Two fire towers are 21 miles apart. Tower B is due East of Tower A. The rangers at Tower A spot a fire at 43°north of east. The rangers at Tower B spot the same fire 31° north of west.
How far is Tower B from the fire? Round to the nearest tenth.

Answer:

Step-by-step explanation:

Percent increase is the percent of the increased value over the initial value.

In our case the increase is represented by the difference of values and the initial value is Value 1.

So the matching choice is D.

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

Answer choices in the comment:

Answer:

First step, correct answer is (3,1)

Step-by-step explanation:

1.it should be x+2(3x-8)=5

2. x+6x-16=5

3.7x=21

4. 7x/7=21/7

5. x=3

then you can eitheir take x+2y=5 or y=3x-8 i suggets taking second option as it is easier, just input values for x in

)  3x-8=y

6. 3(3)-8= 1

7. x=3, y=1

The new odds that the box picked is a special one is 4

Since, there are four boxes that look the same. in one box (the special one), half of the marbles are blue. but only 1/8 of the marbles in the other boxes are blue.

We will have this hypothesis:

The box the blue marble was picked from is the special box.

Prior confidence we had:

Ratio of special boxes to non special boxes=1:3

Now P(blue &special)=1/2, given that a box is selected from the special box, there is 1/2 chance that it is blue

And P(blue & not special)=1/8, given that a box is selected from a non-special box, there is 1/8 chance that it is blue

According to  Baye's factor ,we get:

P(B & S)/P(B & NS)=(1/2)/(1/8)

                               =4

Thus, 4 is the new odds that the box picked is the special one.

To learn more about odds to probability; click here:

https://brainly.com/question/29316520

#SPJ4

They bought  15 acres at $ 4000 per acre and  8 acres at  $6300 per acre

Let,

They bought x acres at $ 4000

and ( 23-x ) acres at $ 6300

From information,

By using algebra,

4000x + 6300(23-x) = 110,400

4000x - 6300x+ 144900 = 110,400

-2300x = 110,400-144900

- 2300x  = - 34500

x =34500 /2300

x = 15

x = 15

They bought 15 acres at $ 4000 per acre

(23 - 15 ) = 8 acres at  $6300 per acre

Hence, they purchased 8 acres for $6300 per acre and 15 acres for $4,000 each.

Learn more about algebra :

brainly.com/question/24875240

#SPJ4

Answer:

Step-by-step explanation:

$9.85   / 10   ≈ $0.99

The blanks are -2 and 0.5 respectively, by solving the expression (8 - 2x) *(-0.25x)

What does the term Algebraic Expression means?

In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.

Solution:

Given the expression, we need to solve it by using the properties of basic multiplication.

= (8 - 2x)*(-0.25x)

= (8*(-0.25x)) + (-2x * (-0.25x))

= -2x + 0.5[tex]x^{2}[/tex]

To learn more about Algebraic Expression from the given link

https://brainly.com/question/22399890

#SPJ9

Answer:

5 feet.

Step-by-step explanation:

if we see that 3 feet is the model and 15 feet is the actual, we find the ratio is 3:15 or 1:5. since the width is 1 foot, then we see the actual is 5 feet long.

Answer:

The error made is that the ASA theorem cannot be used here because the congruent side is not directly in between the two congruent angles in either triangle. Really, the information we are given is Angle-Side-Side, not Angle-Side-Angle, and this is not a congruence theorem unless the triangles given are right triangles.

Using the concepts of co-ordinate geometry, we got that (1.14,3.17) is best set of co-ordinates for the equipment staging if art contractors must locate an equipment staging area to serve the three construction sites, located at (x,y) coordinates (0,3), (1,4) and (5,5).

So, for x co-ordinates how we can find the output, for this we need to find that co-ordinate in which stagging area is maximum.

So that co-ordinate is given = [x-coordinate of point A + x-co-ordinate of point y)/2.0]-1.36

=>the best x-co-ordinate is =[(0+5)/2.0]-1.36

=>the best x-co-ordinate is =1.14,

Similarly, for the y-co-ordinate

the best y-co-ordinate is given by =[[y-co-ordinate of point A+ y-co-ordinate of point B]/2.0] +0.67

=>the best y-co-ordinate is given by =[(0+5)/2/0]+0.67=2.5+0.67

=>the best y-co-ordinate is given by=(

Therefore, the best x and y co-ordinate is (1.14,3.17)

Hence, when art contractors  locate an equipment staging area to serve three construction sites, located at (x,y) coordinates (0,3), (1,4) and (5,5). traffic between the staging area and each of the sites is 30 trips a week, except for the site located at (5,5), which is only 10 trips a week. the best set of co-ordinates for the equipment staging area is (1.14,3.17).

To know more about co-ordinate-geometry, visit here:

https://brainly.com/question/28899589

#SPJ4

Answer:

(7,5)

Step-by-step explanation:

[tex]-3y+4x=13 \implies -15y+20x=65 \\ \\ -5y-6x=-67 \implies 15y+18x=201 \\ \\ \therefore 38x=266 \implies x=7 \\ \\ \implies -3y+4(7)=13 \implies y=5 \\ \\ \therefore (7,5)[/tex]

Answer:

113

Step-by-step explanation:

Finding a remainder seems like you should be dividing. Remember everything is a shortcut for something else in math. So first you learn Long Division, but that's too much writing, so then you learn Synthetic Division, but there's an even shorter shortcut. It is called Remainder Theorem. If you just substitute 3 (because x-3 in the question) into the function, and you calculate it, you get the remainder.

f(x) = 4x^3 + 5

f(3) = 4(3)^3 + 5

f(3) = 4(27) + 5

= 108 + 5

= 113

See image.

The numerical coefficient is -7

From the question,  the expression is given as

-7x

Considering an expression given as

Ax

The numerical coefficient of the above expression is A

When compared to the expression -7x, we have

The numerical coefficient is -7

So, we can conclude that the numerical coefficient of -7x is -7

Read more about expressions at

https://brainly.com/question/4344214

#SPJ1

Answer:

-7

Step-by-step explanation:

The numerical coefficient is -7

a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.

b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.

Given that,

In a typical Chinese restaurant, the Special Dinner is frequently offered, allowing the customer to select one appetizer and one entrée.

We have to find

a) How many unique special dinners are there if there are 8 appetizers and 11 entrees.

b) How many unique special dinners are there if there are 12 appetizers and 7 entrees.

We solve

a) We just multiply

8×11=88

b) 12×7=84

Therefore, a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.

b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.

To learn more about unique visit: https://brainly.com/question/14957572

#SPJ1

Answer:

10 hours

Step-by-step explanation:

since she spent 5 hours writing 10 pages. you just have to multiple by 2 to know how long it will take to write 20 pages

The given quadrilateral PONY is rotated to 180° as P'O'N'Y' and its coordinates are:

So, rotate the given quadrilateral at 180° as follows:

Given quadrilateral: PONY

Rotate to 180° and plot as follows:

Quadrilateral after rotation: P'O'N'Y'

(Refer to the graph attached below)

Therefore, the given quadrilateral PONY is rotated to 180° as P'O'N'Y', and its coordinates are:

Know more about rotation here:

https://brainly.com/question/9993340

#SPJ13

Answer:

P': (2, -7)

O': (2, -3)

N': (6, -3)

Y': (5, -6)

Step-by-step explanation:

Answer: [tex]\sqrt{12x}[/tex]

Step-by-step explanation:

Step-by-step explanation:

[tex]6(8v - 7) - 10 \\ 48v - 42 - 10 \\ 48v - 52[/tex]

Each person need to pay $ 80.88345.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Bill without tax = 105.73

Tax = 6%

So, bill amount after tax = 105. 73 + 105. 73 x 6/100

                                        = 105.73 + 6.3438

                                        = $112.0738

Addition of 20% tip = 112.0738 + 211.46 = $323.5338.

If the amount is divided among 4 people, each will pay

= 323.5338/4

= $ 80.88345

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ1

Answer: y = x - 3

Step-by-step explanation:

Answer:

y = x+3

Step-by-step explanation:

First of all we have to find the equation of the line

Slope-intercept form is:

[tex]y=mx+b[/tex]

Putting the value of slope

[tex]y=x+b[/tex]

Putting the point in the equation

(-4,-1)

[tex]-2=-5+b\\b=-2+5\\b=3[/tex]

So the equation is:

[tex]y=x+3[/tex]

The graph is attached with the answer

Keywords: Equation of line, slope

Learn more about slope at:

brainly.com/question/5565320

brainly.com/question/5663052

#LearnwithBrainly

The equation for the linear equation parallel to BC is:

y = (2/3)*x - 19/3

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

slope = (y2 - y1)/(x2 - x1)

And two lines are parallel if both lines have the same slope and different y-intercept.

So if we want to et a line parallel to BC whose endpoints are (1, 3) and ( 4, 5), the slope should be:

slope = (5 - 3)/(4 - 1) = 2/3

So our line is like:

y = (2/3)*x + b

And this must pass through (2, -5)

Replacing these values we get:

-5 = (2/3)*2 + b

-5 - 4/3 = b

-15/3 - 4/3 = b

-19/3  =b

Then the linear equation is:

y = (2/3)*x - 19/3

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

6

Step-by-step explanation:

The system of equations best represented by the graph are 4x + y = 6 and −2x + y = −5

The solution of the equations plotted in the graph can be found by checking the point of intersection of the lines

By examining the given graph we can guess the x and y values of the point of intersection. We need to guess because we do not have a means of getting the exact value from the graph. I guess x = 1.9 and y = -1.4

In order to find the system of equations represented by the graph, we need to solve the equations given in the option and check which one gives us  x and y values close to what we guessed from the graph

By Solving 4x + y = 6 and −2x + y = −5:

4x + y = 6          (1)

−2x + y = −5      (2)

Using elimination, subtract (2) from (1), this gives:

6x = 11            

x = 11/6 = 1.83

Put x = 11/6 into (1):

4(11/6) + y = 6

y = 6 - 4(11/6)

y = 6 -44/6 = -4/3 = -1.33

Since these calculated values are very close to the guessed values

Therefore, 4x + y = 6 and −2x + y = −5 are the system of equations best

represented by the graph. So option A is the answer

Learn more system of equations on:

https://brainly.com/question/13729904

#SPJ1

The expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. Similarly, any tirigonometric equation can be convereted into other forms of trigonometric functions.

What is trigonometric functions?

Denoting the relation between a right-angled triangle's angle and sides are trigonometric functions, which are periodic functions.

Consider the given expression.

[tex]3-2tan^2x\\[/tex]

Now, substitute [tex]\frac{sinx}{cosx}[/tex] for [tex]tanx[/tex] as follows:

[tex]3-2tan^2x=3-2(\frac{sinx}{cosx})^2\\=3-2(\frac{sin^2x}{cos^2x})[/tex]

Now, all the terms are converted into cos x except the sin x terms in the numerator. Hence, using the relation between sin x and cos x. Substitute [tex]1-cos^2x[/tex] for [tex]sin^2x[/tex].

[tex]3-2tan^2x=3-2(\frac{1-cos^2x}{cos^2x})[/tex]

Now, all the terms are in cos x. Hence, the expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. In the similar way any function can be conveted into other trigonometric functions.

Learn more about trigonometric functions from the following link:

https://brainly.com/question/25618616

#SPJ1

The 3 in the equation is the starting point

Function given:

h(t) = −4.5t2 + 19.6t + 3

At t =0 we get h(0) = 3. This is called the y-intercept

It is the start point indicating the disc was thrown at 3 feet of height.

Using the common convention in geometry the horizontal axis in a graph in represented by the x-axis and the vertical axis in a graph is represented by the y-axis. The intercepts are the points on the graph at which the graph crosses the two axes. The point where the graph is drawn crosses the horizontal axis is called the x-intercept or the x-axis, and when the graph crosses the vertical axis is called as the y-intercept or the y-axis.

I hope this answer helps.

To learn more about intercepts,

https://brainly.com/question/14180189

Answer:

[tex] = 3 + \sqrt{25 } - \sqrt{12} \\ = 3 + 5 - \sqrt{12 \\ } \\ = 8 - \sqrt{12} [/tex]

[tex] = 8 - 2 \sqrt{3} [/tex]

option d is correct

The missing expression in step 2 should be [(6² + 2)/0.5] - 14.8 ÷ 8.

The missing expression in step 6 should be 76 - 1.85.

In order to evaluate this expression, we would apply the PEMDAS rule, where mathematical operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

For step 1, we have the following:

[(6² + 2)/|-0.5|] - 14.8 ÷ 8.

In step 2, we would take the absolute value of -0.5:

[(6² + 2)/0.5] - 14.8 ÷ 8.

Therefore, we would have the quantity of the sum of six squared (6²) plus two (2) divided by 0.25, minus 14.8 ÷ 8

In step 3, we would take the exponent of 6:

[(36 + 2)/0.5] - 14.8 ÷ 8.

In step 4, we would add 36 and 2 together:

[(38)/0.5] - 14.8 ÷ 8.

In step 5, we would divide 38 by 0.5:

76 - 14.8 ÷ 8.

In step 6, we would divide 14.8 by 0.5:

76 - 1.85

In step 7, we would subtract 1.85 from 76 as follows:

Solution = 76 - 1.85 = 74.15.

Read more on step here: https://brainly.com/question/28313300

#SPJ1

The probability of getting a number greater than 4 when the dice is rolled 20 times is 7.

The number on dice greater than 4 is 2 (that is 5 and 6 on dice) thus the probability of getting a number greater than 4 is

P = 2/6

P = 1/3

This is the probability if the dice were rolled once but if the dice were rolled 20 times thus the probability, in this case, needs to be multiplied by 20  

P = 1/3*20

P = 6.66

equivalents to 7

For more information on probability kindly visit to

https://brainly.com/question/20312769

#SPJ4