write the point slope form of the equation of the line described question 17

a. an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 is : 19 +0.04x >23

b. the meaning of the answer to part a is : Cost of Plan 2 > Cost of Plan 1

c.  the number of monthly calls x  is x > 100

What is inequality ?

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Plan 1: $23 per month for unlimited calls

Plan 2: $19 per month + $0.04 per call

Let the number of calls be x

a. 19 +0.04x >23

0.04x >4

x > 100

b. If Plan 1 should be more economical, then the above inequality represents that cost of plan 2 should be more than plan 1. therefore, the plan 2 is greater than plan 1.

On solving the above inequality, we get over 100 calls should be made  so that Plan 1 is more economical than Plan 2.

c. x > 100

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According to the given statement The sum of pair of vectors are  =  (-16 , -28).

The operation of combining two or even more vectors into a vector sum is known as vector addition. The rule for addition and multiplication of two or more vectors is given by the so-called parallelogram law. When two vectors are placed head to tail, the vector total is determined by drawing this same vector from of the free tail towards the free head.

Given two vectors are:

a =(6,-31)

b = (-22,3)

The vector sum is,

M = (a1 + b1, a2 + b2)

   = (Mx, My).

Substitution of the value we  get:

M = (6 + (-22), (-31) + (3))

   = (-16 , -28)

The sum of pair of vectors are  =  (-16 , -28).

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We have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.

Given,

The quantity of medicine added to the original mixture = 15 ounces

New quantity of medicine in the mixture = 18 ounces

Quantity of water in the mixture = 7 ounces

Total new quantity of mixture = 18 + 7 = 25 ounces

Original quantity of medicine in the mixture = 18 - 15 = 3 ounces

Original quantity of water in the mixture = 7 ounces

Total original quantity of mixture = 3 + 7 = 10 ounces

We have to find the amount of water to add into the new mixture to make the proportion of medicine and water same as the original mixture.

Here,

Proportion of medicine and water in original mixture = 3:7

Quantity of medicine and water in new mixture = 18:7

Now,

18 ÷ 3 = 6

Then, 7 × 6 = 42

So, 42 - 7 = 35

Therefore, we have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.

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Triangles are congruent if their matching interior angles and sides are all congruent.

What is congruence in math?

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

Congruent figures: what are they?

What is congruent shapes?

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Answer:

Negative

Step-by-step explanation:

1) Factorizing the expression x⁶ - 729 is; (x + 3)(x - 3)(x⁴ + 9x² + 81)

2) Solving the equation 2x² + 16x – 11 = -7 by completing the square is; x = -4 + √18 or -4 - √18

3) Factorizing x⁴ – 5x² – 36 over the complex numbers is; (x + 3i)(x - 3i)(x + 2)(x - 2)

1) We are given the expression; x⁶ - 729

It can also be written as;

(x²)³ - 9³

Now, from factorization of algebra, we  know that;

a³ - b³ = (a - b)(a² + ab + b²)

Thus;

(x²)³ - 9³ = (x² - 9)((x²)² + 9x² + 9²)

= (x² - 9)(x⁴ + 9x² + 81)

= (x + 3)(x - 3)(x⁴ + 9x² + 81)

2) We want to solve the equation 2x² + 16x – 11 = -7 by completing the square.

Add 7 to both sides to get;

2x² + 16x – 11 + 7 = -7 + 7

2x² + 16x – 4 = 0

Divide through by 2 to get;

x² + 8x – 2 = 0

Add 2 to both sides to get;

x² + 8x = 2

Take half of the x term and square it and then add the result to both sides to get;

x² + 8x + 16 = 2 + 16

Rewrite the perfect square on the left to get;

(x + 4)² = 18

Take square root of both sides to get;

x + 4 = ±√18

Subtract 4 from both sides to get;

x = -4 ± √18

x = -4 + √18 or -4 - √18

3) We want to factorize x⁴ – 5x² – 36

Using the difference of squares identity, we know that;

a² - b² = (a + b)(a - b)

Thus;

x⁴ – 5x² – 36 = (x² + 9)(x² - 4)

Now, (x² + 9) factored over the complex numbers gives;

(x² + 9) = (x + 3i)(x - 3i)

Thus;

x⁴ – 5x² – 36 = (x + 3i)(x - 3i)(x + 2)(x - 2)

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The area of triangle is 12 square units.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Given:

The given points are

A=(1,2)

B=(1,8)

C=(5,2)

According to given question we have

By the use of distance formula , we get

[tex]AC=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AC=\sqrt{(5-1)^{2} +(2-2)^{2} }\\\\AC=\sqrt{(4)^{2} +(0)^{2} }\\\\AC=4 units\\\\\\AB=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AB=\sqrt{(1-1)^{2} +(8-2)^{2} }\\\\AB=\sqrt{(0)^{2} +(6)^{2} }\\\\AB= 6 units[/tex]

Area of right triangle(A) is given by:

[tex]Area =\frac{1}{2} base *height[/tex]

where,

base of the triangle =4 units

height of the triangle =6 units.

[tex]Area =\frac{1}{2} base *height\\\\Area =\frac{1}{2}* 4 *6\\\\Area =12 square units[/tex]

Therefore, the area of triangle is 12 square units.

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Answer:

Recurring Decimal

Recurring Decimal, also called as repeating decimal, is a decimal number only that consists of digits repeating after a fixed interval after the decimal. For example, 46.374374374..., 5173.838383... etc. Decimals can be classified into different categories depending upon what type of digits occur after the decimal point, whether the digits are repeating, non-repeating, end, or unending (infinite digits after the decimal point).

Examples are

0.6666666666,

1.456456456

Step-by-step explanation:

Set as brainliest

The correct answer would be option 2 and 3:

We have to sove the problem by carefully trying to understand the statements

x = largest angle

y =  next largest angle

z = smallest.

1. For the first statement: The measure of the largest angle is 40 degrees less than the sum of the measure of the other two angles.

largest angle < y + z

This would be represented as

x = y + z - 40

2. The largest angle is twice the smaller angle minus 30 degrees.

This is represented as

2 times of smallest = 2 * z = 2z

minus 30 degrees = 2z - 30

Hence the solutions to the question from the option that we have would be the options

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Answer:

2) x=2z−30

3) x=y+z−40

Step-by-step explanation:

Answer:

[tex]y=18x+ 12[/tex]

Step-by-step explanation:

Given equation:

[tex]2+\dfrac{1}{6}y=3x+4[/tex]

Subtract 2 from both sides:

[tex]\implies 2+\dfrac{1}{6}y-2=3x+4-2[/tex]

[tex]\implies \dfrac{1}{6}y=3x+2[/tex]

Multiply both sides by 6:

[tex]\implies 6 \cdot \dfrac{1}{6}y= 6 \cdot3x+ 6 \cdot2[/tex]

[tex]\implies y=18x+ 12[/tex]

Answer: i believe its 3.2 cups per cake

Step-by-step explanation:

9.6 / 3 = 3.2

Answer:

The first 2 and the 2nd to last equations

Step-by-step explanation:

Angles 8 and 10 are alternate interiors, which would only work if m and n are parallel.

Angles 1 and 9 are congruent angles, which would only work if m and n are parallel.

Angle 1 and 3 are on the same line, so that can't prove it.

m8 and m9 could only add up to 180 if m and n are parallel, which makes this also true.

Angles 7 and 10 add up to 180, but can't be congruent.

Answer:

Just graph, first one Y int: 2 and X is rise over run 1 and 2

Step-by-step explanation:

Answer:

"Games played in a workplace environment to achieve status, advancement and money"

Answer:12+2y

Step-by-step explanation:

Answer:

12 + 2y

Hope this helps :)

Step-by-step explanation:

When it says "sum," this means the answer to 2 numbers you add. The first number would be 12, and the other number will be y 2 times. So y plus y equals 2y. The final equation is 12 + 2y.

The distance between each pair of parallel lines with the given equations y = -2x+1 and y = -2x+16 is 15 units.

We can find the points passing through the lines.

Hence,

The points passing through the line y = x - 11  are:-

Let x = 0

y = -2(0) +1

(0,1)

and;

Let x = 1/2

y = -2(1/2) + 1 = -1 +1

(-1/2,0)

The points passing through the line y = -2x + 16 are:-

Let x = 0

y = -2(0) + 16 =16

(0,16)

and;

Let x = 8

y = -2(8) + 16 = -16 + 16

(8,0)

Hence, using distance formula, the distance between the parallel lines will be:-

[tex]\sqrt{(16-1)^2+(0-0)^2} = \sqrt{15^2+0}=\sqrt{225} = 15[/tex] units.

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Answer:

That is wrong it is not $938 its $322

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rate: 54000 brochures per hour

Formula: D=RT   Distance=Rate x Time (In this case distance is the amount)
(I’m not sure if you meant to type 3 1/4 or 314. I’ll include both)
D=54,000(3 1/4)

Two ways

1. 54,000(3 1/4)=175,500

2. 54,000x3 is 162,000, and 1/4 of 54,000 is 54,000/4=13,500. 162,000+13,500=175,500.

(54,000 x 314 = 16,956,000)

Hope this helps!

Using least common multiple (LCM), the Vasquez family both visit their grandmother and host the neighbor hood party after 24 weeks. After 48 weeks, all three events will occur at the same time.

A common multiple is defined as a whole number, that is a shared multiple of each set of numbers. The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers.

If the Vasquez family visit their grandmother every 3 weeks and host a neighbor hood party every 8 weeks, to know when will these event will occur at the same time, solve for the LCM of 3 and 8.

3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . .

8 : 8, 16, 24, 32, 40, . . .

LCM = 24

Hence, after 24 weeks, both will occur at the same time.

To know when will the three events will occur at the same time, solve for their LCM.

3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, . . .

8 : 8, 16, 24, 32, 40, 48, . . .

16 : 16, 32, 48, . . .

LCM = 48

Hence, after 48 weeks, all three events will occur at the same time.

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Answer:

-2/5

Step-by-step explanation:

Hi there!

We find slope by using rise over run.

For this problem, identify two points on the line. I'll use (0, 3) and (5, 1).

[tex] m = \frac{{y} - {y} }{ {x} - {x}}[/tex]

You can plug the coordinates into this formula, making sure they stay in the right order. Subtract the first y coordinate from the second y coordinate, and the first x coordinate from the second x coordinate. (Just make sure one point is on the left, and the other on the right).

[tex] \frac{3 - 1}{0 - 5} = \frac{2}{ - 5} [/tex]

2/-5 is the same as -2/5, so that is your answer

The expression that represents the difference between the student's guess and the actual number of marbles will be 1206 - 2m.

When there are 1206 marbles in a jar and a student makes a guess of m marbles. The expression for the guesses will be:

= 2 × m

= 2m

The expression that represents the difference between the student's guess and the actual number of marbles will be:

= 1206 - 2m

= 2(603 - m)

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Answer:

Step-by-step explanation:

(i)

[tex]2.014^2-2.012^2=\\(2.014+2.012)(2.014-2.012)=\\4.026*0.002=\\0.008052=\\8.052*10^{-3}[/tex]

(ii)

[tex]12^3+8^3=\\(12+8)(12^2-(12)(8)+8^2)=\\20*(144-96+64)=\\20*112=\\2240[/tex]

(iii)

[tex]9^3-5^3=\\(9-5)(9^2+(9)(5)+5^2)=\\4*(81+45+25)=\\4*151=\\604[/tex]

Answer:

why did the teacher give an exam

Answer:

1. Room size (length * width) for carpet

2. From window top to floor for curtains

Step-by-step explanation:

To form a system with an infinite number of solutions, the equation -4x + 6y = 3 must be combined with D. 0.75 + x = 1.5 y.

A system of equations is a set of two or more equations which includes common variables.

To form a system with an infinite number of solutions, the lines should be the same or overlapping. These lines must have the same slope and y-intercept. The equations of these lines must be the multiple of one another.

Given the equation -4x + 6y = 3, rewrite this in the form c + ax = by(same as the form of the choices).

-4x + 6y = 3   ⇒   3 + 4x = 6y

To make 6y into 1.5y, divide both sides by 4.

3 + 4x = 6y   ⇒   0.75 + x = 1.5 y

Hence, the equation -4x + 6y = 3 must be combined with 0.75 + x = 1.5 y to form a system with an infinite number of solutions.

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Answer:

The answer is 36

Step-by-step explanation:

12+6=18

18/3=6

6 squared is 36

36 simplified is still 36