An observer (O) spots a plane flying at a 42° angle to his horizontal line of sight. If the plane is flying at an altitude of 15,000 ft.

Answer:

  y -6 = 1/3(x +3)   or   y = 1/3x +7

Step-by-step explanation:

The slope of the line describing the given path is the x-coefficient, -3. The slope of the perpendicular line will be the negative reciprocal of that:

  m = -1/(-3) = 1/3

The point-slope form of the equation for a line can be used to write the equation for the new path:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

For m=1/3 and (h, k) = (-3, 6), the new path can be represented by ...

  y -6 = 1/3(x +3) . . . . point-slope form

  y = (1/3)x +7 . . . . . . slope-intercept form

Answer:

27 terms

Step-by-step explanation:

a1 = 7

nth term is -175

common difference d= 0-7 = -7 or -7 - 0 = -7

nth term = first term + ( n-1) * common difference

-175 = 7 + ( n - 1 ) * (- 7)

-175 = 7 - 7n + 7

-175 = 14 - 7n

-175-14 = -7n

-189 = - 7n

n= -189 /-7

n=27

Answer:

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Step-by-step explanation:

Given;

Total Months = 14

Total Words = 1920

Required

Find the time spent in Portugal and time spent in Brazil

Let P represent Portugal and B represent Brazil; This implies that

[tex]P + B = 14[/tex] ---- Equation 1

Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that

[tex]130P + 150B = 1920[/tex] --- Equation 2

Make P the subject of formula in equation 1

[tex]P = 14 - B[/tex]

Substitute 14 - B for P in equation 2

[tex]130(14 - B) + 150B = 1920[/tex]

Open Bracket

[tex]1820 - 130B + 150B = 1920[/tex]

[tex]1820 + 20B = 1920[/tex]

Subtract 1820 from both sides

[tex]1820 - 1820 + 20B = 1920 - 1820[/tex]

[tex]20B = 100[/tex]

Divide both sides by 20

[tex]\frac{20B}{20} = \frac{100}{20}[/tex]

[tex]B = 5[/tex]

Substitute 5 for B in [tex]P = 14 - B[/tex]

[tex]P = 14 - 5[/tex]

[tex]P = 9[/tex]

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Answer:

4 meters

Step-by-step explanation:

To do this you would need to know what the area of a rectangle is, it is base times width. So you already know the area so you would just divide it by 5 and you would get the width, which is 4 meters

Answer:

[tex]\boxed{x < 7.5}[/tex]

Step-by-step explanation:

=> 2x < 15

Dividing both sides by 2

=> x < 15/2

=> x < 7.5

Answer:

[tex]\boxed{x<\frac{15}{2}}[/tex]

Step-by-step explanation:

[tex]2x<15[/tex]

Divide both parts by 2.

[tex]\displaystyle \frac{2x}{2} <\frac{15}{2}[/tex]

[tex]\displaystyle x<\frac{15}{2}[/tex]

Answer:

(0,-7)

Step-by-step explanation:

If nay point is form (x,y)

x is abscissa can be also called x axis coordinate

y is ordinate can be also called y axis coordinate

ordiantes are points lying on y axis.

For any point lying on y axis, its x-axis coordinate will be 0

given that ordinate is -7. it means that value of y coordinate is -7

Thus,  coordinates of the point is (0,-7)

The distance between the points (0, 10) and (–9, 1) is 12.73 units.

Given the following data;

Points ([tex]x_1, x_2[/tex]) = 0, -9

Points ([tex]y_1, y_2[/tex]) = 10, 1

To find the distance between the points;

In Mathematics, the distance between two points on a plane is calculated by using the formula;

[tex]Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 }[/tex]

Substituting the points into the formula, we have;

[tex]Distance = \sqrt{(0 - [-9])^2 + (10 - 1)^2} \\\\Distance = \sqrt{(0 + 9)^2 + (9)^2}\\\\Distance = \sqrt{9^2 + 9^2}\\\\Distance = \sqrt{81 + 81}\\\\Distance = \sqrt{162}[/tex]

Distance = 12.73 units

Therefore, the distance between the points is 12.73 units.

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Answer:

Step-by-step explanation:

7(42 ÷ 3) + 4 (72 + 53) + 8 (-3)4

7(14) + 4(125) + 8(-12)

98 + 500 - 96

    598 - 96

        502

Answer:

Step-by-step explanation:

[tex]7(42 \div 3) + 4(72 + 53) + 8 \times ( - 3) \times 4[/tex]

Divide the numbers

[tex] = 7 \times 14 + 4(72 + 53) + 8 \times ( - 3) \times 4[/tex]

Add the numbers

[tex] = 7 \times 14 - 4 \times 125 + 8 \times ( - 3) \times 4[/tex]

Calculate the product

[tex] = 7 \times 14 + 4 \times 125 - 96[/tex]

Multiply the numbers

[tex] = 98 + 500 - 96[/tex]

Add the numbers

[tex] = 598 - 96[/tex]

Subtract the numbers

[tex] = 502[/tex]

Hope this helps..

Best regards!!

Answer:

x -y =4

Step-by-step explanation:

First find the slope

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

   = (1- -4)/(5 - 0)

    = (1+4)/(5-0)

   5/5

   = 1

Then we can use slope intercept form

The slope is 1 and the y intercept is -4

y = mx+b

y = 1x-4

We want it in standard form

Ax + By = C where A is a positive integer

Subtract x from each side

-x +y = -4

Multiply by -1

x -y =4

Answer:

x -y =4

Step-by-step explanation:

Answer:

a) 28 units

b) 0.0262 seconds

c) Minimum height of the nail = 1.923 units

Step-by-step explanation:

a) From the given equation, f(x) = -14×cos(720(t - 10)) + 14 comparing with the equation for periodic function, y = d + a·cos(bx - c)

Where:

d = The mid line

a = The amplitude

The period  = 2π/b

c/b = The shift

Therefore, since the length of the mid line and the amplitude are equal, the diameter of the bike maximum f(x) = -14×-1 + 14 = 28

b) Given that three revolution = 6×π, we have;

At t = 0

cos(720(t-10) = cos(720(0-10))  = cos(7200) = 1

Therefore, for three revolutions, we have

720(t - 10) = 720t - 7200

b = 720

The period = 2π/b = 6·π/720 = 0.0262 seconds

c) The minimum height of the nail is given by the height of the wheel at t = 0, as follows;

f(x) = -14×cos(720(t - 10)) + 14

At t = 0 gives;

f(x) = -14×cos(720(0 - 10)) + 14

Minimum height of the nail = -14×cos(-7200) + 14 = -14×0.863+14 =1.923

Minimum height of the nail = 1.923

Given Information:

Launch angle of projectile = 30°

Initial velocity = V₀ = 30 m/s

Acceleration due to gravity = g = 10 m/s²

Required Information:

Angle with the horizontal after 1.5 sec = ?

Answer:

The angle of the projectile to the horizontal after t = 1.5 seconds is 0°

Step-by-step explanation:

The horizontal component of the velocity is given by

[tex]Vx = V_0 \cos(\theta)[/tex]

Where V₀ is the initial velocity and θ is the launch angle

The vertical component of the velocity is given by

[tex]Vy = V_0 \sin(\theta) - gt[/tex]

Where V₀ is the initial velocity, θ is the launch angle, g is the acceleration due to gravity and t is the time.

So after t = 1.5 sec

The horizontal component of the velocity is

[tex]Vx = V_0 \cos(\theta) \\\\Vx = 30 \cos(\30) \\\\Vx = 30 \times 0.866\\\\Vx = 25.981 \: m/s[/tex]

And the vertical component of the velocity is

[tex]Vy = V_0 \sin(\theta) - gt \\\\Vy = 30 \sin(30) - 10 \times 1.5 \\\\Vy = 30(0.5) - 10 \times 1.5 \\\\Vy = 15 - 15 \\\\Vy = 0 \: m/s \\\\[/tex]

The angel is

[tex]\tan(\theta) = \frac{0}{25.981} \\\\\theta= \tan^{-1}( \frac{0}{25.981}) \\\\\theta= 0[/tex]

Therefore, the angle of the projectile to the horizontal after t = 1.5 seconds is 0°

Answer:

397.7 m²

Step-by-step Explanation:

Step 1: find m < W

W = 180 - (33+113) (sum of ∆)

W = 34°

Step 2: find side UV using the law of sines

[tex] \frac{UV}{sin(W)} = \frac{VW}{sin(U)} [/tex]

[tex] \frac{UV}{sin(34)} = \frac{29}{sin(33)} [/tex]

Multiply both sides by sin(34)

[tex] \frac{UV}{sin(34)}*sin(34) = \frac{29}{sin(33)}*sin(34) [/tex]

[tex] UV = \frac{29*sin(34)}{sin(33)} [/tex]

[tex] UV = 29.8 m [/tex] (approximated)

Step 3: find the area using the formula, ½*UV*VW*sin(V)

area = ½*29.8*29*sin(113)

Area = 397.7 m² (rounded to the nearest tenth.

Answer:

crystal size and rock texture     D

Step-by-step explanation:

:)

Hence, the option (D) is the correct answer i.e., crystal size and rock texture.

What is the texture?

The texture is defined as a tactile quality of an object's surface. It appeals to our sense of touch, which can evoke feelings of pleasure, discomfort, or familiarity.

The texture of an igneous rock is dependent on the rate of cooling of the melt slow cooling allows large crystals to form, fast coolng yields small crystals.

Hence, the option (D) is the correct answer i.e., crystal size and rock texture.

To know more about the texture

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Answer:

A’B’C’

Step-by-step explanation:

Well if triangle ABC is rotated 90 degrees clockwise around the origin it will turn right to create triangle A’B’C’.

P starts at (-3,5)

Move to the right 2 units and you'll get to (-1,5). We add 2 to the x coordinate here.

Then shift the point up three units to get to (-1,8). We add 3 to the y coordinate.

Finally, reflect over the x axis to get the answer (-1, -8)

Note how the y coordinate flipped in sign but the x coordinate stays the same

Answer:

73cm²

Step-by-step explanation:

Area of rectangle=½ length×width

=½×18×7

=63cm²

Area of triangle=½b×h

base=18-13= 5cm

height=11-7 =4cm

½×b×h

½×5×4

=10cm²

Area of total=63+10

73cm²

Answer: 73c2

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

The original number ⇒ 100

100 is increased by 10%

The result is 20% reduced.

Calculate increase.

100 × (1 + 10%)

100 × (1.1)

= 110

Calculate decrease.

110 × (1 - 20%)

110 × 0.8

= 88

Answer:

Volume left in the cylinder if all the cone is made full:

[tex]\bold{345.72 \ ml }[/tex]

Step-by-step explanation:

Given

Radius of cylinder = 5 cm

Height of cylinder = 14 cm

Radius of cone = 6 cm

Height of cone = 20 cm

To find:

Liquid remaining in the cylinder if cone is made full from cylinder's liquid.

Solution:

We need to find the volumes of both the containers and find their difference.

Volume of cylinder is given by:

[tex]V_{cyl} = \pi r^2h[/tex]

We have r = 5 cm and

h = 14 cm

[tex]V_{cyl} = \dfrac{22}{7} \times 5^2\times 14 = 1100 cm^3[/tex]

Volume of a cone is given by:

[tex]V_{cone} = \dfrac{1}{3}\pi r^2h = \dfrac{1}{3}\times \dfrac{22}{7} \times 6^2 \times 20 = \dfrac{1}{3}\times \dfrac{22}{7} \times 36 \times 20 = 754.28 cm^3[/tex]

Volume left in the cylinder if all the cone is made full:

[tex]1100-754.28 =345.72 cm^3\ OR\ \bold{345.72 \ ml }[/tex]

Answer:

26.4ft²

Step-by-step explanation:

I first converted the centimeter values to feet

140Cm x 30.48 = 4.59

70cm x 30.48 = 2.3

the paper required is approximately equal to the area of the pyramid.

area of pyramid is equal to area of triangle + base²

Are of triangle = 1/2 x b xh

= 4 x 1/2 x4.59x2.3 + (2.3)²

= 2 x 4.59 x 2.3 + 5.29

= 26.4 feet²

therefore it will take 26.4 feet² paper to make each tree, including the bottom.

Answer:

It is actually 24500

Step-by-step explanation:

Hope this helped! I had the same lesson.

Answer:

x=1 and y=6

Step-by-step explanation:

10x+2y=22

3x-4y=-21

First at all, you have to multiply both sides of this equation of 10x+2y=22, like this,

2(10x+2y)=2*22

*Put the 2 for the both sides.

Then, expand them.

20x+4y=44

When we have 20x+4y=44, we can eliminate with another equation.

20x+4y=44

3x-4y=-21

So, the first equation has +4y and the second equation has -4y, so we can use elimination method to eliminate one variable.

This time we can sum these equation to get one variable to get the answer easily. Like this...

20x+4y=44

3x-4y=-21

to become...

23x=23

x=23/23

x=1

When we get the equation like this, we can divide 23 by 23, so we can get the value of x. So, the value of x is 1.

When we know x is equal to 1, we can do the last part substitute x=1 into the second equation which is 3x-4y=-21.

The following steps is like this:

Substitute x=1 into 3x-4y=-21,

3(1)-4y= -21

3-4y= -21

Move the 3 to the another side, like this;

-4y= -21-3

-4y= -24

y= -24/ -4

y=6

*Be careful! When you calculate -24/-4 , you have to know how to eliminate the negative sign. (-) / (-) = +

Negative number divided by negative number is equal to positive number.

So, here we go! the value of x is 1 and the value of y is 6.

That is my solution and explanation from me. I hope you can understand. Bye!

Constraint Equations : [tex]X + 2Y \leq 16 , X + Y \leq 9 , 4X + Y \leq 24[/tex]

Time required for producing sound bar 'X' = 1 hour of machine A , 1 hour of machine B , 4 hour of machine C

Time required for producing flat screen TV 'Y' = 2 hours of machine A, 1 hour of machine B, 1 hour of machine C

So, constraint for machine A (needed for sound bar & flat screen TV) : [tex]1X + 2Y \leq 16[/tex]

Similarly, constraint for machine B (needed for X & Y) : [tex]1X + 1Y \leq 9[/tex]

Also, constraint for machine C = [tex]4X + 1Y \leq 24[/tex]

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Answer:

Y=x(t)(0.06) + x

Y =predicted population

X= population currently

t= number of years

Y= 60000(t) + 1000000

Step-by-step explanation:

Let the current population be x

X= 1000000

The rate of increase= 6% each year

Let the the predicted population= y

If the population is to increase by 6% each year the function predicting the population at the future will be

Y=x(t)(0.06) + x

The only changing value in the above formula is the time.

Y= 1000000(0.06)(t) +1000000

Y= 60000(t) + 1000000

Answer: The actual answer is:

next = now x 1.06, starting at 1,000,000

Answer:

  927 cubic inches

Step-by-step explanation:

The area of the octagonal base is ...

  A = (1/2)Pa

where P is the perimeter, and 'a' is the apothem. Using the given numbers, the base area is ...

  A = (1/2)(8·4)(4.83) = 77.28 . . . square inches

The volume of the prism is given by ...

  V = Bh

where B represents the area of the base, and h is the height.

  V = (77.28 in^2)(12 in) = 927.36 in^3

The volume of the prism is about 927 cubic inches.

the answer on edg is 927

Answer:

see below

Step-by-step explanation:

-3.55 g≤ -28.4

Divide each side by -3.55, remembering to flip the inequality

-3.55 g/-3.55≥ -28.4/-3.55

g≥8

Closed circle at 8 and the line goes to the right

here's your answer in the given attachment

Answer:

Solution: {(-1,-8), (0,-6)}

Step-by-step explanation:

y=x^2+3x-6 ............(1)

y=2x-6 ....................(2)

Solution:

by comparison, the right-hand sides of both equations are equal (to y)

x^2+3x-6 = 2x - 6

Transpose and simplify

x^2 -x = 0

x = -1 or x=0

Substitute  x = -1 in (2)

y = 2(-1) -6 = -8  ..............(-1,-8)

substitute x = 0 in (2)

y = 2(0) -6 = -6 ...............(0,-6)

So there are two solutions, corresponding to the intersection of the quadratic and the straight line.

Answer:

Step-by-step explanation:

Vertex of f is (-1, -4) so its range is limited to y≥-4

|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0

Answer:

D

Step-by-step explanation:

i just took the test

Answer:

¿De que solución habla?

Step-by-step explanation:

Answer:

B, D, F

Step-by-step explanation:

edge 2020

Answer:

[tex]\boxed{m<RUS = 65 \ degrees}\\\boxed{m<STU = 90 \ degrees}[/tex]

Step-by-step explanation:

Given that RU = 50°, So Central Angle ROU = 50° too because the measure of arc is equal to its central angle

Now, Let's assume a triangle ROU. It is an isosceles triangle since RO = RU (Radii of the same circle)

So,

∠ORU ≅ ∠OUR (Angles opposite to equal sides are equal)

So, we can write them as 2(∠RUO)

So,

2(∠RUO)+50 = 180 (Interior angles of a triangle add up to 180)

2(∠RUO) = 180-50

2(∠RUO) = 130

Dividing both sides by 2

∠RUO = 130/2

∠RUO = 65 degrees

m∠RUS = 65 degrees  (Both are the same)

In a semi circle (Given that SU is a diameter) , there must be a 90 degrees angle sin it opposite to the diameter.

So,

m∠STU = 90 degrees

From the diagram of circle k(O), m∠RUS = 65° and m∠STU = 90°

Given that:

m∠ORU = m∠OUR (isosceles triangle)

m∠ORU + m∠OUR + m∠ROU = 180° (angle in triangle)

50 + 2 * m∠OUR = 180

m∠OUR = 65°

m∠OUR =  m∠RUS = 65°

m∠STU = 90° (angle subtended at circumference by semicircle).

From the diagram of circle k(O), m∠RUS = 65° and m∠STU = 90°

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Inequalities are used to show unequal expressions; in other words, it is the opposite of equalities.

The inequality that represents the scenario is, [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls Carolina can buy is 713

Given that:

[tex]Entrance\ Fee = \$18[/tex]

[tex]Rate = \$0.08[/tex] per ball

Let:

[tex]B \to Balls[/tex]

The amount (A) Carolina can spend on B balls is:

A = Entrance Fee + Rate * B

This gives:

[tex]A = 18 + 0.08 * B[/tex]

[tex]A = 18 + 0.08B[/tex]

To get $10, Carolina must spend $75 or more.

This means:

[tex]A \ge 75[/tex]

So, the inequality is:

[tex]18 + 0.08B \ge 75[/tex]

The smallest number of balls is calculated as follows:

[tex]18 + 0.08B \ge 75[/tex]

Collect like terms

[tex]0.08B \ge 75 - 18[/tex]

[tex]0.08B \ge 57[/tex]

Divide both sides by 0.08

[tex]B \ge 712.5[/tex]

Round up

[tex]B \ge 713[/tex]

Hence, the inequality is [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls is 713

Learn more about inequalities at:

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Using a linear function, it is found that:

-----------

The linear function for the cost of B paintballs has the following format:

[tex]C(B) = C(0) + aB[/tex]

In which

-----------

Question 1:

Thus:

[tex]C(B) = 18 + 0.08B[/tex]

[tex]C(B) \geq 75[/tex]

[tex]18 + 0.08B \geq 75[/tex], given by option B.

-----------

Question 2:

[tex]18 + 0.08B \geq 75[/tex]

[tex]0.08B \geq 57[/tex]

[tex]B \geq \frac{57}{0.08}[/tex]

[tex]B \geq 712.5[/tex]

Rounding up, she has to buy at least 713 paintballs.

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