If the entire pizza has a 16 inch diameter and is cut into 8 slices. Find the area of a slice of pizza, to the nearest tenth.

Factoring, utilizing square roots, completing the square, and the quadratic formula are the four ways for solving a quadratic equation.

To factor a quadratic equation, do the following:

1. In standard form, transform the equation such that one side is zero.

2. Take into account the non-zero side.

3. Make each component equal to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero).

4. Solve each of the resultant equations.

Factoring cannot solve all quadratic problems. For example, x²- 3x = 3 cannot be solved using this approach. Completing the square is one approach for solving quadratic equations; graphing the result is another.

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Answer:

B. (50)

Step-by-step explanation:

So, looking at PEMDAS,

Parenthesis,

Exponents,

Multiplication,

Division,

Addition,

Subtraction.

We have no parenthesis and no exponents.

But, we have multiplication.

62x1=62

According to the identity property of 1, any number multiplied by 1 retains its identity. In other words, any number multiplied by one remains unchanged. The number remains constant because multiplying by one produces one copy of the number.

So, next, we have an addition problem.

62+2=64.

And now, subtraction.

64-14=50.

So, the final answer is 50 or known as B.

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The solution to the given fractional equation is x = -4

32/x - 8 = 24/x - 10

collect like terms

32/x - 24/x = -10 + 8

(32-24) / x = -2

8/x = -2

cross product

8 = -2 × x

8 = -2x

divide both sides by -2

x = 8/-2

x = -4

Check:

32/x - 8 = 24/x - 10

32/-4 - 8 = 24/-4 - 10

-8 - 8 = -6 - 10

-16 = -16

Therefore, the equation has the solution x = -4

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The discriminant of the equation 2x2 + 5x + 7 = 0 is -31.

The discriminant of a quadratic equation is the expression under the square root symbol in the quadratic formula.

The formula for the discriminant of a quadratic equation is given by:

Discriminant = b2 - 4ac

In this equation, a, b, and c are the coefficients of the quadratic equation, ax2+bx+c=0.

In this case, the coefficients of the equation given are a=2, b=5 and c=7.

Therefore, the discriminant of this equation can be calculated as follows:

Discriminant = b2 - 4ac

             = 52 - 4(2)(7)

             = 25 - 56

             = -31

Therefore, the discriminant of the equation 2x2 + 5x + 7 = 0 is -31.

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Answer:

9

Step-by-step explanation:

810/90 = d

d=90

Answer:

d = 9

Step-by-step explanation:

to solve, divide each term by 90 and then simplify

90d = 180

[tex]\frac{90d}{90}[/tex] = [tex]\frac{810}{90}[/tex]

[tex]\frac{810}{90}[/tex] = 9

[tex]d[/tex] = 9

The side-length of the given square is 4 units and the equation used to represents the length of the diagonal AC is given by y = -x + 6 .

As given in the question,

In the given square ABCD,

Coordinates of the vertices of the square is given by :

A(2,4), B(-2,4), C(-2,8), and D(2,8)

All the side - length of the square are of equal measure.

Side-length of AB = √ ( 4 - 4 )² + ( -2 -2 )²

                              = √ 16

                              = 4 units

Equation of the diagonal AC is given by :

( y - 4 ) / ( x - 2 ) = ( 8 - 4 ) / ( - 2 -2 )

⇒( y - 4 ) / ( x - 2 ) = 4 / -4

⇒ y - 4 = -1 ( x - 2 )

⇒ y = -x + 2 + 4

⇒ y = -x + 6

Therefore, the side-length of the given square is 4 units and equation of the diagonal AC is y = -x + 6.

The given question is incomplete, I answer the question in general according to my knowledge:

Square ABCD with vertices A(2,4), B(-2,4), C(-2,8), and D(2,8) over the x-axis. Find the length of each side and equation to represent the length of diagonal AC of the given square ?

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By using speed calculation and the Pythagorean theorem, it can be concluded that the contestant is moving down at a rate of 11.8 feet/second.

In speed calculation, speed is defined as the distance traveled in a certain unit of time. Speed can be calculated by dividing the distance by time:

Speed = distance / time

We will need the Pythagorean theorem to solve the problem as well. It says that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two shorter sides:

c² = a² + b²

Now we take a look at the problem.

The height of the pole = 50 feet

Distance between pole and anchor = 50 feet

Time = 7 seconds

We want to know the speed of a contestant, that is the distance traveled in 6 seconds.

Let c be the distance traveled, a be the height of the pole and b be the distance between the pole and the anchor.

We will use the Phtagorast Theory to find c:

c² = a² + b²

   = 50² + 50²

   = 2500 + 2500

   = 5000

c = √5000

  = 70.7 feet

Rate or speed the contestant moving down the line:

Rate = distance / time

        = 70.7 / 6

        = 11.8 feet/second

Thus, the contestant is moving down at a rate of 11.8 feet/second.

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[tex]\stackrel{\textit{not distributed yet}}{\cfrac{x+1}{(x-2)(x+1)}\stackrel{\downarrow }{\text{\LARGE -}}\cfrac{x-2}{(x-2)(x+1)}}\implies \stackrel{\textit{already distributed}}{\cfrac{x+1}{(x-2)(x+1)}\stackrel{\downarrow }{\text{\LARGE +}}\cfrac{-x+2}{(x-2)(x+1)}} \\\\\\ \cfrac{x+1-x+2}{(x-2)(x+1)}\implies \cfrac{3}{(x-2)(x+1)}[/tex]

Answer:

The error is in the 3rd step.  The denominator should be 3, not -1.

Step-by-step explanation:

The third step has an error.  The second fraction is subtracted from the first.  The calculation should have been (x+1) - (x-2).  x+1-x+2 = 3.

See the attached worksheet.

Note that in the above distance-time graph, Sue was traveling for 210 minutes, while she was stationary for 150 minutes.

Note that if the x-axis of the graph is calibrated to 30 minutes per unit/calibration. When examined you'd note that the total number of hours of the trip is from 2 pm to 8 pm which is 6 hours or 360 minutes.

The part of the graph that depicts when Sue was traveling is all the part of the pink curve that is at an incline while the part that represents when she was stationary is when the curve was horizontal.

Adding up the minutes when the graph was at an incline gives a total of 210 minutes.

Thus, the number of times Sue spent being stationery is:
360 - 210

= 150 minutes. This also corresponds with the number of times the graph is horizontal.

Thus, Sue was moving for 210 minutes and stationery for 150 minutes.

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Note that in the above distance-time graph, Sue was traveling for 210 minutes, while she was stationary for 150 minutes.

What is the justification for the above result?

Note that if the x-axis of the graph is calibrated to 30 minutes per unit/calibration. When examined you'd note that the total number of hours of the trip is from 2 pm to 8 pm which is 6 hours or 360 minutes.

The part of the graph that depicts when Sue was traveling is all the part of the pink curve that is at an incline while the part that represents when she was stationary is when the curve was horizontal.

Adding up the minutes when the graph was at an incline gives a total of 210 minutes.

Thus, the number of times Sue spent being stationery is:

360 - 210

= 150 minutes. This also corresponds with the number of times the graph is horizontal.

Thus, Sue was moving for 210 minutes and stationery for 150 minutes.

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By using the geometric mean (leg) theorem, the value of x is equal to: B. 2√70

In Mathematics, the geometric mean (leg) theorem states that the altitude which is drawn from the hypotenuse side of a right-angled triangle would divide the hypotenuse side into two (2) equal sides.

According to the geometric mean (leg) theorem, the length of the leg of a right-angled triangle is the geometric mean between its hypotenuse and the segment of the hypotenuse which is adjacent to that leg.

By applying geometric mean (leg) theorem, the length of the altitude can be calculated as follows;

h/6 = 14/h

h² = 14 × 6

h = √84

h = 2√21

By applying Pythagorean theorem to triangle ABC, the hypotenuse (a) can be calculated as follows;

a² = 14² + h²

a² = 14² + (√84)²

a² = 196 + 84

a = √280

a = √4 × √70

a = 2√70

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Answer:

Communitive Property

Step-by-step explanation:

The communitive property: changing the order of the operands does not change the result.

Therefore, 9+1+7 = 9+7+1

This benefits you because during a problem, you can rearrange the order to make it communitive(if needed) and you can make it equal! It also reduces the number of independent basic multiplication facts to be memorized.

The values are calculated as Part A : $3611.6245, Part B : 21.81% and Part C : $1107.75.

Mark Down percentage is the percentage of reduction in the original price of an item.

Mark down percentage = [(original price - selling price) / original price] × 100

Part A :

Original price = $4248.97

Markdown = 15%

0.15 = (4248.97 - x) / (4248.97)

4248.97 - x = 637.3455

x = 4248.97 - 637.3455

x = $3611.6245

Reduced price of the refrigerator is $3611.6245.

Part B :

Selling price = $1270.55

Original price = $1625

Mark up percentage = [(1625 - 1270.55) / (1625)] × 100

                                  = [354.45 / 1625] × 100

                                  = 21.81%

Part B :

Selling price = $886.20

Mark down percentage = 20%

0.2 = (x - 886.2) / x

0.2x = x - 886.2

x - 0.2x = 886.2

0.8x = 886.2

x = $1107.75

Hence the selling price, mark down percentage and original price has been calculated as $3611.6245, 21.81 % and $1107.75 respectively.

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The histogram displays the frequency distribution of a variable in intervals, showing shape, central tendency and variability.

The histogram of the wr.hnd variable in the overview information in R utilizing the hist capability would show a graphical portrayal of the recurrence dissemination of the information. It would show the quantity of perceptions (i.e., the recurrence) in various spans (i.e., canisters) of the wr.hnd variable. This can give knowledge into the appropriation of the information, like the shape, focal propensity, and changeability.

A precise depiction for the histogram of wr.hnd could include:

The histogram shows the recurrence appropriation of the wr.hnd variable.

The wr.hnd variable is partitioned into stretches or canisters, and the level of each bar addresses the quantity of perceptions in that span.

The histogram gives a visual portrayal of the shape, focal propensity, and changeability of the wr.hnd information.

The histogram shows the recurrence circulation of a variable in spans, showing shape, focal propensity and changeability.

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A mixture contains 200 oz of juice that contains 60% tomato juice and 100 oz vegetable juice that contains 20% tomato juice. The concentration tomato juice in the resulting mixture is 40%.

Percentage is used to represent a fraction of a hundred.

Let:

w1 = weight of tomato juice in juice 1

w2 = weight of tomato juice in vegetable juice

Hence,

w1 = 60% x 200 oz = 120 oz

w2 = 20% x 100 z = 20 oz

Total weight of tomato juice = 100 + 20 = 120 oz

Total weight of the mixture = 200 oz + 100 oz = 300 oz.

Hence, the concentration of the tomato juice in the final mixture is:

concentration = total weight of tomato juice/ total weight of mixture

                       = 120/300

                       = 2/5 = 40%

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The symbol used in the ratio is given by :

1. If we are using ' : ' symbol it is called colon.

2. If we are using ' \ ' symbol it is called by.

3. Third way we use word 'to' to represent the ratio.

As given in the question,

Different symbols used to represent the ratio of two numbers.

Let us consider two number be 'x' and 'y'.

1. Ratio can be represented in the form x : y.

Used symbol ' : ' is known as colon.

2. Ratio can be represented by fraction form.

x / y

Here 'x' is called numerator and y is called denominator.

3. Third way to write ratio is word 'to'

x to y.

Therefore, symbols used to represents the ratio of any given numbers is called 'colon' , 'by' , and 'to'.

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The amount of the 60 milligram dose that is still active in the dog’s bloodstream after 3 hours, after 4.25 hours, and after n hours respectively are as follows;

f(3) = 60(0.80)^3.

f(4.25) = 60(0.80)^4.25.

f(n) = 60(0.80)^n.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

Since 20% of the medicine becomes ineffective every hour, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 20 = 80% = 0.8

After 3 hours, the active dose is given by:

f(3) = 60(0.80)^3

After 4.25 hours, the active dose is given by:

f(4.25) = 60(0.80)^4.25

After n hours, the active dose is given by:

f(n) = 60(0.80)^n

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Complete Question:

Medicine taken by a patient breaks down in the patient’s blood stream and dissipates out of the patient’s system. Suppose a dose of 60 milligrams of anti-parasite medicine is given to a dog and the medicine breaks down such that 20% of the medicine becomes ineffective every hour.

How much of the 60 milligram dose is still active in the dog’s bloodstream after 3 hours, after 4.25 hours, and after n hours?

Using proportions and similar triangle theorem, the value of x is 54.6m

A comparable triangle is a triangle that is similar to another triangle in shape but may not be identical in size. If and only if two triangles have equal matching angles and side ratios, two triangles are said to be similar.

In this problem, we can use the concept of proportion and similar triangle theorem to find the value of x.

This is represented mathematically as;

45.5 / 80.5 = x / 96.6

Cross multiply both sides and solve for x

45.5 * 96.6 = 80.5 * x

4395.3 = 80.5x

x = 4395.3 / 80.5

x = 54.6

The value of x is 54.6m

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Answer: $115

Step-by-step explanation:

Since Juan bought 30 books for $2 each, the amount of money he spent was $60. He received 5 free copies, so that makes 35 books total.

Then, Juan sold each copy for $5, which means that the total money he earned is $5*35 = $175

Since he earned $175 and spent $60, his total profit is 175-60 = 115

Answer: $115

The exact magnitude of BD is q - 3p

Consider the following diagram.

Here, in trapezium ABCD, side DC is parallel to side AB

and DC=3AB

Given that M is the midpoint of DC

From definition of midpoint, DM = MC

The magnitude of DM or MC would be

= 1/2 ​DC

= (1/2) × 3 × AB

= (3/2) × AB

= (3/2) p

From given figure we can observe that BD = BC + CD

so, BD = BC - CD

BD = q - 3p​

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The complete question is:

ABCD is a trapezium with AB parallel to DC and DC=3AB. M is the midpoint of DC. AB=p​, BC=q​.

Find the exact magnitude of BD.

The number of different ways the medals can be awarded is (finalists) * (finalists -1) / 2.

We have two medals (gold and silver) and "n" finalists. The question asks for the number of ways the medals can be awarded.

This is a combination problem, where we have to select 2 items (medals) out of n items (finalists) without regard to the order.

The number of ways to select k items out of n items without regard to the order is given by the binomial coefficient (n choose k), which is calculated as:

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items selected and ! denotes factorial.

So, in this problem, we have to calculate the number of ways to select 2 medals out of n finalists, the binomial coefficient is:

nC2 = n! / (2!(n-2)!) = n*(n-1)/2

so the number of different ways the medals can be awarded is n*(n-1)/2

Therefore, the number of different ways the medals can be awarded is (finalists) * (finalists -1) / 2.

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The quote that is an example of negative self-talk is D. "I wonder if this ever gets easier."

Self-talk can be fueled by negative ideas and sentiments and can significantly affect one's sense of self and how they see the world. Negative self-talk has a significant negative effect on self-esteem and unhealthy habits, which can exacerbate problems like addiction and mental health problems.

Negative self-talk can be a symptom of a more serious mental health issue can stem from depression, low self-esteem, and anxiety. But you can also be engaging in bad self-talk because of your habits. Among these behaviors is ignoring relationship issues.

Therefore, option D is correct.

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Answer:

ML = 30

Step-by-step explanation:

Given the figure:

Where MN is parallel to JK, JM = 18, MN = 20, and JK = 32. We need to find the length of ML.

Since MN and JK are parallel lines, this means that ΔMLN and ΔJLK are similar.

This means that the proportion between the lengths of corresponding sides is constant. In particular, we have:

JK/ MN = JN/ML

From the figure:

32/20 = 18+x / x

we solve the equation for x :

8/5 = 18 + x / x

8x = 5 . 18 + 5x

3x = 90

x = 90/3 = 30

Answer:

ML = 30

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A scale factor of 1/3 for the transformation is discovered using proportions.

In accordance with the rule of three, a percentage is a component of a total amount.

If both the new and original dimensions are known, the scaling factor may be determined. A figure's scale factor can be calculated using the following simple formula: Dimension of the original shape minus the dimension of the new shape is the scale factor.

When applying the proportion to this situation, the scale factor of the transformation is 1/3 because each coordinate was multiplied by 3 throughout the transformation process.

A scale factor of 1/3 for the transformation is discovered using proportions.

The complete question is,

DO,K = (9, 6) (3, 2) (3, 2) Scale factor is

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The range of the function is (0, 30), which represents the possible values of the boat's value in thousands of dollars.

An equation is a mathematical statement that uses symbols, numbers, and/or variables to represent a relationship between two or more quantities. It usually contains an equal sign, indicating that the expressions on both sides of the equal sign have the same value. Equations are used to solve problems and find unknown values by manipulating the symbols and solving for the variable.

Here,

The given graph does not represent an exponential function as the values of y do not increase or decrease at a constant rate. However, we can approximate the values and find an exponential function that fits the data points closely.

Using the two given points (0, 30) and (1, 24), we can find the base of the exponential function as follows:

y = abˣ

30 = ab⁰ (at x=0, y=30)

24 = ab¹ (at x=1, y=24)

Dividing the second equation by the first, we get:

24/30 = (ab¹)/(ab⁰)

0.8 = b

Now we can substitute the value of b in one of the equations to find a:

30 = a(0.8)⁰

a = 30

So the exponential function that fits the data points closely is:

y = 30(0.8)ˣ

The y-intercept of this function is 30, which means that the initial value of the boat is $30,000.

The domain of the function is all real numbers (x can be any value representing time in years).

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Answer:

Step-by-step explanation:

2,4

Answer:

x=4

Step-by-step explanation:

3x+4=x+12

     -4    -4

3x=x+8

-x   -x

2x=8

/2   /2

x=4

Answer:

Abigail wants the hairdresser to cut off 1/4 of the total length of her hair, which is 32 inches long.

To find out how many inches the hairdresser cuts, we can multiply the total length of her hair by 1/4:

32 inches * 1/4 = 8 inches

So the hairdresser cuts off 8 inches of Abigail's hair.

The number of such pairs will be 120, which is the same as the result obtained from the formula.

Let A = {0, 1, 5, 8}. The number of distinct pairs of disjoint non-empty subsets of A whose union is A can be calculated using the formula

C(2^n , 2) = C(2^4 , 2) = C(16 , 2) = 120

Therefore, there are 120 distinct pairs of disjoint non-empty subsets of A whose union is A. This can be verified by constructing all the possible pairs of disjoint non-empty subsets of A whose union is A. The number of such pairs will be 120, which is the same as the result obtained from the formula.

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Answer: (3, -3)

Step-by-step explanation:

2x = 4y + 18 => 2x - 4y = 18   (1)

-5x - 6y = 3   (2)

Multiply both (1) by 5, and (2) by -2

10x - 20y = 90   (3)

10x + 12y = -6    (4)

(3)-(4):

-32y = 96

y = -3

x = 3