3xy - 4 - 2y + 7y + 3​

Answer: 5

Step-by-step explanation:

You  can only have real outputs for a root when that root is 0 or higher because you can never take the square root of a negative number

\(f(x) = \sqrt{x-5} +2\)              >Under the root must be 0 or greater

x-5 = 0

x= 5

so x must be 5 or greater

Answer:

224

Step-by-step explanation:

56 * 4 =224

Answer:

224

Step-by-step explanation:

the pattern is 4 times the space the number is in

ex: 4,8,12,16 because 16 is the 4th number and 4x4= 16

hope this helps!

Have a wonderful day :D

In the next 10 years there will be 398 racoons in the state park

The annual increase in the population size is defined as a sum of differences: the difference between births less deaths and the difference between immigrants less emigrants, in a given country, territory or geographic area at a given year.

Using the formula

p(t) = p(o) e^ kt

k = 3.5/100 = 0.035

t = 10 years

p(t) = 280 e^ 0.035 ×10

p(t) = 280e^0.35

p(t) = 280 × 1.42

p(t) = 398( nearest whole number)

therefore be after 10 years there will be 398 racoons in the state park.

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As per the median, the set of data that fulfilling Marjane's requirement is 24, 25, 25, 25, 26, 26 (option c).

In statistics, data is a collection of numbers or values that represent a particular phenomenon. One way to measure central tendency, or the typical or representative value of the data, is through the median and the mode.

The median is the middle value when the data is arranged in numerical order, and the mode is the value that appears most frequently.

The third set of data is 24, 25, 25, 25, 26, 26.

The median is the middle value, which is also (25+25)/2 = 25.

The mode is the value that appears most frequently, which is 25.

Therefore, the mode and median are the same, fulfilling Marjane's requirement.

Therefore, the correct option is (c).

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By taking the quotient between the total debt and the number of people, we conclude that the debt per person is $2,622

To find the amount of debt per person, we need to find the quotient between the total amount of debt and the number of people.

Here the total debt is:

$6.39 billion = $6.39*10^9

And the total number of people is:

2.437 million = 2.437*10^6

Then the quotient is:

Q = ($6.39*10^9)/( 2.437*10^6) = $2.622*10^3

The debt per person is:

Q = $2.622*10^3 = $2,622

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Answer:

B.

Step-by-step explanation:

I might have gotten this wrong but my mind was telling me it was B hope this helped.

Thanks for your time.

(>.<) <3 Kris

Answer:

6%

Step-by-step explanation:

Subtract 4000 from 5200 . This is the amount of interest earned after 5 years.

Divide that by 5. This is the amount earned after 1 year.

What percent is that number of 4000? (6%)

Answer:

A.

10 ounce= 10 dollars

9 ounce = 11.25 dollars

8 ounce = 10 dollars

6 ounce= 7.5 dollars

4 ounce = 5 dollars

2 ounce = 2.5 dollars

1 ounce= 1.25 dollars

B. The cost per ounce is 1 dollar and 25 cents.

Hope this helps a little bit

the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The number of choice out of 7 that consumer have are 42.

The term permutation alludes to a numerical computation of the quantity of ways a specific set can be sorted out. Set forth plainly, a change is a word that depicts the quantity of ways things can be requested or organized. With stages, the request for the course of action matters.

Number of choices of side dishes does a customer have,

total dishes(n)=7 , r = 2

ⁿP₂

⁷P₂

7×6 = 42

Thus required number of ways are 42.

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Answer:

(1/2)m - (3/4)(8) = 16

(1/2)m - 6 = 16

(1/2)m = 22

m = 44

Answer:

0.625 years = 7.5 months

Step-by-step explanation:

Simple interest formula = rxtxp divided by 100

R x T x P / 100 = 30

Substitute all the values we know

3.2 x T x 1500/100 = 30

Simplify and rearrange =

3.2 x T x 1500 = 3000

3.2 x T = 2

T = 2/3.2

T = 0.625

Statement which gives a correct comparison of their rate of savings is "A) Shane is saving $1 more than Adam per day."

The rate of savings per week can be determined by examining the slope of the equations. In this scenario, Adam saves $3 per week, and Shane saves $4 per week. The slope of a line represents the tangent angle it forms with the horizontal axis, denoted as m = tan(x), where x is in degrees. It is also defined as the rate of change of a function.

Now, considering the competition between Adam and Shane to see who can save the most money in one month, we observe that Adam's savings follow a linear function given by the slope-intercept form equation y = 3x + 3. However, the linear function for Shane's savings is not explicitly provided, so we assume it as y = 4x.

In both equations, the slopes represent the rate at which they save money per week, with Adam saving $3 per week and Shane saving $4 per week.

Therefore, statement "A) Shane is saving $1 more than Adam per day" is correct.

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Answer:

4, 802 cans will be collected in two weeks

Step-by-step explanation:

343 aluminum cans = 1 day

? = 2 weeks

2 weeks = 14 days

So, 343 x 14 = 4, 802

The four chief weaknesses of Mesopotamian mathematics were their lack of a formalized system of notation, limited understanding of abstract concepts, absence of proofs, and reliance on concrete examples.

Mesopotamian mathematics, while impressive for its time, had several weaknesses that limited its advancement. Firstly, one of the chief weaknesses was the absence of a formalized system of notation. Unlike later mathematical systems that employed symbols to represent numbers and operations, Mesopotamian mathematics relied heavily on verbal descriptions and geometric diagrams. This lack of a standardized notation made complex calculations and the representation of abstract concepts challenging.

Secondly, Mesopotamian mathematics had a limited understanding of abstract concepts. Their mathematical knowledge was primarily practical and focused on solving real-life problems such as measuring fields, building structures, and conducting trade. They excelled in arithmetic and geometry related to these practical applications but struggled with more abstract mathematical concepts, such as algebra and formalized proofs.

Thirdly, the Mesopotamians did not have a concept of proof in their mathematical practice. While they had algorithms and methods for solving problems, they did not develop a systematic approach to proving mathematical statements. This absence of rigorous proof limited their ability to explore and establish general mathematical principles.

Lastly, Mesopotamian mathematics heavily relied on concrete examples and specific cases. They often approached mathematical problems by providing solutions to specific scenarios rather than developing general formulas or principles. This empirical approach hindered the development of broader mathematical theories and hindered the advancement of mathematics as a discipline.

In summary, the chief weaknesses of Mesopotamian mathematics were the lack of a formalized system of notation, limited understanding of abstract concepts, absence of proofs, and reliance on concrete examples. These limitations prevented the Mesopotamians from achieving a higher level of mathematical abstraction and hindered the development of more sophisticated mathematical theories. However, their contributions laid the foundation for future mathematical advancements in other civilizations.

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Answer:

1) 0.12

2) 52.5

3) 185.32

4) 77.85

5) 313.75

6) 1.536

7) 0.0167

8) 64

9) 21

10) 282.4

11) 136.64

12) 88.56

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

The amount added to each of the 3 sides is a rectangle 6.25 m by 1.5 m.

Then there are two square corners added that each one is 1.5 m by 1.5 m.

Total added area = 3 × 6.25 m × 1.5 m + 2 × 1.5 m × 1.5 m

Total added area = 28.125 m² + 4.5 m²

Total added area = 32.625 m²

The area of each tile is:

0.25 m × 0.25 m = 0.0625 m²

A box of tiles has 25 tiles. The total area covered by a box of tiles is:

25 × 0.0625 m² = 1.5625 m²

The number of boxes need is:

32.625 m² / 1.5625 m² = 20.88

Since 20.88 boxes are needed, but she needs to buy full boxes, she needs 21 boxes of tiles.

Answer: 21

2 x 10^5 miles is the correct answer.

A power of ten in mathematics is defined as one of the integer powers of a number multiplied by ten. Integers can be both positive and negative. To find the multiple of ten, we need to add 10 to itself several times (if the power is a positive integer).

if we have a value that says ten ^5,

then this value is equal to:

= 10 x 10 x 10 x 10 x 10

= 10,0000

Also, by the definition of a multiple of ten, the number 1 is a power of 10 as well if we take the 0th power of 10.

10^0 = 1

Whatever the integer is, it is multiplied by 10 n times. So, the long form of a power of 10 is the number 1, followed by n zeros, where the n number is greater than the 0 value.

Here the distance that is given to us is:

238,855

We can also write it as,

2 x 10 ^ 5.

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The value of x which is hypotenuse is 4 units .

Using pythagoras theorem ,

( a ^ 2 ) + ( b ^ 2 ) = ( h ^ 2 )

where a is the base , b is a side and h is the hypotenuse of a right- angled triangle .

First triangle's hypotenuse = \(\sqrt{2}\)

Second triangle's hypotenuse = \(\sqrt{3}\)

Third triangle's hypotenuse = 2

Therefore ,

Last triangle's hypotenuse = \(\sqrt{15}\)

Hence ,

( \(\sqrt{15}\) ^ 2 ) + [ ( 1 ) ^ 2 ] = x ^ 2

15 + 1 = x ^ 2

16 = x ^ 2

x = 4

Therefore , the value of x which is hypotenuse is 4 units .

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The absolute value inequality that has the solution set x < –7 or x > 5 is

|x + 1| > 6.

When we are given a solution set that involves inequalities, we can use the midpoint of the interval between the endpoints of the solution set as the reference point, and half the length of the interval as the value for c.

We can then use the form |x - b| < c or |x - b| > c to write an absolute value inequality that has the given solution set.

Here we have

The condition x < –7 or x > 5

To write an absolute value inequality that has the solution set x < -7 or x > 5, we can use the form |x - b| > c,

Where b is the midpoint of the interval [-7, 5] and c is half the length of the interval.

The midpoint of the interval [-7, 5] is:

b = (-7 + 5) / 2 = -1

The length of the interval is:

|5 - (-7)| = 12

So half the length of the interval is:

c = 12 / 2 = 6

Therefore,

the absolute value inequality that has the solution set x < -7 or x > 5 is:

|x - (-1)| > 6

Simplifying this inequality, we get:

|x + 1| > 6

Therefore,

The absolute value inequality that has the solution set x < –7 or x > 5 is

|x + 1| > 6.  

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Answer:

cos 315°   =   45° reference angle in the 4th quadrant =  √2 /2

And sin 315°    is the negative of this

So  

z = (3) cos 315°  + ( 3i ) sin 315°  =

[   (3/2)√2  ,  - (3/2) √2 i  ]

Mr. Knapp initially had 61 stamps.

Given that Mr. Knapp had some stamps,

if he gave 7 stamps to each of his children, now he would have 5 stamps left.  

If he gave 8 stamps to each child, he would need 3 more stamps in order for the children to have an equal number of stamps.  

We need to find that how many stamps did Mr. Knapp had.

Let's solve the problem step by step.

Let's assume Mr. Knapp has "x" stamps initially.

According to the first condition, if he gave 7 stamps to each of his children, he would have 5 stamps left.

This can be expressed as:

x - 7c = 5,

where "c" represents the number of children.

According to the second condition, if he gave 8 stamps to each child, he would need 3 more stamps in order for the children to have an equal number of stamps.

This can be expressed as:

x - 8c = -3.

We now have a system of two equations with two variables:

x - 7c = 5,

x - 8c = -3.

Let's use the elimination method to eliminate "x" from the equations:

(x - 7c) - (x - 8c) = 5 - (-3),

x - 7c - x + 8c = 5 + 3,

c = 8.

Now that we know the value of "c" is 8, we can substitute it back into either of the original equations to find the value of "x."

Let's substitute it into the first equation:

x - 7(8) = 5,

x - 56 = 5,

x = 5 + 56,

x = 61.

Therefore, Mr. Knapp initially had 61 stamps.

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To find the factors of the expression 12x^2 - 4x - 1, we can use the factor theorem. The factor theorem states that if a polynomial expression evaluates to zero when a certain value is substituted for the variable, then that value is a factor of the polynomial.

To determine if a certain value is a factor of the expression, we can use synthetic division. Synthetic division involves dividing the polynomial expression by the possible factor to check if the remainder is zero. If the remainder is zero, then the value is a factor.

Let's start by checking if x = 1 is a factor of the expression:

    1 | 12 - 4 - 1
      |     12   8
      |____________
       12   8   7

Since the remainder is not zero, x = 1 is not a factor of the expression.

Next, let's check if x = -1 is a factor of the expression:

   -1 | 12 - 4 - 1
      |    -12  16
      |____________
       12 -16  15

Again, the remainder is not zero, so x = -1 is not a factor of the expression.

Now, let's check if x = 2 is a factor of the expression:

    2 | 12 - 4 - 1
      |     24 40
      |____________
       12  20 39

Once again, the remainder is not zero, so x = 2 is not a factor of the expression.

Finally, let's check if x = -2 is a factor of the expression:

   -2 | 12 - 4 - 1
      |    -24 56
      |____________
       12 -28 55

As we can see, the remainder is not zero, so x = -2 is not a factor of the expression.

After checking all the possible factors, we can conclude that none of the values tested (1, -1, 2, -2) are factors of the expression 12x^2 - 4x - 1.

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The wire should cut at a distance of 33.6

For given question,

Let x be the length of one side of the square.

so, the Perimeter of a square = 4x

For the remaining length of (60 - x) we make a circle.

We know that the Circumference of a circle = 2πr

So, 4x + 2πr = 60

⇒ 2πr = 60 - 4x

⇒ r = (60 - 4x)/2π

⇒ r = (30 - 2x)/π                                            

The area of the square would be,

\(A_s=x^{2}\)

And the area of the circle would be,

\(\Rightarrow A_c=\pi (\frac{30-2x}{\pi} )^2\\\\\Rightarrow A_c=\frac{(30-2x)^2}{\pi}\)

Thus summing the areas we get,

\(\Rightarrow A=A_s+A_c\\\\\Rightarrow A=x^{2} +\frac{(30-2x)^2}{\pi}\)

To find the critical points we differentiate the given area with respect to 'x'

Thus we have,

\(\Rightarrow \frac{dA}{dx}=\frac{d[x^{2} +\frac{(30-2x)^2}{\pi}]}{dx}\\\\\Rightarrow 0=2x - \frac{4 (30-2x)}{\pi} \\\\\Rightarrow 2x = \frac{4 (30-2x)}{\pi}\\\\\Rightarrow x = \frac{60}{\pi}-\frac{4x}{\pi} \\\\\Rightarrow x (1+ \frac{4}{\pi})=\frac{60}{\pi} \\\\\Rightarrow x=8.4\)

Thus the perimeter of square would be, 33.6

And the circumference of circle would be,

60 - 33.6 = 26.4

Thus, cut the wire at a distance of 33.6  and draw this length into a square and the remaining 26.4 into a circle.

Therefore, the wire should cut at a distance of 33.6

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Answer:

1. x + 23 = 41

2. x = 18; solution is 18

Step-by-step explanation:

We can translate the question into an equation. Because the question is asking to find a specific number we don't know the value of, let that unknown number be a variable; x. We know, from the information given in the question, that x added to 23 is equal to 41. When we're adding a number to another number, we use the + symbol. So far, we have x + 23. Now, the last part says "equals 41". We can imply when something equals another thing, we use the = sign. Then, we're left with the equation: x + 23 = 41.

To solve for this equation:

x + 23 = 41

Subtract 23 from both sides:

x + 23 - 23 = 41 - 23

x = 18

Therefore, our solution is 18.

The given matrix is used to answer the following questions:Image: The table above demonstrates a shipping rate schedule that includes shipping classes and weight ranges.

The first column indicates the shipping class, while the top row lists weight limits (pounds). Therefore, the charge for shipping a 1428 pound crate in shipping class (50) is $ 4.70.What are matrices?

Matrices are a collection of numbers that are organized into rows and columns. Matrices are frequently used to depict data that has multiple dimensions. They are utilized to depict data that has been arranged in tabular form, and they are useful for solving linear equations, system equations, and more.

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Answer:

The answer is the third one

-168

Step-by-step explanation:

1. 360

2. 360

3. -168

4. 0

Solution :

1st -

2nd -

3rd -

4th -

Conclusion - only third choice has negative equivalent value