A cell phone company offers its customers two monthly plans. Plan A costs $20 per month plus
$0.15 for each minute used. Plan B costs $15 per month plus $0.20 for each minute used.
Part A
Write equations to represent the cost of each plan.
Plan A
Plan B
Part B
Graph the equations
Part C
For how many minutes is the cost the same?
Show your work.

Answer:

5. The factors of 8 are 1, 2, 4, and 8. The factors of 12 are 1, 2, 3, 4, 6, and 12. The greatest common factor (GCF) is 4.

6. The factors of 10 are 1, 2, 5, and 10. The factors of 15 are 1, 3, 5, and 15. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The GCF is 5.

7. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The GCF is 6.

Answer:

1

Step-by-step explanation:

you should remove 8 out of 10 then 2 will remain

then add negative 5 to both sides then we will left with -3x = -3

divide -3 on both sides we find x = 1

Answer:

x=1

Step-by-step explanation:

-3x + 5= -8 + 10​

Combine like terms

-3x+5 = 2

Subtract 5 from each side

-3x+5-5 = 2-5

-3x = -3

Divide by -3

-3x/-3 = -3/-3

x =1

The equation of the line in slope-intercept form is y= 2x -6.

The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.

Given that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:

y= 2x +c

Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.

2x -3y= 6

When x= 3,

2(3) -3y= 6

6- 3y= 6

3y= 6 -6

3y= 0

Divide both sides by 3:

y= 0

Coordinate that lies on the graph is (3, 0).

Substitute the point into the equation and solve for c:

y= 2x +c

When x= 3, y= 0,

0= 2(3) +c

0= 6 +c

c= -6

Substitute the value of c back into the equation:

Thus, the equation of the line in slope-intercept form is y= 2x -6.

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Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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Using trial and improvement, the approximate value of √220 to the nearest integer is 15.

To find the approximate value of √220 using trial and improvement, we can start by making an initial guess and then refine it until we get closer to the actual value.

Let's begin with an initial guess of √220 = 14.

When we square this guess, 14^2 = 196, which is less than 220. So, we know that the actual value lies somewhere between 14 and the next whole number, 15.

Now, let's try with the number 15. Squaring 15, we get 15^2 = 225, which is greater than 220.

Since the actual value is between 14 and 15, we can try a value closer to 14. Let's try 14.5.

Squaring 14.5, we get 14.5^2 = 210.25, which is still less than 220.

We can continue this process by trying values closer to 14.5 until we find a value that, when squared, is close to 220.

After a few more iterations, we find that 14.9^2 is approximately 220.01, which is very close to 220.

Rounding to the nearest integer, we can say that the approximate value of √220 is 15.

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The volume of wood in a tree varies directly as the height and inversely as the square of the girth. If the volume of a tree is 144 cubic meters when the height is 20 meters and the girth is 1.5 meters, we are to find the volume of a tree with a height of 180 meters and girth of 2 meters.

Let V be the volume of wood in a tree, h be the height and g be the girth. From the information given, we can write the equation relating the variables as: V ∝ h × 1/g²Therefore, V = kh/g², where k is a constant. Using the values of the volume, height and girth given, we can find k as follows: 144 = k × 1.5/1.5² ⇒ k = 144 × 2.25/1.5 = 216. Hence, the equation is: V = 216h/g². When h = 180 m and g = 2 m, the volume of wood in the tree is: V = 216 × 180/2² = 14580 cubic meters. Hence, the volume of the tree with height 180 meters and girth 2 meters is 14580 cubic meters.

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The statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is NOT true.

A. The statement is true. The ratios of the vertical rise to the horizontal run, also known as the slopes, of any two distinct nonvertical parallel lines are equal. This is one of the properties of parallel lines.

B. The statement is true. If two distinct nonvertical lines are parallel, then they have the same slope. Parallel lines have the same steepness or rate of change.

C. The statement is true. Given two distinct lines in the Cartesian plane, the two lines will either intersect at a point or they will be parallel and never intersect. These are the two possible scenarios for distinct lines in the Cartesian plane.

D. The statement is NOT true. Given any two distinct lines in the Cartesian plane, they may or may not be parallel or perpendicular. It is possible for two distinct lines to have neither parallel nor perpendicular relationship. For example, two lines that have different slopes and do not intersect or two lines that intersect but are not perpendicular to each other.

Therefore, the statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is the one that is NOT true.

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Answer:

31.42

Step-by-step explanation:

C=2πr

d= 2r

Solving for C

C = πd = π·10 ≈ 31.41593

Answer:

(a) 31.4 in (b) 37.68 mm

Step-by-step explanation:

a- The circumference of a circle of radius r - or diameter d, is,

C=2\(\pi r\)=\(\pi d\)

In this case, we have that the diameter of the circle is d = 10in. If we use 3.14 for π, the circumference is,

\(C=\pi xd=3.14x10in=31.4in\)

b- - The question gives us a circle with a radius of 6mm and we are asked to find the circumference of the circle.

- To find the circumference of a circle, we simply need to apply the formula for finding the circumference of a circle.

- The formula for the circumference of a circle is:

C=2\(\pi \)×r

where,

r=radius

C= circumference of the circle:

- Thus, we can find the circumference of the circle as follows

r= 6mm

\(\pi \)=3.14

C=2×3.14× 6mm

C= 37.68mm

Final Answer

The circumference of the circle is 37.68 mm

Answer:

x=5

Step-by-step explanation:

They are vertical angles, so they are equal.

22x+5=23x

minus 22x from each side

5=x

and you can switch it around :)

x=5

Answer:

128degrees

Step-by-step explanation:

Note that the given triangle ABC is an isosceles triangle with base angles equal, hence;

m∠BAC = m∠BCA

7x+1 = 5x+9

7x - 5x = 9-1

2x = 8

x = 8/2

x = 4

m∠BAC = 5x+6

m∠BAC = 5(4)+6

m∠BAC = 26 degrees

The vertex angle = 180 - (26+26)

The vertex angle = 180 - 52

The vertex angle = 128degrees

Answer:

c.the area method

Step-by-step explanation:

A scatterplot is a plotting of data that represents the relationship between the two variables that should be numerical in nature. The data points i.e to be shown in a horizontal and vertical axis represent that how much one variable affected by another variable.

In the area method, we plot a data and then draw a shape which can be in oval but it does not include the outliers but the other methods like oval method, divide center method, regression calculator includes the outliers

Therefore the option c is correct

Answer:

c.the area method

Step-by-step explanation:

c.the area method c.the area method c.the area method c.the area methodc.the area methodc.the area methodc.the area method c.the area method c.the area method c.the area method   c.the area method  c.the area method

1. Three examples of situations where consistency is important:

Healthcare: when treating patients, healthcare providers must follow consistent procedures and protocols to ensure that every patient receives the same level of care.

Financial transaction: when making financial transactions, it is important to follow regular security rules to prevent fraud.

Support rules: Adherence to consistent rules and regulations in sports is essential to ensure fair play and the safety of all participants.

2. The number 0 is important in mathematical systems because it represents the absence of a number and serves as a placeholder. Without zero, our mathematical system would be affected in many ways. For example, writing the number 100 would be difficult without the zero. Without the invention of zero, progress in mathematics would have been delayed.

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Answer:

How much is her raise?

Her raise is at 0.345$

Hourly pay after raise?

Her new pay rate is 11.845$/h

Step-by-step explanation:

New hourly pay:

\(11.50 \times 1.03 = 11.845\)

Actual raise:

\(11.845 - 11.50 = 0.345\)

The coordinates of the triangle's image in the question serve as an example of transformation and are A(-2,4), B (-3,7), and C (0,6).

The triangle's coordinates are as follows:

(-6,-1), (-5,2) and (-3,0) (-3,0)

The new points are created when the triangle is mirrored over the line y = 2.

(-6,5), (-5,2) and (-3,4) (-3,4)

Then, we use the translation to translate the triangle's picture.

(x,y) -> (x + 3, y +2)

We thus have:

(-6,5) => (-6 + 3, 5 + 2) = (-3,7) (-3,7)

(-5,2) => (-5 + 3, 2 + 2) = (-2,4) (-2,4)

(-3,4) => (-3 + 3, 4 + 2) = (0,6) (0,6)

Hence, the triangle's image's coordinates are A(-2,4), B (-3,7), and C (0,6) respectively.

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In summary, to find an interval of length 1 and having integer endpoints on which the function has a root, we can use a trial-and-error method to identify intervals that satisfy the given criteria. The choice of interval may depend on the specific function and there may be multiple intervals that satisfy these conditions.

To find an interval on which the function has a root, we need to consider the function's behavior and identify any potential zero crossings. An interval of length 1 with integer endpoints can be represented as [a, a+1] where a is an integer.
One approach to finding a root is to plot the function and visually identify where it crosses the x-axis. Another approach is to use algebra and solve for when the function equals zero. However, without knowing the specific function, we cannot use these methods.
Instead, we can use a trial-and-error method to identify an interval that satisfies the given criteria. For example, we can start by choosing an integer a and evaluating the function at a and a+1. If the function has opposite signs at these two endpoints, then by the Intermediate Value Theorem, the function must have at least one root in the interval [a, a+1].
We can continue this process until we find an interval that satisfies the given criteria. Note that there may be multiple intervals that satisfy these conditions, and the choice of interval may depend on the specific function.

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Answer:

yes it is proportional y is 1.2 times x

not proportional

Answer:

El cliente puede ordenar una comida en 60 formas distintas.

Step-by-step explanation:

El cliente escoge una entrada de las cinco opciones disponibles, luego un plato principal de cuatro opciones disponibles y un postre de tres opciones disponibles. Es costumbre consumir primero una entrada, después un plato principal y finalmente, un postre.

Estadísticamente hablando, se debe considerar un producto de tres combinaciones, puesto que el orden no importa a la hora de pedir, como sigue:

\(n = _{5}C_{1}\times _{4}C_{1}\times _{3}C_{1}\) (1)

Donde:

\(n\) - Total de combinaciones al ordenar una comida (entrada, plato principal, postre)

\(_{5}C_{1}\) - Combinaciones posibles para pedir una entrada.

\(_{4}C_{1}\) - Combinaciones posibles para pedir un plato principal.

\(_{3}C_{1}\) - Combinaciones posibles para pedir un postre.

Ahora, desarrollamos la operación:

\(n = \frac{5!}{(5-1)!}\times \frac{4!}{(4-1)!} \times \frac{3!}{(3-1)!}\)

\(n = 5\times 4\times 3\)

\(n = 60\)

El cliente puede ordenar una comida en 60 formas distintas.

Answer:

57.78

Step-by-step explanation:

90 -(40%*90)

= 90 -36

=54

Tax =7% *54=3.78

Final cost= 54 +3.78 = 57.78

Answer:

\(y = \frac{9}{2} x + \frac{9}{2} \)

Step-by-step explanation:

\(m = \frac{9 - ( - 9)}{1 - ( - 3)} = \frac{18}{4} = \frac{9}{2} \)

\(9 = \frac{9}{2} (1) + b\)

\( \frac{18}{2} = \frac{9}{2} + b\)

\(b = \frac{9}{2} \)

\(y = \frac{9}{2} x + \frac{9}{2} \)

Answer:

3m

Step-by-step explanation:

red wire = 27

black wire= 12

so, we take HCF (highest common factor)

which would be 3 so all the wires would be cut into 3m long.

I hope it helps.

Answer:2m

Step-by-step explanation:

as the factors of 12 are:1, 2, 3, 4, 6 and 12

and the factors of 26 are:1, 2, 13 and 26

so if you are talking meters 2 would be the longest

i hope you get this right x

6 full teams will be made.

If you take 62 and divide it by 9, you'll get a value of 6.88... or it can also be notated as 6 remainder 8. You will be able to make 6 full teams but your last team will only have 8 members, which does not have the full 9 members.

Answer:

Missing side length = 45

Step-by-step explanation:

In this problem, we're trying to find the longest side, or hypotenuse, of the triangle. Luckily, there's a formula to find this!

The Pythagorean Theorem is a formula that allows us to find any of the three sides of a right triangle using the lengths of the other two sides.

The formula is, a² + b² = c², where a and b are the side lengths of the two sides that make the right angle and c is the length of the side across from the right angle, the hypotenuse.

To use the formula, we just have to plug in the lengths of the two sides we know and then solve for the third variable. When we're looking for the hypotenuse length, we'll plug in the values for a and b, then solve for c. The a and b values are completely interchangeable, so it won't matter which side length you plugin for which. You just have to make sure that c is going to be the hypotenuse length.

Let's go ahead and plug in our known values for the equation. We're given the two side lengths 27 and 36, which will be our a and b values. Remember, they're interchangeable!

27² + 36² = c²          Next, we can square the a and b numbers.

729 + 1296 = c²       Now add them together.

2025 = c²                 And finally, square root both sides of the equation.

\(\sqrt{2025}= \sqrt{c^2}\)

45 = c

So, the length of the hypotenuse for this triangle is 45. Now, you can use this formula to solve for any of the three sides of a right triangle when given the other two side lengths.

Answer:

x = 45

Step-by-step explanation:

Forming the equation,

→ (x)² = (36)² + (27)²

Now the value of x will be,

→ (x)² = (36)² + (27)²

→ x² = 1296 + 729

→ x² = 2025

→ x = √2025

→ [ x = 45 ]

Hence, the value of x is 45.

Answer: X is the missing value.

Step-by-step explanation:

Answer:

Delivery Trip: 3 hours

Return Trip: 4 hours

Step-by-step explanation:

d/60 + d/45 = 7

45d/2700 + 60d/2700 = 7

105d/2700 = 7

105d = 18900

d = 180

180/60 = 3

180/45 = 4

Answer:

delivering 180/45 = 4 hours and return trip 180/60 = 3 hours

Step-by-step explanation:

d = unknown number to calculate each trip

\(\frac{d}{45}\) + \(\frac{d}{60}\) = 7

find common denominator (45 * 60 = 2700)

(\(\frac{60}{60}\))*(\(\frac{d}{45}\)) +( \(\frac{45}{45}\))*(\(\frac{d}{60}\)) =7

\(\frac{60d}{2700}\) + \(\frac{45d}{2700}\) =7

\(\frac{60d + 45d}{2700}\) =7

\(\frac{105d}{2700}\) = 7

105d = 7 * 2700

105d = 18,900

d = 18900/105

d = 180

delivering 180/45 = 4 hours

return trip 180/60 = 3 hours

Answer:

B

Step-by-step explanation:

The m to the y can’t equal to m so it’s b

Answer:

1.5 inches po

Step-by-step explanation:

thanks me later

good luck!

Long after Mr. and Ms. Jones has been destroyed from the farm,  the animals called pigs invoke his name to scare the other animals into submission.

Indeed though the ranch possesses all of the necessary accoutrements to make the windmill, but the design presents a number of difficulties.

The creatures in the farm are struggle over how to break the available gravestone into manageable sizes for structure without picks and crowbars, which they're unfit to use.

And they eventually break the problem by learning to raise and also drop big monuments into the chase, smashing them into usable gobbets.

At the time of late summer, the creatures have enough broken gravestone to begin construction.

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Answer:

x=4.2

Step-by-step explanation:

29-3=5x+5

21=5x, x=21/5=4.2

Answer:

A. It increased the number of molecular collisions.