What are the factors of m2-6m+6m-36

Answer:

length = 100 yd, width = 60 yd

Step-by-step explanation:

To solve this problem, you must set up an equation.

We know that he length (l ) is 40 yards greater than the width (w ). That means that the length is equal to the width + 40 yards, which can be written as l = w + 40. If the area of the field is 6000 square yards, that means the length times the width must be equal to 6000. Here is the equation that comes from it:

w * (w + 40) = 6000

You can simplify that even further:

w ^2 + 40w = 6000

Divide both sides by 40 to get rid of the coefficient:

w ^2 + w  = 150

Now subtract w from both sides, then take the square root of both sides:

w = sqrt(150-w)

You could keep simplifying this equation until you finally arrive at your answer:

w = 60.

This means that the length, which is 40 more than the width, is 100.

If you want to prove this answer, just multiply the width by the length, which is 60*100, which gives you 6000 square yards; just what you need!

The value of dimensions of the soccer field, in yards are,

⇒ w = 60, l = 40

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A school is building a rectangular soccer field that has an area of 6000 square yards.

And, The soccer field must be 40 yards longer than its width.

Let width of soccer field = w

Hence, Its length = w + 40

So, We get;

w (w + 40) = 6000

w² + 40w - 6000 = 0

w² + 100w - 60w - 6000 = 0

w (w + 100) - 60 (w + 100) = 0

w = - 100

w = 60

Since, Dimension are always positive.

Hence, w = 60

So, The value of dimensions of the soccer field, in yards are,

⇒ w = 60

l = 60 + 40 = 100

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Answer:

the two integers are 17 and 18

Step-by-step explanation:

Let x represent the smaller integer. Then x+1 is the larger. The problem statement tells us

... 2 × larger = -15 + 3 × smaller

... 2(x+1) = -15 + 3x . . . substitute variable expressions for 'larger' and 'smaller'

... 2x +2 = 3x -15 . . . . . eliminate parentheses

... 17 = x . . . . . . . . . . . . .add 15-2x

The smaller integer is 17, so the larger is 18.

_____

Check

2×18 = 36 = 3×17 -15 = 51-15

Let's take the first number as 'x' ( This would be the smaller number )

Let's take the second number as 'x+1' ( This would be the larger number )

I have taken x and x+1 because both these numbers are consecutive.

Twice the larger number :-

... 2 ( x + 1 )

... 2x + 2

15 less than thrice the smaller number :-

... 3x - 15

The question states that these both values are equal. Hence,

... 2x + 2 = 3x - 15

... 2 + 15 = 3x - 2x

... 17 = x

The value of 'x' is 17

( The smaller number is 17 )

Larger number :-

... x + 1

... 17 + 1

... 18

Hence, the numbers are 17 and 18.

Hope my answer helps!!

Answer:

The answers are: A and D (for anyone else looking for answers)

I will meet my friends at the park if I complete my chores. If I meet my friends at the park, we will go to the duck pond. Therefore, if I complete my chores, we will go to the duck pond.

If Bob reads the book, then he will be prepared for the test. If Bob is prepared for the test, then he will get a good grade. Therefore, if Bob reads the book, he will get a good grade.

I just took the test and my correct answers are in the screenshot below :-)

Hopefully its not too late for brainliest!

Your answer is A. The sum of x and y is a rational number .

Answer:

A) The sum of x and y is a rational number.

Step-by-step explanation:

We will first prove that the given values of x and y are rational and then we will prove the fact that the sum of two rational numbers is a rational number.

A rational number is a number which is in the form [tex]\frac{p}{q}[/tex], where p and q are integers and q ≠ 0.

We can write - 5 as [tex]\frac{-5}{1}[/tex] and clearly 1 ≠ 0.

So, x = -5 is a rational number.

Similarly, y = -4 is also a rational number.

For the second part of the proof, consider any two rational numbers [tex]\frac{p}{q}[/tex] and [tex]\frac{r}{s}[/tex].

Now,

[tex]\frac{p}{q} +\frac{r}{s} =\frac{ps+rq}{qs}[/tex]

Since p, q, r and s are integers, ps + rq is also an integer.

Moreover, since q ≠ 0 and s ≠ 0, qs ≠ 0.

Therefore, [tex]\frac{ps+rq}{qs}[/tex] is also a rational number.

Hence, sum of two rational numbers is also a rational number.

Since x = -5 and y = -4 are rational numbers, x + y = (-5) + (-4) = -9 is also a rational number.

[tex]\bf 8~~,~~\stackrel{8-2}{6}~~,~~\stackrel{6-2}{4}~~,~~\stackrel{4-2}{2}~~,~~\stackrel{2-2}{0}[/tex]

so, as you can see, the common difference is then -2, and the first term is clearly 8, thus

[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\qquad\begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\d=\textit{common difference}\\[-0.5em]\hrulefill\\a_1=8\\d=-2\\n=14\end{cases}\\\\\\a_{14}=8+(14-1)(-2)\implies a_{14}=8-26\implies a_{14}=-18[/tex]

Final answer:

The explicit formula for the given arithmetic sequence is an = 10 - 2n. By applying this formula, we find that the 14th term of the sequence (a14) is -18.

Explanation:

The sequence given is 8, 6, 4, 2, 0, ... and it is decreasing by 2 every term. This is an arithmetic sequence where each term is 2 less than the previous term. To write an explicit formula for an arithmetic sequence, we use the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the term number.

For this sequence, a1 = 8 and d = -2. Substituting these values into the formula, we get an = 8 + (n - 1)(-2). Simplifying this, the explicit formula for the nth term is an = 10 - 2n. To find the 14th term, a14, we substitute n = 14 into the formula: a14 = 10 - 2(14) = 10 - 28 = -18. Therefore, the 14th term of the sequence is -18.

The answer is 2+2=4 LOL

Answer:

4 because two plus two is four minus 0 equals 4

Add 8y+3y=11y

Divide 44/11y=4

Answer= 4

The solution to the equation 8y + 3y = 44 is y = 4.

To solve the equation 8y + 3y = 44, we can combine like terms and solve for y:

Combine like terms on the left side:

8y + 3y = 44

Simplify:

11y = 44

Divide both sides by 11:

11y/11 = 44/11

Simplify: y = 4

Therefore, the solution to the equation 8y + 3y = 44 is y = 4.

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the 7 is in the tenths place

Using Avogadro's number, you can calculate the number of molecules in a mass of water by dividing the number of molecules in a given mass by the mass, then multiplying by the mass you are interested in. Reverse the process to find the mass given the number of molecules.

This question is about molar calculations, or figuring out how many molecules are in a given mass of a substance using Avogadro's number. We can start by calculating how many molecules there are in one gram of water:

First, take the number of molecules in 0.065g of water (2.174 × 10^21), then divide that by 0.065 to find out how many molecules are in 1g. Then, multiply by 200 to find out how many molecules are in 200g of water.

For the second part of your question, we're given the number of molecules and need to find the mass in grams. Reverse the original calculation. If 2.174×10^21 molecules are in 0.065 g of water, then divide 1.271 × 10^28 by 2.174 × 10^21 to find out how many 0.065g portions there are. Then, multiply by 0.065 to get the mass in grams.

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Interesting problem.

A palindrome is a number which is identical when read/interpreted left-to-right or right-to-left.   For example, 14241 is a palindrome, so is 444444.

A three digit palindrome must be made up of two distinct digits only, one for the first and last digits, and one for the middle, for example, 424, or 515, etc.

For a number to be divisible by 9, the sum of the digits must add up to a multiple of 9, such as 0, 9, 18, 27, etc.

We can now form a table of the possible 3-digit palindromes divisible by 9, starting with the first/last digits (=A), and finding the middle digit (=B).  The number is therefore represented by the pattern ABA.

For example, when A=1, we have the number 1B1.  For the number to be divisible by 9, B=7 so that sum=1+7+1=9, which is divisible by 9.

For each value of A (from 1 to 9) we can only find one value of B that makes the number divisible by 9.   Thus we can only find nine such numbers, with A equal to 1 to 9.

Here's a list of the numbers

A   B   number

1    7    171

2   5    252

3   3    333

4   1     414

5   8    585

6   6    666

7   4    747

8   2   828

9   0   909

There are 9 unique 3-digit palindromic numbers that are divisible by 9. This is determined by the rule that a number is divisible by 9 if the sum of its digits is also divisible by 9, considering the constraints of palindromic numbers.

To find 3-digit palindromic numbers that are divisible by 9, we must first understand what qualifies as a palindromic number. A palindromic number is a number that remains the same when its digits are reversed. For a 3-digit number, this means the first and last digits must be the same (i.e., the form is aba, where a and b are digits).

Since our objective is to find those divisible by 9, we must recall the divisibility rule for 9: a number is divisible by 9 if the sum of its digits is also divisible by 9. For a 3-digit palindromic number aba, the sum of its digits is 2a + b. For this sum to be divisible by 9, a and b must be chosen accordingly.

The smallest 3-digit palindromic number is 101, and the largest is 999. To be divisible by 9, the sum of the digits must equal 9, 18, 27,..., or 81 (the largest sum for a 3-digit number where the first and last digits are the same). Since there are 9 possible sums (9 to 81 inclusive), and each sum offers a unique number that satisfies the palindrome and divisibility criteria, there are 9 such numbers.

Therefore, there are 9 unique 3-digit palindromic numbers divisible by 9.

Answer:

75

Step-by-step explanation:

Number of foul shots made by the girl first time = 12

Number of shots missed by the girl first time = 8

Total number of shots played first time = 12 + 8 = 20

Let the number of foul shots made by the girl second time be x

The total number of shots played by the girl second time = 125

Let's set up a proportion,

[tex]\frac{Number of foul shots made by the girl first time}{Total number of shots played first time}[/tex] = [tex]\frac{number of foul shots made by the girl second time}{total number of shots played by the girl second time}[/tex]

=> [tex]\frac{12}{20} = \frac{x}{125}[/tex]

Flip the sides of the equation

[tex]\frac{x}{125} = \frac{12}{20}[/tex]

Multiplying both the sides by 125

[tex]\frac{x}{125}*125 = \frac{12}{20}*125[/tex]

Cancelling out the 125's on the top and bottom from the left side

x = [tex]\frac{12}{20}*125[/tex]

=> x =  [tex]\frac{1500}{20}[/tex]

=> x = 75

Number of foul shots made by the girl if she played 125 foul shots = 75

To find out how many shots the girl made, set up a proportion using the ratio of shots made to shots missed. The girl made 187 shots.

To find out how many shots the girl made, we can set up a proportion using the ratio of shots made to shots missed. The ratio is 12:8. Let's assume the number of shots made is x. We can create the proportion: 12/8 = x/125. Cross-multiplying gives us 8x = 12 * 125. Solving for x gives us x = (12 * 125) / 8. Evaluating this expression gives us x = 187.5. Since we can't have a fraction of a shot, we round down to the nearest whole number. Therefore, the girl made 187 shots.

big oof uh

Russel D Bag

-1/32ac2

You want to cancel out the -32 on the top with the 64 on the bottom leaving -1. Then do the same with the variables.

the answer is

2.25 it is right

it is 2∪ 1/4...............

In a parallelogram, consecutive

angles are supplementary

Answer:

In a parallelogram, consecutive angles are supplementary.

Step-by-step explanation:

Consecutive angles in a parallelogram have a sum of 180°; this means they are supplementary.

All angles in a parallelogram are not necessarily congruent; the second statement is therefore not true.

Consecutive angles in a parallelogram are not necessarily congruent; therefore the third statement is not true.

Consecutive angles in a parallelogram are not complementary, as they add up to 180° instead of 90°.

Amount of soup in each container = 18 ounces

Total number of containers of soup = 6 containers

So, total amount of soup in 6 containers = [tex]6 \times 18[/tex]

= 108 ounces

Total amount of soup for 9 people = 108 ounces

So, amount of soup for 1 people = [tex]108 \div 9[/tex]

= 12

So, each person will get 12 ounces of soup.

Given:

monthly deposit, A=100

rate of interest, i = 1% per month = 0.01 per period

compounding period = 1 month (assumed).

Total payments :

n=60 payments of $100 at the end of the month (beginning of the next month) +

1 payment at the beginning of the first month.

Future value after 60 months

= amount due to 60 monthly payments at end of month + value of first payment

= A((1+i)^n-1)/i  + A*(1+i)^60

=100(1.01^60-1) + 100(1.01^60)

= 8166.967 + 181.670

= 8348.64 (to the nearest cent)

Answer:

8348.64

Step-by-step explanation:

3 * 600 = 1800

Hundreds = 18 hundreds

The father is 27 because when they said 3 TIMES OLDER THEN THE SON he was 9

The father is 24 years old and the son is 6 years old. You know this is right because it shows that the father 4 times older than the son

Answer:

[tex]y = \frac{1}{3}x - 1[/tex]

Step-by-step explanation:

Let the gradient be calculated as follows:

slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

         = [tex]\frac{-7-(-3)}{6-(-6)}\\ = -\frac{1}{3}[/tex]

to find the equation passing through the point we calculate as follows:

[tex]- 3= \frac{1}{3} (-6) + b\\ -1 = b[/tex]

Therefore, the equation of the line is:

[tex]y = \frac{1}{3}x - 1[/tex]

An equation of this graphed line in slope-intercept form is [tex]y=-\frac{1}{3} x-5[/tex].

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-7 - (-3))/(6 - (-6))

Slope (m) = -1/3.

At data point (6, -7) and a slope of -1/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

[tex]y-(-7)=-\frac{1}{3} (x-6)\\\\y+7=-\frac{1}{3} (x-6)\\\\y=-\frac{1}{3} x-5[/tex]

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(3.5x10^-5) (3x10^-10)

Lets break this problem up so that we can answer it more smoothly!

This question can be answered with PEMDAS. 1. Parenthesis, 2. equation, 3. multiplication, 4. division, 5. addiction, and 6. subtraction. As I listed the PEMDAS formula in order, we see that parenthesis comes first.

So,

(3.5x10^-5)

35^-5= 0.000035.

So, we have the first parenthesis equation solved, we will have to multiply the equation we just solved with the next equation because 2 parenthesis' together create a multiplication. For an example, 3(4) would be 12.

(3x10^-10)

30^10= 3e-10

0.000035x3e-10=1.05e-14

Your answer is:

1.05e-14

We are ecstatic to help you and If you have any questions, or if we solved something incorrectly please tell us! Thank you <3

-ExperimentsDIYS

Given that the revenue for each jumbo biscuit sold is $1

Given that the cost to make each jumbo biscuit is $0.20

Then profit on each jumbo biscuit =$1 - $0.20 = $0.80

Since positive profit occurs so producing jubo biscuit is good idea.

Given that the revenue from each regular biscuit is sold at $0.65

Given that the cost to make each regular biscuit is $0.15

Then profit on each regular biscuit =$0.65 - $0.15 = $0.50

Since positive profit occurs so producing regular biscuit is good idea.

As in both business, we are getting positive profit. Infact more profit on jumbo biscuits so YES, bakery can produce 10 regular biscuits and 55 jumbo biscuits.

The bakery can produce 10 regular biscuits and 55 jumbo biscuits. This conclusion is based on calculations showing that the revenue generated from selling these biscuits is higher than the cost to produce them. There are no clear limitations violated.

The bakery can indeed produce 10 regular biscuits and 55 jumbo biscuits, as long as it accounts for the cost associated with making each biscuit. We can calculate this through simple multiplication. The cost to make 10 regular biscuits would be 10 * $0.15 = $1.50, and the cost to make 55 jumbo biscuits would be 55 * $0.20 = $11.00.

The revenue from selling 10 regular biscuits would be 10 * $0.65 = $6.50, and the revenue from selling 55 jumbo biscuits would be 55 * $1 = $55. Hence, the total cost of producing these biscuits is $1.50 (for regular biscuits) + $11 (for jumbo biscuits) = $12.50, while the total revenue generated is $6.50 (from regular biscuits) + $55 (from jumbo biscuits) = $61.50.

The revenue generated ($61.50) is clearly higher than the cost of production ($12.50), so it would be financially feasible for the bakery to produce these biscuits. There are no apparent limitations violated.

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Patrick initially has 600 meters of yarn. After using some to make a hat, he only has 351.1 meters of yarn left, which is not enough to make a scarf that requires 354.03 meters.

To answer this question, we have to perform a subtraction operation on the total lengths of yarn. Initially, Patrick has a 600-meter skein of yarn. After making a hat, he uses 248.9 meters of yarn. To find out how much yarn is left, we subtract the amount used from the total: 600 - 248.9 = 351.1 meters. You then need to check if 351.1 meters are enough to make a scarf that consumes 354.03 meters of yarn. In this case, we can see that Patrick does not have enough yarn left to make the scarf because 351.1 meters is less than 354.03 meters.

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8192, 16 x 8 x 64,  24 = 16, 26= 64, 23= 8

Hey there!

[tex]2^4[/tex] [tex]= 16[/tex]

[tex]2^3[/tex] [tex]= 8[/tex]

[tex]2^6[/tex] [tex]= 64[/tex]

____________________________________________________________

[tex]16(8)[/tex] [tex](64)[/tex]

[tex]16(8)[/tex] [tex]= 128[/tex]

[tex]128(64)[/tex] [tex]= 8192[/tex]

Answer: [tex]8,192[/tex]

Good luck on your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

So, just divide:

52.50 / 6 = 8.75

This means that she earns $8.75 an hour.

If this is her hourly salary, then multiply 8.75 x 11

8.75 x 11 = 96.25

So, if Paula works for 11 hours,  she will earn $96.25!

Remark

I think you can only do this either as a 2 step question or as a proportion. The easiest way is the proportion.

Proportion

6 hours / 52.50 = 11/x      Cross multiply

6*x = 52.50 * 11                Combine the factors on the right

6x =  577.5                       Divide both sides by 6

6x/6 = 577.5/6

x = 96.25                        Answer

Answer:1) B. 240(0.92)^t < 115; 9 days  is the inequality which represents the situation.

2)After t=9 days the amount of the sample be less than 115 milligrams.

Step-by-step explanation:

The amount of sample which Jordan had in starting a =240 milligrams

rate of decreasing it r =8%=0.08

let t be the number of days the amount of sample took to become 115 milligrams then by the exponential decay  function

[tex]f(t)=a(1-r)^t[/tex] where f(t) =115

[tex]115=240(1-0.08)^t....(1)\\\Rightarrow\frac{115}{240}=(0.92)^t\\\Rightarrow0.479=(0.92)^t\\\text{taking log on both sides ,we get}\\log(0.479)=log((0.92)^t)\\\Rightarrow\ log(0.479)=t\ log(.092)\\\Rightarrow\ -0.735=t(-0.0833)....\text{after solving log values}\\\Rightarrow\ t=\frac{-0.735}{-0.833}\approx8.82 days[/tex]or 9 days(approx ).

therefore, after t=9 days the amount of the sample be less than 115 milligrams.

So ,the right inequality which represent the situation is

B. 240(0.92)^t < 115; 9 days (from (1))

Answer:

B.  240(0.92)t < 115

9 days.

Step-by-step explanation:

We are told that Jordan works in a science lab where he is studying the behavior of a certain unstable isotope. He has 240 milligrams of the sample, and the amount of the substance remaining in the sample decreases at a rate of 8% each day. After t days, there are less than 115 milligrams of the substance remaining. We  are asked to write an inequality to represent this situation.

An exponential function representing decay will be our inequality.Let us write an inequality for this situation.

[tex]240(1-0.8)^{t} <115=240(0.92)^{t} <115[/tex], where 240 is our initial amount of substance, 0.8 is decrease factor.

Now let us solve our inequality to find out number of days.

[tex](0.92)^{t} <\frac{115}{240}[/tex]

Upon taking natural log of both sides of inequality,

[tex]ln(0.92)^{t} <ln\frac{115}{240}[/tex]

[tex]t\ln \left(0.92\right)<ln(\frac{115}{240})[/tex]

[tex]-0.08338160t < -0.73570679[/tex]

[tex]t>8.82[/tex]

Upon rounding up our answer to nearest integer we can see that option B is correct. Therefore, our answer will be option B.

because the square root of 4 is 2 and the square root of 9 is 3 which means 2x3=6 and 9x4=36 and the square root of 36 is 6 because 6x6=36

Write f(x) above g(x), as shown below:

 f(x)=2x^2 + 3

- g(x) = x^2 - 7

---------------------   Next, combine the givens in three columns:

(f-g)(x) = x^2 + 10 (answer)

The arithmetic operation of the functions f(x) and g(x) is x² + 10 if  arithmetic operation is (f-g)(x) option (D) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

f(x) = 2x² + 3

g(x) = x² - 7

To find the (f-g)(x)

(f-g)(x) = f(x) - g(x)

Plug the function f(x) and g(x):

The above expression is representing an arithmetic operation of the functions:

(f-g)(x) = f(x) - g(x) = (2x² + 3) - (x² - 7)

(f-g)(x) = 2x² + 3 - x² + 7

(f-g)(x) = x² + 10

Thus, the arithmetic operation of the functions f(x) and g(x) is x² + 10 if  arithmetic operation is (f-g)(x) option (D) is correct.

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