Practice 21: Combine the like terms to make a simpler expression
A. -3n-7+6n + 1
B 7x+5-3x
D. 12x² -5+7x² - 11x
a)
C. 6x + 4 + 15-7x
E 6g + 11 + 8g² - 15w
1 point

The perimeter of the rectangle 24x + 1 feet. The perimeter of a geometric figure is the total length of its sides.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

To find the perimeter of a rectangle, you need to add the lengths of all four sides of the rectangle.

The width of the rectangle is 4x-7.5 feet and the length is 7.5x+8 feet.

The perimeter is therefore equal to 2 times the sum of the width and the length,

= 2 * (4x-7.5 + 7.5x + 8) feet.

This simplifies to 2 * (12x + 0.5) feet,

which is equal to 24x + 1 feet.

The perimeter of the rectangle 24x + 1 feet

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Assume the account earns 7% simple interest. in your account now. You would need to deposit $3,007.52 in your account.

1541 days = 4.2219 years

Hence,

Time = 4.2219 years

Interest rate = 7%

Principal = $4,000

Hence,

4000=Po(1+.07)^4.2219 years

4000=1.33×Po

Po = 4,000 /1.33

Po = $3,007.52

Therefore the amount you need to deposit is  $3,007.52.

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The distance between  Bowtown to Dovebury is 39.

The total distance Dave will drive is 54 miles.

What is meaning of  total distance?

Total distance refers to the actual travel distance between the origin and destination locations of the material.

Given table is

Aranville

24                 Bowtown

37                        20           Cliffton

18                         39               17           Dovebury

From the table, the distance from Bowtown to Dovebury is 39miles.

The distance between Aranville to Cliffton is 37 miles.

The distance between Cliffton to Dovebury is 17 miles.

Dave wants to drive from Aranville to Cliffton and then from Cliffton to Dovebury.

Total distance is (37 + 17) miles = 54 miles

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The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.

It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.

First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.

On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.

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The fourth term of the recursive sequence in this problem is given as follows:

[tex]a_4 = 15[/tex]

The nth term of a recursive sequence is obtained applying the recursive rule n times, considering that the first term of the sequence is given.

The recursive rule for this problem is given as follows:

[tex]a_n = 2a_{n - 1} + 1[/tex]

The first term of the sequence is given as follows:

[tex]a_1 = 1[/tex]

Then the second term of the sequence is given as follows:

[tex]a_2 = 2(1) + 1 = 2 + 1 = 3[/tex]

The third term of the sequence is given as follows:

[tex]a_3 = 2(3) + 1 = 6 + 1 = 7[/tex]

The fourth term of the sequence is given as follows:

[tex]a_4 = 2(7) + 1 = 14 + 1 = 15[/tex]

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The system of equation to describe Tammy and Luke's outcome is as follows:

5x + y = 23

8x + 5y = 30

Tammy and Luke take part in a game in which they earn the same number of points for each catch and lose the same number of points for each miss.

let

x =  number of points for a catch

y = the number of points for a miss.

Tammy makes 5 catches and misses 1, ending the game with 23 points.

Therefore,

5x + y = 23

Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points. Therefore,

8x + 5y = 30

Hence, the combine equation to describe the outcome is as follows:

5x + y = 23

8x + 5y = 30

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The equation is y = 15x + 90. The initial value is 90. Rate of change is: 15.

To host a party at a local restaurant, you must pay $90 to rent it and $15 per guest.

To write a linear equation that models a situation in slope-intercept form, y = mx + b, find the following:

Given the table above, the value of y when x = 0 is 90. This means the initial value (b) = 90.

Using two pairs of values from the table, (0, 90) and (6, 180):

Rate of change (m) = (180 - 90) / (6 - 0) = 15

Substitute m = 15 and b = 90 into y = mx + b, to write the equation:

y = 15x + 90.

The graph of y = 15x + 90 is shown below.

The complete table is:

x   |  y  

0    90

3    135

6    180

9    225

12   270

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Answer:

[tex]x = \frac{26 + 8 \sqrt{10} }{9} [/tex]

or

[tex]x = \frac{26 - 8 \sqrt{10} }{9} [/tex]

Step-by-step explanation:

I apologise for my messy explanation.

The solution of the expression will be;

⇒ x = 5.7

or ⇒ x = 0.07

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ log ₂ (3x + 2) - log ₄ (x) = 3

Now,

Since, The expression is,

⇒ log ₂ (3x + 2) - log ₄ (x) = 3

Solve as;

⇒ log ₂ (3x + 2) - 1/2 log ₂ (x) = 3

⇒ log ₂ (3x + 2) - log ₂ √(x) = 3

⇒ log ₂ (3x + 2) / (√x) = 3

⇒ (3x + 2) / √x = 2³

⇒ (3x + 2) / √x = 8

⇒ (3x + 2) = 8√x

Taking square both side, we get;

⇒ (3x + 2)² = (8√x)²

⇒ 9x² + 12x + 4 = 64x

⇒ 9x² + 12x - 64x + 4 = 0

⇒ 9x² - 52x + 4 = 0

By applying quadratic formula, we get;

⇒ x = - (- 52) ± √ (-52)² - 4×9×4 / 2×9

⇒ x = 52 ± √ 2704 - 144 / 18

⇒ x = 52 ± √2560 / 18

⇒ x = 52 ± 50.6 / 18

This gives two solution as;

⇒ x = (52 + 50.6) / 18

⇒ x = 102.6/18

⇒ x = 5.7

And, We get;

⇒ x = 52 - 50.6 / 18

⇒ x = 1.4 / 18

⇒ x = 0.07

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The correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams

A confidence interval, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.

Since the 95% confidence interval for the mean weight of apples in an orchard at a specific given time is between 147 grams to 151 grams.

This follows that from our definition of confidence interval and 95 % confidence interval, that there is a 95 % confidence that the mean weight of the apples in the orchard lies between 147 grams to 151 grams.

So, the correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams

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David's three exam scores are B. 84, 88, 98

From the information, David took three exams. The median score of his exams was 88, the mean score was 90, and the range was 14.

The scores are 84, 88, and 98. The middle number is 88. It's the median.

The mean is:

= (84 + 88 + 98) / 3

= 270 / 3.

= 90

Range will be:

= Highest number - Lowest number

= 98 - 84

= 14

In conclusion, the correct option is B.

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The amount of money earned by Zach each week will be equal to $9 per week.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given data in the question,

Total amount earned by Zach = $36

The time taken to earn the amount = 4 weeks

Then, the amount earned each week will be.

= $36/4

= $9 per week

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Using the Leading Coefficient Test the end behavior of the function  f(x) = 1234999x as the values of x increase towards infinity, ∞ is the functin also tends to infinity

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = 1234999x

The end behavior is determined by the leading Coefficient = 1234999, the problem has only one variable and hence the leading coefficient

x ⇒ ∞ f(x) ⇒ ∞

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The hypothesis, at the 0.05 significance level,

H₀ : the observed distribution of X may be fitted by the geometric distribution

Hₐ : the observed distribution of X may not be fitted by the geometric distribution

we conclude p-Value > α so, cannot reject null hypothesis. The observed distribution of X may be fitted by the geometric distribution g(x ; 1 / 2), x=1,2,3

A coin is thrown until a head occurs and the number X of tosses recorded.

The probability that head occur on toss ,p = 0.5

Consider the null and alternative hypothesis,

H₀ : the observed distribution of X may be fitted by the geometric distribution

Hₐ : the observed distribution of X may not be fitted by the geometric distribution

The chi square test statistic here as:

χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ

where Oᵢ--> observed value

Eᵢ --> expected value

and the expected frequencies for each X here E(x) = P(X = x) = 256×g(x)

The probability mass function of geometric distribution with parameter 1/2 is g(x) = (1/2)(1 - 1/2)⁽ˣ⁻¹⁾

where x = 0, 1,2 ,3,......

Observed values are f :136 60 34 12 9 1 3 1

Using the data,we calculate the expected values

E₁ = P( x = 1) = 256×g(1) = 256×(1/2)(1/2)⁰

= 128

E₂ = P( x =2) = 256×g(2) = 256×(1/2)(1/2)¹

= 64

E₃ = P( x = 3) = 256×g(3) = 256×(1/2)(1/2)² = 32

E₄ = P( x = 4) = 256×g(4) = 256×(1/2)(1/2)³

= 16

E₅ = P( x = 5) = 256×g(5) = 256×(1/2)(1/2)⁴

= 8

E₆ = P( x = 6) = 256×g(6) = 256×(1/2)(1/2)⁵

= 4

E₇ = P( x = 7) = 256×g(7) = 256×(1/2)(1/2)⁶

= 2

E₈ = P( x = 8) = 256×g(8) = 256×(1/2)(1/2)⁷

= 1

Hence, χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ

= (136 - 128)²/128 + (60 - 64)²/64 + (34 - 32)²/32 + (12-16)²/16 +(9 - 8)²/8 + (1 - 4 )²/4 + (3 - 2)²/2 +(1 - 1)²/1

= 0.5 + 0.25 + 0.125 + 1 + 0.125 + 2.25 + 0.5 =4.75

Significance level is α =0.05

Using the χ² table, the p- value for χ² is 0.6290 .. Now P value > 0.05 , therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we have sufficient evidence here that the frequencies given are fitted by the geometric (p = 0.5) distribution.

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The equation of line that passes through point (-8, 1) and parallel to x - 4y = 4 is x - 4y + 12 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

The given equation is,

x - 4y = 4.

The slope of the given equation,

m = 1/4

The slope of the required line will be equal to given line if line is parallel.

The equation of line that passes through point (-8, 1) and parallel to line x - 4y = 4.

y - 1  = m (x - (-8))

y - 1 = 1/4.(x + 8)

4y - 4 = x + 8

x - 4y + 12 = 0

The required equation of line is x - 4y + 12 = 0.

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Answer:

x = 9

Step-by-step explanation:

Use Vertical Angles and Supplementary Angles to put all the given information inside the triangle.

Then use the idea that the three angles in a triangle add up to 180° to write an equation.

see image.

Actually also--shortcut! The 150° is an exterior angle, so it is equal to the

90° + 5x+15

90 + 5x + 15 = 150

this calculation comes out the same as the other.

Answer:

  x = 9

Step-by-step explanation:

Given a right triangle with an exterior angle of 150°, and a vertical angle to the other acute angle marked as 5x+15, you want to solve for x.

The exterior angle is equal to the sum of the remote interior angles. One of those is the right angle; the other is a vertical angle with respect to the one marked 5x+15. So, we have ...

  150 = 90 + (5x +15)

  45 = 5x . . . . . subtract 105

  9 = x . . . . . . divide by 5

The value of x is 9.

Answer: x = 11

Step-by-step explanation: set both angles equal to 90 bc a triangle is 180 minus the 90 degree angle

Answer:

54.33

Step-by-step explanation:

Answer:

54.33

Step-by-step explanation:

Addition or a calculwtor can be used

We have proved that the ray FE is parallel to the ray GC.

What is meant by parallel lines?

In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.

Angle DEF intersects at B

which results in angle DEF corresponding to the angle  ACG.

As DEF = 45 so angle ACG = 45

So by the above discussion, we can say that the ray FE is parallel to the ray GC.

Hence, we have proved that the ray FE is parallel to the ray GC.

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Answer:

1.135,

3.718,

and 8.389

Step-by-step explanation:

Answer:

[tex]x=-2,\;y\approx\boxed{1.135}[/tex]

[tex]x=1,\;y\approx\boxed{3.178}[/tex]

[tex]x=2,\;y\approx\boxed{8.389}[/tex]

Step-by-step explanation:

Euler's number, denoted as the letter "e", is a mathematical constant approximately equal to 2.7182818 ( 7 d.p.).

To evaluate [tex]y=e^x+1[/tex] for the given values of x, substitute the value of x into the equation and evaluate using a calculator, rounding the final answer to 3 decimal places (nearest thousandth).

[tex]\begin{aligned}x = -2\implies y&=e^{-2}+1\\y&=0.135335...+1\\y&=1.135335...\\y&=1.135\end{aligned}[/tex]

[tex]\begin{aligned}x =1\implies y&=e^1+1\\y&=2.7182818...+1\\y&=3.7182818...\\y&=3.718\end{aligned}[/tex]

[tex]\begin{aligned}x = 2\implies y&=e^{2}+1\\y&=7.389056...+1\\y&=8.389056...\\y&=8.389\end{aligned}[/tex]

Answer:

x = 6

Explanation:

If x is reserved for the number of hours it'll take, then the first equation is saying that $6 is being multiplied by an x amount of hours, which is then added by $30. The second equation states that $11 is being multiplied by an x amount of hours, but there is no flat fee. This makes the equation:

6x + 30 = 11x

The steps to solving this are:

1) Make the variables on one side. In this case, it is easier to put them on the right.

11x - 6x = 5x

5x = 30

2) Divide both sides by 5.

5x / 5 = 30 / 5

x = 6

This means it will take 6 hours for them to charge the same amount of money.

The volume of a sphere is 33409.6 cm³ and the volume of a cube is 8000 cm³. Therefore, the volume of water 8000 cm³ can fit in the sphere.

Given that, a cube with an edge of 20 cm is filled with water.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

We know that, the volume of cube =a³, where a=edge

Here, volume of cube =20³

= 8000 cm³

Radius of sphere is 20 cm

As we know, the volume of sphere = 4/3πr³

= 4/3 ×3.14×20³

= 1.33×3.14×8000

= 33409.6 cm³

The volume of a sphere is 33409.6 cm³ and the volume of a cube is 8000 cm³. Therefore, the volume of water 8000 cm³ can fit in the sphere.

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Class members that should be the public are: Constructors, accessors/ mutators and methods the user needs to manipulate the objects of the class. The correct answer is c. I, III, V.

All members declared in a class as well as all members (apart from constructors and finalizers) defined in all classes in its inheritance structure are considered to be members of the class. Although they are inherited, derived classes cannot access private elements of base classes.

Class members are all the members (apart from constructors and destructors) defined in the class, as well as all the classes in its inheritance structure. Members of a class may be any of the following: Constant values represented by constants. Variables represented by fields.

If you want the class to be instantiated from anywhere, you must make the constructor public. If you want a class to be inheritable and its inherited classes to be instantiated, you must make the constructor protected.

A technique used to regulate changes to a variable is known as a mutator method. They're also frequently referred to as setter methods. A getter, often referred to as an accessor, frequently follows a setter and returns the value of the private member variable.

Therefore, the correct answer is (c). I, III, V.

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Answer:

The inverse of f is x=8

Step-by-step explanation:

I did it

Measure of angle AKQ is 90°.

There are several different kinds of angles in geometry. Angle is one of the most significant and fundamental units. When two rays or lines are connected at their common terminus, an angle is created. Angles are used in many facets of daily life, including the construction of buildings, dams, and statues, starting with a pizza slice. Angle has a crucial role in civil engineering. A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.

Given

Measure of angle AKQ is 90°.

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Answer:

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 110.5° is added to the data, how does the mean change and by how much?

80.41 to 82.7

The mean increases by 2.7°.

The means stays at 80.4°.

The mean stays at 82.7°.

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 58° is changed to 101°, which of the following measures changes the most and what is the new value?

Mean 84°

Range 48°

IQR 32°

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 101° is added to the data, how does the mean change?

80.42 to 82

The mean decreases by 1.6°.

The mean decreases by 8.4°.

The mean increases by 8.4°.

Step-by-step explanation:

The associative property states that the order in which three or more numbers are added or multiplied does not affect the result of the operation. You can apply the associative property to the expressions A. 9-5-2, B. 5+3-2, and D. 7+3+1.

In expression A, 9-5-2, you can rearrange the numbers as follows: 9-5-2 = (9-5)-2 = 4-2 = 2.

In expression B, 5+3-2, you can rearrange the numbers as follows: 5+3-2 = (5+3)-2 = 8-2 = 6.

In expression D, 7+3+1, you can rearrange the numbers as follows: 7+3+1 = (7+3)+1 = 10+1 = 11.

You cannot apply the associative property to expression C, 8÷4÷1, as this is a division expression, and the associative property does not apply to division.

Overall, the associative property allows you to rearrange the order of addition or multiplication of three or more numbers without affecting the result of the operation.

The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A mathematical principle that states the product of a multiplication issue is unaffected by the way the elements are organized.

The associative property for addition and multiplication is valid but not for division.

The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.

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While China has pulled hundreds of millions out of poverty, it has done so at the expense of the right to free speech and government.

China is a Communist country ruled by the Communist Party in a one-party state.

As a result, there are few political liberties because everything must adhere to the party's criteria. This means that while China's economy has been flourishing for decades, lifting people out of poverty has come at the expense of their freedom.

This is why Tiananmen Square movements for democracy were crushed, and Hong Kong protesters are being suppressed.

China is giving its people economic rights by lifting them from poverty, but has taken their political rights away.

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The horizontal force that the student exert on the boat is 120 N toward the front of the boat.

What is third law of Newton ?

As per the third law of Newton, the force exerted by the boat over the student is equal in magnitude to the force that the student exerted on the boat.

So, calculate the force on the student using the second law of Newton, Force = mass * acceleration.

Force on the student = 60 kg * 2.0 m/s^2 = 120 N.

=> horizontal force exerted by the student on the boat = 120 N

Answer: option d. 120 N. toward the back of the boat.

Of course it is toward the back because that is where the student jumped from..

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Answer:

693.2

Step-by-step explanation:

6.932 · 100

Move the point two times to the right

693.2

Answer:

Doing the math, it should be 7.25/1