Susan is choosing tween two cell phone plans that offer the same amount of free minutes.
Plan A charges $29.99 per month with additional minutes costing $0.45
per minute.
Plan B charghes $39.99 a month with addtional minutes costing $0.40 per minute. If the equation for Plan A is
0.45x + 29.99 and the equation for plan E
is 0.40x+ 39.99, then how many addtional minutes, x, will it take for the two plans to cost the same?

The quadratic function is f(x) = x² - 11x + 12 which zeros are 12 and -1

A quadratic function is a polynomial function of the form:

f(x) = ax²+ bx + c

where a, b, and c are constants. The zeros of a quadratic function are the values of x that make the function equal to 0.

To find a quadratic function whose zeros are 12 and -1, we can use the fact that the sum of the zeros of a quadratic function is equal to the negative of the coefficient of the x term (b) and the product of the zeros is equal to the constant term (c).

Using this information, we can set up the following system of equations:

x1 + x2 = -b

x1 × x2 = c

Where x1 and x2 are the zeros of the function.

Substituting the known values of the zeros (12 and -1) and solving for a and c, we get:

12 + (-1) = -b

12 × (-1) = c

Solving for b and c gives us:

b = -11

c = 12

Therefore, a quadratic function whose zeros are 12 and -1 is:

f(x) = a(x - 12)(x + 1)

where a is any non-zero constant.

As per the given question, if we set a = 1, the function becomes:

f(x) = (x - 12)(x + 1) = x² - 11x + 12

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Answer:

Smaller number = 4

Larger number = 13

Step-by-step explanation:

Smaller number = x

Larger number = 4x - 3

Sum of the numbers = 17

x + 4x -3 =  17   {Combine like terms}

   5x - 3 = 17    {add 3 to boht sides}

        5x = 17 + 3

        5x = 20      {Divide both sides by 5}

          x = 20/5

         x = 4

      Larger number = 4x - 3

                               = 4*4 -3

                                = 16 - 3

                                = 13

The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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By using the division property of equality we can divide both sides by -12 to get the solution x = -4

An equation:

A = B

Says that the number A is equal to the number B, so basically, are the same number.

So, if we divide both A and B by the same number C, we will get:

A/C and B/C

And A and B are the same numbers, then A/C and B/C also are the same numbers.

So in an equation, we can divide both sides by the same number (except 0) and the equation will not change.

In this case we have:

-12*x = 48

We could divide both sides by -12, so we will get:

-12*x/-12 = 48/-12

x*(-12/-12) = -4

x = -4

And thus we used the division property of equality to solve the equation.

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Answer:

(2,-1)

Step-by-step explanation:

We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:

4(2y + 4) + 2y = 6

Simplifying the left side:

8y + 16 + 2y = 6

Combining like terms:

10y + 16 = 6

Subtracting 16 from both sides:

10y = -10

Dividing both sides by 10:

y = -1

Now that we know y, we can use the second equation to find x:

x = 2y + 4

x = 2(-1) + 4

x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -1).

The correct answer choice is (2, -1).

Answer:

1191 cm²

Step-by-step explanation:

Area of parallelogram = base X vertical height.

Call the vertical line h.

h/ sin 80  =  7/ sin 10

h = (7 sin 80) / sin 10

= 39.7.

Area of parallelogram = 30 X 39.7

= 1191 cm²

The Area of Parallelogram whose side length is 30 cm is 1,190.952 square cm.

Given:

Side length = 30 cm

Using Trigonometry

tan 80 = P / Base

5.6712 = P / 7

P = 39.6984 cm

Using the formula for Area of parallelogram

= Base x height

= 30 x 39.6984

= 1,190.952 square cm.

Therefore, the area is 1,190.952 square cm.

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Answer:

$374,080.00

Step-by-step explanation:

You want to calculate the interest on $40000 at 5.8% interest per month after 12 year(s).

The formula we'll use for this is the simple interest formula, or:

\(I=P*R*T\)

Where:

P is the principal amount, $40000.00.

r is the interest rate, 5.8% per month, or in decimal form, 5.8/100=0.058.

t is the time involved, 12....year(s) time periods.

Since your interest rate is "per month" and you gave your time interval in "year(s)" we need to convert your time interval into "month" as well.

Do this by multiplying your time, 12 year(s), by 12, since there's 12 months in 1 year.

So, t is 144....month time periods.

To find the simple interest, we multiply 40000 × 0.058 × 144 to get that:

The interest is: $334080.00

Usually now, the interest is added onto the principal to figure some new amount after 12 year(s),

or 40000.00 + 334080.00 = 374080.00. For example:

If you borrowed the $40000.00, you would now owe $374080.00

If you loaned someone $40000.00, you would now be due $374080.00

If owned something, like a $40000.00 bond, it would be worth $374080.00 now.

Answer

Options C and E are the correct answers.

The two options that are indeed vertical asymptotes of this function include

Explanation

Asymptotes are the points on either the x or the y-axis where the graph of the function doesn't touch.

Taking each of the options one at a time, we will know which of them are actually asymptotes.

Option A

x = π

We can see that a line passes through this point,

At x = π, y = 0

This is not an asymptote for this function.

Option B

x = 0

We can see that a line passes through this point,

At x = 0, y = 0

This is not an asymptote for this function.

Option C

x = (3π/2)

We can see that the lines of the function avoid the vertical line of x = (3π/2)

This is an asymptote for this function.

Option D

x = (π/4)

This lies between x = 0 and x = (π/2)

We can see that a line passes through this point,

At x = (π/4), y = -0.5

This is not an asymptote for this function.

Option E

x = (π/2)

We can see that the lines of the function avoid the vertical line of x = (π/2)

This is also an asymptote for this function.

Hope this Helps!!!

Two ways of solving:

1. Convert the fractions to decimals:

3/7 = 0.42857

3/5 = 0.6

0.42857 < 0.6

So 3/7 < 3/5

Second way is to rewrite the fractions with a common denominator:

3/7 = 15/35

3/5 = 21/35

Now compare the numerators:

15 < 21 so 3/7 < 3/5

The dot represents the data point of 5, and there are no other data points to include on the dot plot.

You can still make a dot plot even if you just have one number in the tens by placing a dot on a number line above the number. If your data point is 5, for instance, you can represent it by placing a dot above the tick mark for 5 on a number line that has tick marks for each integer from 0 to 9. Here is an illustration of how the dot plot might appear:

  |      

5  •      

  |      

  |      

  |      

  |      

  |      

  |      

  |      

  |      

  +   -   -    -   -   -   -   -

  0  1   2   3  4  5  6  7

There are no additional data points to place on the dot plot because the dot in this illustration represents the data point of 5.

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Answer: The function h because the graphs of f and h are symmetrical about the line y=x.

The mean and standard deviation of the sampling distribution of the sample mean (average) of the SAT math scores are:

(b) Mean = 515, SD = 114/√100

The mean of the sampling distribution of the sample mean is equal to the population mean (515), because the expected value of the sample mean is equal to the population mean. The standard deviation of the sampling distribution of the sample mean is called the standard error, and it is equal to the population standard deviation divided by the square root of the sample size (114/√100).

The result (b) is determined based on the central limit theorem, which states that as the sample size increases, the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the population mean is 515 and the population standard deviation is 114, so the standard deviation of the sampling distribution of the sample mean is equal to 114/√100. This result can be mathematically proven using the formula for the standard deviation of the sample mean:

SD of sample mean = σ/√n, where σ is the population standard deviation and n is the sample size.

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The answer of the following are; A. 16 yellow marbles were chosen

B. 24 marbles were chosen

C. Not enough information.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are obtained data from the question. This include the following:

marble = 40

Black marble =..?

A. From the question given, 3/5 of the 40 marbles were chosen. It therefore means that 2/5 were not chosen and 16 of these were black.

yellow marble chosen = 2/5 x 40 = 16.

Therefore, 16 yellow marbles were chosen.

B. From the question given, 3/5 of the 40 marbles were chosen.

marble chosen = 3/5 x 40 = 24.

Therefore, 24 marbles were chosen.

C. Not enough information because the number of black marbles in the bag was not given, we can not obtain the total number of marbles that were not chosen.

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Answer:

f(4) is the correct answer which gives the number 27.

The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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The value of length BC is 18.9

Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Therefore,

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

Therefore, the length of BC is 18.9

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In the triangle, the value of the side BC is 18.9cm to 1 decimal place

The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The cosine formula states that

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

In conclusion, the value of  the length of BC is 18.9cm

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Answer:

-10x+25

Step-by-step explanation:

−5(2x−5)

=(−5)(2x+−5)

=(−5)(2x)+(−5)(−5)

=−10x+25

The general form of the equation of a circle is given as:

Where:

(a, b) is the coordinate of the center of the circle

r is the radius of the circle

Now, given the circle in question, with:

(-4, 12) as the coordinate of the center

sqrt(3) as the radius of the circle,

The equation of the circle is as follows:

Therefore, the equation of a circle with center (-4, 12) and radius sqrt(3) is:

(x + 4)^2 + (y - 12)^2 = 3

Step-by-step explanation:

law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides, A, B, C are the corresponding opposite angles.

so,

16/sin(90) = x/sin(30)

16/1 = x/0.5

0.5 × 16 = x

x = 8 units

Pythagoras now gets us half the baseline (and therefore the full baseline) :

16² = x² + (baseline/2)² = 8² + (baseline/2)²

256 = 64 + baseline²/4

192 = baseline²/4

768 = baseline²

baseline = sqrt(768) = sqrt(256×3) = 16×sqrt(3) units

the area of a triangle is

baseline × height / 2

in our case

16×sqrt(3) × 8 / 2 = 16×sqrt(3) × 4 = 64×sqrt(3) units² =

= 110.8512517... units²

Answer:

Step-by-step explanation:

12*4*y

=

4(12y)

.......

Answer:

Step-by-step explanation:

[-5/13] 3/5 +12+13 [-4/5 = - 63/65

This phrase can be used in a variety of contexts, from simple arithmetic problems to more complex Algebraic equations and expressions.

The algebraic expression ÷ 8 can be written in a variety of ways depending on the context and the specific operation being performed. However, in general, the phrase "divided by 8" or "the quotient of x and 8" can be used to represent this expression.

For example, if we have an algebraic expression such as 24 ÷ 8, we can write it as

24 divided by 8

the quotient of 24 and 8

24/8

In each case, the idea is the same: we are dividing 24 into 8 equal parts, or finding how many groups of 8 are contained in 24.

In the context of an algebraic equation or expression, the phrase "divided by 8" is often used to indicate that the variable or expression preceding it is being divided by 8. For example:

3x ÷ 8

(2y + 5) ÷ 8

In these cases, we are dividing the value of 3x or the sum of 2y and 5 by 8. The quotient of these expressions will depend on the specific values of x and y."divided by 8" is a commonly used phrase to represent the algebraic expression ÷ 8. This phrase can be used in a variety of contexts, from simple arithmetic problems to more complex algebraic equations and expressions.

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Answer:

Step-by-step explanation:

Vicky  jogged 4 1/2 miles or 9/2 miles  or 4.5 miles

7/8 of 60 min=(7*60)/8=(7*15)/2= 52.50 min

4.5 miles....................52.50 min

? miles.......................60 min

vicky will have a rate of 5.14 miles/hour

Answer:

253 cm^2

Step-by-step explanation:

Large rectangle (without the cutout)

A = wl

A = 18*18

A = 325

Small rectangle (cutout)

A = wl

A = 12 * 6

A = 72

Substract 72 from 325

Answer: you will multiply the length of its base by its height.

Step-by-step explanation:

The area of square with side length 0f 1/4 inch is equals to 0.0625 square inch.

"A square is a regular quadrilateral, which  has four equal sides and four equal angles. It can also be defined as a rectangle with two equal adjacent sides."

Formula used

Area of square = side × side

According to the question,

We have

Side length of the square = 1/4 inch

                                          = 0.25 inch

Area of square = 0.25 × 0.25

                          = 0.0625 square inch

Hence, area of square is 0.0625 square inch.

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The slope of a line that is parallel to y=5x+3 is 5x.

Two lines must have the same slope to be parallel to each other.

Mikey Johnson shipped out 34 2/7 pounds of electrical supplies. The supplies are placed in individual packets that weigh 2 1/7 pounds each. Therefore, Mikey shipped out 16 packets of electrical supplies.

To solve the problem, we can use the following steps.Step 1: Find the weight of each packet.

We are given that the weight of each packet is 2 1/7 pounds.

To convert this mixed number into an improper fraction, we can multiply the whole number by the denominator and add the numerator.

This gives us: 2 1/7 = (2 × 7 + 1) / 7= 15 / 7 pounds.

Therefore, the weight of each packet is 15/7 pounds.

Now, divide the total weight by the weight of each packet.

We are given that the total weight of the supplies shipped out is 34 2/7 pounds.

To convert this mixed number into an improper fraction, we can multiply the whole number by the denominator and add the numerator.

This gives us: 34 2/7 = (34 × 7 + 2) / 7= 240 / 7 pounds.

Therefore, the total weight of the supplies is 240/7 pounds.

To find the number of packets that Mikey shipped out, we can divide the total weight by the weight of each packet.

This gives us: 240/7 ÷ 15/7 = 240/7 × 7/15= 16.

Therefore, Mikey shipped out 16 packets of electrical supplies.

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