Michael and Zach are hiking in the mountains. They left Michael’s car in the parking lot and walked northwest for 12.4 km to a campsite. Then they turned due south and walked another 7.0 km to a glacier lake. The weather was taking a turn for the worse, so they decided to plot a course directly back to the parking lot. Zach remembered, from the map in the parking lot, that the angle between the path to the campsite and the path to the glacier lake measures about 30°. What compass direction should they follow to return directly to the parking lot?

Answer:

Find the area land of each town.

Let x be the area of town D

then, x+ 30000 is the area of town C

we know that,

the total area of town C and town D is 120,000 square miles.

x+x+30000=120000

2x= 90000

x=45000

Area of town D= 45000 square miles

Area of town C= 45000+30000= 75000 square miles.

Answer:

The remainder is 9

Step-by-step explanation:

x-7=0

x=7

Plug x=7 into the given fxn

-2(7)²+15(7)

-2(49)+105

-96+105

9

Step-by-step explanation:

2x + 28° + 90° = 180° ( The sum of all angle of triangle is 180° )

Now you may add 28° and 90° and subtract it from 180° ...

2x = 62° ..

Now...divide 62 by 2 ...

x = 31°

hence the value of x is 31°....

Answer:

either x = 1.75 or x = 700 , question wasn't clear

Step-by-step explanation:

Because you put the x in front of 20 , you might be meaning x/20 (second answer listed)? Or, you put the variable on the wrong side of 20. (first answer listed)

If you meant to type 20x

35 = 20x

÷20   ÷20     *

1.75 = x

*divide both sides by 20 to isolate x

x = 1.75

(x = [tex]\frac{35}{20}[/tex])

--------------------------------------------------------------------------

If you meant to type x/20

35 = [tex]\frac{x}{20}[/tex]

·20   ·20       *

700 = x

*multiply both sides by 20 to isolate x

700 = x

Answer:

6.28 ft

Step-by-step explanation:

using the formula [tex]\pi d[/tex] to find the circumference of the circle, you substitute the numbers. 3.14(2). 3.14 x 2 = 6.28 hence the answer

The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

The equation is given as:

f(x) = 3x + 3

Express f(x) as y

y = 3x + 3

Swap the positions of y and x

x = 3y + 3

Make y the subject

3y = x - 3

Divide by 3

y = 1/3x - 1

Replace y with the inverse function

f-1(x) = 1/3x - 1

Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

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Step-by-step explanation:

4 + 4 = 8 is one of the two closest double to 3 + 4

W.K.T(we know that )..

4 is 1 more than 3 this means ;

4 + 4 will be 1 more than 3 + 4

4 + 4 = 8 ,so finding 1 Less ;

3 + 4 = 7

here is the answer hope It helped U

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The set of input of the function are {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }

The set of output of the function is a multiple of 40 from 200 to 640

The input of the function can be found as follows:

The camp can only run if we have at least 5 students.

The limits of student is 16.

Therefore, the input are  {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }

The output are the dependent variables or the range. They are gotten when we input the values of the input in the function.

Therefore,

R(n) = 40n

R(5) = 40(5) = 200

R(16) = 40(16) = 640

The output are multiple of 40 from 200 to 640

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Answer:

d

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

[tex]~~~~~-24 = 6x\\\\\\\implies -\dfrac{24} 6 = \dfrac{6x}6\\\\\\\implies x = -4[/tex]

Answer:

B

Step-by-step explanation:

Total money spent = 25 + 30 + 10 + 8 = 73

Per week = 73 / 4 = 18.25

The proposition given by definition of function "division" is false as [tex]\frac{f}{g} \ne {(1, 2)}[/tex] for the former function f = (9, 5) and the latter function g = (9, 0).

In this question we have a definition of division between two functions, consisting in dividing each component of the ordered pair of the former function (f) by the component of the ordered pair of the latter function (g) such that resulting ordered pair is (1, 2).

We must check if the proposition is true for every ordered pair. Let analyze each case:

Case I

[tex]\frac{f}{g} = \left(\frac{1}{1}, \frac{6}{3} \right) = (1, 2)[/tex]

Case II

[tex]\frac{f}{g} = \left(\frac{9}{9}, \frac{5}{0} \right) = (1, NaN)[/tex]

Thus, the proposition is false.

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Answer:

The answer is in Step.

Step-by-step explanation:

Domain: (- inf, + inf)

Range: (- inf, 3]
Increasing: (- inf , 0)

Decreasing: (0 , + inf)
Positive: (- 1 , 1 )
Negative: (- inf , -1) , (1 , + inf)

Maximum: (0,3) or just 3.

Minimum: None.
x-int: -1, 1
y-int: 3

The area of the circle will be equal to 11309.733 square centimetres.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

The area of the circle will be calculated by the following formula:-

Area = πr²

Area = π x ( 60 x 60 )

Area = 3.14 x 60 x 60

Area = 11309.733 square centimeters.

Therefore the area of the circle will be equal to 11309.733 square centimetres.

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The conversion from degree to radian will be 180° = π radian. Then the measure of angle 75° is 1.31 radians.

Conversion means to convert the same thing into different units.

Convert the degree measure to the radian measure.

⇒ 75°

We know the conversion is given as

180° = π radian

   1° = π/180°

Then we have

75° = 75° x π/180° radian

75° = 1.30899 radian

75° ≅ 1.31 radian

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The sentence that correctly compares the two numbers is 5385 > 5.395

Here are inequality signs and what they mean:
Note that

5385 is greater than 5.385. Thus, the correct statement is 5385 > 5.395.

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The probability that the student was NOT a female that got a "C" is 15 / 32.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C =  15 / 32.

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Answer:

  B.  27 < AB < 81

Step-by-step explanation:

The triangle inequality requires that the length of any given side of a triangle be greater than the difference and less than the sum of the other two sides.

__

  54 -27 < AB < 54 +27

  27 < AB < 81

_____

Additional comment

Some versions of the triangle inequality allow the "or equal to" case.

  27 ≤ AB ≤ 81

Apparently, the one used here does not.

If the sum of the two short sides is equal to the long side, the "triangle" looks like a line segment. Its altitude and area are zero.

Answer: Transitive property of congruence

Answer: AAS

Step-by-step explanation:

We know that [tex]\angle TSN \cong \angle HSU[/tex] because they are vertical angles, meaning the triangles are congruent by AAS.

Answer:

22 meters

Step-by-step explanation:

Let x = width of the rectangle

Let y = length of the rectangle

Equation 1

If the length of the rectangle is 6 meters shorter than four times the width then:

⇒ y = 4x - 6

Equation 2

Perimeter of a rectangle = 2(width + length)

If the perimeter is 58 inches, then:

⇒ 58 = 2(x + y)

Solve by substitution

Substitute Equation 1 into Equation 2 and solve for x:

⇒ 58 = 2(x + 4x - 6)

⇒ 58 = 2(5x - 6)

⇒ 58 = 2 · 5x - 2 · 6

⇒ 58 = 10x - 12

⇒ 58 + 12 = 10x -12 + 12

⇒ 10x = 70

⇒ 10x ÷ 10 = 70 ÷ 10

⇒ x = 7

Substitute found value of x into Equation 1 and solve for y:

⇒ y = 4(7) - 6

⇒ y = 28 - 6

⇒ y = 22

Conclusion

The dimensions of the rectangle are:

Therefore, the length of the longer side is 22 meters

The length of the longer side is 22 meters.

Let, one side of the rectangle is x meters.

According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

In this case, the perimeter is 58 meters:

58 = 2 * (x + 4x - 6)

Now, let's solve for x:

58 = 2 * (5x - 6)

58 = 10x - 12

Add 12 to both sides:

58 + 12 = 10x

70 = 10x

Now, divide both sides by 10 to isolate x:

x = 70 / 10

x = 7

So, one side of the rectangle is 7 meters.

Now, we can find the length of the longer side:

Length of the longer side = 4x - 6

Length of the longer side = 4 * 7 - 6

Length of the longer side = 28 - 6

Length of the longer side = 22 meters

Therefore, the length of the longer side is 22 meters.

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The sum of squares of the lengths  of the triangle is 130 and the square of the length of the hypotenuse is 65

This is a triangle with 3 sides and one side is called the hypotenuse which faces one of the angles 90°

Analysis:

distance between two points = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

distance AB with coordinates A(-2,4) B(5,0) = [tex]\sqrt{(5 - -2)^{2} + (0 - 4)^{2} }[/tex] = [tex]\sqrt{65}[/tex]

distance AC with coordinates A ( -2,4) C(2,6) = [tex]\sqrt{(2--2)^{2} + (6-4)^{2} }[/tex] = [tex]\sqrt{20}[/tex]

distance BC with coordinates B(5,0)  C(2,6) = [tex]\sqrt{(2-5)^{2} + (6-0)^{2} }[/tex] = [tex]\sqrt{45}[/tex]

sum of squares of the lengths = [tex](\sqrt{45} )^{2}[/tex] + [tex](\sqrt{65}) ^{2}[/tex] + [tex](\sqrt{20}) ^{2}[/tex] = 65 + 45 + 20 = 130

the square of the length of the hypotenuse = 65

In conclusion, the sum of the squares of the three length is 130 and the square of the hypotenuse is 65

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The total weight of the 100 cantaloupe is 324 pounds

The given parameters are:

Since the number of zeros in 100 is 2;

All Evans needs to do is to move the decimal point in 3.24 two places forward.

i.e. 3.24 becomes 324 when the decimal point is moved

Hence, the total weight of the 100 cantaloupe is 324 pounds

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Answer:

$10955.6157151671

Step-by-step explanation:

Amount [A] = [tex]P(1+r)^{t}[/tex]

Here, P = principal (which is $5000)

r = rate of interest in decimal form(which is 0.04)

t = time in years (which is 20)

Substituting,

[tex]$5000(1+0.04)^{20}[/tex] = $10955.6157151671

So

Hence

Option A

Answer:

Option A

Step-by-step explanation:

y=4x+10

So

Put x ax 12°C

Hence

y=4(12)+10

y=48+10

y=58

Answer:

31°

Step-by-step explanation:

As the opposing side and adjacent side of the angle x are given, we need to take the tan ratio of the angle.

=============================================================

Solving :

⇒ tan x° = 9/15

⇒ tan x° = 3/5

⇒ x = tan⁻¹ (0.6)

⇒ x = 31°

The size of the unknown angle "x"

We'll have to check which is the appropriate one from SOHCAHTOA.

In this question we'll have to use tan because opposite and adjacent is given.

[tex]\large\boxed{Formula: tan(A)= \frac{opp}{adj}}[/tex]

Substitute according to the formula.

[tex]tan \: x= \frac{9}{15}[/tex]

We'll have to use tan inverse.

[tex]x={tan}^{-1}(\frac{9}{15})[/tex]

[tex]x=30.96375653[/tex]

[tex]\large\boxed{x=31° }[/tex]

Hence, the size of the unknown angle "x" is 31°

Answer:

$2142.86

Step-by-step explanation:

The remaining part of her money, after spending 3/5 of it and depositing 1/8 of it is equal to $750.

===============================================================

Retracing the steps :

⇒ She put 1/8 of the remainder in the bank, which gives $750

⇒ R - R/8 = 750

⇒ 7R/8 = 750

⇒ R = 750/7 × 8

⇒ R = 107.142857 × 8

⇒ R = 857.142856

* Don't worry, we'll simplify at the end of the answer *

=============================================================

Now, this remainder is what was left after spending 3/5 of it.

⇒ T - 3/5T = 857.142856

⇒ 2/5T = 857.142856

⇒ T = 857.142856/2 × 5

⇒ T = 428.571428 × 5

⇒ T = $2142.86 (nearest cent)