A plane (at point P) sees a bridge (at point B) at an angle of depression on 28 degrees. The horizontal distance between the plane and the bridge is 3000 feet. Explain which trigonometric equation can be used to solve for the height of the plane (segment PA). What is the height of the plane? You must show all work and calculations to receive full credit. Round your answer to the nearest foot.

The angle x has a measure of 37

Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines

The given parameter is the figure

On the figure, we have the following angle measures

2x, 79, 32 and 5x

The sum of angles in a quadrilateral is 360 degrees

So, we have the following equation

2x + 79 + 32 + 360 - 5x =  360

Evaluate the like terms in the above equation

So, we have the following equation

-3x + 79 + 32  =  0

Evaluate the like terms in the above equation

So, we have the following equation

-3x =  -111

Divide both sides of the equation by 3

x = 37

Hence, the value of x is 37

Read more about angles at

https://brainly.com/question/7620723

#SPJ1

Answer:

The average cost for a gallon of gasoline in 2006 was $2.45. In 2007, the average cost of a gallon of gasoline was $3.29.

As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,

(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.

(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.

As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.

We  are required to determine the correct time domains for four different situations, by observing the plotted graph.

Part (A) is to determine the correct time domain where the water balloon's height remains the same.

From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

Part (B) is to determine the correct time domain where the height of the water balloon is increasing.

From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.

Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.

From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.

Since, [(30/1) > (10/0.5) > (30/3)],

Or, [30 > 20 > 10],

Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).

Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.

Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.

Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.

To learn more about Time Domain, click on the link below.

https://brainly.com/question/21637355

#SPJ1

Slope-intercept form is y = 21.

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

Given that,

The line is horizontal. It means slope of this line is zero. We can use the point-slope form for a linear equation since we know the slope and the point (15, 21).

Point-slope form: [tex](y-y_{1}) = m(x-x_{1})[/tex]

Where,

m = slope and [tex](x_{1}, y_{1})[/tex] is the points.

Then,

[tex](y-y_{1}) = m(x-x_{1})[/tex]

[tex](y-21) = 0(x-15)[/tex]

[tex]y-21 = 0\\y=21[/tex]

Hence, the Slope-intercept form is y = 21.

To learn more about equation of line from the given link:

https://brainly.com/question/18831322

#SPJ9

Answer:

m∠QPT = 32°

Step-by-step explanation:

∠QPT and ∠SPR are vertical angles, meaning that the measure of their angles are congruent (the same).

Vertical angles are formed when two lines intersect, creating opposite angles. Those opposites are congruent (equal).

Step 1: Set the measure of the angles to equal each other.

[tex]\implies m \angle QPT = m \angle SPR[/tex]

[tex]\implies (2x+12) = (4x - 8)[/tex]

Step 2: Subtract 4x from both sides.

[tex]\implies 2x-4x+12 = 4x - 4x - 8[/tex]

[tex]\implies -2x+12 = - 8[/tex]

Step 3: Subtract 12 from both sides.

[tex]\implies -2x+12-12 = - 8-12[/tex]

[tex]\implies -2x = -20[/tex]

Step 4: Divide both sides by -2.

[tex]\implies \dfrac{-2x}{-2} = \dfrac{-20}{-2}[/tex]

[tex]\implies x = 10[/tex]

Step 5: Find the measure of ∠QPT by substituting 10 for x.

[tex]\implies [2(10)+12]^{\circ}[/tex]

[tex]\implies 32^{\circ}[/tex]

Therefore, the measure of ∠QPT is 32°.

Step 1. The expression we have for the graph is:

To find the inequality that represents the graph, we need to solve for y first.

Step 2. Solve for y in the equation:

We can also represent this as follows:

Move 5x to the right side as a -5x:

Move the two that is multiplying on the left side, to divide on the right side:

Simplify:

This is the equation of the line.

Step 3. Find the inequality.

Since the shaded part is below the line, and it has a dotted line, the inequality that represents this is:

Which are the values below the dotted line.

Answer:

The number of tornadoes is 77

total time for occurrence is 70 years

using these

= ( 77/70)

= (  1.1 )

Learn more about recurrence interval:

brainly.com/question/17253648

#SPJ4

The constant of proportionality (K ) we will write

Perimeter = 3 ( side)  where K = 3

Perimeter of any polygon is defined as the sum of all sides of  polygon.

Given polygon is a triangle. A triangle is any polygon which has three sides.

And as the sides of a polygon increases the perimeter also increases.

One can say that perimeter and side of a polygon has a direct relationship.

That is when we write it mathematically we write it like:

Perimeter ( P ) ∝ Sides of polygon

However given is an equilateral triangle

this means that all sides of the triangle are equal

so let us consider the side of the triangle as "s"

Thus we get that perimeter will be 3 times s

which when mathematically written will be:

Perimeter ∝ ( side)

to remove the constant of proportionality (K ) we will write

Perimeter = 3 ( side)  where K = 3

To know more about triangle and proportionality visit:

https://brainly.com/question/15006074

#SPJ13

Answer:

y=2x-5

Step-by-step explanation:

y - 2x = -5
add 2x to both sides.
y=-5+2x

Answer:

y = 2x - 5 is a line. determine the two points that this line intersects with the axes then connect these points to graph it.

Step-by-step explanation:

Given y = 2x -5 set y = 0 then solve for the abscissa

y = 2x - 5

0 =2x - 5

2x=5

x = 5/2

we now have the point (5/2,0)

set now x = 0 then solve for ordinate

y = 2x - 5

y = 2(0) - 5

y = -5

we now have the point (0, - 5)

we now simply draw a line passing thru the two points ( 5/2, 0) and (0, - 5)

kindly see the graph of y = 2x - 5 with points (5/2, 0) and (0, - 5)

Hope this helps

Answer:

Step-by-step explanation:

Answer:

..........

Step-by-step explanation:

.

.

..

.

.

.

.

.

.

The value of x is 4

The value of m ∠VUR = 126°

From the image shown, we have that;

Note that all the sides of a equilateral triangle are equal.

Then, we have;

Now, equate the side lengths of the inscribed triangle, we have;

3x + 8 = 6x - 4

collect like terms

3x - 6x = -4 - 8

subtract the like terms

-3x = -12

Make 'x' the subject of formula

x = -12/-3

Find the quotient

x = 4

Note that m ∠VRS and m ∠VUR are on a straight line, we have;

m ∠VRS +  m ∠VUR = 180

substitute the values

54° +  m ∠VUR = 180

m ∠VUR = 180 - 54

m ∠VUR = 126°

Hence, the values are 4 and 126°

Learn more about rectangles here:

https://brainly.com/question/25292087

#SPJ1

Answer:

a. -5x³ + 29x² - 56x + 15

b. 8x² + 9x + 5

c. 18t³ - 42t² - 14t - 30

d. x³ - 2x² - 5x + 6

e. -2b⁴ + a² + 6b² - 24a

Step-by-step explanation:

a. 3(x³ − x² + 5) − 8(x³ − 4x² + 7x)

3x³ - 3x² + 15 - 8x³ + 32x² - 56x

-5x³ + 29x² - 56x + 15

b. 7x² + 2x + 5 + x(x + 7)

7x² + 2x + 5 + x² + 7x

8x² + 9x + 5

c. 10(t³ − 4t² + 1) − t(2t + 6) + 8(t³ − t − 5)

10t³ - 40t² + 10 - 2t² - 6t + 8t³ - 8t - 40

18t³ - 42t² - 14t - 30

d. (x − 1)(x + 2)(x − 3)

(x - 1)(x + 2)

x(x + 2) - 1(x + 2)

x² + 2x - x - 2

x² + x - 2(x - 3)

x(x² + x - 2) - 3(x² + x - 2)

x³ + x² - 2x - 3x² - 3x + 6

x³ - 2x² - 5x + 6

e. (3a − 2b²)(3a + 2b²) − 3(4a − b²)2 + 2(−2a − b²)(2a − b²)

3a(3a - 2b²) + 2b²(3a - 2b²)

9a² - 6ab² + 6ab² - 4b⁴ - 3(4a − b²)2 + 2(−2a − b²)(2a − b²)

9a² - 4b⁴ - 24a + 6b² + 2(−2a − b²)(2a − b²)

                                                               (−2a − b²)(2a − b²)

                                                              -2a(2a - b²) - b²(2a - b²)

                                                               -4a² + 2ab² - 2ab² + b⁴

                                                                -4a² + b⁴

                                                                 2(-4a² + b⁴)

                                                                  -8a² + 2b⁴

9a² - 4b⁴ - 24a + 6b² - 8a² + 2b⁴

-2b⁴ + a² + 6b² - 24a

In the polygon, The triangles are not similar

The term similar triangles refers to triangles that the ratio of the sides are equal.

In the problem, the sides of the triangles are given as

The ratio of the sides

In DQRS: QR / RS = 4/15 = 0.27

In DUVT: VT / TU = 8/32 = 0.25

0.27 ≠ 0.25

since the ratio of the sides are not equal the two triangles are not similar

Learn more about similar triangles here:

https://brainly.com/question/26068068

#SPJ1

Given the word exprssion:

Seventy less than 9 times a number is 375

Where h represents the number.

We have:

Seventy less than 9 times a number: 9h - 70

Seventy less than 9 times a number is 375: 9h - 70 = 375

Therefore, the equation that is a correct translation of Seventy less than 9 times a number is 375 is: 9h - 70 = 375

ANSWER:

9h - 70 = 375

Answer:

Step-by-step explanation:

The given inequality can be written as 2m - 5/4 ≤ -7/8.

An inequality -7/8 is at most the difference of twice a number m and 5/4 which is 2m - 5/4 ≤ -7/8.

Difference of twice a number 'm' and 5/4 is 2m - 5/4 and this is at most -7/8 means less than or equal to.

∴ The given statement can be written as 2m - 5/4 ≤ -7/8

Answer:

2m - 5/4 ≤ -7/8

Step-by-step explanation:

hope this helps

The lengths of the axes in the elipse are given as follows:

The equation of an elipse of center (x*, y*) is given according to the following rule:

(x - x*)²/a² + (y - y*)²/b² = 1.

The lengths of the axes are given as follows:

In this problem, the equation of the elipse is given as follows:

(x - 3)²/212 + (y + 4)²/224 = 1.

Hence the measures of a and b are calculated as follows:

Hence the lengths of the axes have numeric values given by:

The difference in the measures is because I suppose there was a typo in the equation of the ellipse, but the procedure is as presented in this problem.

More can be learned about the equation of an elipse at https://brainly.com/question/16904744

#SPJ1

According to the given problem,

(i) It is given that,

The cost price of 1000 packets of peanuts = Rs. 50

We need to find the cost price of 1 packet of peanut = [tex]\frac{50}{1000}[/tex] = Rs. 0.05

(ii) Selling price at which Sipho continues to sell 1 packet = Rs. 1

Then Selling price of 1000 packets = 1000 x 1 = Rs. 1000

Then Profit made by sipho = Selling Price - Cost Price

= 1000 - 50

= Rs.950

Profit percentage gained by Sipho = [tex]\frac{Profit}{Cost Price}[/tex] x 1000

= [tex]\frac{950}{50}[/tex] x 1000

= 1900 %

(iii) The profit earned by sipho remains same, we nee to find the cost price at which Sipho should sell 100gm of her peanuts is Rs. 1

(iv) I would advice Sipho to sell peanuts at a selling price more than the cost price in order to gain profit

To learn more about, profit here

https://brainly.com/question/28017453

#SPJ1

Answer:

31cm

Step-by-step explanation:

Add AC and BC together to get AB.

AC = 2x - 13 and

BC = 3x + 4 and

AB = 36 (this is all the given information)

The two smaller pieces can be combined to equal the whole segment.

AC + BC = AB

2x - 13 + 3x + 4 = 36

combine like terms.

5x - 9 = 36

Add 9

5x = 45

Divide by 5.

x = 9

But you're not done because they asked for BC.

BC = 3x + 4

substitute 9 for x.

BC = 3(9) + 4

BC = 27 + 4

BC = 31

BC is 31 cm.

there are two aircraft​ carriers, a and​ b, and carrier a is longer in length than the carrier b. then Carrier A is 2,104 feet and Carrier B is 2,094 feet.

Since there are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B, and the total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet, to determine the length of each aircraft carrier, the following calculation must be performed:

(4,198 - 10) / 2 = X

4.188 / 2 = X

2,094 = X

2,094 + 10 = 2,104

2,094 + 2,104 = 4,198

Therefore, Carrier A is 2,104 feet and Carrier B is 2,094 feet.

the complete question is

There are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B. The total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet.

learn more about of length here

https://brainly.com/question/24085875

#SPJ4

The number of quarters, Richard have is 3 out of 198 coins he have.

For the given question,

The total number of coins Richard have is 18.

The fraction of dimes is 1/3.

1/3 of 18 = (1/3)×18 = 6

The number of dimes is 6.

The fraction of nickles is 1/2.

1/2 of 18 = (1/2)×18 = 9

Let the number of quarters be 'x'.

Total coin = dimes + nickles + quarters.

18 = 6 + 9 + x

x = 18 - 15

x = 3

Thus, the number of quarters, Richard have is 3.

To know more about the fraction, here

https://brainly.com/question/28417000

#SPJ13

The painting is a square, which means all its sides are equal.

If x is the length of one side, then, all the remaining 3 sides also have the same length: x.

The area of a square is the square if its side, then, for a square with sides x:

We know that the area of the painting will be 400 square inches, then:

a. The equation that can be set up to find the length of a side is:

b. We can solve the equation by finding a number that multiplied by itself gives 400. For this case, we have two solutions. 20 and -20, since:

And:

-20 is also a solution because as a negative number, when multiplied by itself, gives a positive one. (A product between negative numbers gives always a positive number).

c. We have two solutions, however, only one of them makes sense: the 20. A negative length makes no sense, so we can discard the second solution (-20).

d. The length of the wood trim needed to go around the painting is then 20 inches. (we should not forget the units.)

Answer:

use a calculator or try math app

The solution of  the value is mathematically given as

√6 =2.449

This is further explained below.

Generally, In mathematics, the term "square root" refers to a component of a number that, when multiplied by itself, results in the same value as the original number.

As an example, both 3 and –3 are square roots of the number 9.

A number y is said to have a square that is equal to a given number x if and only if it satisfies the following condition: y2 = x.

Another way to express this is to say that the number y has the same value as its own square. For example, the square roots of 16 are 4 and -4, since 42 divided by 2 is 16.

In conclusion,

√6 is not -4

because

√6 =2.449

Read more about square roots

https://brainly.com/question/3120622

#SPJ1

Answer:

m<2=m<5=50

m<4=85

m<6=45

Step-by-step explanation:

Answer:

1:85 2:50 3:45 4:85 5:50 6:45

Step-by-step explanation:

pls give brainliest

1 should be like 4 and 3 should be like 6.

Like 6+1 is 130 so 2 is 50

From the given parameter, the total amount that Lou spent on the gas is; $30.8

We are told that Lou​'s car had 6.2 gallons in the 15 gallons in the ​-gallon tank on the coldest day of the year.

Now, Lou filled the tank with gas that cost ​$ 3.50 per gallon.

Thus;

Amount of gas that Lou bought = 15 - 6.2

Amount of gas that Lou bought = 8.8 gallons

Since he bought these gallons at the cost of ​$3.50 per gallon, then it means that;

Total amount he spent = 8.8 * 3.5

Total amount he spent = $30.8

Read more about Algebra Word Problems at; https://brainly.com/question/13818690

#SPJ1

Complete question is;

Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Lou​'s car had 6.2 gallons in the 15 gallons in the ​-gallon tank on the coldest day of the year.

Lou filled the tank with gas that cost ​$ 3.50 per gallon. How much did Lou spend on​ gas?

⇒To get the difference we subtract.

[tex]2.5-7.5=-5\\[/tex]

⇒To get the sum we add.

[tex]2.75+9.55=12.3[/tex]

Goodluck!!

// ignore, made mistake//

Answer:

(4.7) and (5.-7)

Step-by-step explanation:

find the gradient using the formula:

y2-y1 (divide this by the bottom)

x2-x1

-7-7

5-4

=-14/1

-14 is the answer

then you will say y-y1= m(x-x1)

you can choose to sub any point

I will use (4;7)

therefore...

y-7=-14(x-4)

y= -14x+56+7

y= -14x+63