The numbers 840 and 8316, written as the products. of their prime factors, are 840= 2¹ × 3 × 5 × 7 and 8316= 22 x 3³ x 7 x 11. Hence, find
(i) the greatest whole number that will divide both 840 and 8316 exactly,
(ii) the smallest non-zero whole number that is divisible by both 840 and 8316.

Pls help asap​

Two lines are parallel when their slopes are the same

Two lines are perpendicular when the product of their slopes is -1

Two lines are intersect when their slopes are different

Let's define our slopes as m1 and m2, != means not equal

Solution:

1) m1 = m2        Parallel

2) m1*m2=-1     Perpendicular

3) m1*m2=-1     Perpendicular

4) m1=m2         Parallel

5) m1=m2   (-4 = -4)  Parallel

6) m1 != m2     Neither

7) m1 != m2     Neither

8) m1*m2=-1    Perpendicular

Answer:

96 and 270

Step-by-step explanation:

12×8=96

90

×13

180

+90

270

Answer:

-----------------------

The line of sight is the hypotenuse of the 45° right triangle.

As per the property of the 45° right triangle, the length l is:

Answer:77.7f

Step-by-step explanation: pythagorean theorem

55*55=3025

3025*2=6050

square root 6050=77.7

The value of TU is 117.

What is a line segment?

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.

Here, we have

Given: U is between T and V. If TU = 11x − 15, UV = 10x, and TV = 20x − 3.

We have to find the value of TU.

TV = TU + UV

20x − 3 = 11x − 15 + 10x

20x − 3 = 21x - 15

-3 + 15 = 21x - 20x

12 = x

Now, we have TU = 11x − 15.

We put the value of x on TU and we get

TU = 11x − 15

TU = 11(12) - 15

TU = 132 - 15

TU = 117

Hence, the value of TU is 117.

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The deck of cards Jacob got has a volume of 6.833 cubic inches.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given, Jacob received a deck of cards for his birthday. The length, width, and height of the card box are shown below.

Length = 3 1/2 = 7/2

Width = 2 1/2 = 5/2

Height = 2/3

From the general formula of volume:

volume = Length * width *Height

volume = 7/2 * 5/2 * 2/3

The volume of a pack of cards = 35/6 = 6.833

Therefore, the volume of the Deck of cards Jacob received is 6.833 cubic inches.

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The two equivalent expressions that could be used to find the total number of chocolate pieces that Luisa has are given as follows:

To obtain the number of pieces that Luisa has, we must consider that:

Hence the multiplication operation giving the number of pieces is given as follows:

4 x 10 x 8.

The associative property of multiplication states that the order in which 3 or more terms are multiplied does not change the product, hence the equivalent expressions are given as follows:

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except point (5, 7) all given coordinates are on the line.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

given, an equation 2x−y=20

to check what are the coordinate of the equation:

The easiest way to find out if a point falls on a specific line is to plug the first value of the point in for x and the second value for y.

Thus, For Coordinates(10, 0)

2x−y=20

=> 2 * 10 - 0 = 20

=> 20 = 20

Thus Coordinates are on the line.

Thus, For Coordinates(15, 10)

2x−y=20

=> 2 * 15 - 10 = 20

=> 30 -10 = 20

=> 20 = 20

Thus Coordinates are on the line.

Thus, For Coordinates(5, 7)

2x−y=20

=> 2 * 5 - 7 = 20

=> 3 = 20

Thus Coordinates are not on the line.

Thus, For Coordinates(-4, -28)

2x−y=20

=> 2 * -4 - (-28) = 20

=> -8 + 28 = 20

=> 20 = 20

Thus Coordinates are on the line.

Therefore, except point (5, 7) all given coordinates are on the line.

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Answer:

2/5 of income put into savings

Step-by-step explanation:

Let Kory's income be X

1/3 of his income goes to taxes so taxes are X/3

Remaining is (1-  2/3) of income = (2/3 ) X

He spends 4/5 of this remaining amount

So balance after expenditure = (1- 4/5) = 1/5 of the remaining income and this amount is put into savings

Fraction of income in savings = 1/5 x 2/3 X = (2/15)X

So fraction put into savings account is 1/5 of total income

If you find it confusing to work with fractions such as these, I suggest an alternate approach which may make it easier to understand

Pick an amount for total income. Since the denominators are 3 and 5, choose an amount which is divisible by both 3 and 5 or in other words divisible by 15

Let's choose 300, a convenient number

Tax Paid = 1/3 x 300 = 100

Income after tax = 300 - 100 = 200
which is same as 2/3 x 300

Spending = 4/5 x 200 = 160

Balance in savings = 200 - 160 = 40 same as 1/5 x 200

So amount in savings as a fraction of income = 40/300 = 2/15

y = ln( [tex]\frac{x^2+1}{2}[/tex])  is the required equation.

In a graph of an equation, the x-intercept is the point at which the graph of the equation crosses the x-axis. It is the point where the y-coordinate is equal to 0. The x-coordinate of the x-intercept is the solution of the equation when y = 0.

Given that the slope at point (x,y)

and we know that slope at any find is dy/dx

so dy/dx = [tex]xe^-^y[/tex]

=> dy/[tex]e^-^y[/tex] = xdx

=> [tex]e^y[/tex] dy = x dx

intergrating both side we get:

[tex]e^y[/tex] = x²/2 + c

where c is a constant

given x intercept is 1

[tex]e^0[/tex] = 1²/2 + c

=> 1 = 1/2+c

=>  c= 1/2

so [tex]e^y[/tex] = x²/2 + 1/2

taking ln on both side we get:

y = ln( [tex]\frac{x^2+1}{2}[/tex])  is the required equation.

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Option(B) is the correct answer. The answer is - Adding data from a student who is 154 cm tall and weighs 69kg.

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If Joanie is organizing her closet. She has 3 times as many black shirts as gray shirts, plus 3 new black shirts she just bought. The number of gray shirts that Joanie have is: 2.

Let x represent the number of gray shirts

Let Joanie black shirts = 3x + 3

Let Joanie white shirts =  5x - 1

Let Joanie brown shirts =   2x

So,

3x + 3 = 5x - 1

Substract 3 from both side

3x + 3-3 = 5x - 1 -3

3x = 5x -4

Substract 5x from both side

3x-5x = 5x -4 -5x

-2x =  -4

Divide both side by

x = -4/-2

x =2

Therefore, Joanie has 2 gray shirts.

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The maximum number of zeroes in a generic equation with the form axe? + bx4 + cx3 + dx2 is 5.

a) [tex]$ax^{5}[/tex]

b) Factor 2x3 - 9x2 + 7x + 6  is

(x - 3) (x -2) (2x + 1)

c) x = -b / 2a

Replace x by -2, from the vertex:

-2 = -b / 2a

Solve for b:

-b = -4a

Or

b = 4a

By evaluating the equation with the vertex's x-value, we can determine the y-value from the vertex:

y = ax2 + 4ax - 6

Simplify, 6 for y, and -2 for x:

6 = a(-2)2 + 4a(-2) - 6

6 = 4a - 8a - 6

solve for a:

a = -3

Simplifying the above equation,

b = 4a, b = -12

The value for a is -3.

The value for b is -12

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The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption.  P(terriers) = 85% is likely Option B

Generally, Probability is the area of mathematics that deals with providing numerical descriptions of the likelihood that an event will take place or the likelihood that a statement will be correct.

A number between 0 and 1 may be thought of as representing the chance of an event happening, with 0 indicating that the occurrence is impossible and 1 indicating that it will definitely happen.

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Answer:

x=32

x+1=33

Step-by-step explanation:

let the first consecutive integer be 'x'

let the second consecutive integer be 'x+1'

x+x+1=65

2x+1=65

2x=65-1

2x=64

x=64÷2

x=32

x+1=(32+1)

x+1=33

The answer is D. I and II only. The number of people who chose A as their favorite brand could be 30 or 35 since x is rounded to the nearest integer, which is 3. However, it cannot be 45 since 3 is the nearest integer.

1. x is rounded to the nearest integer, which is 3

2. If x is equal to 30, then the number of people who chose A as their favorite brand would be 30

3. If x is equal to 35, then the number of people who chose A as their favorite brand would be 35

4. If x is equal to 45, then the number of people who chose A as their favorite brand would be 45

5. Since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45

6. Therefore, the answer is D. I and II only.

1,150 respondents were asked to select their preferred brand among brands A, B, and C of laundry detergent. x% of those polled indicated that A was their preferred brand. The outcome is 3 if x is rounded to the nearest integer. This means that x could be 30, 35, or 45. However, since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45. Therefore, the answer is D. I and II only, meaning that the number of people who chose A as their favorite brand could be 30 or 35. This is because if x is equal to 30, then the number of people who chose A as their favorite brand would be 30 and if x is equal to 35, then the number of people who chose A as their favorite brand would be 35.

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Trigonometry is the study of relationships between angles and sides of a triangle.

The six trigonometric functions—sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot)—are used to describe the relationships between the angles and sides of any triangle.

The unit circle is a circle of radius one centered at the origin of a Cartesian coordinate system. When we determine the coordinates of points on the unit circle, we are using the six trigonometric functions. The unit circle is used to find the values of the trigonometric functions for angles of measures 0°, 30°, 45°, 60°, and 90°.

In the interval [0, 2π], we can use the unit circle to calculate the trigonometric functions of the angles in both degrees and radians. For example, sin 0° = 0, cos 0° = 1, tan 0° = 0, csc 0° = undefined, sec 0° = 1, cot 0° = undefined. The corresponding values in radians are sin 0 = 0, cos 0 = 1, tan 0 = 0, csc 0 = undefined, sec 0 = 1, cot 0 = undefined.

By using the unit circle, we can find the value of all six trigonometric functions for any angle in the interval [0, 2π], given in degrees or radians. We can also use the unit circle to find the trigonometric functions for any angle in any interval.

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To determine the service fee as a percentage of the deposited amount, we can use the following formula:

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Service fee percentage = (Service fee / Deposited amount) x 100

In this case:

Service fee percentage = (31.74 / 2239.10) x 100 = 1.41%

So, the service fee for depositing the amount of R2239.10 was 1.41% of the deposited amount.

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The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The probability of randomly landing in a particular region of a circular dartboard is 1/6.

The probability of randomly landing in a particular region of a circular dartboard is 1/6. This means that each region of the dartboard is equivalent in size, and thus has the same central angle. Since the dartboard is circular, the total measure of the central angles must add up to 360 degrees. Therefore, the measure of the central angle of each section of the dartboard is 360 divided by 6, which is equal to 60 degrees.

The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The probability of randomly landing in a particular region of a circular dartboard is 1/6.  of randomly landing in a particular region of a circular dartboard is 1/6.

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We can substitute the given values into the expression to find the result:

3s - 4q - m² = 3(-24) - 4(-3) - 4² = 72 + 12 - 16 = 60.

So the expression equals 60 when m= 4, q= -3, and s = -24.

The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.

The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.

y_2(t) = t^2v'(t) + 2t v(t) - y_1(t)

Substituting y_1(t) and y_2(t) in the given equation, we get

t^2v''(t) + 2tv'(t) - 2v(t) = 0

This is a first order linear differential equation and can be solved as

v'(t) = -2v(t)/t

Integrating both sides, we get

v(t) = c/t^2

Therefore, the second solution of the given equation is

y_2(t) = c/t

The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.

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The measure of the angle opposite the side of length 3 is approximately 53.13 degrees.

To find the measure of the angle opposite the side of length 3, we need to use the inverse sine function. The inverse sine function can be written as sin^−1(x). We can use the Pythagorean Theorem to calculate the side length of the triangle, which is 3^2 + 4^2 = 5^2. Therefore, we can use the inverse sine function to calculate the measure of the angle opposite the side of length 3. To do this, we will take the ratio of the side of length 3 to the hypotenuse, which is 3/5. We can then plug this value into the inverse sine function, which gives us sin^−1(3/5). Calculating this value gives us approximately 53.13 degrees, which is the measure of the angle opposite the side of length 3.

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Answer: your answer is c

Step-by-step explanation:

The puffs that the patient will take daily include:

1 puff every 4 hours for 24hrs = 6

1 puff every 6 hours for 24hrs =4

2 puffs every 4 hours for 24hrs =12

2 puffs every 6 hours for 24 hrs =8

From the information, a physician writes a prescription for Proair HFA (albuterol sulfate) for Chronic Obstructive Pulmonary Disease (COPD). The instructions state: Inhale 1 to 2 MDI puffs (90-180mcg) q 4-6 hours.

In this case, it should be noted that puff every 4 hours for 24hrs will be 6 times. Also, 1 puff every 6 hours for 24hrs will be 4 times.

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The monthly cost of x messages is 0.43x + 6 dollars.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given

Cost of message plan for one month = $6

cost for each text = $0.43

The monthly cost is calculated by adding the price of the message plan for one month to the cost of each text message multiplied by the number of messages sent in a month.

Total number of messages sent in a month = x

monthly cost for x text messages = (0.43 * x) + 6

Monthly cost for x text messages = 0.43x + 6 dollars

Hence the cost is 0.43x + 6 dollars.

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You prοbably know our football and basketball teams, but we have 21 Divisiοn I varsity programs that all raise the bar whenever they compete.

There were 465 people whο were surveyed in all.

The attendance at the FSU-Marist game was (M), n(M)=240.

The attendance at the FSU-Butler game was (B), n(B)=200.

The tοtal number οf spectators for the FSU-NC State game was n(NCS)=240.

The cοmbined attendance at the NC State game and the Marist game was n(MNCS)=90.

The cοmbined attendance at the Butler vs. NC State game was n(NCSB)=80.

The cοmbined attendance at the Butler and Marist games was n(BM)=100.

n(MBNCS)=30 peοple attended all three of the games.

When NC State's first football game was οrganised by students in 1892, the school's long histοry of intercollegiate athletics officially started.

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The solution for the inequality |x +1|>-3 is x > -4 or x < -4.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To solve the inequality |x + 1| > -3, we need to consider two cases:

x + 1 > -3: In this case, we can subtract 1 from both sides to get x > -4.

x + 1 < -3: In this case, we can subtract 1 from both sides to get x < -4. However, we also need to reverse the inequality symbol because we are multiplying or dividing by a negative number.

So the solution for the inequality is x > -4 or x < -4.

To get the final solution, we need to consider the combined solution from both cases:

x < -4 or x > -4

This represents as follows:

[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:\mathrm{True\:for\:all}\:x\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

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The ΔBAE is congruent to ΔDAE. ΔBAE and ΔDAE have three corresponding angles that are congruent, so they are congruent.

The Triangle Congruence Theorem states that if two triangles have three corresponding angles that are congruent, then the triangles are congruent.

This can be seen by looking at the angles BAE, BAE, and DAE. All three of these angles are equal, so they are congruent. Additionally, the side lengths of the triangles are the same, so the triangles are also congruent. The Triangle Congruence Theorem is an important tool for determining the congruence of two triangles.

It is used to compare the angles and side lengths of two triangles, and if the angles and side lengths are the same, then the triangles are congruent. When ΔBAE and ΔDAE have the same angles and side lengths, then it is clear that they are congruent.

According to question,

E is the midpoint of,

AC⊥ BD,

As given E is the midpoint of the line ,

So, BE = ED,

further, line AE = AE, because this is the common line between the two triangles.

Also, ∠BED =∠DEA =90°, as AC⊥ BD.

Therefore, the ΔBAE is congruent to ΔDAE.

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Karen divided 560.9 by 10³ and got a quotient of 0.5609 ,therefore he is right.

What do you mean by division?

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

What do you mean by quotient ?

In mathematics, the outcome of dividing two numbers is called the quotient. In other words, the result quotient is obtained by dividing a dividend by a divisor.

How to Divide a Long Number by Decimals?

Hence, Karen divided 560.9 by 10³ and got a quotient of 0.5609.

It is Right answer for the this division, and steps are uploaded in mage kindly see the image also.

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The number of combinations that can be made among eight people is given as follows:

56 combinations.

As there are different roles, the order is important, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

For this problem, two people are selected from a set of 8, hence the number of combinations is given as follows:

P(8,2) = 8!/6! = 8 x 7 = 56 combinations.

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