3. Write the equation of the line passing through (5,-3) and ( -4,4).​

Answer:

Maybe the answer will be C. P ( A and B )

explanation:

I think it is OPTION C , P(A and B)

as this is the only option which has the value of 80, which we got from the table...

The scale factor from the scale drawing to the actual triangle is; 1/3

The area of a triangle is calculated using the formula;

A = ¹/₂bh

Where;

A is area.

b is base.

h is height.

The two sides of the rectangle are 6 units and 3 units. Use the measurements in the formula. "u" is for units.

Thus;

A = ¹/₂(6)(3)  

A = 9 square units

The scale factor, represented by the variable "k", tells you how much a shape enlarged or reduced. If "k" is greater than 1, the shape enlarged. If "k" is greater than 0 and less than 1, the shape reduced

In this case, since the drawing is smaller than the actual triangle, the scale factor will be a fraction less than 1 and greater than 0.

The scale factor is used for side length. When it's used to find a side length, we use "k" multiplied by a side. Since the information we know is area, we find k² first, then isolate "k".

Divide the depicted triangle area by the actual area.

k² = 9 ÷ 81

k² = 1/9

√k² = √(1/9)

k = 1/3

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Answer:

$0.75 per pound

Step-by-step explanation:

To find the unit rate, divide the price by the amount you have.

14.99/20 = 0.7495

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

Given the equation x^2 = 2y.

The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:

To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].

Now we need to find the value of x that will minimize this expression.

We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.

Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T

he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

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Answer:

b. F' (3, 0), G' (-6, -1), H' (-5, -3)

To use spherical coordinates, we need to express x, y, and z in terms of ρ, θ, and φ. The cone z = x2 y2 can be expressed in spherical coordinates as ρ cos(φ) = ρ2 sin2(φ), which simplifies to ρ = sin(φ)/cos(φ) = tan(φ).

The lower sphere has radius 1, so ρ = 1, and the upper sphere has radius 6, so ρ = 6.

Therefore, the limits of integration are 0 ≤ ρ ≤ 6, 0 ≤ θ ≤ 2π, and 0 ≤ φ ≤ arctan(1/6).

The volume element in spherical coordinates is ρ2 sin(φ) dρ dφ dθ, so we can express the integral as:

∫∫∫ e^(x^2+y^2+z^2) dv = ∫₀²π ∫₀^(arctan(1/6)) ∫₀⁶ e^(ρ^2) ρ² sin(φ) dρ dφ dθ

We can evaluate the integral by first integrating with respect to ρ:

∫₀⁶ e^(ρ^2) ρ² sin(φ) dρ = [1/2 e^(ρ^2)]₀⁶ sin(φ) = (1/2)(e^(36) - 1) sin(φ)

Next, we integrate with respect to φ:

∫₀^(arctan(1/6)) (1/2)(e^(36) - 1) sin(φ) dφ = (1/2)(e^(36) - 1)(1 - cos(arctan(1/6))) = (1/2)(e^(36) - 1)(1 - 6/√37)

Finally, we integrate with respect to θ:

∫₀²π (1/2)(e^(36) - 1)(1 - 6/√37) dθ = 2π(1/2)(e^(36) - 1)(1 - 6/√37) = π(e^(36) - 1)(1 - 6/√37)

Therefore, the value of the integral is π(e^(36) - 1)(1 - 6/√37).

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Answer:

The 1st step in evaluating the expression is doing the equation in the paranthesis. PEMDAS states we do the paranthesis 1st.

Answer: 360% - 7 x 180 rotation

Step-by-step explanation: your welcome

This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Solving for the area and scale factor we have:

L= 5 units

W = 2 units

A = (5 x 2)

A = 10 square units.

A= (Scale factor of  L * W)*  L * W

= (2 x 2 x 5 x 2)

A = 40 square units.

A= (Scale factor of  L * W)*  L * W

= (3 x 3 x 5 x 2)

A= 90 square units

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When the confidence level is reduced from 99% to 95%, the confidence interval for the population mean mu based on the given data will likely be wider. The correct option is: "The confidence interval will be wider."

The width of a confidence interval is influenced by the desired level of confidence. A higher confidence level requires a wider interval to capture a larger range of possible population means.

In this case, when the confidence level decreases from 99% to 95%, the interval needs to be narrower to accommodate the reduced confidence requirement.

Since a 99% confidence interval is wider than a 95% confidence interval, reducing the confidence level to 95% will result in a wider confidence interval for the population mean mu based on the given data.

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The value of the expression is 9.

In this question given, we have been given the equation and the values of the letters in the equation that is given. Since we are given the expression, g=2, r=3, and t=11, then we have to slot in the values into the equation and this will be:

r² + (g³ - 8) × 5

= 3² + (2³ - 8) × 5

= 9 + [(8 - 8) × 5]

= 9 + (0 × 5)

= 9 + 0

= 9

Therefore, based on the calculations above, the answer is 9.

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It takes 53 years until we run out of gas.

Given,

Reserves of natural gas = 6500 TCF

Consumption per year = 123 TCF

Therefore,

years left ( x )= Reserves of natural gas / Consumption per year  

                     = 6500/123

                     = 52.8 years

                  x = 53 years approximately

So, it takes 53 years until we run out of gas at this rate of consumption.

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The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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Answer:

Step-by-step explanation:

$1.20 dollars

The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³

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

The base of the pyramid is x cm while the height is x + 2, hence:

Volume of pyramid = (1/3) * area of square base * height = (1/3) * x * x * (x + 2) = (x³ + 2x²)/3 cm³

The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³

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Answer:

43560 I think

Step-by-step explanation:

20 x 11 x 11 x 18

The estimated answer to 78x11.6/391 by rounding each number to 1 significant figure is 2.

By rounding each number to 1 significant figure, we get: 78 -> 80 11.6 -> 10 391 -> 400 Now, we can estimate the answer to 78x11.6/391 by using the rounded numbers: 80x10/400 = 800/400 = 2 Therefore, the estimated answer to 78x11.6/391 by rounding each number to 1 significant figure is 2.

Remember, when rounding a number to 1 significant figure, we look at the first non-zero digit and round it up if the next digit is 5 or greater, or round it down if the next digit is 4 or less.

For example, the number 78 is rounded to 80 because the next digit after the first non-zero digit (7) is 8, which is greater than 5. Similarly, the number 11.6 is rounded to 10 because the next digit after the first non-zero digit (1) is 1, which is less than 5.

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Answer:

4

Step-by-step explanation:

250 - 10 = 240

240/50 = 4.8

You cannot buy 8/10 of a net meaning you can only buy 4

Answer:

4 net in total

Step-by-step explanation:

take ten away and you have $240 and 50+50=100 so 100+100=200

LCM of 15 and 35 = 105

3x5x7 = 105

Answer:

3x5x7

Answer:

Step-by-step explanation:

The integral of the given expression is equal to (n/588)ln|18 - 49y| + (7n/588)ln|147(18 - 49y)| + (n/784)(18 - 49y) + C, where ln denotes the natural logarithm and C is the constant of integration.

First, let's consider the constant term (n/4). The integral of a constant term with respect to y is obtained by multiplying the constant by y and adding the constant of integration C. Therefore, the integral of n/4 is (n/4)y + C.

Next, we'll focus on the rational function (14y - 49y^2) / (147(18 - 49y)). To integrate this, we consult the Table of Integrals and identify a similar form:

∫(1/(a - bx)) dx = (1/b)ln|a - bx| + C,

where a, b, and C are constants. By comparing this form with the rational function in our integral, we can see that a = 18, b = -49, and the constant term is 147. Applying the formula, we have:

∫(14y - 49y^2) / (147(18 - 49y)) dy = (1/(-49))(14/147)ln|18 - 49y| + C1,

which simplifies to -(1/7)ln|18 - 49y| + C1, where C1 is another constant of integration.

Now, combining the results for both terms, we get:

∫(n/4 + 14y - 49y^2) / (147(18 - 49y)) dy = (n/4)y - (1/7)ln|18 - 49y| + C1.

To simplify further, we can rewrite C1 as C2 = C1 + (n/4), yielding:

∫(n/4 + 14y - 49y^2) / (147(18 - 49y)) dy = (n/4)y - (1/7)ln|18 - 49y| + C2.

Finally, we can simplify the expression by combining the constants:

∫(n/4 + 14y - 49y^2) / (147(18 - 49y)) dy = (n/4)y - (1/7)ln|18 - 49y| + (7n/28) + C.

Thus, the integral is equal to (n/588)ln|18 - 49y| + (7n/588)ln|147(18 - 49y)| + (n/784)(18 - 49y) + C, where ln denotes the natural logarithm and C is the constant of integration.

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To find direction numbers for the line of intersection of planes x y z = 3 and x z = 0, find the normal vectors of the first plane and the second plane. Then, cross product the two vectors to get the direction numbers: 1, 0, -1.

To find the direction numbers for the line of intersection of the planes x y z = 3 and x z = 0, we need to find the normal vectors of both planes.

For the first plane, x y z = 3, we can rearrange the equation to the form Ax + By + Cz = D, where A = 1, B = 1, C = 1, and D = 3. The normal vector of this plane is (A, B, C) = (1, 1, 1).

For the second plane, x z = 0, we can rearrange the equation to the form Ax + By + Cz = D, where A = 1, B = 0, C = 1, and D = 0. The normal vector of this plane is (A, B, C) = (1, 0, 1).

To find the direction numbers of the line of intersection, we can take the cross product of the two normal vectors:

Direction numbers = (1, 1, 1) x (1, 0, 1) = (1 * 1 - 1 * 0, 1 * 1 - 1 * 1, 1 * 0 - 1 * 1) = (1, 0, -1).

Therefore, the direction numbers for the line of intersection are 1, 0, -1.

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The answer is letter A. (x + 4)(x - 2)

The answers are the black circles, just we need to change the signs as i did.

Answer:

A

Step-by-step explanation:

Answer:

We recommend to use a rectangular set of coordinates to make the proof  easier to complete.

Step-by-step explanation:

A right triangle is a triangle whose leg are orthogonal to each other, then we need to use a set of coordinates whose axes are orthogonal to each other. Hence, we recommend to use a rectangular set of coordinates to make the proof  easier to complete.

The integer that represents the balance owed on the credit card is -257.

The process of subtracting one number from another is known as subtraction.

Given that, the person owns $225 on the credit card.

The balance owed on a credit card is represented by a negative sign, therefore, the balance on the credit card is.

-255

The balance after making a $55 payment is,

-255 + 55

Now, the balance after purchasing stuff of $87 is,

-255 + 55 + 87

= -257

Hence, the integer that represents the balance owed on the credit card is -257.

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Your answer will be letter C [-4, ∞)

Answer: y=-3x-5

Step-by-step explanation:

(0,-5)   (-1,-2)

\(\displaystyle\\\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}\)

x₁=0     x₂=-1     y₁=-5    y₂=-2

\(\displaystyle\\\frac{x-0}{-1-0}=\frac{y-(-5)}{-2-(-5)} \\\\\frac{x}{-1} =\frac{y+5}{-2+5} \\\\-x=\frac{y+5}{3}\)

Multiply both parts of the equation by 3:

\(-3x=y+5\\\\-3x-5=y+5-5\\\\-3x-5=y\)

\(Thus,\ y=-3x-5\)

The value for the expression is obtained as -7/4.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

To evaluate the expression 12.5 - 31/2 + 1 1/4, we need to convert the mixed number 1 1/4 to an improper fraction -

1 1/4 = 5/4

Now we can substitute the values into the expression and simplify -

Substitute 1 1/4 with 5/4 -

= 12.5 - 31/2 + 1 1/4

= 12.5 - 31/2 + 5/4

Convert 12.5 to an improper fraction with a denominator of 2 -

= 25/2 - 31/2 + 5/4

Get a common denominator of 4 -

= (50)/(4) - (62)/(4) + 5/4

= 55/4 - 62/4

= -7/4

Therefore, the value is -7/4.

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Answer: y=1/3x-6

9y−3x=−54

9y=3x-54

y=1/3x-6

Answer:

$9

Step-by-step explanation:

5 T-shirts, each for $5 is $25

$10 + 8($3) = $10 + $24 = $34

$34 - $25 = $9

Ken owes the store $9