Simplify each expression by combining like terms.
8x + 3 - 5x - 9

Helpp

If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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A 2x3x2 factorial design has three independent variables. What is a factorial design? A factorial design is an experimental design that studies the impact of two or more independent variables on a dependent variable.

The notation of a factorial design specifies how many independent variables are used and how many levels each independent variable has. In a 2x3x2 factorial design, there are three independent variables, with the first variable having two levels, the second variable having three levels, and the third variable having two levels.

The number of treatments or conditions required to create all feasible combinations of the independent variables is equal to the total number of cells in the design matrix, which can be computed as the product of the levels for each factor.

In this case, the number of cells would be 2x3x2=12.Therefore, a 2x3x2 factorial design has three independent variables and 12 treatment groups..

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Answer:

The probability is 1/6

Step-by-step explanation:

Firstly, we need to get the total number of coins

that would be the sum of all the coins present

We have this as;

8 + 10 + 4 + 2 = 24 coins

The number of nickels is 4

So the probability of selecting a nickel is the number of nickels divided by the total number of coins

We have this as;

4/24 = 1/6

Answer:

$10.50 ×14 = 150

Step-by-step explanation:

espero que te sirve

$0.75 is the average price per minute.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

she pays $10.50 to rent the bike for 14 minutes,

i.e. the average price per minute is,

$10.50 /14

=$0.75

Hence, $0.75 is the average price per minute.

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The possibility that the son marry one of girls of the three races based on the dating records is 15%.

We are given that;

The record of 35 times with Asians, 20 times with Blacks and 45 times.

Now,

The probability of marrying an Asian girl is 0.35 * (1 - 0.15) = 0.2975, where 0.15 is the rejection rate by Asian girls.

The probability of marrying a Black girl is;

0.2 * (1 - 0.15) = 0.17, where 0.15 is the rejection rate by Black girls.

The probability of marrying a Caucasian girl is;

0.45 * (1 - 0.15) = 0.3825, where 0.15 is the rejection rate by Caucasian girls.

These probabilities add up to 0.85, which means that there is a 15%

Therefore, by probability the answer will be 15%.

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Answer:

The change in elevation of the seagull is -16 ft

Step-by-step explanation:

Displacement

The displacement, unlike distance, considers the direction of the lengths occurring in the systems.

To solve the problem, we need to set a zero-level reference. Let's assume the sea level as zero height, any position above this reference as positive, and any position below this reference as negative.

The seagull is flying at a height of 10 ft above the ocean. Thus, its position is positive +10 feet.

The seagull then dives into the water to catch a fish at a depth of 6 feet. This position is negative: -6 ft.

The change in elevation is found by subtracting the final elevation and the initial elevation:

change = -6 ft - 10 ft = -16 ft

The change in elevation of the seagull is -16 ft

Answer:

7pi/8

Step-by-step explanation:

Well the arc is 21pi/8 cm. Our formula to find the length of arc is r × theta(angle). Let's take the angle as x.

R × x = 21pi/8

x = 21pi/8 ÷ R = 21pi/8 ÷ 3 = 7pi/8 rad

The rank of the coefficient matrix and the augmented matrix are equal to the number of variables, hence the system has a unique solution.

To solve the system of linear equations using Gaussian Elimination, let's first rewrite the equations in the form of an augmented matrix [A|B]:

| 1   1   -2 | 13 |

| 1  -2  1   | 32 |

| 2  7  -11 | 3  |

Now, let's perform Gaussian Elimination to transform the augmented matrix into row-echelon form:

1. Row2 = Row2 - Row1

  | 1  1  -2  | 13 |

  | 0  -3 3   | 19 |

  | 2  7  -11 | 3  |

2. Row3 = Row3 - 2 * Row1

  | 1  1  -2  | 13 |

  | 0  -3  3  | 19 |

  | 0  5  -7  | -23 |

3. Row3 = 5 * Row3 + 3 * Row2

  | 1  1  -2  | 13 |

  | 0  -3  3  | 19 |

  | 0  0  8   | 62 |

Now, the augmented matrix is in row-echelon form.

Let's apply back substitution to obtain the values of x, y, and z:

3z = 62  => z = 62/8 = 7.75

-3y + 3z = 19  => -3y + 3(7.75) = 19  => -3y + 23.25 = 19  => -3y = 19 - 23.25  => -3y = -4.25  => y = 4.25/3 = 1.4167

x + y - 2z = 13  => x + 1.4167 - 2(7.75) = 13  => x + 1.4167 - 15.5 = 13  => x - 14.0833 = 13  => x = 13 + 14.0833 = 27.0833

Therefore, the solution to the system of linear equations is:

x = 27.0833

y = 1.4167

z = 7.75

The rank of the coefficient matrix A is 3, and the rank of the augmented matrix [A|B] is also 3. Since the ranks are equal and equal to the number of variables, the system has a unique solution.

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The speed of the aeroplane per hour during the journey is (d) 1550 km/hr.

The time the aeroplane would take to reach its destination if it starts on schedule is T.The distance from the starting point to its destination is D.The speed of the plane from the starting point to its destination is S.When the plane starts 1.5 hours late, it takes T + 1.5 hours to reach its destination at the scheduled time.The distance traveled by the plane under this circumstance is still D.

When the pilot increases the speed of the plane by 800 km/h, the time it takes to travel from the starting point to the destination is reduced by 1.5 hours. So, the time taken to travel the distance D is (T - 1.5) hours.The formula to find speed is distance divided by time.Using these values we can find the speed of the aeroplane.

Solving the equation,D/S = T... equation [1]D/S+800 = T - 1.5... equation [2]Substitute the value of T from equation [1] in equation [2], we get:D/S + 800 = D/(S + 800) - 1.5Solving the equation, we get:S2 - 400S - 3,20,000 = 0S = 1550 km/hr

Therefore, the speed of the aeroplane per hour during the journey is (d) 1550 km/hr.

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The arc length is L = 8.831t.

If the curve has position vector p(x) for value of x ranging from x = a to x = b,

then, the curve's length is calculated as:

\(L = \int_a^b ||p'(x)||dx\\\)

You have the following vector:

r(t) = (4 + 5t)i + (8 + 2t)j + (2 - 7t)k, -1sts

r(t) = {(4 + 5t), (8 + 2t), (2 - 7t)}

To find the arc length you use the following formula:

\(L= \int\limits^a_b( {\dfrac{dx}{dt})^2+( {\dfrac{dy}{dt})^2+( {\dfrac{dz}{dt})^2 } \, dt\)   (1)

Where dx/dt, dy/dt and dz/dt are the components of the vector dr/dt.

Then, we have to calculate dr/dt:

dr/ dt = (5, 2 -7)

Next we have to replace in the integral of the equation (1):

\(L = \int\limits^t_0 {\sqrt{5^2 +2^2 + (-7)^2} } \, dx\)

L = 8.831t

Hence, the arc length is L = 8.831t.

The complete question is

"Find the arc length parameter along the curve from the point where t=0 by evaluating the integral s= V(T) dt. Then find the length of the indicated portion of the curve.

r(t) = (4 + 5t)i + (8 + 2t)j + (2 - 7t)k, -1sts"

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Answer:

we can immediately subtract 5$ from the 150$ cost. leaving us with 145$, then we can divide to see if 145 divided by 9 makes sense. it should be around 16.1111 but thats not a valid answer so we round down to 15. 15x9=145

Step-by-step explanation:

Answer:

The total of Jenny's 5 tests = 375

If she wants an average of 77 then

her 6 tests must total 6 x 77 = 462

462 - 375 = 87 which is what Jenny

must score on the sixth test for an

average of 77.

When x = 2 seconds, the area of the circle formed by the ripples in the pool is 625π square inches. This means that after 2 seconds, the circular ripples have spread out and covered an area of 625π square inches on the surface of the water.

To find (A⁰r)(x) when x=2, we need to find the composition of the two functions A(x) and r(x).

Step 1: Substitute x=2 into the function r(x) to find the radius at x=2:
r(2) = 12.5 * 2 = 25 inches

Step 2: Substitute the result from Step 1 into the function A(x) to find the area:
A(25) = π * (25)² = 625π square inches

So, (A⁰r)(x) when x=2 is 625π square inches.

The value 625π square inches represents the area of a circle at x=2 seconds after the pebble was tossed into the pool of water, based on the given functions.

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No, every 2-approximation algorithm for finding a minimum vertex cover is not necessarily a 2-approximation algorithm for finding a maximum independent set.

The reason for this is that the two problems, minimum vertex cover and maximum independent set, are not symmetric in their definitions and objectives.

In the minimum vertex cover problem, the goal is to find the smallest possible set of vertices that covers all edges in the graph. On the other hand, in the maximum independent set problem, the objective is to find the largest possible set of vertices such that no two vertices in the set are adjacent.

An approximation algorithm for the minimum vertex cover problem guarantees that the size of the vertex cover found by the algorithm is at most twice the size of the optimal minimum vertex cover. This means that the algorithm provides a solution that is within a factor of 2 of the optimal solution.

However, this does not imply that the same algorithm will provide a solution within a factor of 2 of the optimal maximum independent set. The reason is that the concepts of vertex cover and independent set are complementary. A vertex cover is a set of vertices that covers all edges, whereas an independent set is a set of vertices with no adjacent vertices.

Therefore, while a 2-approximation algorithm for minimum vertex cover guarantees that the size of the vertex cover is at most twice the size of the optimal solution, it does not necessarily imply that the algorithm will find a maximum independent set with a size within a factor of 2 of the optimal solution.

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It is based on the given information, the only figure that is definitely a reflection of ABCD is ABCD itself.To determine which figures are reflections of ABCD, we need to understand the concept of reflection. In a reflection, the image is created by flipping the original figure over a line of reflection.

From the given options, we need to analyze each figure and check if it can be obtained by reflecting ABCD.

ABCD: This is the original figure itself.

KLMN: Without more information about the figure KLMN and the line of reflection, we cannot determine if it is a reflection of ABCD.

WXYZ: Without more information about the figure WXYZ and the line of reflection, we cannot determine if it is a reflection of ABCD.

PQRS: Without more information about the figure PQRS and the line of reflection, we cannot determine if it is a reflection of ABCD.

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All of the figures that are reflections of ABCD include the following:

B. KLMN

D. WZYX

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

Generally speaking, all congruent geometric figure are reflections of one another. This ultimately implies that, the geometric figures that are reflections of ABCD must be congruent to it and these include the following under a reflection over the y-axis and x-axis:

KLMN

WZYX

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Complete Question:

ABCD ≅ KLMN ≅ PQRS ≅ WXYZ

Given that information, which figures are reflections of ABCD? Check all that apply.

ABCD

KLMN

WXYZ

WZYX

PQRS

There are 30 different ways in which each person in the group can be friends with exactly 2 other people.

To find the number of different ways in which each person in a group of 6 people is friends with exactly 2 other people, we can use the concept of permutations.

Let's start by selecting two friends for the first person. Since there are 5 remaining people in the group, we can select their friends in (5 choose 2) ways. This can be calculated using the formula:

(5 choose 2) = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = 10

Now, we move on to the second person. They also have 5 remaining people to choose their friends from. However, we need to consider that the first person has already chosen two friends, so there are only 3 remaining options for the second person. Therefore, the number of ways to choose friends for the second person is (3 choose 2) = 3.

Continuing this process, we multiply the number of ways to choose friends for each person: 10 * 3 * 1 * 1 * 1 * 1 = 30.

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Answer:

63

Step-by-step explanation:

Based off of the question,we have a word problem that can be interpreted as the following. 6²+3³= ?

6² is the same as 6×6 which is equal to 36, In other words 6×6=36 or 6²=36

3³ is the same as 3×3×3 which is equal to 27, In other words 3×3×3=27 or

3³=27

Now with the product of each value in the word problem we can set up a statement as the following: 36+27= ?

Which when added together gives us the sum of 63, in other terms 36+27=63

concluding in our answer for the initial word problem. (6²+3³=63)

Answer:

8 pizzas for the party

Step-by-step explanation:

The Italian Kitchen Pizzeria charges $12.99

Budget of $115

How many pizzas to buy?

115 / 12.99 ≈ 8.853 pizzas

We can buy 8 pizzas. ( we do not have enough  money for a ninth )

Answer:

A.

Step-by-step explanation:

Given that point P partitions a directed line segment from A to B into the ratio 3:4, we are to determine how close P is to either A or B.

To do this, we take an example.

Let the length of line segment AB be 14 Units.

Since P divides AB in the ratio 3:4

Therefore, from the above, we can conclude that P will be closer to A as its distance from A is shorter than its distance from B.

The correct option is A.

Answer:

Point P partitions the directed line segment from A to B into the ratio 3:4. Will P be closer to A or B? Why?

A number line goes from point A to point B. A line is drawn from point A to point B.

Right Answer  A.)   P will be closer to A because it will be Three-sevenths the distance from A to B.  

Wrong Answer  B.)   P will be closer to A because it will be Four-sevenths the distance from A to B.

Wrong Answer C.)    P will be closer to B because it will be Three-sevenths the distance from B to A.

Wrong Answer D.)   P will be closer to B because it will be Four-sevenths the distance from B to A.

Step-by-step explanation:

The Reduction in the Price of Computer is $56.25

What is Percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. The term 100% refers to one hundred percent. It is denoted by the sign "%".

Solution:

To solve this problem we need to find 15% of $375

15 * 375 / 100 = 56.25 $

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You have the following system of equations:

x + 3y = 1

y = 2x + 5

in order to solve the previous system, replace the expression y = 2x + 5, into the first equation and solve for x, as follow:

x + 3y = 1

x + 3(2x + 5) = 1 apply distribution property

x + 6x + 15 = 1 simplify lef side

7x + 15 = 1 subtrac 15 both sides

7x = 1 - 15

7x = -14 divide by 2 both sides

x = -14/2

x = -7

replace the previous value of x into the second equation to get y:

y = 2x + 5

y = 2(-7) + 5

y = -14 + 5

y = -9

Hence, the solution to the given system of equations is:

x = -7

y = -9

(-7 , -9)

Answer:

The answer would be B

Step-by-step explanation:

From 1 second to 3 seconds Denise had stopped

We can tell that this is true because looking at the graph we can see that from 1 to 3 seconds the distance stayed the same which indicates that Denise was not walking

Answer:

I think it is B  between 1 and 3 bc a flat line shows no progress and the only area where is show a flat line is between 1 and 3 so he stopped walking at that point

Step-by-step explanation:

The Half Angle Formula for Sin is an equation used to find the sine of half of an angle by using the sine of the original angle. It is written as sin(x/2) = ±√(1/2)(1 ± cosx).

The Half Angle Formula for Sin is an equation used to find the sine of half of an angle by using the sine of the original angle. It is written as sin(x/2) = ±√(1/2)(1 ± cosx). The half angle formula is a useful tool for simplifying trigonometric expressions and for finding the exact value of certain angles. The "±" symbol indicates that the sine of the angle can be either positive or negative, depending on the sign of the cosine of the original angle. The ± sign is also used to indicate that the result of the formula can be either an acute or an obtuse angle. The formula is based on the Pythagorean Identity, which states that sin2x + cos2x = 1. By plugging in the value of the original angle into the formula, we can find the sine of the angle. The half angle formula can be used to find the sine of any angle, such as the sine of a right angle or the sine of an obtuse angle. The formula is also useful for finding the sine of angles that cannot be easily measured with a protractor.

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The sample size must be at least 12 if you want the standard error of the sample average to be 1.5.

To find the sample size needed, we can use the formula for standard error:
SE = σ/√n
Where SE is the standard error, σ is the population standard deviation (which is the square root of the variance), and n is the sample size.
In this case, we are given that the population mean is 100 and the variance is 25, so the standard deviation is √25 = 5.
We want the standard error to be 1.5, so we can plug in the values:
1.5 = 5/√n
To solve for n, we can isolate the variable by squaring both sides:
(1.5)^2 = (5/√n)^2
2.25 = 25/n
n = 25/2.25
n ≈ 11.11
So the sample size must be at least 12 (since we can't have a fraction of a person). This will give us a standard error of approximately 1.5.

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Answer:

\(y=\frac{7}{3}x+7\)

Step-by-step explanation:

\(y=mx+b\\\\y=\frac{7}{3}x+b\\ \\7=\frac{7}{3}(0)+b\\ \\7=b\\\\y=\frac{7}{3}x+7\)

For these kinds of problems, the point-slope formula comes in handy.

The point-slope form (y - y1 = m(x - x1) +b) uses the slope and a point given to find the y-intercept, or in this case, the equation of the line.

First, we plug the known #'s into the equation, then solve.

y - 7 = -7/3( x -0)

y - 7 = -7/3x

   +7        +7

y = -7/3x +7

Therefore, the equation of the line is: y = -7/3x + 7

Hope this helps!

Answer:

The probability of selecting a vowel is 5/26

Step-by-step explanation:

The probability of selecting a vowel

= number of vowels/total number of alphabets

The vowels are a,e,i,o,u = 5

Number of alphabets = 26

The probability is 5/26

The marginal utility per dollar spent on the fifth apple is 60. The correct option is D.

The marginal utility simply refers to the change or extra satisfaction derived from the change in consumption.

Hence, the marginal utility of the fifth apple equals :

Difference /change or extra satisfaction derived by consuming one more than 4 apples = (total utility of 5th apple - total utility of 4th apple)

= (250 - 220) = 30

Hence, marginal utility per dollar: Marginal utility/price per apple

Price per apple = $0.5

Marginal utility of 5th apple = 30

Marginal utility of 5th apple = 30 / 0.5

Marginal utility of 5th apple = 60

Therefore, the marginal utility per dollar spent on the fifth apple is 60. The correct option is D.

Complete question :

If the price of an apple is $0.50, the marginal utility per dollar spent for the fifth apple is:

a) 20

b) 30

c) 40

d) 60

Number of apples ____total utility

2__________________130

3__________________180

4__________________220

5__________________250

6__________________270

7__________________280

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Hence the volume of given figure is 4464 \(m^{3}\)

Quadrilaterals make its  faces A cuboid is a six-sided solid shape known as a hexahedron in geometry. . A cuboid is similar to a cube or a Cuboid as like a short cube.  in the  cuboid can become a cube by variation the angles between the faces or the lengths of the edges.

A measurement of three-Dimensional space is volume. It is frequently expressed quantitatively using US-standard units or SI-derived units, as well as several imperial or Volume and the notion of length are connected.

According to figure ,

The volume of given figure = the volume of upper cuboid +the volume of lower cuboid

we know the the volume of cuboid = l*b*h \(m^{3}\)

so, V = \((l_1*b_1*h_1)+(l_2*b_2*h_2)\\\)

∴V=(11*(30-(9+9)*12) +(30*12*8)

∴V=(11*(30-18)*12) +(30*12*8)

∴V=(11*12*12) +(30*12*8)

∴V=(11*144) +(30*96)

∴V=1584 +2880

∴V=4464  \(m^{3}\)

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The proportion relation between the number of games and the price is given by the proportionality constant k = 4.5

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the number of games be represented as x

Let the cost for the total number of games be y

And , the values of x = { 2 , 5 , 7 }

Now , the values of y = { 9.00 , 22.50 , 31.50 }

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

On simplifying , we get

9 = k ( 2 )

Divide by 2 on both sides , we get

k = 4.5

And , 22.50 = k ( 5 )

Divide by 2 on both sides , we get

k = 4.5

Therefore , the proportionality constant is k = 4.5

Hence , the proportion is y = 4.5x

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The complete question is :

At a flea market, used computer games are sold at the prices shown in the table below.

Number of Games Price ($)

2 9.00

5 22.50

7 31.50

Do the Number of the games and price form a proportional relationship? choose correct response

1. Yes there is a constant of proportionality of 11.25.

2. Yes there is a constant of proportionality of 4.50.

3. No there is not a constant of proportionality.

4. No the Slope is 4.5

x=4

y=2

solve the equations together to get value of x and y

Answer:

The value are

x=4

y=2

Step-by-step explanation:

x+y=6 1

x-y=2 2

Using Substitution Method

From equation 2

x=y+2 3

input equation 3 into equation 1

(y+2)+y=6

y+y+2=6

2y+2=6

2y=6-2

2y=4

divide both sides by 2

2y/2=4/2

y=2

input into equation 3

x=y+2

x=2+2

x=4