HELP!! Triangle MNO is dilated to create triangle PQR on a coordinate grid. You are given that angle N is congruent to angle Q. What other information is required to prove that the two triangles are similar?

a. The Length of the fence around the field = perimeter of quarter circle is  892.7 ft.

b. The area of the outfield is 39,584 sq. ft..

Note that:

a. The length of the fence around the field = perimeter of the quarter circle fence

= 2r + 1/4(2πr).

r = 250 ft

Put in the value

The length of the fence around the field = 2(250) + 1/4(2 × π × 250)

= 892.7 ft.

b. Size of the outfield = area of the full field (quarter circle) - area of the infield (cicle)

= 1/4(πR²) - πr²

R = radius of the full field = 250 ft

r = radius of the infield = 110/2 = 55 ft

Put in the values

Size of the outfield = 1/4(π × 250²) - π × 55²

= 49,087 - 9,503

= 39,584 sq. ft.

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Answer: y = 1.8

x = -0.8

Step-by-step explanation:

From equation 1, x = -8 + 4y

Substitute this in equation 2,

3 (-8 + 4y) + 8y = 12

-24 + 12y + 8y = 12

20 y = 12+ 24

20 y = 36

y = 36/20

y = 1.8

Substitute value of y in any equation: x = -0.8

Answer:

see photo

Step-by-step explanation:

Arrange your terms

substitute

solve for y

solve for x

Answer:

x=3 and y=−2

Step-by-step explanation:

Multiply the first equation by 4,and multiply the second equation by 3.

4(2x−3y=12)

3(3x+4y=1)

Becomes:

8x−12y=48

9x+12y=3

Add these equations to eliminate y:

17x=51

Then solve17x=51for x:

17x=51

17x

17

=

51

17

(Divide both sides by 17)

x=3

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

2x−3y=12

Substitute3forxin2x−3y=12:

(2)(3)−3y=12

−3y+6=12(Simplify both sides of the equation)

−3y+6+−6=12+−6(Add -6 to both sides)

−3y=6

−3y

−3

=

6

−3

(Divide both sides by -3)

y=−2

Answer:

\((3,-2)\)

Step-by-step explanation:

\(2x-3y=12\)

\(2(3)-3(-2)=12\)

\(6--6=12\)        Two negative signs together makes a addition

\(3x+4y=1\)

\(3(3)+4(-2)=1\)

\(9-8=1\)            

The solution to this expression (√5 - 3√2)(√5 + 3√2) is equal to -13.

In Mathematics and Geometry, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:

a² - b² = (a + b)(a - b).

Where:

a and b represent numerical values (numbers or numerals).

Based on the information provided, we have the following mathematical expression:

(√5 - 3√2)(√5 + 3√2);

By comparison, we have the following:

(√5 - 3√2)(√5 + 3√2) = (a + b)(a - b)

a² - b² = (√5)² - (3√2)²

a² - b² = 5 - 18

a² - b² = -13.

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Answer:

The answer is 26 is after 34.

The pattern is x - 8 = y.

Step-by-step explanation:

Good luck! <3

The total number of garment to be replaced is 294

Percentage” is used to refer to a general relationship rather than a specific measure. Percentage can also be said as per 100 of something. Cent means 100.

The total garment in the warehouse is 14000 garments.

1.5% of the garments were damaged

= 1.5/100 × 14000

= 1.5 × 140

= 210 garments

0.6% were lost

= 0.6/100 × 14000

= 8400/100

= 84 garments

Each garments are replaced when they are lost or damaged.

Therefore the total number of garments replaced is

= 210 + 84

= 294 garments

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We need to identify the function among the given options which is guaranteed by the Extreme Value Theorem to have an absolute maximum on the interval [0,4].What is the Extreme Value Theorem? The extreme value theorem says that a function on a closed interval must have a maximum and a minimum value.

The correct option is-C

In other words, there is an absolute maximum and an absolute minimum value. It is an important theorem in calculus. Let's check the given options for the absolute maximum on the interval [0,4]:a. y=tan⁡x As the function

f(x)=tanx is not continuous on the interval [0,4], it is not guaranteed to have an absolute maximum on the interval [0,4]. Therefore, option a is incorrect .b

. y=tan⁻¹xAs the function

f(x)=tan⁻¹x is not continuous on the interval [0,4], it is not guaranteed to have an absolute maximum on the interval [0,4].

Therefore, option b is incorrect. c.

y=x²−16/x²+x−20 Let's check the critical points of the function

f(x)=x²−16/x²+x−20 by finding its derivative and equating it to zero:

f '(x)= (2x(x² - 20) + (x² - 16)(2x + 1))/ (x² + x - 20)²=0On solving this equation,

we get x=-4, 0, and 4. Now we will check the function values of these critical points as well as at the endpoints of the given interval:[0,4]. We get: f(0) = -4 and

f(4) = 4/3 Since f(4) is greater than all other values, the absolute maximum of f(x) is at

x=4.Therefore, option c is correct .d. y=1/e^x-1As the function f(x)=1/e^x-1 is not continuous on the interval [0,4], it is not guaranteed to have an absolute maximum on the interval [0,4].

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Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).

The horizontal distance from the tower to the fire is 7 feet

The term "angle of depression" describes the angle created by a horizontal line and the line of sight from the observer's eye to a location below their horizontal line of sight. It is often calculated by descending from the horizontal line.

The angle of depression is a term that is frequently used in discussions of observations or measurements involving objects that are below the observer's location in geometry and trigonometry.

We know that;

Tan 3 = x/140

x = 140 Tan 3

x = 7 feet

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The value of the card was declining over the period  is from the month of January 2020 to July 2020.

To determine the period over which the value of the card was declining,

Identify the range of values for which the derivative of the function V(m) is negative.

Let's find the derivative of the function V(m),

V'(m)

= dV(m)/dm

= 500m - 3500

To determine when the value of the card is declining,  find when V'(m) is less than zero.

Setting V'(m) < 0,

⇒500m - 3500 < 0

Solving for m,

⇒500m < 3500

⇒m < 7

The value of the card is declining for values of m less than 7.

Since m represents the approximate number of months since the start of 2020,

The declining period can be determined as the time from the start of 2020 to the 7th month.

Hence, the period over which the value of the card was declining is from January 2020 to July 2020.

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Answer:

3 dollars

Step-by-step explanation:

20 dollars is his total

$20-2 dollar water bottle=18

18 dollars divided by 6 cupcakes equals 3 dollars for each cupcake.

Answer:

D

Step-by-step explanation:

Answer:

Two pairs of parallel sides

Step-by-step explanation:

The given transformation performed on parallelogram RSTU = 180° clockwise rotation

Given that a rotation is a form of rigid transformation, the shape and size of the preimage RSTU will be equal to the the shape and size of the image R'S'T'U'

Therefore, RSTU ≅ R'S'T'U' and R'S'T'U' is also a parallelogram with two pairs of parallel sides.

Answer:

A circal graph also known as a pie chart

Step-by-step explanation:

THe world precentage gives it away

Based on the calculations, we find that the sample with the smallest estimated standard error is option c, where n = 100 with s^2 = 100. The estimated standard error for this sample is 1. Therefore, the correct answer is option c.

The estimated standard error is a measure of the variability of the sample mean and is calculated using the sample size (n) and the sample variance (s^2). A smaller value for the estimated standard error indicates less variability in the sample mean.

To determine the sample with the smallest estimated standard error, we compare the combinations of sample size and sample variance provided:

a. n = 25 with s^2 = 100

b. n = 25 with s^2 = 400

c. n = 100 with s^2 = 100

d. n = 100 with s^2 = 400

To calculate the estimated standard error, we take the square root of the sample variance divided by the sample size:

Standard Error = √(s^2 / n)

Comparing the given options, we can calculate the estimated standard errors for each case:

a. Standard Error = √(100 / 25) = √4 = 2

b. Standard Error = √(400 / 25) = √16 = 4

c. Standard Error = √(100 / 100) = √1 = 1

d. Standard Error = √(400 / 100) = √4 = 2

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Answer:

Step-by-step explanation:

We must use system of equations:

horses = h     chickens = c

horses have 4 legs & chickens have 2 and there are 120 legs total so to set up the first part of the equation...

4h + 2c = 120

They both have only 1 head each and there are 48 heads total so to set up the second part of the equation...

h + c = 48

Now we combine the equations and solve:

4h + 2c = 120

h + c = 48

Now we solve...

4h + 2c = 120

h = 48 - c         (subtract c on both sides to single out h)

--------------------

4(48 - c) + 2c = 120

192 - 4c + 2c = 120

-192                  -192

----------------------------

-2c = -72           (divide both sides by -2)

c = 36

Now we go back and find the value of h...

h = 48 - c

h = 48 - 36

h = 12

So there are 36 chickens & 12 horses!

La solución de la ecuación de valores absolutos es x = - 1 y la solución de la inecuación de valores absolutos es x ≥ 9/2 ∨ x ≤ 3.

En esta pregunta debemos resolver una ecuación de valores absolutos y una inecuación de valores absolutos, cuya resolución requiere la aplicación de la definición de valor absoluto y procedimientos algebraicos:

|3 x - 1| = |3 · x + 7|

\(\left|\frac{3\cdot x - 1}{3\cdot x + 7} \right| = 1\)

Por definición de valor absoluto:

\(\frac{3\cdot x - 1}{3\cdot x + 7} = 1\,\lor\,-\frac{3\cdot x - 1}{3\cdot x + 7} = 1\)

\(3\cdot x - 1 = 3\cdot x + 7\,\lor \,- 3\cdot x + 1 = 3\cdot x + 7\)

\(NaN \,\lor \, 6\cdot x = -6\)

x = - 1

|4 · x + 3| ≤ 15

Por definición de valor absoluto:

- 4 · x + 3 ≥ - 15 ∨ 4 · x + 3 ≤ 15

- 4 · x ≥ - 18 ∨ 4 · x ≤ 12

x ≥ 9/2 ∨ x ≤ 3

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Answer:  D) reflection across y = -x

Explanation:

When we reflect over y = x, we basically swap x and y. So for instance, the point (3,1) becomes (1,3).

When reflecting over y = -x, we will do the same thing but we'll make each coordinate swap in sign from positive to negative (or vice versa). The rule for reflecting over y = -x is \((x,y) \to (-y,-x)\)

So if we apply that rule to point A(3,1) then it becomes A ' (-1, -3).

Similarly, B(1,5) moves to B ' (-5, -1)

Finally, C(6,9) becomes C ' (-9, -6)

In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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Answer: aaaaaaaaaaaaaaaa

Step-by-step explanation: what is this first grade

Answer:

please see answers below

Step-by-step explanation:

1) 5/10 X 5 = (5 X 5)/ 10 = 25/10 = 2.5

2) 3/5 X 10 = (3 X 10) /5 = 30/5 = 6

3) 5/6 X 3 = (5 X 3)/6 = 15/6 = 5/2 = 2.5

4) 5/6 X 12 = (5 X 12)/6 = 60/6 = 10

5) 3/5 X 20 = (3 X 20)/5 = 60/5 = 12

6) 2/3 X 8 = (2 X 8)/3 = 16/3

7) 2/9 X 3 = (2 X 3)/9 = 6/9 = 2/3

8) 4/7 X 21 = (4 X 21)/7 = 84/7 = 12

The solution to the given initial value problem is y(t) = (1/4)(e^3t - e^2t). To solve the given initial value problem, we first find the characteristic equation associated with the homogeneous equation.

y" - 3y + 2y = 0. The characteristic equation is r^2 - 3r + 2 = 0, which can be factored as (r - 1)(r - 2) = 0. This yields two distinct roots: r1 = 1 and r2 = 2. Since the roots are distinct, the general solution to the homogeneous equation is given by h(t) = c1e^t + c2e^2t, where c1 and c2 are arbitrary constants to be determined. Applying the initial conditions y(0) = 0 and y'(0) = 0, we find that c1 = -c2 = 0.

Next, we seek a particular solution to the non-homogeneous equation y" - 3y + 2y = e^3t. Since the right-hand side is an exponential function with the same form as the characteristic equation, we assume a particular solution of the form p(t) = Ae^3t, where A is a constant to be determined.

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The miles per gallon does the car get on the trip is 6.3 miles per hour and the number of gallons required for the car to travel 549 miles is 87.14 gallons

The rate of a function is also known as its slope. According to the question, if an automobile travels 305 miles on 16 2/3 gallons of gasoline, the unit rate is calculated as;

Unit rate = 305/16(2/3)

Convert mixed fraction to improper

Unit rate = 305/(50/3)
Unit rate = 105 * 3/50
Unit rate = 6.3 miles per hour

Hence the miles per gallon does the car get on the trip is 6.3 miles per hour.

To determine how many gallons would be required for the car to travel 549 miles, this is expressed as;

Number of gallons = 549/6.3
Number of gallons = 87.14gallons

Hence the number of gallons required for the car to travel 549 miles is 87.14 gallons

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All the measures of central tendency are, The median, The mode, and The mean.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some measures,

A. The median

B. A sample statistic

C. The mode

D. The lowest value

E. The mean

We know that;

The four measures of central tendency are mean, median, mode and the midrange.

Here, mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.

Hence, All the measures of central tendency are, The median, The mode, and The mean.

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In the Subgame Perfect Equilibrium of a Stackelberg model, firm 1 chooses a number, and firm 2 chooses a function. Therefore, option (d) is the correct answer.

The Subgame Perfect Equilibrium (SPE) is a solution concept in game theory that analyzes strategic decision-making in sequential games. In a Stackelberg model, firm 1 acts as the leader and sets its output level first, followed by firm 2 as the follower, who observes firm 1's output before making its decision.

In the Subgame Perfect Equilibrium of this model, firm 1 chooses a number (output level) while firm 2 chooses a function (strategy). This implies that firm 1's decision is made independently as a quantity, and firm 2, observing firm 1's choice, formulates its strategy based on that information.

Therefore, option (d) is the correct answer: Firm 1 chooses a number, and firm 2 chooses a function in the Subgame Perfect Equilibrium of a Stackelberg model.

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