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The vector PQ is given by the addition of the components of the two vectors i.e. →PQ = →Q + →P

Vector is a quantity having magnitude as well as direction and is used to denote the mathematical and geometrical direction of the given quantity.

For example : Velocity, Displacement etc.  

Let us first assume that,

P(x,y,z) and Q(u,v,w)

Now, we need to find the vector PQ

→PQ = →Q + →P

= (ui + vj + wk ) + (xi + yj + zk)

= (ui + xi ) +(vj  + yj) + (wk +zk)

= (u+x) i + (v + y) j + (w + z)k

= →PQ

For example : Let P(1,2,1) and Q ( -1, -2,4)

Then,  →PQ = →Q + →P

= (1i + 2j + 1k ) + (-1i + (-2)j + 4k)

=  (1-1) i + (2 -2) j + (1 + 4)k

= oi+0j +5j

= 5j

Hence, the vector PQ is given by the addition of the components of the two vectors.

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The approximate circumference of the path Round to the nearest hundredth is 93.12 feet.

A circle's outside boundary is called the circumference and can be measured, or calculated, by using

Circumference = 2πr

where r is the radius of circle.

Now it is given that,

circumference of pond = 68 feet

⇒ 2πr = 68

⇒ r = 34/π

⇒ r = 10.82 feet

Now it is also given that, The outer edge of the path is going to be 4 feet from the pond all the way around

⇒ Radius of path, R = r + 4

⇒ Radius of path, R = 10.82 + 4  

⇒ R = 14.828

So,circumference of the path = 2πR

⇒ circumference of the path = 2π*14.828 = 93.119 feet

⇒ circumference of the path Round to the nearest hundredth = 93.12 feet

Thus, the approximate circumference of the path Round to the nearest hundredth is 93.12 feet.

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The knowledge of  how many more minutes m you can use during the rest of the month is given by the linear inequality 648 + m ≤700, where 'm' is the minutes on the cell phone or simply m ≤ 52

It is given that the  monthly minutes on your cell phone can add up to no more than 700 minutes so the highest limit is 700

And You have already used 648 minutes so this is our base for the formation of linear inequality

We are provided to use 'm' for rest of  the minutes on the cell phone

Hence, we can form a linear inequality using the three points as the sum of already used minutes and the maximum minutes that can be used in this month is at most  700 minutes is given by 648 + m ≤700

This can also be simplified as

m ≤ 700 - 648

m≤52

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The ordering of the number is 6.286  , 6.628 , 6.826

According to the question we have been given three numbers which are

     6.826 , 6.628 and 6.286

We need to arrange in ascending order that is from least number to the greatest number.

when we arrange number in ascending order for decimal number we first look at the number before the decimal point then if they are all same then we look at the number after the decimal point. After the decimal point the first number is compared which is closest to the decimal point.

If we look into this question the number before decimal points are all same thus we will look the numbers after the decimal point. Therefore we will arrange according to the first  number after the decimal that is 8 , 6 and 2

Hence the ordering the number we get:

      6.286  , 6.628 , 6.826

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Answer:

Step-by-step explanation:

Answer:

I'm pretty sure the answer is E

You can add the distance she travelled upwards to her new distance to get her old distance.

Essentially, 21.6 + 61.9 = 83.5.

This means she was 83.5 feet below sea level, before ascending 61.9 feet to 21.6 feet below sea level.

Answer: she was 83.5 feet below sea level, before ascending 61.9 feet to 21.6 feet below sea level.

Step-by-step explanation:

Answer: 36

Step-by-step explanation:

XZ=XY+YZ

48=12+YZ

48-12=12-12+YZ

YZ=48-12

YZ=36

Using it's concept, there is a 0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

A standard deck is given by 4 suits of 13 cards, each with either a number from 1 to 10 or one letter from A, Q or K, hence:

Hence the probability is given by:

p = 48/51 x 45/50 x 42/49 = 0.726.

0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).

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The area of the figure is 289 square unit

The area of a rectangle can be calculated by multiplying the length and the width of the shape.

Given that

But the length and the width have two equal opposite sides. The shape is a square

20 - x = 3x + 8

20 - 8 = 3x + x

12 = 4x

x = 12/4

x = 3

L = 20 - 3 = 17

B = 3(3) + 8

B = 9 + 8

B = 17

A = 17 x 17

A = 289 square unit

Therefore, the area of the figure is 289 square unit

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He estimates that he will stand 6 feet 9 inches tall when he is 20 years old. His prediction is correct.

Given: Growth per year = 3 inches

Height at 15 yrs of age = 5'6''

Height at 20 yrs of age = 6'9''(predicted)

We know that Jesse grows 3 inches every year.

In 5 years(15yrs - 20yrs) his growth = 5 × 3 = 15 inches.

At 15 years(present) height = 5'6''

At 20 years (future) height = 5'6'' + 15'' = 6'9'' (since, 1ft = 12 inches)

Thus, Jesse's prediction is correct

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Answer:

Yes, that means the whole fraction is negative.

Also for future note, if the negative is on the top or bottom, the fraction will still be negative. Unless it says to simplify.

Hope this helps!

Answer:

d = 13

Step-by-step explanation:

19d - 16d - d - d - 1 = 12

19d + (-16 - 1d - 1d) - 1 = 12

19d + (--18d) - 1 = 12

19d - 18d - 1 = 12

1d = 12 + 1

d = 13

Check:

19*13 - 16*13 - 13 - 13 - 1 = 12

247 - 208 - 26 - 1 = 12

39 - 27 = 12

Answer:

[tex]81x {}^{6} - 108 { \times }^{5} + 54 { \times }^{4} - 12 { \times }^{3} + { \times }^{2} [/tex]

Answer:

ue7e7373777 is is and 88877376363778

Answer:

7

Step-by-step explanation:

5x + 3 = 38

5x + 3 - 3 = 38 - 3

5x = 35

5x ÷ 5 = 35 ÷ 5

x = 7

The value of A in the 4-digit number is 5.

Given the information provided in the question, the 4-digit number is a multiple of 15. A multiple of a number is the product of an integer and that number.

The multiple of a number is divisible by that number. For example, a multiple of 2 is 20. This is because 2 multiplied by 10 is equal to 20 and 20 is divisible by 2 to yield a value of 10.

The multiplies of 15 either have a unit value of 5 or 0.

If A is 5, the number becomes 3555.

3555 / 15 = 237

If A is 0, the number becomes 3050

3050 / 15 = 203.333

Thus, the value of A is 5 because 3555 is divisible by 15.

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The correct answer is A. 13.

We have been given equation. Now, to find the value of x, we will take square root. So, solving the mathematical expression now -

x = √169

Taking square root to find the value of x

x = 13

Since the number is positive. the square root of the number will also be positive.

Hence, the solution to equation is A. 13.

Further to cross check, we can also square the resultant number.

On squaring the number 13 for validation of our result, we get 169. It is the same number as in mathematical expression provided to us. Thus, our resultant solution to equation is correct.   

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The complete question is -

What are the solutions to the equation x² = 169? Choose all answers that are correct. A. 13 B. –13 C. 84.5 D. –84.5

The product of the smallest and largest integer is 672

Represent the smallest even integer with x.

So, the other even integers are x + 2 and x + 4

The sum is represented as

x + x + 2 + x + 4 = 18 + 5/2x

Evaluate the like terms

3x + 6 = 18 + 5/2x

Evaluate the like terms

1/2x = 12

Multiply by 2

x = 24

The largest integer is x + 4

So, we have

x + 4 = 24 + 4

x + 4 = 28

The product of the smallest and largest integer is

Product = 24 * 28

Evaluate

Product = 672

Hence, the product of the smallest and largest integer is 672

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The value of b is b=p-a.

Given the equation is p=a+b.

A pair of inverse operations is defined as two operations to be performed on a number or. variable,  always returns the original number or variable And inverse means opposite.

equation means a mathematical statement with the symbol "equal" between two expressions of equal value. This is represented by '='.

The given equation is p=a+b.

Now, we will apply the inverse operations on both sides.

Subtract a from both sides, we get

p-a=a+b-a

Now, we will simplify the above equation, we get

p-a=b

Hence, the value of b from the given equation p=a+b is b=p-a.

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Answer:

Step-by-step explanation:

990 x 70% = 693 people

The coordinates of the centroid of Δ ABC is y = -1/3x + 2.

The slope of the line is the rise-to-run ratio or the rise divided by the run. It expresses the slope of a line in the coordinate plane. Finding the slope of a line is similar to determining the slope between two points.

The midpoint D of AC is (-3+4/2, 3-3/2) or (1/2, 0).

Note that DB is a line that connects the vertex B and D, the midpoint of AC.

The slope of the line DB is ((5-0)/(2-1/2)) or 10/3.

The equation of DB is

y - 5 = 10/3 (x - 2)

simplifying the above equation, we get

y - 5 = 10x/3 - 20/3

y - 5 + 5 = 10x/3 - 20/3 + 5

y = 10x/3 - 5/3

Use the same method to find the equation of the line between point A and the midpoint of BC.

Therefore, the coordinates of the centroid of Δ ABC is y = -1/3x + 2.

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Answer:

70 miles per hour

Step-by-step explanation:

take 875mi and divide by how long it took: 12.5 hours

Answer:

x | y

-2. -2

-1. 2

0. 6

1. 10

2. 14

how many numbers do we have between each number on Y? 4

Step 1

this you have to use this data to make your function

f(x)=4X

Always you have to use the spaces times X

Step 2

We have to calculate what do we need to satisfy the function, in this case we have to add 6

f(x)=4x+6

Answer: x=1

Step-by-step explanation:

x-5=2x-6

x-5+6=2x-6+6

x+1=2x

x-x+1=2x-x

2x-x=1

x=1

Answer: x = 1

Step-by-step explanation:

fewer or less than means minus -

difference of x and 5 = x - 5

6 fewer = - 6

twice the number of x = 2x

x - 5 = 2x - 6

x = 2x - 6 + 5

x -2x = - 6 + 5

- x = - 1

x = 1

checking

1 - 5 = 2(1) - 6

4 = 2 - 6

4 = 4

Answer:

well done .....I hope it's helpful

The two decimal numbers that are greater than 5.06 and less than 5.13 are 5.09 and 5.1.

It should be noted that decimals simply means.the numbers that aren't whole numbers.

It should be noted that this is a straight forward question.

Here, the two decimal numbers that are greater than 5.06 and less than 5.13 are 5.09 and 5.1.

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The equation of the line in point-slope form, which passes through the pair of points located at (-4 , 10) and (-6 , 15), is y - 10 = -5/2(x + 4).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (-4 , 10) and (-6 , 15).

m = (y2 - y1)/(x2 - x1)

m = (15 - 10)/(-6 - -4)

m = 5/-2

m = -5/2

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = -5/2 and (x1 , y1) = (-4 , 10)

(y - 10) = -5/2(x - -4)

y - 10 = -5/2(x + 4)

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