use the completing the square method to solve the equation x^2 + 16x + 2.

a) North Carolina has 4,910,119 more people than South Carolina

b) the population of North Carolina is 2.06 times larger than that of South Carolina

Step-by-step explanation:

a)

Here the question is asking "how much larger is the population of North Carolina than South Carolina". This means that we have to compare the absolute value of the population of North Carolina with the population of South Caroline.

We have:

NC = 9,535,483 is the population of North Carolina

SC = 4,625,364 is the population of South Carolina

In order two compare the two, we have to calculated the difference between NC and SC. Plugging into a calculator, we get:

[tex]NC-SC=9,535,483-4,625,34=4,910,119[/tex]

So, North Carolina has 4,910,119 more people than South Carolina.

b)

In this question, we are asked "how many times larger is North Carolina’s population than South Carolina’s population". This is equivalent to ask what is the ratio between the population of North Carolina to that of South Carolina.

As we said before, we have:

NC = 9,535,483 is the population of North Carolina

SC = 4,625,364 is the population of South Carolina

And by calculating the ratio, we find:

[tex]\frac{NC}{SC}=\frac{9,535,483}{4,625,364}=2.06[/tex]

So, the population of North Carolina is 2.06 times larger than that of South Carolina.

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Answer: the population of North Carolina is 2.06 times larger than that of South Carolina.

Answer: 8 3/7

Step-by-step explanation:

32/7 + 3 6/7

= 32/7 + 27/7

= 59/7

= 8 3/7

Hope this helps!

Hello! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

So you are adding fractions, but not just any fractions, mixed numbers.

So, to start you are gonna wanna turn these mixed numbers into improper fractions.

Here are the steps!

1. Multiply the whole number by the denominator

2. Add that to the numerator

3. Write the number you now have over the original denominator

So 4 4/7 = 32/7

3 6/7 = 27/7

You can only add or subtract fractions with like denominators. This just means denominators with the same number. In our case, we already have like denominators. They are both seven! So the adding process easy. Simply add the numerators and keep the denominators the same!

32 + 27= 59/7

Bam! 59/7 is your answer! If you would like to turn this back into a mixed number, here are the steps:

1. Divide numerator by denominator

2. Put that number as the whole number

3. Use the remainder as the numerator

4. Keep the same denominator

So, 59/7 = 8 3/7

So your answer is 59/7, or, 8 3/7.

Have a great day! And feel free to reply with any questions! (〃^∇^)ﾉ

Answer:

1) the set of all points in a plane that are at a given distance from a given point in the plane

2)a chord of a circle that contains the center of the circle

3)circles that have equal radii

4)two or more circles that lie in the same plane an have the same center

5)a segment joining the center of a circle to a point of the circle

Answer:

21.6

Step-by-step explanation:

18 is the 100% of the given number, 120% is 18 + 20% of 18

to find 20% of 18 we multiply 18 by 20 and the divide it by 100

18 × 20 ÷ 100 = 3.6 now add this to 18 and the answer is 21.6

Answer:

21,6

Step-by-step explanation:

120% × 18 =

= 120×18/100

= 2160/100

= 21,6

x - 6 = - 3 + 8

x = 5 + 6

x = 11

3w - 8w = 35

- 5w = 35

5w = - 35

w = - 35 : 5

w = - 7

3(3x - 3) = 10x

9x - 9 = 10x

- 9 = 10x - 9x

x = - 9

Answer:

1. x = 11,

2. w = -7,

3. x = -5

4. x = -5

5. x = -9

Step-by-step explanation:

1. x-6 = -3+8

x - 6 = 8 -3

x - 6 = 5

Adding 6 to both sides:

x - 6 + 6 = 5 + 6

x = 11

2. 3w - 8w = 35

3w - 8w = 35

-5w  = 35

Divide both sides by -5

-5w/-5 = 35/-5

w = -7

3. - 4 x - 4 x = 44 - 4

- 4 x - 4 x = 44 - 4

-8x = 40

Divide both sides by -8

-8x/-8 = 40/-8

x = -5

4. 5 -8 = 3x +2 - 2x

Collecting like terms and rearranging equation

3x - 2x = 5 - 8 - 2

x = 5 - 10

x = -5

5. 3(3x - 3) = 10x

3(3x - 3) = 10x

Expanding and removing parenthesis

9x - 9 = 10x

Collecting like terms and rearranging equation

10x - 9x = -9

x = -9

Answer:

0

Step-by-step explanation:

The period of the function [tex]y=\tan x[/tex] is equal to [tex]\pi.[/tex]

To find the exact value of [tex]\tan (6\pi)[/tex], first note that we can skip 6 periods of this function, so

[tex]\tan (6\pi)=\tan 0[/tex]

Use definition of [tex]\tan:[/tex]

[tex]\tan 0=\dfrac{\sin 0}{\cos 0}[/tex]

Since

[tex]\sin 0 = 0\\ \\\cos 0=1,[/tex]

we have that

[tex]\tan (6\pi)=\tan 0=\dfrac{\sin 0}{\cos 0}=\dfrac{0}{1}=0[/tex]

Answer:

10 hours

Step-by-step explanation:

Let [tex]N[/tex] represent the distance the train heading north has traveled

Let [tex]S\\[/tex] represent the distance the train heading south has traveled

Let [tex]t[/tex] represent the number of hours that has passed

[tex]N=25t\\S=35t[/tex]

[tex]600=N+S[/tex]

[tex]600=25t+35t\\600=60t\\t=10[/tex]

Nancy and Matilda will meet in 3 hours.

Step-by-step explanation:

Given,

Distance to cover = 60 miles

Speed of Matilda = 12 miles per hour

Speed of Nancy = 8 miles per hour

Combined speed of Nancy and Matilda = 8+12 = 20 miles per hour

Let,

x be the time taken by them

Distance = Speed * Time

[tex]60=20*x\\60=20x\\20x=60[/tex]

Dividing both sides by 20

[tex]\frac{20x}{20}=\frac{60}{20}\\x=3[/tex]

Nancy and Matilda will meet in 3 hours.

Keywords: distance, speed

Learn more about distance at:

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In 3 hours Nancy and Matilda meet.

Given

Nancy and Matilda are 60 miles apart, cycling towards each other on the same road.

Matilda rides 12 miles per hour and Nancy rides 8 miles per hour.

Speed is defined as the ratio of distance and time.

The time will take to meet Nancy and Matilda is given by;

[tex]\rm \dfrac{12}{8}=\dfrac{x}{60}\\\\8 \times x=60\times 12\\\\8x=720\\\\x = \dfrac{720}{8}\\\\x=90[/tex]

Therefore.

The time taken to meet them is;

[tex]\dfrac{12}{8}+\dfrac{90}{60}\\\\1.5+1.5= 3[/tex]

Hence, in 3 hours will they meet.

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Answer: 200%

Step-by-step explanation:

We are asked to find the percent increase in student fees. The amount of increase in student fees is given by

final amount − initial amount = increase

12,000 − 4,000 = 8,000

We can now find the percent increase by finding what percent the amount of increase is of the initial amount. In other words, we want to find what percent 8,000 is ... of 4,000.

Let p be the percent. The question can be translated into an equation.

8,000  {is}  {what percent}     {of}  4,000

8,000  {=}   {          P          }     {x}   4,000

To solve for p, we can now divide each side by 4,000 and simplify.

8,000 = 4,000p

p=2

To convert p to a percent, multiply 2 by 100.

2 x 100

=200%

It follows that the percent increase in student fees was 200%.

Answer:

200%

Step-by-step explanation:

Find the amount of change.

12,000−4,000=8,000

Find the percent.

Change is what percent of the original amount?

Let p= the percent.

8,000 is what percent of 4,000?

Translate to an equation and simplify.

8,000 = p⋅ 4,000=

8,000 = 4,000p

Divide both sides by 4,000 and change to percent form.

2=p

200%=p

Answer:

84

Step-by-step explanation:

Using PEMDAS: (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

7*(3+9)

7*(12)

84

Answer:

83

Step-by-step explanation:

Answer:

1) D

2) A, D, F

3) 3.5 mph

4) equation in explanation $15

Step-by-step explanation:

4) equation: 27.50-12.50

Answer: 1/5

Step-by-step explanation: To find the probability of selecting a mint out of the jar, we use our ratio for the probability of an event which is shown below.

(P) event = number of favorable outcomes/total number of outcomes.

Since there are 7 mints in the jar, the number of favorable outcomes is 4 and since there are 35 candies in all,

the total number of outcomes is 35.

Therefore, the probability of selecting a mint is 7/35.

Notice however that 7/35 is not in lowest terms so we need to divide the numerator and denominator of 7/35 by their greatest common factor of 7 to get 1/5.

So our final answer for the probability of selecting a mint is 1/5.

The difference between four times a number and one can be expressed as 4x - 1, where "x" represents the number. This expression involves multiplying the number by 4 and then subtracting 1.

The difference between four times a number and one can be succinctly expressed as the result of multiplying that number by four and then subtracting one from the product. In mathematical notation, this difference can be represented as:

4x - 1

Here, "x" represents the unknown number, and we are performing two operations: multiplying it by 4 and subtracting 1 from the result. Let's break this down further:

Four times a number: When you multiply a number by 4, you are essentially scaling it up by a factor of 4. For example, if the number is 5, then four times that number would be 4 * 5 = 20.

Subtracting one: After obtaining the result of four times the number, we subtract 1 from it. In our example, if the number is 5, then after four times the number (20), subtracting 1 results in 19.

So, the difference between four times a number and one is the value obtained after performing these two steps. It's a simple arithmetic expression that can be calculated for any given value of "x."

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Answer:

C - 8

Step-by-step explanation:

153 - 81 = 72

72 ÷ 9 = 8

Answer:

C) 8

I looked at the other answer at the bottom.

Answer:

Step-by-step explanation:

Example:  (cx)×(ax + b) comes out to acx^2 + bcx, which is a linear quadratic (highest power of x is 2).

the product of a linear monomial and a linear binomial will be

[tex]\rm = (cx)\times(ax + b)[/tex]   which will comes out to  [tex]\rm acx^2 + bcx[/tex] that is a linear quadratic higgest power of x

Lets understand,

A Linear monomial is an Expression that has only one given term & whose power or highest degree is one. It cannot take any addition or subtraction signs monomial is an linear expression that has only a single non-zero term. Monomials can be numbers, variables, or numbers multiplied with variables.

Examples of linear monomial:-

For example, [tex]\rm 2, ab, and\; 42\;xy[/tex] are examples of a monomial. A few other examples of monomials are [tex]\rm 5x, 5x^3 , 7xy,x^5 .[/tex]

Therefore, the product of a linear monomial and a linear binomial will be

[tex]\rm = (cx)\times(ax + b)[/tex]   which will comes out to  [tex]\rm acx^2 + bcx[/tex] that is a  quadratic with higgest power of x.

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Answer:

overlapping lines

Step-by-step explanation:

look at shown picture

Answer:

5y-x

MathMathMathMath

The question involves discovering rules for completing mathematical tables and requires skills in pattern recognition, multiplication, and data organization.

The student's question requires finding a rule for each given table and writing the missing number. Utilizing mathematical skills to recognize patterns or apply known operations is the key to solving these problems. For example, when asked about the cube of a number such as (74)³, one would have to multiply 74 by itself three times to get the result. This translates to 74 * 74 * 74, which can also be expressed as 7.4 * 102 * 7.4 * 102 * 7.4 * 102. Furthermore, when working with tables of data, it's essential to organize the data accurately and calculate additional information such as relative frequency when required.

In another instance, if you're given a list of numbers corresponding to particular data points, like the roster of students or experimental results, the task could involve identifying patterns or utilizing statistical tools to complete the tables.

It's important to show work and approach each problem methodically, confirming the application of correct mathematical rules. By doing so, you gain deeper understanding and enhance your problem-solving skills.

Step-by-step explanation:

Formula of straight line is given as:

[tex]y= mx + c[/tex]

Where m = is the gradient or slope & c = y-intercept.

Answer:

T   = 0.05x + 35

D  = 0.03x + 55

Step-by-step explanation:

i) On the last weekend in November both Terri and Donna earned from sales the amount of x.

ii) Terri pays the amount T = 0.05x + 35

iii) Donna pays the amount D  = 0.03x + 55

Answer:

Net Change in Geno's Field Position = 22 yards

Step-by-step explanation:

Assuming Geno initial position before change is 0

Geno Gained 4 yards three times = 4*3 = 12yards

Geno lose 1 yard twice = 1*(-2) = -2yards

Geno Gained 6 yards twice = 6*2 = 12yards

Net Change in Geno's Field Position = 12 + (-2) + 12 yards

                                                            = 22 yards

Answer:

Step-by-step explanation:

8y-24=8(y-3)

Answer:

Total population = 200

Step-by-step explanation:

recaptured tagged/recaptured total ≈ tagged/total population

The best estimate for the total population of Robin's is 200.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given that,

Number of robins which are tagged = 20

Let x be the total population of robins.

Her catches some other robins.

Number of robins that he catched = 120

Number of robins he catched also is tagged = 12

We can write the expression as,

20 / x = 12 / 120

Cross multiplying, we get,

12x = 120 × 20

12x = 2400

x = 2400 / 12

x = 200

Hence the number of robins is 200.

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trying to find the system to the solution you have to put in into slope intersecpt form so y=mx+b

so 4=m(3)+b

12=b

y=3x+12

The rate of the cabin cruiser in calm water is 9 mph and the rate of the current 3 mph

Step-by-step explanation:

Given:

Speed of cabin cruiser travelling with then current =  12 mi in 1 h.

Against the current, it took 2 h to travel the same distance.

To Find:

The rate of the boat in calm water and the rate of the current = ?

Solution:

Let  boat speed in calm water  be s

Let rate of the current  be c

Then

(s-c) = effective speed upstream

and

(s+c) = effective speed downstream

Writing a distance equation for each trip:

distance  = [tex]time \times \text{effective speed}[/tex]

1(s + c) = 12

2(s - c) = 12

On the first equation divide both sides by 1

On the second equation divide both sides by 2

s + c = 12

s - c = 6

Now addition of the above two equations gives

2s = 18

s = 9 mph, boat speed in calm water

Lets substitute s value to find  c value

s + c = 12

9 + c = 12

c = 12 - 9

c = 3 mph is the current

Final answer:

The cabin cruiser's rate in calm water is 9 mph, and the rate of the current is 3 mph.

Explanation:

To solve this problem, we will let c represent the rate of the current and r represent the rate of the cabin cruiser in calm water. When traveling with the current, the effective speed of the cruiser is r + c, and against the current, it is r - c.

Using the given information:

Now we can set up a system of equations:

Adding these two equations, we get:

2r = 18

Dividing both sides by 2, we find r = 9 mph. Thus, the rate of the cabin cruiser in calm water is 9 mph. To find the rate of the current, plug r = 9 into either of the original equations. Let's use equation (2):

9 - c = 6

Subtracting 9 from both sides, we find c = 3 mph. So the rate of the current is 3 mph.

Answer:

36 tables are used to seat  the students at the banquet: 12 rectangular and 24 round.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Round tables = 8 seats

Rectangular tables = 12 seats

Ratio of round tables to rectangular tables = 2:1

Number of students = 336

2. How many tables are used to seat 336 students at the banquet, if no table has an empty seat?

x = Number of rectangular tables

2x = Number of round tables

Let's solve for x, using this equation:

12x + 8 (2x) = 336

12x + 16x = 336

28x = 336

x = 336/28

x = 12 ⇒ 2x = 24

12 + 24 = 36

36 tables are used to seat  the students at the banquet: 12 rectangular and 24 round.

Answer:

36

Step-by-step explanation:

Answer:

He bikes 1.6 km per hour.

Step-by-step explanation:

If he bikes 3.2km un 2 hours, then:

3.2 km / 2 hours = 1.6 km / hour

4 cubic feet

Step-by-step explanation:

Step 1:

Length of the concrete beam = 6 feet

Side for the square base = 8 inch = 8/12 feet

So, volume of the concrete beam = 6*(8/12)*(8/12)= 2.67 cu ft

Hence mass of the beam = density of the beam * volume

= 150 * 2.67 = 400 kg

Step 2:

we need the the weight of sand equivalent to the concrete beam.

Mass of the sand bags = den of sand * vol

=> 100 * volume of sand = 400

=> Volume of sand = 400/100 = 4 cu feet.

Answer:

-6

Step-by-step explanation:

the first part is equal to -8 and then you add two which is -6

Answer:

New average = 85.9.

Step-by-step explanation:

Yes, the new class average can be calculated.

The New total of the scores = 37*86 + 76 + 81 + 97

= 3436.

The new total of examinations sat = 37 + 3 = 40.

Therefore the new class average =  3436 / 40

= 85.9