A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that apply.

The measure of the missing side lengths of the triangle is adjacent side = 5 and hypotenuse =  5√2.

What are trigonometric ratios?

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle.

To find the side of a right triangle:

A right-angle triangle has one of its angles as 90 degrees.

Therefore,

using trigonometric ratios,

tan 45 = opposite/adjacent

tan 45 = opposite / 5

opposite side = (tan 45)  * 5

opposite side = 1 * 5 = 5

Therefore,

adjacent side = 5

sin 45 = opposite / hypotenuse

1/√2  = 5 / hypotenuse

hypotenuse = 5√2 /1

hypotenuse =  5√2

Hence, the missing side lengths of the triangle are adjacent side = 5 and hypotenuse =  5√2.

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The distance Joe climbed up the ladder is c.

3.22 + b2 = 2.42 is the correct equation.

What is the Pythagoras theorem?

The Pythagorean theorem is a fundamental concept in geometry and mathematics, named after the ancient Greek mathematician Pythagoras. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

3.22 + b2 = 2.42 is the correct equation that represents the situation of Joe's position on the ladder. It uses the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the lengths of the other two sides (the horizontal and vertical distances from the base of the ladder to Joe's feet). In this case, c is the distance that Joe climbed up the ladder, and b and a are the horizontal and vertical distances, respectively.

So, by solving the equation:

3.22 + b2 = 2.42

b = √ (2.42 - 3.22)

Then use the Pythagorean theorem again to find the length of the ladder (c)

c = √(3.22 + b^2)

Hence, the distance Joe climbed up the ladder is c.

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The 95.2 kilograms of potatoes  by the shop order. With the unit sign kg, the kilogram serves as the International System of Units' unit of mass.

A shop sells potatoes and carrots

let c = carrots

let p = potatoes

let TW = Total weight

The shop orders 50.4 kg more potatoes than carrots

p = 50.4 kg + c

Total weight = Mass of p + Mass of c

TW = 50.4 kg + c + c = 50.4 kg + 2c …. (i)

32% of the total weight is carrots

c = (32 /100 )  * Total weight = 0.32 TW

TW = c / 0.32 …. (ii)

50.4 kg + 2c = c / 0.32

Multiply all through by 0.32

16.128 + 0.64c = c

c -  0.64c  = 16.128

0.36 c = 16.128

c = 16.128 / 0.36 = 44.8 kg

Potatoes = 50.4 kg + c = 50.4 kg + 44.8 kg = 95.2 kg

Hence, the answer is 95.2 kg ordered by the shop.

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No, the ordered pair (-2, 2) is not a solution of the linear inequality because it does not satisfy the inequality.

An ordered pair is a pair of numbers that are related to each other in a specific order. An ordered pair can be used to represent a point on a graph. In order for an ordered pair to be a solution of a linear inequality, it must satisfy the inequality. This means that the ordered pair must make the inequality true when it is substituted into the equation. For example, if the linear inequality is "x + 2 > 3," then for (-2, 2) to be a solution, it must make the inequality true. This would mean that -2 + 2 > 3, which is not true, so (-2, 2) is not a solution of the linear inequality.

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Things that must you include in every confidence argument you write in order to receive full points and have a complete argument are:

Confidence argument is An explanation for why there should be confidence is emphasized in a confidence argument (a case mostly supported by evidence that a process is safe).

The system's overall assurance case must have certain elements in a confidence argument. This contains:

Your question is incomplete but most probably your full question attached below

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Since AD is the angle bisector of <BAC, then BD is 1.9 inches.

An angle bisector is a line that divides a given angle into two equal measure after its construction.

Given that AD is the angle bisector of <BAC, then we have;

From triangle ADC, applying the Pythagorean theorem;

/Hyp/^2 = /Adj/^2 + /Opp/^2

4^2 = 3^2 + AD^2

16 = 9 + AD^2

AD^2 = 16 - 9

         = 7

AD = 7^1/2

     = 2.64

AD = 2.6

So that, from triangle ABD we have;

/Hyp/^2 = /Adj/^2 + /Opp/^2

3.2^2 = 2.6^2 + BD^2

10.24 = 6.76 + BD^2

BD^2 = 10.24 - 6.76

         = 3.48

BD = 3.48^1/2

     = 1.8655

BD = 1.9 inches

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​Extraneous Solutions arise due to the squaring of both sides of a square root equation which will result in 2 solutions (the positive and negative number).

When you are solving equations with square roots, you have to always check whether your answer is correct by substituting with the variable. If the solution does not support the equation it is known as an extraneous solution.

One of the numbers in the solution of an extraneous problem will be an extraneous solution or an extra solution which does not fulfil the original equation.

For example,

x = 4 (original equation)

Squaring both sides of the equation

x² = 16

x = -4, 4

Substituting x = -4 into the original equation

-4 is not equal to 4

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Answer:

You should expect to draw a consonant about 560 times.

Step-by-step explanation:

The word FOOTBALL has 5 consonants - F, T, B, L and L. Therefore, you should expect to draw a consonant 5 times out of every 8 draws. 5/8 = 0.625, so for 840 draws you should expect to draw a consonant approximately 840 x 0.625 = 560 times.

The number of times you should expect to draw a consonant is 525.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

The letters from the word FOOTBALL are written on 8 cards with one letter on each card.

One card will be drawn randomly and then placed back into the stack.

Number of consonants in the word = 5 [F, T, B, L and L]

Total number of letters = 8

Probability of finding consonant each time = 5/8

If this experiment is repeated 840 times,

Number of times you should draw a consonant = 840 × (5/8) = 525

Hence the required number of times is 525.

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The distance of the given point ( -3 , 5 ) from y - axis is equal to 3 units in the left direction ( negative x-axis).

As given in the question,

Given coordinates points in the coordinate plane is given by :

( - 3 , 5 )

Let us consider a horizontal line with the given coordinates on y - axis.

Coordinates on y-axis of the horizontal line are:

( 0 ,5 )

Distance between ( -3 ,5 ) and ( 0 , 5 ) is equal to :

= √ ( 5 - 5)² + ( 0 -(-3))²

= √ 9

= ±3

(-3,5) is in the second quadrant which is in the left direction of y-axis.

Therefore, the distance between the given point and y-axis is given by 3 units in the left direction.

The above question is incomplete , the complete question is :

Find the distance of the point (-3,5) from y-axis.​?

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The distance that is closes to the distance that Steven walked around the pool is B. 62. 83 ft

The perimeter of a circle refers to the distance around that circle and it is also called the circumference of the circle.

This circumference can be found by the formula:

= π x diameter

This means that the closest distance that Steven walked around the circular swimming pool is:

= π x 20

= 62. 86 ft

In conclusion, the distance that Steven was able to walk around the pool is closest to 62. 83 ft.

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The mean of the data in the dot plot is equal to 1.6.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Based on the dot plot, the number of jokers include the following:

Number of jokers                frequency            

0                                               1

1                                                1

2                                               2

3                                               1

Next, we would determine the total number of jokers as follows;

Total number of jokers = 0 + 1 + 2 + 2 + 3

Total number of jokers = 8

Now, we can calculate the mean of the data as follows;

Mean = F(x)/n

Mean = 8/5

Mean = 1.6.

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The scale factor is 3. The segment JA' is a transformation of JA.

What is the scale factor?

A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller). For example, we can enlarge a rectangle with sides of 2 cm and 4 cm by multiplying each side by a number, say 2.

The unit of scale factor is unitless.

Given that the length of the segment JA is 7 in. and the line segment JA' is 21 in.

The ratio of the final length and the original length is the scale factor.

Therefore, JA'/JA = 21/7 = 3

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A possible second point with a y-coordinate of 8 is equal to 5.

In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;

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

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following slope and data points on the line:

Points on x-axis = (1, 2).

Points on y-axis = (_, 8).

Slope, m = 3/2

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

Slope, m = (y₂ - y₁)/(x₂ - x₁)

3/2 = (8 - 2)/(x₂ - 1)

3/2 = 6/(x₂ - 1)

Cross-multiplying, we have:

3(x₂ - 1) = 12

x₂ - 1 = 12/3

x₂ - 1 = 4

x₂ = 4 + 1

x₂ = 5

In conclusion, we can logically deduce that the second point (x₂) is 5.

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-16 5/7 is the additive inverse of 16 5/7.

An additive inverse of a number is the value, which on adding with the original number results in zero value.

given a number 16 5/7

The additive inverse of a number is the number that completes the number to '0' when added.

thus,

the additive inverse of  16 5/7 is -  16 5/7.

Therefore, the additive inverse of 16 5/7 is -16 5/7.

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Complete question:

What is the additive inverse of 16 5/7?

Thus the numbers are 1411 and 1079 respectively.

Answer:

it is + 10 then + 4 and that is how you get your answer

(a) There are four aces in a standard deck of playing cards: the ace of clubs, the ace of diamonds, the ace of hearts, and the ace of spades.

There are 48 cards that are not queens, so there are 4 × 48 = 192 ways to pick two successive cards from a deck of playing cards so that the first is an ace and the second is not a queen.

(b) There are 13 spades in a standard deck of playing cards, but one of them is the queen of spades.

Therefore, there are 12 spades that are not queens, so there are 12 × 48 = 576 ways to pick two successive cards from a deck of playing cards so that the first is a spade and the second is not a queen.

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The relation between logarithmic function and exponential function is they both are inverse of each other.

As given in the question,

Relation between logarithmic function and exponential function is given by:

Therefore, relation between the logarithmic function and the exponential function is  that both are inverse of each other.

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Answer: The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) should be followed to get the correct result.

-3(2) = -6

2^2 = 4

3(-2) = -6

-6 + 4 + (-6) = -8

Therefore, "-3(2)+2^2+3(-2) = -8"

Step-by-step explanation:

Quick Answer:

The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), should be followed to obtain the correct result.

The answer is -8

Explanation:

PEDMAS stands for :

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

So,

-3(2) = -6

2^2 = 4

3(-2) = -6

-6 + 4 + (-6) = -8

As a result, the correct response is, -8

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The age of the rock is 4.5 billion years. Since the ratio of the remaining amount of uranium-238 is half of the original amount.

What is decay?

The half-life of a quantity is the time it takes to reduce to half of its initial value. In nuclear physics, the term is commonly used to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used to describe any type of exponential decay in general.

Given that a rock that originally had a mass of 1.00 gram.

The formula of decay is

A(t) = A₀ (0.5)^(t/ti)

Putting A₀ = 1.00 gram, A(t) = 0.50 gram, ti = half life = 4.5  billions = 4500000000.

0.50 = 1 (0.5)^(t/4500000000)

0.5 = (0.5)^(t/4500000000)

Taking logarithm function on both sides:

log (0.5) = log[(0.5)^(t/4500000000)]

Applying the power rule of logarithm:

log (0.5) = (t/4500000000)]log[(0.5)

Cancel out log (0.5) from both sides:

1 = t/4500000000

t = 4500000000

t = 4.5 billions

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On assuming the given Hexagons are similar then the changes that will result in pair of Non Similar Hexagons is :

(c) adding 15° to angles G, H, and I and subtracting 15° from angles J, K and L .

The Hexagons are said to be similar if they have matching sides in the same proportion .

If the same operation is performed on every side of the hexagon , then the hexagon will remain similar ,

So , from the given operation , the operation that is not performed on each side or on each hexagon , it will result in  Non similar hexagon .

The operation performed in option (c) performs addition on G, H, I and subtraction on angles J, K, L .

Therefore , it will result in Non Similar Hexagons .

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Answer:

To reflect a triangle across the y-axis, you need to negate the x-coordinate of each vertex.

The original triangle with vertices (1, 3), (2, 5), and (4, 3) will be reflected across the y-axis to become a new triangle with the following vertices: (-1, 3), (-2, 5), and (-4, 3).

Keep in mind that a reflection across the y-axis means that the object is flipped along the y-axis. Therefore, the x-coordinate of each vertex is multiplied by -1, which flips the object horizontally.

Answer:

21/10

Step-by-step explanation:

42/20

divide both numerator and denominator by 2

=21/10

So, none of these sides can be the sides of a right triangle.

In a right triangle, one of the sides is the hypotenuse and the other two sides are called legs. The hypotenuse is always the longest side and the side opposite the right angle. The two legs are the shorter sides and the sides that form the right angle.

In the given triangle 2.5 cm, 6.5 cm, 6cm none of these sides can be the sides of a right triangle because according to the Pythagorean theorem, In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, for a right angled triangle with legs of 6cm and 6.5cm the hypotenuse must be greater than 6.5cm and smaller than sqrt(6^2 + 6.5^2) = 8.66cm but the hypotenuse is 2.5cm which is less than 6.5 cm. So it is not a right triangle.

It is important to note that in a right triangle, one of the angles is always 90 degrees and is called the right angle. The side opposite to the right angle is the hypotenuse and the other two sides are the legs.

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The three types of graphs are bar graphs, line graphs and pie chart

The three types of graphs can be noted as -

Bar graph - It is a form of a chart in which distinct values or data sets are represented by rectangular bars. The bars, which can be horizontal or vertical, can be used to compare various values or data sets. A bar graph might be used, for instance, to compare the population of several cities or the sales of various items.

Line graph - It changes or trends over time are represented by a series of points connected by lines. To track changes in data, such as stock prices, temperature, or population increase, line graphs are frequently utilised. The progression of the data through time can be demonstrated by the line.

Pie chart - This chart employs a circular shape divided into wedges to depict percentages or proportions of a whole. The size of wedges indicates the percentage or proportion of each wedge's respective category, with each wedge standing for a separate category. A pie chart could be used to display the allocation of revenue among various departments within a corporation or the breakdown of spending in a budget.

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The number that represent the product of ac is 18 and the sum of b is -9 .

The factored form of the trinomials is (x-3)(x-6)

An algebraic statement with three on-zero terms separated by + or - is called a trinomial. A trinomial exists when three monomials are separated by addition or subtraction. The formula for a quadratic trinomial is ax² + bx + c, where a, b, and c are real, non-zero values.

An algebraic statement with variables and constants is a quadratic trinomial. It is written as ax² + bx + c, where a, b, and c are real non-zero values and x is the variable. Leading coefficient "a," linear coefficient "b," and additive constant "c" all refer to the same constant. A quadratic trinomial is also used to explain the discriminant D, which is expressed as D = b² - 4ac and determines the quantity of an expression. The discriminant aids in categorizing the many quadratic trinomial instances. A quadratic equation, such as ax² + bx + c = 0, is one in which the value of a quadratic trinomial with a single variable is zero.

The trinomial is x² - 9x + 18

In the expression ax² + bx + c

here a = 1,  b = -9 and c = 18

The term that represent the product of ac = 1* 18 = 18

The term represent the sum of b = -9

Factoring The trinomial we get,

x² -9x + 18

= x² - 3x - 6x + 18

= x(x-3) -6(x-3)

=(x-3)(x-6)

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This exponential function can be used to model the value of a dirt bike valued at $9000 over time. The function expresses the amount of value the bike loses each year, which is 18%. This means that the value of the bike decreases by 18% each year.

f(x) = 9000(0.82)^x

After 4 years, the bike costs $6955.12.

f(x) = 9000(0.82)^x

After 100 years, the bike costs $8.87.

This exponential function can be used to model the value of a dirt bike valued at $9000 over time. The function expresses the amount of value the bike loses each year, which is 18%. This means that the value of the bike decreases by 18% each year. After 4 years, the bike would cost $6955.12. After 100 years, the bike would cost $8.87. This exponential function can be used to determine the value of the bike at any given time, depending on the number of years that have passed since the bike was purchased.

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The value for x is 53 given the total area of the parallelogram and the triangle is 120 square meters.

To find the area of the parallelogram and the triangle, we can use the formulas for the area of a parallelogram and the area of a triangle. The area of a parallelogram is base times height, so in this case it would be 1298 = 1032 square meters.

The area of a triangle is (1/2) base heights, so for this case, it would be (1/2)1298 = 520 square meters. To find the value of x, we can use the given information that the total area of the parallelogram and the triangle is 120 square meters.

We can set up an equation: 1032 + 520 = 120. Solving for x, we get x = 53.

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The solution set for the system of inequalities is (-1, -2).

Option A is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

y ≤ 3x + 1 ____(1)

x - y > 1 _____(2)

From (1 ) and (2) we get,

y = 3x + 1

Substituting in x - y = 1

x = 1 + y

x = 1 + 3x + 1

x - 3x = 2

-2x = 2

x = -1

Substituting in x = 1 + y

-1 = 1 + y

y = -1 - 1

y = -2

This means,

The solution set is (-1, -2).

Thus,

The solution set is (-1, -2).

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