which of the following functions is graphed below ?

The graphed rational function is:

[tex]f(x)= \frac{6}{x + 2}[/tex]

Here we can see that we have a rational function of the form:

[tex]f(x) = \frac{q(x)}{p(x)}[/tex]

Now we notice two things, as x increases, we have a horizontal asymptote that tends to zero.

Then q(x) is a constant, let's say:

q(x) = k

We also can see that we have a vertical asymptote at x = -2, then:

p(x) = (x + 2)

So the rational function is:

[tex]f(x) = \frac{K}{x + 2}[/tex]

Now, notice that when x = 0, the curve intercepts the y-axis at y = 3, then if we evaluate the function in x = 0 we must get:

[tex]f(0) = 3 = \frac{K}{0 + 2} = \frac{K}{ 2} \\\\3*2 = K = 6[/tex]

Then the rational function is:

[tex]f(x)= \frac{6}{x + 2}[/tex]

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Answer:

35.3

Step-by-step explanation:

please mark brainliest

Answer:

35.3

Step-by-step explanation:

Answer:

JL = 14

Step-by-step explanation:

N represents the center of the rhombus

Then

N is the midpoint of the diagonal (line segment) JL

Then

JL = 2 × NL

    = 2 × 7

    = 14

Answer:

first of all its not d since the y intercept is negitive

then its not b since its sloping down

so the slop is either 7/5 or 5/7

since rise/run it has to be 7/5

Hope This Helps!!!

Answer:

[tex]y = - \frac{3}{4}x + 3[/tex]

Step-by-step explanation:

the standard form of any straight line is:

y = m × x + c

where: y is the y value of the point

x is the x value of the point

m is the gradient/slope

SOLUTION

[tex]y = mx + c \\ 6 = - \frac{3}{4} ( - 4) + c \\ c = 3[/tex]

Answer:

c or b

Step-by-step explanation:

Answer:

Answer:B

Step-by-step explanation:

I did the test and got it right the person above help thx

Step-by-step explanation:

5x-16 = 3 (10+x)

=> x= 23

Answer:

Y=−4y/v +4x/v

Step-by-step explanation:

Divide each term in by v and simplify.

Answer:

$1503.08 per month

Step-by-step explanation:

The height of the building is 19.02 feet, for a 20-ft ladder to lean against the building at an angle of 72 degrees.

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angle triangle.

Let h represent the height of the building, hence:

sin(72) = h/20

h = 19.02 feet

The height of the building is 19.02 feet, for a 20-ft ladder to lean against the building at an angle of 72 degrees.

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The height reached by the ladder of height 20-ft. inclined at 72° is approximately 19.02-ft.

Length of the ladder = 20 feet

Angle between the ground and ladder = 72°

Height reached by the ladder = Required

Solution:

From the definition of the sine of an angle, we have;

[tex]sin (\theta) = \mathbf{ \frac{opposite \: side}{hypotenuse}} [/tex]

The length of the ladder = The hypotenuse side = 20 ft.

The opposite side to the angle 72° = The height reached by the ladder

Which gives;

[tex]sin (72 ^ {\circ})= \frac{height \: reached}{20} [/tex]

Height = 20 × sin(72°) = 19.02

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Hello,

2/9 - 1/9 = (2 - 1)/9 = 1/9

Answer:

Step-by-step explanation:

Answer:

[tex]y\ne-5[/tex]

Step-by-step explanation:

So you have the equation:

  [tex]x=\frac{10}{5+y}[/tex]. As you may know, you cannot divide by 0, so y has to be restricted in a way that the denominator is never equal to 0. So to find when y makes the denominator 0, simply set the denominator equal to 0, and solve for y. This gives you the equation: 5+y = 0, y=-5. So the y value CANNOT be equal to -5. Because it makes the denominator 0. so [tex]y\ne-5[/tex] would be the restriction.

Answer:

Question 5:

a) 65 degrees

b) 11

Question 6:

a) 15.6

b) 6.4

Question 7:

a) 10

b) 20

Question 8:

a) EF = 14.4

Question 9:

a) x = 6

b) y = 22.5

Step-by-step explanation:

tan is 15/8

Since cos = adjacent/ hypotenuse

Adjacent = 8

Hypotenuse = 17

Let's find opposite

Using the Pythagoras theorem

Opposite ^2 = Hypotenuse^2 - adjacent^2

Opposite = [tex]\sqrt{17^2 - 8^2}[/tex]

Opposite = [tex]\sqrt{289 - 64}[/tex]

Opposite = [tex]\sqrt{225}[/tex]

Opposite = 15

Tan = opposite/ adjacent

Tan = 15/ 8

Thus, tan is 15/8

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Answer:

The correct system of inequalities is b.

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is

[tex](\sqrt{2},\sqrt{-2}  )[/tex] and [tex]((7+\sqrt{2)} ,(7+\sqrt{-2}))[/tex]

We have given that,

f(x) = 2x^2 + x + 4

x                          g(x)      

-2                               1      

  -1                              3        

  0                              5      

  1                              7

  2                              9

A polynomial function is a relation where a dependent variable is equal to a  polynomial expression.

A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.

The general form of a polynomial expression is:

a₀ + a₁x + a₂x² + a₃x³ + ... + anxⁿ.

The highest power to a variable is the degree of the polynomial expression. When degree = 2, the function is a quadratic function.

When degree = 1, the function is a linear function.

The quadratic function is given to us:f(x) = 2x^2 + x + 4.

We need to determine the linear equation g(x).

Since it's a linear equation we use the two-point method to determine the equation.

y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)

We take the points g(-2) =1, g(-1) = 3

g(x) - g(1) = ((g(-2)-g(-1))/(-2+1))*(x-1)or,

g(x) - 1 = ((-2-(-1))/(-2+1))*(x-1)or, g(x) - 1 = -1(-x+1)or,

g(x) = x - 1 + 1 = x

∴ g(x) = x , is the linear function g(x)

We are asked to find the solution to the system of equations f(x) and g(x).To find the solution we need to check what is the common solution to both f(x) and g(x).

For that, we equate f(x) and g(x).2x^2 + x + 4 = x or, 2x² - x +x- 4 = 0or, 2x^2  - 4 = 02(x^2-2)=0x^2-2=0[tex]x^2-\sqrt{2}=0[/tex][tex](x-\sqrt{2}) (x+\sqrt{2})=0[/tex][tex](x-\sqrt{2})=0 \\x=\sqrt{2}  or x=-\sqrt{2}[/tex]g(-1) = 3(from the table)[tex]g(\sqrt{2})=\sqrt{2}  \ and \ g(\sqrt{-2}) =-\sqrt{2}[/tex][tex]f(\sqrt{2}) = 2(\sqrt{2} )^2 + (\sqrt{2} ) + 3\\=2(2)+\sqrt{2} +3\\=7+\sqrt{2}[/tex][tex]g(-\sqrt{2} )= 2(\sqrt{-2} )^2 + (\sqrt{-2} ) + 3\\=2(2)+\sqrt{-2} +3\\=7+\sqrt{-2}[/tex]

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is [tex](\sqrt{2},\sqrt{-2}  )[/tex] and [tex]((7+\sqrt{2)} ,(7+\sqrt{-2}))[/tex]

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Answer:

[tex]y = \frac{1}{2} x + \frac{5}{2} [/tex]

Step-by-step explanation:

Since the line with equation y = 1 - 2x has slope -2, we need to find the equation of the line with slope 1/2.

[tex]3 = \frac{1}{2} (1) + b[/tex]

[tex]3 = \frac{1}{2} + b[/tex]

[tex]b = \frac{5}{2} [/tex]

[tex]y = \frac{1}{2}x + \frac{5}{2} [/tex]

Answer:

Step-by-step explanation:

14+(−7)+7

Now −7 is the idea or the construct that is the complete opposite of 7, when it comes to additive regions. So, they would cancel out.

And we are left with

14.

Answer: x=1

Step-by-step explanation:

1/2+3/2=2^x

4/2=2^x

2=2^x

x=1

Here is the completed table:

                        Original  Ratio   Amount (g)

Sugar                       3                           18

Cinnamon                2                           12

Total topping          5                             30

Original ratio of Cinnamon = total topping - original ratio of sugar

5 - 3  = 2

Amount of Sugar = (12 x 3) / 2 =18g

Total toppings = 18 + 12 = 30g

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Hello,

Answer:

4,8

Step-by-step explanation:

what would be 12% of 40 ?

12% × 40 = 12/100 × 40 = 0,12 × 40 = 4,8

Answer:

The inverse of the given function is [tex]$t(d)=\frac{d}{50}$[/tex]. The time taken to travel 180 miles is 3.6 hours.

Step-by-step explanation:

It is given that a car travels at a constant speed of 50 miles per hour. A function for distance traveled is also given as d(t)=50t.

It is required to find the inverse of the function by expressing the time travel in terms of distance traveled and also find t(180).

To find the inverse, express time traveled in terms of distance traveled using normal algebraic methods and then substitute 180 for t and explain its results.

Step 1 of 2

The given function is d(t)=50t.

Consider d(t) as d and t as t(d) and rewrite the equation.

The rewritten function is d=50 t(d)

Divide by 50 on both sides of the equation.

[tex]$$\begin{aligned}&d=50 t(d) \\&\frac{d}{50}=\frac{50 t(d)}{50} \\&t(d)=\frac{d}{50}\end{aligned}$$[/tex]

Step 2 of 2

Substitute 180 for $t$ in the simplified expression and interpret the results.

[tex]$$\begin{aligned}&t(d)=\frac{d}{50} \\&t(d)=\frac{180}{50} \\&t(d)=3.6\end{aligned}$$[/tex]

The time taken to travel 180 miles is 3.6 hours.

sec ^6 A−tan ^6A=(1+tan ^2A−tan ^2 A)(1+tan ^4

A+2tan ^2 A+tan ^2 A+tan ^4 A+tan ^4 A)

sec ^6 A−tan ^6 A=1+3tan ^2 A+3tan ^4A

L.H.S. = R.H.S.

Hence proved

Step-by-step explanation:

♡´･ᴗ･`♡

Answer:

y < 3x + 2

Step-by-step explanation:

We will be solving this in slope-intercept form, which is a form that gives us the slope and the y-intercept of the graph explicitly:

[tex]y=mx+b[/tex], m is the slope and b is the y-intercept

We are given that everything to the left of the resulting line is shaded, so we know that the inequality sign will be < (less than). That already eliminates the second and fourth options. We also know the y-intercept, or the point where the graph crosses the y-axis and x is 0. because it is given to us (2, which comes from the point (0,2)). To figure out the slope, we can use the formula since we are given two points [(-3, -7) and (0, 2)] the line passes through. The formula, which is mapped out below, tells us that the slope is just the difference in rise (vertical movement) divided by the difference in run (horizontal movement).

[tex]m=\frac{-7-2}{-3-0} =\frac{-9}{-3} =3[/tex]

Now we have all the information we need to find the inequality. The slope is 3, the y-intercept is 2, and the sign is <. The first inequality fits these criteria, meaning the correct linear inequality is y < 3x + 2

Surface area of A = 50 square inches, S.A of B = 120 square inches, S.A of C = 60 square inches, S.A of D = 50 square inches, S.A of E = 60 square inches, S.A of F = 120 inches.

S.A of the box = 460 square inches.

A cuboid is a three dimensional solid shape made of 6 rectangles.

Analysis:

surface area of A = surface area of D which is the smallest from the diagram = 5 x 10 = 50 square inches

surface area of C = surface area of E = the second largest = 5 x 12 = 60 square inches

surface area of B = surface area of F = 10 x 12 = 120 square inches

surface area of shape = 2( 50 + 60 = 120) = 2(230) = 460 square inches.

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The function is decreasing on the interval (–3, ∞). Therefore, the correct option is B.

A linear function can be represented by a line. The standard form for this equation is: ax+b where,

a= the slope

b= the constant term that represents the y-intercept.

The domain of a function is the set of input values for which the function is real and defined.

Here, the function is decreasing on the interval (–3, ∞).

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In this case using the elimination method is actually easier, but the question asks you to use substitution method so....

2x+y= -10

3x-y=0

1st equation: It is better to isolate 2x on both sides because the y is going to be positive no matter what, 2x+y=-10 => y=-2x-10

If you isolated 3x for the 2nd equation, the y will be negative, and you have to divide the whole equation by -1 to make it positive

Now we got y=-2x-10, lets substitute it in the 2nd equation and solve for x:

3x-(-2x-10) = 0

5x+10=0

5x=-10

x=-2

Now lets solve for y:

3(-2)-y=0

-6-y=0

y=-6

Lets see if the same is applicable for 1st equation

2(-2)+(-6)=-10

-10=-10

Yess!!

(-2,-6) is the solution

The answer to the question is explained at the beginning

Hope it helps!

The values of a and b are 4 and -3

To solve for a, we make use of the function f(x).

x    f(x)

2     4

0     5

2     a

3     7

Remove the x values 0 and 3

x    f(x)

2     4

2     a

The above table implies that:

f(2) = 4 and f(2) = a

Substitute 4 for f(2) in f(2) = a

4 = a

Rewrite as:

a = 4

To solve for b, we make use of the function g(x).

x    g(x)

2     b

0     0

2     -3

3     -4

Remove the x values 0 and 3

x    g(x)

2     b

2     -3

The above table implies that:

f(2) = b and f(2) = -3

Substitute -3 for f(2) in f(2) = b

-3 = b

Rewrite as:

b = -3

Hence, the values of a and b are 4 and -3

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Complete question

Use the Symmetry of a Function to Find Coordinates

f is an even function             g is an odd function

x    f(x)                                        x             g(x)

2     4                                          2              b

0     5                                          0              0

2     a                                          2              -3

3     7                                          3              -4

Find a and b

Answer:

4, 3

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

A

I solved on paper it took me 45 mins