Which is true regarding the graphed function f(x)? f of 0 = 3 f of 5 = negative 1 f of 3 = 2 f of 2 = negative 2

Answer:

[tex]\tan \theta = \dfrac{8}{15}[/tex]

Step by step explanation:

[tex]\text{Given that,}\\\\~~~~~~~\sin \theta = \dfrac{8}{17}\\\\\implies \sin^2 \theta = \dfrac{64}{289}\\\\\implies 1-\cos^2 \theta = \dfrac{64}{289}\\\\\implies \cos^2 \theta = 1-\dfrac{64}{289}\\\\\implies \cos^2 \theta = \dfrac{225}{289}\\\\\implies \cos \theta =\pm\sqrt{\dfrac{225}{289}}\\\\\implies \cos \theta = \pm\dfrac{15}{17}[/tex]

[tex]\text{In quadrant I, all ratios are positive, so,}~ \cos \theta = \dfrac{15}{17}\\\\\text{Now,}\\\\\tan \theta = \dfrac{\sin \theta }{\cos \theta}\\\\\\~~~~~~~~=\dfrac{\tfrac{8}{17}}{\tfrac{15}{17}}\\\\\\~~~~~~~~=\dfrac{8}{17} \times \dfrac{17}{15}\\\\\\~~~~~~~=\dfrac{8}{15}[/tex]

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

so in this case we have the provided ones (2005 , 12000) and (2010 , 12250)

[tex](\stackrel{x_1}{2005}~,~\stackrel{y_1}{12000})\qquad (\stackrel{x_2}{2010}~,~\stackrel{y_2}{12250}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12250}-\stackrel{y1}{12000}}}{\underset{run} {\underset{x_2}{2010}-\underset{x_1}{2005}}} \implies \cfrac{12250 -12000}{2010 -2005}\implies \cfrac{250}{5}\implies \underset{\textit{rate of change}}{50}[/tex]

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

Answer:

  65.9 ft

Step-by-step explanation:

The Law of Sines tells us the relationship between an angle and the opposite side. We are given the angle opposite the given side, but we need the angle opposite the side of interest.

__

The sum of angles in a triangle is 180°, so the measure of the angle at the balloon is ...

  angle C = 180° -75° -60° = 45°

Then the distance between Amaya and Rochelle (c) is ...

  c/sin(C) = r/sin(R)

  c = r×sin(C)/sin(R) = (90 ft)×sin(45°)/sin(75°)

  c ≈ 65.8846

Amaya and Rochelle are about 65.9 feet apart.

Answer:

Compound interest, or 'interest on interest', is calculated using the compound interest formula.

The formula for compound interest is A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods.

Step-by-step explanation:

The system of equations that models the given situation is given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

He had 25 customers, hence:

x + y = 25.

He charges $15 for a single lawn and $25 for a front and back lawn, and made a total of $475, hence:

15x + 25y = 475

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The number of seconds it takes until the ball reaches max height is 2 seconds and the maximum height is 112 feet, and the number of seconds it takes until the ball hits the ground will be 6.9 seconds.

When a body is thrown in the air then the motion under the gravity is known as projectile motion.

A person standing close the the edge on the top of a 80 foot building throws a baseball vertically upward. the quadratic function

h(t) = -8t² + 32t + 80 models the ball's height above the ground, h(t), in feet, t seconds after it was thrown.

The number of second to reach at maximum height will be

We know that at maximum height, the rate will be zero. Then we have

       h'(t) = 0

-16t + 32 = 0

            t = 2 seconds

Then the maximum height will be

h(t) = -8(2)² + 32 x 2 + 80

h(t) = -32 + 64 +80

h(t) = -32 + 144

h(t) = 112 feet

Then the number of the seconds to reach at the ground will be

-8t² + 32t + 80 = -80

-8t² + 32t + 160 =0

t² - 4t - 20 = 0

Then t will be

[tex]\rm t = \dfrac{-(4) \pm \sqrt{(-4)^2 - 4 * 1 * -160}}{2*1}[/tex]

Then we have

t = 6.9 and -2.9

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Answer:

Step-by-step explanation:

x + x + 36 = 180

2x + 36 = 180

2x = 144

x = 72

Answer:

c (2,0) and (-2,0) I hope ot helps

Answer: B

[tex]f(x) = 7x-2[/tex] and        [tex]g(x) = \frac{x+2}{7}[/tex]

How to solve:

check if the composite functions of f(x) and g(x) are equal to x (this means they are inverses)

f[g(x)] = x

g[f(x)] = x

Step-by-step explanation:

Checking A.

[tex]f(x) = \frac{5}{x} -2[/tex]

[tex]g(x) = \frac{x+2}{5}[/tex]

[tex]f(g(x)) = f(\frac{x+2}{5} ) = \frac{5}{\frac{x+2}{5} } -2[/tex]

This does not equal x, so we know these are not inverses

Checking B.

[tex]f(x) = 7x-2[/tex]

[tex]g(x) = \frac{x+2}{7}[/tex]

[tex]f(g(x)) = f(\frac{x+2}{7} ) = 7(\frac{x+2}{7}) - 2 = x+2-2 = x[/tex]

[tex]g(f(x)) = g(7x-2) = \frac{7x-2 + 2}{7} = \frac{7x}{7} = x[/tex]

since both f(g(x)) = x and g(f(x)) = x, we can determine that they are inverses of each other.

The required total distance the ball travels, approximately, is 180 feet.

Let's denote the height of the first fall as a (initial height of 60 feet), and the distance covered during each rebound as r (two-thirds the distance of the previous fall).

The first fall distance (a) is 60 feet.

The first rebound distance (r) is (2/3) * 60 feet.

The total distance covered during the first fall and rebound cycle is:

60 + (2/3) * 60 = 60 + 40 = 100 feet.

Now, for the subsequent cycles, the ball will continue to fall and rebound in the same pattern:

Second fall distance = r * a
                                  = (2/3) * 60
                                  = 40 feet.

Second rebound distance = r*(2/3) * 60
                                            = (2/3) * 40
                                            = 80/3 feet.

The total distance covered during the second fall and rebound cycle is:

40 + (80/3) ≈ 66.67 feet.

The pattern will continue for the subsequent cycles.

To represent this as an infinite geometric series, we can write:

Total distance = [tex]a + (a * r) + (a * r^2) + (a * r^3) + ...[/tex]

Where:

a = 60 feet (height of the first fall)

r = 2/3 (rebound factor)

Using the formula for the sum of an infinite geometric series:

Total distance = a / (1 - r)

Total distance = 60 / (1 - 2/3)

Total distance = 60 / (1/3)

Total distance = 60 * 3

Total distance = 180 feet.

Therefore, the total distance the ball travels, approximately, is 180 feet.

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Answer: 6.64

Step-by-step explanation:

[tex]A=\frac{1}{2}(4.7)(3.2)(\sin 62^{\circ}) \approx \boxed{6.64}[/tex]

Answer:

i can't see the question i would love to help though

Step-by-step explanation:

No it can't be factored , whenever there is addition between two squares , the expression can't be factored

Answer:

[tex]\text{P(green)} =\frac{45}{139}[/tex]

Step-by-step explanation:

The total number of candies is :

= 42+45+20+32

= 139

Then

we have 45 green out of 139 candies.

Then

[tex]\text{P(green)} =\frac{45}{139}[/tex]

Note : 45/139 is already simplified.

Answer:

No, it is not the same thing.

Step-by-step explanation:

Hope this helps!

Answer + Step-by-step explanation:

» ABC ≅ DBE

» DE // AC  

(properties of the mid-segment of a triangle)

» Length of DE = 1/2 length of AC  

(properties of the mid-segment of a triangle)

» ∠BDE = ∠DAC

(Corresponding angles)

Considering the given function, we have that:

a) D(12) = 2600, which means that after 12 hours of driving, the family is 2600 miles from home.

b) D(t) = 2490 when t = 14, which means that the family is 2490 miles from home after 14 hours of driving.

The distance that the family is from home, after t hours of driving, is given by:

D(t) = 3260 - 55t.

Then, after 12 hours, the distance is given by D(12), that is:

D(12) = 3260 - 55 x 12 = 2600.

D(12) = 2600, which means that after 12 hours of driving, the family is 2600 miles from home.

D(t)=2490, hence:

3260 - 55t = 2490

55t = 770

t = 770/55

t = 14

D(t) = 2490 when t = 14, which means that the family is 2490 miles from home after 14 hours of driving.

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Answer:

Center: (6, -12)

Radius: 4

Step-by-step explanation:

Complete the squares

[tex]x^2+y^2-12x+24y-10=6\\\\x^2-12x-10+y^2+24y=6\\\\x^2-12x-10+46+y^2+24y+144=6+46+144\\\\(x^2-12x+36)+(y^2+24y+144)=196\\\\(x-6)^2+(y+12)^2=196[/tex]

Comparing with the standard form equation [tex](x-h)^2+(y-k)^2=r^2[/tex], since [tex]r^2=196[/tex], then the radius of the circle is [tex]r=14[/tex]. Also, the center of the circle would be [tex](h,k)\rightarrow(6,-12)[/tex].

The area of the target which earns 30 points on a throw.

[tex]\huge\boxed{Formula: a= \pi{r}^{2}}[/tex]

[tex]4+3[/tex]

[tex]=7[/tex]

Let's solve

We have to find the answer in terms of π so, we'll just have to multiply the radius by itself.

[tex]a={7}^{2}[/tex]

[tex]\large\boxed{a= 49 \pi\: {in}^{2}}[/tex]

Hence, the area of the target which earns 30 points on a throw is 49π square inches.

Answer= Option B

Answer:

Step-by-step explanation:

Answer:

C: is a function because each input (x) has exactly one output( y).

Step-by-step explanation:

A function is when one input (x) has exactly one output (y).

A: is not a function because -4 is paired with two different y values.

B: is not a function because -4 is paired with two different y values.

C: is a function because each input (x) has exactly one output( y).

D: is not a function because -1 is paired with two different y values.

Answer:

2,4,8,11,22, or 44

Step-by-step explanation:

To figure out how many rings would be in each full row with no leftovers, we need to find all the factors of 88 (outside of 1 and 8) which are 2,4,8,11,22, and 44. Since the question does not give any more information on how big the rows need to be, I can't narrow this down any further, however if I had to choose I would say rows of 8 by 11 would be the best.

Hope this helps! :)

The series is a convergence series and the sum of the series is -8/3

The series is given as:

[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]

The above series has the following properties:

Start by calculating the absolute value of the common ratio

Absolute value = |-1/2|

This gives

Absolute value = 1/2

The above value is less than 1.

It means that the series converges.

This is calculated using:

[tex]S_{\infty} = \frac{a}{1 -r}[/tex]

So, we have:

[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]

Evaluate the sum

[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]

Evaluate the quotient

[tex]S_{\infty} = \frac{-8}{3}[/tex]

Hence, the sum of the series is -8/3

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Answer:

Step-by-step explanation: