The sides of a rectangle have length x+1 and width x-5. which equation below describes the area A of the rectangle in terms of x?​

The value of x will be cos^-1 549/900.

What is Law of Cosine ?

The relationship between a triangle's side lengths and the cosine of its angle is known as the law of cosines. Additionally known as the cosine rule.

We know that ,

a²= b²+c² - 2bc cosα, where α is the angle between b and c.

Here, b = 18 , c= 25, a = 20 and cos x

So, a²= b²+c² - 2bc cosα

     (20)² = (18)² + (25)² - 2×18×25 cos x

     400 = 324 + 625 - 900 cos x

    900cos x = 549

         cos x = 549/900

 hence, x = cos^-1 549/900

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X for type 1 cabinets = 30

Y for type 2 cabinets = 80

And that proven that type 2 cabinets (Y) produced exceeded more than twice the number of type 1 cabinets (X)

As per the equations stated

X + Y = 110  ……….. (1)

Y = 2x + 20  …...... (2)

We substitute Y at equation (1) with equation (2), to find X

X + Y = 110

X + (2X + 20) = 110

3X + 20 = 110

3X = 110 – 20

3X = 90

X = 90 / 3

X = 30

Then, We substitute value X at equation (1 ) with the value that we have discovered before

X + Y = 110

30 + Y = 110

Y = 110 – 30

Y = 80

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Therefore 128 ways that Peter can make 8 steps and land back at vertex A.

There are two possible directions for each step that Peter can take, either clockwise or counter-clockwise.

Therefore, for 8 steps, there are 2^8 = 256 possible ways that Peter can make the steps. However, only half of these ways will end with Peter back at vertex A, since the other half will have him end at the opposite vertex.

Therefore, there are 256/2 = 128 ways that Peter can make 8 steps and land back at vertex A.

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The formula for a circle's sector's area is /360o (r2), where r is the circle's radius and is the sector's angle.

Formula for a Sector's Circumference

The following is the formula for a circle's sector's perimeter:

Sector perimeter equals radius plus radius plus arc length.

Sector perimeter equals 2 radius plus arc length.

The relation is used to compute arc length:

Arc length is equal to l = (/360) 2r.

Therefore,

Sector perimeter: 2 Radius + ((/360) 2r)

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Assuming that r is the circle's radius and that is the sector's angle, the formula for the area of a circle's sector is /360o (r2).

A circular sector (also known as a circle sector or a disc sector; symbol: ) is the area of a disc (a closed region bordered by a circle) enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger as the major sector.

The radius of the circle, r, and the sector angle (in degrees) that the arcs at its centre subtend are also given. A = 1/2 r2 gives the area if the subtended angle is provided in radians.

The area, A, of just the segment may be calculated using the following formula if you know the circle's radius, r, and the sector's central angle,, in degrees.

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The value of the given expressions is p = -1.281, though it is also possible for p = 0.781 to be the value.

Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, slope-intercept form, and point-slope form are the three primary formats for linear equations. In a mathematical expression known as an equation, the equals sign appears. Algebra is used in a variety of equations. When you don't know how much to compute in math, you use algebra to approximate the answer.

given

-4p^2=2p-4

p=(-1-sqrt(17))/4=-1.281

p=(-1+sqrt(17))/4=0.781

The value of the given expressions is p = -1.281, though it is also possible for p = 0.781 to be the value.

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Answer:

30%

Step-by-step explanation:

The level of decay is determined by the number raised to the power.

y = 0.4(0.7)^t

If you had 1^t, there would be no decay or growth since 1^t is always 1.

Instead, you have 0.7^t

As t increases, 07^t decreases. That is where the decay comes from.

Now look at 0.7

In the general decay equation, you have

y = a(1 - r)^t

r is the rate of decay.

Here we have 0.7

0.7 = 1 - 0.3

the rate of decay is 0.3 or 30%

Answer:

The equation y = 0.4(0.7)^t represents an exponential decay of 30%. The decay rate is determined by the value in the parentheses, which in this case is 0.7. To calculate the decay rate, you can subtract this value from 1, giving you 1 - 0.7 = 0.3, or 30%.

Step-by-step explanation:

The final image of K would be at (3,-1) after the given sequence of transformation Segment JK.

Dilation is a process for creating similar figures by changing the size.

Segment JK has endpoints J(2,4) and K(6,2).

A dilation by a factor of 1/2 means that each coordinate value will be multiplied by 1/2.

The dilation of segment JK with a scale factor of 1/2 would shrink the segment by half, so the coordinates of K would be (3,1).

Reflecting over the x-axis would change the sign of the y-coordinate, so the final image of K would be at (3,-1).

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(a) To determine if it is possible to prepare 21 goodie bags exactly, we need to check if 450 notebooks and 315 fridge stickers can be divided equally into 21 goodie bags without any leftovers.

To do this, we can use the greatest common divisor (GCD) of 450 and 315, which is 15. If the GCD is not 1, it means that the two numbers cannot be divided exactly, so it is not possible to prepare exactly 21 goodie bags with 450 notebooks and 315 fridge stickers.

(b) To find the largest number of goodie bags that can be prepared, we can use the least common multiple (LCM) of 450 and 315. The LCM is 990, which means that 990 notebooks and 990 fridge stickers can be divided into the same number of goodie bags without any leftovers. Therefore, the largest number of goodie bags that can be prepared is 990/450 = 990/315 = 2.

(c) Using the answer from (b), we can calculate how many notebooks and fridge stickers will be in a goodie bag. If we divide 990 by 2, we get 495. Therefore, there will be 495 notebooks and 495 fridge stickers in each goodie bag.

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Graphs 1 and 2's respective inequalities are n14 and n14.

"Inequality" is the term used in mathematics to describe a connection between two expressions or values that is not equal to one another.

the first graph

line excluding number 14 is extending to the left.

The disparity is as;

n < 14.

Within Graph 2,

The number 14 is part of a line that is diverging to the right.

The disparity is as;

n≥14

As a result, graphs 1 and 2's respective inequalities are n14 and n14.

Graph 1 and Graph 2 each have n14 and n14 inequalities.

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first statement is true, the equation shows a linear but not proportional.

The equation which has two variables with first order term and only a constant available in the equation is termed as linear equation. Example of a linear equation, y =mx + b

Given, an equation, y = 225x + 200

where x and y are two variables

x denotes the number of hours the field is being rented

y denotes the total cost

constant 200 implies the flat rate for renting the field.

If we compare this equation to the standard form of linear equation, y = mx + b, where m = slope and b is the y intercept.

 we will find that the above two equation is similar and therefore the equation given in question is a linear relationship.

the coefficient 225 is the slope of equation and the constant 200 is the y intercept.

this given equation is not a proportional relationship.

The first statement is true.

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Answer:

0.6  cause I got it correct.

Answer: its number 2

Step-by-step explanation:

The difference between the value predicted by the regression and the observed value for a given data point is known as the residual. The residual calculation offers a useful indicator of how well your model matches the given data set.

The discrepancies between actual and expected data values are known as residuals in statistical or machine learning models.

They serve as a diagnostic tool for evaluating a model's quality. They are also called mistakes.

The table below's main column, Inflation, displays information on US inflation for each month of 2017. The Predicted column displays forecasts from a model that aims to forecast the pace of inflation.

The residuals are calculated as follows: Residual = Inflation - Predicted. They are displayed in the Residual column. In the instance of the data for January 2017, the model projected 1.8%, but the observed inflation was 0.5%, leaving a residual of -1.3%.

Hence, The residual calculation offers a useful indicator of how well your model matches the given data set.

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So on solving the provided question we can say that coefficient of x^2 in  x³ +4x² -7x -2 is 1.

A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include:  The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example  Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.

here,

coefficient of x^2 in  x³ +4x² -7x -2 is 1

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The correct dot plot for the given data would be option A. Number of Errors for the Week for Workstations.

A dot plot is a graph that displays the frequency of a data set by plotting a dot above the number for each occurrence of that number. The x-axis represents the data values and the y-axis represents the frequency of each data value.

In this case, the data represents the number of errors each workstation makes during the week, so the correct way to display the data in a dot plot would be to have the x-axis represent the number of errors and the y-axis represents the frequency of each error. Each dot on the dot plot would be above the number of errors for each workstation.

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Symbolic Form:

P: National elections deteriorate into TV popularity contests

Q: Smooth-talking morons will get elected

The argument can be expressed as:

If P then Q

Therefore, if not P then not Q

This is a valid argument as it follows the logical form of Modus Ponens. We can verify this using a truth table:

P | Q | P → Q | ¬P | ¬P → ¬Q

T | T | T       | F  |  T

T | F | F       | F  |  T

F | T | T       | T  |  T

F | F | T       | T  |  T

The truth table shows that the argument is valid because the final column (¬P → ¬Q) is true for all four cases. This indicates that if the symbolic form of premise (P) is false, then the conclusion (Q) must also be false.

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The correct statement regarding the similarity of triangles GHJ and FHK is given as follows:

Triangle FHK is similar to triangle GHJ by the SAS Similarity Theorem.

Similar triangles are triangles that share these two features given as follows:

For this problem, the similar triangles are given as follows:

FHK and GHJ.

They are similar because:

As they have two proportional side lengths, along with the angle between them, the congruence theroem is the SAS theorem.

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The percent of monthly earnings that Vera spends on phone apps is 4%.

The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

Since Vera spent 0.04 of of the earnings on a new phone apps, the percent of monthly earnings did she spend on phone apps will be:

= 0.04.

= 4/100

= 4%

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Answer:

90 calories in a 6 ounce bottle

Step-by-step explanation:

6oz/x

10oz/150

150 divided by ten is 15

15 times 6 equals 90

Answer: 90 calories is in 6 ounce bottle which is 90

In the word problem ,the total cost for cruise for total family is $5475.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here the Total members of the Harrison family = 3

Cost of cruise per person = $1825

Now, Total cost for cruise of Harrison family is,

=> Total members × Cost per person

=> 3 × 1825

=> $5475

Hence the total cost for cruise for total family is $5475.

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r<15 because I am smart dont doubt me

You swam 50 yards more than your friend.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, you swam 4 sets of 200 yards and your friend swam 5 sets of 150 yards.

Total number of yards you swam 4×200

= 800 yards

Total number of yards your friend swam 5×150

= 750 yards

Number of yards more you swam =800-750

= 50 yards

Therefore, you swam 50 yards more than your friend.

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A dodecagon or 12-gon is a twelve-sided polygon.

One of the polygonal shapes with 12 sides, 12 vertices, and 12 angles is the dodecagon. A dodecagon is a two-dimensional plane figure, just like other polygons. 12 equal sides and 12 equal angles make up a standard dodecagon polygon.

Dodecagons that are irregular have uneven sides and angles. Dodecagons can also be concave or convex polygons. The dodecagon's inner angles add up to 1800° in total.

The word dodecagon is derived from Greek words, ‘dodeka‘ which means ‘twelve’, and ‘gon‘ means ‘sides’.

Thus, A dodecagon or 12-gon is a twelve-sided polygon.

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Answer:

30 Oranges

Step-by-step explanation:

The ratio of apples to oranges is 4:3.  For every 4 apples there are 3 organges.  We can write that as 4A/3O, where A and O are Apples and Oranges.  This can be rewritten as percentages of each fruit.  A bag of 7 would have 4 Apples (4/7) or 0.5715 [57.15%] and 3 Oranges (3/7) or 0.4285 [42.85%].

A bag of 70(A and O) can be determined to have:

Apples:  70*(0.5715) =  40 Apples, and

Oranges:  70*(0.4285) = 30 Oranges

Answer:

Step-by-step explanation:

Question 4 I got something different x= 5, y= -4 (double check my work to make sure i used correct equation and all)

Also for slopes does your teacher want you to include the "x". Cuz when I think of slope its only the "m" part which means it should only be -1, -4 but its your call.

The distance that light will travel in 3 years, given the speed it travels in one year is

The notion of a Light Year allows us to quantity the distance that light travels in an entire year. This has allowed scientists to quantify with more ease, the distance to other galaxies and planets.

The distance that light travels in a year is 5. 88 x 10¹² miles.

In 3 years therefore, the distance would be:

= 3 x ( 5.88 x 10 ¹²)

= 17.64 x 10 ¹² miles

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The partial fraction decomposition of the function is[tex]\\& \Rightarrow \frac{1}{x^2+x^4}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1}\end{aligned}[/tex]

In algebra, a rational fraction—that is, a fraction where the numerator and denominator are both polynomials—can be partially decomposed or expanded by adding a polynomial (potentially zero) and one or more fractions with a lower denominator to the original fraction.

In symbols, the partial fraction decomposition of a rational fraction of the [tex]{\textstyle {\frac {f(x)}{g(x)}},}[/tex]

[tex]{\displaystyle {\frac {f(x)}{g(x)}}=p(x)+\sum _{j}{\frac {f_{j}(x)}{g_{j}(x)}}}[/tex]

Where p(x) is a polynomial, [tex]g_{j}[/tex] for each j is a power of an irreducible polynomial (which cannot be factored into polynomials of positive degrees), and [tex]f_{j}[/tex] for each j is a polynomial with a smaller degree than this irreducible polynomial's degree.

The numerical values of the coefficients is [tex]\frac{1}{x^2+x^4}$[/tex].

Now,

[tex]$\begin{aligned} x^2+x^4 & x^2+x^4 \\ = & x^2\left(1+x^2\right)\end{aligned}$[/tex]

Therefore, the form of the partial fraction decomposition is

[tex]\begin{aligned}& \frac{1}{x^2\left(1+x^2\right)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1} \\& \Rightarrow \frac{1}{x^2+x^4}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1}\end{aligned}[/tex]

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Answer: X=19

Step-by-step explanation:

x^2=361

Square root both sides to get rid of the exponent above x.

     [tex]\sqrt{x^2}[/tex]=[tex]\sqrt{361}[/tex]

      x=19

Therefore , the solution of the given problem of equation comes out to be k1 = - 0.67 and k2 = -0.1.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A scientific statement that verifies the equality of two formalisms is known as an equation in algebra. For instance, the pieces ptdc + 6 and 12 are separated by an equal sign in the solution obd + 6 = 12. The relationship between the two phrases on either flank of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 4x – 4 = 0.

Here,

If y varies in this case simply also as square of x

k is the proportionality constant, and

y = kx² in mathematics.

Considering y = -54 and x = 9,

y = kx²

k = y/ x²

k = -54/ 9²

k = -54/81

k1 = - 0.67

Moreover, if y=-11/3 and x=6,

k = y/x²

k = -3.667/ (6)²

k = -3.667/36

k2 = -0.1

Therefore , the solution of the given problem of equation comes out to be k1 = - 0.67 and k2 = -0.1.

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