Kurt is flying his airplane over a
campground. He spots a small fire below at
an angle of depression of 32°. If the
horizontal distance from Kurt's plane to the
fire is 3600 feet, find the approximate
altitude of his plane.
A. 2,250
B. 2,575
C. 2,825
D. 3,150

Answer:

[tex]x = 19[/tex]

Step-by-step explanation:

Given

[tex]\angle 1 = 4x + 9[/tex]

[tex]\angle 2 = x - 14[/tex]

See attachment

Required

Find x

From the attached image, we have:

[tex]\angle 1 +\angle 2 = 90[/tex]

Because the sum of both angle corresponds to the right angle between n and m

So, we have:

[tex]4x + 9 + x - 14 = 90[/tex]

Collect like terms

[tex]4x + x = 90 - 9 +14[/tex]

[tex]5x = 95[/tex]

Divide by 5

[tex]x = 95/5[/tex]

[tex]x = 19[/tex]

The volume of a rectangular box can be found by multiplying the length, width, and height of the box together. So if the volume of the box is x³+x²-4x-4 cubic inches, the length is x+1 inches, and the width is x-2 inches, we can set up the equation h = (x³+x²-4x-4) ÷ (x²-x-2).

The formula for the volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height of the box. This formula can also be written as V = l×w×h.

In the question you provided, the volume of the rectangular box is given as x³+x²-4x-4 cubic inches, and the length and width are given as x+1 inches and x-2 inches, respectively. With this information, we can set up an equation using the formula for the volume of a rectangular box:

(x+1)(x-2)(h) = x³+x²-4x-4

where h is the height of the box in inches. To solve for h, we can divide both sides of the equation by (x+1)(x-2) to get:

h = (x³+x²-4x-4) ÷ (x+1)(x-2)

And Now we can simplify the expression using standard algebraic operations.

h = (x³+x²-4x-4) ÷ (x²-x-2)

You can now substitute any value of x to find the height of the box.

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The angle that the golfer has between the spectator and the hole is 60°. Therefore, option A is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.

Let the angle that the golfer has between the spectator and the hole be x

Here, sin 120°/200 =sin x/140

0.8660/200 =sin x/140

0.00433 = sin x/140

sin x=0.866

x=60°

Therefore, option A is the correct answer.

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Hi hi! The answer would be 22.7°, I took the test a while ago.

Answer: A) Domain: All real numbers , Range: All real numbers

Step-by-step explanation: Since the line of the graph continued to infinity, the answer for both domain (goes from Left to right) and range (goes up to down) would be all real numbers

As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.

Given that it has three sides and three vertices, a triangle is a polygon. It is one of the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon because it has three sides and three corners. The points at which the three sides of the triangle converge are referred to as its corners. Three triangle angles can be multiplied to get 180 degrees.

given

p is the midpoint of GI

GP = PI , PN = AP ( as mid point )

∠APG = ∠IPN ( as vertical opp. angle )

∠A = ∠N ( given )

so by ASA congruency ΔAPG = ΔIPN

As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.

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Answer: -14

Step-by-step explanation:

Answer:B all integers

Step-by-step explanation: took the test

The option second all integers are correct because for every value of the x the function will always give an integer value.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function

f(x)= 4[X-3]+ 2

f(x) represents the greatest integer function, which means for every value of the x the function will always give an integer value.

The function will be discontinuous for all integers.

Thus, the option second all integers are correct because for every value of the x the function will always give an integer value.

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Complete the table with values 3, 2, 24 and 10 respectively

The constant of proportionality is the ratio of the y value to the x value i.e.

constant of proportionality (k) = y/x

The table can be completed by determining the constant of proportionality. That is:

k = y/x

where y = hours and x = magnets

k = 4/12 = 1/3

when y = 1:

1/3 = 1/x

x = 3

when x = 6:

1/3 = y/6

y = 2

when y = 8:

1/3 = 8/x

x = 24

when x = 30:

1/3 = y/30

x = 10

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Answer:

0.2 x 25 = 5

0.3 x 75=22.5

22.5+5=27.5

Step-by-step explanation:

Answer:

I believe the answer is D.

[tex]\huge\boxed{Answer\hookleftarrow}[/tex]

D

[tex]\huge\boxed{Explanation\hookleftarrow}[/tex]

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If you list the number of tickets sold over time, the kind of sequence will you see is a geometric sequence.

What is a geometric sequence?

A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Here,

We assume that the variable x represents the number of tickets sold previously (initial year) and it sold 7 times as many tickets each year as it did the year before, a mathematical expression that models this situation is given by geometric sequence:

x, 7x, 49x, 343x, .....

Verification:

7/1 = 49/7 = 343/49 = 7

Hence, this is a geometric sequence.

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Answer:

472

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

[tex]f(x)=a^x[/tex]

x  is the exponent, so [tex]f(b)=a^b \text{ and }f(c)=a^c[/tex].

That makes [tex]f(b) \cdot f(c) =(a^b)(a^c)=a^{b+c}[/tex].

b + c is the exponent, so it takes the place of x.

[tex]a^{b+c}=f(b+c)[/tex]

Answer:

2x−3=x

Move all terms containing x

to the left side of the equation.

Subtract x

from both sides of the equation.

2x−3−x=0

Subtract x

from 2x

x−3=0

Add 3

to both sides of the equation.

x=3

The ordered pair (x, y) for the given line can be obtained from the graph as (-4, 1).

A straight line can be written in the form of an equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

The graph of the line is given.

In order to find the coordinate of a point do as follows,

Draw a perpendicular line from any point on the line to the x-axis.

The intersection of this line with the x-axis will give the x-coordinate.

Similarly, find the y-coordinate by drawing a perpendicular line to the y-axis.

Applying the above procedure, a point is obtained as (-4, 1).

Hence, the ordered pair for the line shown in the graph is (-4, 1).

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An acute angle, θ, is in a right triangle such that sin of theta is equal to 3 over 8 period  The value of cot θ is (√55)/3.

To determine the value of cot(θ), Since is an angle in a right triangle and sin() = 3/8, we obtain:

cot(θ) = (√55)/3

In light of the fact that is an acute angle in a right triangle, we may calculate:

sin(θ) = 3/8

Keep in mind:

Hypotenuse = ((opposite cathetus)2 + (adjacent cathetus)2), where sin() = (opposite cathetus)/(hypotenuse)

Next, we have:

contrary cathetus = 3

Using the formula hypotenuse = 8 = (3 + neighboring cathetus)2,

In order to solve this for the nearby cathetus, we obtain:

(82 - 32) = 55 adjacent cathetus

And we are aware of:

(Cot) = (nearby cathetus) (opposite cathetus)

Next, we have:

cot(θ) = (√55)/3

The value of cot θ is (√55)/3.

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Answer:

17 is the correct answer

Answer:

I think it's the remaining students, 17.

Step-by-step explanation:

15 + 18 = 33 (students that like one subject but not the other)

33 + 5 = 38 ( adding 5 because of the 5 student that dislike both)

38 is the number of students that either don't like both subjects or like one but now the other, so now you would subtract it by the total number of students (55).

55 - 38 = 17

The remaining students are who I believe like both subjects. The remaining number of students are 17.

Answer:

13

Step-by-step explanation:

He starts with 45 pencils (3x15) in total. Then he gives 32 to each student. He is left with 13 (45-32) pencils.

Answer:

Solution given:

function of g(x)=?

when

x=0

y=3

so

g(x)=-3f(x) is a function of g.

Let

Face changed to opposite means coefficient is negative

Streched by 3 [-6/-2=3]

Answer:

The Measure of angle 1 is 68

The Measure of angle 2 is 112

The Measure of angle 3 is 68

The Measure of angle 4 is 112

Step-by-step explanation:

Answer:

First Question - 74.25

Second Question - 23.92

Hope this helps you out

Answer:

[tex]\displaystyle x=\frac{1}{5}y^2[/tex]

Step-by-step explanation:

[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]

Answer:

1

Explanation:

Radius = C/2π

C is 6.28 and 2*pi is also 6.28

So 6.28/6.28 = 1.

Answer: the answer is 1

Step-by-step explanation:

The function f(g) is 8/(8+9x) and the function g(f) is -8x/(x-9).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=x/(x-9) and g(x)= -8/x.

1) f(g)

Here, f(-8/x)= -8/x ÷ (-8/x -9)

= -8/x ÷ (-8-9x)/x

= -8/x × x/(-8-9x)

= 8/(8+9x)

2) g(f)

Now, -8/x/(x-9)

-8x/(x-9)

3) f(f)

Here, f(f) = x/(x-9) ÷ (x/(x-9) -9)

= x/(x-9) ÷ ((x-9x+81)/(x-9))

= x/(x-9) × (x-9)/(-8x+81)

= x/(-8x+81)

4) g(g)

Now, -8/(-8/x)

= 64/x

Therefore, the function f(g) is 8/(8+9x).

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Answer:

50

Step-by-step explanation:

2000/40=50

Answer:

The train travels 50 miles per hour

Step-by-step explanation:

You can solve this by dividing 2,000 by 40.

Answer:

8 hours

Step-by-step explanation:

21/3=7 and 56/7=8

Answer:

She worked for 8 hours

Step-by-step explanation:

She earned $21 for 3 hours 21 divided by 3 is 7 so $7 an hour. She made $56 so 56 divided by 7 = 8 hours

Answer: x=0

Step-by-step explanation:

2(2)=4

4+x=4

-4 on both sides

so x=0

Answer:

B) x = 0

Step-by-step explanation:

We will get our equation in here first. Our equation is:

2 * 2 + x = 4

We simplify the multiplication giving us:

4 + x = 4

Finally, we subtract 4 from both sides to find the value of x. We get:

x = 0.

So the correct answer is B) x = 0.

Hope this helped!

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Explanation:

There are 170 million martians surveyed, note the "170" in the bottom right hand corner.

Of this total, there are 48 million who have completed 4 (or more) years of college. Refer to the bottom of the "4 or more" column.

This must mean that 170 - 48 = 122 million martians have not completed 4 or more years of college. This figure of 122 is effectively the sum of nearly everything in the bottom row, except for the 48 and the 170. In other words, 27+51+44 = 122.

We divide the values 122 over 170, and reduce fully, to get the answer we're after.

122/170 = (2*61)/(2*85) = 61/85

This can be thought of as "if we had 85 million people total, then 61 million of them did not complete 4 or more years of college".

Side note: 61/85 = 0.7176 = 71.76% approximately

The probability that a randomly selected martian, has not completed four years (or more) of college is P = 0.72.

We want to find the probability that a randomly selected martian over the age 25, is not completed over 4 years of studies.

In the table, we can see that we have a total of 170 Martians.

Of these 170, only 48 have completed more than 4 years of college.

Then: 170 - 48 = 122 have not completed 4 years or more.

Then the probability that a randomly selected martian has not completed 4 years or more of college is:

P = 122/170 = 0.72

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Answer:

oof...so sorry bro...

Step-by-step explanation:

9- left side of 10

-4 - right side of -5

2 - two points to the right of zero

so sorry if i am wrong..