What is the slope of each of these three graphs?

Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

        |\

        | \

   h    |  \   9 ft

        |   \

        |    \

        |     \

        -------

        6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.

The direct method of Lyapunov is a technique used in the analysis of the stability of a dynamical system. It involves the use of a Lyapunov function to determine whether a system is stable or not.

A Lyapunov function is a scalar function V(x) that is defined on the state space of a dynamical system, where x is the state of the system. The function is chosen such that it is positive definite, i.e., V(x) > 0 for all x except possibly at the origin, where V(x) = 0. The time derivative of the Lyapunov function along the trajectories of the system, denoted by V'(x), is also chosen to be negative definite or negative semi-definite, i.e., V'(x) < 0 or V'(x) ≤ 0 for all x except possibly at the origin.

The direct method of Lyapunov uses this Lyapunov function to determine the stability of the system. If a Lyapunov function can be found that satisfies the above conditions, then the system is said to be stable or asymptotically stable, depending on whether V'(x) is negative definite or negative semi-definite, respectively. If a Lyapunov function cannot be found, then the stability of the system cannot be determined using this method.

In addition to determining stability, the direct method of Lyapunov can also be used to determine instability. If a Lyapunov function can be found that satisfies the above conditions, but with V'(x) positive definite or positive semi-definite instead of negative definite or negative semi-definite, respectively, then the system is unstable.

Overall, the direct method of Lyapunov provides a powerful tool for analyzing the stability of a wide range of dynamical systems, including linear and nonlinear systems, time-invariant and time-varying systems, and continuous and discrete-time systems.

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the probability that the next 3 cards are also spades is 0.0156.

There are 13 spades in a deck of 52 cards. The probability of each card being a spade is 13/52 or 0.25. The probability that the next 3 cards are also spades is 0.25 x 0.25 x 0.25 = 0.016. Therefore, the probability that the next 3 cards are also spades is 0.0156.

1. Calculate the probability of one card being a spade: 13/52 or 0.25

2. Calculate the probability of the next 3 cards being spades: 0.25 x 0.25 x 0.25 = 0.016

3. Round the answer to four decimal places: 0.0156

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Answer:

4

Step-by-step explanation:

Line f is 4 units from the x-axis.

Answer:

7.3333, so if you round down, 7.

Step-by-step explanation:

5 1/2 divided by 3/4 is 7.3333

Answer:

0.95

Step-by-step explanation:

The points after the decimal place are SF (significant figures/digits)

Answer:

Step-by-step explanation:

2-(-1\8)±-7\4 then

2 plus 1\8 plus -7\4

2 plus 1\8 plus -14\8

2 -13\8

2= 16/8

3\8?

Answer:

3/8

Step-by-step explanation:

Substitute given information into given equation

b=2, c=-7/4

2-(-1/8) + - 7/4

Make 2 into 16/8 (by multiplying it by 8/8 To make denominator the same)

16/8 -(-1/8) + -7/4

17/8 (Because when negative and negative will make positive)

17/8+ -7/4

Make -7/4 into -14/8 (by multiplying it by 2/2 To make denominator the same)

17/8 -14/8 (Because negative and positive will make negative)

3/8 is the final answer

I hope this helps, dont hesitate to ask for any question.

Mark me as brainliest is appreciated.Tq!!

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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The area of the circular shaded area is of 116.113 cm².

The area of a circle of radius r is given by pi multiplied by the radius squared, as follows:

A = πr²

For this problem, the shaded area is the area of the larger circle subtracted by the area of the smaller circle. We have that:

Hence the area of the larger circle is given by:

Al = π(6.5)² = 132.732 cm².

The area of the smaller circle is given by:

As = π(2.3)² = 16.619 cm².

Hence the shaded area is given by:

A = Al - As = 132.732 - 16.619 = 116.113.

The shaded area is of 116.113 cm².

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Answer:

\( 770 = 5\pi r^2\)

If we divide both sides by \( 5\pi\) we got:

\( \frac{770}{5\pi} = r^2 \)

And taking square root we got:

\( r = \sqrt{\frac{770}{5\pi}}= 7.001 ft\)

And rounded to the nearest whole number we got 7 ft

Step-by-step explanation:

For this case we know that the hieght of a right cylinder is 5 ft and the volume is given by:

\( V = 5 \pi r^2 \)

And we know that the volume \( V = 770 ft^3\) and we want to solve for r so we can set up the following equation:

\( 770 = 5\pi r^2\)

If we divide both sides by \( 5\pi\) we got:

\( \frac{770}{5\pi} = r^2 \)

And taking square root we got:

\( r = \sqrt{\frac{770}{5\pi}}= 7.001 ft\)

And rounded to the nearest whole number we got 7 ft

\( \: \: \: \)

\(y = - 7\)

Step-by-step explanation:

\(y = x - 7\)

\(y = 0 - 7\)

\( = y - 7\)

Apply the slope-intercept formula y = mx + b. Two variables are the slope and y-intercept.

y = (1)x + (-7)

The slope is one, and the y-intercept is -7.

Answer:

340.2

Step-by-step explanation:

18.0 x 18.9 = 340.2

Answer:

18.0x18.9=340.2

Step-by-step explanation:

Answer:d

Step-by-step explanation:

The answer is d. None of the above is true.

To calculate velocity, we need to use the equation:

Velocity = M * P / Y

Given:

M = 1,000

P = 2.25

Y = 2,000

Plugging in the values:

Velocity = 1,000 * 2.25 / 2,000

Simplifying:

Velocity = 2.25 / 2

The result is:

Velocity = 1.125

Therefore, the correct answer is: d. None of the above is true.

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Answer:

10 cm wide, 20cm long

Step-by-step explanation:

That's what I got

Answer:

lol lots of luck

Step-by-step explanation:

Answer: A. 90° clockwise, E. 270° counterclockwise

Answer:

\(m=\frac{3}{5}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (8, 4)

Point (3, 1)

Step 2: Find slope m

The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.

When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.

Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.

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Answer: To find the x-intercept of a line, we set y equal to 0 and solve for x. To find the y-intercept of a line, we set x equal to 0 and solve for y.

For the line 5x + 17y = -25, we set y equal to 0 to find the x-intercept:

0 + 17y = -25

17y = -25

y = -25/17

Since we set y equal to 0, the x-intercept is (0, 0).

For the line 6x - 7y = -21, we set x equal to 0 to find the y-intercept:

6x - 7y = -21

-7y = -21

y = 21/7

Since we set x equal to 0, the y-intercept is (0, 21/7).

Therefore, the x-intercept of the line 5x + 17y = -25 is (0, 0) and the y-intercept of the line 6x - 7y = -21 is (0, 21/7).

Answer:

the cost that used to frame the math certificate is $847.80

Step-by-step explanation:

The computation of the cost that used to frame the math certificate is shown below:

= 27 wide × 20 tall × $1.57 per centimeter

= $847.80

Hence, the cost that used to frame the math certificate is $847.80

The value of \(\sqrt{x}(\pi-\sqrt{x} \cdot 17) x^2\) is \(\pi x^2 \sqrt{x}-17 x^3\)

\($$\begin{aligned}& \sqrt{x}(\pi-\sqrt{x} \cdot 17) x^2 \\& =x^2 \sqrt{x}(\pi-17 \sqrt{x})\end{aligned}$$\)

Apply the distributive law: \($\quad a(b-c)=a b-a c$\)

\($$\begin{aligned}& a=\sqrt{x} x^2, b=\pi, c=\sqrt{x} \cdot 17 \\& =\sqrt{x} x^2 \pi-\sqrt{x} x^2 \sqrt{x} \cdot 17 \\& =\pi x^2 \sqrt{x}-17 x^2 \sqrt{x} \sqrt{x} \\& 17 x^2 \sqrt{x} \sqrt{x}=17 x^3 \\& =\pi x^2 \sqrt{x}-17 x^3\end{aligned}$$\)

What is distributive law?

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true. For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

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Answer:

..........................................

Answer:

B

hope it helps

Answer:

What is the question??

Step-by-step explanation:

After factorization, the absolute value of the variable 'x' is 9.

What is factorization method?

The factorization method is used for the quadratic based equation whose highest degree is either two or more than two. Depending upon the degree of the variable, the number of factors are calculated. And by substituting the calculated value to check whether the answer is correct or not.

According to the question, the given linear equation is: |2x - 4| = 15

Now, to calculate the value of the variable 'x' by using factorization method. And to remove the bars which represent absolute value that means positive values

Required expression: |2x - 4| = 15

⇒ 2x = 15 + 4 = 19

⇒ x = 19/2 = 9.5

After factorization, the absolute value of the variable 'x' is 9.

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Step-by-step explanation:

Hey there!

Simply work with it.

As it is a Right angled triangle, taking angle 40° as a reference angle. Then,

Length of board = hypotenuse = 15 feet.

To find: height of ladder = perpendicular.

Now,

Taking sin ratio,

\( \sin = \frac{p}{h} \)

\(sin \: 40 = \frac{p}{15} \)

or, as in per the given sin value is 0.6428

so,

\(0.6428 = \frac{p}{15} \)

or, 15 × 0.6428 = p

or, p = height of ladder = 9.642.

Therefore, p = height of ladder = 10 feet. { rounding off we get 10 feet as answer}.

Hope it helps...

Answer:

Step-by-step explanation:

x          -  age of a son three years ago

3x        -  age of a father three years ago

x + 3      -  age of the son now

3x + 3       -  age of the father now

x + 3 + 5       -  age of the son in five years time

3x + 3 + 5       -  age of the father in five years time

in five years time, the father will be twice as old as his son, so:

3x + 3 + 5 = 2(x + 3 + 5)

3x + 8 = 2x + 16

3x - 2x = 16 - 8

  x = 8

x + 3 + 4       -  age of the son in four years time

8 + 3 + 4 = 15

3x + 3 + 4       -  age of the father in four years time

3×8 + 3 + 4 = 31    

the sum of their ages in four years time:

15 + 31 = 46

Answer: She would need 188 square inches of wrapping paper .

Step-by-step explanation:

Given:  The base of the box is a rectangle and has a length and width of 4in and 7in respectively.

The height of the box is 6 inches.

Surface area of cuboid = 2(lw+wh+hl) , where l = length , w = width and h = height.

Surface area of box = 2 (4 x 7+ 4 x 6 + 7 x 6)

= 2 (28+24+42)

= 2 (94)

= 188 square inches.

Hence,  she would need 188 square inches of wrapping paper .