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 435 m to the second vertex and 656 m to the third vertex. The angle between the lines of sight to the second and third vertices is 49°. Calculate how much fencing he would need to enclose his entire field.

Answer:

D, B, B

Step-by-step explanation:

Question 1: D

We need to solve for x.

z = 2π * (x / y)¹/²

z = 2π * (x¹/² / y¹/²)

z = 2π * (√x / √y)

z = √x * 2π / √y

√x = √y * (z / 2π)

x = y(z /2π)²

Question 2: B

(x⁵ + x⁴) / (x³ + x²)

= x⁴(x + 1) / x²(x + 1)

= x⁴ / x² = x⁽⁴⁻²⁾ = x²

Question 3: B

Let's try out A. Substituting p = 1, q = 1:

√1 * √1 = √(1 + 1)

1 * 1 = √2

1 = √2 FALSE

Let's try B. Substituting p = 2, q = 2:

√2 * √2 = √(2 + 2)

√4 = √4 TRUE so the answer is B.

Answer:

1.44 pounds

Step-by-step explanation:

From the above question, we are told that:

The shop has 3 for 2 offer on chocolate bars going on .This means a customer can buy 2 chocolates get 1 free, for the price of 2 chocolates, a customer can get 3 chocolates.

If the price of 1 chocolate bar = 72p

2 chocolate bars =

72p × 2

= 144p

Hence, Sian spends 144p

We are asked to convert our answer to pounds

The symbol p represent pence in money form

Hence,

100p(pence) = 1 pound

144p(pence) = x

100p × x = 144p × 1

x = 144p/100p

x = 1.44 pounds

Therefore, Sian spends 1.44 pounds

Answer:

Area of rectangle=9×17=153 SQ.ft

Area of semi-circle=π9'2/2

Area of traingle=(1/2)×7×9=31.5

The area of the composite figure is 325.17 square feet

The figure is a composite figure with the following shapes

The dimension of the shapes are:

The area of each shape is:

Semicircle

A = 0.5πr²

This gives

A = 0.5 * 3.14 *9^2 = 127.17

Triangle

A = 0.5 * base* height

This gives

A = 0.5 * 9 * (26 -9 - 7) = 45

Rectangle

A = Length * Width

This gives

A = 9 * (26 - 9) = 153

The area of the figure is the sum of the areas of the individual shapes.

So, we have:

Total = 127.17 + 45 + 153

Evaluate

Total = 325.17

Hence, the area of the composite figure is 325.17 square feet

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Answer:

560,317.460

Step-by-step explanation:

The computation of copies that have been sold is shown below:-

we assume the number of copies is x

So, the number of copies in the first month is

= [tex]\frac{6.3}{100} x[/tex]

As per the situation the number of sold copies is 35,300 so the equation will be

[tex]\frac{6.3}{100} x = 35,300[/tex]

[tex]6.3x = 35,300\times 100[/tex]

[tex]x = \frac{35,300\times 100}{6.3}[/tex]

after solving the above equation we will get the number of copied that have been sold to date

= 560,317.460

Answer:

Estimate of crowd is 27456.

Step-by-step explanation:

Given that a square of 5 by 5 can have 13 students.

Area of a square = [tex]side^2[/tex] = 25

Area of 25 can have 13 students.

Now, it is given that 10 feet square are used for crowd.

Area of square of side 10 feet  = 100

So, area of 100 can have 13 [tex]\times[/tex] 4 = 52 people from crowd

Now, it is given that the parade route is 1 mile long.

1 mile = 5280 feet

1 mile = 528 [tex]\times[/tex] 10 feet

It means that there are 528 number of such squares on the 1 mile section of the parade route.

Kindly refer to the attached image as well.

So, number of people or the estimate of the size of crowd is:

528 [tex]\times[/tex] 52 = 27456

Answer:

D) had been trained over the past two years and that they had

Step-by-step explanation:

In the context, the sentence speaks of something that happened in the past, so 'had been' is required and also it speaks of parallelism of events, as an estimation is being made so,  parallelism should be maintained.

Hence, option (D) satisfies the two requirements. And eliminate option A, B, C and E.

Thus, (D) is correct.

Answer:

12,138 people

Step-by-step explanation:

Create an equation using the basic exponential growth equation:

y = a(1 + r)^t, where a is the initial amount, r is the growth rate as a decimal, and t is the amount of time in years.

Plug in the values we know

y = a(1 + r)^t

y = 8200(1 + 0.04)^10

y = 8200(1.04)^10

= 12,138 people

Answer:

10/36 or 5/18 is the fraction of the wall that is limestone. In percentage form it would 27.77..% or could be rounded to 27.8%

Step-by-step explanation:

a no. is divisible by 4 if the last two digits are a mutiple of 4

Answer:

(i), (iii), (v).

Step-by-step explanation:

If a number is divisible by 4 then its last 2 digits are divisible by 4.

For example 23408 is because 08  is divisible by 4.

Answer:

  7

Step-by-step explanation:

Working backward, we can find Bob's initial product.

We subtracted 3 to get 1, so we had 4.

We divided by 5 to get 4, so we had 20.

We added 6 to get 20, so we had 14

After Bob multiplied the two numbers together, he had 14. We know that 14 is the product of 2 and 7. The odd number is 7.

Answer:

the inverse is f(x) = 2x - 2

Step-by-step explanation:

Inverse operation in this equation is basically switching the x and y:

y = x/2 + 1

x = y/2 +1

x - 1 = y/2

2x - 2 = y

Answer:

A conjunction is true in region  

✔ B  <--- Answer

A disjunction is true in region(s)  

✔ A, B, and C  <--- Answer

A disjunction is false in region(s)  

✔ D  <--- Answer

Step-by-step explanation:

I took the assaignment aswell

A conjunction is true in the region  

✔ B  ← Answer

A disjunction is true in the region(s)  

✔ A, B, and C  ← Answer

A disjunction is false in the region(s)  

✔ D  ← Answer

A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.

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Answer:

Step-by-step explanation:

1.

[tex](3,1) and\:perpendicular \:to \: y = -x+1\\(3,1) = (x,y)\\m = -1\\In\: perpendicularism ; m_2 = \frac{-1}{m_1} \\m_2 = \frac{-1}{-1} \\m_2 =1\\y = mx+c\\1 = 1(3) +c\\1=3+c\\1-3=c\\-2 =c\\Substitute \:new \:values\:into\\y =mx+c\\y = 1x -2\\y = x-2[/tex]

2.

[tex](-1,7) =(x_1,y_1)\\\\5y = 4x+5\\\\Write\:in\:y=mx+c\:form\\\frac{5y}{5} = \frac{4}{5} x + \frac{5}{5} \\y = \frac{4}{5} x +1\\m = \frac{4}{5} \\\\y -y_1=m(x-x_1)\\y-7=\frac{4}{5} (x -(-1)\\y -7 = 4/5(x+1)\\y -7 = 4/5x +4/5\\\\y = \frac{4}{5} x+\frac{4}{5} +7\\\\y = \frac{4}{5} x +39/5[/tex]

Answer:

41

Step-by-step explanation:

Points are:

Distance between these points:

Answer is 41

Answer:

[tex]\Huge \boxed{41}[/tex]

Step-by-step explanation:

Easy way to find the distance between the two numbers is by taking the sum of the absolute values of these numbers.

[tex]|-13| + |28|[/tex]

The absolute value tells the distance of the numbers from zero.

Solving for absolute value.

[tex]13+28[/tex]

Adding the numbers.

[tex]41[/tex]

The distance between -13 and 28 on the number line is 41.

Answer:

(4x + 5)(x² + 25)

Step-by-step explanation:

Given

4x³ + 5x² + 100x + 125 ( factor the first/second and third/fourth terms )

= x²(4x + 5) + 25(4x + 5) ← factor out (4x + 5) from each term

= (4x + 5)(x² + 25)

Answer:

Step-by-step explanation:

From science fiction to science fact, there is a concept that suggests that there could be other universes besides our own, where all the choices you made in this life played out in alternate realities. The concept is known as a "parallel universe," and is a facet of the astronomical theory of the multiverse.

Answer:

to be honest I'm not sure

Answer:

a.) 98°

Step-by-step explanation:

Angle 5 and angle 8 (82°) are supplementary angles. This means that their sum will make a straight angle of 180°. Make an equation:

[tex]82+x=180[/tex]

Solve for x, the value of angle 5:

[tex]x=180-82\\\\x=98[/tex]

Angle 5 has a  measure of 98°.

Now we know the measure of angle 5. Angle 4 and angle 5 are alternate interior angles, so they are congruent. Therefore, angle 4 has a measure of 98°.

:Done

Answer:

4y

Step-by-step explanation:

youd have to combine like terms..

Answer:

4y

Step-by-step explanation;

since they have something in common which is y,it is possible to subtract.we would be focusing more on the numbers than letters.The like term which is y just paves a way for these numbers to be subtracted.Hence, 6y -2y= 4y

or you can do it this way also

they have something in common which is y,so we factorise

y(6-2)

y(4)

hence y(4) also means 4 x y= 4y

Answer:

B. 90°

Step-by-step explanation:

Quadrilateral inscribed in the circle with center O is a cyclic quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

Therefore,

(b + d) + (32° + 58°) = 180°

b + d + 90° = 180°

b + d = 180° - 90°

b + d = 90°

Answer:

16/27

Step-by-step explanation:

First let's convert this info an equation and then we will solve.

(2/3) * (8/9) = ?

( 2 * 8 ) / ( 3 * 9 ) = ?

( 16 ) / ( 27 ) = ?

16 / 27 = ?

So our fractional answer is 16/27.

In words this would be sixteen over twenty seven.

Cheers.

Answer:

15/9

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

The correct statements are (a), (c) and (d).

Step-by-step explanation:

The information provided is:

The total charge for Elegance Home Architects, if the Nelsons choose them will be:

Total for Elegance = 75 × h = 75h.

Suppose  the Nelsons hire the design firm for 15 hours.

Total for Elegance = 75 × h = 75 × 15 = $1,125

Total for Rock = 500 + (50 × h) = 500 + (50 × 15) = $1,250

So, the  Elegance Home Architects will be cheaper.

Suppose  the Nelsons hire the design firm for 25 hours.

Total for Elegance = 75 × h = 75 × 25 = $1,875

Total for Rock = 500 + (50 × h) = 500 + (50 × 25) = $1,750

So, the Rock the House Digital Designs will be cheaper.

Thus, the correct statements are (a), (c) and (d).

Answer:

a)  

Step-by-step explanation:

We have been given a function . We are asked to find the domain of our given function.

We can see that our given function is a rational function and numerator of our given function is a square root.

To find the domain of our given function, we will find the number that will make our denominator 0 and the domain of square root function will be the values of x that will make our numerator non-negative.

Undefined points for our given function:

The domain of denominator is all values of x, where x is not equal to negative 4 and positive 6.

Non negative values for radical:

The domain of numerator is all value of x greater than or equal to negative

Upon combining real regions and undefined points for our given function, the domain of our given function will be all values of x greater than or equal to negative 1, where x is not defined for 6.

Therefore, domain of our given function is .

Answer:

The question seems to be incomplete, so i will answer in a general way.

Ok, i guess that here we have two vectors:

a = (Ax, Ay) and b = (Bx, By).

Now we have that:

c = a + b = (Ax, Ay) + (Bx, By) =  (Ax + Bx, Ay + By).

Now, to calculate the magnitude of a vector (x, y) we have:

√(x^2 + y^2)

Then the magnitude of c will be:

IcI = √( (Ax + Bx)^2 + (Ay + By)^2)

And for the direction:

First, the direction is already defined by the vector c.

But a more exact (and easy to read) way is:

When we have a vector (x, y).

The angle between this vector and the x-axis is given by:

Tan(θ) = y/x.

Then in the case of c.

Tan(θ) = (Ay + By)/(Ax + Bx)

θ = ATan( (Ay + By)/(Ax + Bx) )

Answer:

12.53 miles

Step-by-step explanation:

6² + 11² = x²

36 + 121 = x²

157 = x²

x = 12.53 miles

The distance from town A to town C would be; 12.53 miles.

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

We are given that Town B is 6 miles due north of town A, and town C is due east of town A. It is 11 miles from town B to town C.

Therefore,

6² + 11² = x²

36 + 121 = x²

157 = x²

x = 12.53 miles

Hence, the distance from town A to town C would be; 12.53 miles.

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Answer:

Rational

Step-by-step explanation:

If you can write it as a fraction (=ratio), it is rational.

-6/10 = -0.6

Answer: 7000

Note: 5 and up rounds up. 4 and below rounds down.

4 < 5 so that means we won't need to round up we round down.

7412 = 7000

If we were to round up then the answer would of been 7500.

Answer:

145 ft below sea level

Step-by-step explanation:

40 + 105 = 145

Answer:

145 feet

Step-by-step explanation: