Draw an isospeles right triangle on the coondinate plane so that the midpoint of its hypotenuse is the origin. Label the coordinates of each vertex.

Answer:

Step-by-step explanation:

Angle (3x+31)° and angle (2x-6)° are supplementary angles

(3x + 31)° + (2x - 6)° = 180°

5x + 25° = 180°

5x = 155°

x = 31°

-----------------

check

3 * 31 + 31 + 2 * 31 - 6 = 180

180 = 180           (remember PEMDAS)

the answer is good

Answer:

the value it's -21

Step-by-step explanation:

5×(-4)+3×(-5)+14=

-20 + (-15) + 14=

-20 -15 + 14=

-35 + 14=

-21.

Answer:

opposite

Step-by-step explanation:

Answer:

£4240

Step-by-step explanation:

2%of 4000=80

80x3=240

4000+240=4240

Answer:

- 9 < x < - 3

Step-by-step explanation:

- 53 < 9x + 1 < - 26 ( subtract 1 from each interval )

- 54 < 9x < - 27 ( divide each interval by 9 )

- 6 < x < - 3

9.233050612 is a rational number.

Real numbers that can be expressed as a ratio of two integers, such as P/Q, where Q is not equal to zero, are referred to as rational numbers. Finite or repeating numbers are included in the category of rational numbers.

Real numbers are referred to as irrational numbers if they cannot be represented as the ratio of two integers. These are composed entirely of non-terminating, non-repeating numbers.

The given number 9.233050612 can be written in the form P/Q as :

9.233050612 = [tex]\frac{9.233050612}{1000000000}[/tex]

Hence, the given number is a rational number.

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The correct question is:

"9.233050612 is a rational or irrational number"

On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] the final answer in scientific notation is 3.5 ×[tex]10^{8}[/tex] .

The quantity 3.185 times ten raised to the seventeenth power can written as 3.185 × [tex]10^{17}[/tex] .

The quantity 9.1 times ten raised to the eighth power can written as 9.1 × [tex]10^{8}[/tex] .

On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] ,

( 3.185 × [tex]10^{17}[/tex] )/( 9.1 × [tex]10^{8}[/tex] ) = 0.35 × [tex]10^{17-8}[/tex] = 0.35 ×[tex]10^{9}[/tex] = 3.5 ×[tex]10^{8}[/tex] (in scientific notation)

Scientific notation is a floating-point system in which the numbers are expressed as the products consisting of a number between one to ten multiplied by an appropriate power of ten.

On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] the final answer in scientific notation is 3.5 ×[tex]10^{8}[/tex] .

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The equation of the line in slope-intercept form is  y = (2/5)x + (-3/2)  .

The equation of a line in slope-intercept form can be written as follows,

y = mx + c                                                       equation 1

m in the above equation represents slope of the line and c represents the intercept.

The given equation is (x/6) - (5/12)y = 5/8 .

To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as

(x/6) - (5/12)y = 5/8

On multiplying both sides of above equation by (12/5), we will get

   (2/5)x - y = 3/2

⇒ y = (2/5)x + (-3/2)                                                 equation 2

On equating equation 1  and equation 2, we will get

Slope of the line = m = 2/5

Intercept = c = -3/2

The equation of the line in slope-intercept form is  y = (2/5)x + (-3/2) .      

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Answer:

-1/2

[tex] - \frac{1 }{2} [/tex]

First the two fours cancel out so it's becomes

[tex] \frac{1 - 3}{4} [/tex]

then subtract

[tex] \frac{ - 2}{4} [/tex]

simplify

[tex] \frac{ - 1}{2} [/tex]

Isabel to complete one full rotation is 12 seconds.

In statistics, what does a probability mean?

In every 2 seconds the ride rotates 60º.

So, it takes 6 turns to rotate 6 × 60º or 360º.

Therefore, the time it takes

Isabel to complete one full rotation is 12 seconds.

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27 is the number that is a coefficient.

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.

A coefficient is a number or an alphabet that is multiplied by a variable of a single term or the terms of a polynomial. For example, in the term 7x, 7 is the coefficient. The coefficient of x in the term 3xy is 3y.

The variable is a symbol for a value we don't know yet. It is usually a letter like x or y.

In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

In the expression 38 + 27y the coefficient of y is 27, 38 is the constant and y is the variable.

we can identify a coefficient since it is always associated with a variable.

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you can either graph this or plug in values.

[tex]f(x)=3+\frac{1}{3}x[/tex]

[tex]f(-1)=3+\frac{1}{3}(-1)\\\\f(-1)=3-\frac{1}{3}\\\\f(-1)=2\ \frac{2}{3}\\\\f(0)=3\\\\f(1)=3\ \frac{1}{3}[/tex]

[tex]\therefore[/tex] we can conclude that this function is linear.

Also here is a graph

Answer:

UT=27

ST=18

RV=15

US=15

Step-by-step explanation:

If the entirety of RT is 30, then you'd divide that by 2 to receive the number for both RV and VT. 30 divided by 2 is 15.

Because RVS and UVT are vertical, they are both 27. Similarly, RVU and SVT are vertical to each other, so SVT is the same as RVU which is 18.

Hope this helps.

Answer:

x=2

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

3(4x-2)=2(5x+3)

12x-6=10x+6

    +6       +6

12x=10x+12

-10x -10x

2x=12

Divide by 2.

x=6

Hope this helps.

Step-by-step explanation:

Looks like it's a piecewise defined function. Where you see a circle, means it's not inclusive so at f(1) it should be define at y=3

The domain is  f[tex]o[/tex]g(x)= -30x+7

The domain is all the real numbers.

Given that f(x)=-5x-3 and g(x)=6x-2.

f[tex]o[/tex]g=f(g(x))

   =f(6x-2)-3

   =-5(6x-2)-3

   =-30x+10-3

f[tex]o[/tex]g =-30x+7

The domain is all the real numbers.

What is domain?

Specific to the internet, the term domain can refer to how the internet is structured, and domain also refers to how an organization's network resources are organized. In general, a domain is an area of control or a sphere of knowledge.

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The explicit formula is [tex]a_n = 2^{n-1}.10[/tex]

A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence. There are many types of sequences such as recursive sequences, arithmetic sequences, special sequences, quadratic sequences, geometric sequences etc.

Some examples for sequence are :

2,4,6,8,10,12

3,9,27,81,243

The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.

In a sequence , first term always known as initial term.

and difference between two terms are known as common difference. It is denoted by d.

General form of sequence is :

[tex]a_1,a_2,a_3,----,a_n[/tex]

where , [tex]a_n[/tex] = last term in sequence.

According to question,

[tex]a_1 = 10[/tex] and [tex]a_n=2a_{n-1}[/tex]

first find the sequence ,

[tex]a_2= 2 a_{2-1} = 2 a_1 = 2(10) = 20\\\\a_3= 2 a_{3-1} = 2 a_2= 2(20) = 40\\\\a_4= 2 a_{4-1} = 2 a_3= 2(40) = 80[/tex]

Thus sequence is 10,20,40,80,...

and the explicit formula for sequence is :

[tex]a_n = 2a_{n-1}\\= > a_n = 2(2a_{n-2}) = 2^2 a_{n-2}\\= > a_n = 2^2 (2a_{n-3}) = 2^3 a_{n-3}\\ .\\.\\= > a_n = 2^{n-1} a_{n-(n-1)} \\ = > a_n = 2^{n-1} .a_1 = 2^{n-1}.10[/tex]

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Answer: $3.40 per pint

Step-by-step explanation:

1 gallon=8 pints

3 gallons * 8 pints/1 gallon=

3*8/1=

3*8=24 pints in 3 gallons

$81.6 for 24 pints of paint

81.6/24=$3.40 per pint

  8. (-3)+4

= -24 +4

= -20

In algebraic equation or polynomial equation is an equation of the frame P=0 where P could be a polynomial with coefficients in a few field, regularly the field of the rational numbers.

algebraic equation, statement of the equality of two expressions defined by applying to a set of factors the algebraic operations, namely, expansion, subtraction, increase, division, raising to a control, and extraction of a root.

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Answer:

He shot a total of 2,415 free throws. He shot 255 on the 20th day.

Step-by-step explanation:

Rita has a head start, has she began her race 28 Mile ahead of the starting  point.

Since they moved at a constant speed, then there speed is the same through out the journey.

Speed is given by the slope:

(y2 - y1) / (x2 - x1) = (130 - 65) / (2 - 1) = 65 / 1 = 65 mph

Roger's starting position, when t = 0

t = 1 ; distance = 65 miles

t = 0 ; 65 - speed per hour = 65

At t = 0 ; 65 - 65 = 0 miles

Hence, Roger does not have a head start.

For Rita :

Speed is also constant :

Speed or rate = slope of the graph :

(y2 - y1) / (x2 - x1) = (158 - 93) / (2 - 1) = 65 / 1 = 65 mph  

Rita's starting position, when t = 0

t = 1 ; distance = 93 miles

t = 0 ; 93 - speed per hour

At t = 0 ; 93 - 65 = 28 miles

Hence, Rita has a head start of 28 miles.

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They can set up total 30 tables in 5 hours.

Multiply in mathematics refers to the continual addition of sets of same size.

2 × 3 = 6

It can be interpreted this way:

Three times two equals six.

Three times two equals six.

Six is two threes.

Given,

Andersons can set up 6 tables in 1 hour

Tables they can set up in 5 hours = 5 × 6

= 30

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Answer:

y is equal to 18

Step-by-step explanation:

[tex]3y+20-20=5y-16-20\\3y=5y-36\\3y-5y=5y-36-5y\\-2y=-36\\\frac{-2(y)}{-2}=\frac{-36}{-2}\\(\frac{-a}{-b} = \frac{a}{yb}) =\frac{2y}{2}\\\frac{2(y)}{2}=y\\=\frac{36}{2}\\=18\\y = 18[/tex]

If you double or halve the length of each of Pythagorean triplet the resulting triangle will always be Right Triangle.

Pythagoras Theorem states that the sum square of two sides of triangle is equal to the  square of longest side.

Let us take Pythagorean triplet as (6,8,10).

where base=6

perpendicular = 8

hypotenuse = 10

Part(a)

Let us double the length of each value

base = 12

perpendicular = 16

hypotenuse = 20

By Pythagoras Theorem

[tex]base^{2} +perpendicular^{2} =hypotenuse^{2}[/tex]

[tex]12^{2} +16^{2} =20^{2} \\ \\ 144+256=400\\ \\ 400=400[/tex]

Therefore the Triangle will be a Right Triangle as Pythagoras Theorem is satisfied.

Part (b)

Let us halve the length of each value

base=3

perpendicular = 4

hypotenuse = 5

By Pythagoras Theorem

[tex]base^{2} +perpendicular^{2} =hypotenuse^{2}\\\\3^{2} +4^{2} =5^{2}[/tex]

[tex]9+16=25\\ \\ 25=25[/tex]

Therefore the Triangle will be a Right Triangle as Pythagoras Theorem is satisfied.

Therefore ,  If you double or halve the length of each of Pythagorean triplet the resulting triangle will always be Right Triangle.

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The equation of the circle with radius 1 and center at (-6 , 10) is (x + 6)^2 + (y - 10)^2 = 1.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (-6 , 10)

r = 1

(x - -6)^2 + (y - 10)^2 = 1^2

(x + 6)^2 + (y - 10)^2 = 1

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Answer: The graph of f(x) is shifted to the right to create g(x).

Step-by-step explanation:

g(x) is the graph of f(x) shifted right 3 units.

There are 4 graph in the given picture. The 4th graph is the function other 1st, 2nd and 3rd graph are not a function.

Given that,

There are 4 graph in the given picture.

We have to find the graph is function or not.

We have to perform the vertical line test.

Use the vertical line test to determine whether a graph accurately represents a function. If a vertical line is moved across it and only ever touches it at one point, the graph is said to be a function. The graph is not a function if the vertical line traverses it more than once.

We have to draw the vertical lines on a graph if the vertical line touches the graph more then 1 then it is not a function if it touches 1 time then it is a function.

1st graph is not a function.

2nd graph is not a function.

3rd graph is not a function.

4th graph is a function.

Therefore, the 4th graph is the function other 1st, 2nd and 3rd graph are not a function.

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Answer:

1. translate

2.rotate

explanation:

first, translate a to the next quadrant.

second, rotate it 180 degrees.

Answer:

Figure A translated 2 figures down and mirrored to the right.

Figure A then rotated 180 degrees.