What is the greatest common factor of 16 , 24 , 48

Exponent rules are those laws that are applied to exponent-based expressions to make them simpler. The principles of exponents make it simple and rapid to execute numerous arithmetic operations like addition, subtraction, multiplication, and division. These guidelines are also useful for reducing the complexity of numbers that have complex powers incorporating fractions, decimals, and roots.

Exponent rules, commonly referred to as the "laws of exponents" or "properties of exponents," facilitate the task of simplifying exponent-based statements. These guidelines are useful for reducing the complexity of expressions whose exponents are decimals, fractions, irrational numbers, or negative integers.

When an exponent is a negative number, we apply the negative law of exponents. This rule states, "The reciprocal should be taken to convert any negative exponent into a positive exponent." The change in sign of the exponent values moves the expression from the numerator to the denominator.

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The factors of the expression is 3x²(x+5)(x+5) .

Factors of a number are defined as the numbers which divide the given number completely.

For an algebraic expression the factors of the expression are smaller polynomials which divide the given expression completely.

Factors of algebraic expression can be  calculated by the following methods:

The given polynomial is of the form:

3x⁴ + 30x³ + 75x²

Taking 3x² common from all the terms we get:

3x² (x² + 10x + 25)

Now we use middle- term factorization method to factor (x² + 10x + 25)

3x² (x² + 5x + 5x + 25)

or, ( 3x² ){x ( x + 5 ) + 5 ( x + 5 )}

or, 3x² (x + 5) (x + 5)

or, 3x²  (x + 5)²

Hence the factors of the expressions are: 3x²  (x + 5)²

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Factor completely:  3x⁴ + 30x³ + 75x²

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Answer:

y = −2x + 8

Step-by-step explanation:

y = −2x + 8, the answer is this because, in order to find the slope, you must use the formula y2-y1/x2-x1, and the y-intercept is found by using the formula y=mx+b, in which b is the y-intercept which leads to the awnser,  y = −2x + 8.

Hi! Your answer is y = −2x + 8

Step-by-step explanation:

In order to find the slope, you have to use y2-y1/x2-x1 for the formula. The y-intercept can be found by using the formula y=mx+b. This means b is the y-intercept which makes the answer:  y = −2x + 8.

Hope this helps! Have a good day :)

The given statement is true that for a given non-zero vector v in r³ there is a unique unit vector parallel to it.

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Answer: 9x^2+6x

Step-by-step explanation:

(4x^2 - 2x) - (-5x^2 - 8x)=

4x^2 - 2x +5x^2 + 8x=

4x^2+5x^2 - 2x + 8x=9x^2+6x

Answer:

x² + y² = z²

Step-by-step explanation:

(a)

Using the right triangle altitude theorem,

x/z = p/x

x² = pz

(b)

y/z = q/y

y² = qz

(c)

x² + y² = pz + qz

x² + y² = z(p + q)

z = p + q

x² + y² = z × z

x² + y² = z²

It should be noted that y=x+8 is not an inverse variation.

The relationships between variables that are expressed in the form of y = k/x, where x and y are two variables and k is a constant number, are known as inverse variations. According to this statement, if the value of one item rises, the value of the other quantity falls.

Ab example is when a constant of variation is k = xy = 5(2) = 10 if y changes inversely as x and x = 5 when y = 2. Consequently, xy = 10 is the equation that describes this inverse variation.

Therefore, it should be noted that y=x+8 is not an inverse variation.

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Answer: 124 degrees ==> Option 3

Step-by-step explanation:

ABC=ABX+XBC

ABX=XBC     ==> bisected angles are equal since when an angle is bisected, it is divided into two equal angles. Hence:

ABC=XBC*2

ABC=62*2

ABC=124 degrees ==> Option 3

Answer:

42, 12)

Step-by-step explanation:

Let the present ages of the father and son be x years and y years respectively.

According to the question,

Condition I,

Three years ago the sum of the ages of the father and his son was 48 years.

or,(x−3)+(y−3)=48

or,x−3+y−3=48

or,x−6=48−y

or,x=54−y - (i)

Condition II,

Three years hence the father's age will be three times the son's age,

or,(x+3)=3(y+3)

or,x+3=3y+9 - (ii)

Put value of x from equation (i) in equation (ii), we get,

or,(54−y)+3=3y+9

or,54−y=3y+9−3

or,54−6=3y+y

or,48=4y

or,y=484

∴y=12

Put the value of y in equation (i), we get,

or,x=54−12

∴x=42

So, (x,y) = (42, 12)

Therefore, the required present ages of the father and the son are 42 years and 12 years respectively.

Answer: Give me 11 min

Step-by-step explanation:

Answer:

Interest = Rs. 1297.26

Step-by-step explanation:

To calculate the final amount, we can use the following formula:

[tex]\boxed{A = P(1 + \frac{r}{100})^n}[/tex],

where:

A = final amount

P = principal (initial) amount

r = rate

n = time in years,

and then we can subtract the initial amount from the final amount to find the interest.

We have been told in the question that the principal, P = Rs. 10,000; and the time is [tex]2\frac{1}{2}[/tex] years, therefore n = 2.5. The rate is 5%, therefore r = 5.

Using this information, and the formula above, we can calculate the final amount:

[tex]A = 10000(1 + \frac{5}{100})^{2.5}[/tex]

⇒ [tex]A = 10000(1.05)^{2.5}[/tex]

⇒ [tex]A = \bf 11297.26[/tex]

Now that we know what the final amount was, we can calculate the interest by subtracting the initial amount from it:

Interest = 11297.26 - 10000

             = 1297.26

Therefore the interest was Rs. 1297.26.

The Absolute Difference and the Relative Difference is  mathematically given as

Absolute Difference = $40;

Relative Difference = 19%. Option B

This is further explained below.

Generally, Divide the difference in values by the value that was used initially, and you will get the relative difference between the two values: difference original value

Perform the conversion to get a percentage out of this amount. If there was a rise in value, we would say there was an increase of x %.

We state there was an x % decline in the value if there was a decrease in the value. x represents the number that was arrived at by us.

In conclusion, since we are comparing A from be we have

Absolute Difference = 250-210

Absolute Difference = $40;

and

Relative Difference =  (Original-ref)/ref

Therefore

Relative Difference 250-210/210

Relative Difference=19%

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Answer:

a^2-b^2=(a + b) (a - b) is the formula

Given that Q is a point between P and R, the numerical values of x, segment PQ, QR and PR are 11, 30, 22 and 52 respectively.

Given the data in the question;

Since Q is a point between P and R.

PR = PQ + QR

Plug in the given values and solve for x.

5x - 3 = ( 2x + 8 ) + ( x + 11 )

5x - 3 = 2x + 8 + x + 11

5x - 3 = 3x + 19

5x - 3x = 19 + 3

2x = 22

x = 22/2

x = 11

Numerical value of segment PQ when x = 11 will be;

PQ = 2x + 8 = 2(11) + 8 = 30

Numerical value of segment QR when x = 11 will be;

QR = x + 11 = (11) + 11 = 22

Numerical value of segment PR when x = 11 will be;

PR = 5x - 3 = 5(11) - 3 = 52

Given that Q is a point between P and R, the numerical values of x, segment PQ, QR and PR are 11, 30, 22 and 52 respectively.

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Answer:

6

12

1

2

Step-by-step explanation:

In 1, is 4. Okay, this a good answer.

The probability that the product of the two rolls is a multiple of 3 is 1/2.

Probability:

Probability mean the fraction of the possibility of the required event.

The formula for the probability is

P(E) = n(E)/n(S)

Where

P(E) = Probability of the event

n(E) = number of required event

n(S) = Total number of event

Given,

Juan rolls a fair regular octahedral die marked with the numbers 1 through 8.

Then Amal rolls a fair six-sided die.

Here we need to find the  probability that the product of the two rolls is a multiple of 3.

We know that,

On both dice, only the faces with the numbers 3,6 are divisible by 3.

Let

P(a) = 2/8

P(a) = 1/4

it is  the probability that Juan rolls a 3 or a 6,

and Similarly,

P(b) = 2/6

P(b) = 1/3

Is the probability of Amal does.

By the Principle of Inclusion-Exclusion,

[tex]\[P(a \cup b) = P(a) + P(b) - P(a \cap b) = \frac{1}{4} + \frac{1}{3} - \frac{1}{4} \cdot \frac{1}{3} = \frac{1}{2} \Rightarrow \mathrm{(C)}\][/tex]

Thus the total probability is 1/2.

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The location of point D on the number line is -5.15625

The given parameters are:

A = 5

B = -10

AC : CB = 1 : 3

This means that

C = AC/(AC + AB) * (A - B)

This gives

C = 1/4 * (5 + 10)

Evaluate

C = 3.75

Also, we have:

BD : DC = 3 : 5

So, we have:

D = BD/(BD + DC) * (B - C)

This gives

D = 3/8 * (-10 - 3.75)

Evaluate

D = -5.15625

Hence, the location of point D on the number line is -5.15625

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The height of the building = 1026.328ft

Given the angle of elevation = 11°

The angle of elevation is the angle formed between the horizontal distance to the base of the building and the line of sight to the top of the building.

We know that tan x = opposite side/adjacent side.

Here the opposite side gives the height of the building and the adjacent side is the distance to the base of the building on the ground.

Distance to the base of the building on the ground = 1 mile = 5280 ft.

So tan 11° = h/5280

⇒ h= tan 11° x 5280 = 0.194 x 5280 = 1026.328 ft

So the height of the building = 1026.328 ft

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The number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) will be D. A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.

It should be noted that a number line is used to illustrate the intervals between the numbers given.

Therefore, the number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) will be a number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right

In conclusion, the correct option is D.

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The median of the data set given for the tips (in dollars) earned in the last hour by waiters in a Japanese restaurant is determined as: 28.

]The median of any given data set is the data value that lies at the center of the data set when ordered.

Given the data set, 30,17,47,47,26,17,36,31,21,17, order the data set from the least to the greatest:

17, 17, 17, 21, 26, 30, 31, 36, 47, 47

The center or middle of the data set is 28.

Thus, the median of the data set given for the tips (in dollars) earned in the last hour by waiters in a Japanese restaurant is determined as: 28.

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Answer:

Hello,

Answer d

Step-by-step explanation:

Since x=y then 3v-1=2v+6 ==> v=7

Answer d

Answer:

b=2/3

Step-by-step explanation:

Let's solve the equation step by step

( b ) = 2/3

Remove bracket

b=2/3

By using the given pair of values we can see that the constant of proportionality is 8, and the proportional relation is:

y = 8*x

A proportional relation is a linear relation with an y-intercept of 0, so these are written as:

y = a*x

Where a is the constant of proportionality.

By knowing a pair of values x and y, we can find the value of a. In this case we can see that when x = 3, y = 24, replacing that in the general equation we get:

24 = a*3

24/3 = a = 8

Then the constant of proportionality is 8, and the proportional relation is:

y = 8*x

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Answer:

Option 1

Step-by-step explanation:

Perpendicular lines form right angles

Parallel lines never intersect.

Answer:

[tex]\sf x = -1 + \sqrt{5}\:i,\: -1 - \sqrt{5}\:i[/tex]

Explanation:

[tex]\sf \rightarrow x^2 + 2x +6 = 0[/tex]

[tex]\sf use\:quadratic\:formula: x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \: \: ax^2 + bx + c = 0[/tex]

comparing identify:

Substitute inside the formula:

[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{2^2 - 4(1)(6)}}{2(1)}[/tex]

evaluate:

[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{4 - 24}}{2}[/tex]

[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{- 20}}{2}[/tex]

[tex]\rightarrow \sf x = \dfrac{ -2 \pm 2\sqrt{5}\:i}{2}[/tex]

[tex]\rightarrow \sf x =-1 \pm \sqrt{5}\:i[/tex]

[tex]\rightarrow \sf x = -1 + \sqrt{5}\:i,\: -1 - \sqrt{5}\:i[/tex]

The experimental research has two key advantages over correlational studies.

1. The possibility of random assignment

2. Causal connections can be assumed.

Correlational studies merely examine the data that already exists, whereas experimental studies give the researcher the opportunity to influence the study's factors. Researchers can make inferences about how changes in one variable affect changes in another through the use of experimental investigations.

The factors in a correlation study are out of the control of the researcher or research team. The researcher merely measures the information she discovers in the outside world. She can then determine whether changes in one are related to changes in the other, or if the two variables are correlated. In such a study, experimenters gather existing data and use statistical methods to examine it, such as economic statistics from governments. The findings of correlation studies can lead to hypotheses that can be verified through a more focused experimental one.

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The point G on AB such that the ratio of AG to GB is 3:2 is; G(4.2, 2)

How to partition a Line segment?

The formula to partition a line segment in the ratio a:b is;

(x, y) = [(bx1 + ax2)/(a + b)], [(by1 + ay2)/(a + b)]

We want to find point G on AB such that the ratio of AG to GB is 3:2.

From the graph, the coordinates of the points A and B are;

A(3, 5) and B(5, 0)

Thus, coordinates of point G that divides the line AB in the ratio of 3:2 is;

G(x, y) = [(2 * 3 + 3 * 5)/(2 + 3)], [(2 * 5 + 3 * 0)/(2 + 3)]

G(x, y) = (21/5, 10/5)

G(x, y) = (4.2, 2)

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[tex]9.6\times 10^9~~ = ~~(2\times 10^5)(4.8\times 10^n)\implies \cfrac{9.6\times 10^9}{2\times 10^5}~~ = ~~4.8\times 10^n \\\\\\ \cfrac{9.6}{2}\times \cfrac{10^9}{10^5}~~ = ~~4.8\times 10^n\implies 4.8\times 10^{9-5}~~ = ~~4.8\times 10^n \\\\\\ 4.8\times 10^4~~ = ~~4.8\times 10^n\implies \cfrac{4.8\times 10^4}{4.8}=10^n\implies \cfrac{4.8}{4.8}\times 10^4=10^n \\\\\\ 1\times 10^4=10^n\implies 10^4=10^n\implies 4 = n[/tex]

Answer:

es equivalente al es 54x

Answer: 63.5

Step-by-step explanation:

90 - 26.5 = 63.5