which postulate or theorem can be used to prove <RPQ = <RNM​

slope = m = (4 - 0) / (1 - 0) = 4

y = mx + b

y = 4x + b

substitute (0, 0) to find b

b = 0

y = 4x

Step-by-step explanation:

are you sure there is no other given info? do you have to solve in terms of m and D?

Answer:

ok

Step-by-step explanation:

The vector <5√74 / 74, - 7√74 / 74> is the unit vector in the direction of <5, - 7>.

Vectors are described by two features: (i) magnitude, (ii) direction. The magnitude is the quantity associated with a vector and determine by Pythagorean theorem, and the direction indicates the "distribution" of the magnitude along the ortogonal axes of the vector. Unit vectors are vectors of magnitude 1 and we can determine it by using the following definition:

[tex]\vec u[/tex] = <x, y> / ||<x, y>||

Where ||<x, y>|| = √(x² + y²)

Please notice that [tex]\vec u[/tex] represents the unit vector.

If we know that <x, y> = <5, - 7>, then the unit vector is:

Magnitude

||<x, y>|| = √[5² + (- 7)²]

||<x, y>|| = √74

Unit vector

[tex]\vec u[/tex] = <5, - 7> / √74

[tex]\vec u[/tex] = <5 / √74, - 7 / √74>

[tex]\vec u[/tex] = <5√74 / 74, - 7√74 / 74>

<5√74 / 74, - 7√74 / 74> is the unit vector in the direction of <5, - 7>.

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By the zero vector property x=y.

Suppose for full generality that V is any vector space and x,y,z is any vector in V. Suppose, x+z = y+z. Show that x=y. Since z is in v, there exists a vector z in v, such that

= z + (-z) = 0, because x+y=y+z

Thus x+z=y+z

= (x+z)+(-z) = (y+z)+(-z) and thus

= x+(z+(-z)) = y + (z+(-z)) because addition is associative in vector

= x+0 = y+0 because additive inverse exists in a vector

= and thus x=y by the properties of zero vector

Also according to the question, it is now proved that x+z=y+z implies x=y and v has the cancellation property.

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Answer:

#0.85

Step by step:

13.60/16 = #0.85

pls give me brainliest

pls:(

Answer:

[tex]y=\frac{1}{2}x-5[/tex]

B: smaller rate of change but night y intercept

Step-by-step explanation:

y intercept is -5 because when x is zero y is -5

Now to find slope

-1-(-3)/8-4

-1+3/4

2/4

1/2

Now we can put it in an equation

y=1/2x-5

2nd question

-6-4/0-2

-10/-2

5

-6 is greater then -10 so the y intercept is bigger

So B is correct

Answer: i'm writeing this so you can mark the other person brainliest

Step-by-step explanation:

The difference is 4[tex]x^{2}[/tex] - 14x - 4

Given,

In the question:

To find the difference:

The difference of [tex]2x^2-9x+8[/tex] subtract from [tex]6x^2 -5x-12[/tex] .

Now, According to the question:

Based on the given condition:

Formulate:

[tex]6x^2 -5x-12[/tex] -  [tex]2x^2-9x+8[/tex]

Simplify and expand:

[tex]6x^2 -5x-12[/tex]  - [tex]2x^2-9x+8[/tex]

Reorder and gather like terms:

[tex](6x^2-2x^2)[/tex] + (-5x - 9x) + (-12 + 8)

Collect coefficient of like terms

(6 - 2)[tex]x^{2}[/tex] + (-5 -9)x + (-12 + 8)

Calculate the sum or difference:

4[tex]x^{2}[/tex] - 14x - 4

Hence, The difference is 4[tex]x^{2}[/tex] - 14x - 4 .

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The amount earned as commission in 2011 is $44928

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

Commission percentage = 12%

Average sales per week = $7200

The amount earned as commission in the 2011 is then calculated as

Amount = Commission percentage x Average sales per week x Number of weeks

Substitute the known values in the above equation

So, we have

Amount = 12% x 7200 x 52

Evaluate

Amount = 44928

Hence, the commission amount is $44928

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The value of x in the given equation is x = -12/35

From the question, we are to solve the given linear equation.

The given linear equation is

-4 1/5x = 1.44

To solve the given equation, we will determine the value of x in the equation.

First, we will convert 4 1/5 to an improper fraction

-4 1/5 = -21/5

Also,

We will convert 1.44 to a fraction

1.44 = 144/100 = 36/25

Now,

-21/5(x) = 36/25

-21(x) × 25 = 36 × 5

x = (36 × 5) / (-21 × 25)

x = -180/525

x = -12/35

Hence, the value of x is x = -12/35

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Answer:

[tex] \sf \: \frac{7}{12} [/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: \frac{1}{4} + \frac{1}{3} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{1}{4} + \frac{1}{3} [/tex]

[tex] \sf \rightarrow \: \frac{(1) \times 3}{(4) \times 3} + \frac{(1) \times 4}{(3) \times 4} [/tex]

[tex] \sf \rightarrow \: \frac{3}{12} + \frac{4}{12} [/tex]

[tex] \sf \rightarrow \: \frac{(3 + 4)}{12} [/tex]

[tex] \sf \rightarrow \: \frac{7}{12} [/tex]

Hence, the answer is 7/12.

Answer:

  y = 9x -78

Step-by-step explanation:

You want the equation y + 6 = 9(x − 8) written in slope-intercept form.

Solve for y and simplify.

  y +6 = 9x -72 . . . . . . . . eliminate parentheses

  y = 9x -78 . . . . . . . . . subtract 6

__

Additional comment

The given equation is written in point-slope form. It has a slope of 9 and goes through the point (8, -6).

Slope-intercept form is ...

  y = mx +b

where m is the slope and b is the y-intercept.

Answer:

B

Step-by-step explanation:

Alright, to start off... we need to find a range of value that sqr 74 is between.

To do that, we can check by just trying some random numbers.

Let's try 8 -- 8^2 is 64. Let's try 9 -- 9^2 is 81. So the sqr 64 is 8 and sqr 81 is 9.

sqr 74 is between sqr 64 and sqr 81, so the statement is true. However, the multiple-choice has decimal numbers, meaning that they want us to be more specific.

First, we can cross out 9.5, because we don't want to expand our range, we want to keep it as accurate as possible.

That leaves us 8.5

To find if 8.5 fits the criteria, meaning that it can't be larger than sqr 74, we can use two methods.

The first method is preferred, you simply need to multiply them. I hope you know how to do that by hand. We get 72.25

The second method is less preferred but works. We need to approximate the value by finding the mean of 64 and 81, because 8.5 is the mean of 8 and 9. The approximate value should be very close to the true value. By doing (81+64)/2, we get 72.5

Now, double-check: is the 74 between 72.25 and 81? Yes, it is!
Hence, that gives us the answer that sqr74 is between 8.5 (sqr 72.25) and 9 (sqr 81)

Answer:

[tex]f( x) = x2 - 7 x[/tex]

Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.

Given function is: [tex]f(x) = -2x^{2}+12x+5[/tex]

[tex]f(x) = a(x-h)^{2} +k[/tex] , where (h,k) is the vertex

Apply completing the square method to find vertex

[tex]f(x) = -2x^{2}+12x+5\\\\f(x) = -2(x^{2}-6x)+5[/tex]

Lets take half of coefficient of x is -6

divide by 2 that is -3

square it [tex](-3)^{2}[/tex] that is 9

Add and subtract 9

[tex]f(x) = -2(x^{2}-6x+9-9)+5[/tex]

Take out -9 and multiply by -2

[tex]f(x) = -2(x^{2}-6x+9)+18+5\\\\f(x) = -2(x^{2}-6x+9)+23[/tex]

Now factor the parenthesis part

[tex]f(x) = -2(x-3)^{2} +23[/tex]

The value of h=3  and k=23

So vertex is (3,23)

The value of 'a' is -2, it means the parabola is upside down. so vertex is maximum

Hence the answer is the vertex is maximum at (3,23)

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Answer: 10

Step-by-step explanation: The least common denominator is 10 because both integers 2 and 10 have a LCM OF 10. Your welcome. :’j

Answer: 10

Step-by-step explanation: The least common denominator is 10, cuz it is the lowest common multiple of 10 and 2, 2 × 5 =10, 10× 1 = 10. they r both common multiples.

By evaluating a linear equation, we will see that after two seconds there are 93 gallons of fuel.

We know that the tank initially has 103 galons of fuel, and we know that it releases 5 gallons per second at a constant rate.

So, after x seconds, the amount of fuel inside the container is:

F(x) = 103 - x*5

so we have a linear equation.

The amount of fuel in the tank after 2 seconds is given by:

F(2)=  103 - 2*5 = 103 - 10 = 93

After 2 seconds there are 93 gallons of fuel.

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The percentage of games which Jay won is 44 percent.

This is referred to as a number or ratio expressed as a fraction of 100 and is usually denoted as %.

Percentage is calculated by : parts/whole × 100.

In this scenario we can deduce that the part is 154 while the whole is 350. Therefore: 154/350 × 100 = 44 percent.

Hence the most appropriate choice is 44 percent.

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From the given relative frequency table , answer of the following questions are as follow:

a. Percentage of students those who have completed the exam review with the condition that they have passed the exam is given by 55%.

b.  Percentage of students those who have completed the exam review with the condition that they have failed the exam is given by 10%.

c. Yes, there is association between the two completing the exam review and passing the exam is only 55%.

As given in the question,

From the given relative frequency table , answer of the following questions are as follow:

Total percentage of students completing the exam review = 65%

a. Completed the exam review with the condition that they have passed the exam = 55%

b. Completed the exam review with the condition that they have failed the exam = 10%

c. Yes, there is association between the two completing the exam review and passing the exam is only 55% and those who have completing the exam review but failed are 10%.

Therefore, from the given relative frequency table , answer of the following questions are as follow:

a. Percentage of students those who have completed the exam review with the condition that they have passed the exam is given by 55%.

b.  Percentage of students those who have completed the exam review with the condition that they have failed the exam is given by 10%.

c. Yes, there is association between the two completing the exam review and passing the exam is only 55%.

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The rectangle with the sides 4 and 3 is the required rectangle.

The correct option is third shape.

Area is the amount of area occupied by an object's flat (2-D) surface or shape.

The area of the triangle,

= 1/2 x base x height

= 1/2 x 6 x 4

= 12 square millimeters.

And rectangle has the same area as the triangle.

The rectangle with the sides 4 and 3 is the required.

Therefore, the rectangle with the sides 4 and 3 is the required rectangle.

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The height of woman who has a shoulder width of 18.5 inches is 74 inches.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Height of woman = 64 inches

Shoulder width = 16 inches

So, ratio = Height :  shoulder width = 64:16

let the height of a woman who has a shoulder width of 18.5 inches be x.

So, x:18.5.

Now,

64 / 16 =  x/ 18.5

4= x/18.5

x= 74

Hence, the height of woman who has a shoulder width of 18.5 inches is 74 inches.

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Answer:

x = 139°

Step-by-step explanation:

The sum of the internal angles of a triangles is 180°

a + 59 + 80 = 180

a = 180 - 139

a = 41°

a and x are supplementary angles. Supplementary angles sum 180°.

Then:

a + x = 180

41 + x = 180

x = 180 - 41

x = 139°

The number 1.23 x 10⁶ without scientific notation is 12,30,000.  

Scientific notation is a way to display extremely big or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper.

We use positive exponents for base 10 when expressing any huge integers in scientific notation. For example:

500000 = 5 x 10⁵, where 5 is the positive exponent.

We use negative exponents for base 10 when expressing any small integers in scientific notation. For example:

0.00005 = 2 x 10⁻⁵, where -5 is the negative exponent.

Here we have

The number 1.23 x 10⁶

We need to write the given number without scientific notation

In the given number the exponent of 10 = 6 and positive

Then we need to move the decimal place 7 places to the right or multiply the given decimal number with 1000000

Therefore,

1.23 x 10⁶ = 1.23 × 1000000 = 12,30,000.  

Hence,

The number 1.23 x 10⁶ without scientific notation is 12,30,000.

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The unit rate of three dollars for 2 1/2 hours of work is 1.2.

The rate is a ratio of change in one quantity with respect to other. The unit rate is a rate such that the denominator of the rate must be one. An item's unit rate is its rate for one of them. How many units of the first type of quantity are needed to make up one unit of the second type is expressed using a unit rate (or unit ratio).

Now, finding the unit rate for three dollars for 2 1/2 hours of work,

Unit rate [tex]=\frac{3}{2.5}[/tex]

= 1.2

Therefore, the unit rate of three dollars for 2 1/2 hours of work is 1.2.

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The values (d,n) that will be the solution of the equation are

A. (0,445)

D.(118,209)

E.(172,101)

The equation that we have in this problem is:

0.10d+0.05n=22.25

here

d is the number of dimes

n is the number of nickels

Diego collected a total of $22.25 and put it in the jar.

Simply substitute each pair (d,n) into the left term of the equation and see if the answer is 22.25 to determine which values can be the equation's solutions.

Now,

A. (0,445)

0.10d+0.05n=22.25

0.10(0)+0.05(445)=22.25

22.25=22.25

Yes, The point satisfy the condition.

B. (0.50,435)

0.10d+0.05n=22.25

0.10(0.50)+0.05(435)=22.25

21.08≠22.25

No, The point does not satisfy the condition.

C. (233,21)

0.10d+0.05n=22.25

0.10(233)+0.05(21)=22.25

24.35≠22.25

No, The point does not satisfy the condition.

D.(118,209)

0.10d+0.05n=22.25

0.10(118)+0.05(209)=22.25

22.25=22.25

Yes, The point satisfy the condition.

E.(172,101)

0.10d+0.05n=22.25

0.10(172)+0.05(101)=22.25

22.25=22.25

Yes, The point satisfy the condition.

Therefore, The values (d,n) that will be the solution of the equation are

A. (0,445)

D.(118,209)

E.(172,101)

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Answer:

-5

Step-by-step explanation:

We need to find the value of y to find the value of 8y + 3. So,

-11y - 9 = 2

Add 9 on both sides

-11y = 11

Divide 11 by -11

y = -1

Step 2:

8 x -1 + 3

-8 + 3

-5

So the value of 8y + 3 is -5

Answer:

Option C: 5

Step-by-step explanation:

1st coin = $8

2nd coin = $16

3rd coin = $32

4th coin = $64

5th coin = $128

Total spent = $248

The rectangular coordinates are

a. (1,0,0) ⇒ (x,y,z) = (0,0,1)

b. (18,1/3,1/4) ⇒ (x,y,z) = (11.022,11.022,9)

Let us take ( x, y, z ) as cartesian or rectangular coordinates and ( r, Θ, ∅ ) are the spherical coordinates, then

x   =   r.sinΘ.cos∅      →   1

y   =   r.sinΘ.sin∅       →   2

z   =   r.cosΘ               →   3

According to the given problem,

a.)   ( 1, 0, 0 )  =   ( r, Θ, ∅ )

Substitute the values r = 1, Θ = 0 and ∅ = 0 in 1, 2, 3.

1 ⇒ x   =   r.sinΘ.cos∅          

           =   1.sin0.cos0

           =   1.0.1

      x   =   0

2 ⇒ y   =   r.sinΘ.sin∅

            =   1.sin0.sin0

            =   1.0.0

      y   =   0

3 ⇒ z   =   r.cosΘ

            =   1.cos0

            =   1.1

       z   =   1

∴   ( x, y, z )   =   ( 0, 0, 1 )

b.)   ( 18, π/3, π/4 )   =   ( r, Θ, ∅ )

Substitute the values r = 18, Θ = π/3 and ∅ = π/4 in 1, 2, 3.

1 ⇒ x   =   r.sinΘ.cos∅

           =   18.sinπ/3.cosπ/4

           =   18.√3/2.1/√2

      x   =   11.022

2 ⇒ y  =   r.sinΘ.sin∅

           =   18.sinπ/3.sinπ/4

           =   18.√3/2.1/√2

       y  =   11.022

3 ⇒ z   =   r.cosΘ

            =   18.cosπ/3

            =   18.1/2

       z   =   9

∴   ( x, y, z )   =   ( 11.022, 11.022, 9 )

Therefore the rectangular coordinates for the spherical coordinates of

a. ( 1, 0, 0 )   is   ( 0, 0, 1 )

b. ( 18, 1/3, 1/4 )   is   ( 11.022, 11.022, 9 )

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The equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18]). So option(1) is correct.

Equivalent expressions are expressions that work the same way despite their appearance. When we plug in the same value(s) for the variable, two algebraic expressions have the same value (s).

Equivalent means that different terms and expressions with similar values are considered equal in mathematical form.

The given expression is

[(1.3^3)/(1.2^4)]^-6

Apply the indices power law to the above expression.

[(1.2^4)/(1.3^3)]^6

The exponents are then expanded using the power law of indices.

(1.2^[4x6])/(1.3^[3x6])

(1.2^[24])/(1.3^[18])

Hence, the equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18])

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