Proving that a quadrilateral is a parallelogram quiz part 1:
State which method we can use to show that the quadrilateral is a parallelogram. a. Both pairs of opposite angles are congruent.
b. Both pairs of opposite sides are congruent.
c. Both pairs of diagonals bisect each other.
d. Both pairs of opposite sides are parallel.

The outside dimensions of the house are 11' 9" x 15' 11".

To determine the outside dimensions of the house, we need to take into account the thickness of the interior and exterior walls.First, we'll calculate the thickness of the interior walls. The interior walls are made of 2x4 (31/2") lumber with 1/2" drywall on both sides.

This means that each interior wall adds an additional 3 1/2" + 1/2" + 1/2" = 4 1/2" to the overall width and height of the house. Next, we'll calculate the thickness of the exterior walls. The exterior walls are made of 2x6 (51/2") lumber with 1/2" drywall on the interior and 7/16" siding with 35/8" brick on the exterior.

This means that each exterior wall adds an additional 5 1/2" + 1/2" + 7/16" + 3 5/8" = 8 11/16" to the overall width and height of the house. To calculate the outside dimension of the house, we will add the thickness of the interior and exterior walls to the dimensions of the interior rooms.

The outside dimension of the house will be:

Width = 11' 3" + 4 1/2" + 8 11/16" = 11' 9"

Height = 15' 7" + 4 1/2" + 8 11/16" = 15' 11"

So the outside dimensions of the house are 11' 9" x 15' 11".

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Question

The interior wall of a residence consists of a 2 × 4 (31/2") with 1/2" sheetrock on both sides. Exterior walls are 2 × 6 (51/2") construction with 1/2" sheetrock on the interior and 7/16" sheeting with 35/8" brick on the exterior. Determine the outside dimension of a house if there are two interior rooms with an interior wall. One room's dimensions I 11' 3", and Room 2 dimensions I 15' 7". How do I solve this?

Solving the system of equations by the method of elimination we get

x = 7 and y = 7/3

Here we are given the system of equations:-

x - 3y = -2                                                         [1]

x + 3y = 16                                                        [2]

Since nothing is mentioned we will use the method of elimination for the question

Subtracting equation [2] rom [1] we get

-6y = -14

or, y = 14/6

or, y = 7/3

Now adding equation [1] and [2] gives us

2x = 14

or, x = 14/2

or, x = 7

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Complete Question

What is the solution to this system of linear equations

x - 3y = -2,

x + 3y = 16

The conjecture for the relationship between the volume of the two spheres is "the volume of a sphere with radius 2y is 8 times greater than the volume of a sphere with radius y."

A conjecture is an educated guess or a hypothesis about a mathematical statement that has not yet been proven. It can be based on patterns or observations and can lead to further exploration and eventually a proof or disproof.

The formula for the volume of a sphere is given by (4/3)πr³, where r is the radius of the sphere. To compare the volumes of two spheres with different radii, we can substitute their respective radii into the formula.

If we let the radius of one sphere be y, then the volume of that sphere can be represented as (4/3)πy³. If we let the radius of the other sphere be 2y, then the volume of that sphere can be represented as (4/3)π(2y)³. Dividing the latter by the former, we get (4/3)π(2y)³ / (4/3)πy³ = (2y)³ / y³ = 8.

Thus, the volume of a sphere with a radius equal to 2y is 8 times greater than the volume of a sphere with a radius equal to y.

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Answer:

2x-2y

Step-by-step explanation:

1/3x + 2y + 5/3x - 4y

= 1/3x + 5/3x - 4y  + 2y

=6/3 x -2y

=2x-2y

The inequality equation is x ≤ ( -12 )

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

( 1/4 )x  ≤  -3   be equation (1)

On simplifying the equation , we get

x/4 ≤ -3

Multiply by 4 on both sides of the equation , we get

x ≤ ( -3 ) ( 4 )

x ≤ -12

Therefore , the value of x is less than or equal to -12

Hence , the inequality equation is x ≤ -12

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The height of the board up the side of the building is 7.5 feet.

An 8-foot-long board is leaning against a building. The angle formed by the ground and the board is 70 degrees.

The height of the board to the side of the building can be calculated as follows:

Therefore, the situation forms a right-angle triangle.

Using trigonometric ratios,

sin 70° = opposite / hypotenuse

sin 70° = x / 8

cross multiply

x = 8 sin 70°

x = 8 × 0.93969262078

x = 7.51754096629

Therefore,

distance of the board up the building  = 7.5 feet

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Rounded to the nearest foot, the height of the tree is 31 feet.

Height is a measurement of distance from the ground to the top of an object, such as a person, animal, or building. It is typically measured in centimeters (cm) or feet and inches. Height is an important measurement for medical professionals, as it can provide insight into a person's overall health and wellbeing.

Using the tangent formula in trigonometry, the height of the tree can be calculated as follows:
tan(angle of elevation) = Opposite/Adjacent
tan(angle of elevation) = 47/h
h = 47/tan(angle of elevation)
Therefore, the height of the tree is h = 47/tan(angle of elevation) = 47/tan(47°) = 47/1.53 = 30.78 feet
Rounded to the nearest foot, the height of the tree is 31 feet.

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Complete Question:
From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is : height of the tree to the nearest foot. The height of the tree is feet. Round your answer to the nearest foot. with explanation. (And photo in question)

Answer:

Step-by-step explanation:

okay bc the inches is 26 so the answer is 88

bc if u subtract this 26 with this 1 its will. be 25 so add 50 to 25 it will be 88

Translation, rotation, and reflection are three of the fundamental transformations.

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Answer:

5%

Step-by-step explanation:

First, you do:

$2100/7 = $300

Then you do:

r x 6000 = $300

r = 300/6000 = 0.05

Finally, you do:

0.05 x 100 = 5%

So the interest rate is: 5%

About 285 numbers lie between the values 10 and 14. (option C).

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or a Gaussian distribution. In statistics and the natural and social sciences, normal distributions are crucial concepts.

There are 600 numbers and their mean is 10 where the standard deviation is 2.

47.5% of the numbers should fall between 10 and 14, as expected. In a normal distribution, 47.5% of the sample size will fall between the mean and two standard deviations on either side of it.

By doing calculation on option C, we got that = [tex]\frac{285}{600}*100=47.5[/tex]

Hence, option C is correct, i.e., about 285 numbers would lie between the values 10 and 14.

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The graph that makes the increase in life expectancy from 1975-2000 appear to be relatively small is given by the following option:

b. A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 0 to 100 in increments of 10.

The total increase is given as follows:

80 - 76.6 = 3.4 years.

Hence the higher the difference between the bounds of y, the smaller the difference will appear, meaning that the graph is given by option b.

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From probability of occurence of events the large box holds 180 hats.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows

Let us check a simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

The probability is classified into theoretical probability and experimental probability.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Here we have 60 hats in the mall box.

And a large box holds 180% as many hats as the mall box is given.

So, 180/100 ×60 = 180

Therefore, from probability of occurence of events the large box holds 180 hats.

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The factored form of given equation 9x² - 12x + 4 is (3x - 2)(3x - 2).

The given expression is 9x² - 12x + 4

By splitting the middle term, let us factor this polynomial.

To identify the factors we have to consider factors of 36 as (9 × 4)

9x²- 6x - 6x + 4

=3x(3x - 2) - 2(3x - 2)

=(3x - 2)(3x - 2)

Another example of a quadratic polynomial can be taken to demonstrate similar factorization:

x² + 9x + 20

= x² + 5x + 4x + 20

= x × (x + 5) + 4 × (x + 5)

= (x + 5)(x + 4)

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The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

You should perform x trials until you observe a success.

We have given that,

There are exactly two possible outcomes success and failure.

We have to determine the following is NOT a common characteristic of a binomial distribution.

By process of elimination:-

A binomial experiment is a statistical experiment that must meet certain requirements

All trials are independent.

There are a fixed number of n trials.

The probability of success, p, is the same for each trial.

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The value of Angle ADB, which is the angle created while moving from A to D to B. Angle ABM is the angle created while moving from point A to point B to point M is [tex]41^{0}[/tex]

Due to the fact that angle ADB is an inscribed angle, its measure is halved compared to the angle of the arc that it intercepts. In other words, the angle is 40 degrees in length, which is equal to half of an 80 degree angle.

By adding up all of your balances at the end of each day for each eligible month, you may get your average daily balances (ADB) by dividing that amount by the number of days in that qualifying month.

3x - 16 = 9x + 4

4x = 20 x = 5 m

with BCE: 9 (5) + 4 = 49°

m with ADB = 41°

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No, the Sine law cannot be used directly on right triangles.

What is right triangle?

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). The angle that measures 90 degrees is formed by two sides of the triangle, called the legs, and the third side, called the hypotenuse, is the side opposite the right angle. The legs of the right triangle are perpendicular to each other, meaning they form a 90 degree angle.

What is law of sines?

The sine law, also known as the "law of sines," is a mathematical relationship that relates the lengths of the sides of a triangle to the sines of its angles. the law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

What is Pythagorean theorem ?

The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, can be used to solve for unknown side lengths in a right triangle. This theorem is particularly useful in trigonometry, geometry and navigation.

A right triangle is a special type of triangle that has one angle that measures exactly 90 degrees (a right angle). Since the sine law relates the lengths of the sides of a triangle to the angles, it can be used to solve for unknown side lengths or angles in a right triangle, as long as the other side lengths and angles are known.

However, it is important to note that the sine law is typically used to solve for unknowns in non-right triangles, where the angle measures are not known. In a right triangle, the Pythagorean theorem can be used instead, which relates the length of the hypotenuse to the lengths of the legs.

So, Sine law cannot be used directly on right triangles, but it can be used in solving triangles which includes right triangles as well.

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There are eight perfect squares from 1 to 100 (i.e., except 1 and 100). They are represented as 4, 9, 16, 25, 36, 49, 64 and 81.

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, we can say that a perfect square is a number that can be expressed as the product of an integer by itself or as the second power of an integer. Perfect Square Formula : Let us consider if N is a perfect square of a whole number x, then N can be represent as the product of x and x = x². So, the perfect square formula formula is , N = x². For example, If x = 3, and N = x². This means, N = 3× 3 = 3² = 9 . Here, 9 is a perfect square because it is equal to the square of a whole number, 3. We have to determine the number of perfect squares from 1 to 100.

1² = 1 ; 2² = 4 ; 3² = 9 ; 4² = 16 ; 5² = 25 ; 6² = 36 ; 7² = 49 ; 8² = 64 ; 9² = 81 ; 10² = 100

As we get, there are 10 perfect squares from 1 to 100. But, in actual manner they are only 8 perfect squares from 1 to 100 after excluding 1 and 100.

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Nata was using the partial products method to solve the multiplication problem 42 × 15. She likely wrote 20 because she was finding the product of 42 and 10, which is 420. Writing 20 was likely a shorthand for the digit 2 in 420.

In the partial product method, each digit of one number is multiplied by each digit of another number, keeping each digit in its original place. Place value is typically used to calculate the partial product. To get the product of two-digit numbers, we employ the partial product method.

The partial products method involves breaking down one factor into its place value components and multiplying each component separately, then adding the products together to get the final answer.

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A suspension bridge: a parabola represents the profile of the cable of a suspended-deck suspension bridge.

A graph is a topic which gives us the numerical facts into visual form.

That is, a graph gives the visual representation of the data collected.

The towers supporting the cable of suspension bridge are 15m apart and 12m above the bridge it supports.

Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.

lets have the bridged centered at the origin

Three points are needed on the parabola

x = 0, y = 20

x = -7.5, y = 12

x = +7.5, y = 12

using the form ax^2 + bx + c = y, we know that c=20

x=-7.5, y = 12 and x =+7.5, y = 12; write two equations

-7.5^2a - 7.5b + 20 = 12

+7.5^2a + 7.5 + 20 = 12

use elimination

56.25a - 7.5b + 20 = 12

56.25a + 7.5b + 20 = 12

addition eliminates b

112.5a + 40 = 24

112.5=16

a = 16/112.5

a = 0.1422

Now we can write the equation

y = 0.1422x^2 + 2

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She did not find the correct solution. She graphed the bottom equation of the System incorrectly.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

According to the Problem

y = 3x - 3.....(1)

2x + 2y = 8........(2)

Substitute the value of y from equation 1 to equation 2

2x + 2(3x -3 ) = 8

2x + 6x -6 = 8

8x = 14

x = 1.75

Tus,

y = 3 * 1.75 - 3

y = 2.25

Therefore, she did not find the correct solution to the system of equations.

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The team Seahawk has a larger mean value of about 23 inches.

The three main methods for identifying the average value of a set of integers are mean, median, and mode.

Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.

The middle value in a list that is arranged from smallest to greatest is called the median.

The value that appears the most frequently on the list is the mode.

We know the mean of a data set is [tex]\frac{1}{n}\sum_{i=1}^{n} x_i[/tex].

So, The mean of Pelicans is, [tex]\frac{1}{15}\sum_{i=1}^{n} x_i[/tex].

= (1/15)×[20 + 20 + 22 + 21 + 22 + 23 + 22.5 + 24 + 21.5 + 22 + 23.5 + 22 + 23.5 + 22 + 24.5].

= (1/15)×[333.5].

= 22.23.

The mean of Seahawks is,

= (1/15)[21 + 23.5 + 23.5 + 22.5 + 23 + 21 + 23.5 + 23.5 + 22.5 + 23 + 21 + 23.5 + 23.5 + 22.5 + 23].

= 22.7.

So, Seahawks have a larger value of about 23 inches.

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According to definition of proportional ratios, 15 / 20 is not a multiple of 20 / 21.

In this problem we find two ratios in fraction form, both are proportional if the numerator and denominator of one of them are multiple of the corresponding elements of the other. First, write the fraction with the lowest numerator:

15 / 20

Second, multiply numerator and denominator by 4 / 3:

[15 · (4 / 3)] / [20 · (4 / 3)]

20 / 26.667

Ratio 15 / 20 is not proportional to ratio 20 / 21.

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Answer:

Image result for System with one solution 1 3 System with no solutions System with infinite number of solutions 2x 2y 8 and 3x 3y 12 3x 3y 12 and 5x 5y 10 y 4 x and y x 2

You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.

Step-by-step explanation:

Answer:

1) 2x + 2y = -8 and 3x + 3y = - 12: Infinite: the lines are the same.

2) - 3x + 3y = 12 and 5x + 5y = 10: One solution (-3.10)

3) y +4 =-x and y = -x + 2: No solutions. Parallel

Step-by-step explanation:

See the attached worksheet. All three explanations are used to identify the three systems of equations. Some of the equations are equal to each other, apparent only when one rearranges the equations.

The solution set of the expression is y > -5

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

-y-8<-3 ory+5>19

Express the inequality properly

So, we have the following expression

-y - 8 < -3 or y + 5 > 19

Collect the like terms

This gives

-y < 8 - 3 or y > 19 - 5

Evaluate the like terms

This gives

-y < 5 or y > 14

Rewrite as

y > -5 or y > 14

When combined, we have:

y > -5

Hence, the solution set is y > -5

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Complete question

For the following inequality expression, determine the solution set

-y-8<-3 ory+5>19

Answer:

s - 1 - t(s - 1)/(r + 1)

Step-by-step explanation:

x/(s - 1) + t/(r + 1) = 1

x/(s - 1) = 1 - t/(r + 1)

x = s - 1 - t(s - 1)/(r + 1)

To find the median of a cumulative frequency graph the median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.

When a set of numbers is arranged in ascending order of magnitude, the middle number is known as the median. A collection of n numbers has a median value of (n+1)/2. N is the cumulative frequency in the case of a cumulative frequency curve.

The median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.

Create the cumulative frequency curve using the numbers provided first. Mark the point with the highest cumulative frequency, then draw a line perpendicular to the Y-axis that precisely passes through it. The lowest cumulative frequency is then marked, and a line is drawn parallel to the X axis. Mark the place where these two lines intersect.

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Answer:

-1/2, 5/3

Step-by-Step Explanation:

6z^2 - 7z - 5 = 0

=> 6z^2 - 10z + 3z - 5 = 0

=> 2z(3z - 5) + 1(3z - 5) = 0

=> (2z + 1)(3z - 5) = 0

=> z = -1/2, 5/3

Hope it helps.

If you have any query, feel free to ask.

Between these two integers the following surds lie

(1) √5 = 1-5

(2)√1 = 1-2

(3)√107 = 1-107

(4)√3​  = 1-3

There are two simple steps to surd simplification:

Split the number within the root into its prime factors. √50=√(5×5×2)

Based on the root write the prime factors, outside the root. In case of square root, write one factor outside the root, for every two similar factors within the root.

√18+√50.

Root of any whole number must always be greater than 1 as

√1 = 1

√2 = 1.41 > 1

Therefore, Between these two integers the following surds lie

(1) √5 = 1-5

(2)√1 = 1-2

(3)√107 = 1-107

(4)√3​  = 1-3

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The Hall family utilizes sprinklers for 15 hours compared to the 35 hours used by the Nguyen family.

The Hall family utilizes sprinklers for 15 hours compared to the 35 hours used by the Nguyen family.

Let h and n represent the amount of hours each household uses its sprinkler, the Halls and the Nguyens, respectively.

They use for a total of 50 hours, thus either h + n = 50 or h = 50 - n.

Additionally, their total water output is 1050 L, thus we may use the equation below.

35h + 15n = 1050

Replace h with h = 50 - n to get

35(50 - n) + 15n = 1050

1750 - 35n + 15n = 1050

35n - 15n = 1750 - 1050

20n = 700

34 hours, n

15 hours equal 50 h, 50 n, and 35 n.

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