HELP.............................! !

(a) Using the distributive property ( x + 7 )² is equal to x² + 14x + 49.

(b) When x = 3, the expressions  ( x + 7 )² and x² + 14x + 49 are equal.

Consider the expression ( x + 7 ),

Now when we square the expression we get,

( x + 7 )²  = ( x + 7 ) ( x + 7 )

Using the distributive property,

( x + 7 )²  = x( x + 7 ) + 7( x + 7 )

Again by using distributive property,

( x + 7 )²  = x² + 7x + 7x + 49

( x + 7 )²  = x² + 14x + 49

(b) For the expressions ( x + 7 )² and x² + 14x + 49,

When x = 3,

( x + 7 )² = ( 3 + 7 )²

( x + 7 )² = 10²

(x + 7 )² = 100

When x = 3,

x² + 14x + 49 = 3² + 14 × 3 + 49

x² + 14x + 49 = 9 + 42 + 49

x² + 14x + 49 = 100

Hence, the expressions (x+7)² and  x² + 14x + 49 are equal when x = 3.

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Answer:

AC = 15

AB = 3

BC = 12

Step-by-step explanation:

AB + BC = AC

3x + (4x + 8) = 5x + 10

3x + 4x - 5x = 10 - 8

2x = 2

x = 1

AC = 5x + 10 = 5(1) + 10 = 15

AB = 3x = 3

Bc = 4x + 8 = 12

Answer:

2

Step-by-step explanation:

2 ^ 9 is already way more than 82 so yea it has to be 2

The number that is halfway between the numbers -46.3 and 46.31 will be 46.305.

We are given the two numbers:

- 46.30 and 46.31

Now, we need to find a number that is halfway between the given numbers.

For this, we need to find the mid point between the two numbers that is given to us.

Mid point is calculated as:

| x | + | y | / 2

Substituting the values in the expression, we get that:

46.3 + 46.31 / 2

= 92.61 / 2

= 46.305

Therefore, we get that, the number that is halfway between the numbers -46.3 and 46.31 will be 46.305.

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The solution of the given equations is x=-7 and x=3.

The given equation is x² + 5x - 12 = | x + 3| + 7.

A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values such that, when substituted for the unknowns, the equation becomes an equality.

Now, x² + 5x - 12 = | x + 3| + 7 can be rewritten as

x² + 5x - 12 = x + 3 + 7

⇒x² + 5x - 12 = x+10

⇒x² + 5x - 12 -x - 10=0

⇒x² +4x -22 =0

From the obtained graph, the solution of equations is x=-7 and x=3.

Therefore, the solution of the given equations is x=-7 and x=3.

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Answer:

22 - 4x

Step-by-step explanation:

4(3-x) + 10  Distribute the 4

4(3) - 4x +10

12 - 4x +10

22 - 4x

Answer:

false

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

to determine if (9, 10 ) is a solution, substitute x = 9 into the equation and if y = 10 then it is a solution.

y = 2(9) - 8 = 18 - 8 = 10

then (9, 10 ) is a solution of the equation

Answer:

$2.08 per pound  

Step-by-step explanation:

1.52+1.08= 2.6pound

6.50/2.6=$2.5 per 2.6 Ibs

(turn the pound to a whole number)

2.6/2= 1.3 so 2,6/1.3= 2Ibs

(what you do to one side must be done to the other)

$2.5/1.3 =2.08

Answer: 1.75 minutes

Step-by-step explanation:

6 gallons per minute.

14.5-4=10.5

10.5/6=1.75 minutes

Answer:

The slope is 4

Step-by-step explanation:

This equation is in slope intercept form

y = mx+b

where m is the slope and b is the y intercept

y = 4x-7

The slope is 4 and the y intercept is -7

The k has interval notation(7,13).

Given that 5< k-2<11

Remove all of the teams from the inequality's center that don't contain k.

Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

So, 5+2<k<11+2

7<k<13

Therefore, The interval notation for k is (7,13).

Equations in mathematics are not always balanced on both sides using a 'equal to' symbol. Sometimes it's a 'not equal to' relationship, as though something is more than or less than the other. In mathematics, an inequality is a relationship that results from a non-equal comparison of two numbers or other mathematical expressions. Inequalities are mathematical expressions that fall within the category of algebra.

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The relative frequency of adults who are engaging in less than the minimum amount of recommended moderate-intensity physical activity weekly is 92.16%.

The term 'relative' refers to an event that is being thought of in relation to or in proportion to another event.

As, per the given question.

The minimum standard for moderate-intensity aerobic activity weekly is 150 min.

All the values which are less than 150 min will be considered as the below specified standard for moderate-intensity aerobic activity.

The relative frequency for 0 - 49 min is 47.54%.

The relative frequency for 50 - 99 min is 32.77%.

The relative frequency for 99 - 149 min is 11.85%.

Thus, the cumulative of all relative frequencies will be;

= 47.54% + 32.77% + 11.85%

= 92.17%

Therefore, the percentage of adults who get less than the recommended amount of moderate-intensity physical activity per week is 92.16%.

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The complete question is -

The center for disease control and prevention (cdc) states that adults should engage in at least 75 min of vigorous-intensity aerobic activity or 150 min of moderate-intensity aerobic activity weekly. researchers gathered data from a random sample of adults who participated in the 2011–2012 national health and nutrition examination survey (nhanes).

What is the relative frequency of adults who are engaging in less than the minimum amount of recommended moderate-intensity physical activity weekly (less than 150 min)? Give your answer to two decimal places.

The hypothesis is called the alternative hypothesis test.

According to the statement

We have to explain about the alternative hypothesis.

So, For this purpose, we know that the

The alternative hypothesis is one among ll|one amongst |one in every of} two mutually exclusive hypotheses in a hypothesis test. the choice hypothesis states that a population parameter doesn't equal a specified value.

From the given information:

she randomly selects houses during this neighborhood and compares their estimated market price within the current year to their estimated value within the previous year. suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market price of the previous year from the value of the present year.

Then

the alternative hypothesis test usually suggests that there's an opportunity of variation (difference) within the data observed.

Hence, since we are told the "real real estate agent believes that the values of homes within the neighborhood she works in have increased (the chance of variation) from last year," which "each difference is calculated by subtracting the market price of the previous year from the market price of this year," we are able to reach the conclusion that this can be an example of an alternate hypothesis test.

So, The hypothesis is called the alternative hypothesis test.

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Answer:

Step-by-step explanation:

Convert 576 from base 10 to following bases:

first of all  convert 576 from base 10 to base 2 we got this

1001000000_2

now  then convert  576 from base 10 to base 3 we got this

210100_3

now then convert 576 from base 10 to base 4 we got this

21000_4

now then convert 576 from base 10 to base 5 we got this

4301_5

now then convert 576 from base 10 to base 6 we got this

2400_6

now then convert  576 from base 10 to base 7 we got this

1452_7

now then convert 576 from base 10 to base 8 we got this

1100_8

now then convert 576 from base 10 to base 9

710_9

Only in base 5 does it end in 1.

referred by  www.web2.0calc.com

So only in base 5 does it end in final digit of 1.

A Binary operation can be considered as a function whose input is two elements of the same set S and whose output also is an element of S. S . Two elements a and b of S can be written as a pair (a, b) of elements in S.

So first of all convert 576 from base 10 to following bases:

first of all  convert 576 from base 10 to base 2 we will get this 1001000000_2

Then convert  576 from base 10 to base 3 we will get this 210100_3

Then convert 576 from base 10 to base 4 we will get this 21000_4

Then convert 576 from base 10 to base 5 we will get this 4301_5

Then convert 576 from base 10 to base 6 we will get this 2400_6

Then convert  576 from base 10 to base 7 we will get this 1452_7

Then convert 576 from base 10 to base 8 we will get this 1100_8

Then convert 576 from base 10 to base 9 we will get this 710_9

Therefore only in base 5 does it end in final digit of 1.

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The simplified form of the expression is equivalent to 3c - 19

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as the addition, subtraction, division and multiplication.

Given the expression below;

2 (1.5c - 2.5) + 7 + 17

Expand

2(1.5c) - 2(2.5) + 7+ 17

3.0c - 5.0 + 24

3c - 19

Hence the simplified form of the expression is equivalent to 3c - 19

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well, let's convert the mixed fraction to improper fraction firstly, then let's check their difference.

[tex]\stackrel{mixed}{15\frac{3}{5}}\implies \cfrac{15\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{78}{5}}\qquad \impliedby \textit{that's for just 1 day} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE after 6 days}}{\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} }\implies \cfrac{468}{5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{change in bushels}}{\cfrac{468}{5}~~ - ~~\cfrac{78}{5}}\implies 78\qquad \impliedby \textit{so 6 days later he's got 78 more bushels}[/tex]

Answer:

1.  x^-3

2. b^7

Step-by-step explanation:

I am pretty sure those are the answers. I'm not 100%

The linear function that represents the line giving by the point slope equation y-2=4(x-3) is f(x) = 4x - 10

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Also note that f(x) = y

Isolate the y then add 2 from both sides:

y - 2 = 4(x-3)

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

y = 4(x-3) + 2

Note that the equation is : y = 4(x-3) + 2

Now Distribute 4 to all terms within the parenthesis

y = 4(x-3) + 2

y = 4x - 12 + 2

Simplify. Combine like terms

y = 4x - 10 ; or f(x) = 4x - 10.

Hence, The linear function that represents the line giving by the point slope equation y-2=4(x-3) is f(x) = 4x - 10

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Answer:

√15, -14, 20.151155111555...

Step-by-step explanation:

it's a square root (not perfect), negative, and never ending decimal

Answer:

It would have to be [tex]\sqrt{15}[/tex].

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Hope this helps!

Have a great day and God bless! :)

Answer:

(M U C) ∩ V = {3, 5}

Subsets: { }, {3}, {5}, {3, 5}

Step-by-step explanation:

M = {2, 3, 4, 5}

C = {4, 6, 8, 10}

V = {3, 5, 7, 9}

(M U C) ∩ V =

= ( {2, 3, 4, 5} U {4, 6, 8, 10} ) ∩ {3, 5, 7, 9}

= {2, 3, 4, 5, 6, 8, 10} ∩ {3, 5, 7, 9}

= {3, 5}

Subsets: { }, {3}, {5}, {3, 5}

Answer: ( -2, 4)

Step-by-step explanation:

The length of the new garage will be approximately 8.83 meters.

The length is referred as the side of a rectangle or a square. Ideally we use length to measure the larger side of a rectangle, but for a square all sides are equal and so can be called length.

The are of a square is given by the square of any side .

Given the area of the square is 52 square meters.

The new are of the square is 50% more.

Increased amount =  50% of 52 = 26 meters²

New area of square = 52 + 26 meters² = 78 meters²

Now we know that the area of a square is given by (side)² .

Therefore  (side)²= 78

or, side = √78

or, side = 8.8317...

or, side ≈ 8.83 meters

Therefore the length of the new garage is approximately 8.83 meters.

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Answer:

A) The percentage of the bacteria increasing each hour is 15% per hour

B) When t=0 the population of bacteria is 3000 bacteria

C) After 24 hours the a sensible degree of accuracy in population is about 85875 (since only whole numbers count)

Step-by-step explanation:

A) To find the percentage of the bacteria increasing each hour the growth rate needs to be determined. To find it you need to subtract 1.15 by since the formula for exponential growth is a(1+r)^t one is added to the rate so to inverse it 1.15 needs to be subtractied by one to get 0.15. At this point you found the decimal rate to find the percentage you multiply 0.15 by 100 to make it a whole number and it results in 15%

B) To determine the size if the population when t=0 you substitute the variables t for 0 to get 3000×1.15^0 to get 3000 (remember anything times 0 is 0). Another way is to keep in mind that 3000 is the initial amount because that's the number with no variable with it.

C) To find the population after 24 hours substitute t for 24. After substituting t and multiplying 3000×1.15^24 the exact answer is 85875.52857. To find the answer in a sensible degree of accuracy you would round it to the nearest whole number which is 85876 since the dight in the tenths place is 5 or greater than the answer is rounded up by one.

Lisa bowling score is 100.

John bowling score is 282.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Lisa and John are bowling.

Johns score is three times the difference of Lisa's score and 6.

The sum of their scores is 382.

Now, Let Lisa bowling score = x

Then, John bowling score = 3 (x - 6)

Since, The sum of their scores is 382.

Hence,

x + 3 ( x - 6 ) = 382

After solving,

x + 3x - 18 = 382

4x = 382 + 18

4x = 400

x = 100

Hence, Lisa bowling score = x = 100

And, John bowling score = 3 (x - 6)

                                       = 3 (100 - 6)

                                       = 3 × 94

                                       = 282

Therefore, Lisa bowling score is 100.

And, John bowling score is 282.

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4.8 packages will need for the use of one year.

No. of used packages of printer paper during 10 months = 4 Packages

As we know that there is 12 months in a year,

To determine the number of packages need for the year, first we have to find the number of package is being use in one month.

S0,  No. of used package in 1 month = 4/10 = 0.4 Package

Now, we will determine the number of packages for the use of one year, by multiplying the No. of used package in 1 month with 12.

No. of packages for the use of one year = 12 × 0.4

                                                                   = 4.8 Packages

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Answer: 117in^3

Step-by-step explanation:

Based on the number of movies that each of the 8 students saw in the past year, the mean number of movies is 12.875 movies

To find the mean of a distribution of numbers such as the number of movies seen in the past year, sum up the number of movies watched and then divide it by the number of students.

The mean number of movies watched by the students is therefore:

= Sum of movies watched / Number of students

= (6 + 14 + 14 + 16 + 14 + 18 + 15 + 6) / 8 students

= 103 / 8

= 12.875 movies

Rest of the question is:

Find the mean number of movies that the students saw.

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Answer:

U = 4

Step-by-step explanation:

We take 3/9 and simplify it, making 1/3.

We multiply both by 12 to eliminate denominators, so the new numbers are 4 and U.

U = 4