what is the equation 2(h+3.5)=-11

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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Answer:

Best answer choice seems to be C.

Step-by-step explanation:

Time required to form 3,000,000 bacteria from 10 if it will double every hour = 18.2years.

The phrase exponential refers to a high number expressed in smaller terms, or something that grows at an ever-increasing rate. 25 is shown as 5x5 as an example of an exponential. The erosion that is occurring on the Holderness coast in eastern England is an example of exponential erosion.

Using the formula of exponential growth:

y = a*b^t

a = reflects the initial bacterial population

t =  represents the doubling.

the information given

a = 10

t = 1 hour

After 1 hour, the number of bacteria multiplies by 2, so:

y = 2 × 10 = 20

So that:

20 = 10 × b^1

Dividing through by 10 gives:

2 = b

solving this we get an equation:

y = 10(2)^t

Solving for 3,000,000 bacteria.

Substituting the value in the formula:

3000000 = 10(2)^t

3000000/10 = (2)^t

300000 = (2)^t

Applying the log of both sides, it gives:

Log 300000 = tlog2

5.477 = 0.301t

t = 5.477/0.301

t = 18.2 years

Time required to form 3,000,000 bacteria from 10 if it will double every hour = 18.2years.

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Given the length and perimeter, the width of the rectangle is 38 inches.

Hence, option A) 38inches is the correct answer.

The perimeter of a rectangle is expressed mathematically as;

P = 2( l + w )

Given the data in the question;

Let "x" represent the width of the rectangle.

To determine the width of the rectangle, plug the given values into the formula above and solve for x.

P = 2( l + w )

220  = 2( (2x - 4) + x )

220 = 2( 2x - 4 + x )

220 = 2( 3x - 4 )

Apply distributive property

220 = 2( 3x - 4 )

220 = 2(3x) + 2(-4)

220 = 6x - 8

Collect like terms

220 + 8 = 6x

228 = 6x

6x = 228

x = 228/6

x = 38

Now, since "x" represent the width of the rectangle,

The width of the rectangle w = x = 38 inches.

Given the length and perimeter, the width of the rectangle is 38 inches.

Hence, option A) 38inches is the correct answer.

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

Step-by-step explanation:

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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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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It should be noted that since Taylor got 3(4x) and the correct expression is 3(4x + 1), he is incorrect.

It should be noted that the expression given is illustrated as 12x+3=3(4x).

We need to solve this:

12x + 3

It should be noted that the common factor is 4.

Therefore, 12x + 3 = 3(4x + 1)

Therefore, since Taylor got 3(4x). He is incorrect.

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Taylor's work:

12x+3=3(4x)

Taylor's Check:3(4x)=12x

Is this correct?

Answer:

Step-by-step explanation:

Group of six

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 constant of proportionality for the ratio of green team students to gray team students is 7/8.

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.

It can be expressed in different ways:

1) Use the ":" to separate the values : a : b

2) Use the word "to" : a to b

3) Write it in fraction: a / b

The ratio that relates two given values is called the constant of proportionality, a/b.

If the green team has 42 students, and the gray team has 48 students, then the ratio of green team students to gray team students can be written as:

42 : 48 or 42 to 48 or 42/48

To simplify the ratio, divide both numbers in the ratio by the same number until they cannot be divided any more.

Divide both number by 6.

42 : 48 = 7 : 8 or 7/8

Hence the constant of proportionality is 7/8.

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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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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:7

Step-by-step explanation:

just gotta add it up all good

Answer:

7

Step-by-step explanation:

The square root of 60 minus 11 would be plotted on a number line in between −3 and 8, but closer to 8.

A straight line with numbers placed at equal intervals or segments along its length. Number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.

Given:

The square root of 60 minus 11 would be plotted on a number line.

According to given question we have

We know that the  square root of 60

=

[tex]\sqrt{60} \\\\=7.74[/tex]

So, By the statement square root of 60 minus 11 we have,

=7.74-11

=-3.25

So, in the number line the points are lies in between −3 and 8, but

closer to 8.

Therefore, the square root of 60 minus 11 would be plotted on a number line in between −3 and 8, but closer to 8.

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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 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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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:

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

Answer: 195

Step-by-step explanation:

65%=65/100

300 * 65/100=

300 * 6.5/10=

300 * 13/20=

3900/20=

390/2=195

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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one serving is 432/19=27

27g are in one serving

Sophiya has to pay 2.2 dollars for per pound of pretzel sticks.

Unitary method is a mathematical technique for first obtaining the value of a single unit then deriving the given units by multiplying it with the single unit.

The cost per pound of pretzel sticks can be obtained by the unitary method.

Given that 5 pounds of pretzels costs 11 dollars,

Now to obtain the cost of per pound of pretzel sticks we'll put the total cost at the numerator and the total weight of the pretzel sticks on the denominator.

∴ Per pound of pretzel costs (11/5) dollars which is,

= 2.2 dollars per pound of pretzel sticks.

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Answer:

the throwing back by a body or surface of light, heat, or sound without absorbing it.

"the reflection of light" The reflection factor of a body is the ratio of the light reflected by the body to the incident light.

Answer:

Step-by-step explanation:

acute

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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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:4/9

Step-by-step explanation:

Find the GCD

8/2

18/2

Answer:

4/9

Step-by-step explanation:

Let's simplify the value,

→ 8/18

→ (8 ÷ 2)/(18 ÷ 2)

→ 4/9

Thus, the value is 4/9.