Given the table below, write a linear equation that defines the
dependent variable, t, in terms of the independent variable, a.

The angle of elevation from the stake up to the tent pole is, 54.55°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A 19 ft rope is tied from the top of a tent pole, It is the hypotenuse length.

Also, The state is 11 feet away and it is the adjacent length.

We know, cos = adjacent/hypotenuse.

cos = 11/19.

Ф = cos⁻¹(0.58).

Ф = 54.55°.

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Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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To solve the given Bernoulli equation, we can use a substitution technique to transform it into a linear equation. By making a suitable substitution and simplifying the equation.

The Bernoulli equation is of the form y' + P(x)y = Q(x)y^n, where n is a constant.

In this case, the given Bernoulli equation is 3xy + 2y = 3x sin(?) y".

To solve this equation, we make a substitution by letting u = y^(1-n). Differentiating u with respect to x gives du/dx = (1-n)y^(-n)y'. Substituting this into the equation and simplifying, we obtain the linear equation (1-n)du/dx + (1-n)P(x)u = (1-n)Q(x).

Now we have a linear equation in terms of u, which can be solved using standard linear equation techniques. Once we find the solution for u, we can substitute it back into the expression u = y^(1-n) and solve for y in terms of x.

By following this substitution and solving process, we can find the solution for the given Bernoulli equation and express y in terms of x.

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Answer:

I would say it's B. false

Answer:

False

Step-by-step explanation:

Look at the inputs (x-values)

If the inputs are the same, the relationship is Not a function.

Inputs (x-values), cannot share the same output (y-values).

Example:

Inputs      Outputs

3              2    

2              5

8              5

3              6

In the input there are two 3's which causes this to not be a function.

(Outputs can have the same numbers repeating just not inputs.)        

Answer:

I'm sorry I wish if I could help you but not sure of the answe

Answer:

B.

Symmetric Property

Step-by-step explanation:

Answer:

x = 12.5

Step-by-step explanation:

The phrase "Twice the number of x"  = 2x

2x = 25 ⇒ Divide both sides by 2

2x ÷ 2 = 25 ÷ 2

x = 12.5

-Chetan K

Answer: 3/4 *3/4 *3/4 = 27/64 this is the proabability that is DOES snow every day. 1-27/64 = 37/64 this is the proabability that is DOES NOT snow EVERY day. 1/(4^3) = 1/64 IS the probability that is does not snow AT ALL for the 3 days.

Step-by-step explanation:

Answer:

y = 4x - 12

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = E(4, 4) and (x₂, y₂ ) = F(2, - 4)

m = \(\frac{-4-4}{2-4}\) = \(\frac{-8}{-2}\) = 4 , then

y = 4x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 4), then

4 = 16 + c ⇒ c = 4 - 16 = - 12

y = 4x - 12 ← equation of line

Answer:

y = -4x + 17

Step-by-step explanation:

Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.

The total cost  of he meat with tax and tip is $ 22.42

To calculate the total cost with tax and tip, we need to follow these steps:

multiply the meal cost by the tip rate. when  the tip rate is 18%, we have:

Tip amount = $19.00 * 0.18 = $3.42

Add the meal cost, sales tax, and tip amount to get the total cost:

Total cost = Meal cost + Sales tax + Tip amount

= $19.00 + $3.42

= $ 22.42

Therefore, the total cost with tax and tip is $22.42

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Input data

Last week

Coffee for $12.80

Current week

15 % Discount

How cost 2 3/4 pounds

Procedure

The total cost of coffee would be

Now let's apply the discount

d = discount

The final cost would be

The tatoal cost would be $ 29.92

Answer:

it going be b 65.75

Step-by-step explanation:

just did test

The total amount of money put down by Xi-ling monthly  is mathematically given as

y=65.75

Question Parameters:

Xi-ling has a net income that is 5% of her monthly salary of $2,315. Xi-ling would like to keep a net income of $50

Generally,  5% of her monthly salary   is mathematically given as

x=0.05*2315

x=115.75

Therefore, if she has a net income equal to 115.75

y=115.75-50

y=65.75

Xi-ling puts y=65.75 towards paying down debt each month.

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The triple integral is equal to ∫∫∫ f(x, y, z) dV using spherical coordinates is equal to 64π/21 .

Use spherical coordinates to evaluate this triple integral over the given region.

The region p < 2 is a sphere centered at the origin with radius 2.

In spherical coordinates, this region can be described by,

0 ≤ ρ ≤ 2

0 ≤ θ ≤ 2π

0 ≤ φ ≤ π

The volume element in spherical coordinates is ρ² sin φ dρ dφ dθ.

The triple integral can be written as,

∫∫∫ f(x, y, z) dV

= \(\int_{0}^{2}\int_{0}^{\pi}\int_{0}^{2\pi }\) (ρ² sin φ)(ρ⁴ sin²φ cos²θ sin²θ) dρ dφ dθ

= \(\int_{0}^{2}\int_{0}^{\pi}\int_{0}^{2\pi }\)  (ρ⁶ sin³φ cos²θ sin⁵ θ) dρ dφ dθ

= \(\int_{0}^{2}\)(ρ⁶/7) \(\int_{0}^{\pi }\) (sin³ φ) \(\int_{0}^{2\pi }\) (cos² θ sin⁵θ) dθ dφ dρ

The innermost integral evaluates to π/8.

The second integral can be evaluated using the substitution u = cos φ, du = -sin φ dφ, which gives,

\(\int_{0}^{\pi }\)(sin³ φ) dφ

= -\(\int_{1}^{-1}\)(1-u²) du

= 4/3

The outer integral evaluates to (2⁷)/7.

Triple integral is equal to

∫∫∫ f(x, y, z) dV

= (2⁷/7) (4/3) (π/8)

= (32/7)π/6

= 64π/21

Therefore, the triple integral is equal to ∫∫∫ f(x, y, z) dV = 64π/21 .

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Step-by-step explanation:

Hey there!

The equation of a st.line passing through point is;

(y + 6) = m1(x+3).........(i). [ Use one point formula]

y = -4x + 1............(ii)

Comparing 2nd equation with y = mx+c, we get;

Slope (m2) = -4.

For parallel lines;

\(m1 = m2\)

(i.e m1=m2 = -4)

Putting value of slope in 1st equation,

\((y + 6) = - 4(x + 3)\)

Smplify them to get equation.

\((y + 6) = - 4x - 12\)

\(y = - 4x - 12 - 6\)

\(y = - 4x - 18\)

Therefore the required equation is y = -4x-18.

Hope it helps..

The probability that they have an average weight of greater than 10 pounds and less than 15 pounds is 0.84134

In this question we have been given there are 250 dogs at a dog show who weigh an average of 15 pounds, with a standard deviation of 6 pounds. of 10 dogs are chosen at random.

We need to find the probability that they have an average weight of greater than 10 pounds and less than 15 pounds.

Given, μ = 12, σ = 8, n = 4

P(X > 8)

= P(z > (8 - 12 / 8/√4))

= P(z > -1)

= 1 - P(z ≤ -1)

= 1 - [1 - P(z ≤ 1)]

=  P(z ≤ 1)

= 0.84134

Therefore, the required probability is 0.84134

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Step-by-step explanation:

Continuous compounding formula

FV = PV e^(rt)      PV = $  700   r = .05  t = 12

FV = future value =  $ 700 e^(.05 * 12) = $ 1275.48

Answer:

The measurement of angle B is 135°

The measurement of angle A is 60°

The measurement of angle C is 75°

Step-by-step explanation:

Angle A is the same value of 60, Angle B is pretty much just 180 - 45, and so is angle C.

The limit of the \(\lim_{x \to \infty}\)(√(81x² + x) - 9x)  by simplifying it is equal to 1/18.

To find the limit of the expression\(\lim_{x \to \infty}\) (√(81x² + x) - 9x), simplify the expression first,

\(\lim_{x \to \infty}\)(√(81x² + x) - 9x)

= \(\lim_{x \to \infty}\)(√(81x² + x) - 9x) × (√(81x² + x) + 9x) / (√(81x² + x) + 9x)

= \(\lim_{x \to \infty}\) ((81x² + x) - (9x)²) / (√(81x² + x) + 9x)

= \(\lim_{x \to \infty}\) (81x² + x - 81x²) / (√(81x² + x) + 9x)

= \(\lim_{x \to \infty}\)x / (√(81x² + x) + 9x)

= \(\lim_{x \to \infty}\) (x / x) / (√(81x² + x) / x + 9x / x)

=\(\lim_{x \to \infty}\) 1 / (√(81 + 1/x) + 9)

As x approaches infinity, 1/x approaches 0.

Therefore, simplify the expression further,

\(\lim_{x \to \infty}\)1 / (√(81 + 1/x) + 9)

= 1 / (√81 + 9)

= 1 / (9 + 9)

= 1 / 18

Hence, the limit of the given expression as x approaches infinity is 1/18.

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The above question is incomplete, the complete question is:

Find the limit. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.) lim x→∞ (√( 81x² + x )- 9x)

The square is a useful technique in various mathematical applications, such as solving quadratic equations,  the Vertex of a parabola, or converting a quadratic equation into vertex form

The process of rewriting a quadratic equation so that one side is a perfect square trinomial is indeed called "completing the square." It is a technique used to solve quadratic equations and also to convert them into a specific form that makes further manipulation easier.

Completing the square involves manipulating the quadratic equation by adding or subtracting a constant term in order to create a perfect square trinomial on one side of the equation. The goal is to express the quadratic equation in the form of (x + p)² = q, where p and q are constants.

The steps to complete the square for a quadratic equation in the form ax² + bx + c = 0 are as follows:

1. Divide the equation by the coefficient of x², so that the coefficient becomes 1.

2. Move the constant term (c) to the other side of the equation.

3. Add the square of half the coefficient of x to both sides of the equation.

4. Factor the perfect square trinomial on the left side of the equation.

5. Take the square root of both sides of the equation.

6. Solve for x by setting up two separate equations, one positive and one negative.

Completing the square is a useful technique in various mathematical applications, such as solving quadratic equations, finding the vertex of a parabola, or converting a quadratic equation into vertex form. It allows for easier analysis and simplification of quadratic expressions and helps in understanding the properties of quadratic functions.

In summary, completing the square is the name of the process used to rewrite a quadratic equation so that one side is a perfect square trinomial. It involves manipulating the equation to create a squared binomial expression, making it easier to solve or analyze the quadratic equation.

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Answer:

28>x

Step-by-step explanation:

7>x/4

remove the denominator by multiplying both sides by 4

4×7>x/4×4

28>x

Answer:

B

Step-by-step explanation:

the change in y and x are the same between the three points.

Answer:

2

Step-by-step explanation:

Hey there!

The equation is asking us, c x c = 4

What is c?

Well the only number that is equal to 4 when you square it is 2

If billion dollars in taxes were collected in 2005, then 30 billion was collected in 2017.

In 2005 the population was 2 million and it had increased to 3 million by 2017.

If 20 billion dollars in taxes were collected in 2005 then we have to determine how much tax was collected in 2017.

The amount of taxes of the city is proportion to the population of that city.

Tax(T) = kP(Population)

where k is a constant.

In 2005 Population = 2 millions and T = 20 billion. So

20 = 2k

Divide by 2 on both side, we get

k = 10

In 2017 Population = 3 millions and k = 10. So the tax collection in 2017 is:

t = 10 × 3

t = 30 billion

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The complete question is:

The amount of taxes a city collects is proportional to the population of the city. In 2005 the population was 2 million and it had increased to 3 million by 2017. If 20 billion dollars in taxes were collected in 2005 how much was collected in 2017? billion dollars help?

Answer:

it doesn't change

Step-by-step explanation:

Rounded to the nearest inch, the length of the diagonal of the desktop screen is approximately 23 inches.

To find the length of the diagonal of the desktop screen, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Given:

One side of the desktop screen = 14 inches

The other side of the desktop screen = 18 inches

Let's denote the length of the diagonal as d.

Using the Pythagorean theorem, we have:

d² = 14² + 18²

d² = 196 + 324

d² = 520

Taking the square root of both sides to solve for d:

d ≈ √520

d ≈ 22.803

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The double integral of the function 1L 4x² dA over the region D can be found by following these steps: determine the limits of integration, set up the double integral, integrate with respect to y, integrate with respect to x, and calculate the result.

To evaluate the double integral of the function 1L 4x² dA over the region D, where D is the region in the first quadrant bounded by y = 7x and y = -x³, follow these steps:

1. Determine the limits of integration: To find the limits of integration, first find the points of intersection between y = 7x and y = -x³. Set the two functions equal to each other and solve for x:

7x = -x³
x³ + 7x = 0
x(x² + 7) = 0

The points of intersection are x = 0 and x² + 7 = 0 (which has no real solutions). So, the limits of integration for x are [0, x₁], where x₁ is the positive root of x² + 7 = 0.

2. Set up the double integral: The double integral can be set up as follows:

∬ₐᵦ 4x² dy dx

Here, a and b represent the limits of integration for x (0 and x₁), and α(y) and β(y) represent the limits of integration for y.

3. Integrate with respect to y: Since there is no y in the function 4x², the integral with respect to y becomes:

∫ₐᵦ (4x²) * (β(y) - α(y)) dx

The functions y = 7x and y = -x³ can be rewritten as x = y/7 and x = \(-y^{\frac{1}{3} }\) respectively. So, β(y) = y/7 and α(y) = \(-y^{\frac{1}{3} }\). Thus, the integral becomes:

∫₀ˣ₁ (4x²) * (y/7 - (\(-y^{\frac{1}{3} }\))

4. Integrate with respect to x: Now, we need to integrate the function with respect to x:

∫₀ˣ₁ (4x²) * (y/7 - (\(-y^{\frac{1}{3} }\)) dy = (4/3)x³(y/7 - \((-y^{\frac{1}{3} })\) evaluated from x=0 to x=x₁.

5. Calculate the result: After evaluating the expression, the result is the value of the double integral over the region D.

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The correct point-slope equation for the line that passes through the point (-4,-2) and is parallel to the line given by y = 5x + 44 is: A. y + 2 = 5(x + 4)

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since the line is parallel to y = 5x + 44, the slope is equal to 5.

At data point (-4, -2) and a slope of 5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-2) = 5(x - (-4))  

y + 2 = 5(x + 4)

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Answer: $200,000

Step-by-step explanation:

Simple interest equation:

A= P (1 +rt)

P= $100,000

r= 0.05%

t=  20 years

A= 100,000 (1+(0.05x20))

A= $200,000