To indirectly measure the distance across a lake, Ethan makes use of a couple
landmarks at points B and C. He measures AE, EC, and DE as marked. Find the
distance across the lake (BC), rounding your answer to the nearest hundredth of a
meter.

We can find the unit price of a ticket by dividing the number of purchased tickets by the total price, like this:

Then, the unit price of the tickets is $0.15

Answer: 2%

Step-by-step explanation:

Exponential growth functions are of the form [tex]P(1+r)^t[/tex], where r is the rate of change. From the equation, we see that r=0.02, and converting this to a percentage, we get 2%.

Answer: 120

Step-by-step explanation:

All angles in a triangle add up to 180. The third angle in the triangle is 60. A straight line is always 180, and line TU intersects it. So, subtract 60 from 180 and you get 120.

Answer:

120 degrees

Step-by-step explanation:

70 + 50 = 120 (exterior angle of a triangle)

The point of intersection is a point where the value of both functions will be the same thus the point of intersection of the lines y = −10x − 3 and −y = 11x + 5 is at (-2,17).

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given lines,

y = −10x − 3

−y = 11x + 5 → y = -11x - 5

The value of the function at the point of intersection is always the same.

So,

−10x − 3 = -11x - 5

-10x + 11x = -5 + 3

x = -2

So,y = -10(-2) - 3 = 17

Hence "The point of intersection is a point where the value of both functions will be the same thus the point of intersection of the lines y = −10x − 3 and −y = 11x + 5 is at (-2,17)".

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1.

Algebra:

Graph:

2.

Words:

x is greater than 3 or x is less than minus 2

Graph:

3.

Words:

x is greater than minus 1 and x is less than 2.

Algebra:

Interior Angle Theorem asserts that the alternate interior angles that result when two parallel lines are cut by a transversal are equivalent.

If m2 + m28 = 180 then we get ∠2 + ∠8 = 180°

Lines that are parallel to one another on a plane do not intersect or meet at any point.  They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines.

Two lines are said to be parallel if a transversal and two matching angles it forms are congruent.

Verification of Parallel Lines

When two lines are intersected by a transversal and the opposing interior angles line up, the intersected lines are said to be parallel. Two lines are said to be parallel if they are divided by a transversal such that their opposing exterior angles are equivalent.

Therefore,

Given line m is parallel to line m

Interior Angle Theorem asserts that the alternate interior angles that result when two parallel lines are cut by a transversal are equivalent.

Alternate Exterior Angles are congruent if a transversal cuts two parallel lines. When a transversal cuts two parallel lines, the resulting angles are congruent.

Therefore, ∠2 = ∠6

∠2 + ∠4 = 180° ( Sum of the angles on a straight line is 180°)

∠6 + ∠8 = 180° ( Sum of the angles on a straight line is 180°)

∵  ∠2 = ∠6

∴ ∠6 + ∠8 = 180° ⇒ ∠2 + ∠8 = 180°

∠2 + ∠8 = 180° , Hence Proved.

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Answer:  [tex]3\sqrt{2}+3\sqrt{5}[/tex]

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

Work Shown:

[tex]\sqrt{3}\left(\sqrt{6}+\sqrt{15}\right)\\\\\sqrt{3}*\sqrt{6}+\sqrt{3}*\sqrt{15}\\\\\sqrt{3*6}+\sqrt{3*15}\\\\\sqrt{18}+\sqrt{3*3*5}\\\\\sqrt{9*2}+\sqrt{9*5}\\\\\sqrt{9}*\sqrt{2}+\sqrt{9}*\sqrt{5}\\\\3\sqrt{2}+3\sqrt{5}\\\\[/tex]

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

Explanation:

I distributed and used the idea that sqrt(A*B) = sqrt(A)*sqrt(B) to combine square roots, but also to break them up when factor out the largest perfect square factor.

Optionally for the last step, you could factor out 3, but your teacher may want you to leave it like shown.

We are looking for the point at which the compensation from Plan A is less than the compensation from Plan B.

Plan A = 850 +0.1x

Plan B= 1050+(x-7000)(0.14)

Plan A < Plan B

850 +0.1x <1050+(x-7000)(0.14)

then we sill simplify

850+0.1x < 1050+0.14x-980

850+0.1x<70+0.14x

then we isolate the x

0.1x-0.14x<70-850

-0.04x<-780

x>-780/-0.04

x>19500

In this case the monthly sales x need to be greater than 19500 (x>19500), in order that Plan B were better than plan A.

We have the following:

Therefore:

3x+6=4x+7 //// = //// 3x-1=4x

3(x+6)=4x+7 //// = //// 3x+18=4x+7

4x+3x=7-6 //// = //// 7x=1

Answer:

the value of x is 32 degree

Step-by-step explanation:

100 + 68 +x = 180

168 +x=180

x= 180- 168

x= 32 degree

The equation for F is,

Determine the value of F.

Thus value of F is 210.

Since P(t) models the number of people on a beach, t hours past midnight, hence P(10)=N means that there were N people on the beach at 10 am

The sum of the interior angle of a polygon with 10 sides is equal to 1440°

If it can be expressed as 360n, then n is

The solution of 3x−10>5 inequality is x>5 and is graphed with the image attached.

what is inequality?

Given inequality,

3x−10>5

3x>5+10

3x>15

x> (15/3)

x>5

The solution of 3x−10>5 inequality is x>5 and is graphed with the image attached.

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The most appropriate choice for maxima and minima of a function will be given by

Rectangle of length 72 feet and breadth 36 feet has largest area

What is maxima and minima?

Maxima of function f(x) is the maximum value of the function and minima of function f(x) is the minimum value of the function.

Here,

Let the length be x feet and breadth be y feet

The farmer has 144 feet of fencing

Three of the sides will require fencing and the fourth wall already exists.

So,

x + y + y =1 44

x + 2y = 144

Area of rectangle(A) = xy [tex]ft^2[/tex]

                               = (144 - 2y)y

                               = [tex]144y - 2y^2[/tex]

[tex]\frac{dA}{dy} = \frac{d}{dy}(144y - 2y^2)[/tex]

     = [tex]144 - 2\times 2y^{2-1}\\144 - 4y[/tex]

For largest area,

[tex]\frac{dA}{dy} = 0[/tex]

[tex]144 - 4y = 0 \\4y = 144\\y = \frac{144}{4}\\y = 36[/tex]

[tex]\frac{d^2A}{dy^2} = \frac{d}{dy}(144 - 4y)\\=0-4\\=-4 < 0[/tex]

Hence area is maximum

For largest area, y = 36 feet

[tex]x = 144 - 2\times 36\\x = 144-72\\[/tex]

[tex]x = 72[/tex] feet

So length of rectangle is 72 feet, breadth of rectangle is 36 feet

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Okay, here we have this:

Considering the provided equation, we are going to solve the system using an augmented matrix and Gauss-Jordan Elimination. So we obtain the following:

Finally we obtain that the solution to the system is:

The circumference of the circle is

205 air conditioners must be produced and sold to have a yearly profit of $45,000.

As per the relation representing p and x, x is the number of air conditioners so p must be the profit. Keep the value of profit to find the value of x.

45000 = x² + 15x - 100

Shifting 100 to Left Hand Side of the equation

45000 + 100 = x² + 15x

Performing addition on Left Hand Side of the equation

45100 = x² + 15x

Rearranging the equation

x² + 15x - 45100 = 0

Factorising the equation to find the value of x

x² + 220x - 205x - 45100 = 0

x(x + 220) -205 (x + 220) = 0

(x - 205) (x + 220) = 0

x = 205, - 220

The number of air conditioners produced and sold can not be negative. So, the value of x and hence the number of air conditioners is 205.

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Answer:

y=2/3x+4

Step-by-step explanation:

The pancakes stall sells total 12 combinations of pancakes.

What is Combination?

Combinations are mathematical operations that count the number of potential permutations for a set of elements when the order of the selection is irrelevant.

According to the given data:

Savory pancakes can have 3 toppings in any combination.

Therefore, total number of savory pancake combinations = 3 x 2 x 1 = 6

For sweet pancakes jams can either have ice cream or fresh cream.

Therefore combinations with ice cream = 3

And combinations with fresh cream = 3

Hence total combinations for sweet pancakes = 3 + 3 = 6

Now, total pancakes combination = 6 + 6 = 12

So, the stall sells 12 combinations of pancakes.

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let's recall the vertical line test, if a vertical line hits the graph or points twice, then is NOT a function.  Check the picture below.

A very easy way to find out if a graph is a function is to use the vertical line test.

Look at each graph and mentally draw a vertical line that goes through each of its points.

If that line goes through more than one point (2, 3, 4...) then that graph is not a function.

That's because a function, is an equation for which each input (x value) has exactly one output (y value). There cannot be two points of the same x value, with two different y values.

Answer:  If we take the aerobics class, then we will be in good shape for the ski trip

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

Explanation:

The conditional statement in bold is of the form "If P, then Q" where

P and Q are placeholders for logical statements, in much a similar fashion that x = 2 has x as a placeholder for the number 2.

Considering a parabolic equation with a vertex of (-7,-2) and directrix of x = -1. This is a horizontal parabola

The directrix of a parabola is a straight line perpendicular to the axis of symmetry of the parabola.

The directrix does not touch the parabola

A parabolic equation is also called quadratic equation.

Since the directrix is perpendicular to the axis of symmetry of the parabola it means that if:

The axis of symmetry says if the parabola is vertical or horizontal, when the axis of symmetry is parallel:

In the given problem, the directrix is given at x, the axis of symmetry is along the x direction and hence a horizontal parabola

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Answer:

The solution to the inequality is;

Explanation:

Given the inequality;

Firstly, let's multiply both sides of the equation by 9;

Then we can multiply both sides by -1.

Note that when we multiply both sides by a negative number(-1) the sign will change;

So;

The solution to the inequality is;

Explanation

Question 10

We are asked to write the quadratic eqation that has the solutions of x=3 and x =-7

To do so, we will make use of

So we will follow the steps below

substituting the above, we will have

Therefore, the quadratic equation is

Answer:

-1.12 or -28?/25 or -1 3/25

Step-by-step explanation:

Below is the figure of the triangle

We have three unkown variables which are x, y, and z

Firstly, let us find the unknown side z

To find z, we will be applying SOH CAH TOA

The longest side is z

The opposite sides is 39

Find x

X can be find by applying the SOH CAH TOA

Let z = opposite

let x = adjacent

Find y

let y = adjacent

x = Hypotenus

Applying SOH, CAH TOA

Answer:

  33w² +660w

Step-by-step explanation:

You want the expression for the volume of a cuboid with dimensions in inches of 33, (w+20), and (w).

The volume of a cuboid is the product of its dimensions:

  V = HLW

  V = (33)(w +20)(w) = 33(w² +20w)

  V = 33w² +660w . . . . expression for volume

__

Additional comment

Comparing coefficients, you see ...

Given the function below,

Let us now plot the graph in order to obtain the end behaviours.

From the graph above, we can conclude that

Hence, the correct answer is Option D.

Answer: 1 minute

Step-by-step explanation:

First elevator's rate is 200 meters per second

Second's rate is 250

In one second, they would travel 450 meters

Answer:

Step-by-step explanation: