an airplane flying at an elevation of 3,500 ft., directly above a straight highway. two motorists are driving cars on the highway on opposite sides of the plane. the angle of depression to one car is 31 degrees and to the other is 53 degrees. how far apart are the cars?

Answer:

4/6 and 6/9

Put 6 in both the boxes as the both ratios will be equal to 2/3 if 6 is put.

Answer:

[tex] \frac{4}{6} \: and \: \frac{6}{9} [/tex]

Answer: 2

Step-by-step explanation:

if you plug in -6 into x, we get

36 - 36 + 2

the 36s will cancel each other out, leaving us with only 2 as our final answer.

Answer: -70

Step-by-step explanation:

-[tex]6^{2}[/tex] + 6(-6)+2

= -36 - 36 + 2

= - 70

Answer:

11/48

Step-by-step explanation:

x-2/5=2/3-3x-2/6

collect like terms

x-2/5 + 3x = 2/3 - 2/6

taking LCM on both sides

[(x-2) + 5(3x)]/5 = [2(2) -2]/6

(16x - 2)/5 = 2/6

cross multiply

6(16x - 2) = 5(2)

96x - 12 = 10

96x = 22

therefore; X = 22/96

= 11/48

CHECK:

(11/48 - 2)/5 = 2/3 - 3(11/48) - 2/6

(-85/48)/5 = 2/3 - 11/16 - 2/6

-85/48 × ⅕ = -17/48

-17/48 = -17/48

Answer:

[tex]x=\frac{11}{60}[/tex]

Step-by-step explanation:

Given the equation

[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{2}{6}[/tex]

Lets solve for x.

Simplify the right side of the equation.

Cancel the common factor of 2 and 6 .

Factor 2 out of 2 .

[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{2(1)}{2(3)}[/tex]

[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{1}{3}[/tex]

Combine the numerators over the common denominator.

[tex]x-\frac{2}{5}=-3x-\frac{2-1}{3}[/tex]

[tex]x-\frac{2}{5}=-3x-\frac{1}{3}[/tex]

Move all terms containing x to the left side of the equation.

Add [tex]3x[/tex] to both sides of the equation.

[tex]x-\frac{2}{5}+3x=\frac{1}{3}[/tex]

Add [tex]x[/tex] and [tex]3x[/tex].

[tex]4x-\frac{2}{5}=\frac{1}{3}[/tex]

Move all terms not containing x to the right side of the equation.

Add [tex]\frac{2}{5}[/tex] to both sides of the equation.

[tex]4x=\frac{1}{3}+\frac{2}{5}[/tex]

To write [tex]\frac{1}{3}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{5}{5}[/tex] .

[tex]4x=\frac{1}{3}*\frac{5}{5} +\frac{2}{5}[/tex]

To write [tex]\frac{2}{5}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{3}{3}[/tex]

[tex]4x=\frac{1}{3}*\frac{5}{5} +\frac{2}{5}*\frac{3}{3}[/tex]

Simplify.

Write each expression with a common denominator of 15 , by multiplying each by an appropriate factor of 1 .

[tex]4x=\frac{11}{15}[/tex]

Divide each term in [tex]4x=\frac{11}{15}[/tex] by 4 and simplify.

[tex]x=\frac{11}{60}[/tex]

Answer:

a₈ = - 1280

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 10 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-20}{10}[/tex] = - 2 , then

a₈ = 10 [tex](-2)^{7}[/tex] = 10 × - 128 = - 1280

The 8th term of geometric sequence is -1280

Step of calculate geometric sequence

This is a geometric sequence. The geometric number sequence is characterized by the presence of a ratio (the ratio between the next term and the previous term). The next term is the product of the previous term with the ratio. Another sequence called arithmetic sequence is characterized by the presence of difference (the difference between the next term and the previous term).

10, -20, 40, ...

We will first analyze the things that can be found in the three numbers in the sequence. The thing to look for is the first term (a) and also the ratio (r). The first term can also be written as U1, where the 2nd term is U2, and the n-th term is Un.

[tex]a = 10[/tex]

[tex]r=\frac{U2}{U1}[/tex]

[tex]r=\frac{-20}{10}[/tex]

[tex]r=2[/tex]

When the first term (U1) and ratio (r) have been obtained, then we can find the 8th term by substitute it in the formula.

[tex]Un=ar^{n-1}[/tex]

With that formula, let's find the 8th term.

[tex]U8=10(-2)^{8-1}[/tex]

[tex]U8=10(-2)^{7}\\U8=10(-128)\\U8=-1280[/tex]

Learn more about geometric sequence here: https://brainly.ph/question/5507726

#SPJ1

At point 1, the carrying capacity is both the area is around 5, and therefore it can very well be said that growth rate in Area A is at a much higher pace than that of Area B. And that can subsequently be verified from the succeding graph.

What is Carrying Capacity?

The quantity of humans, other living species, or crops that a place can support without negatively impacting the environment is termed as carrying capacity.

To learn more about Carrying Capacity from the given link

https://brainly.com/question/14645317

#SPJ1

Let's solve your system by substitution.

4x−4y=8 and 5x−3y=18

Step: Solve 4x−4y=8 for x:

4x − 4y = 8

4x − 4y + 4y = 8 + 4y (Add 4y to both sides)

4x = 4y + 8

[tex]\frac{4x}{4} = \frac{4y + 8}{4}[/tex]

x = y + 2

Step: Substitute y + 2 for x in 5x − 3y = 18:

5x − 3y = 18

5(y+2) − 3y = 18

2y + 10 = 18  (Simplify both sides of the equation)

2y + 10 + (−10) = 18 + (−10)  (Add -10 to both sides)

2y = 8

y = 4

Step: Substitute 4 for y in x = y + 2:

x = y + 2

x=4+2

x=6  (Simplify both sides of the equation)

Answer:

x = 6 and y =4

Solving the inequality -6.6 < 1.7 + u for u, the solution is simplified as: u > -8.3 or -8.3 < u.

In maths, an inequality is defined as a statement that is used to compare two quantities that are unequal. For example, we can state that 5 is greater than 3 + 1, or 5x is less than 4x + 3x. We can equally state that a given value of a variable can be equal to or greater than a number, and so on.

Basically, we are comparing two unequal quantities when we state inequalities.

Given the inequality, -6.6 < 1.7 + u, we are asked to solve the inequality for u. That is, we need to find the possible value that u represents in the inequality or that would make the inequality true.

Therefore:

-6.6 < 1.7 + u

Subtract 1.7 from both sides

-6.6 - 1.7 < 1.7 + u - 1.7 [subtraction property of equality]

-8.3 < u

It can be rewritten as:

u > -8.3

Learn more about inequality on:

https://brainly.com/question/11613554

#SPJ1

The volume in liters a person uses daily is about 90 liters which is equivalent to 23.48 gallons

Information given in the question

everyday a person uses about 90 liters of water at home

6 gallons is about 23 liters

how many liters of water does a person use at home daily = ?

Volume is a three dimensional calculation, the formula depends on the object. how ever the calculation is usually done by area * height or thickness

the unit for volume can liters, gallons, cubic meters, and so on

The question have it that a person uses about 90 liters of water daily converting this quantity in gallon is done by

= 90 liters * 6 gallons / 23 liters

= 90 * 6 / 23

= 23.48 gallons

Learn more about volume calculation here:

https://brainly.com/question/12410983

#SPJ1

Check the picture below.

Answer:

3.7miles

Step-by-step explanation:

divide the length value by 1.6

As per given information about change in uplift it occurs at the rate of 0.1 m per 1,000 years then change in uplift over 1,000,000 years is equal to 100m.

As given in the question,

Rate of occurring of uplift is equal to 0.1m per 1000 years

Represent the given relation in equality form we get,

Change of uplift in 1000 years  = 0.1 m

⇒ 1 year = 0.1 m / 1000

⇒ 1,000, 000 years = ( 0.1 m / 1,000 ) × 1,000, 000

⇒ 1,000, 000 years =  ( 1 m / 10,000 ) × 1,000, 000

⇒  1,000, 000 years =  100 m

Therefore, for given information about change in uplift it occurs at the rate of 0.1 m per 1,000 years then change in uplift over 1,000,000 years is equal to 100m.

Learn more about uplift here

brainly.com/question/6036848

#SPJ4

The equation for the proportional relationship is y = 65x

The animal shelter wants to track its profit for each animal that is

adopted.

The cost of each animal adoption = $65

Consider the number of animal adoption = x

Consider the total profit from animal adoption = y

From the given the details, we can say that the profit from the animal adoption is directly proportional to the number of animal adoption,

Then the relationship will be

y ∝ x

y = kx

Here the cost of each animal adoption is k = 65

Then the equation will be

y = 65x

Hence, the equation for the proportional relationship is y = 65x

Learn more about proportional relationship here

brainly.com/question/12917806

#SPJ1

A six sided dice is tossed twice. The probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss is 1/9 .

A dice has six faces or sides and it is throws twice . When a dice is toss first time,

Total possible outcomes on toss = 6 ={ 1,2,3,4,5,6}

In our first toss we want to get 1 or 2

So, favourable outcomes of getting 1 or 2 = 2

Probability of getting 1 or 2 on first toss= favourable cases /total outcomes = 2/6 = 1/3

For second toss, we want to get a1 or a2 again.

Total possible outcomes = 6

Probability of getting a1 or a2 on second toss= 2/6= 1/3

Now, Multiply these probsbilites togethers and chance of getting 1 or 2 on first and second which is 1/3× 1/3 = 1/9

Hence , probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss is 1/9.

To learn more about Probability , refer:

https://brainly.com/question/29312865

#SPJ4

Answer:2

Step-by-step explanation:i did it

The point at which this cable would pass through the road shown is at the y-intercept of (0, -17/2).

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the road shown in the graph above, the points on the line include the following:

Points (x, y) = (0, -2)

Points (x, y) = (-3, 0)

Substituting the given points into the formula, we have;

Slope, m = (0 + 2)/(-3 - 0)

Slope, m = 2/-3

Slope, m = -2/3.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-2/3 × m₂ = -1

-2m₂ = -3

m₂ = 3/2

At point (7, 2), a linear equation for the line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - 2 = 3/2(x - 7)

y - 2 = 3x/2 - 21/2

y = 3x/2 - 21/2 + 2

y = 3x/2 - 17/2

At the y-intercept of (0, -17/2), the cable pass through the road.

Read more on slope here: brainly.com/question/3493733

#SPJ1

The expressions that represent the total weekly wages of Rita is 11r + 32 and of Tina is 11t.

We are given;

Rita and Tina each make $11 an hour working as cashiers at a supermarket.

Last week, Rita worked r hours while Tina worked t hours.

Rita also worked overtime hours during the week, for which she was paid an extra $32 flat wage.

We need to find the expressions that represent the total weekly wages of both Rita and Tina.

Let us form an algebraic expression for both one by one;

For Rita:

Number of hours Rita worked for = r

Cost per hour = $ 11

The amount for overtime Rita earned = $32

So, the equation expressing the total weekly wage for Rita = 11r + 32.

For Tina :

Number of hours Tina worked for = t

Cost per hour = $ 11

So, the equation expressing the total weekly wage for Tina = 11t.

Thus, the expressions that represent the total weekly wages of Rita is 11r + 32 and of Tina is 11t.

To learn more about algebraic expression visit:

https://brainly.com/question/28884894

#SPJ1

Answer: 3/5

Step-by-step explanation:

              Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side, divided by the length of the hypotenuse: The other trigonometric functions of the angle can be defined similarly; for example, the tangent is the ratio between the opposite and adjacent sides. As stated, the values and.

Answer: 4,375 rs

Step-by-step explanation:

25% × 17,500 = 4,375

Answer:

$4375

Step-by-step explanation:

25 percent *17500 =

(25:100)*17500 =

(25*17500):100 =

437500:100 = 4375

Now we have: 25 percent of 17500 = 4375

The answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5).

A projectile is fired vertically upward, and its height s(t) in feet after t seconds is given by the function defined by

s(t) = -16t² + 800t + 600.

To find out

(a) From what height was the projectile fired

Given height functions: s(t) = -16t² + 800t + 600

Now,

[tex]s^{'}(t)[/tex] - -32t+800

(b) Now, to find the time it will attain maximum height,

[tex]s^{'}(t)[/tex] = 0

-32t = -800

t = 25 seconds

(c) The maximum height it will reach

= [tex]-16*(25)^{2} + 800*25+600[/tex]

= -10000+20000+600

= 10,600 feet

(d) Between what two times (in seconds, to the nearest tenth) will it be more than 5000 ft above the ground

By putting x = 3

[tex]P(3) = 4*(3)^{3}-50 * (3)^{2}-8*3+6[/tex]

= 108-90-24+6

= 114-114

= 0

Therefore x = 3 is a zero of P(x)

(e) How long to the nearest tenth of a second will the projectile be in the air

Now, factoring,

[tex]f(x) = x^{3}+3x^{2} -13x-15\\ \\= x^{3}+x^{2} +2x^{2}+2x-15x-15\\ \\ = (x+1)(x^{2} +5x-3x-15)\\\\= (x+1)(x(x+5)-3(x+5))\\\\=(x+1)(x-3)(x+5)[/tex]

Hence the answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5)

To learn more about equations click here https://brainly.com/question/22688504

#SPJ9

Asymptote indicates that as time increases, the number of bacteria approaches 0.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

Once an antibiotic is given, number of bacteria decreases at a rate of 15% /day.

There were about 15,000 bacteria prior to the treatment.

The line y = 0 is an asymptote of the graph.

The y-intercept is 15,000.

The y-intercept represents the number of bacteria when treatment began.

The asymptote indicates that as time increases, the number of bacteria approaches 0.

Hence, asymptote indicates that as time increases, the number of bacteria approaches 0.

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ1

Answer:

Absolutely correct. you got the answer

The Submarine is 7.74 Km away from its base .

In the question ,

it is given that ,

the distance travelled by Submarine from base in East direction = 4.2 Km

let the distance from base to east direction be denoted by AB ,

that means AB = 4.2 Km

the distance travelled by Submarine from East to North direction = 6.5 Km

let the distance from east to north direction be denoted by BC .

that means BC = 6.5 Km

the given situation form a right triangle ,

So , the distance from submarine to its base is the hypotnuse of the right triangle , that is AC .

So By Pythagoras Theorem ,

AC² = AB² + BC²

Substituting the values , we get

AC² = 4.2² + 6.5²

AC² = 17.64 + 42.25

AC² = 59.89

AC = √59.89

AC = 7.7388

AC = 7.74

Therefore ,  The Submarine is 7.74 Km away from its base .

The given question is incomplete , the complete question is

A Submarine travel 4. 2 km due Eat from it base and then turn and travel due North for 6. 5 km. How far away is the submarine from it base ?

Learn more about Pythagoras Theorem here

https://brainly.com/question/21926466

#SPJ4

Answer:

40 questions

Step-by-step explanation:

100-85=15

15/100=6/x

cross multiply

15x=100(6)

15x=600

x=40

there were 40 questions on the test

hopes this helps please mark brainliest

The value of x on the frequency density axis is 200.

What is frequency?

The frequency of a repeated event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to underline differences with spatial and angular frequencies, respectively.

What is density?

The mass of a substance per unit of volume is its density. Density is most frequently represented by the symbol, however, the Latin letter D may also be used.

Here, we have

x is about half of the number of beehives producing 16 to 18 kg of honey, for the middle blue bar.

x = half of 400

x = 200

Hence, The value of x on the frequency density axis is 200.

To learn more about the frequency from the given link

https://brainly.com/question/254161

#SPJ9

Answer:yes

Step-by-step explanation:

yes

Answer:

  about 21.3 cm²

Step-by-step explanation:

Given a triangle with three sides 6 cm, 8 cm, and 12 cm, and smallest angle 26.4°, you want the area.

  A = 1/2ab·sin(C)

  A = 1/2(12 cm)(8 cm)·sin(26.4°) ≈ 21.34 . . . . square units

The semiperimeter is ...

  s = (6 +8 +12)/2 = 13

The area is ...

  A = √(s(s -a)(s -b)(s -c))

  A = √(13·(13 -12)(13 -8)(13 -6)) = √(13·1·5·7) = √455

  A ≈ 21.33 . . . . square centimeters

The area of the triangle is about 21.3 cm².

__

Additional comment

The problem with over specifying the dimensions of a geometry problem is that it is often difficult to make them consistent. Here, the area values agree to three significant figures. That is about all we can expect, given the angle precision is 3 significant figures.

Your answer depends on the set of dimensions you choose to use. It will be different yet if you use the Law of Sines to find angle A or B for the Sine Formula, especially if you round the angle value to tenths.

The attachment shows the solution using side lengths only.

The expression y = 660(0.902)ˣ represents a decay , the rate of decrease is 9.8% .

In the question ,

it is given that ,

the the exponential function is y = 660(0.902)ˣ

we need to determine that , the equation represents a growth or decay .

0.902 is the variable that will determine a growth or decay .

Since, 0.902 is less than 1 , so it represents a decay function .

To find the rate we subtract 0.902 from 1

= 1 - 0.902

= 0.098

= 9.8% decrease rate

Therefore , The expression y = 660(0.902)ˣ represents a decay , the rate of decrease is 9.8% .

The given question is incomplete , the complete question is

Identify if it's Growth or Decay , and determine the percentage rate of increase or decrease , the function is y = 660(0.902)ˣ ?

Learn more about Growth and Decay here

https://brainly.com/question/22392518

#SPJ1