Given: Quadrilateral PAST, TX = AX; TP || AS
Prove: Quadrilateral PAST is a parallelogram.

The amount the gambler can win in this fractional game that pays a 10 to 1 with a 1/12 chance of winning is $2,500.

A fractional betting or game allows the gambler to calculate the winning from their betting when it is compared with their stake.

The number on the left-side represents the winning, while the number on the right side of the fractional odds represents the stake (investment).

When the gambler wins, they receive 10x their stake.  The expected amount to be won is computed as the total stakes, multiplied by the winning probability and the fractional odds.

Fractional odds of winning = 10/1

Chance of winning = 1/12

Number of independent games played = 150 times

Bet each time = $20

Total bets = $3,000 ($20 x 150)

Amount won = $2,500 ($3,000 x 1/12 x 10/1)

Thus, the amount the gambler can win in this fractional game that pays a 10 to 1 with a 1/12 chance of winning is $2,500.

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How much do you expect to win?

Answer:

B, C, A

Step-by-step explanation:

Don't really know how to explain this.

The given exponential function exists [tex]f(x)=3(1/3)^x[/tex] . The growth value of the function is 1/3.

An exponential function exists a mathematical function of the following form: [tex]f ( x ) = a^ x[/tex].

where x exists a variable, and a exists a constant named the base of the function.

An exponential function exists of the form [tex]f(x)=ab^x[/tex]

where a ≠ 0, b > 0, b ≠1, and x exists any real number.

when b > 1, the graph increases.

when 0 < b < 1, the graph decreases.

a = initial value

r = growth or decay rate

x = number of time.

The given exponential function exists [tex]f(x)=3(1/3)^x[/tex]

The function exists a stretch of the function [tex]f(x)= (1/3)^x.[/tex]

Therefore, the correct answer is the growth value of the function is 1/3.

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The age of the grandfather in years according to the task content is; 84.

It follows that the age of the grandfather and granddaughter are; x and y respectively.

Hence, the two equations which follow are;

x = 12y

x + y= 91

Hence, the age of the grandfather, x can be evaluated as follows;

x = 12(91-x)

13x = 1092

x = 1092/13

x = 84 years.

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Step-by-step explanation:

we use the point-slope approach :

y - y1 = m(x - x1)

m is the slope, and (x1, y1) is a point on the line.

so,

1.

y - 2 = 7(x - 1) = 7x - 7

y = 7x - 5

2.

y - -1 = -1×(x - 3) = -x + 3

y + 1 = -x + 3

y = -x + 2

3.

y - 5 = -4(x - -2) = -4x - 8 (3x a "-" is a "-" for 8)

y = -4x - 3

4.

y - 5 = 5/3 × (x - 3) = 5x/3 - 5

y = 5x/3 or 5/3 × x

Answer:

1. [tex]7x-y=5[/tex]

2. [tex]x+y=2[/tex]

3. [tex]4x+y=-3[/tex]

4. [tex]5x-3y=0[/tex]

Step-by-step explanation:

Since we already know the slope and the coordinates of one point, first use the point-slope form to create an equation.

[tex]y-k=m(x-h)[/tex]

[tex]y-2=7(x-1)[/tex]

[tex]y-2=7x-7[/tex]

[tex]7x-y=5[/tex]

[tex]y+1=-1(x-3)[/tex]

[tex]y+1=-x+3[/tex]

[tex]x+y=2[/tex]

[tex]y-5=-4(x+2)[/tex]

[tex]y-5=-4x-8[/tex]

[tex]4x+y=-3[/tex]

[tex]y-5=\frac{5}{3} (x-3)[/tex]

[tex]y-5=\frac{5}{3}x-5[/tex]

[tex]3y-15=5x-15[/tex]

[tex]5x-3y=0[/tex]

Considering that it is a triangle, the range of the possible lengths, x, of the third side of the tile is: (1, 17).

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

Hence, if 9 is the greater side:

8 + x > 9

x > 1.

If 8 and 9 are the smaller sides:

x < 8 + 9

x < 17.

Hence the range of possible lengths is:

(1, 17).

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Answer:

a₈ = - 10935

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 5 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-15}{5}[/tex] = - 3 , then

a₈ = 5 × [tex](-3)^{7}[/tex] = 5 × - 2187 = - 10935

Step-by-step explanation:

Set up a system of equations,

Consective numbers appear before and after so we need two number such that

[tex]x + 1 = y[/tex]

or

[tex]x - y = - 1[/tex]

Likewise, we also know that

[tex]4x + 3y = 157[/tex]

Let multiply the top equation by 3.

We get

[tex]3x - 3y = - 3[/tex]

Then we add the bottom equation to that

[tex]4x + 3y = 157[/tex]

[tex]7x = 154[/tex]

[tex]x = 22[/tex]

Then we plug in x for the original equation,

[tex]22 + 1 = 23[/tex]

So the two numbers are 22,23.

Las cuentas de Dmitri de menor a mayor se ordenan: retiro, cheques y ahorros.

Para organizar las cuentas bancarias de Dmitri de menor a mayor debemos observar cuidadosamente los valores de cada una. Adicionalmente para organizarlas por valor absoluto nos fijamos únicamente en el número sin tener en cuenta el símbolo, en ese caso el valor de cheques pierde su símbolo negativo.

Entonces las cuentas quedarían organizadas así:

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Answer:

For every x value, the y value would be double of the x value. (ex, x=2, y=4)

Step-by-step explanation:

If you look closely at every x value and see their y-values for the ordered pair, you will see that the x-value in question was doubled in order to find the y-value. This will result in the linear equation: [tex]y=2x[/tex].

Answer:

6288388288288828ffjfjjrjir

There will be total 14 hard centred and 14 soft centred choclates in the box.

The ratio is the division of the two numbers.

For example, a/b where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that in the question hard-centred and soft-centred chocolates in the ratio 5 : 2

Hard centred/ Soft centred = 5/2

And total

Hard centred + Soft centred = 49

Now let say hard centred is H and soft centred S

H/S = 5/2 and H + S = 49

Now H = (5/2)S put into second equation

(5/2)S + S = 49

S(7/2) = 49

S = 14 now put into second equation

H + 14 = 49 = 35 hence hard centred will be 35 and soft centred will be 14.

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The perimeter of the triangle whose coordinates are A (2, 2), B (3, 3), and C (4, 2) is 4.828

We can determine the perimeter of a triangle with vertices by utilizing the distance formula.

Given that, we have the vertices (x₁,y₁), (x₂, y₂), (x₃, y₃). Then the length of each sides can be expressed as follows:

SIde AB = [tex]\mathbf{\sqrt{(x_1 -x_2)^2 +(y_1 -y_2)^2}}[/tex]

Side AC = [tex]\mathbf{\sqrt{(x_1 -x_3)^2 +(y_1 -y_3)^2}}[/tex]

Side BC = [tex]\mathbf{\sqrt{(x_2 -x_3)^2 +(y_2 -y_3)^2}}[/tex]

Replacing the values of the coordinates into the given formula above the perimeter of the triangle is 4.828

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I give u the answers of first and second one.

thank you

brainlist please

Answer:

First answer is 9 or 1 . Second answer is 7 or -7.

Step-by-step explanation:

[tex](x-5)^{2} =16[/tex]

[tex]x-5 = 4[/tex]  or [tex]x - 5 =-4[/tex]

so [tex]x = 9[/tex] or [tex]x = 1[/tex]

[tex]2x^{2} = 98[/tex]

[tex]x^{2} =49[/tex]

[tex]x=7[/tex] or [tex]x = -7[/tex]

Answer: C: [tex]D\cap F = \{2, 4, 6, 8\}[/tex]

Step-by-step explanation:

Let's first find the specific numbers that are in sets D and F.

[tex]D=\{0,1,2,\ldots\}[/tex], as D has all whole numbers.

[tex]F=\{2,4,6,8\}[/tex], as all of these numbers are even, greater than or equal to two, and less than nine.

Since all the numbers in F are whole numbers, all of them would be in D. Hence, the intersection of both would just be {2, 4, 6, 8}.

[tex]D\cap F = \{2, 4, 6, 8\}[/tex]

The solution will illustrate that the equation has one solution at x=0.

Given that  adds 2 to both sides, the equation 4x = 3x results.

An algebraic equation may be described as a mathematical declaration wherein expressions are set the same as every other.

The equation is 4x=3x.

As given that add 2 on both sides, we get

4x+2=3x+2

Now, we will subtract 3x from both sides, we get

4x+2-3x=3x+2-3x

x+2=2

Further, we will subtract 2 from both sides, we get

x+2-2=2-2

x=0

Hence, When adds 2 to both sides, the equation 4x = 3x results that the equation has one solution x=0.

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Answer:

18

Step-by-step explanation:

3*3*3 = 27, assuming all 3 digits can occupy each space

However, 0 cannot start a number, so it becomes:

3*3*2, which is 18.

The value of x when y = 1.728 and z = 5 in the inverse variation y = (k × x²) / z³ is 36

The types of variation are;

y = (k × x²) / z³

where,

If y = 12, x = 4 and z = 2

y = (k × x²) / z³

12 = (k × 4²) / 2³

12 × 2³ = k × 4²

12 × 8 = k × 16

96 = 16k

k = 6

Find x when y = 1.728 and z = 5

y = (k × x²) / z³

1.728 = (6 × x) / 5³

1.728 × 5³ = 6x

1.728 × 125 = 6x

216 = 6x

x = 216/6

x = 36

Therefore, value of x when y = 1.728 and z = 5 in the inverse variation y = (k × x²) / z³ is 36

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The widgets should be sold for $22.08 for the company to make the maximum profit.

To maximize a function, y = f(x), we differentiate it with respect to x, to get y' = f'(x). Equate it to zero to get the points on inflections.

Differentiate y' = f'(x) again with respect to x, to get y'' = f''(x), and put in the points of inflections to check whether y'' is greater than or less than zero. If it is greater than zero, then we have a minimum, and if it is less than zero, then we have a maximum.

In the question, we are given a profit function y, with respect to the sale price of each widget x. We are asked to find the sale price that maximizes the profit.

The function given is:

y = -30x² + 1325x - 8569.

Differentiating this with respect to x, we get:

y' = -60x + 1325.

To find the point of inflection, we equate this to zero, to get:

0 = -60x+ 1325,

or, x = 1325/60 = 22.0833

Now, we differentiate, y' = -60x + 1325, with respect to x, to get:

y'' = -60 < 0, thus we have a maximum at x = 22.0833.

Thus, the widgets should be sold for $22.08 for the company to make the maximum profit.

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Answer:

20 units

Step-by-step explanation:

7×50×5 = 1750 minutes

1750minutes/60minutes = 29.161 hours

The stock worth when she sells it eight years later $545, If the stock decreases at a rate of 15% per year for eight years.

According  to the question,

Petra opens her mail one day to find that an anonymous donor has given her $3000 cash. She sets aside $1000 to refurnish her apartment, and decides to invest the other $2000.

If the stock decreases at a rate of 15% per year for eight years. In order to find the stock worth when she sells it eight years later we have the formula

Value of stock after 'n' years = Principal[1-Rate/100]ⁿ

Value of stock after '8' years = 2000[1-15/100]⁸

= 2000[1-0.15]⁸

=2000[0.85]⁸

=2000[0.2725]

=545$

Hence, the stock worth when she sells it eight years later $545, If the stock decreases at a rate of 15% per year for eight years.

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Answer:

Step-by-step explanation:

The double number line that shows the other values of packages and pencils is A. A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48.

It should be noted that a number line simply means a line which numbers are marked a intervals to illustrated numerical operations.

In this case, the double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48 illustrate this information

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Answer: B

The main word that gives the answer away is product, which means to multiply.

Answer:

11.4 feet

Step-by-step explanation:

1/1.9 = h/w  (h= height, w=width)

Solving for w, gives you the formula

w = (1.9)h

This means the width is 1.9 times the height.

Use the formula to find the width where the height is 6 feet.

h = 6

w = (1.9)(6) = 11.4

The width is 11.4 feet.

The length and the width of the rectangle are 10 inches and 6 inches respectively.

In the question, we are given that the length of a rectangle exceeds its width by 4 inches, and the area is 60 square inches.

We are asked for the length and the width of the rectangle.

We assume the width (w) of the rectangle to be x inches.

Its length (l), exceeds its width (w) by 4 inches.

Thus, its length (l) = x + 4 inches.

Now, the area can be calculated using the formula, A = l*w, where A is its area, l is its length, and w is its width.

Thus, the area = (x + 4)x = x² + 4x.

But, we are given that the area is 60 square inches.

Putting the value, we get a quadratic equation:

x² + 4x = 60.

or, x² + 4x - 60 = 0,

or, x² + 10x - 6x - 60 = 0,

or, x(x + 10) - 6(x + 10) = 0,

or, (x - 6)(x + 10) = 0.

By the zero-product rule, we get:

Either, x - 6 = 0, or, x = 6,

or, x + 10 = 0, or, x = -10, but this is not possible as the width of a rectangle cannot be negative.

Thus, the width = x = 6 inches.

The length = x + 4 = 10 inches.

Thus, the length and the width of the rectangle are 10 inches and 6 inches respectively.

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Answer:

(8 , 5)

Step-by-step explanation:

• Marty would get the best view ,if he stood at the midpoint

of the line that connect the park to the high school .

• On the coordinates plane ,the park is located at (-4 , -11)

and the high school is located at (20 , 21) .

•• Calculating the midpoint (best position) :

Let M(x , y) be the midpoint.

[tex]x=\frac{-4+20}{2} =8[/tex]

[tex]y=\frac{-11+21}{2} =5[/tex]

Answer:

(8, 5)

Step-by-step explanation:

Given points:

To find the point that is between and equidistant from the High School and the park, use the formula for midpoint between two points.

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

[tex]\textsf{Let }(x_1,y_1)=(20,21)[/tex]

[tex]\textsf{Let }(x_2,y_2)=(-4,-11)[/tex]

Substitute the endpoints into the formula:

[tex]\implies \textsf{Midpoint} =\left(\dfrac{-4+20}{2},\dfrac{-11+21}{2}\right) = (8,5)\end{aligned}[/tex]

Therefore, the point at which Marty would get the best view is (8, 5).

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2000 feet can be represented as 20 blue whales in a row of each 100 feet.

What is a blue whale?

I feet = 30.48 centimeters

To explain what the length of 2000 feet looks like:

Take the example of a blue whale of 100 feet.

Now, imagine placing up 20 blue whales one behind the other.

20 × 100 feet = 2000 feet

Therefore, 2000 feet can be represented as 20 blue whales in a row of each 100 feet.

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