The length of the roller coaster track from the top of a hill to the bottom of the hill is 125 feet at a 53°C angle with the vertical. If the position at the top of the hill is (x, y) , use function notation to describe the translation to the bottom of the hill. Round to the nearest foot.

Answer:

Step-by-step explanation:

Simplify:

31−(5−3⋅4)*2+26÷4=

31-(5-12)*2+6.5=

31-(-7)*2+6.5=

31+14+6.5=

51.5

Answer: h=60 feet

Step-by-step explanation:

h=4+60t-16t²

h(2)=4+(60)(2)-(16)(2)²

h(2)=4+120-(16)(2)(2)

h(2)=124-64

h(2)=60 feet

Answer:

11.55

Step-by-step explanation:

The angle of depression, at which Tom threw the paper is 14.93°

In this question,

Tom throws a paper from a height of 4 feet, and it lands 15 feet from the car.

We need to find the angle of depression, at which he threw the paper.

Consider the following diagram.

Let the θ be the angle of depression, at which he threw the paper.

Consider the tangent of angle θ.

⇒ tan(θ) = 4/15

⇒ θ = [tex]tan^{-1}(\frac{4}{15} )[/tex]

⇒ θ = 14.93°

Therefore, the angle of depression, at which Tom threw the paper is 14.93°

Learn more about the angle of depression here:

https://brainly.com/question/13514202

#SPJ4

Answer: -8

Step-by-step explanation:

Answer:

Step-by-step explanation:

d

Answer:

Step-by-step explanation:

15. True

16. False

17. True

18. True

Answer:

15 )true because they are opposite angles.

16) false 2 and 4 are opposite angles so should be the same value.

17 true ) because angle 4+1=180.

18 true) because the two angles make a 180 degree.

Answer:

c = 110.25

(r + 10.5)²

Step-by-step explanation:

Hello!

Perfect Square Trinomial: [tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

21r is basically 2 times r and b, the missing number.

The missing number, b, would be 10.5

Now c is basically b², so we just have to simplify 10.5²:

c should be 110.25 for it to be a Perfect Square Trinomial. The factored form would be (r + 10.5)².

An interior angle of a regular polygon has a measure of 108°. It is a 5 sided polygon known as pentagon.

What shape does the Pentagon have?

What do you call a shape with five sides?

Learn more about Pentagon

brainly.com/question/17054992

#SPJ4

Answer:

The period would be 2 years

Step-by-step explanation:

[tex]\frac{12}{5}[/tex] = [tex]2\frac{2}{5}[/tex] revolutions per second is the unit rate.

An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

1) Convert mixed fractions into fractions.

[tex]6\frac{2}{5}[/tex] = [tex]\frac{((6*5) + 2)}{5}[/tex] = [tex]\frac{32}{5}[/tex]

[tex]2\frac{2}{3}[/tex] = [tex]\frac{((2*3) + 2)}{3}[/tex]  =  [tex]\frac{8}{3}[/tex]

2) [tex]\frac{32}{5}[/tex] ÷ [tex]\frac{8}{3}[/tex] ; where [tex]\frac{32}{5}[/tex] is the 1st fraction and [tex]\frac{8}{3}[/tex] is the 2nd fraction

a) Find the second fraction's reciprocal:

  From [tex]\frac{8}{3}[/tex] to [tex]\frac{3}{8}[/tex]

b) Multiply the first fraction by the second fraction's reciprocal, which is 32/5, 5/3, or (5/3), to get 96/40.

c) Simplify the fraction.

Divide 96 / 40 by 4 to get 24/10.

Divide 24/10 by 2, and the result is 12/5. The 96/40 simple fraction

[tex]\frac{12}{5}[/tex] = [tex]2\frac{2}{5}[/tex] revolutions per second is the unit rate.

To learn more about unit rate visit:

brainly.com/question/28394073

#SPJ9

[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\textsf{Parallel lines have the same slope, thus:}[/tex]

[tex].\qquad\bullet\sf{Slope\:of\:the\:line\:that's\:parallel\:to\:the\:given\:line: \dfrac{1}{3}}[/tex]

[tex]\textsf{Next, we'll apply the \textbf{Point-Slope Formula:}}[/tex]

[tex].\qquad\bullet\sf{y-y_1=m(x-x_1)}[/tex]

[tex]\textbf{\underline{Setting the values:}}[/tex]

[tex].\qquad\bullet\sf{y_1=2}\\.\qquad\bullet m=1/3\\.\qquad\bullet x_1=6}}[/tex]

[tex]\textbf{\underline{Plugging in the values:}}[/tex]

[tex].\qquad\bullet\sf{y-2=\dfrac{1}{3} (x-6)}\\\\.\qquad\bullet y-2=\dfrac{1}{3}x-2}\\\\.\qquad\bullet y=\dfrac{1}{3} x}[/tex]

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\large\overbrace{\underbrace{\textsf{\textbf{Reflection - RoSe}}}}^\star_\star[/tex]

By combining the like terms, the simplified form of the expression x(3-y)+y(x+6) is 3x+6y

Given,

The algebraic expression = x(3-y)+y(x+6)

Apply distributive property and expand the term

x(3-y)+y(x+6)=3x-xy+xy+6y

Combine like terms

3x-xy+xy+6y= 3x+6y

Hence, by combining the like terms, the simplified form of the expression x(3-y)+y(x+6) is 3x+6y

Learn more about distributive property here

brainly.com/question/5637942

#SPJ4

The solution of the given equation -3(x-4)=2(x+8) is at x = -4/5.

According to the given question.

We have a linear equation in one variable.

-3(x-4)=2(x+8).

As we know that,the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the given equation is given by

-3(x - 4) = 2(x + 8)

⇒ -3x + 12 = 2x + 16

⇒ -3x - 2x = 16 - 12

⇒ -5x = 4

⇒ x = -4/5

We get the solution of the given equation is at x = -4/5.

Now, we can check that x = -4/5 is a solution of the given equation or not.

Therefore,

L.H.S

= -3(-4/5 - 4)

= 12/5 + 12

= (12 + 60)/5

= 72/5

Similarly,

R.H.S

= 2(-4/5 + 8)

= -8/5 + 16

= -8 + 80/5

= 72/5

So, L.H.S = R.H.S

Hence, the solution of the given equation -3(x-4)=2(x+8) is at x = -4/5.

Find out more information about equation here:

https://brainly.com/question/15549034

#SPJ4

The point X on AB such that the ratio is 1.25 units.

XB=AX×3

AX+XB=AB

AX+(AX×3)=AB

AX×4=AB

AX×4=9

AX=2.25

X=-1+2.25

X=1.25 units

Ratio shows how often one number is contained in another. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). The proportions of oranges to the overall amount of fruit are 8:14 for oranges and 6:8 (or 3:4) for lemons (or 4:7).

The quantities in a ratio can be of any form, including counts of people or things, measures of lengths, weights, or times, etc.

Hence , the Coordinate in units: (2,1.25).  In most contexts, both numbers are restricted to be positive.

To know more about ratio, visit :

brainly.com/question/1649297

#SPJ1

It should be noted that the value of to 3x-4will be -12.

It should be noted that this simply has to do with multiplication.

In this case we have to multiply the values that are given.

Also, it's important note that minus multiplied by plus is minus.

Therefore, (3 × -4) = -12.

Learn more about multiplication on:

brainly.com/question/10873737

#SPJ1

answer:

5

explanation:

(5*5) + 3=28

(7*5) - 7= 28

The equation of the line for given values is y = -5x - 7.

When you know the slope of the line to be investigated and the provided point is also the y intercept, you may utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

The standard equation of straight line is y = mx + c.

Given m = -5 and y - intercept is -7

So, the equation of the line becomes y = -5x - 7

To learn more about equation of the line from given link

https://brainly.com/question/18831322

#SPJ4

The value of expression is 33

For evaluating the expression, we will keep the given values of variables in the expression. Further solving will be done according to the mathematical operators.

Rewriting the equation -

Value = 11 (a + 2b) + 2 (a - 2b)

Now keeping the values of variables in expression -

Value = 11 (-3 + 2×4) + 2 (-3 - 2×4)

Firstly solving the brackets

Value = 11 ( -3 + 8) + 2 (-3 - 8)

Value = 11 (5) + 2 (-11)

Performing multiplication

Value = 55 - 22

Performing subtraction

Value = 33

Hence, the expression for the given values of the variables is 33.

Learn more about evaluation of expression -

https://brainly.com/question/28581449

#SPJ4

The equation in point-slop form of the line line having the slope m=-1 and that contains the point (-2,3)  is y-3=-1(x+2)

Given,

The slope m = -1

The point = (-2,3)

We know the point-slope form,

[tex]y-y_{1}=m(x-x_{1})\\[/tex]

Substitute the values in the equation

y-3=-1(x-(-2))

y-3=-1(x+2)

Hence, the equation in point-slop form of the line line having the slope m=-1 and that contains the point (-2,3)  is y-3=-1(x+2)

Learn more about point-slope form here

brainly.com/question/24436844

#SPJ4

Step-by-step explanation:

$2.88 per pound

so, then how much for e.g. 2 pounds ?

right : the price for 1 pound plus 1 pound = 2×$2.88 = $5.76

and so on.

therefore, 3.9 pound cost :

3.9 × $2.88 = $11.232 ≈ $11.23

Answer:

11.232

Step-by-step explanation:

3.9×2.88=11.232

The equation of a line with slope = 0 and y-intercept = (0,-2) is: y = -2

Now,

Given:

To find: Equation of the line

Finding:

Now, we know that the slope-point form method to find the equation of a line, requires only two things: slope of the line and coordinates of the y-intercept.

The equation so given by the method: y = mx + c, where

m = slope of the line

c = y-intercept

On substituting the given values in the above equation, we get:

=> y = 0x - 2, which the required equation of the line.

Hence, The equation of a line with slope = 0 and y-intercept = (0,-2) is: y = -2.

To learn more about equation of a line to a curve, refer to the link: brainly.com/question/13763238

#SPJ4

The division of given rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex] is [tex]\frac{3(x-2)}{4(x+3)}[/tex] provided x ≠ -3

In this question,

we have been given a complex rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex]

We need to find the division of given rational expression.

We rewrite given rational expression as,

[tex]\frac{\frac{3x-6}{12x-24}}{\frac{x^2+5x+6}{3x^{2} -12}}\\\\\\= \frac{3x-6}{12x-24}\times \frac{3x^2-12}{x^2+5x+6}[/tex]

First we simplify the quadratic expression x² + 5x + 6

x² + 5x + 6

= x² + 3x + 2x + 6

= x(x + 3) + 2(x + 3)

= (x + 3)(x + 2)

And the simplified form of quadratic expression 3x² - 12 would be,

3x² - 12

= 3(x² - 4)

= 3(x² - 2²)

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

So, the given rational expression would be,

[tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12} \\\\\\ = \frac{3x-6}{12x-24}\times \frac{3x^2-12}{x^2+5x+6}\\\\\\=\frac{3(x-2)}{12(x-2)}\times \frac{3(x+2)(x-2)}{(x+3)(x+2)}[/tex]

[tex]\\\\=\frac{3}{12}\times \frac{3(x-2)}{(x+3)}\\\\\\=\frac{3(x-2)}{4(x+3)}~~~~~~~~~~~~~(provided~~x\neq -3)[/tex]

Therefore, the division of given rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex] is [tex]\frac{3(x-2)}{4(x+3)}[/tex] provided x ≠ -3

Learn more about the rational expression here:

https://brainly.com/question/13015660

#SPJ4

The probability that it hits region I is 15%.

Probability:

Probability means the possibility of the required event.

The formula for the probability is written as,

P(E) = n(E)/n(S)

Where,

P(E) is the probability of an required event

n(E) is the number of possible outcomes

n(S) is the total number of events.

Given,

At a carnival, the object of a game is to throw a dart at the board and hit region III.

Here we need to find the probability that it hits region I.

Consider the board was look like the following figure.

Then based on the given figure,

First, we have to find the total area of the board and the area of the required region.

And then we have to compare it to calculate the Probability.

So, the total area of the board is,

=> total area of the board = (10 + 30)(10 + 15)

=> total area of the board = 1000 in²

Now, the The area of the region I is

=> Area = (10)(15)

=> Area = 150 in²

Therefore, the probability that it hits region I is

=> P = 150/1000

=> P = 15/100

=> P = 15%

Therefore, the probability that it hits region I is 15%.

To know more about Probability here.

https://brainly.com/question/15729871

#SPJ4

Answer:

2x² - 25x + 90

Step-by-step explanation:

→ Replace every x in 2x² + 5x + 15 with -x + 5

2 × ( -x + 5 )² + 5 ( -x + 5 ) + 15

→ Simplify

2 ( x² - 10x + 25 ) - 5x + 25 + 15

→ Expand

2x² - 20x + 50 - 5x + 40

→ Simplify

2x² -25x + 90

Answer:

F

Step-by-step explanation:

La respuesta es f porque la tasa vigente en el lado x es por 2 y la tasa vigente en el lado y es por 12.