And,

B( -b/m, 0) ----> B'( -b/m + a, 0 + b)

B( -b/m, 0) ----> B'( -b/m + a, b)

To find the equation of the line's translation, we use the points A and B ′:

m' = (2b - b)/[a  - (-b/m +a)]

m' = b/(b/m)

m'  =m

And,

y−yA' = m' (x−xA')

y−2b=m(x−a)

y=mx−am+2b

The translation of the line's x and y intercepts are:

Put x=0

⇒y = m⋅0−am+2b

⇒y = 2b−am

And, put y=0

⇒0 = mx−am+2b

⇒x = a - (2b/m)

Therefore, the equation of the translate line is found to be  y = mx − am + 2b.

And, the value of the y-intercept is found to be 2b−am.

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According to the question, the given parameters of a triangle Δ IJK is given below:

j = 960 inches, i = 200 inches and ∠I = 68 degree.

As we know, the sum of the angle of a triangle is 180 degree.

Therefore, ∠I + ∠J + ∠K = 180 degree

Substituting above values in the given expression, we get:

∠J + ∠K = 180 - 68 = 112 degree

For isosceles triangle, two sides are equal. Therefore, ∠J = 56 degree

Hence, the calculated value for the ∠J is 56 degree.

What is triangle?

In the geometry of mathematics, the triangle can be defined as a polygon shape which has three edges as well as three vertices. There are three different forms of triangle which are known as scalene, isosceles and equilateral triangle.

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For given situation the events are dependent.

In this question,

Alita's basketball team is in the final four.

we have been given two events.

event A: Alita's basketball team win.

event B: Alita's basketball team play in the championship game.

From given condition, If they win, they will play in the championship game.

We can clearly observe that the occurrence of event B is dependent on the other event A.

If event A occurs only then event B would be true.

Therefore, for given situation the events are dependent.

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No, the regular polygon pentagon will not tessellate in the plane.

A tessellation or tiling is the seamless application of one or more geometric shapes, known as tiles, to a surface, frequently a plane. Tessellation in mathematics can be expanded to include other geometries and higher dimensions.

A tiling constructed of materials like cemented ceramic hexagons or squares is referred to as a real-world tessellation. Such tilings may be ornamental designs or serve practical purposes such providing long-lasting and water-resistant pavement, floor, or wall coverings.

Tessellations were historically employed in Islamic art, such as the Moroccan architecture and the ornamental geometric tiling of the Alhambra palace. They were also used in Ancient Rome.

Regular polygons tessellate if their interior angles divide by 360° evenly or if the total of their interior angles is a factor of 360°. A tessellation is a pattern made of identical forms that fit together seamlessly.

So lets find out how pentagon won't tessellate.

First we find the measure of the interior angles of pentagon,

[tex]\frac{540\°}{5} = 108\°[/tex]

Now divide the interior angle by 360°

[tex]\frac{360\°}{108\°}[/tex] = 3.333

Hence, the measure of the interior angle does not divide by 360°.

Therefore, we conclude that the regular polygon pentagon will not tessellate in the plane.

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Volume of baseball is 1.24 times greater than volume of tennis ball.

We are given the diameter of baseball and tennis ball. So, firstly we will calculate the volume of tennis ball and baseball.

Volume of ball = 4/3πr³, where r stands for radius of ball.

Taking value of π as 3.14.

Volume of tennis ball = 4/3×π×2.7³

Volume of tennis ball = 82.4 m³

Volume of baseball = 4/3×π×2.9³

Volume of baseball = 102.1 m³

Now, finding the number of times volume of baseball is greater than volume of tennis ball.

Comparison -  volume of baseball ÷ volume of tennis ball

Comparison - 102.1 ÷ 82.4

Comparison - 1.24

Hence, volume of baseball is 1.24 times of volume of tennis ball.

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A scatter plot is a series of points plotted on horizontal and vertical axes. If there is no correlation between variables, the points appear randomly scattered on the coordinate plane. If the correlation is high, the points will be clustered around a straight line. A scatter chart is a data visualization tool that helps show trends.

The scatter plot shows not only the correlation's magnitude but also the correlation's direction.

As the vertical (or Y-axis) variable increases, the correlation is positive as the horizontal (or X-axis) variable increases.

The correlation is negative if the y-axis variable decreases and the x-axis variable increases, or vice versa.

The correlation is zero if none of the above criteria can be established.

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The solution to the equation (2x - 20)/3 = 2x of temperature change gives x = -5.

The given equation is;

(2x - 20)/3 = 2x

Simplify the equation;

2x - 20 = 6x

Bring variables together;

6x - 2x = -20

4x = -20

Divide by 4

x = -5

Therefore, the solution to the equation (2x - 20)/3 = 2x of temperature change gives x = -5.

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Δp≥5.2755∗10−25ms−1

According to the Heisenberg uncertainty principle, we have

δx∗δp≥ℏ2

Since Δx=1angstrom=10−10m,

Δp≥6.626∗10−344∗3.14∗10−10

Δp≥5.2755∗10−25ms−1

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The required value of y is 21.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be a constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx,      —-- 1

Now, find k for given x = 3 and y = 7, we need to put these values in equation 1, i.e.

7 = k(3)

k = 7/3

k = 7/3

Further calculate y for given x = 6 and constant of proportion = 7/3 i.e.

y = (9)(7/3)

y = 21

Hence, the required value of y is 21.

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Answer:

x = 2

y = 17

Step-by-step explanation:

Rule that applies to this question: Opposite sides of a parallelogram are equal.

Therefore:

x+2 = 4

x = 4 - 2

x = 2

y-5 = 12

y = 12 + 5

y = 17

The simple interest earned on the principal of $550 is $12.1.

The formula for simple interest is;

SI = PRT/100

where,

P is principal amount = $550

R is rate of interest = 4.4%

T is the total time in year; 6 months = 0.5 years.

Put the values in formula;

SI = 550×4.4×0.5 / 100

On simplification;

SI = 12.1

Thus, the simple interest incurred on the deposited principal is $12.1.

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A line segment is also a line but a line with finite length and fixed endpoints. The given statement "Lines p and q intersect in points M and N" can never be true.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

A line segment is also a line but a line with finite length and fixed endpoints.

The given statement "Lines p and q intersect in points M and N" will never be true, this is because two straight lines can only bisect once, therefore, at only a single point.

Although, the line may also bisect each other at infinite points but only if the line overlap with one another.

Since it is given that bisect each other at two points M and N.

Hence, The given statement "Lines p and q intersect in points M and N" can never be true.

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R (-90°) = (x, y) — > (y, -x)  is the x - and y -coordinates change.

How is a point rotated with respect to the origin?

As it turns out, however, I don’t need to look at options. I can tell you that a clockwise rotation of 90° of a point about the origin is actually considered a rotation of -90°.

(For positive rotations are counterclockwise, while negative rotations are clockwise.) The rule for the type of rotation you speak of is

R (-90°) = (x, y) — > (y, -x)

One more point, if I may. It appears that you copied this problem verbatim right out of a textbook.

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3/5w - 1/5w +10 = 4

First, simplify 3/5w - 1/5w

2/5w + 10 = 4

Then, subtract each side by 10

2/5w = -6

Multiply each side by the denominator

2w = -30

Then divide each side by 2

w = -15

9.27  rounded to 2 decimal places is 9.27

The important thing to remember is that you should round 9.270 to two digits or places after the decimal point. As a result, we wish to do rid of the final digit in 9.270. We utilize the following Two Decimal Places Rules to find the answer by removing the final digit in 9.270:

Rule #1 for two decimal places: If the final digit in 9.27 is less than 5, it should be removed.

Two Decimal Places Rule #2: If the second-to-last digit in 9.27 is less than 9 and the previous digit is 5 or greater, the last digit must be removed and one added to the second-to-last digit.

Three Decimal Places Rule #3: If the final digit in a number, such as 9.27, is five or more, the second to last digit is nine, and the third to last digit is less than nine, the last digit is eliminated, the second to last digit is changed to zero, and the third to last digit is increased by one.

Fourth Rule of Two Decimal Places: Add 1 to the value on the left side of the decimal point and change the right side of the decimal point to 00 if the final digit in 9.270 is 5 or more, the next-to-last digit is 9, and the next-to-last digit is 9.

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Exact Form:

23

266

Decimal Form:

0.08646616...

The restriction on the variable x for the expression 5x+15/10x-10÷x²+6 x+9/3x²-3 is  x ≠ -3 .

Restriction in algebraic expression is defined as the value that makes the denominator as 0  or the whole expression as not defined.

For Example: 1/(x+2)   , here the restriction is x ≠ -2 as -2 will make the denominator 0.

In the given question

[tex]=\frac{5x+15}{10x-10} \div\frac{x^{2} +6x+9}{3x^{2} -3}[/tex]

rewriting the expression

[tex]=\frac{5x+15}{10x-10} \times\frac{3x^{2} -3}{x^{2} +6x+9}[/tex]

Simplifying the numerator and denominator we get

=5(x+3)/10(x-1) x 3(x² -1)/(x²+3x+3x+9)  ...( by splitting the middle term )  

=5(x+3)/10(x-1) x 3(x-1)(x+1)/(x+3)(x+3)  ...( using identity a²-b²=(a+b)(a-b)   )

On further simplifying we get ,

=5*3*(x+1)/10(x+3)

=3(x+1)/2(x+3)

For finding restriction;

denominator, 2(x+3)≠0

means (x+3)≠0 ⇒ x ≠ -3.

Therefore , the restriction on the variable x is x ≠ -3 as -3 will make the expression not defined, and the value after division is 3(x+1)/2(x+3).

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Answer:$19,829.10

Step-by-step explanation:

Compounded quarterly so use [tex]A = P(1+\frac{r}{n})^{nt}[/tex]

-Quarterly means 4 times a year

Initial Amount (P) = $4700
Rate = 5.8%

Time = 25 years

Plug everything into equation

[tex]A = 4700(1+\frac{0.058}{4})^{4*25}[/tex]

Insert into calculator and get:

$19,829.0996305 which is approximately $19,829.10

Round to the nearest hundredth because when dealing with money there are only two decimal places.

Answer:

$19,829.10

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=4700\left(1+\dfrac{0.058}{4}\right)^{4 \times 25}[/tex]

[tex]\implies \sf A=4700\left(1+0.0145\right)^{100}[/tex]

[tex]\implies \sf A=4700\left(1.0145\right)^{100}[/tex]

[tex]\implies \sf A=4700(4.2189573...)[/tex]

[tex]\implies \sf A=19829.0996...[/tex]

Therefore, the account balance after 25 years will be $19,829.10 (nearest cent).

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Answer:

81

Step-by-step explanation:

6 multiplied by 13.5 gives the answer 81.

Answer: 81

Step-by-step explanation:

[tex]13.5*6=\\\\13.5*2*3=\\\\27*3=\\\\81[/tex]

The number of miles in a day at which the rental costs for Company A and Company B are the same will be 200 miles.

We are given that:

For Company A:

Fixed cost = $ 110

Variable cost = $ 0.20 per mile

For Company B:

Fixed cost = $ 70

Variables cost = $ 0.40 per mile

Let the number of miles in a day be x.

So, the equation for rental cost for company A will be:

Rental cost = 110 + 0.20 x

The equation for rental cost for company B will be:

rental cost = 70 + 0.40 x

Now, put both rental cost equal.

110 + 0.20 x = 70 + 0.40 x

0.40 x - 0.20 x = 110 - 70

0.20 x = 40

x = 40 / 0.20

x = 200 miles.

Therefore, the number of miles in a day at which the rental costs for Company A and Company B are the same will be 200 miles.

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Answer:

2x+y

Step-by-step explanation:

They have 2 bags containing "x" counters and 1 containing "y" counters. So 2 multiply the number of x since there are 2 bags + y because y also contains counters we need to add. (I'm pretty sure)

Answer: x=+27

Step-by-step explanation:

[tex]\huge\qquad\underline{{\tt answer : - }} [/tex]

[tex]x+12=2x-15 \\ x - 2x = - 12 - 15 \\ - x = - 27 \\ x = 27[/tex]

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The two inequalities are:

y = 20x when x ≤ 6  and y = 15x when x > 6

The scenario given here is of a chicken that is being roasted. To solve this problem, we will take y as the time required to roast the chicken and x as the lbs of the chicken. (weight)

Now two different conditions are applied depending upon the lbs of the chicken the taken to roast the chicken will vary,

20min/lb for a chicken weighs as much as 6lb.

y = 20x when x ≤ 6

15 min/lb for a chicken weighs more than 6lb.

y = 15x when x > 6

The above two equations are the two inequalities that represent time needed to roast both the chicken.

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When an angle exists encircled by a circle, its measure exists equivalent to the intercepted arc's measure divided by two. The measure of m DH is 162.

The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc. Anywhere on the circle that the sides of an inscribed angle intersect to produce an intercepted arc can serve as the angle's vertex.

Angles with vertices on a circle and that cross an arc on the circle are said to be inscribed angles. Half of the intercepted arc's length and half of the central angle's length intersecting that same arc make up the measure of an inscribed angle. Congruent inscribed angles are those that intersect the same arc.

According to the Inscribed Angle Theorem, an inscribed angle's measure is equal to half of its intercepted arc's measure. Congruent inscribed angles are those that intersect the same arc.

An angle's measure is equal to the intercepted arc's measure divided by two when it is surrounded by a circle.

m DH = 2(m ∠F) = 162

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