A plane flies from Dubbo on a bearing of 139° for 852 km, then turns and flies on a bearing of 285° until it is due west of Dubbo. How far from Dubbo is the plane, to the nearest km?

Answer:

Below.

Step-by-step explanation:

I can do this using calculus but the algebra will be a bit messy.

Let the 2 equal sides of isosceles triangle be x and the base be y units long.

Then perimeter p = 2x + y.

Area A = 0.5yh  where h is the altitude of the triangle.

h =  sqrt [x^2 - (0.5y)^2]

=  [x^2 - (0.5y)^2]^0.5

So A = 0.5y * [x^2 - (0.5y)^2]^0.5

From the perimeter formula y = p - 2x so:

A = 0.5(p-2x) * [x^2 - (0.5(p-2x)^2]^0.5

A = 0.5(p-2x) * [x^2 - 0.25(p^2 - 4xp + 4x^2)]^0.5

A = 0.5(p-2x) * [x^2 - 0.25p^2 + xp - x^2]^0.5

A = (0.5p-x) * [xp - 0.25p^2]^0.5

We now find the derivative and equate it to zero to find the value of x which corresponds to a maximum area.

We use the product rule:

dA/dx =   (0.5p-x)* 0.5(xp - 0.25p^2)^(-0.5) * p  - 1(xp - 0.25p^2)^0.5 = 0

p(0.5p - x) / (2((xp - 0.25p^2)^0.5 -  (xp - 0.25p^2)^0.5 = 0

p(0.5p - x) / (2((xp - 0.25p^2)^0.5 =  (xp - 0.25p^2)^0.5

Now multiplying though by (2((xp - 0.25p^2)^0.5 :-

p(0.5p - x) = 2 (xp - 0.25p^2)

0.5p^2 - px = 2px - 0.5p^2

p^2 = 3px

x = p^2/3p = p/3

So for a maximum value of the area x = p/3.

But y = p - 2x

         = p - 2(p/3)

          = p -  2/3p

           = p/3

- but we've just shown that x = p/3

That means that x = y and the triangle is Equilateral.

Answer:

b

Step-by-step explanation:

the answer is b if values are plugged in to function

Answer:

y = -(x - 2)² - 4

Step-by-step explanation:

The vertex form an equation is given as :

Substitute any point in the table to find a :

Hence, the final equation :

a)    Line parallel to the line 3x+5y=-10 is -6x-10y=9

b)    Line parallel to the line 2y-4x=5 and which goes through the point

       (3,7) is y= 2x-1.

c)      Line perpendicular to the line 8x+6y=-1 and which goes through the

        point (-2,1) is 4y= 3x+ 10

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y.

a) Equation parallel to 3x+5y=-10 is

    -6x-10y=9

So, it satisfies:  [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}[/tex]

b)given equation into the form of y=mx+c,

     2y-4x=5

we can find the gradient of the line.

  2y= 5+4x

  y= [tex]\frac{5}{2}[/tex] + 2x

Hence, the gradient is 2.

As, Parallel lines have the same gradient

Thus the line would also have a gradient of 2.

Substitute m=2 into the equation:

y= 2x +c

To find the value of c, substitute a pair of coordinates.

When x=3, y=7,

7= 2(3) +c

7= 6 +c

c=6-7

c= -1

So, equation of line be: y= 2x-1.

c) Given: 8x+6y=-1

     6y= -1-8x

     y= [tex]\frac{-1}{6} -\frac{4}{3}x[/tex]

Hence, m= [tex]-\frac{4}{3}[/tex]

We know, if two lines are perpendicular have m and m' as slope then,

m*m'=-1

[tex]\frac{-4}{3} *m'=-1[/tex]

 m'= [tex]\frac{3}{4}[/tex]

Now, y= [tex]\frac{3}{4}[/tex] x +c

Put x= -1 and y=1

then, 1= [tex]\frac{3}{4}[/tex] (-2) + c

         c= [tex]\frac{5}{3}[/tex]

So,  y= [tex]\frac{3}{4}[/tex] x + [tex]\frac{5}{2}[/tex]

     4y= 3x+ 10

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No, there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one are congruent to the included angle and corresponding two sides of the other triangle.

Two figures are congruent if their vertices can be mapped into one another by appropriate rigid transformation or a combination of rigid transformations. Examples of the transformation are; reflection, dilation, rotation and translation.

Comparing the two figures, it would be observed that they are not congruent. Since there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.

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Answer:not congruent.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

In 3 options, the coefficient of x on both sides is the same. Hence, they will all have no solution. The only one which has exactly one solution is :

Answer:

Keen

Step-by-step explanation:

Favorite shoe brand = Keen

Answer:

Nike

Step-by-step explanation:

Nike shoes are great and comfy

Answer:

1/3 is the same as 0.33...(The decimal continues on from here.)

Answer:

[tex]\displaystyle \frac{4}{3}\text{cm}^2/\text{min}[/tex]

Step-by-step explanation:

Given

[tex]\displaystyle \frac{dV}{dt}=10\:\text{cm}^3/\text{min}\\ \\V=s^3\\\\SA=6s^2\\\\\frac{d(SA)}{dt}=?}\:;s=30\text{cm}[/tex]

Solution

(1) Find the rate of the cube's edge length with respect to time at s=30:

[tex]\displaystyle V=s^3\\\\\frac{dV}{dt}=3s^2\frac{ds}{dt}\\ \\10=3(30)^2\frac{ds}{dt}\\ \\10=3(900)\frac{ds}{dt}\\\\10=2700\frac{ds}{dt}\\\\\frac{10}{2700}=\frac{ds}{dt}\\\\\frac{ds}{dt}=\frac{1}{270}\text{cm}/\text{min}[/tex]

(2) Find the rate of the cube's surface area with respect to time at s=30:

[tex]\displaystyle SA=6s^2\\\\\frac{d(SA)}{dt}=12s\frac{ds}{dt}\\ \\\frac{d(SA)}{dt}=12(30)\biggr(\frac{1}{270}\biggr)\\\\\frac{d(SA)}{dt}=\frac{360}{270}\biggr\\\\\frac{d(SA)}{dt}=\frac{4}{3}\text{cm}^2/\text{min}[/tex]

Therefore, the surface area increases when the length of an edge is 30 cm at a rate of [tex]\displaystyle \frac{4}{3}\text{cm}^2/\text{min}[/tex].

Answer:

Jeff, 4.5 hours; Julia 9 hours.

Step-by-step explanation:

To solve the problem, we need to write two equations using the given information.

So, writing the first equation we have:

We know that Jeff can weed the garden twice as fas as his sister Julia, so:

Also, from the statement we know that they can weed the garden in 3 hours, so, writing the second equation we have:

Then, we need to substitute the first equation into the second equation in order to isolate Julia's rate, so, solving we have:

We have that Julia could weed the garden by herself in 9 hours.

So, calculating how long will it take to Jeff, we have:

We have that Jeff could weed the same garden by himself in 4.5 hours.

hope this helps!

To solve this problem, we need to use combination which is statistical tool to determine the number of ways an event may occur. The combination to select a 5 a side team from 12 students is 792.

This a mathematical technique that is used to determine the number of possible arrangements in a collection of items where the way they're arranged does not matter.

Data;

The combination for this would be

[tex]C = ^1^2C_5 = 792[/tex]

The combination to select a 5 a side team from 12 students is 792.

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His new balance after the check is deducted will be $370.09

From the question, we have the following parameters:

The new balance is then calculated using:

New balance = Initial Balance - Check

So, we have:

New balance = 415.01 - 44.92

Evaluate

New balance = 370.09

Hence, his new balance will be $370.09

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Answer:

c

Step-by-step explanation:

Answer: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

Step-by-step explanation:

First, we can ensure that 12 is the median by putting it in the middle and putting the same amount of numbers to its left and right side. To make the values have a mean of 12, the easy why to do it is to subtrate one as you move to the left and add one as you move to the right, that way they will cancel each other out and keep the mean at 12. The answer has a total of 11 values, has more than 3 values that are different, and has a mean and median of 12.

7+8+9+10+11+12+13+14+15+16+17=132

132/11=12

There are 5 values to each side of 12, making 12 the median.

Answer:

A

Step-by-step explanation:

|-20| = 20 the positive value of -20

20 is not < 20 so A is false

All the rest are true
(B) |9| = 9

(C) |-20| = 20 > 9

(D) |9| = 9, |20| = 20 and 9 < 20

Answer:

See below for proof of identity.

Step-by-step explanation:

Since both terms of [tex]\sin^3\theta+\cos^3\theta[/tex] are perfect cubes, we can use the formula [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex] where [tex]a=\sin\theta[/tex] and [tex]b=\cos\theta[/tex]:

[tex]\displaystyle \frac{\sin^3\theta+\cos^3\theta}{\sin\theta+\cos\theta}\\\\\frac{(\sin\theta+\cos\theta)(\sin^2\theta-\sin\theta\cos\theta+\cos^2\theta)}{\sin\theta+\cos\theta}\\ \\\frac{(\sin\theta+\cos\theta)(1-\sin\theta\cos\theta)}{\sin\theta+\cos\theta}\\\\1-\sin\theta\cos\theta[/tex]

Thus, the identity is proven.

The functions f(x) and h(x) have an axis of symmetry of x = 2 and a maximum

The functions are given as:

A quadratic function can be represented as:

y = ax² + bx + c

y = a(x - h)² + k

In both cases, when a < 0; the function has a maximum.

This means that all three functions have a maximum.

Next, we determine the axis of symmetry:

Using the above forms, we have:

f(x) = -x² + 4x + 2

Axis of symmetry, x = -4/(2 * -1)

x = 2

g(x) = -(x + 2)² - 5

Axis of symmetry, x = -2

h(x) = -2(x − 1)(x − 3)

Expand

h(x) = -2x² - 8x + 8

Axis of symmetry, x = -8/(2 * -2)

x = 2

This means that f(x) and h(x) have an axis of symmetry of x = 2

Hence, the functions f(x) and h(x) have an axis of symmetry of x = 2 and a maximum

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Step-by-step explanation:

2x + 18

x = 18÷2

x=9

hence the answer is 9

Answer:

it would be a

Step-by-step explanation:

8x4=32

The base of the given triangle is calculated as: 16 ft

The formula that is used to calculate the area of a triangle is expressed as:

Area of triangle= ½ × base × height

We are given that:

Area = 32 ft²

Height = 4 ft

Thus:

32 = ½ × base × 4

32 = 2 * base

base = 32/2

base = 16 ft

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Answer:

Step-by-step explanation:

Questions:

To find:

Solutions:

First, do switch sides.

[tex]\Longrightarrow:\sf{3.1-12.5\left|1-0.8x\right|=5.6}[/tex]

Multiply by 10 from both sides.

[tex]\Longrightarrow: \sf{3.1*10-12.5|1-0.8x|*10=5.6*10}[/tex]

Solve.

31-125|1-0.8x|=56

Subtract by 31 from both sides.

[tex]\Longrightarrow: \sf{31-125\left|1-0.8x\right|-31=56-31}[/tex]

Solve.

[tex]\Longrightarrow: \sf{-125\left|1-0.8x\right|=25}[/tex]

Divide by -125 from both sides.

Solve.

[tex]\Longrightarrow: \sf{\dfrac{-125\left|1-0.8x\right|}{-125}=\dfrac{25}{-125}=\boxed{\sf{No\ solutions.}}}[/tex]

I hope this helps, let me know if you have any questions.

There are no solutions.

Answer:

Hypotenuse = 17

Step-by-step explanation:

if: a = 8, b = 15 c = hypotenuse:

[tex]c=\sqrt{a^{2}+b^{2} }[/tex]

[tex]c = \sqrt{(8)^{2} +(15)^{2} } =\sqrt{64+225}=\sqrt{289} =17[/tex]

Hope this helps

Answer:

a=646.84   c=113.04

Step-by-step explanation:

Answer:

4th graph

Step-by-step explanation:

I believe that they are just saying f(x) and then adding 2 to each of the corrdnants to x+2 y+2

Answer:

See below ~

Step-by-step explanation:

The +2 in the equation : f(x) + 2, indicates the y-intercept of the graph lies at (0, 2). The 4th graph (attached below) is the correct answer.

The value of x in the given equation [ √( 1 + (25/144) ) = 1 + (x/12) ] is 5.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given that;

First, we square both sides

√( 1 + (25/144) ) = 1 + (x/12)

(√( 1 + (25/144) ))² = (1 + (x/12))²

1 + (25/144) = 1 + ( x²/144)

Collect like terms

1 - 1 + (25/144) = ( x²/144)

25/144 = x²/144

We cross multiply

25 × 144 = x² × 144

Multiply each sides by 1/144

x² = 25

x = √25

x = 5

Therefore, the value of x in the given equation [ √( 1 + (25/144) ) = 1 + (x/12) ] is 5.

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Answer:

x= -64°, y= -63°, z=-57°

Step-by-step explanation:

→Solution,

Here,

60°=(-y-3)°[The opposite sides of a parallelogram are equal]

⇒y= -60°-3°

⇒y= -63°

⇒60°+(-2x-8)°=180°[Sum of co-interior angles is 180°]

⇒52°-2x=180°

⇒52°-180°=2x

⇒x= -128°/2

⇒x= -64°

⇒60°+(-2z+6)°=180°[Sum of co-interior angles is 180°]

⇒66°-2z=180°

⇒66°-180°=2z

⇒z= -114°/2

⇒z= -57°

Answer:

35

Step-by-step explanation:

Answer:

(-2, -1)

Step-by-step explanation:

The easiest way to approach this problem is to think of each quadrant as being 90 degrees. As you can see, each quadrant has a 90 degree angle.

If we were to move 2 quadrants (or 180 degrees) clockwise, we would end up in the third quadrant (- , -)

Because we are moving clockwise on the graph, the shape would also turn clockwise. 180 degrees is the halfway point, so the shape will appear to be upside down.

If you're a visual learner, I'd recommend finding a website with an online graph (something like desmos or geogebra) that would allow you to actually graph the points and change their position with commands.

Hope this helps :)

Answer:

The answer is 405

Step-by-step explanation:

FIrst you would do 27 times 30 which is 810 then you would divided by 2 which in turn gives you 405

Hope this helped!

Answer:

[tex] \sqrt{ - 100} = 10i = 0 + 10i[/tex]

Answer:

18

Step-by-step explanation:

[tex]184 \times 3 = 59 \div 2 = \times \frac{?}{?} [/tex]