which two equivalent to 4(7x + 2 + x)?

The area of the new triangle is  600ft²

To increase the size of a triangle by a scale factor of 10/3, multiply each dimension of the triangle by 10/3.

The new dimensions of the triangle will be:

10/3 × 9ft = 30ft

10/3 × 12ft = 40ft

The area of a triangle is given by the formula A = 1/2  × b  ×h,

where b is the length of the base and h is the height of the triangle.

Thus, the area of the new triangle will be:

A = 1/2  × 30 × 40 = 600ft²

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Miguel only wins $2 in one of the six tournaments, and he only loses $1 in the other five.

Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a large group of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.

given

We identify the chips so that we can check all six events. Let's say two chips each have a designated 1: R1 and B1 (as if they were red and blue). Let's now consider all possible combinations.

There are 4 options for the first chip, and 3 options remain for the second chip.

There are 12 combinations as a result. There are just six combinations since we don't care about the sequence; for instance, R1, 3 is the same as R1, 3 to us. (R1, B1), (R1, 3), (R1, 5), (B1, 3), and (B1, 5) are the combinations (3,5) Miguel only wins $2 in one of the six tournaments, and he only loses $1 in the other five.

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Answer:

The scale of the model is (21 ft / 3 in) = 7 ft / 1 in. So an 84 foot building would be (84 ft / 7 ft) * 1 in = 12 inches tall in the model.

Step-by-step explanation:

hope it helps

Answer:

588 inches

Step-by-step explanation:

First, find the scale factor of the model by dividing the height of the real building by the height of the model: 21 ft / 3 inches = 21/3 = 7

7 inches/ft

Then, multiply the scale factor by the height of the 84 foot building to find the height of the model: 7 inches/ft * 84 ft = 7*84 = 588

588 inches

Answer: what

Step-by-step explanation:

The reference angle of 7pi/4 is pi/4

The acute angle formed by the terminal arm or side and the x-axis is known as the reference angle.

There is always a positive reference angle. The reference angle is, in other words, the angle formed by the terminal side and the x-axis. It must always be positive and less than 90 degrees.

considering angle 7 pi/4, the angle is pi/4 away from 2 pi.

7 pi/4 + pi/4 = 8 pi/4 = 2 pi

We can therefore conclude that 7 pi/4 is an angle on the third quadrant and the reference angle is pi/4.

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The required first five terms of the sequence are 2, 10, 50, 250, and 1250.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The first five terms of the sequence, a(n), defined by the recurrence relation a(n+1) = 5a(n) and a(1) = 2, are as follows:

a(1) = 2

a(2) = 5a(1) = 5 × 2 = 10

a(3) = 5a(2) = 5 × 10 = 50

a(4) = 5a(3) = 5 × 50 = 250

a(5) = 5a(4) = 5 × 250 = 1250

Therefore, the first five representations of the sequence are 2, 10, 50, 250, and 1250.

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Answer:

[tex]\frac{13}{17}[/tex]

Step-by-step explanation:

just a tip use math-way in the future it's always been great

Hope this helps!

Hello there!

Answer:

[tex](9, +\infty)[/tex]

Step-by-step explanation:

It has no real roots only if

[tex] \sqrt{b {}^{2} - 4ac } [/tex]

has no roots. That means that b² - 4ac is smaller than 0:

[tex]b {}^{2} - 4ac < 0 \\ 12 {}^{2} - 4 \times 4 \times k < 0 \\ 144 - 16k < 0 \\ 144 - 144 - 16k < - 144 \\ - 16k < - 144 \\ k > 9 \\ k \: \: \: in \: \: \: (9, +\infty)[/tex]

we can approach this from the standpoint of the discriminant, if the discriminant is negative then we only get complex roots or namely "imaginary" solutions or values, well, let's check before that happens, when the discriminant is 0.

[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+k} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]

[tex]0=(12)^2 - 4(4)(k)\implies 0=144-16k\implies 16k=144 \\\\\\ k=\cfrac{144}{16}\implies k=9\hspace{5em} \stackrel{if~k > 9\textit{, then we land on negative territory}}{{\Large \begin{array}{llll} k > 9 \end{array}}}[/tex]

a) The patient weight in pounds is 234 lbs.

b) The patient weight in kilograms is 106.36 Kg.

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

The patient’s weight is 245 lbs.

Each week patient loses = 1 Kg

So, In 5 week patient loses = 5 Kg

As, 1 kg = 2.2 lbs

In 5 week patient loses = 11 lbs

a) The weight of the patient after 5 weeks = 245 lbs. - 11 lbs.

                                                                      = 234 lbs.

b) The weight of the patient after 5 weeks =  234 lbs.

The weight of the patient after 5 weeks in Kg

= 234 lbs x 1 kg per 2.2 lbs.

= 106.36 kg

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On solving the provided question, we can say that - by the help of unitary method the value of 9 units will be

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

cost for the 12 classes = $72

cost of 1 unit = $6

cost of 9 units = $54

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Answer:A two-way table, also known as a contingency table, is a way to organize and present categorical data in a tabular format. It can be used to show the relationship between two categorical variables, such as whether a student lives with a grandparent and the number of people who live in their home.

Based on the information you provided, the two-way table would look like this:

More than 4 people | 6 | 10

4 or fewer people | 4 | 30

It should be noted that the information you provided does not add up to 50 students.

Total for students living with grandparents: 10,

Total for students with more than 4 people: 6+10 =16.

Let me know if this table is incorrect and I'll provide you with more information

Step-by-step explanation:

The next step in the series is, shown in Option C.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

There are three steps are shown.

Now, In first step, only one line shown.

In second line the line is left to first line.

And, So on.

Hence, The next step in the series is, shown in Option C.

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For this problem, we know that the line's function is equal to 3 if X isn't 0. That means that for every X that isn't 0, we'll have a line at y = 3 (since we know that g(x) is just fancy for y!). We're also given that if X is equal to 0, it must be at y = 4.

Therefore, your graph should have a straight line through y = 3 EXCEPT at x = 0! At x = 0 you should just have a shaded dot at y = 4.

Need to find the x and y: The Graph asking in question is attached below:

A graph is a type of data structure used to represent relationships between different objects. It consists of nodes, which are connected by edges. The nodes represent the objects, while the edges represent the relationships between them. Graphs can be used to represent many different types of information, such as road networks, social networks, and even computer networks. Graphs can be used to solve a variety of problems, such as finding the shortest path between two nodes, or finding the most efficient way to route data throughout a network. Graphs can be represented in a variety of ways, such as in the form of a table, a map, or a diagram. In addition, graphs can be used to represent abstract concepts such as relationships between individuals.

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Step-by-step explanation:

first of all, if he continuously earns only $160 per month (or at least in that dimension), then he will not have to pay any income tax.

but to do the exercise :

100% = $160

1% = 100%/100 = 160/100 = $1.60

10% = 1% × 10 = 1.6 × 10 = $16

he earns after tax

160 - 16 = $144

FYI :

when we combine all the calculations above into one sequence, then we know

100% - 10% = 90%

and 90% of 100% is 100% × 0.9

and so he earns after tax

160 × 0.9 = $144

Rami's glass is fuller than Will's glass by 1/8

From the question, we have the following parameters that can be used in our computation:

Rami's glass is 1/2 full. Will's glass is 3/8 full.

Convert the fractions to decimal

This gives

Rami's glass is 0.5 full. Will's glass is 0.375 full.

0.5 is greater than 0.375

So, Rami's glass is fuller

To do this, we calculate the difference

So, we have

Difference = 0.5 - 0.375

Evaluate

Difference = 0.125

Rewrite as

Difference = 1/8

Hence, it is 1/8 fuller

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The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .

Given equations ,

[tex]x^{2}[/tex] + 81 = 0  ,[tex]x^{2}[/tex]-22 = -26 , 3[tex]x^{2}[/tex]-18=21 ,2[tex]x^{2}[/tex] +15 = -13

What is Quadratic equation ?

quadratic equation can be defined as the equation which is in the form of a[tex]x^{2}[/tex]+bx + c = 0 .

where a,b,c are constants .

By solving we get ,

[tex]x^{2}[/tex] +81 = 0

[tex]x^{2}[/tex] = -81

x = 9i , -9i

[tex]x^{2}[/tex] - 22 = -26

[tex]x^{2}[/tex] = -26 + 22

[tex]x^{2}[/tex] = -4

x = 2i,-2i

3[tex]x^{2}[/tex] - 18 = 21

3[tex]x^{2}[/tex] = 18+21

3[tex]x^{2}[/tex] = 39

[tex]x^{2}[/tex] = 13

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex]

2[tex]x^{2}[/tex] +15 = -13

2[tex]x^{2}[/tex]  = -13-15

2[tex]x^{2}[/tex]  = -28

[tex]x^{2}[/tex]  = -14

x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i

Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .

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Taking into account the definition of a system of linear equations, the number of sodas and hot dogs sold is 92 and 45 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

The values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y= 137

x= y + 47

To solve a system of equations by the substitution method, an unknown quantity must be solved in one of the equations. Substitute the expression of this unknown in the other equation, obtaining an equation with only one unknown and thus be able to solve it. The value obtained is substituted in the equation in which the unknown appeared. In this way, the two values obtained constitute the solution of the system.

In this case, substituting the second equation in the first one you get:

y + 47 + y= 137

Solving:

y+ y= 137 -47

2y= 90

y= 90÷2

y= 45

Replacing this value in the second equation, you get:

x= 45 + 47

x= 92

Finally, the number of sodas sold is 92 and the number of hot dogs sold is 45.

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The action which would be better is the latter since it provides a higher average return in the span of 5 years.

This is referred to as the concept of increasing a firm's worth to increase the value of stockholders' shares and it is usually considered a long-term goal.

In this scenario, the action which involves the stock price rising from Rs. 1600 to Rs. 3000 provides a higher average return in the span of 5 years which is a long-term goal since it is assumed that shareholders invest in a company to meet their long-term financial goal and the corporate actions which have these general tendencies is lending to people and organizations at a proposed interest rate.

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Work Shown:

[tex]\left(3\text{x}^2\text{y}^5\right)^3\\\\\left(3\right)^3\left(\text{x}^2\right)^3\left(\text{y}^5\right)^3\\\\27\text{x}^{2*3}\text{y}^{5*3}\\\\27\text{x}^{6}\text{y}^{15}\\\\[/tex]

Explanation:

The outer exponent 3 is "distributed", so to speak, to each term inside the parenthesis. This isn't the actual distribution rule. But we can think of it as such. This is what's happening in the second step.

So we'll cube the coefficient 3 to get 3^3 = 27, and we'll cube x^2 to get x^6, and finally cube y^5 to get y^15.

I used the rule [tex](a^b)^c = a^{b*c}[/tex] for the third step.

Answer:y=

Step-by-step explanation:Firstly let's find the slope which is (7-7)/(4-(-3))=0. Using the point slope formula y-y1=m(x-x1) we plug in one of the points and simplify y-7=0(x-4). Simplifying and solving for y gives us y=

x = 3/4 is the correct solution of the given expression.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

The expression Lin tried to solve
8(x-3)+7=2x(4-17)

Simplifying the expression,
8x - 24 = 2x(-13)
8x - 24 = -26x
8x+26x = 24
32x = 24
x = 24/32
x = 3/4

Thus, x = 3/4 is the correct solution of the given expression.

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In order to win his master's tournament, William needs to make the most of his strengths and use the strategies that best suit his playing style.

Mathematics is the study of numbers, shapes, and patterns. It is a universal language that helps us to understand and describe the world around us. Math is used to solve problems and to make predictions. It is used to analyze data and to make decisions. Math is a powerful tool that allows us to communicate ideas and to make sense of the world. Math helps us to understand the physical laws that govern the universe and to make sense of our ever-changing world.

First and foremost, he needs to focus on improving his technical skills. He should practice using a variety of shots and playing on different surfaces. This will give him the confidence and control he needs to succeed.

William should also develop a strategy for each match. This should include analyzing his opponent’s playing style and strengths, understanding the court conditions, and setting a specific set of goals for each game. He should also practice mental conditioning to help him stay focused and be able to handle the pressure.

Finally, William should take care of his physical health. This includes getting enough sleep, eating healthy, and exercising regularly. He should also make sure he is properly hydrated and fueled during the tournament.

By taking the necessary steps and making the most of his strengths, William can put himself in a good position to win the tournament. With hard work and dedication, he can make his dream a reality.

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In order to win his master's tournament, William needs to make the most of his strengths and use the strategies that best suit his playing style.

Mathematics is the study of numbers, shapes, and patterns. It is a universal language that helps us to understand and describe the world around us. Math is used to solve problems and to make predictions. It is used to analyze data and to make decisions. Math is a powerful tool that allows us to communicate ideas and to make sense of the world. Math helps us to understand the physical laws that govern the universe and to make sense of our ever-changing world.

First and foremost, he needs to focus on improving his technical skills. He should practice using a variety of shots and playing on different surfaces. This will give him the confidence and control he needs to succeed.

William should also develop a strategy for each match. This should include analyzing his opponent’s playing style and strengths, understanding the court conditions, and setting a specific set of goals for each game. He should also practice mental conditioning to help him stay focused and be able to handle the pressure.

Finally, William should take care of his physical health. This includes getting enough sleep, eating healthy, and exercising regularly. He should also make sure he is properly hydrated and fueled during the tournament.

By taking the necessary steps and making the most of his strengths, William can put himself in a good position to win the tournament. With hard work and dedication, he can make his dream a reality.

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The value of the x is 10.

What is the exterior angle theorem?

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.

We have given,

angles of the triangle:

Interior angles :

∠D = 2x + 7,

∠E = 26°,

Exterior angle:

∠C = 6x - 7

To find x = ?

few common properties about the angles of a triangle:

A triangle has 3 internal angles which always sum up to 180 degrees.

It has 6 exterior angles and this theorem gets applied to each of the exterior angles.

Note that an exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.

Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon.

So,

∠C  = ∠D + ∠E

6x - 7 = 2x + 7 + 26,

6x - 7 - 2x - 7 = 26,

4x - 14 = 26,

4x = 40

x = 40/4

x = 10,

Hence, the value of the x is 10.

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Answer:

4 7

Step-by-step explanation:

The proof that the angles m<1 = m<4 is shown below

From the question, we have the following parameters that can be used in our computation:

Measure of angles

The angle measurements are then given as

m<1 + m<2 = 90 and m<3 + m<4 = 90

The relationship to prove is also given as

m<1 = m<4

Using the above as a guide, we have the following:

Subtract the equations m<1 + m<2 = 90 and m<3 + m<4 = 90

This gives

m<1 + m<2 = 90

-(m<3 + m<4 = 90)

Evaluate the difference

m<1 + m<2 = m<3 + m<4

When both sides of the angle equations are compared, we have:

m<1 = m<4

m<2 = m<3

Ignoring the second equation, we have

m<1 = m<4

Hence, the measure of the angles has been proved

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Answer:

[tex]4x^2+4vx + v^2[/tex]

Step-by-step explanation:

[tex](2x+v)^2 \\(2x)^2+2(2x)(v)+(v)^2\\4x^2+4vx + v^2[/tex]

To find the sum or difference we must know what k is however you can simplify the expression by rewriting and removing the parenthesis furthermore collecting the like terms to get the solution.

Attached photo shows the steps to the solution :P