A farmer has a field in the shape of a triangle. The farmer has asked the manufacturing class at your school to build a metal fence for his farm. From one vertex, it is 435m to the second vertex and 656m to the third vertex. The angle between the lines of sight to the second and third vertices is 49 degrees. Calculate how much fencing he would need to enclose his entire field.

Complete Question: Which of the following is an example of the difference of two​ squares?

A x² − 9

B x³ − 9

C (x + 9)²

D (x − 9)²

Answer:

A. [tex] x^2 - 9 [/tex].

Step-by-step explanation:

An easy way to spot an expression that is a difference of two squares is to note that the first term and the second term in the expression are both perfect squares. Both terms usually have the negative sign between them.

Thus, difference of two squares takes the following form: [tex] a^2 - b^2 = (a + b)(a - b) [/tex].

a² and b² are perfect squares. Expanding [tex] (a + b)(a - b) [/tex] will give us [tex] a^2 - b^2 [/tex].

Therefore, an example of the difference of two squares, from the given options, is [tex] x^2 - 9 [/tex].

[tex] x^2 - 9 [/tex] can be factorised as [tex] x^2 - 3^2 = (x + 3)(x - 3) [/tex].

Division is one of the four fundamental arithmetic operations. Andrew is faster than Noah.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that Andre can now complete 135 multiplication facts in 90 seconds.

A.) If Andre is answering questions at a constant rate, then the number of facts that Andre can answer per second can be written as,

Number of facts per seconds = 135 facts / 90 seconds

                                                 = 1.5 facts per seconds

B.) Noah also works at a constant rate, and he can complete 75 facts in 1 minute. Therefore, the number of facts that Noah can answer per second can be written as,

Number of facts per seconds = 75 facts / 60 seconds

                                                 = 1.25 facts per seconds

Now, since the number of facts that Andrew can read in a second is 1.5 facts, while the number of facts that Noah can read in a second is 1.25 facts.

Hence, Andrew is faster than Noah.

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Answer:

900cm^3

Step-by-step explanation:

1 cm= 10 mm

x=300mm (criss cross)

1cm*300mm/10mm= 10mm*x/10mm

30cm=x

30cm=300mm

1m=100cm

0.2m=x

1m*x/1m=0.2m*100cm/1m

x=0.2*100cm

x=20cm

0.2m=20cm

l=15cm

w=30cm

h=20cm

v=l*w*h

v=15cm*30cm*20cm

v=450cm^2*20cm

v=900cm^3

Answer:

9000cm^3

Step-by-step explanation:

Width:300mm=30cm

Height:15cm=15cm

Depth:0.2m=20cm

V=DxWxH

V= 20x30x15

V=9000cm^3

Answer:

Step-by-steIn order to go to college, Chris goes from working full-time making $30,000 per year to working part-time at half the salary for two years. The cost of his education will be $5,000. If Chris makes $35,000 per year after getting his degree, approximately how many years will it take him to recover his investment? *

it would take him 7 years to recover the 35,000 he invested

p explanation:

he was in college two years and it cost him a total of 5000 and he lost 30000 from the two years he worked part time

Answer:

1. [tex]\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}[/tex]

2. [tex]y(40) = 110.873 \ kg[/tex]

Step-by-step explanation:

Given that:

A very large tank initially contains 100 L of pure water.

Starting at time t = 0 a solution with a salt concentration of 0.8kg/L is added at a rate of 5L/min.

. The solution is kept thoroughly mixed and is drained from the tank at a rate of 3L/min.

As 5L/min is entering and 3L/min is drained out, there is a 2L increase per minute. Therefore, the amount of water at any given time t = (100 +2t) L

t = (50 + t ) L

Since it is given that we should  consider y(t) to be the  amount of salt (in kilograms) in the tank after t minutes.

Then , the differential equation that  y satisfies can be computed as follows:

[tex]\dfrac{dy}{dt}=rate_{in} - rate_{out}[/tex]

[tex]\dfrac{dy}{dt}=(0.8)(5) -\dfrac{y(t)}{100+2t} \times3[/tex]

[tex]\dfrac{dy}{dt}=(0.8)(5) -\dfrac{3y}{100+2t}[/tex]

[tex]\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}[/tex]

How much salt is in the tank after 40 minutes?

So,

suppose : [tex]e^{\int \dfrac{3}{100+2t} \ dt} = (t+50)^{3/2}[/tex]

Then ,

[tex]( t + 50)^{3/2} y' + \dfrac{3}{2}(t+50)^{1/2} y = 4(t+50)^{3/2}[/tex]

[tex]( t + 50)^{1.5} y' + \dfrac{3}{2}(t+50)^{0.5} y = 4(t+50)^{3/2}[/tex]

[tex][y\ (t + 50)^{1.5}]' = 4(t+ 50)^{1.5}[/tex]

Taking the integral on both sides; we have:

[tex][y(t + 50)^{1.5}] = 1.6 (t + 50)^{2.5} + C[/tex]

[tex]y = 1.6 (t+50)+C(t+50)^{-1.5}[/tex]

[tex]y(0) = 0 = 1.6(0+50) + C ( 0 + 50)^{-1.5}[/tex]

[tex]0 = 1.6(50) + C ( 50)^{-1.5}[/tex]

[tex]C= -1.6(50)^{2.5}[/tex]

[tex]y(40) = 1.6 (40 + 50)^1 - 1.6 (50)^{2.5}(50+40)^{-1.5}[/tex]

[tex]y(40) = 144 - 1.6 \times 17677.66953 (90)^{-1.5}[/tex]

[tex]y(40) = 144 - 1.6 \times 17677.66953 \times 0.001171213948[/tex]

[tex]y(40) = 144 - 33.12693299[/tex]

[tex]y(40) = 110.873 \ kg[/tex]

Answer:

1.  1 * [tex]x^{3/6}[/tex] = [tex]x^{3/6}[/tex] (it will be equal to the sixth root of x cube)

2.  No, the expression [tex]x^{3}[/tex] X [tex]x^{3}[/tex] X [tex]x^{3}[/tex] will be equal to [tex]x^{3 + 3 + 3 }[/tex] since the powers of      numbers with the same base are added

3. B and D   1/[tex]x^{-1}[/tex] is the same as 'x'

as mentioned in the last answer, powers of numbers with same base are added. hence, option D will be [tex]x^{3/3}[/tex] which will be equal to x

Answer:

x = 7

Step-by-step explanation:

5x + 9 = 6x + 2

5x - 6x = 2 - 9

-x = -7

x = 7

probe:

5*7 + 9 = 6*7 + 2

35 + 9 = 42 + 2 = 44

Answer:

x = 11

Step-by-step explanation:

The angles shown are alternate exterior angles.  If they are equal, then the lines are parallel

5x+9 = 6x-2

Subtract 5x from each side

5x-5x+9 = 6x-5x-2

9 = x-2

Add 2 to each side

9+2 = x

11 =x

The correct answer is C) 50 parents of college students from the state

Explanation:

The purpose of representative samples is to study a population by only selecting a small group in it. Due to this, the individuals selected as part of the sample need to match the characteristics of the population being studied.

In this context, if the focus is the opinion of parents about college tuition fees in a specific state, it is expected the sample includes parents of college students rather than students, citizens, etc. because the opinion of parents of college students is being evaluated. Moreover, those parents selected should have children in the state being studied. According to this, the correct option is C because this includes individuals who can appropriately represent the population that is being analyzed.

Answer:

50 parents of college students from the state.

Step-by-step explanation:

Sophia Statistics

Answer:

There is no opposite of 0.

Step-by-step explanation:

There cannot be a zero the opposite of zero. If there was, then there would be two 0's, and there is only one.

Answer:

1. 0.5 for x, 3 for y

2. 1.5 for x, 9 for y

3. 2.5 for x, 15 for y

Step-by-step explanation:

I will explain later if you still need help...but you said you need it fast, so I don't want to be too slow.  :)

Answer:

588.76

Step-by-step explanation:

Commission is 7% of total

Total selling price of 516 crates of oranges:

Commission amount:

Answer:

The 90% confidence interval is  [tex]0.445< p < 0.456[/tex]

Step-by-step explanation:

From the  question we are told that

  The sample  size is  [tex]n = 17592[/tex]

  The number of  binge  drinkers is  [tex]k = 7851[/tex]

Given that the  confidence level is  90%  then the level of significance is mathematically represented as

          [tex]\alpha = (100 - 90)\%[/tex]

          [tex]\alpha = 0.10[/tex]

The critical value  of  [tex]\frac{\alpha }{2}[/tex]  from the normal distribution table  is  [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

The  sample  proportion is mathematically represented as

      [tex]\r p = \frac{ 7851}{ 17592}[/tex]

      [tex]\r p = 0.45[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{ \frac{x}{y} } * \sqrt{\frac{\r p(1 - \r p )}{n} }[/tex]

       [tex]E =1.645 * \sqrt{\frac{ 0.45 (1 - 0.45 )}{17592} }[/tex]

      [tex]E =0.00617[/tex]

The  90%  confidence interval is mathematically represented as  

      [tex]\r p -E < p < \r p +E[/tex]

      [tex]0.45 -0.00617 < p < 0.45 + 0.00617[/tex]

      [tex]0.445< p < 0.456[/tex]

Answer:

144

Step-by-step explanation:

Hello, please consider the following.

[tex]x^2-24x+c[/tex]

is a perfect square means that the discriminant is 0.

[tex]\Delta = b^2-4ac=24^2-4c=0\\\\<=>24^2-4c =0<=> 4c=576\\\\\text{We divide by 4}\\\\c= \dfrac{576}{4}=144[/tex]

Thank you

The value of c which make a perfect square trinomial is,

⇒ c = 144

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ x² - 24x + c

Now, We can it squared as;

⇒ x² - 24x + c

⇒ x² - 2 × 12x + 144

⇒ x² - 24x + 12²

⇒ (x - 12)²

Thus, The value of c which make a perfect square trinomial is,

⇒ c = 144

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Answer:

"proportional to"

Step-by-step explanation:

The sign ∝ means 'is proportional to'. This is used to show that one variable of value is proportional to another value or variable.

Example:

Hope this helps.

Step-by-step explanation: The figure shown here is a straight path between points that extends forever in both directions, so it's called a line.

Since a line doesn't have endpoints, it doesn't matter which

two points on the line we use to name the line.

I have attached 5 possible names for the line below.

Answer:

Step-by-step explanation:

e Because lines continue infinitely, we can name them forwards or backwards. We can also use any two points on a line to identify it, unlike with rays or segments. The l and the end of the line can also be used to identify it.

Different names for the line include: DE ED DF FD and line l.

Answer:

the simple multiplier is equal to 4

Step-by-step explanation:

In an economic model,

Y=  C + I + G + (X - M)

the average expenditure Y must be equal  to the totality of the output

If C = 3 + 0.75Y

where;

marginal propensity to consume MPC = 0.75

Then,

Y = 3 + 0.75Y + 2 + 1

Y = 6+0.75 Y

Y - 0.75 Y = 6

0.25 Y = 6

Y = 6/0.25

Y = 24

However,  the simple multiplier can be expressed as:

[tex]=\dfrac{1}{1 - MPC}[/tex]

[tex]=\dfrac{1}{1 - 0.75}[/tex]

[tex]=\dfrac{1}{0.25}[/tex]

= 4

Answer:

2 < x < 3

Step-by-step explanation:

Set A)

3x + 4 ≥ 13

3x ≥ 9

x ≥ 3

Set B)

0.5x + 3 ≤ 4

0.5x ≤ 1

x ≤ 2

Plot it out on a number line, and you'll see that 2 < x < 3

Answer:

It's A

Step-by-step explanation:

Answer:

or,6x+6=9x-9

or,6+9= 9x-6x

or,15=3x

or,15/3=X

therefore,X=5ans

Answer:

x=3

Step-by-step explanation:

32/24=(6x+6)/(9x-9)

simplify by 8 in the left

4/3=6(x+1)/9(x-1)

simplify by 3 in the right

4/3=2(x+1)/3(x-1)

*3           *3

4=2(x+1)/(x-1)

(x+1)/(x-1)=4/2=2

so x+1=2(x-1)=2x-2

-x                     -x

1=x-2

+2    +2

3=x

so x=3

verify  (6*3+6)/(9*3-9)=32/24

24/18=32/24

simplify by 6  in the left

4/3=32/24

simplify by 8   in the right

4/3=4/3   TRUE

Answer:

Speed= 67.5 miles per hour

Step-by-step explanation:

Google maps has told Juanita that her car trip will be 32 miles.

Juanita has already gone 14 miles.

Remaining miles left to travel

= 32-14

Remaining miles left to travel

= 18 miles

She has only 16 minutes to reach her destination.

The required speed for her to reach her destination

= Distance/time

Her time = 16 minutes

Her time = 16/60

Her time =4/15 hours

Speed= distance/time

Speed= 18 /(4/15)

Speed=18* 15/4

Speed= 67.5 miles per hour

Juanita needs to drive at 67.5 miles per hour to arrive in 16 more minutes

The total distance (D) is given as:

[tex]\mathbf{D = 32miles}[/tex]

She has traveled 14 miles;

So, the remaining distance (d) is:

[tex]\mathbf{d = D -14}[/tex]

This gives

[tex]\mathbf{d = 32 -14}[/tex]

[tex]\mathbf{d = 18}[/tex]

Speed is calculated as:

[tex]\mathbf{Speed = \frac{distance}{time}}[/tex]

Where: distance = 18 miles and time = 16 minutes

So, we have:

[tex]\mathbf{Speed = \frac{18\ miles}{16\ minutes}}[/tex]

Convert time to hour

[tex]\mathbf{Speed = \frac{18\ miles}{16/60\ hour}}[/tex]

So, we have:

[tex]\mathbf{Speed = \frac{18 \times 60\ miles}{16\ hour}}[/tex]

[tex]\mathbf{Speed = \frac{1080\ miles}{16\ hour}}[/tex]

Divide

[tex]\mathbf{Speed = 67.5\ miles/ hour}[/tex]

Hence, the speed is 67.5 miles per hour

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If you have tickmarks on the segment, on a blank piece of paper, then you count out the spaces to get the length of the segment. This is assuming the tickmarks are properly spaced out. If there aren't any tickmarks, then you'll have to use a ruler to find the length. Either way, a ruler is encouraged.

The coordinate plane makes things easier to find the length of any segment. Use either the pythagorean theorem or the distance formula to find the length of the segment.

Answer:

3.14

Step-by-step explanation:

Los primeros tres son 3.14

Answer:

30.4 days or 31 days

Step-by-step explanation:

553 - 112 = 441

it took 30 days for 441 cases

30 / 441 = 0.06802721088

1000 - 553 = 447

0.06802721088 x 447 = 30.4081632653

30.4 days or 31 days

Answer:

coordinates of the centroid = [tex](\frac{2}{3} , \frac{2}{3} )[/tex]

Step-by-step explanation:

The curves to be plotted are : y =2x, y = 0, x =1

The coordinates of the centroid ( visually estimated ) can be found by first calculating the area of the region

A = [tex]\int\limits^1_0 {2x} \, dx[/tex]  =   2[tex](\frac{x^2}{2} )[/tex] hence A = 1

attached below is the remaining part of the solution

Answer:

-625,3125

Step-by-step explanation:

Im not saying this is correct but it looks like its multipling by 25

Answer:

5x^2 -2x +4

Step-by-step explanation:

(8x^2 + 9) - (3x^2 + 2x + 5)

Distribute the minus sign

(8x^2 + 9) - 3x^2 - 2x - 5

Combine like terms

5x^2 -2x +4

Answer:

100 dinners

Step-by-step explanation:

There are 4 choices for the appetizer, 5 choices for the main course and 5 choices for the dessert so the total number of dinners that are possible is 4 * 5 * 5 = 100.

Answer:

Step-by-step explanation:

Using the Distributive Property of Multiplication, we get

12

---- - 12x. or 4 - 12x, or 4(1 - 3x)

 3

Answer:

Yes, this is a function

Step-by-step explanation:

This relation is function because 1 x value corresponds to 1 y value

Answer:

Step-by-step explanation:

Hello,

-1 <= -1 < 0

so f(-1)=-1

0 <= 0.5 < 1

so f(0.5)=0

1 <= 1 < 2

so f(1)=1

Thank you.