How are natural and whole numbers different ?

Answer:

3x^2 - 48 = 0

Step-by-step explanation:

The roots of a quadratic equation whose roots are -4 and 4, means that valid solutions for the quadratic equation are -4 and 4.

The two forms we know for the quadratic equation are the factored binomials:

(ax + cy)(bx + dz) = 0

and the full equation

ax^2 + bx + c = 0

We will start with the factored form:

(x + 4) ( x - 4) = 0

Note that if we solve this, we get the roots:  x + 4 = 0  ==> -4 && x - 4 = 0 ==> 4

Now we apply foil to get the unfactored form:

(x + 4) (x - 4) = 0

x * x + x * -4 + 4 * x + 4 * -4 = 0

x^2 + -4x + 4x + -16 = 0

x^2 - 16 = 0

And now we want the leading coefficient to be 3.

3x^2 - 16  = 0

This looks like what we want; however, now with the leading 3, our solutions are no long +4 and -4.  So, we need to re-evaluate.

Going back to the binomials with the idea of a leading 3, let's rewrite them to still give us the solutions 4 and -4, but with the 3 included:

(3x + 12) (x - 4) = 0

Note, we simply multipled one binomial by 3 to maintain the roots of the original, but also incorporate the leading 3.

3x + 12 = 0              x - 4 = 0

3x = -12                        x = 4

x = -4

So now, we simply apply foil to this new equation of binomials to get our final quadratic equation:

(3x + 12) (x - 4) = 0

3x * x + 3x * -4 + 12 * x + 12 * -4 = 0

3x^2 + -12x + 12x + -48 = 0

3x^2 - 48 = 0

This is our quadratic equation we wish to use.

Note, we could have gotten this same equation by simply multiplying the original (x^2 - 16) = 0 by 3.

Cheers.

Answer:

Step-by-step explanation:

6 + 8 + p = 14 + p

Answer: 14+p

Step-by-step explanation:  We have to add these numbers-

6 + 8 + p

14+p

(Since we don't know the value of p this is how far we can simplify )

Answer:

-12

Step-by-step explanation:

a + b

a = -46

b = 34

-46 + 34 = -12

Answer:

Step-by-step explanation:

150 students/3 classes= 50 students per class

Answer:the answer would be 2.5/5

Answer:

$170.14

Step-by-step explanation:

4,861 / 1,000 = $4.861 per gallon

35 x $4.681 = $170.135, so you need to round up to the nearest penny

Step-by-step explanation:

For 1000 gallons=$4861

For 1 gallon =$4861/1000

For 35 gallons=$4861/1000 x 35=170.135

Answer:

The number of years needed is 15.75 years.

Step-by-step explanation:

The investment amount (present value) = $200

Interest rate =4.5%

Double of investment = $400

Now we have to find the time or number of years in which the investment amount will be doubled. So, just use the below formula to find the number of years.

Future value = present value ×(1+interest rate)^n

400 = 200×(1+4.5%)^n

N = 15.75 years

The number of years required to double the amount is 15.75 years.

quadrant 4

.................

Answer:

Quadrant 4

Step-by-step explanation:

In Quadrant 4 the x-axis is positive (+) and the y-axis is negative (-). Here is the point plotted on a coordinate grid to help you understand better.

Hope this helps :)

The domain is the set of possible x values or inputs. We list each unique x value once (ignoring any repeats)

The range is the set of possible y outputs. Convention is to sort the values from smallest to largest.

This relation is not a function because the x value x = 5 corresponds to multiple y values.

Answer:

Yes

Step-by-step explanation:

6,000 is 10 times greater than 60

Answer:

m ≈ 3

Step-by-step explanation:

3.53631284916 x 10^3 ≈ 3 x 10^3

Answer:

The other lockers that were changed exactly 3 times are:

Locker 1 and Locker 7

Step-by-step explanation:

Question: What other lockers were changed exactly 3 times?

Answer: Lockers 1 and 7

How?

Locker 1 was opened by a student other than student 1; it was closed by a student other than student one; and it was opened by student 1.

Same happened with Locker 7.

The relationship between these numbers is an associative relationship.

Answer:

Any number less than -13.

Step-by-step explanation:

If the number is real and rational and non-natural, this means that it can be any number in the negative number space.

Additionally, since the number has to be less than -13, then the number could be any number less than -13.

With all these things considered, the number is any number less than -13 that is real and rational.

Cheers.

Answer:

x^2 - 8x + 9

Step-by-step explanation:

Please write x2+9-8x as x^2 + 9 - 8x.  The " ^ " indicates exponentiation.

Next, please write x^2 + 9 - 8x in descending powers of x:

x^2 - 8x + 9

Answer:

the last one is the only one with a y intercept of -1

Step-by-step explanation:

Answer:

Dhshshshhshsjehsjsjjsjssjsjsjsjsjsjjshhdhddhhdjdjddjdjjhdhdkdhjsdfggdhjjjjd

Step-by-step explanation:

Answer:

9 - 21x  

Step-by-step explanation:

Simplify the following:

7 (1 - 3 x) + 2

Hint: | Distribute 7 over 1 - 3 x.

7 (1 - 3 x) = 7 - 21 x:

7 - 21 x + 2

Hint: | Add the numbers in -21 x + 2 + 7 together.

Add like terms. 2 + 7 = 9:

9 - 21 x

Hint: | Factor out the greatest common divisor of the coefficients of 9 - 21 x.

Factor 3 out of 9 - 21 x:

Answer: 3 (3 - 7 x)

(of the given solutions it's the only correct one, but can be further simplifued to 3 (3 - 7 x)

Any two parallel lines always have the same slope (but different y intercepts)

The equation of the green line is y = (8/5)x+6

The equation of the red line is y = (8/5)x-3

Slope intercept form is y = mx+b with m as the slope and b as the y intercept.

The slopes must be the same so that each time the line goes up some amount, we move to the right the same amount. Think of a set of stairs to possibly visualize what I mean. If the slopes are different (even slightly), then the lines will intersect at some point and we wouldn't have parallel lines.

Divide US population by Vermont :

3x 10^8 / 6x10^5

3/6 = 1/2 = 0.5

10^8 / 10^5 = 10^3

0.5 x 10^3 = 500

The answer is 500 times

All we need to do is divide.

3*10^8/6*10^5

0.5^8-5

0.5^3

500

Therefore, the answer is 500 times.

Best of Luck!

Answer:

10.8 meters

Step-by-step explanation:

1.2 times 9 minutes= 10.8

Answer:

10.8 meters

Step-by-step explanation:

9 * 1.2 = 10.8

Answer:

Equation to represent all number of points = |4|

Step-by-step explanation:

We are told that a player either wins or loses 4 points during each turn. This means a player could either gain 4 points or loose 4 points. When writing this in Mathematical terms its means either -4 or +4.

Now, since possible number of turns is -4 or 4, then we can represent this with the absolute value symbol.

Thus, it's |4|

Answer:

thousands place

Step-by-step explanation:

Answer:

x + 3.5

Step-by-step explanation:

You are adding

hopefully this helps you:)

The answer would be

B. 9

Answer:

Step-by-step explanation:

4x^2(x^2 - 5x + 6)

4x^2(x - 3)(x - 2)

Answer:

[tex]90^\circ[/tex]

Step-by-step explanation:

Given two non zero vectors, [tex]\vec a, \vec b[/tex].

Let the angle between the two vectors = [tex]\theta[/tex]

Given that:

[tex]|\vec a+\vec b|=|\vec a-\vec b|[/tex]

Let us have a look at the formula for magnitude of addition of two vectors:

[tex]|\vec x+\vec y|=\sqrt{x^2+y^2+2xycos\theta}[/tex]

Where [tex]\theta[/tex] is the angle between the two vectors.

formula for magnitude of subtraction of two vectors:

[tex]|\vec x-\vec y|=\sqrt{x^2+y^2-2xycos\theta}[/tex]

As per the given condition:

[tex]\sqrt{a^2+b^2+2abcos\theta}=\sqrt{a^2+b^2-2abcos\theta}[/tex]

Squaring both sides:

[tex]a^2+b^2+2abcos\theta=a^2+b^2-2abcos\theta\\\Rightarrow 2abcos\theta=-2abcos\theta\\\Rightarrow cos\theta = -cos\theta\\\Rightarrow 2cos\theta = 0\\\Rightarrow cos\theta = 0\\\Rightarrow \theta = 90^\circ[/tex]

So, the angle between the two vectors is: [tex]90^\circ[/tex]

Answer: c) 91.68 < μ < 98.32

Step-by-step explanation:

Let μ  be the mean score of all students.

Let [tex]\overline{x}[/tex] represents the sample mean score.

As per given , we have

Sample size : n= 30

Sample mean : [tex]\overline{x}=95[/tex]

Sample standard deviation: [tex]s=6.6[/tex]

Significance level [tex]\alpha=0.01[/tex]

Now, Confidence interval of mean when population standard deviation is unknown is given by :-

[tex]\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}[/tex]

Degree of freedom = n-1 = 29

Critical two-tailed t-value : [tex]t_{0.01/2,29}=t_{0.005,29}=2.756[/tex] [By students' t distribution table]

Confidence interval of mean will be:

[tex]95\pm (2.756)\dfrac{6.6}{\sqrt{30}}\\\\=95\pm (2.756)\dfrac{6.6}{5.47722557}\\\\=95\pm (2.756)(1.205)\\\\=95\pm 3.32\\\\= (95-3.32, 95+3.32)\\\\=(91.68,\ 98.32)[/tex]

i.e. a 99% confidence interval for the mean score of all students : 91.68 < μ < 98.32

So correct option is c) .

Answer:

the perimeter is 13yd + 13yd + 5yd +5yd = 36yd

the area is 5yd + 5yd = 10yd, 10yd × 12yd ÷ 2 = 60yd

Answer:

The coordinates of point P are (2,5)

Step-by-step explanation:

We know that point P divides AB internally in the ratio 3:2, that is AP/PB = 3/2,

we thus use the formula for internal division.

Let A = (x₁, y₁) = (-4, 8), B = (x₂, y₂) = (6, 3) and P = (x, y)  

So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

where m = 3 and n = 2

Substituting the values of the x coordinates of A and B into x, we have

x = (mx₂ + nx₁)/(m + n)

x = (3 × 6 + 2 × (-4))/(3 + 2)

x = (18 - 8)/5

x = 10/5

x = 2

Substituting the values of the y coordinates of A and B into y, we have

y = (my₂ + ny₁)/(m + n)

y = (3 × 3 + 2 × 8)/(3 + 2)

y = (9 + 16)/5

y = 25/5

y = 5

Therefore, the coordinates of point P are (2,5)