what do the numbers 1 through 10 add up to

The point where two lines meet is known as an angle.

What are some applications of two column proofs?

A two-column proof moves a reader from premise to conclusion by using a table to give a logical argument and assigning each column to carry out a specific task.

Given the following angles from the diagram

m < 2 = m < 4

m < 2 = 100°

Prove that m<3 = 70⁰

m<2 = m<4 (vertically opposite angles)

m<3 and m<4 are supplementary, hence

m < 3 + m < 4 = 180°      ( linear pair )

Substitute m<4 = 110⁰ into the expression

m < 3 + 110 = 180

m < 3 = 180 - 110

m < 3 = 70

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The complete question is -

Complete the two column proof. given 2=4 m<2=110 prove m<3=70

Answer:

d = 4

Step-by-step explanation:

the nth term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₄ = 27 , then

a₁ + 3d = 27 → (1)

Also

a₁ + a₄ = 42 ← substitute a₄ = 27

a₁ + 27 = 42 ( subtract 27 from both sides )

a₁ = 15

substitute a₁ = 15 into (1)

15 + 3d = 27 ( subtract 15 from both sides )

3d = 12 ( divide both sides by 3 )

d = 4

Step-by-step explanation:

the area of a rectangle is

length × width

or

base × height

it all depends on how you make the 2 dimensions.

anyway, the area is in our case

2×6 = 12 square units

A right angle is an angle of 90 degrees. A right angle is formed when two lines that are perpendicular to each other intersect. A right angle assumes the shape L.

Parallel lines are lines that do not meet or intersect at any point no matter how long they are extended. The sided of most quadrilaterals are parallel to each other and intersect at right angles. For example: squares and rectangles.

In our question, Jacqui will know that each pair of opposite sides are parallel since the corners are right angles, each pair of opposite sides will be perpendicular to the same line. As a result, each pair of opposite sides will be parallel.

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The perimeter of the shape is => 50cm.

Here, we have,

given that,

from the given diagram, we get,

there are two rectangles.

we get,

perimeter of one rectangle is:

2( 3+ 7) cm

=20 cm

perimeter of the other rectangle is:

2(4+11)

= 30cm

so, total perimeter = (20+30) =50cm

Hence, the perimeter of the shape is => 50cm.

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Answer:

Step-by-step explanation:

Question 1:

0.42 repeating is rational. A rational number is any integer, fraction, terminating decimal, or repeating decimal.

11/3 = rational. A rational number is any integer, fraction, terminating decimal, or repeating decimal.

6.25 is a rational number. A rational number is any integer, fraction, terminating decimal, or repeating decimal.

16[tex]\pi[/tex] = irrational irrational number, any real number that cannot be expressed as the quotient of two integers.

0.01045 is rational. A rational number is any integer, fraction, terminating decimal, or repeating decimal.

[tex]\sqrt{\frac{3}{16} }[/tex] = Irrational number because it cannot be expressed as a fraction of two whole numbers and it has no accurate decimal equivalent.

[tex]\sqrt{48}[/tex] = The square root of 48 is not a rational number, as it cannot be expressed in the p/q form.

[tex]\sqrt{\frac{16}{81} }[/tex] = rational. The square root of (16/81) is the same as the square root of 16 divided by the square root of 81. You can divide the fraction inside the radical before or after you calculate the square root. The result will be the same.Here we first calculate the square root of the numerator and the square root of the denominator separately, and then we divide the two:  √16   √81  =    4   9  ≈  0.4444 Alternatively, we first divide 16 by 81 and then do the square root of the quotient:√16/81 ≈ √0.1975 ≈ 0.4444

Question 2:

[tex]\frac{\sqrt{6} }{\sqrt{5} }[/tex] = irrational. Irrational number because it cannot be expressed as a fraction of two whole numbers and it has no accurate decimal equivalent.

[tex]\frac{\sqrt{6} }{5}[/tex] = irrational number because it cannot be expressed as a fraction of two whole numbers and it has no accurate decimal equivalent.

[tex]\sqrt{30}[/tex] = the square root of 30 is not a rational number. It is an irrational number, as it cannot be expressed in the form of p/q.

[tex]\frac{\sqrt{5} }{6}[/tex] = irrational number, as it cannot be expressed in the form of p/q.

[tex]\frac{\sqrt{30} }{5}[/tex] = irrational since there is no exact square root for 30 and 5.

Question 3:

[tex]\sqrt{68}[/tex] = 68 is not an exact square root so it is about 8.24621125124….. about 8.25 or 8.3 or just 8.

[tex]\sqrt{45}[/tex] x [tex]\sqrt{96}[/tex] = 12[tex]\sqrt{30}[/tex]

Answer:

5! = 120

Step-by-step explanation:

using the definition of factorial !

n! = n(n - 1)(n - 2) .... 3 × 2 × 1 , then

5! = 5 × 4 × 3 × 2 × 1 = 20 × 12 × 1 = 120

During surgery, the average flow rate of the medications administered to the patient is 23 milliliters per hour.

Flow rate, denoted by Q, is defined as the amount of volume V flowing after time t. The formula for flow rate is given by:

Q = V/t

where V is volume and t is time.

For the two medication administered, given the flow rate and time, solve for the volume of each, and its total volume.

V = Q/t

1 : V1 = Q1t1 = (14ml/h)(150 minutes)(1hour/60 minutes)

V1 = 35 ml

2 : V2 = Q2t2 = (30 ml/h)(4hrs)

V2 = 120 ml

Solving for the average flow rate by dividing the sum of the volume to the sum of the time.

Qave = (V1 + V2)/(t1 + t2)

Qave = (35 + 120)ml/(2.5 + 4)hrs

Qave = 23.84615385 ml/h

Rounding off to the nearest whole number.

Qave = 23 ml/h

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Answer:

whether the transaction

is a purchase or sale. Write a formula for the advisor's

commission. Let D represent the value of one transaction.

Give two examples of how this financial advisor could earn a

commision of $1000

Step-by-step explanation:

Answer:

none

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have

[tex]f(x) = 6x + 5[/tex]

[tex]g(x) = 3x[/tex]

To find the value of either of these functions for a specific value of x, simply substitute that value into the corresponding function equation.

[tex]\bold{f(2)}[/tex]
Substitute x with 2 in 6x + 5
==> [tex]6\cdot \:2+5=17[/tex]   (Answer)

[tex]\bold{g(4)}[/tex]
Substitute x with 4 in g(x) = 3x
==> [tex]3 \cdot4=12[/tex]  (Answer)

[tex]\bold{f(-2)}[/tex]
Substitute x with -2 in 6x + 5
[tex]6\left(-2\right)+5=-7[/tex]  (Answer)

[tex]\bold{g(0)}[/tex]
Substitute x with 0 in g(x) = 3x
==> [tex]3\cdot0=0[/tex]  (Answer)

[tex]\bold{f(\frac{1}{2})}[/tex]
Substitute x with [tex]\frac{1}{2}[/tex] in 6x + 5
==>  [tex]6\cdot \frac{1}{2}+5 = 3 + 5 = 8[/tex]   (Answer)

[tex]\bold{g(-4)}[/tex]
Substitute x with -4 in g(x) = 3x
==> [tex]3\left(-4\right) = -12[/tex]  (Answer)

The complete table of values of the absolute value equation is

x | y

-3 | [5]

-1 | [3]

0 | [2]

1 | [3]

3 | [5]

The absolute value equation of the function is given as

y = |x| + 2

On the incomplete table of values, we have the following x values

x = -3, -1, 0, 1 and 3

Next, we substitute x = -3, -1, 0, 1 and 3 in the equation y = |x| + 2

So, we have:

y = |-3| + 2 = 5

y = |-1| + 2 = 3

y = |0| + 2 = 2

y = |1| + 2 = 3

y = |3| + 2 = 5

So, the complete table of values of the absolute value equation is

x | y

-3 | [5]

-1 | [3]

0 | [2]

1 | [3]

3 | [5]

See attachment for the graph of the absolute value equation

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The number of possible ways to create the flag with 6 colors in total and 3 colors to be used in the flag is 30 ways.

We are given that:

Total colors in a palette = 6 colors.

Colors to be used in making of the flag = 3 colors.

So, by using the permutations, we get that:

Number of possible ways to create the flag = 6 × 5 ways.

Number of possible ways to create the flag = 30 ways.

Therefore, we get that, the number of possible ways to create the flag with 6 colors in total and 3 colors to be used in the flag is 30 ways.

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Answer: 5. 420,  6. 450,  7. 750,  8. 756

Step-by-step explanation:

The value for f(g(x))  =[tex](\frac{x^{2} +5}{2} )[/tex]

                       g(f(x))  =[tex](\frac{x+5}{2} )^2[/tex]

Given:

     f(x)=x+5/2  and g(x)=x²

Take,    g(x) = x²

substitute x = f(x)  into the function g(x). Then:

           g(f)x)) =[tex](\frac{x+5}{2} )^2[/tex]

Now, the next step is to substitute  g(x) into the function f(x)

          f(x) = x+5/2

         f(g(x)) =[tex](\frac{x^{2} +5}{2} )[/tex]

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The hatched percentage is the 50% of the total area of the rectangle, the correct option is a.

Let's define the height of the rectangle as H and the length as L, then the area of the rectangle is:

L*H

Now we can see that the hatched area is defined by two right triangles, both of height H and of bases b₁ and b₂, such that:

b₁ + b₂ = L

Then the area of these triangles is:

[tex]A = b_1*H/2 + b_2*H/2 = (b_1 + b_2)*H/2 = L*H/2[/tex]

This is half the area of the rectangle, so the hatched percentage is the 50%.

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The graph of ordered pairs that shows a proportional relationship is; B: On a coordinate plane, points (negative 2, negative 3) and (2, 3) are plotted.

We are given different ordered pairs as seen in the given options to find the one that represents a proportional relationship.

Now, the option that will have the ratio of its' y-coordinates as (y2/y1) = 1 would be the one that shows a proportional relationship.

Looking at the options, the only option that meets the criteria of (y2/y1) = 1  is option B.

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The required interquartile range of the data set along the median is 300.

The question has given, the median of a data set is 760, the third quartile is 950, and the first quartile is 650,
To determine the interquartile range.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
The first quartile is 650,
The third quartile is 950,
Since, the interquartile range is given as,

IQR = third quartile  - first Quartile
IQR = 950 - 650
IOR = 300

Thus, the required interquartile range of the data set along the median is 300.

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The correct option is C. (-2346) is the real number.

A real number is any number which can be discovered in the real world.

For the given options in the question;

Any negative number raised to any root and fractional power given a imaginary number which is a part of complex number.

Thus, only option C which have (-2346) is the real number more specifically negative integer.

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The correct question is-

Which of the following is equivalent to a real number?

A. (-324)¹/₄

B. (-6745)¹/³

C. (-2346)

D. (-874)¹/₂

The domain of given points are :

IR x ≠ ± √2

Points of discontinuity - x = ± √2 ( non removable / asymptote )

x - intercept =± √-5/2 , y -  intercept = 5/2

Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).

y=2x²+5 / x²-2 x

= 2[tex]x^{2}[/tex]+5/(x-√2)(x+√2)

The domain of given points are :

IR x ≠  ± √2

Points of discontinuity - x = ± √2 ( non removable / asymptote)

x-intercept :

2√10x=2[tex]x^{2}[/tex]+5+2√10x

2[tex]x^{2}[/tex] = -5

[tex]x^{2}[/tex]=-5/2

x = ±√-5/2

y - intercept :

2 * [tex]0^{2}[/tex] + 5 / ( 0-√2)(0+√2)

= 5/2

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The money that the employee earn by working 25 hours in one week is $400.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let f(x) represent the amount of money that the employee earn by working x hours. If the employee work more than 20 hours, then:

f(x) = 15x + 5(x - 20)

For 25 hours:

f(25) = 15(25) + 5(25 - 20) = 400

The money that the employee earn by working 25 hours in one week is $400.

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Answer:Sect A

1)X1=-3,X2=-2

2)X1=-3/4,X2=3

3)X1=-2/3,X2=5/2

4)X1=-2,X2=4

5)X1=1/2,X2=3

6)X1=-4,X2=4/3

Answer: Sect B

1)X1=-5,X2=-3

2)X1=3,X2=4

3)X1=-5,X2=3

4)X1=4,X2=7

5)X1=-5,X2=6

6)X1=-13,X2=2

7)X1=-3,X2=8

8)X1=-7,X2=-2

9)X1=2,X2=16

10)X1=8,X2=9

section a:

1. x = -2, -3

2. x = 3, [tex]-\frac{3}{4}[/tex]

3. x = [tex]\frac{5}{2},-\frac{2}{3}[/tex]

4. x = -2,4

5. x=3, 1/2

6. 4/3, -4

section b

1.x=-3,-5

2. x= 4,3

3. x = 5

4. x =-4,-7

5. x=6,-5

6. x=2,-13

7. x=8,-3

8. x= -2, -7

9. x= 16, 2

10. x= 9,8

section a:

1.

(x + 2)(x + 3)= 0

x + 2 = 0   x + 3 = 0

x + 2 - 2 = 0 - 2      x + 3 - 3 = 0 - 3

x = -2    x = -3

2.

(4x + 3)(x - 3)=0

4x + 3 = 0     x - 3 = 0

4x + 3 - 3 = 0 - 3          x - 3 + 3 = 0 + 3

4x = -3      x = 3

4x = - 3 / 4

x = [tex]-\frac{3}{4}[/tex]       x = 3

3.

(2x-5)(3x+2)=0

 2x-5=0    3x+2=0

 2x-5+5=0+5    3x+2-2=0-2

 2x= 5       3x=-2

 2x=5/2     3x=-2/3

 x= 5/2        x= [tex]-\frac{2}{3}[/tex]

4.

(4x+8)(2x-8)=0

4x + 8 = 0    2x - 8= 0

4x = -8        2x = 8

4x = -8/ 4       2x=8/2

x=-2              x=4

5.

(5x-15)(4x-2)=0

5x-15=0      4x-2=0

5x = 15        4x=2

5x = 15 /5         4x=2/4

x=3, 1/2

6.

(9x-12)(5x+20)=0

9x -12=0     5x+20=0

9x=12       5x=-20

9x = 12/ 9    5x= -20/5

x= 4/3       x = -4

The equation that can model the situation will be 150 + 5n and 20n

Moving Company = 150 + 5n  

(n = the number of boxes)

Taxi = 20n

The break-even point is when these are the same.

150 + 5n = 20n

150 = 15n

n = 150/15 = 10

So with 10 boxes, it costs the same ($200) either way.

With 11 boxes, the Moving Company costs $205

With 11 boxes, the Taxi would cost $220.

It is cheaper to use the moving company with 11 or more boxes.  

Another example of a real life situation that would use systems of equations and write the system is that Company A charges a flat rate of $150, and an additional $5 for each box asn there is another taxi service that would charge $20 for each box.

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The cost of each bag of gummy bears= $1

Let,s take the cost of a bag of gummy bears to be x and the cost of each chocolate bar to be y.

So from the given question, we get out the first equation as

7 x + 3 y = $22 ------(1)

and the second equation is

3 x + 1 y = $ 8 -------(2)

We have to find the value of x and y by which we will get to know about the cost of each bag of gummy bears and chocolate bar respectively.

Now we have to multiply the second equation with 3

(3 x + 1 y = $8 ) *

we will get :

9 x + 3 y = $ 24 -------( 3)

After equating equations (1 ) and (3)

we get

7 x + 3y = $22-------(1)

9x + 3 y= $24-------(3)

By subtracting of the equation (1) and (3) we get

-2 x = - $2

i.e., x = $1

Now to get the value of y we can put the value of x in any of the above- given equation

Let us put it on equation number (2)

3x + 1 y = $8

= 3 * 1 + y = $ 8

= 3 + y = $ 8

=y = $5

From this, we get the value of x = $1 and y = $ 5 which are the value of gummy bear and chocolate bar

We have to find the value of each gummy bar which is $1

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Answer:

y = x + 1

Step-by-step explanation:

An x-intercept of 1 would have the coordinates (-1, 0)

Slope can be found with rise / run. In this case, rise (the number of units going up) would be 6, because 6 - 0 = 6. The run would also be 6 because 5 - (-1) = 6. Following the formula, the rise divided by the run, 6 / 6 = 1, so the slope is 1.

We also have to consider the y-intercept, hence the intercept in the name Slope Intercept Form ( y = mx + b). You can find this by substituting coordinates for y and x, using the slope, and solving for b.

Either (-1, 0) or (5, 6) can be used.

6 = 5(1) + b

6 = 5 + b

b = 1, because 5 + 1 = 6

Answer:

u need to put a picture of the lines so we know what ur talking about

The function rule g(x) after the given transformations of the graph of f(x)= 3x is g(x) = 1/9x

Transformation techniques -

The act of shifting an object's location on the xy plane is referred to as transformation.

Given the parent function

f(x) = -3x

If the function is not reflected over x-axis, the resulting function will be f(x) =  3x

If the resulting function is compressed by a factors of 1/8, hence the final function rule will be;

g(x) = 1/9( 3x)

g(x) = 1/9x

Hence the function rule g(x) after the given transformations of the graph of f(x)=3x is g(x) = 1/9x.

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The number of more drapery pieces than upholstery pieces does Brandon have is 2.03 pieces

Number of pieces of upholstery fabric = 23 3/5 ÷ 2 5/6

= 118/5 ÷ 17/6

= 118/5 × 6/17

= 708 / 85

= 8 28/85

Number of pieces of drapery fabric = 18 1/2 ÷ 2 5/6

= 37/2 ÷ 17/6

= 37/2 × 6/17

= 222/34

= 6 18/34

= 6 9/17

How many more drapery pieces than upholstery pieces does Brandon have = 708 / 85 - 222/34

= (24072-18204) / 2890

= 5,868 / 2890

= 2.03 pieces

Therefore, the number of more drapery pieces than upholstery pieces does Brandon have is 2.03 pieces

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Lifesaver:

∠A = ∠C

⇒ AB = BC (Equal angles have equal sides opposite to them)

⇒ 5x+6 = 3x+14

⇒ 5x-3x = 14-6

⇒ 2x = 8

⇒ x= 4