What is the value of the rational expression x^2-2x-3/4x^2-12 when x = 3?

a) -1/4
b) 0
c) 1/4
d) Undefined

Answer:

(A) Joel wants to find the quotient of a number and four, minus thirteen.

Step-by-step explanation:

The correct description that can be written as the expression [tex]\frac{n}{4}[/tex] - 13 is 'Joel wants to find the quotient of a number and four, minus thirteen'.

Mathematically, an expression is a combination of numbers, variables, operations, and functions that are combined according to specific rules to represent a mathematical computation or relationship. It can be thought of as a mathematical phrase or formula.

By combining numbers, variables, operators, and functions, mathematical expressions can represent a wide range of computations and relationships.

Expressions are fundamental in mathematics as they allow us to represent and manipulate mathematical concepts, solve equations, evaluate formulas, and analyze mathematical relationships. They are used in various areas of mathematics, including algebra, calculus, geometry, and more.

Hence, the expression [tex]\frac{n}{4}[/tex] - 13 can be written as 'Joel wants to find the quotient of a number and four, minus thirteen'.

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Answer: Option b

[tex]M=24[/tex]

Step-by-step explanation:

We have the following list of data

36 20 35 13 30 14 36 11 29 19 22 40 34 17 26 21

The list contains 16 data.

The first step to calculate the median is to order the data from least to highest

11,13,14,17,19,20,21,22,26,29,30,34,35,36,36,40

Now mark the two central values of the data set

11,13,14,17,19,20,21         [22,26]       29,30,34,35,36,36,40

The median of the data is the average of the two central values

[tex]M=\frac{22+26}{2}[/tex]

[tex]M=24[/tex]

Note that the median is the central value of the ordered data set

Answer:

Step-by-step explanation:

Answer

Given

the relative frequency tables in the figure below (Note: the tables are not in the same order as in the problem statement)

Find

which table is best suited to answer the question

A) the percentage of home viewers who prefer to watch horror movies

B) the percentage of people surveyed who prefer to watch comedy movies at home

C) the percentage of viewers with a preference for drama who watch at the theater

Solution

The figure shows the best choices for answering A, B, and C.

table 2 is best for A (it is normalized by viewing location)

table 3 is best for B (it is normalized over the whole sample)

table 1 is best for C (it is normalized by genre)

Range is all the y values included in the graph. Look at the image below for the y values:

As you can see the highest y value this graph reaches is 6 and the lowest is -5 therefore the range is...

-5 ≤ g(t) ≤ 6

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

(8x - 7)(

The x^2 term has to come out to 8x^2.

The 8 is already there.

So your first term in the second factor is x.

(8x - 7) ( x

Now the question is what is the sign after the x. Since the question shows +7 the only way that can happen is if both signs in the factors are the same.

Since (8x - 7) has been given to you and you need 7 to come out plus, then the sign after x must minus. Both signs must be the same.

(8x - 7)(x -

Last, what comes after the minus sign? You already have a minus 7 so you need something to multiply by 7 to get seven.

That should be a one.

(8x - 7)(x - 1)

x - 1 is you answer. I leave you to check the middle term. It is - 15

Answer:

Step-by-step explanation:

The intersection is the point where two equations meet. It is calculated by substituting terms into the equations involved. For the given systems of equation, calculations are as follows:

2x - y = 6

y = 2x - 6

We substitute the equation above to the second equation.

5x + 10y = –10

5x + 10( 2x - 6 )= –10

Simplifying, 

5x + 20x - 60 = -10

25x = 50

x = 2

Therefore, the intersection has the value of x equal to 2.

Answer with Step-by-step explanation:

The point of intersection of the graphs of system of equation is the solution to the system of equations.

So, we need to find the solution of the system of equations:

2x – y = 6

5x + 10y = –10

Multiplying first equation by 10 and add it to second equation.

5x+10y+10(2x-y)= -10+60

5x+10y+20x-10y=50

25x=50

⇒ x=2

Hence, value of x where the graphs of the equations  

2x – y = 6

5x + 10y = –10 intersect is:

x=2

Answer:

The correct answer option is quadratic, because the height increases and then decreases.

Step-by-step explanation:

We are given the following data in the table which represents the height of an object over  time:

Time (s)          Height (ft)

     0                      5

      1                     50

     2                     70

     3                     48

We know that in situation where the values increase and then decreases, a quadratic model is used.

From the values given in the table, we can see that the values of height first increased and then decreased with the increase in time.

Therefore, the model used is quadratic, because the height increases and then decreases.

Answer:

Step-by-step explanation:

Answer:

38.5

Step-by-step explanation:

7 times 5.5

Answer:

The set of ordered pair are { (-12,-18),(-3,-3), (0,2),(3,7),(12,22)}

Step-by-step explanation:

we have

[tex]f(x)=\frac{5}{3}x+2[/tex]

Find the values of f(x) for the domain values

For x=-12

substitute

[tex]f(-12)=\frac{5}{3}(-12)+2=-18[/tex]

The ordered pair is (-12,-18)

For x=-3

substitute

[tex]f(-3)=\frac{5}{3}(-3)+2=-3[/tex]

The ordered pair is (-3,-3)

For x=0

substitute

[tex]f(0)=\frac{5}{3}(0)+2=2[/tex]

The ordered pair is (0,2)

For x=3

substitute

[tex]f(3)=\frac{5}{3}(3)+2=7[/tex]

The ordered pair is (3,7)

For x=12

substitute

[tex]f(12)=\frac{5}{3}(12)+2=22[/tex]

The ordered pair is (12,22)

Answer with explanation:

The given function is

   [tex]f(x)=\frac{5x}{3}+2\\\\x=-12,-3,0,3,12\\\\f(-12)=\frac{5\times -12}{3}+2\\\\f(-12)=-20+2\\\\f(-12)=-18\\\\f(-3)=\frac{5 \times -3}{3}+2\\\\f(-3)=-5+2\\\\f(-3)=-3\\\\f(0)=\frac{5\times 0}{3}+2\\\\f(0)=2\\\\f(3)=\frac{5\times 3}{3}+2\\\\f(3)=5+2\\\\f(3)=7\\\\f(12)=\frac{5\times 12}{3}+2\\\\f(12)=20+2\\\\f(12)=22[/tex]

So, the ordered pair will be

   (-12, -18),(-3,-3),(0,2),(3,7),(12,22)

Answer:

x = 6.93

Step-by-step explanation:

If a tangent and a secant are drawn to a circle from the same exterior point, the square of the length of the tangent is equal to the product of the total length of the secant and the length of the external segment of the secant.

From the given diagram,

(8+4)×4=x²

12×4=x²

48=x²

x=√48

x=6.93

x=7 to the nearest whole number.

Final answer:

The future value of the house will be approximately $232,810.10 in 10 years, calculated by compounding the initial value of $130,000 at an annual growth rate of 6%.

Explanation:

To calculate the future value of a house appreciating at a certain rate, we can use the compound interest formula: [tex]Future\ Value = Present\ Value \* (1 + growth/decay rate)^{number of periods[/tex]

In this scenario, the house is appreciating, which means it's increasing in value over time.

We're given that the initial amount (Present Value) is $130,000 and the growth rate is 6% per year.

The function that represents the situation is:
Future Value = $130,000 × (1 + 0.06)¹⁰

To find the value of the house in 10 years, we simply plug in the values:

Future Value = $130,000 × (1 + 0.06)¹⁰
Future Value = $130,000 × (1.06)¹⁰
Future Value = $130,000 × 1.790847
Future Value = $232,810.10 approximately

Therefore, the house will be worth approximately $232,810.10 in 10 years, and this represents growth, not decay.

Answer:

y = 4x^5 - 12x^4 + 6x and

y = 5x^3 - 2x

Step-by-step explanation:

The system of equations that can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x are;

y = 4x^5 - 12x^4 + 6x and

y = 5x^3 - 2x

We simply formulate two equations by splitting the left and the right hand sides of the given equation.

The next step is to graph these two system of equations on the same graph in order to determine the solution(s) to the given original equation.

The roots of the given equation will be given by the points where these two equations will intersect.

The graph of these two equations is as shown in the attachment below;

The roots are thus;

x = 0 and x = 0.813

To calculate the total surface area of a hemisphere with a radius of 8 cm, we use the formula A = 3πr², resulting in a total surface area of approximately 602.9 cm² to one decimal place.

The question asks us to work out the total surface area of a hemisphere with a radius of 8cm and provide the answer to one decimal place. The total surface area of a hemisphere is given by the formula A = 2πr² + πr², where π is approximately 3.14 and r is the radius of the hemisphere. The first part 2πr² represents the curved surface area, and the second part πr² represents the area of the circular base.

Substituting 8 cm for r:

A = 2π(8²) + π(8²) = 2π(64) + π(64) = 128π + 64π = 192π cm²

Converting π to 3.14:

A = 192(3.14) = 602.88 cm². Therefore, the total surface area of the hemisphere is approximately 602.9 cm² to one decimal place.

The total surface area of this hemisphere is approximately 603.2 cm².

Calculating the Total Surface Area of a Hemisphere

To find the total surface area of a hemisphere with a radius of 8 cm, we need to consider both the curved surface area and the base area.

Curved Surface Area: The formula for the curved surface area of a hemisphere is given by 2πr², where r is the radius. Substituting the given radius (8 cm), we get:

Curved Surface Area = 2π(8 cm)² = 2π(64 cm²) ≈ 2 × 3.1415927 × 64 = 402.1 cm² (rounded to one decimal place)

Base Area: The base of the hemisphere is a circle with the area given by the formula πr². Using the radius (8 cm), we get:

Base Area = π(8 cm)² = π(64 cm²) ≈ 3.1415927 × 64 = 201.1 cm² (rounded to one decimal place)

Total Surface Area: To find the total surface area, we sum the curved surface area and the base area:

Total Surface Area = 402.1 cm² + 201.1 cm² = 603.2 cm²

Therefore, the total surface area of the hemisphere is approximately 603.2 cm².

Answer:

x + 2y = - 2

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (8, - 5)

m = [tex]\frac{-5-0}{8+2}[/tex] = [tex]\frac{-5}{10}[/tex] = - [tex]\frac{1}{2}[/tex]

y = - [tex]\frac{1}{2}[/tex] + c ← partial equation of line

To find c substitute either of the 2 points into the partial equation

Using (- 2, 0), then

0 = 1 + c ⇒ c = - 1

y = - [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form

Multiply through by 2

2y = - x - 2 ( add x to both sides )

x + 2y = - 2 ← in standard form

Final answer:

The importance of graphs in representing solutions to systems of inequalities for purchasing decisions.

Explanation:

Katie's Situation:

Each small tub costs $3, and each large tub costs $4.

Katie needs to buy at least 7 tubs and has $24 in her wallet.

Graph Representation: The graph with the shaded region where the solution to the system of inequalities lies would show the combinations of small and large tubs Katie can buy within her budget.

Answer:

x+y=40liters

10%x+5%y=8%×40

(2x+y)/20=8%×40

(2x+y)=64

x=24

y=16

Answer:

21 rides, with $0.50 left.

Step-by-step explanation:

All rides cost $1. Note that you cannot take half a ride, and so the cents (0.50) is out of the question. Divide 21 with 1:

21/1 = 21

Angela can ride up to 21 rides.

~

Answer:

60 x^3 y^7

Step-by-step explanation:

3x^3 = 3*xxx

12y^7 = 3*4 yyyyyyy

15xy^3 = 3*5 xyyy

We need to have the minimum of each for the least common multiply

For the numbers there is a 3 a 4 and a 5

For the x , the minimum is xxx

For the y, the minimum is yyyyyyy

Least common multiple: 3*4*5 xxx yyyyyyy

                                       60 x^3 y^7

Answer:

Step-by-step explanation:

[tex]\dfrac{x}{5}+1=7\qquad\text{subtract 1 from both sides}\\\\\dfrac{x}{5}+1-1=7-1\\\\\dfrac{x}{5}=6\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup^1\cdot\dfrac{x}{5\!\!\!\!\diagup_1}=5\cdot6\\\\x=30[/tex]

Answer:

The slope is 2.

Step-by-step explanation:

X - intercepts are also known as zeros. To solve this simply take each factor of the polynomial and set it equal to zero. Solve for x then you'll have your x - value of the x intercept.

x - 1 = 0

x - 1 +1 = 0 + 1

x = 1

x - 4 = 0

x - 4 + 4 =0 +4

x = 4

x + 7 = 0

x + 7 - 7 = 0 - 7

x = -7

^^^All the above are the x values of the x - intercepts

The answer is...

C. (1 , 0) (4, 0) ( -7, 0)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: a dilation and a rotation

Step-by-step explanation:

From the given figure it can be seen that ΔABC is reduced to ΔA"B"C" so there must be dilation.

Also, when there is rotation about point C to create ΔA"B"C".

Therefore, the transformations could have occurred to map ΔABC to ΔA"B"C" are a dilation and a rotation.

Answer:(x+1) (x+8)

Step-by-step explanation:

Answer:

(x + 8)(x + 1)

Step-by-step explanation:

Consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 9)

The factors are + 8 and + 1, since

8 × 1 = 8 and 9 + 1 = 9, hence

x² + 9x + 8 = (x + 8)(x + 1) ← in factored form

Convert the fractions to decimals:

1/8 = 0.125

2/3 = 0.666

3/5 = 0.6

Now arrange from largest to smallest

2/3, 3/5, 1/8

Answer:

2/3 biggest

3/5

1/8 smallest

Answer:

522.9 revolutions /min

Step-by-step explanation:

Given Diameter, D = 27 inches

Circumference, C = πD = 3.142 x 27 = 84.82 inches

(recall 1 mi = 63360 in)

Car speed is 42 mph =  42 mph x 63,360 inches / mile = 2,661,120 inches / hr

(recall 1 hour = 60 min)

Hence car speed becomes

= 2,661,120 inches / hr ÷ 60 min/hr

= 44,352 inches / min

Number of revolutions / min

= speed in inches/min ÷ circumference

= 44,352 ÷ 84.82 = 522.9 revolutions /min

To find out how fast a tire with a diameter of 27 inches is turning for a car moving at 42 mph, you first convert miles per hour to inches per minute, then calculate the tire's circumference in inches, and divide the car's speed by this circumference. The calculated result is approximately 523.05 revolutions per minute.

To answer this question, we first need to convert the information about speed and tire diameter to compatible units. We'll convert the car speed from miles per hour (mph) to inches per minute since the diameter of the tire is given in inches.

Since 1 mile equals 63,360 inches, 42 mph is equal to 42*63360 = 2,661,120 inches per hour. As there are 60 minutes in an hour, that comes out to 2,661,120/60 = 44,352 inches per minute.

Next, we will find the circumference of the tire, which is its diameter multiplied by pi. Therefore, we have a circumference of 27 inches * 3.14 (pi) = 84.78 inches.

Finally, to find out how many times the tire rotates in a minute, we divide the car's speed in inches per minute by the tire's circumference in inches. This means the tires are making 44,352/ 84.78 ~= 523.05 revolutions per minute.

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Answer:

the value of 7x-y is -14.

Step-by-step explanation:

When x=2 and y=4,

To find the value of 7x - y when x =2, y = 4, this means when ever you see x, put 2 in replacement, y, put 4 respectively.

7x - y = 7(2 - 4)

14 - 28

= -14.​

The value of the expression 7x - y is 10 if the values of x and y are 2 and 4 respectively.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The expression is:

= 7x - y

The value of x and y is given:

x = 2

y = 4

Plug the above values in the expression 7x - y

= 7(2) - 4

= 14 - 4

= 10

The linear expression can be defined as the relation between two expressions, if we plot the graph of the linear expression we will get a straight line.

If in the linear expression, one variable is present, then the expression is known as the linear expression in one variable.

Thus, the value of the expression 7x - y is 10 if the values of x and y are 2 and 4 respectively.

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Answer:

1 - 12x + 60x^2 - 160x^3 + 240x^4 - 192x^5 + 64x^6

Step-by-step explanation:

So we need to know the 7th line of pascals triangle so let us write it out

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1 <----- This one

Now we know we will need coefficients of x from 0 to 6, let us call this i, and for each of these the coefficient is

(-2)^i * (1)^(6-i) * number in pascals triangle

Hence

i = 0, 1 * 1 * 1 = 1

i = 1, -2 * 1 * 6 = -12

i = 2, 4 * 1 * 15 = 60

i = 3, -8 * 1 * 20 = -160

i = 4, 16 * 1 * 15 = 240

i = 5, -32 * 1 * 6 = -192

i = 6, 64 * 1 * 1 = 64

Hence (1-2x)^6 = 1 - 12x + 60x^2 - 160x^3 + 240x^4 - 192x^5 + 64x^6