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Addition of algebraic terms

(6a+4b-7c) + (12a-10b+15c)

⇒ simplify each term

⇒6a+4b-7c+12a-10b+15c

⇒18a-6b+8c

subtraction  of algebraic terms

(7x-12y+18z) -(3x+18y-10z)

⇒ 7x-12y+18z-3x-18y+10z

⇒4x-30y+28z

: A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  25  is the square of  5

Check : 4 is the square of 2

Check :  a2  is the square of  a1

Factorization is :       (5a + 2)  •  (5a - 2)

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Given u = (-1, 3), v = ( 2, 4) , and w = (2, -5), by applying scalar multiplication of vectors, ³/₂ v = (3, 6)

In the 2D coordinate system, vectors can be split into x-component and y-component.

We can write, for example, a vector s = (4,–1), which means:

x-component = 4

y-component = –1

Some vector operations:

In the given problem:

u = (-1, 3), v = ( 2, 4) , and w = (2, -5)

Then,

³/₂ v = ³/₂ . (2, 4)

          = ( ³/₂ . 2, ³/₂ . 4)

          =(3, 6)

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Answer:

b > 5/6 or b < 11/6

Step-by-step explanation:

1.  Divide both sides by -4
[tex]\dfrac{-4(|6b-8|)}{-4} < \dfrac{12}{-4}[/tex]

2. Simplify above
[tex]|6b-8| > -3[/tex]

3. The absolute value of an expression means that the expression can be positive or negative
Here |  | represents the absolute value of 6b-8

For an absolute value to satisfy the above inequality
either 6b - 8 > -3 or 6b - 8 < - (-3)

(This follows from the fact that if |x| > -a, x > -a
or x < -(-a) ) which is the same as x < a

First case: 6b - 8 > -3:

6b - 8 + 8  > -3 + 8     ( Add 8 to both sides)
==> 6b > 5
==> 6b/6 > 5/6                   (Divide both sides by 6)
==> b > 5/6  

Second case: 6b - 8 < 3
6b −8 + 8 <3 + 8                    (Add 8 to both sides)
==> 6b<11                                    

==> 6b/6 < 11/6    (Divide both sides by 6)

==> b < 11/6

Answer:

38.97 kilograms

Step-by-step explanation:

38 ones and 97 hundredths

38                  0.97

38.97

The mean of Christopher's test score throughout the year is 80.5

Christopher scores during the World Cultures and Geography class for the past year are

87, 90, 77, 68, 65, 62, 75, 83, 98, 100

The mean can be calculated as follows

87+ 90+77+ 68+ 65+62+75+83+98+100/10

= 805/10

= 80.5

Hence the the mean of Christopher's test score throughout the year is 80.5

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The time taken to hit the ground is 13 seconds.

It should be noted that the function that was given based on the information is:

h(t) = 16t²

where h = height

t = time

Therefore, when the height is 2704ft, the time will be:

h(t) = 16t²

2704 = 16t²

t² = (2704 / 16)

t² = 169

t = ✓169

t = 13

The time taken is 13 seconds.

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When you take the square root of 11, the result is neither a terminating nor a repeating decimal. Therefore, it is: 2. irrational number.

In Mathematics, there are six (6) common types of numbers and these include the following:

An irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11.

In conclusion, when you take the square root of 11, the result is neither a terminating nor a repeating decimal. Therefore, it is an irrational number.

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one serving is 432/19=27

27g are in one serving

Answer: Y= -2/-18 or Y= 0.1111X=-2(-0.1111) +1or X=0.77778

Step-by-step explanation:

Fractions are in their simplest form when they have no common divisors other than 1 at their top and bottom. That is, the top and bottom cannot be divided further and remain integers.

You may also hear the simplest form called "lowest term".

In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:

3^(1/2) 12^(1/2)

Simplify the following:

sqrt(3) * sqrt(12)

sqrt(12) = sqrt(2^2×3) = 2 sqrt(3):

sqrt(3)×2 sqrt(3)

sqrt(3)×2 sqrt(3) = 3×2:

3×2

3×2 = 6:

Answer:

6

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Answer:

Parallel lines have the same slope, so the slope of the other line is also 1/6

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the other line is also 1/6

The total simple interest paid by her is R6,600 and the rate of simple interest  is 22%.

Given that

To find

So, according to the question

We have,

After trading in and depositing, the balance was as follows:

= Cost of television - Selling price of old television - Deposit by her

= 20,000 - 3,000 - 2,000

= R15,000

The total simple interest paid by her in 2 years:

= (900 x 2 x 12months) - 15,000

= R6,600

The rate of simple interest given by her in 2 years:

= (6,600 / 2 years) / 15,000

= 22%

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The equation of the circle with center at (-1, 5) and passes through the point (2, 9) is equal to (x + 1)² + (y - 5)² = 25.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

Next, we would determine the length of the radius (r) by using the distance formula. Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substituting the given parameters into the formula, we have;

Radius = √[(2 - (-1))² + (9 - 5)²]

Radius = √[(2 + 1)² + (4)²]

Radius = √[3² + 4²]

Radius = √[9 + 16]

Radius = √25

Radius = 5 units.

For the equation of a circle, we have:

(x - h)² + (y - k)² = r²

(x - (-1))² + (y - 5)² = 25

(x + 1)² + (y - 5)² = 25

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Complete Question:

Write the equation of the circle with center at (-1, 5) and passes through the point (2, 9).

Answer:

x=g/6

Step-by-step explanation:

because if u do the inverse of multiplication which is division on both sides it gives u that and solves for x

Answer:

A. Shawn's Poster

Step-by-step explanation:

It uses perimeter, and the formula is L*W.

Christie hiked 1/4 and Jackie hiked 3/5  MORE. More means Subtraction so it would be  [tex]\frac{3}{5} -\frac{1}{4}[/tex]

Same thing for the other two. They represent subtraction because of their keywords. Here is a list below of what you need to look for, for each control (+,-,x,÷)

Hope this helps

~R3VO

Expression as a single natural logarithm is 1.38629436112

ln 24- ln 6

ln(24/6)

ln 4 = 1.38629436112

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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Answer: 195

Step-by-step explanation:

65%=65/100

300 * 65/100=

300 * 6.5/10=

300 * 13/20=

3900/20=

390/2=195

Damian should cut the ribbons into pieces of 21 meters.

To answer this, we need to find the maximum common factor between the two lengths of ribbon, which are 63 and 105.

If we rewrite both of these numbers as a product between prime factors we get.

63 = 3*3*7

105 = 3*5*7

Then the maximum common factor between these two numbers is 3*7 = 21

Then we conclude that Damian should cut the ribbons into pieces of 21 meters.

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The multiplicative inverse of a number is  a number that when multiplied by the original number gives the product as 1. The multiplicative inverse of 'a' is denoted by a-1 or 1/a. In other words, when the product of two numbers is 1, they are said to be multiplicative inverses of each other. The multiplicative inverse of a number is defined as the division of 1 by that number. It is also called the reciprocal of the number. The multiplicative inverse formula says that the product of a number and its reciprocal is 1.

There are various types of numbers like natural numbers, fractions, unit fractions, negative numbers, etc. Let us understand the multiplicative inverse formula for each type of number.

Natural numbers are counting numbers starting from 1. The multiplicative inverse of a natural number a is 1/a.

Multiplicative Inverse of Integers

Finding the multiplicative inverse of positive integers is the same as natural numbers (explained above). Just like positive integers, the product of a negative number and its reciprocal must be equal to 1. Thus, the multiplicative inverse of any negative number is its reciprocal. For example, (-6) × (-1/6) = 1, therefore, the multiplicative inverse of -6 is -1/6. Note that the multiplicative inverse of a negative number is always negative. And, in the multiplicative inverse of a negative integer, the negative sign will attach to the numerator, and not with the denominator.

How to Find Multiplicative Inverse of a number :

The multiplicative inverse of a number is also known as its reciprocal. It is very easy to find the multiplicative inverse of a number using the following steps:

Step 1: Divide the given number by 1.

Step 2: Write it in the form of a fraction. Say, the reciprocal of a is 1/a.

Step 3: Simplify and get the answer.

Let us find the multiplicative inverse of 2/3. The first step is to divide it by 1, which will result in 1/(2/3) = 3/2. Therefore, the reciprocal of 2/3 is 3/2.

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Answer:

the answer for this question is -3,248

Answer:

Step-by-step explanation:

Group of six

The correct option is D. V = 30-0.1t² ; represents the the volume of water in m³ after t minutes of pumping.

For the given question;

The values for the time of pumping and the volume of water is given;

use them to find the equation which represents their relation.

when, time t = 5

put the values in the options.

a. V = 30 - 2.5 × 5 = 17.5    .....(wrong)

b. V=30 - 0.5 × 5 = 27.5       .....(correct)

c. V = 30 - 0.5 × 25 = 17.5     ......(wrong)

d. V = 30 - 0.1 × 25 = 27.5      ........(correct)

Now, check at time t = 10 just for the correct value.

b. V = 30 - 0.5 × 10 = 25 .....incorrect

d. V = 30 - 0.1 × 100 = 20   ......correct

Therefore, the relation of the water pumped with time is given by the relation; V = 30-0.1t².

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The complete question is-

The table shows the volume of water in cubic meters, V, in a tank after water has been pumped out for a certain number of minutes.

Which equation could represent the volume of water in cubic meters after t minutes of water being pumped out?

A. V = 30-2.5t

B. V = 30-0.5t

C. V = 30-0.5t²

D. V = 30-0.1t²

The value expression represents another method of computing the product given

Thus option A. (-1)((1 × 76) + (0.45 × 76)) has value -110.2 . So it is correct option.

-1.45*76 =-110.2

Now checking all the option one by one if any option has the value -110.2

then it is correct

A. (-1)((1 × 76) + (0.45 × 76))

   (-1)(76 + 34.2)

   =-110.2

B. (-1)(-1.45 - 76)

     (-1)(-77.5)

   = 77.5

C. (-1)(-1.45 + 76)

  (-1)(74.5)

  = -74.5

D. (-1)(-1.45 × 76)

   (-1)(-110.2)

= 110.2

Thus option A. (-1)((1 × 76) + (0.45 × 76)) has value -110.2 . So it is correct option.

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Answer:    

x=-9 , x=-8 , x=15 , x=-13 , x=3 , x=-4 , x=5 , x=6 , x=-24 , x=-7 , x=-16

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

1.2(3x+2y)

add in our X and Y number

1.2(3(4) + 2(4))

Do the multiplication

1.2(12 + 8)

Distribute 1.2

14.4 + 9.6

add them together and you get

24

The inverse for the function f (x) = ∛x / 3 will be f ⁻¹ (x) = 3 x³.

We are given the function:

f (x) = ∛x / 3

we need to find the inverse of the function.

First we will write the function in the form of x.

y = ∛x / 3

y³ =  x / 3

3 y³ =  x

x = 3 y³

So, the inverse function will be:

f ⁻¹ (x) = 3 x³

Therefore, the inverse for the function f (x) = ∛x / 3 will be f ⁻¹ (x) = 3 x³.

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Rebeeca’s histogram most likely shape will be Skewed to the left.

The histogram shows a symmetrical data distribution. A distribution is symmetrical if a vertical line can be drawn at any point in the histogram such that the shapes to the left and right of the vertical line are mirror copies of each other.

The mean and the median both reflect the skewing, but the mean reflects it more so. This is because the mean and median are measures of central tendency. Because in Rebecca’s data the mean is smaller compared to the median, it makes the histogram skewed to the left. If the median were to be smaller than the mean, it would be skewed to the right.

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Answer:7

Step-by-step explanation:

just gotta add it up all good

Answer:

7

Step-by-step explanation: