What is 2x^2-13x+15?

Answer: The angle of depression would be 26.57°

Step-by-step explanation: Please refer to the attached picture for further details.

What harry has done has effectively led to the formation of a right angled triangle. As shown in the diagram, the camera has been mounted at a height of 8 feet above the ground. Also he mounts the camera at a horizontal from the entrance, which puts the camera at 16 feet away from the entrance (not from the ground). In order to capture every movement at the entrance, the camera range would be determined by an angle which covers everything from top to bottom of the entrance. That gives you the angle of depression which is at the point labelled CAMERA in the triangle.

Having determined two sides and an angle (unknown) in a right angled triangle, we shall use the trigonometric ratios as follows;

Tan ∅ = Opposite/Adjacent

Where the opposite is 8 (side facing the reference angle) and the adjacent is 16 (side that lies between the reference angle and the 90 degree angle)

Tan ∅ = 8/16

Tan ∅ = 0.5

By use of a calculator,

∅ = 26.5650

∅ ≈ 26.57

Therefore the angle of depression of the surveillance camera should be 26.57°

How I got that answer:

The graph shows the two points (0,-4) and (-2,2) are on the parabola. The x coordinates of both points are from x = 0 and x = -2 as given in the instructions. Compute the slope of the line through those points. The slope of this line is the exact same as the average rate of change from x = -2 to x = 0.

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

m = (2 - (-4))/(-2-0)

m = (2 + 4)/(-2-0)

m = 6/(-2)

m = -3

A negative slope means the line slopes downhill as you move from left to right. This is a negative average rate of change.

Answer:

9.5 gallons

Step-by-step explanation:

Josh mixed 2 cartons of orange juice, 3 bottles of soda water and 6 cans of

cocktail fruits to make a fruit punch.

Each carton of juice is 1 gallon and 3 quarts.

Therefore, 2 cartons will be:

2 * (1 gallon + 3 quarts) = 2 gallons and 6 quarts

1 quart = 0.25 gallon

6 quarts = 6 * 0.25 = 1.5 gallons

Therefore, Josh poured 3.5 gallons of orange juice.

Each soda water bottle contains 6 quarts. There are 3 bottles of soda water.

Therefore, the number of gallons that the soda water bottle contains is:

3 * 6 * 0.25 = 4.5 gallons

The  cans of cocktail fruit are 2 pints each. There are 6 cans of cocktail fruit.

1 pint = 0.125 gallon

2 pints = 0.25 gallons

=> 6 cans of cocktail fruit is:

6 * 0.25 = 1.5 gallons

The amount of fruit punch that Josh made is the sum of all components:

3.5 + 4.5 + 1.5 = 9.5 gallons

Using the appropriate arithmetic operation, the total measure of the fruit punch in gallons is 9.5 Gallons

Recall :

Orange juice :

2 cartons = 2(1.75) = 3.5 gallons

Soda water :

3 bottles = 3(6 × 0.25) = 4.5 gallons

Cocktail juice :

6 cans = 6(2 × 0.125) = 1.5 gallons

Total gallons in mixture :

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Answer:

V=π*r^(2)*h/3

Step-by-step explanation:

Answer:

  P = (2, 3)

Step-by-step explanation:

P is a local minimum, so can be found from the upper zero of the derivative.

  y' = 0 = 3x^2 -8x +4

  0 = (3x -2)(x -2)

  x = 2/3, x = 2

So, the x-coordinate of P is 2. The y-coordinate is found by evaluating the function:

  y = ((x -4)x +4)x +3 = ((2 -4)2 +4)2 +3 = 3

The coordinates of P are (2, 3).

__

A graphing calculator confirms this result.

Answer:

the newer moat is 169 cm longer than the older one

Step-by-step explanation:

in order to find the difference in length of the two castles, we will first find the perimeters of the two castles then calculate the difference in the perimeters:

old castle:

dimension = 484cm by 386cm

perimeter = 484 + 386 = 870 cm

new castle:

dimension = 725cm by 314cm

perimeter = 725 + 314 = 1039 cm

difference =  1039 - 870 = 169 cm

The total length of the moats used is equals to the perimeter of the sand castles, therefore, the newer moat is 169 cm longer than the older one.

Answer:

Look I know I'm about 2 1/2 years late but the answer is not 169 or whatever the person above me said, it's 660 I answered this before.

Answer:

43.30 km^2

Step-by-step explanation:

Since the shape is a regular polygon, the sides of the triangle are equal (10km) now find the area on the triangle using herons formula

Working:

Side is 10

Perimeter= 30km

Semiperimeter (s) = 15km

Formula= √s(s-a)(s-b)(s-c)

= √15(15-10)(15-10)(15-10)

= √15*5*5*5

=5√5*15

=5√75

= 5*8.66

= 43.3 km^2

Answer:

43.3

Step-by-step explanation:

since it is a regular polygon thus it is a equilateral triangle where all sides are the same and all angles are 60

use formula 1/2 x a x b x sin C where a and b are sides and C is the angle

1/2 x 10 x 10 x sin 60 = 43.30

or method 2 is using Pythagoras theorem by drawing a perpendicular height to length 10km

h = [tex]\sqrt{10^{2} - (10/2)^{2} } = \sqrt{75} \\[/tex]

area of triangle = 1/2 x 10 x [tex]\sqrt{75}[/tex] = 43.30

Answer: The negative solution is -2

Step-by-step explanation:

[tex]5x+14=x^2\\x^2-5x-14=0\\\\(x-7)(x+2)=0\\x_1=7\\x_2=-2[/tex]

Answer:

2040

Step-by-step explanation:

34x60=2040

Answer:

2040

Step-by-step explanation:

So we multiply them on a calculator.

Answer: 2ab - e/3 - 3d

Step-by-step explanation:

2ab - 1/3e - 3d

= 2ab - 1e/3 - 3d

= 2ab - e/3 - 3d

Answer:

5a

Step-by-step explanation:

[tex]5\cdot \:a\\\\[/tex]

5 multiply a

5a

Answer:

common ratio(r) = 10

place of the term = n

a = 3

now

sequence of 1 term = ar^(n-1)

= 3×10^(1-1)

= 3× 10^0

= 3×1

= 3

sequence of 2 term = ar^(n-1)

= 3×10¹

= 30

and so on

Answer:

A triangle has side lengths 18, 24, x.

18 + 24 = x

18 squared + 24 = x

(18 + 24) squared = x squared

18 squared + 24 squared = x squared

Step-by-step explanation:

The right triangle hypotenuse has its length 18² + 24² = x².

In a right triangle, the "side opposite to the right angle is hypotenuse".

According to the question,

In right angle triangle,  sides are 18, 24, x. Where 'x' is the hypotenuse  of the right angle triangle. In right angle the opposite angle is 90⁰ . In order

to find hypotenuse,  

18 + 24 = x

18² +24 =x

(18+  24) ² = x²

18² + 24² = x²

Hence, the right triangle hypotenuse has its length 18² + 24² = x².

Learn more about hypotenuse here

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#SPJ2

Answer:

54

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

b = a² + 2a

Step-by-step explanation:

a + 1 = √(b + 1)

(a + 1)² = b + 1 (Square both sides)

a² + 2a + 1 = b + 1 (Expand left side)

a² + 2a = b (Subtract 1)

Answer:

b) 15 winners

Step-by-step explanation

if 3 winners get $720,000 each that means there is $2,160,000 total. So if each winner gets $144,000 each that means there are 15 winners.

(2,160,000/ 144,000)

Answer:

x= -1

Step-by-step explanation:

Solving through linear equation,

-0.1x + 3/10= 4/10

Bring 3/10 to the other side making it minus

-0.1x = 4/10 - 3/10

-0.1x = (4-3)/10

-0.1x= 1/10

Bring -0.1 to the other side n divide

x= 1/10 ÷ -0.1

( Note that -0.1 is the same as -1/10)

x = 1/10 ÷ -1/10

= 1/10*-10/1

= -10/10

= -1

Answer:

first number is 5

second number is 7

Step-by-step explanation:

let x and y represent the first and second number

5x - 2y = 11 ........ equation 1

3x - 2y = 11.......... equation 2

so by elimination, equation 1 minus equation 2

5x - 3x - 2y - 2y = 11 - 1

2x = 10

x = 5

therefore the first number is 5

put x = 5 into equation 1

5x - 2y = 11

5(5) - 2y = 11

25 - 2y = 11

-2y = 11 - 25

-2y = - 14

y = 7

therefore the second number is 7

hope it helps .

Answer:

the hardcover is 19.95, and the parback is 6.65. enjoy.

Answer:

Step-by-step explanation:

5. a) ∠1 and ∠2 are remote interior angles of ∠ACD so that means that ∠ACD = ∠1 + ∠2

   b) Because an exterior angle is the sum of its two remote interior angles it makes sense that an exterior angle is greater in measure than either of its remote interior angles.

6. BD = DB  Reflexive property

    ∠3 = ∠5, ∠4 = ∠6  Alt. int. angles

    ΔADB = ΔCDB   ASA

7. AB = BC Def. of midpoint

   ∠1 = ∠2 Given

   ∠BAE = ∠CBD Corresponding angles

   ΔBAE = ΔCBD ASA

    ∠D = ∠E CPCTC

Answer:

A..... I guess the answer must be A

Answer: No slope

Step-by-step explanation: The line is going straight down.

Answer:

13, 050

Step-by-step explanation:

15,000 by 13% = 1,950

15,000-1,950= 13, 050

Answer:

46.8 kg

Step-by-step explanation:

78 * 0.6 = 46.8

Answer:

Cam has b-7 dollars

Step-by-step explanation:

Answer:

8/25

Step-by-step explanation:

4/5 *2/5

Multiply the numerators

4*2 = 8

Multiply the denominators

5*5 = 25

8/25

Answer:

The answer would be 8/25 or 0.32

Answer:

Option(1) is the correct answer to the given question .

Step-by-step explanation:

let     [tex]x1, y1=\ (2, 3)[/tex]

[tex](x2,y2)=(\sqrt{15,3} \ )[/tex]

[tex](x3,y3)=\ (4,8)[/tex]

Now we know that

[tex]Area=\ \frac{1}{2} |x1(y2-y3)\ + \ x2(y3-y1)\ + x3(y1-y2)[/tex]

Now putting this value in the formula we get

[tex]\frac{1}{2}|2(3-8)\ +\sqrt{15}(8-3)\ * 4(5-3)|[/tex]

[tex]=\ \frac{1}{2}\ *9.3649[/tex]

=4.6824

Therefore option(1) is the correct answer .

Answer:

Option(1) is the correct answer to the given question .

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

f(x)=72-4x

72-4x=0

4x=72

x=18

f(x)<=18