Name the property that the statement illustrates.
If ZABC - ZDEF and ZDEF ZGHI, then ZABC - ZGHI.

Hello there! GraceRosalia is here to help! :)

(+2)=2

2+8=10

4-4=0

4+8=12

1+10=11

0+9=9

5-1-5

12-7=5

hope it helps

P(x) = -2x² + 130x - 2000 when x is the price of each game to make the game profitable, the price should be at least $ 25 and no more than $ 40.

Quadratic equations are polynomial equations of degree 2 in one variable of the form f(x) = ax2 + bx + c = 0, where a, b, c, R, and a 0 are all zeros. It is the generic form of a quadratic equation in which 'a' is referred to as the leading coefficient and 'c' is referred to as the absolute term of f. (x). The roots of the quadratic equation (,) are the values of x that fulfil the quadratic equation.

There will always be two roots to the quadratic equation. Roots might be real or fictitious in nature.

p(x) = -2x² + 130x - 2000

The game will be profitable if P (x) > 0.

-2x² + 130x - 2000 > 0

-x² + 65x - 1000 > 0

x² - 65x + 1000 > 0

x(x-25) - 40(x -25) > 0

x>25 x < 40.

Therefore, price should be at least $ 25 and no more than $ 40.

The values of variables that satisfy the given quadratic equation are referred to as its roots. In other words, if f() = 0, x = is a root of the quadratic equation f(x).

The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.

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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.

Answer:

Answer:

\(x = \frac{z-5}{y}\)

Step-by-step explanation:

1. Because the problem is asking to solve for x, we have to isolate that variable.

2. (Solving)

Step 1: Subtract 5 from both sides.

Step 2: Divide both sides by y.

Therefore, \(x = \frac{z-5}{y}\)! I hope this helped you.

The value of variable x that makes -4x-(-10 - 8x) = -(12x-14) true is 1/4. thus, option c is correct.

An equation's unknown numerical value is represented by a symbol (typically a letter) called a variable in algebra. X and Y, which are real-number unknowns, as well as z, which are complex-number unknowns, as well as t, r, and s are frequently used variables (arc length).

Given

-4x-(-10 - 8x) = -(12x-14)

-4x + 10 + 8x = -12x + 14

4x + 10 = 14 - 12x

4x + 12x = 14 - 10

16x = 4

x = 4/16

x = 1/4

Thus, Option C is correct, x = 1/4

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Answer: 25 pi

Step-by-step explanation:

Solution:

Step-1: Find the slope of the line.

Formula: Rise/Run = y₂ - y₁/x₂ - x₁

Step-2: Find the y-intercept of the line.

The y-intercept of the line is the point that intersects the y-axis.

Step-3: Create the equation.

Answer:

180

Step-by-step explanation:

Answer:

149°

Step-by-step explanation:

let the remaining side of the triangle a,

now,

63°+86°+a=180°(sum of angles of a triangle)

149°+a=180°

a=180°-149°

a=51°

again,

x+a=180°(being linear pair)

x+51°=180°

x=180°-51°

•°•x=149°

If the Levene's test for homogeneity of variances is significant when you run a t-test, indicating that the assumption of equal variances is violated, you should consider using alternative statistical tests that do not assume equal variances, such as Welch's t-test or a non-parametric test.

The Levene's test is used to assess whether the variances of different groups in a study are equal. When the test is significant, it indicates that the assumption of equal variances is violated, meaning that the variability between groups is not the same. In such cases, using a regular t-test that assumes equal variances may lead to incorrect conclusions.

To address this issue, you can employ alternative statistical tests that are more appropriate for unequal variances. One option is to use Welch's t-test, which does not assume equal variances and adjusts the degrees of freedom accordingly. This test provides reliable results even when variances differ significantly between groups.

Another option is to consider non-parametric tests, such as the Mann-Whitney U test, which do not rely on the assumption of equal variances or normal distribution. These tests are suitable when dealing with non-normal data or when the assumption of equal variances is violated.

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C 72°

Answer:

we have

f(c)=9/5C+32

now

22°C to °F

°C=22°

we have

f(c)=9/5C+32

f(c)=9/5*22+32=71.6≈72

answer is

22°C=72°F

Answer:  \(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boldsymbol{72^\circ F}\)

Step-by-step explanation:

\(\displaystyle\ \Large \boldsymbol{} f(c)=\frac{9}{5} c+32 \ \ in \ \ our \ \ case \\\\\\\\f(22)=\frac{9\cdot 22}{5} +32=39,6+32=7\underline1,6\approx72^\circ F\)

Given that,

The given equation is 5x + 2y= -10

To find,

Draw the graph for the above equation.

Solution,

We can first find the points of the above equation.

x     0      -2

y     -5     0

Now plot the points in the graph.

The attached figure shows the graph for this equation. The points are (0,-5) and (-2,0).

Answer:

You did! well done

Step-by-step explanation:

Given that ∠A = 37°, ∠C = 72°, and b = 18, we can use the Law of Sines to solve the triangle and find the missing values. We need to determine ∠B, side a, and side c. ∠A represents the angle opposite side a, ∠B is opposite side b, and ∠C is opposite side c.

To find ∠B, we can use the fact that the sum of angles in a triangle is 180°. Therefore, ∠B = 180° - ∠A - ∠C. Substituting the given values, ∠B = 180° - 37° - 72° = 71°. To find side a, we can use the Law of Sines: a/sin(∠A) = b/sin(∠B). Plugging in the known values, we have a/sin(37°) = 18/sin(71°). Solving for a, we find a ≈ 11.73. To find side c, we can use the Law of Sines again: c/sin(∠C) = b/sin(∠B). Substituting the given values, we have c/sin(72°) = 18/sin(71°). Solving for c, we find c ≈ 18.91.

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Answer:

The slope is 3/2, and the y-intercept (b) is -1

Step-by-step explanation:

The slope-intercept form is y=mx+b. m is the slope and b is the y-intercept.

Answer:

The correct answer is $6,373.02.

We can use the formula for present value of an annuity:

PV = PMT x ((1 - (1 + r/n)^(-n*t)) / (r/n))

Where PV is the present value, PMT is the monthly payment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the values, we get:

PV = 300 x ((1 - (1 + 0.12/12)^(-12*2)) / (0.12/12))

PV = $6,373.02

Therefore, the present value of Maria's investment is $6,373.02.

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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Given parametric equations are x(t) = Ln(t) and y(t) = (Ln(t))^2. We have to graph the given parametric equations using ln restrictions without a calculator or desmos.

Here, we are going to find the value of t, which helps us to graph the given parametric equation using ln restrictions.Step-by-step explanation to find the value of t are:We have,

x(t) = Ln(t) ⇒ t = e^x(t) ....(1)y(t) = (Ln(t))^2⇒ t = e^(y(t)/2) ...

.(2)From (1) and (2),

we get e^x(t) = e^(y(t)/2)e^(2x(t)) = y(t) ...

(*)We know that the domain of ln x is (0, ∞). Let's determine the range of x(t) and y(t):From equation (1), if t → 0, then x(t) → - ∞From equation (1), if t → ∞, then x(t) → ∞From equation (2), if t → 0, then y(t) → 0From equation (2), if t → ∞, then y(t) → ∞Now,

we can graph the given parametric equations using the following steps: Assign values to t such as

t = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, .7, 0.8, 0.9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Step 2: Calculate x(t) and y(t) corresponding to t values.Step 3: Plot the points obtained in step 2.Step 4: Join all the points obtained in step 3 using a smooth curve.The graph of the given parametric equation is shown below.

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Answer:

x= 12

Step-by-step explanation:

First, we can note that the angles in a pentagon add up to 540°

We can, using the image below, conclude that angles a+b+c+d+f=540

Furthermore, a is on a straight line with 7x+4, and so on, so

180-(7x+4)= a

176-7x=a

180-(4x+1) = b

179-4x = b

180-(9x-6) = c

186 - 9x = c

180 - (4x+9) = d

171 - 4x = d

180 - (5x+4) = f

176 - 5x = f

a+b+c+d+f = 540

176-7x + 179-4x + 186 - 9x + 171 - 4x + 176 - 5x = 540

888 - 29x = 540

348 = 29x

x = 12

Determining (a) a and b by the method of least squares:  a = 1.084 and b = 3.061. (b) The standard deviations of a and b:  σ_a = 0.107 and σ_b = 0.090. (c) To plot the fit on log-log paper, logarithm of both sides of the equation y = a sin(2Tx) to get ln(y) = ln(a) + 2T ln(x) and plot ln(y) against ln(x).

(a) Using the method of least squares, the values of a and b can be determined by minimizing the sum of the squares of the residuals between the data and the function y = a sin(2Tx). Solving for a and b, we get a = 1.084 and b = 3.061.

(b) The standard deviations of a and b can be calculated using the following equations:

σ_a = √(Σ(residuals²)/(n-2)) * √(1/(nΣ(x²)-Σ(x)²))

σ_b = √(Σ(residuals²)/(n-2)) * √(n/(nΣ(x²)-Σ(x)²))

Using the given data and the values of a and b from part (a), we get σ_a = 0.107 and σ_b = 0.090.

(c) To plot the fit on log-log paper, we can take the natural logarithm of both sides of the equation y = a sin(2Tx) to get ln(y) = ln(a) + 2T ln(x) and plot ln(y) against ln(x). The resulting plot should be a straight line with slope 2T and intercept ln(a). We can then plot the given data on the same log-log paper and compare the fit with the data.

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Complete question:

The following data follows the functional form y-ax sin(2Tx)

X 0.25 0.75 1.25 1.75 2.25 2.75

Y 3.09 -1.21 0.84 -0.69 0.49 -0.44

(a) Determine a and b by the method of least squares

(b)Determine  the standard deviations of a 'and b' namely, the corresponding constants of the linearized fit.

(c) Plot the fit on log-log paper along with the data.

The correct option is (c). If the coefficient of correlation is -.4, then the slope of the regression line must be negative.

The coefficient of correlation tells us about the direction and strength of the linear association between two variables. It is used to determine how strong or weak a relationship is between two variables. The coefficient of correlation ranges between -1 to 1.

If the correlation coefficient is negative, then it tells us that as the value of one variable increases, the value of the other variable decreases. That is, the variables move in the opposite direction. When the slope of the regression line is negative, it indicates that as the value of the independent variable increases, the value of the dependent variable decreases. Therefore, the correct answer is option (c).

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Answer:

y + 9 = -2(x - 10)

The correct answer is d.

The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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To verify Stokes's Theorem, we need to evaluate the line integral of the vector field F around the closed curve C and the double integral of the curl of F over the surface S enclosed by C.

Given the vector field F(x, y, z) = (-y + z)i + (x - z)j + (x - y)k and the surface S defined by z = √(1 - x² - y²), we can use Stokes's Theorem to relate the line integral and the double integral.

First, let's calculate the line integral of F along the closed curve C. We parameterize the curve C using two parameters u and v:

x = u,

y = v,

z = √(1 - u² - v²),

where (u, v) lies in the domain of S.

Next, we need to compute the dot product F · dr along C:

F · dr = (-v + √(1 - u² - v²))du + (u - √(1 - u² - v²))dv + (u - v)d(√(1 - u² - v²)).

To calculate the line integral, we integrate this expression over the appropriate limits of u and v that define the curve C.

To evaluate the double integral of the curl of F over the surface S, we need to compute the curl of F:

curl(F) = (∂Q/∂y - ∂P/∂z)i + (∂R/∂z - ∂P/∂x)j + (∂P/∂y - ∂Q/∂x)k,

where P = -y + z, Q = x - z, and R = x - y.

Substituting these values, we can find the components of the curl:

curl(F) = (2x - 2y)j + (2y - 2z)k.

Next, we calculate the double integral of the curl of F over the surface S by integrating the components of the curl over the projected region of S in the xy-plane.

By comparing the results of the line integral and the double integral, we can verify Stokes's Theorem.

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Answer:

centre =

diameter = ab

radius = (ab)/2

Step-by-step explanation: hope this helps

Answer:

a = 35

Step-by-step explanation:

\(a^2+b^2=c^2\\a^2+12^2=37^2\\a^2+144=1369\\a^2=1225\\a=35\)

The calculated volume of the model space is 1657.92 cubic inches

From the question, we have the following parameters that can be used in our computation:

The model space made from:

The volume of the model space is calculated as

Volume = Cone + Cylinder + Hemisphere

Using the volume formulas, we have

Volume = 1/3πr²h + πr²h + 2/3πr³

Substitute the known values in the above equation, so, we have the following representation

Volume = 1/3 * 3.14 * 6² * 8 + 3.14 * 6² * 8 + 2/3 * 3.14 * 6³

Evaluate

Volume = 1657.92

Hence, the volume of the model space is 1657.92 cubic inches

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Answer:

Left side simplifies to (-2/3)^1 and the right side simplifies to (-2/3)^(-n) which means 1 = -n so n = -1.

Antonio is 6 years old, and Alberto is 10 years old.

Solution: Let's assume that Antonio's age is x. Therefore, Alberto's age is x+4 (since Alberto has four more years than Antonio). Now, as the product of their ages is 60, we can make an equation out of it: x(x+4) = 60x² + 4x - 60 = 0(x+10)(x-6) = 0. Either (x+10) = 0 or (x-6) = 0. Hence, x = -10 or x = 6. But we can see that it's not possible to have negative age. Therefore, we can use x=6. That means Antonio's age is 6 years old. Then, Alberto's age is x+4=6+4=10 years old.

Equations act as a scale of balance. If you've ever seen a balancing scale, you know that it needs to have an equal amount of weight on both sides in order to be deemed "balanced". The scale will tip to one side if we just add weight to one side, and the two sides will no longer be equally weighted. Equations use the same reasoning. Anything on one side of the equal sign must have the exact same value on the opposite side in order for it to not be considered unequal.

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