(Show full work please) Carter spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 7250 feet.
Carter initially measures an angle of elevation of 16 to the plane at point A. At some
later time, he measures an angle of elevation of 26° to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest foot if necessary

Answer:

[tex]\frac{2}{3} \ part \ of \ right \ angle \ is \ \frac{1}{6} \ part \ of \ a \ whole \ wheel.[/tex]

Step-by-step explanation:

[tex]\frac{2}{3} \ of \ a \ right \ angle \ = \frac{2}{3} \times 90^{\circ} = 60^{ \circ}\\\\A \ whole \ wheel \ is \ = 360^ {\circ}\\\\[/tex]

Now to find what part of 360 is 60 :

[tex]Let \ it \ be \ x\\\\x \times 360 = 60 \\\\x = \frac{60}{360} = \frac{1}{6}[/tex]

Therefore ,

          [tex]\frac{2}{3} \ part \ of \ right \ angle \ is \ \frac{1}{6} \ part \ of \ a \ whole \ wheel.[/tex]

Answer:

y = -2x + 2

Step-by-step explanation:

Given the following data;

Points on the x-axis (x1, x2) = (2, -1)

Points on the y-axis (y1, y2) = (-2, 4)

To find the equation of line in slope intercept form;

First of all, we would determine the slope of the line.

Mathematically, slope is given by the formula;

[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]

[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

Substituting into the equation, we have;

[tex] Slope, m = \frac {4 - (-2)}{-1 -2} [/tex]

[tex] Slope, m = \frac {4 + 2}{-1 -2} [/tex]

[tex] Slope, m = \frac {6}{-3} [/tex]

Slope, m = -2

Next, we would use the following formula to find the equation of the line;

y - y1 = m(x - x1)

Substituting into the formula, we have;

y - (-2) = -2(x - 2)

y + 2 = -2x + 4

y = -2x + 4 - 2

y = -2x + 2 = mx + c

9514 1404 393

Answer:

  D.  21/2

Step-by-step explanation:

It is probably easiest to add up the three terms.

For n=1, the first term is ...

  8(1/4)^(0) = 8

The second term is ...

  8(1/4)^1 = 2

The third term is ...

  8(1/4)^2 = 8/16 = 1/2

The sum of the series is ...

  8 + 2 + 1/2 = (16 +4 +1)/2 = 21/2

Answer:

???

Step-by-step explanation:

Answer:

Step-by-step explanation:

a1=5

d=2-5=-3

[tex]a_{n}=5+(n-1)(3)\\a_{n}=5+3n-3\\a_{n}=3n+2[/tex]

We are given the system of equations -:

[tex] \large{ \begin{cases} 2x + 3y = - 14 \\ y = 6x + 22 \end{cases}}[/tex]

Since the second equation is y-isolated equation. It can be substituted as y = 6x+22 in the first equation.

[tex] \large{2x + 3(6x + 22) = - 14}[/tex]

Expand 3 in the expression so we can combine like terms and isolate x-variable.

[tex] \large{2x + 18x + 66 = - 14}[/tex]

Then combine like terms.

[tex] \large{20x + 66 = - 14}[/tex]

Get rid of 66 from the left side by subtracting both sides by itself.

[tex] \large{20x + 66 - 66 = - 14 - 66} \\ \large{20x = - 80}[/tex]

To finally isolate the variable, divide both sides by 20 so we can leave x only on the left side.

[tex] \large{ \frac{20x}{20} = \frac{ - 80}{20} }[/tex]

Simplify to the simplest form.

[tex] \large{x = - 4}[/tex]

Normally, we have to find the y-value too but since we only find x-value. The answer is x = -4.

Answer

I hope this helps! If you have any questions or doubts regarding my answer, explanation or system of equations, feel free to ask!

Answer:

A. x = -2

C. x = -4

Step-by-step explanation:

y = 6x + 22

2x + 3•(6x+22) = -14

20x = - 80

x = -4

y = 6x+22

y = 6(-4)+22 = -2

Answer:

The marked price of the article was $ 6000.

Step-by-step explanation:

Since the cost price of an article was $ 4000, to find the marked price of the article so that there will be profit of 20% after allowing a discount of 20%, the following calculation must be performed:

4000 x X x 0.8 = 4000 x 1.2

4000 x X x 0.8 = 4800

4000 x X = 4800 / 0.8

4000 x X = 6000

X = 6000/4000

X = 1.5

4000 x 1.5 = 6000

Therefore, the marked price of the article was $ 6000.

Answer:

C

Step-by-step explanation:

The pattern seems to go as follows:

1. Top left portion is in blue

2. Top left portion is in blue as well as the rest of the upper half filled with red.

3. Another portion of blue is added directly underneath the red.

This leads me to believe that the colors are alternating from blue to red to blue to finally, red. This makes your answer C. Please let me know if you still need help!

Answer:

x = 6, y = 12

x = 7  y = 14

Step-by-step explanation:

im pretty sure that right, hope this helps!

Answer:

N' (-8,9) K' (-8,3) L' (-2,3) M' (-2,9)

Step-by-step explanation:

To translate the square 3 units to the left you would subtract 3 from the x-coordinates of the points shown.

The coordinates of the translated square KLMN is given by K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the square be represented as KLMN

Now , the coordinates of the square KLMN is

K ( -5 , 3 ) L ( 1 , 3 ) M' ( 1 , 9 ) N' ( -5 , 9 )

Now , let the translated square be represented as K'L'M'N'

When translating the square to three units to the left , the x coordinate of the square gets reduced by 3

So , the new coordinate of the square will be ( x - 3 , y )

Substituting the values in the equation , we get

K' = K ( -5 - 3 , 3 )

L' = L ( 1 - 3 , 3 )

M' = M ( 1 - 3 , 9 )

N' = N ( -5 - 3 , 9 )

So , on simplifying the equation , we get

The translated square is K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)

Hence , the translated square is K' ( -8,3 ) L' ( -2,3 ) M' ( -2,9 ) N' ( -8,9 )

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Answer:

5

Step-by-step explanation:

275x5= 1375

1375+55=1430

Answer:

No, the function is not continuous at x=

Answer:

5x+4y=24

Step-by-step explanation:

So Ax+By=C is the standard form equation of a line.

y=mx+b (in which m is the slope and b is the y-intercept) is the equation that most people start off with.

Since the line intersects the y-axis at (0,6), the y-intercept is 6.

So, we can substitute 6 with b, which is y=mx+6.

Now, we can find the slope (m) by either inserting a known point (x,y) or using rise/run. Either way, you get the slope as -5/4 because we go five units DOWN and four units RIGHT from (0,6), one known point, to (4,1), another known point.

The y=mx+b equation becomes: y=(-5/4)x+6.

Now, we subtract (-5/4)x on both sides to get (5/4)x+y=6

Multiply 4 on both sides because standard form requires no fractions or decimals.

The final answer is 5x+4y=24.

That's your answer, fully simplified!

Answer:

1,188,137,600 possible combinations

Step-by-step explanation:

The first three and last two digits can be any letter while the middle two digits can be any number.

26*26*26*10*10*26*26=1,188,137,600

Answer:

a11 = 8+(11-1)6

a11 = 8+54

a11=68

hopefully this is correct

Step-by-step explanation:

15 + 36 not-equals 41, so those lengths will not form a triangle.

15 squared + 36 squared = 1,521

41 squared = 1,681

Since a squared + b squared not-equals c squared, it will not be a right triangle.

15 squared + 36 squared = 297

41 squared = 82

Step-by-step explanation; did it on the website euphoria

The translation of the parent function is f ( x ) = | x + 6 | which is shifted 6 units to the left

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the transformation of the function be a translation , where

The parent function is f ( x ) = | x |

And , the translated function is f ( x ) = | x + 6 |

So , original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

And , the function is translated 6 units to the left

Hence , the translated function is f ( x ) = | x + 6 |

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Write z in polar form:

z = 1 + √3 i = 2 exp(i π/3)

Taking the square root gives two possible complex numbers,

√z = √2 exp(i (π/3 + 2kπ)/2)

with k = 0 and k = 1, so that

√z = √2 exp(i π/6) = √(3/2) + √(1/2) i

and

√z = √2 exp(i 7π/6) = -√(3/2) - √(1/2) i

Answer: Number “2”

Step-by-step explanation: I took the ck-12 Applications with Inequalities

Answer:

iii) a=3b/2

Step-by-step explanation:

7a-2b= 5a+b

7a-5a=2b+b

2a=3b

a=3b/2

I hope this helps!

Answer:

0.624

Step-by-step explanation:

Number who have run a red light = 315

Number who haven't run a red light = 190

From the data :

The total number of people sampled = total possible outcome = (315 + 190) = 505

Selecting a person at random, probability that the selected person has run a red light :

P = required outcome / Total possible outcomes

Required outcome = Number who have run a red light = 315

P(having run a red light) = 315 / 505 = 0.624

Answer:

Step-by-step explanation:

11.04 = 10(1.02)^n

1.104 = 1.02^n

ln 1.104 = ln 1.02^n

ln 1.104 = n ln 1.02

n = ln 1.104/ ln 1.02

n = 4.99630409516

4.99 can be rounded to 5.

So a reasonable domain would be 0 ≤ x < 5

PART B)

f(0) = 10(1.02)^0

f(0) = 10(1)

f(0) = 10

The y-intercept represents the height of the plant when they began the experiment.

f(1) = 10(1.02)^1

f(1) = 10(1.02)

f(1) = 10.2

(1, 10.2)

f(5) = 10(1.02)^5

f(5) = 10(1.1040808)

f(5) = 11.040808

f(1)=10(1.02)^1

f(1)=10.2

Average rate= (fn2-fn1)/(n2-n1)

                     =11.04-10.2/(5-1)

                    =0.22

the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

Answer:

a÷(b+c)≠(a÷b)+(a ÷c)

Step-by-step explanation:

To verify that a÷(b+c)=(a÷b)+(a ÷c)

Using the values ;

a=10 , b=5 , 6=2​

plugging the values into a÷(b+c) should give the same result as (a÷b)+(a ÷c) ;

That is, right hand side = left hand side

a÷(b+c) = 10 ÷ (5+ 2)

a÷(b+c) = 10 / 7

Also;

(a÷b)+(a ÷c) = (10/5) + (10/2) = 2 + 5 = 7

Given the result, it can be seen that ;

RHS ≠ LHS

10/7 ≠ 7

Answer:

8

Step-by-step explanation:

Let the unknown number be x.

Therefore, we can write the question as a mathematical statement and this will be:

3x^2 - 137 = 55.  (Note: ^2 = to the power of 2 or "squared"

(In the question, we can break it up as being three times of a square of a natural number = (3x^2) and 137 is subtracted from = (- 137) and the result is 55 = (= 55). Therefore, this gives 3x^2 - 137 = 55

Then, we add 137 first to get rid of the (-137)

Therefore:

3x^2 = 192

Then, we divide 3 from both sides to get rid of the (3) in (3x^2).

Therefore,

x^2 = 64.

So, we square root 64. This gives

x = 8.

Therefore, the answer is 8.

Answer: D

Step-by-step explanation:

set the functions to subtract

Answer:

No it is not fair how can two people win

Answer:

Mean = 4.8875

Median = 4.6

Mode = 4.5 and 7.7

Step-by-step explanation:

Mean is the sum of total of data divided by the sample size

Sum total = 1.5 + 4.7 + 6 + 7.7 + 7.7 + 4.5 + 2.5 + 4.5

Sum total = 39.1

Sample size = 8

Mean = 39.1/8

Mean = 4.8875

To get the median we need to first rearrange

1.5, 2.5, 4.5, 4.5, 4.7, 6, 7.7, 7.7

Median = 4.5 + 4.7/2

Median = 4.6

Hence the median is 4.6

Mode is the value occuring the most. Since 4.5 and 7.7 both occurs twice, hence the mode of the data is 4.5 and 7.7

Answer:

y = 30.96

Step-by-step explanation:

take 23 degree as reference angle

using tan rule

tan 23 = opposite / adjacent

0.42 = 13/y

y = 13/0.42

y = 30.96