A rectangle has a length of x centimeters and a width of 20 centimeters.
Which expression represents the perimeter of the rectangle?

Answer: The answer is -34 3/16

Step-by-step explanation:

−51/2 + 63/4(−41/4)

=−51/2 + −2583/16

= −2991/16

= -34 3/16

Answer:

3.7252903e-9

Step-by-step explanation:

(((128^(negative 3)) / 4)*(2^(negative 3))) / 4 = 3.7252903e-9

The situations are classified as survey, observational study or experiment as follows:

3. Experiment.

4. Observational study.

5. Survey.

6. Survey.

7. Survey.

The definitions for each of these three cases are given as follows:

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The activity that burns calories at a faster rate is; Basketball

The general equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given the equation;

y = 11x that represents the calories Jamila burns when cross-country skiing, where x is time in minutes and y is number of calories

Thus, the rate at which calories are burned is 11 calories per minutes.

In hours, this is; 60 * 11 = 660 calories per hour

From the graph, we see that the rate at which calories are burned = 1500 calories for every 2 hours. Thus;

Rate at which calories are burned = 1500/2 = 750 calories per hours

This is more than that burned when skiing

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The second inequality in the system tells us about the budget of the cost of each package of notepad.

A mathematical comparison of two integers or algebraic expressions that uses the terms greater than, larger than or equal to, less than, or less than or equal represents inequalities.

Given that the budget for the notepads is $160.

Assume the cost of package of 24 is $16 for each package and the cost of package of 6 is $5.40 for each package.

The second inequality in the system of equations represents the equation of the budget that would be spent to buy the notepads.

Hence, 16x +5.40y ≤ 160 represents the budget.

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The probability of (A, A) if two cards are randomly selected with replacement is B. one ninth.

It is important to note that probability is the chance that a particular thing or event will happen. It is the occurence of likely events.

In this situation, a set of 3 cards, spelling the word ADD, are placed face down on the table and we want to determine P(A, A) if two cards are randomly selected with replacement.

The probability will be:

P(A) × P(A)

= 1/3 × 1/3

= 1/9

In conclusion, the correct option is B.

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Answer:

20 months

Step-by-step explanation:

Define the variables:

Create an equation for the total costs of renting each apartment:

To calculate how many months it will take for the costs to be the same, substitute the equation for Apartment A into the equation for Apartment B and solve for m:

[tex]\implies 1000 + 1200m = 1500 + 1175m[/tex]

[tex]\implies 1000 + 1200m - 1175m = 1500 + 1175m - 1175m[/tex]

[tex]\implies 1000 + 25m = 1500[/tex]

[tex]\implies 1000 + 25m - 1000 = 1500 - 1000[/tex]

[tex]\implies 25m = 500[/tex]

[tex]\implies 25m \div 25 = 500 \div 25[/tex]

[tex]\implies m = 20[/tex]

Therefore, it will take 20 months for the costs to be the same.

Check by substituting m = 20 into both equations:

[tex]\begin{aligned}\textsf{Apartment A}: \quad c &= 1000 + 1200(20)\\ &= 1000 + 24000\\ &= 25000\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Apartment B}: \quad c &= 1500 + 1175(20)\\ &= 1500 + 23500\\ &= 25000\end{aligned}[/tex]

As the total cost for both apartments is $25,000 after 20 months, this proves that it will take 20 months for the costs to be the same.

Answer:The slope is 9, for every X value it goes up 9 times the Y value, so the Slope is 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

What you do if first you draw your rectangle. You name length as x (as told in the question) and width as x-3 (since the width is 3 feet less). To obtain the area you have to do x × (x-3) because to find area you do length × width right.

So area is x(x-3) and it also tells you that area is 54 there

That's how you get x(x-3)=54

Now to solve it, you have to expand

x(x-3)=54

x²-3x-54 = 0 (you have to factorise this now)

(x+6) or (x-9) = 0

x = -6 or x = 9

As you can see you have two answers there. We have to eliminate the -6 because length can never be negative. The logic is simple, any length you take for example on a ruler (it has to be 0 or above) you can measure 1 feet, 2 feet, even 100 feet but you can't measure less than 0 right?

So the final answer is that x=9 and x represents the length

So length = 9

The two functions are not inverses of one another.

A relation is a function if it has only One y-value for each x-value.

The given two functions are F(x)=5x+2

G(x) = x-2/5

Now we need to verify whether these two are inverses of one another

F(G(x)=F(x-2/5)

=5(x-2/5)+2

=5x-2+2

=5x

Now G(F(x))=G(5x+2)

=5x+2-2/5

=5x+8/5

F(G(x) is not equal to G(F(x)).

Hence, the two functions are not inverses of one another.

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Answer:

a) $720.00

b) $882.00

Step-by-step explanation:

For part a) Shawna works 40 hours at $18.00 per hour.

Multiply to find the amount of money she made that week.

40 hrs × $18/hr

= 40 × 18

= 720

Shawna made $720.00

For part b) we can use the answer for part a, but she worked 6 hours more beyond the fulltime 40 hours. The 6 additional hours should be paid as overtime.

Her regular rate is $18/hr. Her overtime rate is "time-and-a-half" Multiply to find that pay rate.

18 × 1.5

= 27

For overtime, Shawna will earn $27/hour.

SO now part b)

She worked 46 hours.

40 × 18 = 720 and

6 × 27 = 162

Regular pay + overtime

= 720 + 162

= 882

Shawna will earn $882.00

(** if you have been studying basic math or basic algebra, this calculation totally works. But if you have been studying labor laws and intricasies of payroll processing, it could be that there is not enough information.)

The 4 basic types of lines are  Curved Lines, Straight Lines, Horizontal Lines, and  Vertical Lines.

How do lines work?

A straight group of points that stretch in opposing directions is what is known as a line.

the 4 basic types of lines are:

a) Curved Lines: A curved line is any line that is not straight. A curve results from a point that is not moving in a straight line.

b) Straight Lines: A straight line is the shortest path between any two points. We obtain a straight line if a point moves only in that direction.

c) Horizontal Lines: A horizontal line is any straight line that extends from left to right. Vertical lines are perpendicular to the y-axis and parallel to the x-axis.

d) Vertical Lines: From top to bottom or bottom to up, vertical lines are straight up and down. A vertical line is perpendicular to the x-axis and parallel to the y-axis.

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Yes

We can use increasingly specific terms to describe numbers and categories they fit in such as rational and irrational numbers.

Rational Numbers

A rational number is defined as a number that can be written as a non-complex fraction. Another way to say this is that rational decimals will always either terminate or repeat. For example, if you have 0.333 repeating forever, that would be a rational number.

The number we are given, -1.63, terminates. Thus, it must be a rational number. Additionally, -1.63 can be written as [tex]-\frac{163}{100}[/tex], so it is a rational number.

Other Categories

As stated above, there are lots of categories numbers can fall into. Rational and irrational are extremely broad groups that all real numbers can fit into. Integers, whole numbers, and natural numbers are all more specific groups that include fewer and fewer numbers. Integers are all rational numbers that are not fractions or decimals. Whole numbers are all non-negative integers. Natural numbers are all non-zero whole numbers.

Answer:

First put a point on 2. That would be the y-intercept.

Then you will move 7 units down and move 2 units to right.

Step-by-step explanation:

This is most I can help you. I understand how you feel. I also was struggling with this topic too. Hope this helps. :)

The notes are £20 and £5. And the coins are £0.50 and £0.20.

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.

Nick buys some fruits for £25.70. There are eight distinct coin denominations in the euro series: 1, 2, 5, 10, 20, and 50 cents, as well as £1 and £2.

The number 25.70 is expanded. Then we have

£25.70 = £20 + £5 + £0.50 + £0.20

The notes are £20 and £5. And the coins are £0.50 and £0.20.

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Answer: sin(f) are correct trigonometric ratios for triangle DEF.

Step-by-step explanation: Sin(d) = cos(e) = tan(d) = sin(e) = tan(d) = sin(f)

It will take approximately 6.5 years for the price of gasoline and oil to be equal.

To solve this problem, we need to set up a system of equations to represent the changing prices of gasoline and oil over time. Let "t" be the number of years that have passed.

The price of gasoline after "t" years is:

$2.27 - $0.03/2 months * 12 months/year * t years = $2.27 - $0.18t

The price of oil after "t" years is:

$0.45 + $0.05/6 months * 12 months/year * t years = $0.45 + $0.10t

To find the value of "t" for which the two prices are equal, we can set the two expressions equal to each other and solve for "t":

$2.27 - $0.18t = $0.45 + $0.10t

$1.82 = $0.28t

t = 6.5 years

Therefore, it will take approximately 6.5 years for the price of gasoline and oil to be equal.

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The height of Veronica's scale model in  inch is 10.5 inch.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

3 inches = 50 feet.

So, 1 feet = 3/50 inch

Then, height of Concert Venue in feet

175 feet = 175 x 3/50

             = 525/50

             = 105/ 10

              = 21/2

              = 10.5 inch

Hence, the height is 10.5 inch.

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Answer:

[tex]\frac{1875}{100}[/tex]

Step-by-step explanation:

18[tex]\frac{75}{100}[/tex]  For the numerator: multiply 100x18 and then add 75

[tex]\frac{1875}{100}[/tex]

got the wrong answer, sorry

The supplementary in the Diagram are Angles 1 and 2.

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.

From the diagram Angles 1 and 2 are angles on a straight line

Angles on a straight line are equals to 180 degree

hence, the supplementary angles are angles 1 and 2

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The steps to  solve a line segment problem is

1. Draw a diagram of the line segment.

2. Label the endpoints and any given information.  

3. Use the given information to calculate the length of the line segment.

4. Use the Pythagorean Theorem to calculate the length of the line segment, if needed.  

5. Solve for the unknown variable.  

To solve a line segment problem, you must first draw a diagram of the line segment. Label the endpoints and any given information, such as the length of one of the sides of the line segment. Then you can use the given information to calculate the length of the line segment. If the length of the line segment is unknown, you can use the Pythagorean Theorem to calculate the length. After that, solve for the unknown variable, and then check your answer. With these steps, you can solve any line segment problem.

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Answer:

it's very simple D

if you throw -ve sign to g(x) sign will change

and do simple calculation

Answer:

To find the difference between the two functions, we can subtract g(x) from f(x):

f(x) - g(x) = (5x² - 2x + 7) - (2x² + 6x + 3)

= 5x² - 2x + 7 - 2x² - 6x - 3

= 3x² - 8x + 4

Therefore, the difference between the two functions is f(x) - g(x) = 3x² - 8x + 4, which is answer D.

Step-by-step explanation:

The equation that represents the given word problem is y = 5 + 15x.

A mathematical definition of an equation is a claim that two expressions are equal and joined by the equal sign. It consists of coefficient, variable operator and constants.

Let the total charges be y and the number of hours be denoted by x.

It is given that for gas the flat fee is $5 this is represented as:

y = 5

Now, $15 per hour is represented as 15x, and the equation becomes:

y = 5 + 15x

Hence, the equation that represents the word problem is y = 5 + 15x

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The segment lengths for this triangle are given as follows:

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

There are three triangles in this problem, all of which are similar.

The length of segment PX can be obtained with triangles PQR and PXY, as follows:

PX/30 = 10/40

PX/30 = 1/4

4PX = 30

PX = 7.5.

The length of segment XQ is found applying the segment addition postulate, as follows:

PQ + XQ = 30

7.5 + XQ = 30

XQ = 22.5.

The length of segment XY can also be obtained with the similarity of triangles PXY and PQR, as follows:

XY/36 = 10/40

XY/36 = 1/4

4XY = 36

XY = 9.

The length of segment ZW is obtained with the similarity of triangles PZW and PQR, as follows:

ZW/36 = 24/40

ZW/36 = 0.6.

ZW = 36 x 0.6

ZW = 21.6.

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The sum and difference between nine-tenths and seven-eighths is 71/40 and 1/40, calculated by addition and subtraction.

As per the fact, representing the words in numbers. So, nine tenths will be represented as: 9/10

Seven eighths: 7/8

Calculating the sum and difference as follows -

Sum = 9/10 + 7/8

Taking LCM we get 40

Sum = 9×4 + 7×5/40

Performing multiplication on Right Hand Side of the equation

Sum = 36 + 35/40

Sum = 71/40

Difference = 9/10 - 7/8

Difference = (9×4) - (7×5)/40

Performing multiplication on Right Hand Side of the equation

Difference = 36 - 35/40

Difference = 1/40

Hence, sum is 71/40 and difference is 1/40.

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The choice of method to the solution of the \pair of equations is substitution method.

In a pair of equations, we can use substitution method or any other method to solve the equations.

The given pair of equations is

y=-x+5 and

y=-x+3

The first thing is to write the two equations where the constant stays at the right hand side and the two variables stay at the left hand side tyo give

y+x = 5 and

y+x=3

Then we use substitution method to solve for x and y

In this case, make x the subject of the relation in equation 1

x=5-y

Then substitute x=5-y in equation 2

That is 2y = 5

then y = 2.2

Sibstitute y=2.2 in equation  to get x=5-2.2

Therefore the value of x=2.8

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The way that the exponent illustrated as x ^7/3 can be written is 3✓x^7

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Expressing large numbers in terms of powers is known as an exponent. Therefore, the exponent describes the number of times a number has been multiplied by itself.

Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is written as bn. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to base multiplication when n is a positive integer; therefore, bn is the result of multiplying n bases:

In this case, it should be noted that x ^7/3 will simply be the cube root of x raised to power 7. This is illustrated as x ^7/3.

Therefore, the correct option is C.

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Answer:

77.77

Step-by-step explanation:

The new value =

77 + The value of the percentage increase =

77 + (1% × 77) =

77 + 1% × 77 =

(1 + 1%) × 77 =

(100% + 1%) × 77 =

101% × 77 =

101 ÷ 100 × 77 =

101 × 77 ÷ 100 =

7,777 ÷ 100 =

77.77

Answer:

= 77.77

Step-by-step explanation:

1% = 1/100 = 0.01

Then:

77*0.01 = 0.77

77 increased 1% is:

77 + 0.77 = 77.77

Answer:

see explanation

Step-by-step explanation:

calculate the slope m of the line using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 3 ) and (x₂, y₂ ) = (- 9, 6 )

m = [tex]\frac{6-(-3)}{-9-4}[/tex] = [tex]\frac{6+3}{-13}[/tex] = - [tex]\frac{9}{13}[/tex]

• Parallel lines have equal slopes.

Thus slope of a parallel line is m = - [tex]\frac{9}{13}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{9}{13} }[/tex] = [tex]\frac{13}{9}[/tex]