Write a paragraph proof to prove that if P, Q, R, and S are collinear, PQRS, and O is the midpoint of PR, then R is the midpoint
of QS.

Because PQ RS and congruent segments have ___ lengths, PQ = ___ Because Q is the midpoint of PR, ___ so R is the midpoint of QS. PQ ___ By the Select Choice Property of Equality. QR

The values of the radical expressions are [tex]\frac{5x^4z^3}{7y}[/tex] and [tex]2x^2y\sqrt{5z}[/tex]

Expressions are mathematical statements that are represented by variables, coefficients and operators

Expression 1

Here, we have

[tex]\sqrt{\frac{25x^8z^6}{49y^2}}[/tex]

Take the square roots of 25 and 49

So, we have

[tex]\frac{5}{7}\sqrt{\frac{x^8z^6}{y^2}}[/tex]

Next, we apply the law of indices in simplifying the radical expressions

This gives

[tex]\frac{5}{7}\frac{x^{(8/2)}z^{(6/2)}}{y^{(2/2)}}[/tex]

Evaluate

[tex]\frac{5}{7}\frac{x^4z^3}{y}[/tex]

Rewrite as

[tex]\frac{5x^4z^3}{7y}[/tex]

Expression 2

Here, we have

[tex]\frac{\sqrt{100x^4y^2z}}{\sqrt 5}}[/tex]

Take the square roots of 100

So, we have

[tex]10\frac{\sqrt{x^4y^2z}}{\sqrt 5}}[/tex]

Rationalize

[tex]10\frac{\sqrt{5x^4y^2z}}{5}[/tex]

Next, we apply the law of indices in simplifying the radical expressions

This gives

[tex]10\frac{\sqrt{5z}x^{4/2}y^{2/2}}{5}[/tex]

Evaluate

[tex]2\sqrt{5z}x^2y[/tex]

Rewrite as

[tex]2x^2y\sqrt{5z}[/tex]

Hence, the solution is  [tex]2x^2y\sqrt{5z}[/tex]

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Answer:

16!

Step-by-step explanation:

The sequence shows that from left to right, the numbers are being divided by two (or multiplied by 1/2). So, for that reason I think that the answer must be 16.

Answer:

A

Step-by-step explanation:

it reflects over the y axis

The coordinates of the vertices of triangle A'B'C' after a reflection over the y-axis to triangle ABC are: C. A' = (3, -3), B' = (6, -3), C' = (5, -6), D' = (0, -6).

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (x, y).

By applying a reflection over the y-axis to triangle ABC, the coordinates of the vertices of the image triangle A'B'C' include the following:

(x, y)                    →            (x, y)

Point A = (3, -3)   →  Point A' = (3, -3)

Point B = (6, -3)   →    Point B' = (6, -3)

Point C = (5, -6)   →     Point C' = (5, -6)

Point D = (0, -6)   →     Point D' = (0, -6)

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The scale factor of figure A to figure B is 5/2

A scale factor can be defined as the ratio of the scale difference between  a given original shape and a new shape.

It is seen as a number from which the size of a dimensional shape or figure can be transformed with respect to its original size or magnitude.

It is also described as the ratio between corresponding measurements of an object and a representation of that object.

The formula for scale factor is expressed as;

Scale factor = Dimension of the new shape ÷ Dimension of the original shape

This is so for the downgrading of a shape

Now, we have;

Scale factor = Adjacent of the triangle A/adjacent of triangle B

Scale factor = 10/ 4

Reduce to simply forms

Scale factor = 5/ 2

Hence, the scale factor is 5/2

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Z is Odd.

Eg :- The Association between Height and Age

This is a relation since you would get various heights if you entered a specific age and checked all the persons of that age. Nevertheless, if you were to look at a person's height over time, it would depend on their age.

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Triangle A is right angled triangle

Triangle B is right angled triangle

Triangle C is obtuse angled triangle

Triangle D is acute angled triangle

In right angled triangle one of the three angles in the triangle is 90 degrees

In acute angled triangle all the angels in the triangle is less than 90 degrees

In obtuse angled triangle one of the three angles in the triangle is greater than 90 degrees

In triangle A one of the angle is 90 degrees, then the triangles is right angled triangle

In triangle B one of the angle is 90 degrees, then the triangles is right angled triangle

In triangle C one of the angle is greater than 90 degrees, then the triangle is obtuse angled triangle

In triangle D all the angles are less than 90 degrees, then the triangle is acute angled triangle

Hence, Triangle A is right angled triangle

Triangle B is right angled triangle

Triangle C is obtuse angled triangle

Triangle D is acute angled triangle

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The total surface area of the pyramid (a) is  624.32 cm² , and of pyramid (b) is 265.6 m²  .

The Total Surface Area of the Pyramid with pentagon base can be calculated using the formula

TSA = 5/2*b(a+s) ,

where b is the base length (side of pentagon)

s is the slant height ,

a is the apothem

and the Total Surface Area of the Pyramid with square base can be calculated using the formula .

TSA = b² + 2bs

where , b is the base and

s is the slant height .

Pyramid (a)

we can see from the figure that ,the pyramid has a pentagon base ,

So, the TSA will be 5/2*b(a+s) ,

in the figure , given that height =12 cm , apothem = 7.8cm

we find the slant height by Pythagoras theorem

(slant height)²=(height)²+(apothem)²

(slant height)² = 12² + 7.8²

(slant height) = √(12² + 7.8²)

(slant height) = √(144+60.84)

(slant height) = 14.3 cm

Substituting in TSA formula , TSA = 5/2*b(a+s)

we get ,

TSA = 5/2*11.3(7.8+14.3)

= 2.5*11.3(22.1)

= 28.25*22.1

=624.32 cm²

Pyramid (b)

we can see from the figure that ,the pyramid has a square base ,

So, the TSA will be b² + 2bs,

in the figure , given that height =12 m , apothem = 4 m

we find the slant height by Pythagoras theorem

(slant height)²=(height)²+(apothem)²

(slant height)² = 12² + 4²

(slant height) = √(12² + 4²)

(slant height) = √(144+16)

(slant height) = 12.6 m

Substituting in TSA formula , TSA = b² + 2bs

we get ,

TSA = 8² + 2*8*12.6

= 64 + 16*12.6

= 64 + 201.6

= 265.6 m²

Therefore , the total surface area of the pyramid (a) is 624.32 cm²  , and of pyramid (b) is 265.6 m² .

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Answer:

x = 40

Step-by-step explanation:

We just have to manipulate the terms, putting each term that has the variable "x" on one side of the equation like this:

5x + 8 = 7x - 72​

5x - 7x = - 72 - 8​

-2x = -80

x = -80/--2

x = 40

Answer:

x = 40

Step-by-step explanation:

Given equation:

[tex]5x+8=7x-72[/tex]

Add 72 to both sides:

[tex]\implies 5x+8+72=7x-72+72[/tex]

[tex]\implies 5x+80=7x[/tex]

Subtract 5x from both sides:

[tex]\implies 5x+80-5x=7x-5x[/tex]

[tex]\implies 80=2x[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{80}{2}=\dfrac{2x}{2}[/tex]

[tex]\implies 40=x[/tex]

Therefore, the solution to the given equation is x = 40.

Given vector v as a linear combination of the standard unit vectors i and j would be, vec v = 10 i -4 j

In this question, we have been given a vector whose initial point is (-2, -1) and the final point is (8, -5)

We need to write vector v as a linear combination of the standard unit vectors i and j.

Let (x1, y1) = (-2, -1) and (x2, y2) = (8, -5)

We know that for vector A having initial point (x1, y1) and terminal point (x2, y2), a linear combination of the standard unit vectors i and j is:

vec A = (x2 - x1)i + (y2 - y1)j

So, for given vector it would be,

vec v = (x2 - x1) i + (y2 - y1) j

vec v = (8 - (-2)) i + (-5 - (-1)) j

vec v = (8 + 2) i + (-5 + 1) j

vec v = 10 i -4 j

Therefore, given vector v as a linear combination of the standard unit vectors i and j would be, vec v = 10 i -4 j

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Answer:

Step-by-step explanation:

Answer:

78, 3, 28, 42

Step-by-step explanation:

This appears to be a repeating sequence of four numbers:

72, 3, 28, 42

so the missing 4 numbers must be as above

The function which represents the relation between the perimeter and the length of the square is; y = 4x.

For the given question;

Let x be the side of the square.

Let y be the perimeter of the square.

Perimeter is 4 times the side of the square.

Then,

Perimeter = 4×side

y = 4x.

Thus, the function which describes the relation between the perimeter and the side of square is y = 4x.

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Answer:2 to the 5, 8 to the 2, and 4 to the third

Step-by-step explanation:

2x2x2x2x2=64

8x8=64

4x4x4=64

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:slope(m) = \dfrac{5}{2} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Slope (m) of a line can be calculated by using this formulae :

[tex]\qquad \tt \rightarrow \: m = \dfrac{rise}{run} [/tex]

Considering two points [ (60 , 0) and (80 , 50) ]

[tex]\qquad \tt \rightarrow \: m = \dfrac{y2 - y1}{x2 - x1} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{50 - 0}{80 - 60} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{50}{20} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{5}{2} [/tex]

So, slope of given line is 5/2

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

To convert Celsius to Fahrenheit, we take the given Celsius measurement, multiply it by 1.8, and add 32, and vice versa.

To convert Celsius to Kelvin, we add 273 into the given Celsius measurement, and vice versa.

1) 18oC to F and to K

18oC = 18 x 1.8 + 32 = 64.4oF = 18 + 273 = 291oK

2) 95oF to C to K

95oF = (95-32) : 9/5 = 35oC = 35 + 273 = 308oK

Answer:

The total of all calories in a coffee with milk and sugar, is somewhere between 120 and 180. A couple of cups per day could easily add a lot of calories to the 2 000 calories needed per day.

Step-by-step explanation:

Answer:

A standard coffee with whole milk and sugar contains around 140 calories. This number can increase depending on the type of milk used, as well as the amount of sugar added.

The items matched in the left column to the items in the right column are

Ratio is the number representing a comparison between two named things or quantities.

1. total to fish

= 8 : 3

2. starfish to fish

= 5 : 3

3. starfish to total

= 5 : 8

4. fish to starfish

3 : 5

In conclusion, the ratio of the total to fish to starfish is 8 : 3 : 5

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Answer:

2.4x10^6

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

assuming everyone takes their own car, 9.75+17.75 * 7 = 192 I don’t know the state tax, because each state is different but 192 gives about $3 worth of room for tax. If the tax is higher in your state maybe I’d answer with 6 people. Hope this helped!

23

Explanation

Complementary angles are pair angles with the sum of 90 degrees, so we can say that

are complementary angles, therefore

Step 1

so,we need to equals to 90 and solve for x

so, the answer is

23

I hope this helps you

Answer:

x < 0.5

Step-by-step explanation:

2(1 - x) > 2x ( divide both sides by 2 )

1 - x > x ( add x to both sides )

1 > 2x ( divide both sides by 2 )

0.5 > x , that is

x < 0.5

The hiking trail that has the least change in elevation, related to sea level, is:

Southern Moon.

The change in altitude of each trail is calculated as the subtraction of the highest altitude by the lowest altitude, that is:

Change in elevation = highest altitude - lowest altitude.

For Eastern Point, the change is given as follows:

Change = 78 - (-85) = 78 + 85 = 163 feet.

(subtracting by a negative is the same as adding to the positive of the number).

For Northern Star, the change is given as follows:

Change = 34 - (-150) = 34 + 150 = 184 feet.

For Southern Moon, the change is calculated as follows:

Change = 48 - (-62) = 48 + 62 = 110 feet.

The smallest amount is of 110, hence Southern Moon has the least change in elevation relative to sea level.

The table is shown by the image at the end of the answer.

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Answer: 18>=S>=-9

Explanation:

There are 29 nickels and 12 dimes in the piggy bank.

In this question, we have been given a piggy bank contains 2.65$ in nickels and dimes.

We need to find the number of nickels and dimes if the number of nickels is 7 less than three times the number of dimes.

Let x be the number of nickels and y be the number of dimes.

We know that, 1 dollar = 20 nickels

and 1 dollar = 10 dimes

So, we get an equation

0.05x + 0.1y = 2.65                   ...........(1)

Also the number of nickels is 7 less than three times the number of dimes.

x = 3y - 7                      .................(2)

Substitute above value of x in equation (1)

0.05(3y - 7) + (0.1)y = 2.65

0.15y - 0.35 + 0.1y = 2.65

0.25y = 2.65 + 0.35

0.25 y = 3

y = 12

Substitute above value of y in equation  (2)

x = 3(12) - 7

x = 29

Therefore, there are 29 nickels and 12 dimes in the piggy bank.

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The triangle is Isosceles and Acute.

From the given data, the coordinates of the three points of the triangle are, A(2, 3), B(8, 3), and C(5, 6).

applying the distance formula, D = √((x2-x1)²+(y2-y1)²) the distance AC and BC are obtained as 3√2 and the distance AB as 2√3.

From this, it can be concluded that AC=BC≠AB.

thus since two of the sides, AC and BC are equal and the third side AB is not equal to AC and BC hence the given triangle is an isosceles triangle.

To check whether the given triangle is right, acute.

A right triangle is a triangle with one of its angles equal to 90 degrees.

An acute triangle is a triangle with all three of its angles less than 90 degrees.

An obtuse triangle is a triangle with at least one of its angles greater than 90 degrees.

To check whether the given triangle is right, acute, or obtuse we use the law of cosines.

To find the angle of a triangle given 3 of its sides, let the angle between the sides AB and AC be A then,

cos(A) =  (AC² + AB² − BC²)÷(2×AB×AC).

cos(A) = (3√2² + 2√3² - 3√2²)÷(2×2√3×3√2) =2÷√6

[tex]cos^{-1}[/tex](2÷√6) = 39.182.

Let the angle between the sides AB and BC be B then,

cos(B) =  (BC² + AB² − AC²)÷(2×AB×BC).

cos(B) = (3√2² + 2√3² - 3√2²)÷(2×2√3×3√2) =2÷√6

[tex]cos^{-1}[/tex](2÷√6) = 39.182.

Let the angle between the sides AC and BC be then,

cos(C) =  (AC² + BC² − AB²)÷(2×AC×BC).

cos(C) = (3√2² + 3√2² - 2√3²)÷(2×3√2×3√2) =2÷3

[tex]cos^{-1}[/tex](2÷3) = 53.544.

Since all the angles A, B, and C is less than 90 degrees the triangle is acute.

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Answer:

-1.5 goes in between -2 and -1

3/2 goes in between 2 and 1 but closer to 1

-2/3 goes in between 0 and -1 but closer to 0

I’m not very sure about -4/3 but I think it goes in between -2 and -1 but closer to -1 than 3/2

Step-by-step explanation:

By using a translation rule, the coordinates of C' are (- 1, - 2). (Correct choice: E)

Triangles are defined by the locations of its three vertices on Cartesian plane and we must find the locations of the images of the three vertices after applying a translation rule. In this case, we must translate each vertex  2 units upward and 4 units to the right. The general translation formula is described below:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that C(x, y) = (- 5, - 4) and T(x, y) = (4, 2), then the location of the image of point C is:

C'(x, y) = (- 5, - 4) + (4, 2)

C'(x, y) = (- 1, - 2)

The coordinates of C' are (- 1, 2).

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