If the slope is 26.5° what is the rise per meter

Answers

Answer 1

Answer: Rise / run = tangent of the angle.

Tan(26.5) = 0.49858... , so the rise per meter is about 1/2 meter.

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If sin α=(12/13), and cos α=(5/13), then tan α = ?

Can anyone answer question 15 and 16

Answers

15) (6x²y³)(3xy²z⁵) = 18x³y⁵z⁵

16) area of square with side lengths (x-3) units

area of a square = a²
A = (x-3)²
A = (x-3)(x-3)
A = x(x-3) -3(x-3)
A = x² - 3x -3x + 9
A = x² - 6x + 9

Area of a rectangle with a length of x units and a width of (x-5)units

Area of a rectangle = length * width
A = x * (x-5)
A = x(x-5)
A = x² - 5x

Value of x for Area of square and Area of rectangle to be equal.

Area of square = Area of rectangle
x² - 6x + 9 = x² - 5x
x² - x² - 6x + 5x = -9
-x = -9
x = -9/-1
x = 9

x² - 6x + 9 = x² - 5x
9² - 6(9) + 9 = 9² - 5(9)
81 - 54 + 9 = 81 - 45
90 - 54 = 36
36 = 36

Graph y = 5x and y = log5x on a sheet of paper using the same set of axes. Use the graph to describe the domain and range of each function. Then identify the y-intercept of each function and any asymptotes of each function. Explain also.

Answers

Answer:

1) For $y=5x$

A) Domain= $(-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]$

B) Range= $(-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]$

C) y-intercept = 0

D) Asymptote= No asymptote

2) For $y=log_5x$

A) Domain=Domain= $(0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]$

B) Range= $(-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]$

C) y-intercept = None

D) Vertical Asymptote: x=0

Step-by-step explanation:

Given : $y=5x$ and $y=log_5x$

Refer the graph attached.

1) In equation (1) $y=5x$

→The domain is the set of all possible values in which function is defined.

y=5x is a linear polynomial defined on all real numbers.

Domain= $(-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]$

→Range is the set of all values that function takes.

It also include all real numbers.

Range= $(-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]$

→y-intercept- Value of y at the point where the line crosses the y axis.

put x=0 in equation y=5x we get, y=0

Therefore, y-intercept = 0 (We can see in the graph also)

→An asymptote is a line that a curve approaches, but never touches.

Asymptote= No asymptote

2) Now in equation (2) $y=log_5x$

Domain= $(0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]$

because log function is not defined in negative.

Range= $(-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]$

y-intercept - None

Vertical Asymptote: x=0

A) Domain= (-∞, ∞) for all x

B) Range= (-∞, ∞) for all y

C) y-intercept = 0

D) Asymptote= No asymptote

A) Domain=(0, ∞) for all x > 0

B) Range= (-∞, ∞) for all y

C) y-intercept = None

D) Vertical Asymptote: x=0

Here, we have,

Function 1: y = 5x

Domain: The domain of this function is all real numbers because there are no restrictions on the values that x can take.

Range: The range of this function is also all real numbers because for every value of x, we can find a corresponding y value by multiplying it by 5.

Y-intercept: To find the y-intercept, we set x = 0 and solve for y. Substituting x = 0 into the equation, we get y = 5(0) = 0. Therefore, the y-intercept is (0, 0).

Asymptotes: There are no asymptotes in this linear function.

Function 2: y = log₅x

Domain: The domain of this function is all positive real numbers because the logarithm function is only defined for positive values of x.

Range: The range of this function is all real numbers because the logarithm function can produce any real number output.

Y-intercept: To find the y-intercept, we set x = 1 and solve for y. Substituting x = 1 into the equation, we get y = log₅(1) = 0. Therefore, the y-intercept is (0, 0).

Asymptotes: The logarithmic function has a vertical asymptote at x = 0 because the logarithm is undefined for x ≤ 0. Additionally, there is no horizontal asymptote.

When plotting these functions on the same set of axes, we will observe that the graph of y = 5x is a straight line passing through the origin (0, 0) with a slope of 5.

The graph of y = log₅x will appear as a curve that starts at the point (1, 0) and approaches the vertical asymptote x = 0 as x approaches zero.

The two graphs will intersect at the point (1, 0) because log₅1 = 0.

To learn more on function click:

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How many liters will a U.S. 6-quart container hold? Round your answer to the nearest hundredth

Answers

You are given volume of 6 USquart. You are required to convert this into liters and be rounded off to thenearest hundredth. Keep in mind that forvolume, every one liter is equal to 1.05669 US quart. So you need to divide the6 US quart. This is equal to 6.34014 liters. To round of the nearest hundredth,the ocation of the hundredth is the four in 6.34014. since after four iszero, the round off rule states that from 0-4, the preceding number remainsunchanged. So the final answer is 6.34 liters.

6 quarts can hold 6.34 liters.

ALGEBRA HELP !!!!! Which of the following is the simplest form of this expression? —photo attached

Answers

$\displaystyle \frac{ \sqrt[5]{a^4}}{ \sqrt[3]{a^2}}= \frac{a^{(4)/(5)}}{a^{(2)/(3)}}=a^{(4)/(5)- (2)/(3)}=a^{(12-10)/(15)}=\boxed{a^{(2)/(15)}}$

Answer is: A. a^(2/15)

Choose a method that can be used to solve this system of equations by elimination.2x - 2y = 24
4x + 7y = -40

1. Subtract 2x from both equations and solve the first equation for y.

2. Multiply the first equation by -2 and add the second equation.

3. Add the first equation to the second equation and subtract 6x from both sides of the equation.

4. Subtract 7y from the second equation and add the first equation.

Which one of these steps is the correct way of solving by elimination?

Answers

The method that should be selected is

2. Multiply the first equation by -2 and add the secondequation.

Elimination method:

In the elimination method, we can either add or subtract the equations to get an equation in one variable. At the time When the coefficients of one variable are opposites, so we can add the equations to eliminate a variable and when the coefficients of one variable are equal we can subtract the equations to eliminate a variable.

Learn more about an equation here: brainly.com/question/17599700

Answer:

Step-by-step explanation:

if we multiply the first equation by neg 2, the 4x's cancel out.

Tiffany pays $40 for 160 minutes of talk time on her cell phone. Hpw how many minutes of talk time does she get per dollar?

Answers

the answer is ............................4

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