If g(x) = 3x − 4, what is the value of g−1(g(13))?

A. 17/3

B. 35

C. x+4/3

D. 13

The rate at which her shadow is lengthening is 2.5ft/sec

To get the rate of her shadow lengthening, we will use the similarity theorem of a triangle.

Find the triangle attached. From the triangle;

Substitute the sides as given in the diagram:

[tex]\frac{12}{x+a} =\frac{5}{x}\\12x = 5(x+a)\\ 12x=5x+5a\\7x = 5a[/tex]

Differentiate both sides with respect to t

[tex]7\frac{dx}{dt} = 5\frac{da}{dt} \\7\frac{dx}{dt}=5(3.5)\\7\frac{dx}{dt}=17.5\\\frac{dx}{dt} = 2.5ft/sec[/tex]

The rate at which her shadow is lengthening is 2.5ft/sec

Learn more on similar triangles here: https://brainly.com/question/2644832

The height of the tree will be 45 feet.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

A tree is standing next to a 40-foot-high building. the tree has an 18-foot shadow, while the building has a 16-foot shadow.

Let x be the height of a tree. Then we have

x / 18 = 40 / 16

x = 45 feet

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ2

Answer:

Deductive reasoning

Step-by-step explanation:

Given : John concludes that, since (x-5) is a factor of the polynomial [tex]x^2-25[/tex], if he performed the long division [tex](x^2-25)\div (x-5)[/tex], the remainder would be zero.  

To find : This is an example of ___________ reasoning [tex]x^2-25[/tex]?

Solution :

The above situation make conclusion when we know the fact that (x-5)

is the factor as the factor of polynomial divide it completely.

Therefore, This is the example of deductive reasoning.

Deductive reasoning is the process by which a person makes conclusions based on previously known facts.

Answer:

its B

Step-by-step explanation:

Answer:

B. [tex]\text{cos}(52^{\circ})[/tex].

Step-by-step explanation:

We have been given a right triangle. We are asked to complete our given statement.

[tex]\text{sin}(38^{\circ})[/tex] equals ___.

We will use identity [tex]\text{sin}(x)=\text{cos}(90-x)[/tex] to solve our given problem.

[tex]\text{sin}(38^{\circ})=\text{cos}(90^{\circ}-38^{\circ})[/tex]

[tex]\text{sin}(38^{\circ})=\text{cos}(52^{\circ})[/tex]

Therefore, [tex]\text{sin}(38^{\circ})[/tex] equals [tex]\text{cos}(52^{\circ})[/tex].

Answer:

11x^3 - 2x^2 + 3x + 11

Step-by-step explanation:

we need to find the sum of 4x^3 + 2x^2 - 4x + 3 and 7x^3 -4x^2 + 7x + 8

To find the sum we add both the polynomials

4x^3 + 2x^2 - 4x + 3 + 7x^3 -4x^2 + 7x + 8

To add the polynomials we combine like terms

4x^3 + 7x^3 = 11x^3

2x^2 - 4x^2 = -2x^2

-4x+7x= 3x

3+8 = 11

So final expression is 11x^3 -2x^2 +3x+11

Answer:

[tex]\theta[/tex] is located in 3rd Quadrant.

Step-by-step explanation:

We are given that [tex]cos\,\theta[/tex]  is negative  and [tex]tan\,\theta[/tex]  is positive

We have to find Quadrant in which [tex]\theta[/tex] is located.

We have 4 Quadrants.

In 1st Quadrant , All trigonometric ratios are positive.

In 2st Quadrant , sin and cosec are positive while others are negative.

In 3rd Quadrant , tan and cot are positive while others are negative.

In 4th Quadrant , cos and sec are positive while others are negative.

Therefore, According to given information [tex]\theta[/tex] located in 3rd Quadrant.

Answer:100,000,000 tons

word form: one hundred million tons

Step-by-step explanation:

r/5 - 6 = -1

add 6 to both sides

r/5 = 5

multiply both sides by 5

r = 5 *5 = 25

r = 25

The values of sine, cosine, and tangent for angle θ, where (1, -1) is on its terminal side, are sin(θ) = -1, cos(θ) = 1, and tan(θ) = -1, knowing that the point lies in the fourth quadrant.

To find the values of the sine, cosine, and tangent of an angle θ where the point (1, -1) is on its terminal side, we first recognize that this point lies in the fourth quadrant of the coordinate system. In this quadrant, cosine is positive, and sine and tangent are negative.

The point (1, -1) gives us the x and y coordinates on the Cartesian plane, which correspond to the lengths of the adjacent side and the opposite side of the right-angle triangle formed by the radius (hypotenuse) from the origin to the point, and the axes. Assuming we're dealing with a unit circle (which has a radius of 1), we can directly use the coordinates (1, -1) to find the cosine and sine:

Hence, for angle θ, cos(θ) is 1, sin(θ) is -1, and tan(θ) is -1.

To find out how many hits each player had, we set up a system of equations and solve for the variables. Pedro had 2474 hits and Ricky had 1197 hits.

To solve this problem, we need to set up a system of equations. Let's represent the number of hits Pedro had as x and the number of hits Ricky had as y. We are given that their combined hits is 2671, so we can write the equation:

x + y = 2671

Additionally, we are given that Pedro had 277 more hits than Ricky. This can be represented as:

x = y + 277

We can now substitute the second equation into the first and solve for y:

y + 277 + y = 2671

2y = 2394

y = 1197

Now we can substitute the value of y back into the first equation to solve for x:

x + 1197 = 2671

x = 2474

Therefore, Pedro had 2474 hits and Ricky had 1197 hits.

https://brainly.com/question/29050831

#SPJ12

when m = 5:

2k = 5+3

2k = 8

k = 8/2

k=4

when m = 7

2k = 7+3

2k =10

k = 10/2

k = 5

when m = 9

2k = 9+3

2k = 12

k = 12/2

k = 6

k = {4,5,6}

The given function 3xy = 27 is not a linear function.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

A linear function is defined as when the function has the highest degree of expression is 1, such as y = mx + c.

here,
Given function,
3xy = 27,

Simplifying the function,
3xy = 27
xy = 27/3
y = 9/x

Since, from the definition of the function, the given function is 9 reciprocal of x and is said to be a reciprocal function.

Thus, the given function 3xy = 27 is not a linear function.

Learn more about function here:

brainly.com/question/21145944

#SPJ2