Trapezoid PQRS has vertices P(0, 0), Q(0, 4), R(6, 4), and S(12, 0).
What is the length of the midsegment?

please help me its the last question on this test and i only have 20 mins left of this class

Answer:

w = 0, z = − 2

Step-by-step explanation:

The solution for the given system of equations is: w = 0 and z = -2.

What is a system of equations?

A system of equations is a collection of two or more equations with the same set of unknowns. For a system to have a unique solution, the number of equations must equal the number of unknowns.

The equations are as follows:

[tex]3w-4z=8[/tex]-------- (1)

[tex]2w+3z=-6[/tex]-------(2)

The solution for the above equation,

Multiply the equation 1 by 2,

⇒([tex]3w-4z=8[/tex]  )*2 --------- (3)

Multiply the equation 2 by 3,

⇒([tex]2w+3z=-6[/tex] )*3 --------(4)

Now solve equations 3 and 4 to get,

⇒ [tex]-17z=34[/tex]

⇒ [tex]z= -2[/tex]

Now substitute the value of z in equation 1,

⇒  [tex]3w-4(-2)=8[/tex]

⇒ [tex]\\3w=0[/tex]

⇒ [tex]w=0\\[/tex]

Hence we can conclude that the solution for the given system of equations is w = 0 and z = -2.

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A cosine and sine function can be expressed in terms of an imaginary exponential using Euler's formula: e^(iθ) = cos(θ) + i*sin(θ).

This formula can be derived by using the Taylor series for e^x, and replacing x with iθ.

A cosine and sine function can be expressed in terms of an imaginary exponential using Euler's formula: e^(iθ) = cos(θ) + i*sin(θ).

Conversely, an imaginary exponential can be expressed in terms of cosine and sine by solving for θ in the above equation. This can be done by taking the inverse cosine and inverse sine of both sides to get θ = cos^(-1)(e^(iθ)) = sin^(-1)(i*sin(θ)). Combining these equations gives θ = sin^(-1)(i*(e^(iθ) - cos(θ))).

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The domain of a function refers to the set of all possible inputs for the function.

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The difference between the area of triangle ABC and the area of triangle EFJ is 0 square unis

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

Trapezoid ABCD and trapezoid EFGH are congruent.

From the complete question added as an attachment

We can see that the two triangles have the same base and the same height due to the congruence of the two trapezoids

This means that their areas are equal

The difference between equal values is 0

Hence, the area difference is 0

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The figure of the coterminal angle of 300° on a circle in standard position is attached in the solution.

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.

Coterminal angles are two angles in the standard position where one angle is a multiple of 360 degrees larger or smaller than the other. That is, if angle A has a measure of M degrees, then angle B is co-terminal if it measures M +/- 360n, where n=0,1,2,3, ...

Starting from that position, 300° is drawn by moving around the circle to the left "counter-clockwise" and ending at the 300° measure.

The negative coterminal angle is the angle that would end in the same place if we went to the right instead of right on the circle. It is equal to the original 300° minus 360°

Coterminal angles Ac to angle A may be obtained by adding or subtracting k⋅360° or k × (2π)

Hence, Ac = A + k⋅360°, if A is given in degrees.

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The criterion that she should use to prove that triangles RST and XYZ are congruent are:

i. Hypotenuse Leg (HL)

ii. Side-Angle-Side (SAS)

When the corresponding properties i.e. length of sides and measure of internal angles of two or more triangles are equal, then the triangles are said to be congruent. The relations can be shown using some theorems.

From the given triangles RST and XYX, it can be observed that;

TR ≅ XZ

RS ≅ XY

<R ≅ <X   (given)

<T ≅ <Z   (given)

Angles R and X are included angle of the triangles. Thus, the criterion that can be used to show that triangles RST and XYZ are congruent at;

i. Hypotenuse Leg (HL)

ii. Side-Angle-Side (SAS)

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The fraction of water left from the bottle which was 1 liter is 3/4 liter.

Fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, from the bottle which was 1 liter, Juan drank 1/4. The amount that is left will be:

= 1 - 1/4

= 3/4

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Answer:

The gutters are 24 ft above the ground. For safety, the distance a ladder reaches up a wall should be four times the distance from the bottom of the ladder to the base of the side of the house. Therefore, the ladder must be 6 ft from the base of the house.

Answer:

Step-by-step explanation:

1.50/6 = 0.25

3/5 = 0.6

0.25*2 = 0.5

0.6*3 = 1.8
1.80+0.50 = 2.30

$2.30

Answer:

The two numbers are 17 and 7

Step-by-step explanation:

Translate this word problem into a math equation

If we let x and y be the two unknown numbers

One-half the sum of two numbers is 12 ==>

So one equation is 1/2(x + y) =12

Multiplying throughout by 2 gets rid of the denominator:
2 x 1/2 x (x + y) = 2 x 12

x + y = 24   (1)

One of the numbers is three more than two times the other number:
x = 2y + 3

or

x - 2y = 3  (2)

Equation (2) - Equation (1) =>

x + y - (x -2y) = 24 - 1
x + y - x + 2y = 21

3y = 21

y = 21/3

y = 7

With y = 7, substituting in equation 1 gives

x + y = 24

x + 7 = 24

x = 24-7

x = 17

The two numbers are 17 and 7

The probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear is 21/36

What is Probability ?

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes

Given ,

A bowl at a delicatessen contains a mix of 15 apples, 12 oranges, and 9 pears

so , we have to find  the probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear.

Choosing orange or a pear ,

= 12c1 + 9c1

= 12+9

= 21

Total = 36.

Probability = 12 + 9 / 36

= 21 / 36 .

Therefore , The probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear is 21/36

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I will order a pizza tonight only if we eat dinner at home is a conditional statement.

Sentences are groups of words that convey complete and logical meaning. They have subjects and predicates. It can be in form of exclamation and questions consisting of main and subordinating clauses.

Conditional statements are sentences where the subordinating clause influences whether the action that will be performed or not in the main clause. In these statements, the subordinating clause is also called the antecedent, and the main clause is called the consequent.

There are two types of Conditional statements, they are Implicative and predictive statements. Implicative sentences are based on facts whereas predictive statements depend on a situation dependent on a hypothetical case.

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The  difference in the account balances at the end of the loan terms is, $1770.87. So option B is correct

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

Given that,

Offer 1-  5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term Offer

Offer 2-  3.75% annual interest compounded monthly for a 66-month term

In offer 1,

Total amount A  = $32487.50

In offer 2,

Total amount =

[tex]A = P[ 1 + r/n]^{nt}[/tex]

[tex]A = 25000[ 1 + 0.0375/12]^{12*5.5}[/tex]

A = $30,716.63

Difference = 32487.50 - 30716.63

                  = $1770.87

Hence, the difference in account balance is $1770.87

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According to the Greek geocentric paradigm, a planet moves retrogradely when it actually goes backward in its orbit around Earth. So the option b is correct.

The geocentric paradigm, also known as geocentrism, which is frequently and particularly shown by the Ptolemaic system, is an outdated explanation of the cosmos that places Earth at its center. The Sun, Moon, stars, and planets all orbit Earth according to the majority of geocentric models.

Since humans have been gazing up at the stars for thousands of years, our perception of what the Universe looks like has undergone a significant transformation.

In time, humanity also realized that the Earth was a sphere and developed logical justifications for how other heavenly bodies behaved. By classical antiquity, scientists had developed theories about how the planets moved and how all the celestial bodies interacted. This led to the development of the now-defunct Geocentric model of the cosmos, which described how the Sun, Moon, and firmament revolved around our earth.

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The complete question is:

In the Greek geocentric model, the retrograde motion of a planet occurs when (a) Earth is about to pass the planet in its orbit around the Sun. (b) the planet actually goes backward in its orbit around Earth. (c) the planet is aligned with the Moon in our sky.

Answer:

1015

Step-by-step explanation:

29 es un número primo.

Por tanto:

29*35 = 1015

El mínimo común múltiplo de 29 y 35 es:

1015

Transformation includes changing the position of a shape.

The sequence of metamorphosis is 90 degrees counterclockwise gyration, followed by a vertical restatement to the right by 2 units.

What's meant by sequence?

The ordered brace- rule for each are :

(x,y)⇒ (-y,x) and (x,y)⇒(x+2,y)

The sequence of metamorphosis.

From the figure, we observed that ABC was rotated and also restated

So, the sequence of metamorphosis on ABC are

90 degrees counter clockwise gyration.

Vertical restatement to the right by 2 units.

The ordered brace rule :

When a point is rotated 90 degrees counter clockwise, the rule of metamorphosis is :

x, y)->(- y, x)

When a point is restated 2 units right, the rule of metamorphosis is :

x, y)->( x 2, y)

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Transformation includes changing the position of a shape.

The sequence of metamorphosis is 90 degrees counter clockwise gyration, followed by a vertical restatement to the right by 2 units.

The ordered brace- rule for each are :

(x,y)⇒ (-y,x) and (x,y)⇒(x+2,y)

The sequence of metamorphosis.

From the figure, we observed that ABC was rotated and also restated

So, the sequence of metamorphosis on ABC are

90 degrees counter clockwise gyration.

Vertical restatement to the right by 2 units.

The ordered brace rule :

When a point is rotated 90 degrees counter clockwise, the rule of metamorphosis is :

x, y)->(- y, x)

When a point is restated 2 units right, the rule of metamorphosis is :

x, y)->( x 2, y)

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Answer:

c

Step-by-step explanation: got it     right on test

The linear function that models the graph is given as follows:

a) y = -2x/3 - 4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -4, hence the intercept b is obtained as follows:

b = -4.

When x increases by 6, y decays by 4, hence the slope m is obtained as follows:

m = -4/6

m = -2/3.

Hence the function is defined as follows:

y = -2x/3 - 4.

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True. The three numbers can be the measures of the sides of a triangle.

What is the triangle inequality theorem?

The triangle inequality theorem is a fundamental principle in Euclidean geometry that states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This means that in any triangle, no side can be longer than the sum of the other two sides.

The three numbers 4, 7, and 8 can be the measures of the sides of a triangle. This is because of the triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for any triangle, the sum of two sides must always be greater than the third side.

For example, in this case,

4 + 7 = 11 > 8,

7 + 8 = 15 > 4,

4 + 8 = 12 > 7

Hence, 4, 7, and 8 can be the measures of the sides of a triangle, so the correct response would be "True".

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It will take 51 days to fill the Olympic sized pool.

Time and work have a relationship that is

Work Completed is equal to Time x Rate of Work.

Alternately, Rate of Work = Time Taken / 1.

Alternatively, Time Taken = 1 / Rate of Work

Considering that,

Pool volume is 6.6043 x 105 gallons, or 6,600,430 gallons.

9 litres of water are delivered through a hose every minute.

Therefore, the amount of water delivered by hose every hour is equal to (9 * 60) gallons.

Water provided by hosen each day is equal to (9 * 60 * 24) gallons, or 12,960 gallons.

Thus, the amount of time needed to fill the pool is equal to 6,600,430/12960.

There are 50.9 days needed to fill the pool.

51 days were needed to fill the swimming pool.

The Olympic-sized pool will therefore fill in 51 days.

The Complete Question is Olympic sized pool.

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Answer:

224 total cookies sold

Step-by-step explanation:

if 9 sugar with every 5 cholates then, 144/9 = 16

so there were 16 times 5 cookies were sold with means

80 cholate cookies were sold

80+ 144= 224

:)

The value of x which makes the equation true is 15.

What is the system of equations?

A system of equations is a set of two or more equations that contain multiple variables. These equations are typically used to describe a real-world situation and are solved simultaneously to find the values of the variables.

To solve a system of equations for unknown variables, you can use one of several methods, such as substitution, elimination, or graphing.

To solve a system of equations such as x-4=11, you have to find the value of x which will make the equation true.

x-4=11

x=15

Hence, the value of x which makes the equation true is 15.

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Chung is going to be able to get the representative sample by carrying out a random selection.

It would be helpful to get the multiple samples because it is a way w=of getting the true representation of sample.

Chung could generate a representative sample by randomly selecting a group of teachers from the school population and surveying them about their hobbies.

It would be helpful to generate multiple samples because, with only one sample, there's always a chance that the sample is not truly representative of the population. By generating multiple samples, Chung can compare the results and see if there is a consistent pattern among the samples, which would increase the likelihood that the results are representative of the population.

Additionally, by comparing multiple samples, Chung can also estimate the degree of variability in the population and the sample, this allow him to have more robust conclusions.

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The length of AC of the given right angle triangle is; AC = 8

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse, Opposite and the adjacent side.

Now, the given triangle is a right angle triangle and using Pythagoras theorem, we can say that;

AC = √(BC² - AB²)

Thus;

AC = √(10² - 6²)

AC = √64

AC = 8

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Answer:

c

Step-by-step explanation:

it is 4×+5 which is easy as u tines it by fixing the sum into parts and its eisier

Answer:

x > 0

Step-by-step explanation:

An open circle means less than or greater than the number it is on.

A closed circle means less than or equal to, or greater than or equal to the number it is on.

This graph has an open circle on zero with the arrow pointing to the right.

so x>0