A book club charges a membership fee of $20 and then $12 for each book purchased. Write a function to represent the change, y, of membership in the club based on the number of books purchased, x.

You can use the sin function to solve this.

Think of a triangle with the conveyor being the longest side (hypotenuse). The height (the vertical side) is H=17m. The angle of elevation is a=36.2. We are looking for length of the hypotenuse, L.

The sin is the ratio of height to hypotenuse: sin(36.2) = H/L = 17/L

Now solve for L:

L = 17/sin(36.2) = 17m/0.59 = 28.78m

The conveyor needs to be approx. 28.8m long to get close to the max. efficient angle.

the answer is c) 0.375, a number that terminates.

Answer:

D- 0.375 with a repeating bar over 375., a number that repeats

Step-by-step explanation:

Convert 3 over 8 to a decimal and tell whether it terminates or repeats.

A- 3.8, a number that terminates

B- 3.8 with a repeating bar over 8., a number that repeats

C- 0.375, a number that terminates

D- 0.375 with a repeating bar over 375., a number that repeats

The difference between whole numbers and integers is that whole numbers do not include negative numbers, whereas integers do. Therefore, the same rule used by integers can be used with whole numbers, so long as negative numbers are not used.

The rule for subtracting integers applies to whole numbers because whole numbers are integers. In subtraction, we change the sign of the subtracted number and then add, a principle that works with both negative and whole numbers.

The rule for subtracting integers can indeed be used to subtract whole numbers because whole numbers are a subset of integers. Integers include all positive whole numbers, zero, and their negative counterparts. When we look at the subtraction of integers, for example, 5 - 3 = 2, we can also see this as adding the opposite, 5 + (-3) = 2. Similarly, if you subtract a negative number, like subtracting -6 from 2, it becomes 2 - (-6) = 2 + 6 = 8. Hence, even with whole numbers, we are using the same principles.

When subtracting whole numbers, you follow the same process: change the sign of the number being subtracted and proceed with addition. If the numbers have different signs, you subtract the smaller number from the larger and retain the sign of the larger number. The basic principle to use in working with addition and subtraction of integers is changing subtraction into addition and the paying attention to the signs.

The universality of mathematical rules applies regardless of where or when, meaning subtraction of whole or negative numbers follow the same fundamental principles.

Answer:

9.5

Step-by-step explanation:

X=2:        16+5-10=11 21-10=11=11=11

Combine Like Terms: 11 = 8x + 5 - 5x

First combine the ones with variables:

11 = 3x +5

Then combine ("move") 5 to 11.

6=3x

Divide.

Final Answer

2=x

Hope that helps :)

-edited-

y-intercept is -6 (0,-6) and the x-intercept is -3 (-3,0)

To create a line segment that is twice as long as a given segment, use a compass and straightedge to draw two intersecting arcs and connect the intersection point with one endpoint of the given segment.

To create a line segment that is twice as long as a given segment using a construction tool or a compass and straightedge, follow these steps:

https://brainly.com/question/31666029

#SPJ12

20 plus 10 equals 30.

I believe the answer is B, but I'm not 100% sure. :)

the answer is 5.

                                                hope it helps

The answer is 857011

Answer : The correct answer is, 857011

Step-by-step explanation :

We are given an expression :

A value that is [tex](879000-21989)[/tex]

The mathematical operation used in the expression is subtraction.

Calculating the value of given expression, we get:

[tex](879000-21989)=857011[/tex]

Hence, the value of the expression is 857011.

the 1st 10 prime numbers are ..wait let me look at my notes from 8th grade..oh found them here they are

2,3,5,7,11,13,17,19,23 and 29

hoped this helped:)

3x - 5y = 6

-3x         -3x

      -5y = -3x + 6

       [tex]\frac{-5y}{-5} = \frac{-3x}{-5} + \frac{6}{-5}[/tex]

          [tex]y = \frac{3}{5}x - \frac{6}{5}[/tex]  ⇒  m = [tex]\frac{3}{5}[/tex]

perpendicular slope (m⊥) = [tex]-\frac{5}{3}[/tex]

Point-Slope equation:

m = [tex]-\frac{5}{3}[/tex]    (x₁ , y₁)= (-8, 0)

y - y₁ = m(x - x₁)

y - 0 = [tex]-\frac{5}{3}[/tex](x - (-8))

    y = [tex]-\frac{5}{3}[/tex](x + 8)

    y = [tex]-\frac{5}{3}x - \frac{40}{3}[/tex]

The mean [tex]\mu =11.5[/tex] pounds;

the standard deviation is [tex]\sigma =2.7[/tex] pounds.

Let the variable [tex]X[/tex] be the weight of male babies less than 2 months old. It is normally distibuted with a law

[tex]X\sim N(11.5, 2.7^2).[/tex]

Find the variable

[tex]Z=\dfrac{X-\mu}{\sigma},[/tex] that is normally distributed with a law

[tex]Z\sim N(0, 1).[/tex]

Part A.

If X=15 pounds, then

[tex]Z=\dfrac{15-11.5}{2.7}\approx 1.2963[/tex] and

[tex]Pr(X<15)=Pr(Z<1.2963)\approx 0.9032[/tex]

Part B.

If X=15 pounds, then

[tex]Z=\dfrac{15-11.5}{2.7}\approx 1.2963.[/tex]

If X=13 pounds, then

[tex]Z=\dfrac{13-11.5}{2.7}\approx 0.5555[/tex] and

[tex]Pr(13<X<15)=Pr(0.5555<Z<1.2963)\approx 0.9032-0.7123=0.1909[/tex]

Part C.

If X=17 pounds, then

[tex]Z=\dfrac{17-11.5}{2.7}\approx 2.0370[/tex] and

[tex]Pr(X>17)=Pr(Z>2.0370)=1-Pr(Z<2.0370)\approx 1-0.9793=0.0207.[/tex]

This means that approximately 2% of babies are born with weight more than 17 pounds and, therefore, seems to be quite unusual for a baby.

Using standard normal distribution properties, we calculate that about 90.32% of babies weigh less than 15 pounds, around 19.07% of babies weigh between 13 and 15 pounds and just 2.07% of babies weigh more than 17 pounds, which is considered unusual.

These questions are solved using the properties of the normal distribution. The standard score (or z-score) is calculated with the formula z = (x-μ)/σ where x is the value, μ is the mean, and σ is the standard deviation.

For babies that weigh less than 15 pounds: Z = (15-11.5)/2.7 = 1.30. You then use a standard normal table (also called a z-table) to find the proportion associated with this z-score, which is about 0.9032. Therefore, about 90.32% of babies weigh less than 15 pounds.

For babies that weigh between 13 and 15 pounds you need to find the z-scores for both weights and identify the difference. Therefore, for 13 pounds, z = (13-11.5)/2.7 = 0.56, and for 15 pounds z=1.30 as calculated before. The odds of a weight between the two is approximately 0.9032 - 0.7125 = 0.1907. So, about 19.07% of babies weigh between 13 and 15 pounds.

For a baby to weigh more than 17 pounds, you again calculate the z-score which results in z = (17-11.5)/2.7 = 2.04. The proportion associated with this z-score is about 0.9793 but since we want to find the proportion of babies weighing more than 17 pounds we do 1 - 0.9793 = 0.0207 meaning only about 2.07% of babies weigh over 17 pounds. This is well below 5%, so it is considered unusual.

https://brainly.com/question/34741155

#SPJ3

We can figure this out by applying proportionality.

25/5 = 5.

We know the multiplier is 5 between the fraction on the right and the fraction on the left, so we need only to multiply 8 by 5.

8 * 5 = 40.

Your answer is C.

A) 3y - x = 10 is the correct answer! (I just graphed it on Desmos.com)

Step-by-step explanation: usatestprep approved

The estimated value can be given by 21.76

To solve this expression, let's just:

[tex]\\\large \sf 102.3 \div 4.7 = 21.7659574468\\[/tex]

We can make the approximation to the first two numbers after the point, thus having the result

[tex]\red{\boxed{\large \sf \approx 21.76}}[/tex]

So, the answer will be 21.76

Answer:

20

Step-by-step explanation:

Answer:

x = -6 and x=3

Step-by-step explanation:

We have been given the equation to solve

[tex](x-2)(x+9)=4x[/tex]

Let us simplify the left hand side of the equation using FOIL (first outer in last).

[tex]x^2+9x-2x-18=4x\\\\x^2+7x-18=4x\\\\x^2+3x-18=0[/tex]

Now, let us find the factors using AC method.

Middle term 3x can be written as 6x - 3x

[tex]x^2+3x-18=0\\\\x^2+6x-3x-18=0\\\\x(x+6)-3(x+6)=0\\\\(x+6)(x-3)=0\\\\x=-6,3[/tex]

Now, let us check the solution by plugging values in the original equation

For x= -6

[tex](-6-2)(-6+9)=4(-6)\\\\(-8)(3)=-24\\\\-24=-24\Rightarrow\text{ True}[/tex]

Thus, x=-6 is a solution.

For x= 3

[tex](3-2)(3+9)=4(3)\\\\(1)(12)=12\\\\12=12\Rightarrow\text{ True}[/tex]

Thus, x=3 is a solution.

Therefore, the solutions are x = -6 and x=3

Solution

1. The algebraic expression =  -0.5n - 3.8, where n is the number of minutes.

2. Here the variable "n" represents the number of minutes.

Thank you.

For this case we have the following data:

In this way, the depth of the diver for a certain number of minutes is given by:

[tex]3.8 + 0.5x[/tex], where x represents the number of minutes

Answer:

Question 1: [tex]3.8 + 0.5x\\[/tex]

Question 2: x represents the number of minutes

Respuesta: El noveno piso costara $16 millones

Solucion:

El primer piso costara $12 millones y cada piso sucesivamente al segundo $500,000 mas que el piso precedente.

Esta es una progresion aritmetica, porque cada valor se obtiene sumandole al valor anterior un valor constante que es la razon "r". En este caso la razon es:

r=$500,000

Que en millones de dolares es:

r=$0.5 millones

Tenemos el primer valor: El primer piso costara $12 millones:

a1=$12 millones

Y necesitamos el costo del noveno piso, o sea el noveno valor: a9=?

Tenemos esta formula para calcular el valor de un termino cualquiera "an" de una progresion aritmetica, conociento el  primer termino de la misma:

an=a1+(n-1)r

En este caso n=9, entonces sustituyendo en la formula anterior:

a9=a1+(9-1)r

a9=a1+8r

Reemplazando los valores dados en la formula de arriba:

a9=$12 millones+8($0.5 millones)

a9=$12 millones+$4 millones

a9=$16 millones

the length of each equal side is 10 ft

the length of the third side is 2 ft

let x be the length of the third side the equal sides are 4x + 2

given perimeter == 22, then

x + 4x + 2 + 4x + 2 = 22

9x + 4 = 22 ( subtract 4 from both sides )

9x = 18 ( divide both sides by 9 )

x = 2 and 4x + 2= 10

The length of the third side (base) of the isosceles triangle is 2 feet, and the other two equal sides are each 10 feet long, with the perimeter totaling 22 feet.

To solve for the lengths of the sides of an isosceles triangle given its perimeter, we can set up an equation. Let's denote the length of the third side (base) as x feet.

Since the triangle is isosceles, we know that the other two sides (legs) have equal lengths, each being 2 feet more than 4 times the length of the third side. Therefore, these equal sides are each 4x + 2 feet long. The perimeter of the triangle is the sum of the lengths of all three sides, which is given as 22 feet.

So, the perimeter equation is:
x + (4x + 2) + (4x + 2) = 22
This simplifies to:
9x + 4 = 22
Solving for x, we get:
x = 2 feet.

Now we know the third side (base) is 2 feet long. The length of each equal side can now be calculated:
4(2) + 2 = 10 feet.

Therefore, the length of each equal side is 10 feet and the length of the third side is 2 feet.

Because the distance to both chords are the same (5.70) and both chords are 90 degrees from the 5.70 line, both chords are identical.

Chord AB = 5, so chord CD is also 5.

The answer will be 5.

Solving a system of linear equations involves finding the point where the two equations intersect when plotted on a graph. This can be done using a graphing calculator by first entering the equations into the calculator, then finding the point of intersection, which represents the solution.

To start solving the given system of linear equations: 2.1x+4.2y=14.7 and −5.7x−1.9y=−11.4, you first need to enter them into your graphing calculator. The intersection point of the two lines represented by these two equations will be your solution. If you don't see a clear intersection point, use the Intersection tool in your graphing calculator, which will provide the respective x and y coordinates of the intersection. This represents the solution to your set of equations.

For instance, if you have a calculator where you can plot both equations on the same graph, find the intersection point, the result is the solution of the system. If the graphing calculator finds an intersection at (x,y), that means x is the solution for the variable x and y is the solution for the variable y. This process is analogous to figuring out where the two lines would cross if you graphed them on a sheet of paper.

https://brainly.com/question/11897796

#SPJ12

To solve a system of linear equations using a graphing calculator, you first need to rewrite the equations in slope-intercept form: y = mx + b. Then input these equations into the graphing calculator. The intersection of the two graphs is the solution.

To solve the given system of linear equations—[tex]2.1x+4.2y=14.7[/tex]and [tex]-5.7x-1.9y=-11.4[/tex]—using a graphing calculator, you first have to rewrite the equations in slope-intercept form (y = mx + b), where 'm' represents the slope and 'b' represents the y-intercept.

To do this, isolate 'y' in both equations. For the first equation, you would do the following:

Repeat the same process with the other equation and you will have two equations with 'y' isolated. Input these two equations into your graphing calculator. Where the graphs intersect represents the solution to the system of equations, that is, the values of x and y that satisfy both equations.

https://brainly.com/question/11897796

#SPJ12

Answer:

Mary's Age = 12

Hector's Age = 2 x 12 - 5

                      = 24 - 5 = 19 years old

Jason is making a mistake in calculating the distance between the two points on a coordinate plane. The correct formula to find the distance between two points is the distance formula, which uses the Pythagorean theorem.

Jason is making a mistake in calculating the distance between the two points. The formula to find the distance between two points in a coordinate plane is the distance formula, which uses the Pythagorean theorem. The correct formula is:

Distance = sqrt((x2-x1)^2 + (y2-y1)^2)

Using the formula with the points (4, 4) and (-4, -4), the distance should be:

Distance = sqrt((-4-4)^2 + (-4-4)^2) = sqrt((-8)^2 + (-8)^2) = sqrt(64 + 64) = sqrt(128) = 8*sqrt(2)

So the distance between the two points is 8 times the square root of 2, not just 8. Jason made a mistake by adding the absolute values of the coordinates instead of using the distance formula correctly.

https://brainly.com/question/25841655

#SPJ3

Greetings, the answer is 11.

Steps:

9+6=15

-4·15

-60

The correct answer is -60

It is simple. There are 3 pizzas and 26.28 total. We are suppose to find for each pizza.

26.28/3=8.76

B. $8.76 per pizza

Answer

B. $8.76

I got it right and also if you multiply 8.76 by 3 you get 26.28 and the same goes for 26.28 divided by 3 which equals 8.76.

The cost function for renting a limo for the prom is Cost(c) = 200 + 25c, where c is the number of passengers. The domain is {4, 6, 8, 10}, representing the possible number of passengers (4 to 10). A table of values for this domain shows the total costs at 300, 350, 400, and 450 respectively for groups of 4, 6, 8, and 10 passengers.

To calculate the cost of renting a limo for the prom including the cost of refreshments based on the number of passengers, we can define a function Cost(c) where c represents the number of passengers. The function can be written as:

Cost(c) = 200 + 25c

The domain of this function is the set of all possible numbers of passengers, which ranges from 4 to 10 (counting in groups of two, since each friend brings a date). Therefore, the domain is {4, 6, 8, 10}.

Next, we'll create a table of values with this domain to calculate the costs associated with each potential number of passengers:

(4, 300)

(6, 350)

(8, 400)

(10, 450)

Each ordered pair represents (number of passengers, total cost).

4-2x≤-3 so basically you are trying to find x so the best inequality for this equation would be less than or equal to  hoped this helped have a great day :)

Answer:

4 - 2x < 3

Step-by-step explanation:

Given,

The measured temperature in Toronto = 4°C,

∵ the temperature started dropping 2°C every hour,

So, the decrement in temperature after x hours = 2x degree celsius,

∴ The total temperature after x hours = original temperature - decrement in the temperature,

= 4 - 2x

According to the question,

Total temperature would be below -3°C,

4 - 2x < 3

Which is the required inequality.

The equation of a line formula is y=mx+b.

y = 1/4x - 2

m= 1/4

b= -2

Answer"

y=4x+-2

Step-by-step explanation:

8 + 3 *X = 2^2 + X^2

Simplify:

8 + 3x = 4 +x^2

Subtract x^2 from each side:

8 + 3x - x^2 = 4

subtract 4 from each side:

8 + 3x -x^2 -4 = 0

Simplify:

3x - x^2 +4 = 0

Factor

-(x-4)(x+1) =0

X = 4, -1

The answer would be 4.

Hi Slyther,

Answer - B. 4

8 + 3 * x = 2^2 + x^2

8 + 3 x 4 = 2^2 + 4^2

8 + 12 = 4 + 16

20 = 20