When a sprinkler is installed in the ground, the spray of water goes up and falls in the pattern of a parabola. The height, in inches, of a spray of water is given by the equation h(x)=160x−16x2 where x is the number of feet away from the sprinkler head the spray is. What is the height of the spray 2 feet away from the sprinkler head?

Answer: x=45

Step-by-step explanation:

To solve for x, we first need to understand the figure. We know TV and RS are parallel lines. If we extend TV to the left, we get a straight line parallel to RS. By Alternate Interior Angles, We know ∠R is equivalent to ∠T on the very left. Therefore, we can set it equal to 180° and solve.

x+2x+x=180          [combine like terms]

4x=180                  [divide both sides by 4]

x=45

Now, we know x=45.

Answer:

The polar coordinates appear in the form (r, θ), where r is the the radius from the center and θ is the angle. To get the radius, do the following.

[tex]r = \sqrt{x^2 + y^2} = \sqrt{1^2 + (-1)^2} = \sqrt{2}\\[/tex]

You can get the angle visually by drawing a point (1, -1) on a graph and seeing that it is 45 degrees from the top right quadrant (you can tell its 45 because both x and y have the same magnitude). Since there are 360 degrees, 360 - 45 = 315.

If you would like to find it mathematically, this is the way to do it

[tex]\theta = atan(y/x) = -45[/tex]

Notice that -45 degrees is just 360 - 45 = 315

Your answer would be

[tex](\sqrt{2}, 315)[/tex]

The best answer from the choices provide is x = -1 or x = -1

Given the expression

[tex]x^2 + 2x + 1 = 0[/tex]

Factorizing the given expression

[tex](x^2 +x)+(x + 1) = 0\\[/tex]

Factor out the common variable from both brackets

[tex]x(x+1)+1(x+1)=0\\(x+1)(x+1)=0\\x+1 \ and \ x+1=0\\x =0-1 \ and \ x=0-1\\x=-1 \ and \ x =-1[/tex]

Hence the best option is x = -1 or x = -1

Learn more about factorization here: https://brainly.com/question/16099992

The solutions for [tex]f(x) = x^{2}+2\cdot x + 1 = 0[/tex] are [tex]x_{1} = x_{2} = -1[/tex].

We can estimate the roots by a numerical approach, which consists in evaluating the quadratic function ([tex]f(x) = x^{2}+2\cdot x + 1 = 0[/tex]) for a set of values of [tex]x[/tex]. We consider the set of values between [tex]-4\le x \le 4[/tex]:

[tex]\,\,\,\,\,\,x \,\,\,\,\,\,\,\,f(x)\\-4\,\,\,\,\,\,\,\,\,\,\,\,9\\-3\,\,\,\,\,\,\,\,\,\,\,\,4\\-2\,\,\,\,\,\,\,\,\,\,\,\,1\\-1\,\,\,\,\,\,\,\,\,\,\,\,0\\.\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,1\\.\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\,\,4\\.\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,9\\.\,\,\,3\,\,\,\,\,\,\,\,\,\,\,\,\,16\\.\,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,25\\[/tex]

According to the previous input, we conclude that roots of the quadratic formula are [tex]x_{1} = x_{2} = -1[/tex].

The solutions for [tex]f(x) = x^{2}+2\cdot x + 1 = 0[/tex] are [tex]x_{1} = x_{2} = -1[/tex].

Answer: A' (-4,0)

Step-by-step explanation:

Answer:

100km

Step-by-step explanation:

Time taken to travel to Bangi:

x/80 hours

15min = 1/4hrs

Time taken to travel back:

x/80 - 1/4

x= x/(x/80-1/4)

x^2-100x=0

x(x-100)=0

x=0 (rejected) or x=100

Answer:

B. 100km

Step-by-step explanation:

Brainliest please

Answer:

2100

Step-by-step explanation:

28.34 rounds to 30

We look at the 8 which is greater than 5 and rounds the 2 to 3

69.72 rounds to 70

We look at the 9 which is greater than 5 and rounds the 6 to 7

30*70

2100

Answer:

\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}

\begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)=1\:\\ \:\mathrm{Interval\:Notation:}&\:f\left(x\right)=1\end{bmatrix}

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

The axis of symmetry passes through the vertex of the graph

It is a vertical line with equation

x = c ( c is the x- coordinate of the vertex )

vertex = (6, 1 ) with x- coordinate 6 , then

equation of axis of symmetry is x = 6

Answer:

here you go! with step by step so you can do it next time

Answer:

-7/8

Step-by-step explanation:

cross multiply first then expand the equations when you cross multiply it will be

(3x+3)(x+4)=(3x+2)(x-1)

3x(x+4)+3(x+4)=3x(x-1)+2(x-1)

3x²+12x+3x+12=3x²-3x+2x-2

3x²+15x+12=3x²-x-2

3x²-3x²+15x+x=-2-12

16x/16=-14/16

x=-14/16

simplified to

-7/8

I hope this helps

Answer:

a

Step-by-step explanation:

vì số âm không nằm ở dưới

Answer:

y = 2/3x - 13/3

Step-by-step explanation:

Implying the x and y coordinates, you get this.

I dont know the answer lol but imma say B

Answer:

[tex]{ \sf{ {(x - 2)}^{2} + {(y + 8)}^{2} = 4}}[/tex]

Answer:

Center is (2, -8) and radius =2

h = 2 and k = -8

Filling in this equation:

(x -h)² + (y -k)² = radius²  we get:

(x - 2)^2 + (y--8)^2 = 2^2 which equals

(x-2)^2 + (y +8)^2 = 4

Source: http://www.1728.org/circleqn.htm

Step-by-step explanation:

Answer:

1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.

Step-by-step explanation:

The order in which the teachers are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

1 from a set of 2(Either Mrs. Vera or Mr. Jan).

3 from a set of 18 - 2 = 16. So

[tex]C_{2,1}C_{16,3} = \frac{2!}{1!1!} \times \frac{16!}{3!13!} = 1120[/tex]

1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.

Answer:

10

Step-by-step explanation:

1x2x2.5=5

5/0.5=10

Answer:

= 40 cubes

Step-by-step explanation:

volume = 2.5×2×1 = 5cm^2

volume of cubes = 0.5×0.5×0.5 = 0.125cm^2

5÷0.125 = 40

= 40 cubes

Answer:

D

Step-by-step explanation:

I took the quiz

Answer:

Download gauthmath it will help Jesus loves you

Answer:

I think this is the right answer but last two signs are incorrect

Hope this will help

Answer:

i dont know

Step-by-step explanation:

Answer:

43

Step-by-step explanation:

First you divide the opposite side from the angle by the hypotenuse.

33/44

then you take the inverse sine of 33/44, resulting in

43.43°, which rounds to 43°

Answer:

"A number, y, is equal to the difference of a larger number and 3."

[tex]y=x-3[/tex]

You can rearrange this equation to find the matching answer choice:

[tex]y-x=-3\\x-y=3[/tex]

"The same number is one third of the sum of the larger number and 9."

[tex]y=\frac{1}{3} (x+9)[/tex]

You can rearrange this equation to find the matching answer choice:

[tex]y=\frac{1}{3} x+3\\3y=x+9\\3y-x=9\\x-3y=-9[/tex]

Answer:

The Angle-Side-Angle Theorem (ASA) states that if two angles and their included side are congruent to two angles and their included side to another triangle, then these two triangles are congruent.

Step-by-step explanation:

found this on varsitytutors.com

Answer:

y x

-1 0

1 1

3 2

5 3

This is a table that follows the above function

Answer:

23•1

Step-by-step explanation:

83°/360°×100km=23•1

Answer:

True

Step-by-step explanation:

assuming that you meant to write

cot (x-π//2) = - tan x

the identity is TRUE because,

- you can graph cot (x-π//2)  and  - tan x, and see that the graphs overlap

OR

-you solve for cot (x-π/2)

useful to know is that :

cot x=1/tan x, tan x = sin x/cos x,  

cos(x) =cos(-x), sin(-x) = -sin x,

cos(π/2 -x) =sin x, sin (π/2-x) =cos x

cot (x-π/2) = 1/tan (x-π/2) , yet tangent is sin x/cos x

cot (x-π/2) = cos (x-π/2) /sin (x-π/2) , factor -1

cot (x-π/2) = cos -(π/2-x) /sin -(π/2-x),  use facts: cos(x) =cos(-x), sin(-x) = -sin x

cot (x-π/2) = cos (π/2-x) / -sin (π/2-x), use cos(π/2 -x) =sin x, sin (π/2-x) =cos x

cot (x-π/2) = sin x / -cos x , again sin x /cos x = tan x

cot (x-π/2) = -tan x

Answer:

A

Step-by-step explanation:

Heron's formula finds the area of any triangle.

Area = sqrt(s*(s - a)*(s-b)*(s-c) )

s = (a + b + c)/2

a = 8

b = 16

c = 12

s = 36/2 = 18

s-a = 18 - 8 = 10

s-b = 18 - 16 = 2

s-c = 18 - 12 = 6

Area = sqrt(18*10*2*6) = sqrt(2160)

Area = 12*sqrt(15)

Area = 46.4758

Now x is easily found. It is the altitude to 16

Area = 1/2 16 * h

46.4758 * 2 / 16 = h

h = 3*sqrt(15)/2

h= 5.81

Answer:

-(5^N)

Step-by-step explanation:

The sequence is a negated 5 to the N power

ex.) -(5^0) = -1

-(5^1) = -5

-(5^2) = -25

-(5^3) =125

Answer:

56 + 77 + 88 + 99 = 320km²

Step-by-step explanation:

A triangular prism has 5 sides. We can start with the top and bottom, which have a base of 7 km and a height of 8km, making each of their areas equal to 7 * 8/2 = 28. Adding those up, we get 28+28 = 56 km² as the surface area of the top and bottom portions.

Next, we have the face that has 7 as the base and 11 as the height. The area of that is 7 * 11 = 77km²

After that, we have the face with 8 as the base and 11 as the height, making the area of that 8 * 11 = 88km²

Finally, we have the face with 9 as the base and 11 as the height, making that area 9 * 11 = 99km²

Adding these all up, the total surface area is

56 + 77 + 88 + 99 = 320km²

Answer:

A) (-8, -16)

B) (0, 48)

C) (-4, 0), (-12, 0)

Step-by-step explanation:

A) the vertex is the minimum y value.

extremes of a function we get by using the first derivation and solving it for y' = 0.

y = x² + 16x + 48

y' = 2x + 16 = 0

2x = -16

x = -8

so, the vertex is at x=-8.

the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16

B) is totally simple. it is f(0) or x=0. so, y is 48.

C) is the solution of the equation for y = 0.

the solution for such a quadratic equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case here

a=1

b=16

c=48

x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =

= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)

x1 = -8 + 4 = -4

x2 = -8 - 4 = -12

so the x- intercepts are (-4, 0), (-12, 0)

Answer:

a = -3

Step-by-step explanation:

f(x) = 5x³+4x²+3x-4a

f(-1) = 8

therefore , x = -1

substituting x = -1 in 5x³ + 4x² +3x-4a

5(-1)³ + 4(-1)² + 3(-1) - 4a. = 8

-5 + 4 -3 - 4a = 8

-8 + 4 -4a = 8

-4 - 4a = 8

shifting -4 from LHS to RHS

-4a = 8+4

-4a = 12

[tex] - a = \frac{12}{4} [/tex]

therefore

-a = 3

a = -3

ANS = the value of a = -3

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