Find the total surface area of the prism. 8.6. 7. 14.5.

There are 50 ways for Marvin to reach his destination without passing through the forbidden point.

To solve this problem, we can use the unitary method. This method involves breaking the problem down into smaller, simpler units to solve it more easily.

In this case, we can break the path from Marvin's starting point to his destination into two smaller paths. The first path is from (0,0) to (1,4), and the second path is from (1,4) to (4,6).

There are five paths from the bottom left corner to the point (1,4) that do not go through the forbidden point.

Once Marvin reaches the point (1,4), he can only go up or to the right to reach his destination. So, we need to count the number of ways to get from (1,4) to (4,6)

We can visualize this by drawing another grid and counting the paths:

In total, there are

=> 5 x 10 = 50

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The two values of y such that the barn is 50 yards from the well are given as follows:

y = -47 and y = 53.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the following equation:

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

For this problem, we have that D = 50, hence the equation is given as follows:

sqrt[(-2 - (-2))² + (y - 3)²] = 50

y - 3 = ±50.

Hence the values of y are given as follows:

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Answer: The distance between Star B and Star C can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side). In this case, the lengths of the two shorter sides are the distances from Star A to Star B (50 lightyears) and from Star A to Star C (120 lightyears).

So, we have:

(Star B to Star C)^2 = (Star A to Star B)^2 + (Star A to Star C)^2

(Star B to Star C)^2 = 50^2 + 120^2

(Star B to Star C)^2 = 2500 + 14400

(Star B to Star C)^2 = 16900

Taking the square root of both sides:

Star B to Star C = √16900

Star B to Star C = 129 lightyears

So, Star B and Star C are 129 lightyears apart.

Step-by-step explanation:

Answer:

I have graphed it and attached it in the explanation part.

Step-by-step explanation:

Out of three tables given, only second table ( when we take the order from top to bottom )satisfies this.

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

Given are three tables in x and y and we have to find which table shows a linear relation.

We know in  a linear relation between x and y the graph would be a straight line and also the slope would be constant

i.e. change of y/change of x for any pair in the table would be a constant.

Out of three tables given, only second table ( when we take the order from top to bottom )satisfies this.

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The statements that are true about rectangles are mentioned in options  

A,B,C,E.

Rectangles -A shape with four sides and internal angles is a rectangle. The lengths of the other two sides are offset by two. The rectangle's diagonal sides are of identical length.

The opposite sides of a rectangle are equal and parallel to one another.

The diagonals cut each other in half, but not exactly.

All diagonals are the same length.

The rectangle's diagonals line up.

The total internal angles add up to the same value

Every internal angle has the same value.

A rectangle has congruent angles on all sides.

A rectangle's opposing angles are congruent.

We may thus infer that the statements about rectangles in the options are accurate based on the aforementioned features.

Q. Select all the statements that are true about rectangles.

A Diagonals are congruent.

B Diagonals bisect angles.

C Opposite angles are congruent.

D Diagonals are perpendicular.

E Diagonals bisect each other.​

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The transformations are matched accordingly is given below.

A function transformation takes whatever the underlying function f (x) is and "transforms" (or "equates") it, which is a fancy way of saying you alter the equation and shift the graph over.

Parent function is given as f(x) = 2x - 6

The transformations are shifts f(x) 4 units down

f(x) → f(x) - 4

⇒ g(x)= 2x - 6 - 4 = 2x - 10

Then stretches f(x) by a factor of 4 away from the x-axis

f(x) → 4*f(x)

⇒ g(x) = 4(2x - 6) = 8x - 24

Now shifts f(x) 4 units right

f(x) → f(x - 4)

⇒ g(x) = 2(x - 4) - 6 = 2x - 14

To compresses f(x) by a factor of toward the y-axis (must be 4)

f(x) → f(4x)

⇒ g(x) = 2*4x - 6 = 8x - 6.

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The value of x is given as follows:

x = 131º.

An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.

Hence the measure of the top angle of the bottom triangle is given as follows:

a = 180 - 98

a = 82.

The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence, considering that the sum of the measures of the internal angles of a triangle is of 180º, their measures are given as follows:

2b + 82 = 180

2b = 98

b = 49.

Considering the vertical angles, the base angles of the top triangle are given as follows:

b = 49.

Hence the value of x is given as follows:

x = 180 - 49

x = 131º.

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Answer: 27

Step-by-step explanation:

8^x+1 = 64

8^x+1 = 8²

x+1 =2

x = 2 - 1

x = 1

To Find :

3^2x +1

Substitute the value of x :

3^2(1)+ 1

3^2+1

3^3

27

Check the picture below.

In 30 years, the amount that Jenna will have is $411, 235

This account balance is as a result of Jenna's annuity payments.

The amount that Jenna's account will be worth in 30 years can be found by the future value of annuity formula which is :

= Annuity deposited periodically x Future value of annuity factor, 10 % , 30 years

Annuity deposited periodically = $ 2, 500

Future value of annuity factor = 164.49402268886

The value of the account balance will be:

= 2, 500 x 164.49402268886

= $411, 235

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Answer: $411,235, Annuity Payments

Step-by-step explanation:

I have took the test and know the answer is correct

The actual amount of sale for each bake is $214. As Miguel said it is $215 which is very close to the actual amount, it is reasonable.

To determine if Miguel's estimate of $215 per bake sale is reasonable, we can start by calculating the average amount of money the scout troop made per bake sale. We do this by dividing the total amount they earned by the number of sales they had, as follows:

Total amount earned = $1,498

Number of bake sales = 7

Average amount earned per bake sale = Total amount earned ÷ Number of bake sales

= $1,498 ÷ 7

= $214

This calculation shows that the average amount the scout troop made per bake sale was $214. This means that if they had charged a consistent price for all of their baked goods at each sale, they would have made an average of $214 per sale.

Now, we can compare this average to Miguel's estimate of $215 per bake sale. Since his estimate is very close to the actual average, we can conclude that it is reasonable.

It is possible that the scout troop charged slightly different prices for their baked goods at each sale, which could explain the small discrepancy between the actual average and Miguel's estimate. However, given that the difference between the two values is only $1, it is likely that Miguel's estimate is a good approximation of the actual amount.

Moreover, it is reasonable to assume that the scout troop earned the same amount at each bake sale, especially if they had a set price for their baked goods.

If they had charged different prices at each sale, it would have been more difficult to estimate the average amount they earned per sale, and it would have been less likely that Miguel's estimate of $215 per bake sale would have been close to the actual average.

Therefore, based on the calculation and the context of the problem, we can conclude that Miguel's estimate of $215 per bake sale is reasonable.

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The slope of the line that models this situation is equal to 2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (0, 8).

Points on y-axis = (4, 20).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (20 - 4)/(8 - 0)

Slope, m = 16/8

Slope, m = 2.

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The percentage multiplier to find the 53% of a price is 0.53

The given percentage value = 53%

Percentage of a quantity is defined as the number or the ratio, that can be expressed as the fraction of 100. To find the percentage of a number, divide the number by the whole quantity and multiply by 100. Percentage of a number is usually expressed as by using percentage sign "%"

Here we have to find the percentage multiplier

To find the percentage multiplier divide the given percentage by 100

The percentage value = 53%

The percentage multipler = 53 / 100

Divide the numbers

53 / 100 = 0.53

Therefore, the percentage multiplier is 0.53

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Answer:

(4,3)

Step-by-step explanation:

Using trigonometric ratio, the height of the pole is approximately 60 feet

The angle of elevation is the angle between the horizontal and a line from the observer to a point above the horizontal. In other words, it is the angle between the ground and the line of sight to an object above the ground.

Using trigonometric ratio to solve the angle of elevation problem, the height of the pole can be calculated using the tangent of the triangle.

tanθ = opposite / adjacent

tan 55 = x / 42

x = 42 * tan 55

x = 59.98 ft≅ 60 feet

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Work Shown:

i = P*r*t

900 = 6000*r*1

r = 900/6000

r = 0.15

That converts to 15% after moving the decimal point 2 spots to the right. It's the same as multiplying by 100.

3 is the minimum number of guesses required to guarantee that you know the number.

If we use a binary search approach, we can guess the number in a minimum number of steps.

First, we guess the middle number, which is 8. If the answer is higher, we can eliminate all the numbers from 1 to 8, because they are lower than the answer.

Then we guess the middle number of the remaining numbers, which is 12. If the answer is lower, we can eliminate all the numbers from 12 to 15, because they are higher than the answer.

We have now eliminated half of the remaining numbers, and we are left with 6 and 7. We can guess either of these numbers, and we will know the answer with a total of three guesses.

Therefore, we can guarantee that we know the number in three guesses using this binary search approach.

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Answer:

Step-by-step explanation:

its C

Answer:

(12m+10)(2m-2)

hope this helps

It will take 20 pounds for both charges to be the same.

An equation containing variables with its highest power as one is called linear equation.

To ship a package,

UPS charges $4 for the first pound and $0.50 for each additional pound.

FedEx charges $6 for the first pound and $0.40 for each additional pound.

These can be written in the linear equation form as,

Let p be the pound charges by both UPS and FedEx,

then, 4+0.50p-------(1)

6+0.40p-----(2)

When the charges are same, (1)=(2)

4+0.50p = 6+0.40p

⇒0.10p=2

⇒p=20

Hence, this means that, it will take 20 pounds for both charges to be the same.

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Answer:

A.7

Step-by-step explanation:

You first have to add 8 and -15

Then, find the absolute value

So, the answer is 7

The expression that represents the value of the stock after two years in terms of x is 1.6144x

After the first year, the value of the stock increased by 39%, which means that the stock's new value will be -

x + 0.39x = 1.39x

After the second year, the value of the stock decreased by 16%, which means that the stock's new value will be -

1.39x - 0.16(1.39x) = 1.16(1.39x)

Simplifying this expression, we get,

1.16(1.39x) = 1.6144x

Therefore, the expression that represents the value of the stock after two years in terms of x is 1.6144x.

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The complete question is -

Aubrey bought stock in a company two years ago that was worth x dollars. During the first year that he owned the stock, it increased by 39%. During the second year the value of the stock decreased by 16%. Write an expression in terms of x that represents the value of the stock after the two years have passed.

The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.

Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

The diagonals of the rhombus will be the same as the dimension of the rectangle that is 8 cm and 6 cm.

Then the area of the rhombus is given as,

A = (Product of diagonal of rhombus) / 2

A = (8 x 6) / 2

A = 48 / 2

A = 24 square centimeters

The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.

The diagram is shown below.

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An inverse relationship is also known as a negative relationship, because the correlation coefficient, is negative in an inverse relationship. Correct option is B.

An inverse relationship is a type of relationship between two variables in which they move in opposite directions. As one variable increases, the other variable decreases. In other words, when one variable changes, the other variable changes in the opposite direction.

For example, in the context of physics, the distance between two objects and the gravitational force between them have an inverse relationship. As the distance between the objects increases, the gravitational force between them decreases, and vice versa.

An inverse relationship is also known as a negative relationship. This is because the correlation coefficient, which measures the strength and direction of the relationship between two variables, is negative in an inverse relationship.

A correlation coefficient of -1 indicates a perfect inverse relationship, while a correlation coefficient of 0 indicates no relationship, and a correlation coefficient of 1 indicates a perfect positive relationship.

In contrast, a direct relationship, also known as a positive relationship, is a type of relationship between two variables in which they move in the same direction. As one variable increases, the other variable also increases, and vice versa.

In summary, an inverse relationship is a negative relationship in which two variables move in opposite directions, while a direct relationship is a positive relationship in which two variables move in the same direction.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{4} {x}^{2} - 4 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{4} {x}^{2} = 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} = 4 \times 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \sqrt{4 \times 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \pm4[/tex]

[ but since we have been asked for positive solution, it will be 4 ]

Hence, the correct choice is : A.) 4

The value of x and y in the geometric sequence are 1/r and 1

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

If the first term of the sequence is a ,second term is ar , third term = ar²

r = ar²/ar

In the sequence 2y, 2xy, 2, xy/2, ...

r = 2y/2xy

therefore r = 1/x

r = 2/2xy

r = 1/xy

therefore 1/x = 1/xy

therefore y = 1

x = 1/r

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The factors of the cubic function f(x) = 64x³ + 27 are (4x + 3) and (16x² − 12x + 9). The correct answer would be options (A), and (D).

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original.

The cubic function is given in the question, as follows:

f(x) = 64x³ + 27

The above expression can be rewritten as:

f(x) = (4x)³ + (3)³

Compare the sum of cubic formula a³ + b³ = (a + b)(a² - ab + b²) and we get

f(x) = (4x + 3)(16x² − 12x + 9)

Thus, the factors of the cubic function are (4x + 3) and (16x² − 12x + 9).

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Rounded to the nearest minute, the answer is 12 minutes.

The expressions can contain variables, constants, mathematical operations, and functions. An equation can be used to represent a relationship between two or more variables, and it is often used to solve problems by finding the values of the variables that satisfy the equation.

The radius of the Ferris wheel is half its diameter, which is 20/2 = 10 meters. When the Ferris wheel makes a full revolution, a person riding it will pass the loading platform twice: once on the way up and once on the way down. The highest point reached by the Ferris wheel is at the top, which is 10 + 1 = 11 meters above the ground.

To find out how many minutes of the ride are spent higher than 19 meters above the ground, we need to figure out at which times the rider is at or above this height. Let's call h(t) the height of the rider at time t. We know that h(t) is a sinusoidal function with a period of 10 minutes, an amplitude of 10 meters, and a vertical shift of 11 meters. In other words, we can write:

h(t) = 10 sin(2πt/10) + 11

To find out when h(t) is greater than 19, we solve the inequality:

10 sin(2πt/10) + 11 > 19

Subtracting 11 from both sides, we get:

10 sin(2πt/10) > 8

Dividing by 10, we get:

sin(2πt/10) > 0.8

The sine function is greater than 0.8 at two times in each period: once when it is increasing from 0.8 to 1, and once when it is decreasing from 1 to 0.8. We can find these times by solving the equations:

sin(2πt/10) = 0.8

sin(2πt/10) = -0.8

Using a calculator, we find that these equations have solutions at:

t = 1.167, 8.833, 3.5, 6.5

These times represent the four moments during the 10-minute period when the rider is at or above 19 meters. The first and fourth of these moments occur in the first half of the period, and the second and third occur in the second half.

Therefore, the total time spent higher than 19 meters is:

(8.833 - 1.167) + (6.5 - 3.5) = 11.6667 minutes

Rounded to the nearest minute, the answer is 12 minutes.

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