Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

The figure shows two right trapezoids. Trapezoid A B C D has right angles at B and C. Angle B is adjacent to the shorter parallel side. Angle C is adjacent to the longer parallel side. Angle A is obtuse. Angle D is acute. Sides A B and C D are parallel. The sides in order of length from shortest to longest are B C, A D, A B, and C D. Trapezoid R S P Q has right angles at S and P. Angle S is adjacent to the shorter parallel side. Angle P is adjacent to the longer parallel side. Angle R is obtuse. Angle Q is acute. Sides R S and P Q are parallel. The sides in order of length from shortest to longest are S R, R Q, R S, and P Q.

The two figures shown above are congruent. Identify the corresponding sides and angles.

Answer:

Line 1

Step-by-step explanation:

Slope = (y₂ - y₁)/(x₂ - x₁)

Now, in line 1, all the y coordinates are equal, meaning, that y₂ - y₁ = 0 no matter what. Hence, line 1 is the answer.

Cheers!

The expression can be used Jake paid each night for the hotel is:

x = d/5 - $50

Now, According to the question:

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

The given data is:

He bought a plane ticket for $250 and stayed in a hotel for 5 nights.

The price d is equal to $250 + 5 prices of staying in a hotel for a night.

If we let "x" be the price per night then we can get the following:

The expression will be:

d = $250 + 5x

5x = d - $250

[tex]x = \frac{d - 250}{5}[/tex]

x = d/5 - $50

Hence, The expression can be used Jake paid each night for the hotel is:

x = d/5 - $50.

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The ratio of the musicians to fashion professionals is 13 : 32

Total number of people on the guest list= 45

Number of musicians= 13

Number of fashion professionals = Total number of people on the guest list - Number of musicians

= 45 - 13

= 32 people

The ratio of the musicians to fashion professionals = 13 : 32

Ultimately, based on the given situation the ratio of musicians to fashion professionals = 13 : 32

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Answer: y = -3x + 2

Step-by-step explanation:

ur welcome

Answer:

B and C I think.....

Step-by-step explanation:

it makes sense cuz if u make a line it'll kinda go through.

Answer:

Step-by-step explanation:

The orthocenter

The correct answers are 1, 2, and 5 AB=BC,AD=2AC and BD=CD.

Circle is a two-dimensional shape made up of points that are all the same distance from the center point. This distance is called the radius. Circles are one of the most fundamental shapes in geometry, and can be found in nature in many places, from the sun to the rings of Saturn. Circles can also be used to create other shapes such as ellipses, sectors and arcs.

1. The two circles have the same radius.

2. The two circles intersect at two distinct points.

3. The line segment connecting A and C is the diameter of the larger circle.

4. The line segment connecting A and C is the radius of the smaller circle.

5. The two circles have different radii.

6. The two circles have the same circumference.

The correct answers are 1, 2, and 5.

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The (a) and (c) statements are correct out of five statements are (a) and (c) and other statments i.e., (b), (d) and (e) are too generalised statements.

We have a sample of midterm grades for five students are following 69, 62, 79, 87, 73. Average Formula : It is also called the arithmetic mean, which is calculated by dividing the sum of all given observations to the total number of observations.

Average = (a₁+ a₂+ a₃+ ---+ aₙ )/n

where, a₁, a₂,a₃,--,aₙ --> Obersvations

n --> number of observations

So, Average midgrade is written as

= (69+62+79+87+73)/5 = 370/5 = 74

a) Average of midgrade for the sample of five students is equals to 74, so it is a correct statement.

b) Statement (b) is too generalised because the average 74 is base only on a sample of five students not for all students.

c) A sample five students is selected from population (all students), so the average misgrade 74 of five students referred as estimate for all students who took the exam. Thus, it is correct statement.

d) This statement is too generalised because it is possible that the population deviates from this sample of five students.

e) This statement is too generalised because it is possible that the newly added five students could have different grades which may be lower than 62 and greater than 87.

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Complete question:

A sample of midterm grades for five students showed the following results: 69, 62, 79, 87, 73. which of the following statements are correct, and which should be challenged as being too generalized?

(a) the average midterm grade for the sample of five students is 74.

(b) the average midterm grade for all students who took the exam is 74.

(c) an estimate of the average midterm grade for all students who took the exam is 74.

(d) more than half of the students who take this exam will score between 67 and 82.

(e) if five other students are included in the sample, their grades will be between 62 and 87.

Therefore , the solution of the given problem of triangle comes out to be height x is 20 m.

Polygons include triangles since they have four sides or more. It has a simple, geometric shape. The letters ABC make up a triangle, which is a square angle. Euclidean geometry results in a single rectangle or square so when sides remain not coincident. Because they have 3 components and three corners, triangles are polygons. A triangle's corners are where its three sides meet. The total of the angles in a triangle is 180 degrees.

Here,

Given :

Area of triangle is  120 m².

the base length is 12m

To find the height = x,

=>Area = 1/2 * base * height

=> 120  = 1/2 * 12 * x

=> 120 = 6 *x

=> x = 120/6

=> x =20

Therefore , the solution of the given problem of triangle comes out to be

height x is 20 m.

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Answer:

Step-by-step explanation:

It will take 3 hours and 40 minutes for a car to travel 200km at an average speed of 55km/hr.

200km / 55km/hr = 3.63 hrs

3.63 hrs x 60 minutes/hr = 218 minutes

218 minutes - 60 minutes = 158 minutes

158 minutes / 60 minutes = 2.63 hrs

2.63 hrs + 1.37 hrs (3.63 hrs - 2.26 hrs) = 3.40 hrs

To calculate how long it will take a car to travel 200km at an average speed of 55km/hr, you first need to divide the distance (200km) by the speed (55km/hr). This gives you 3.63 hours. To convert this to minutes, you need to multiply this by 60 minutes/hour, which gives you 218 minutes. Subtracting 60 minutes from this gives you 158 minutes. To convert this to hours, you need to divide by 60 minutes/hour which gives you 2.63 hours. Then, you need to add 1.37 hours (3.63 hours - 2.26 hours) to get a total of 3.40 hours. Therefore, it will take 3 hours and 40 minutes for a car to travel 200km at an average speed of 55km/hr.

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There are several strategies for resolving systems of linear equations, including:

(1) Graphing Techniques

(2) The Substitution Method

(3) Using a linear combination

(4) The Matrix Approach

(1) Graphing Techniques: Useful if you simply need a broad answer or are certain that the intersection takes place at an integer location. To find where the two lines intersect, just plot them.

(2) The Substitution Approach: To begin, a linear equation for y must be resolved in terms of x. Substitute that expression for y in the other linear equation after that. A formula will be given to you in x. You'll know the intersection's x-coordinate if you can figure this one out. Insert x into either equation to get the equivalent y-coordinate.

(3) Using a linear combination: Add (or subtraction) a multiple of one equation to (or from) the other equation to make the x-terms or y-terms cancel out. Solve for x (or y, depending on which is left) before substituting to get the other coordinate.

(4) The Matrix Approach: This is actually just a streamlined notation of the Linear Combination approach.

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Answer: the bench is 138.6 inches long

Answer:

1

Step-by-step explanation:

According to Theorem 6.1C, a quadrilateral's subsequent angles are supplementary if it is a parallelogram.

One of the most fundamental geometric shapes is the square. This particular parallelogram contains four sides that are identical to one another and four right angles. Due to its two sets of parallel sides and four right angles, a square is also a rectangle.

A parallelogram's consecutive angles are congruent. A parallelogram's diagonals cut each other in half. A rhombus has four right-angled angles. A rhombus has consecutive sides that are congruent. Conclusion 6.3C. A parallelogram becomes a rectangle if one of its angles is a right angle.

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The population will reach 700,000 in the year 2044. The equation to calculate this is t = ln(700000/776000)/(-0.015), which gives t = 42.

1. We are given the population of San Francisco in 2002, which is 776,000.

2. We are also given the equation P=776000e^-0.015, which is a model for the population of San Francisco over time.

3. We need to figure out when the population will reach 700,000.

4. To do this, we need to rearrange the equation to solve for t, the number of years since 2002.

5. Rearranging the equation gives us t = ln(700000/776000)/(-0.015).

6. Plugging in our values gives us t = 42.

7. This means that the population of San Francisco will reach 700,000 in the year 2044 (i.e. 42 years since 2002).

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The additional angles are P and Q. The measure of angle P = 116 if the measure of angle Q is 64º

Additional angles add up to 180.

P+Q = 180

P +64 = 180

Subtract 64 from each side

P = 180-64

P =116

The complete question is:

Angle P and angle Q are supplementary angles. If the measure of angle Q is 64º, find the measure of angle P.

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The circumference of a circle with given radius is 30.1 meters.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Also, it has rotational symmetry around the center for every angle.

Given the radius of the circle = 4.8 m

to find the circumference,

circumference of a circle is given by

C = 2πr

where r = radius = 4.m

C = 2π(4.8)

C = 2(3.14)(4.8)

C = 30.144 m

C = 30.1 m

Hence the circumference is 30.1 metres.

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There are 1e-6 cubic meters in a cubic centimeter.

A centimeter is a metric unit of measurement used for measuring the length of an object. It is written as cm. It can also be defined as the unit of length in the International System of Units (SI), the current form of the metric system. It is equivalent to 1/100 meters.

A meter has 100 centimeters.

10 millimeters make one centimeter.

The centimeter can be written as cm.

While calculating the surface area of an object, the unit of measurement becomes cm².

While measuring the volume of an object, the unit of measurement becomes cm³.

Thus, There are 1e-6 cubic meters in a cubic centimeter.

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y =-1/2x+7 is the equation of the line that is parallel to 2x+4y=6 and passes through the point (6, 4).

Parallel to 2x+4y=6 and passing through(6,4) 2 x 4y = 6

Find the slope of this line and make y the subject 4y=-2x 6

By Dividing the equation by 4 we get:

y=-1/2 x + 3/2

Compare this equation with y=mx+b

slope m=-1/2

The slope of a line parallel to the above line will be the same

The slope of the required line will be - 1/2

m=-1/2,  at the point (6,4)

Finding b by plugging the values of m & the point in y=mx+b

4=-3+b

b= 7

m=-1/2

Plug value of the slope and b in y = mx +b

The required equation is y=-1/2x+7

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Answer:

what is the question?

Answer to what?

Answer: [tex]4\sqrt{26}[/tex]

Step-by-step explanation:

This is a rather tricky question at first, but it's easy when you figure out the trick.

The key here is using the Pythagorean theorem twice.

We see that the big triangle is divided by its height into two smaller ones.

First, use the Pythagorean theorem on the triangle on the left to find the height.

height = [tex]\sqrt{80-64}=\sqrt{16} =4[/tex]

Now that we know the height is 4, we can use the Pythagorean theorem on the triangle on the right to find x.

x = [tex]\sqrt{20^{2}+4^{2} } =\sqrt{416} = 4\sqrt{26}[/tex]

And there we have our final answer.

The height of the triangle will be equal to 16.4 cm.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that the two sides of the right-angle triangle are a = 10 cm and b = 13 cm.

The height of the triangle will be calculated as,

c² = a² + b²

c² = 13² + 10²

c² = 169 + 100

c = √( 269 )

c = 16.4 cm

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Mackenzie owed $100 after -4 weeks. This means that after 4 weeks, the amount she owed was $100 less than it was at the start.

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Answer:

160 cups are in 10 gallons

On solving the algebraic expression 4nm^0 × 2m^4n^3, the value is obtained as 10368.

What is algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

The given algebraic expression is -

4nm^0 × 2m^4n^3

The values for n and m is given as 2 and 3 respectively.

Substitute the values of n and m in the algebraic expression.

= 4nm^0 × 2m^4n³

= 4(2)(3)^0 × 2(3)^4(2)³

Use the exponents rule -

= 4(2)(1) × 2(81)(8)

Use the arithmetic operation of multiplication -

= 8 × 1296

= 10368

Therefore, the final value is obtained as 10368.

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If m=3 and n=2. What is 4nm^0 x 2m^4n^3 ?

The points D(3,-5), E(3, 4), and F(-4, 3) form a triangle. Then 26.701 unit is the perimeter of the triangle.

The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it. The perimeter of the form is equal to the algebraic sum of each side's length. For the various geometric forms, there are formulae accessible. The radius of a shape's edge is known as the perimeter. The length of the shape's edge is measured by its perimeter. All of the shape's sides added together provide it. It just has one dimension and uses linear units to represent itself. In contrast, area quantifies how much space a form takes up.

The points D(3,-5), E(3, 4), and F(-4, 3) form a triangle.

DE = [tex]\sqrt{(3-3)^2+ (4 +5)^2}[/tex]

DE = 9 units

EF = [tex]\sqrt{(-4-3)^2+ (3-4)^2}[/tex]

EF = √50 units

DF = [tex]\sqrt{(-4-3)^2 + (3+5)^2}[/tex]

DF = √113 units

So, the perimeter of the triangle DEF = sum of all three sides

= 9 units +  √50 units + √113 units

= 26.701 unit

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Answer:

250

Step-by-step explanation:

The length of the rectangular garden is 23 feet.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given that,

Length of the rectangular garden is 5 feet longer than its width.

Let w be the width of the rectangle.

Then w + 5 is the length of the rectangle.

Area of a rectangle = Length × Width

Area is given as 414 square feet.

(w + 5) w = 414

w² + 5w - 414 = 0

Factorizing,

(w - 18) (w + 23) = 0

w - 18 = 0, then w = 18

w + 23 = 0, then w = -23

w = -23 is not possible for the width.

So w = 18 feet

Length of the rectangle = w + 5 = 18 + 5 = 23 feet

Hence 23 feet is the length of the rectangle.

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When we say "solve for K" we mean to isolate K by itself on one side of the equal sign. You can do this by "moving" things from one side to the other using mathematical rules.

What does it mean to solve for K?

To isolate K by itself on one side of the equal sign is what we mean when we say "solve for K." Using mathematical principles, you can accomplish this by "moving" objects from one side to the other. The most crucial rule is that anything you do to one side of the equation must also be done to the other.

The K value, also known as the bending limit, of a cyclotron is the ratio between the obtainable energy and the charge-to-mass ratio, where is the particle's kinetic energy, m is the number of atoms, and k is the variational constant. By dividing the y-coordinate by the x-coordinate, we can calculate k when given any position because it is constant (the same for every point).

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