Can someone please help i don’t understand at all :/

Can Someone Please Help I Dont Understand At All :/

Answers

Answer 1

Using the Segment Addition Postulate, considering the congruent segments and the trisection, the missing lengths of the segments are given by the following items:

CH = 4.HI = 4.ID = 4.CB = 12.AC = 6.AE = 12.A to F = 4.GE = 4.FB = 8.DG = 8.

What is the segment addition postulate?

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

For this problem, two other concepts are important, given by the bullet points below:

Congruence: Congruent segments have the same length.Trisection: A trisection of a segment divides the segment into three segments of equal lengths.

CD = 12, hence, considering the trisection: (12/3) = 4.

CH = 4.HI = 4.ID = 4.

CD is also congruent to CB, hence:

CB = 12.

CE = 6, and AE = 2CE, hence:

AC = 6.AE = 12.

Due to the postulate, since DG = 8 and GE = 12, and the entire lengths are of 12, and considering the congruence:

A to F = 4.GE = 4.FB = 8.DG = 8.

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Related Questions


Find the average rate of change of g(x) = 3x³ + 1 from æ =
- 1 to x = 4.

Answers

The average rate of change or the slope is found as 39.

What is the definition of line slope/ average rate of change?A line's slope is a measure of its steepness and orientation. The slope of a line can be calculated using any 2 different points on that line.The slope of a line formula calculates the ratio of "vertical change" to "horizontal change" between two distinct points on a line.The net change in y coordinates is Δy, while the net change in x coordinates is Δx.

The slope of the line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

The function is given as;

g(x) = 3x³ + 1

The points are; -1 and 4.

Put x = -1

g(-1) = 3(-1)³ + 1

g(-1) = -2

Put x = 4

g(4) = 3(4)³ + 1

g(4) = 193

The points are;

(x₁ ,y₁) = (-1, -2)

(x₂, y₂) = (4, 193)

Put the values in the slope formula;

m = (193 + 2)/(4 + 1)

m = 195/5

m = 39

Thus, the value of the average rate of change is 39; which is also the slope of the function.

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Please help me understand this
2x+3=7x

Answers

Answer:

x = 3/5

Step-by-step explanation:

Isolate the x by subtracting 2x from both sides

2x + 3 = 7x

-2x        -2x

3 = 5x, Then divide by 5 on both sides

x = 3/5

Answer:

[tex] \sf \large \: x = \frac{3}{5} [/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

2x+3=7x

Step 1: Subtract 7x from both sides.

2x+3−7x=7x−7x

−5x+3=0

Step 2: Subtract 3 from both sides.

−5x+3−3=0−3

−5x=−3

Step 3: Divide both sides by -5.

−5x/−5 = −3/−5

x=3/5

Someone help me outtt

Answers

Answer:

I THINK ITS B

Step-by-step explanation:

CORRECT ME IF I'M WRONG!!!

Need help ASAP! (algebra 2)
•Write a system of equations that can model the situation: A moving company charges a flat rate of $150, and an additional $5 for each box. If a taxi service would charge $20 for each box, how many boxes would you need for it to be cheaper to use the moving company, and what would be the total cost?
•Create another example of a real life situation that would use systems of equations and write the system.

Answers

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

How to illustrate the information?

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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Let f(x)=7 x+5 and g(x)=x². Perform each function operation and then find the domain of the result.
f/g(x)

Answers

The domain of the result f/g(x) is (7 /x ) + (5/x^2).

The two functions are:

f(x) = 7x + 5

and

g(x) = x^2

For calculating f/g(x)

f/g(x) is equivalent to f(x) / g(x)

Hence (f / g)(x) = f(x) / g(x)

                        = 7x + 5 / x^2

                        = (7 /x ) + (5/x^2)

the domain of the result f/g(x) is (7 /x ) + (5/x^2).

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An employee earns $15 an hour for the first 20 hours worked during the week. The employee earns an extra $5 per hour for every additional hour over 20 hours worke per week. The scenario is represented by the function f(x). How much does the employee earn by working 25 hours in one week?

Answers

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

What is an equation?

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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x^2 + 9x + 14 = ( x+_)(x+_)


quickly!!!

Answers

Answer:

[tex](x+7)(x+2)[/tex]

Step-by-step explanation:

We have the equation:

[tex]x^{2} +9x+14[/tex].

The factors of 14 are 1, 2, 7 and 14.

Now, all we have to do is find two numbers that add up to 9.

We see that 2 and 7 add up to 9.

Therefore,

[tex]x^2+9x+14=(x+7)(x+2)[/tex]

Hope this helped! Have a great day!

Answer:

(x+7)(x+2)

Step-by-step explanation:

x^2+2x+7x+14           (Because 7 and 2 add to give 9 and multiply to give 14)

x(x+2) +7(x+2)            (Take out common factors, factorising)

(x+2)(x+7)                   (Put the things common in a bracket together and the bits that are outside in another bracket)

How do you write this in slope intercept form

11. Passes through x-intercept at -1 and (5, 6)

Answers

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

What values of x and y satisfy the system of equations 10x=5y−8 15x=−5y−2?

Answers

[tex]\begin{array}{llll} 10x=5y-8\\\\ 15x=-5y-2\\\\ \end{array}\implies \stackrel{\textit{using elimination}}{\begin{array}{llll} 10x-5y=-8\\\\ 15x+5y=-2\\\cline{1-1} 25x+0=-10 \end{array}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]25x=-10\implies x=\cfrac{-10}{25}\implies x=-\cfrac{2}{5} \\\\\\ \stackrel{\textit{substituting "x" in the 1st equation}}{10\left(-\frac{2}{5} \right)=5y-8\implies }-4=5y-8\implies 4=5y\implies \cfrac{4}{5}=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} \left( -\frac{2}{5}~~,~~\frac{4}{5} \right) \end{array}}~\hfill[/tex]

Brandon has 23 3/5 yards of upholstery fabric and 18 1/2 yards of drapery fabric into 2 5/6 yard pieces. How many more drapery pieces than upholstery pieces does Brandon have?

Answers

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

Fraction

Upholstery fabric = 23 3/5 yardsDrapery fabric = 18 1/2 yardEach fabric piece = 2 5/6 yards

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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How do I do this ???

Answers

-2 | 2
-1 | -1
0 | 4
1 | -7
2 | -10

The mass of a bar of chocolate is 1800g
The density of the chocolate is 9g/cm
Find the mass of the ball in kg

Answers

The mass of the bar of chocolate in kilogram, kg is calculated to be 1.8kg

How to find the mass of the bar in kg

Given data

mass of a bar of chocolate is 1800g

density of the chocolate is 9g/cm

density is defined the ratio of mass and volume. therefore the density of the chocolate will be the ratio of the mass of the chocolate bar to the volume of the chocolate. this represented mathematically as:

The mass of the bar of chocolate is given in grams as 1800g

converting the unit to kg is done as follows

if 1kg is equal to 1000g, then how many kg is 1800g

= 1800 / 1000

= 1.8 kg

hence the mass of the chocolate bar in kg is 1.8 kg

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x + 2y3z = 25
3x - 3y + 4z = -23
-4x+y-z = -25

Answers

Values of x y z for system of equation are

x=[tex]\frac{565}{54}[/tex]

y=[tex]\frac{703}{54}[/tex]

z=[tex]\frac{-23}{6}[/tex]

we have system of equation as follows

x + 2y+3z = 25

z=(25-x-2y)/3..........(A)

3x - 3y + 4z = -23

z=(3y-3x-23)/4........(B)

-4x+y-z = -25

z=(25-4x+y)..............(C)

Equating we get

(25-x-2y)/3=(3y-3x-23)/4=(25-4x+y)

Solving this we get

x=[tex]\frac{565}{54}[/tex]

y=[tex]\frac{703}{54}[/tex]

z=[tex]\frac{-23}{6}[/tex]

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Solve for x
−6−(−4x+2)−x=-(5x-2)

Answers

Answer: x=5/4

Step-by-step explanation:

−6−(−4x+2)−x=-(5x-2)

−6+4x-2−x=-5x+2

-x+4x-6-2=-5x+2

3x-8=-5x+2

3x-8+8=-5x+2+8

3x=-5x+10

3x+5x=-5x+5x+10

8x=10

x=10/8

x=5/4

Hi there,

I hope you and your family are staying safe and healthy during this anomalous time.

[tex]-6 -(-4x + 2) - x = -(5x-2)[/tex]

The first step is to distribute

[tex]-6 + 4x - 2-x=-(5x-2)[/tex]

Now let's subtract the numbers

[tex]-8 +3x = -(5x-2)[/tex]

[tex]3x - 8 = -(5x-2)[/tex]

[tex]3x - 8 = -5x+2[/tex]

[tex]3x = -5x + 2 +8\\3x = -5x +10[/tex]

[tex]3x + 5x = 10 \\8x = 10\\x = \frac{10}{8}[/tex]

Once we simplify that, we get:

[tex]x = \frac{5}{4}[/tex] as the answer

Happy to help! All the best this semester.


Find the domain, points of discontinuity, and x - and y - intercepts of each rational function. Determine whether the discontinuities are removable or non-removable. y=2x²+5 / x²-2 x

Answers

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

What is rational functions ?

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).

CALCULATION

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 cube root of 125 − 14 ÷ 2)(3 − 5)2 step by step

Answers

Answer:

18

Step-by-step explanation:

[tex] \sf( \frac{ ∛125 \: - \: 14 }{2})(3 - 5)2[/tex]

Apply rule: ([tex] a[/tex]) = [tex] a[/tex]

[tex] \sf( \frac{ ∛125 \: - \: 14 }{2}) = \: \sf\frac{ ∛125 \: - \: 14 }{2}[/tex]

[tex] = \sf \frac{∛125 \: - \: 14 }{2}(3 - 5)2[/tex]

Substract the numbers (3-5) = (-2)

[tex] = \sf \frac{∛125 \: - \: 14 }{2}( - 2)2[/tex]

Change 2 to fraction: [tex] \sf \frac{2}{1} [/tex]

[tex] = \sf \frac{∛125 \: - \: 14 }{2} \times \frac{2}{1} ( - 2)[/tex]

Cross- cancel common factor 2

[tex] = \sf \frac{∛125 \: - \: 14 }{1} ( - 2)[/tex]

Let's calculate [tex] \sf \frac{∛125 \: - \: 14 }{1} [/tex]

[tex] = \sf \frac{∛125 \: - \: 14 }{1} [/tex]

Apply a fraction rule = a/1 = a

[tex] = \sf ∛125 \: - \: 14 [/tex]

[tex] \sf = - 9[/tex]

[tex] \sf \: = - 9( - 2)[/tex]

[tex] \sf \: = 18[/tex]

(Equivalent Algebraic Expressions LC)
Simplify this please!!!

Answers

Answer: X^3 / Y^5

The first answer choice

Step-by-step explanation:

Nick has $50 to spend during fall break. he decides to spend $10 each day. which equation represents the amount of money nick has left, y, and the number of days x?

Answers

Answer:

$50 = 5 days

$40 = 4 days

$30 = 3 days

$20 = 2 days

$10 = 1 day

Step-by-step explanation:

hope this helps = )


An environmental equipment supplier sells hemispherical holding ponds for treatment of chemical waste. The volume of a pond is V₁=1/2(4/3 π r₁³) , where r₁ is the radius in feet. The supplier also sells cylindrical collecting tanks. A collecting tank fills completely and then drains completely to fill the empty pond. The volume of the tank is V₂=12 π r₂², where r₂ is the radius of the tank.
b. You want to double the radius of the pond. How will the radius of the tank change?

Answers

The radius of the tank should increase √ 2 times.

We are given that:

To fill a pond whose volume is given as V₁ = 1 / 2 (4 / 3 π r₁³), we need a cylindrical tank whose volume is given by V₂ = 12 π r₂².

This means that the volume of the pond should be equal to the volume of the cylinder.

So, we get that:

1 / 2 (4 / 3 π r₁³) = 12 π r₂².

4 / 3 π r₁³ = 24 π r₂²

r₁³ = 18 r₂²

r₂ = √ ( r₁³ / 18)

r₂ = r₁ / 3 √r₁ / 2

Now, we will double the radius of the pond.

So, r₁ will become 2 r₁

Substituting it, we get that:

R₂ = 2r₁ / 3 √2r₁ / 2

R₂ = 2r₁ / 3 √r₁

So, we can see that:

R₂ / r₂ = 2r₁ / 3 √r₁ / (r₁ / 3 √r₁ / 2)

R₂ / r₂ = 2 / √2 = √ 2

Therefore, the radius of the tank should increase √ 2 times.

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Rewrite in simplest rational exponent form
Show each step of your process.

Answers

The simplest rational exponent form is [tex]x^\frac{3}{4}[/tex] .

A rational exponent is defined as an exponent that can be expressed as p/q. where q ≠ 0. The common notation for rational exponents is x^m/n. where x is the base (a positive number) and m/n is a rational number.An exponential expression of the form am has a rational exponent if m is a rational number. Powers and roots of numbers are represented together in rational exponents.

We have given a rational exponent [tex]\sqrt{x} .\sqrt[4]{x}[/tex] .     ...(1)

By formula [tex]\sqrt[4]{x}[/tex] can be written as [tex]x^\frac{1}{4}[/tex] and [tex]\sqrt{x}[/tex] can be written as [tex]x^\frac{1}{2}[/tex] .

Put in equation (1) , we get

    [tex]\sqrt{x} .\sqrt[4]{x}=x^\frac{1}{2} .x^\frac{1}{4} \\[/tex]              ...(2)

Using formula [tex]a^\frac{m}{n} \times a^\frac{p}{q} = a^{\frac{m}{n} +\frac{p}{q} }[/tex]  

Equation (2) can be written as

                                       [tex]\sqrt{x} .\sqrt[4]{x}=x^{\frac{1}{2} +\frac{1}{4}}\\\\\sqrt{x} .\sqrt[4]{x}=x^{\frac{2+1}{4} }\\\\\sqrt{x} .\sqrt[4]{x}=x^{\frac{3}{4} }[/tex]

Hence , on simplification , we get  [tex]x^\frac{3}{4}[/tex] .

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4. Use the equations below to find the indicated values.
a. f(x) = 6x +5
i) f(2)=
b. g(x) = 3x
i) g(4) =
ii) f(-2) =
ii) g(0) =
iii) f(1/2) =
iii) g(-4)=

Answers

Answer:

f(2) = 17g(4) = 12f(-2) = -7g(0) = 0f(1/2) = 8g(-4) = -12

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)


                                     

Use breaking apart to complete the calculation. 4 X 23 =​

Answers

Using breaking apart technique 4 X 23 = 92

What does the multiplication breaking apart technique entail?

To make the multiplication process simpler, you split up one or more of the numbers. It also explains why you would "carry" a number to the following column.

What does it mean to disintegrate?

split apart definitions. verb: break anything down into its component parts. substitute words: separate, dismantle, take apart

According to the given question

4×23 = (20×4)+(3×4)

         =80+12

          =92

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A:B = 6:7 and A=30. Find B.
Please help me out with this, i dont know how to work it out, thank you.​

Answers

Step-by-step explanation:

it is a ratio, and as such it is simply a fraction.

we can also write it

A/B = 6/7

and it gives us the same information.

and so,

30/B = 6/7

30 = 6B/7

210 = 6B

B = 210/6 = 35

Rational Or Irrational? PLEASE hurry!!!

Answers

Answer:

-1.7 = rational

1.083 = rational

1.22345721 = rational

-1.090909 = rational

Step-by-step explanation:

Use the interactive to graph a line with a slope of zero and passing through the point (0,4).

Which statements are true for the graph? Check all that apply.
The line is horizontal.
The line is vertical.
The line goes through (0,0).
The line goes through (4,4).
The x-values are all 0.
The y-values are all 4.

Answers

the answer is “horizontal line”

Answer:

THE CORRECT ANSWER'S ARE A,D AND F

Step-by-step explanation:

did the test on edge .

A polygon has vertices A (5, -1), B (21, 11), C (26, -1), and D (2, -8).
Part A. What is the perimeter of ABCD to the nearest tenth of a unit?
Part B. What is the area of ABCD to the nearest tenth of a square unit?
Enter the correct answers in the boxes.
A. Perimeter: units
B. Area: square units

Answers

Check the picture below.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad B(\stackrel{x_2}{21}~,~\stackrel{y_2}{11}) ~\hfill AB=\sqrt{(~~ 21- 5~~)^2 + (~~ 11- (-1)~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 16 )^2 + ( 12)^2}\implies \boxed{AB=20}[/tex]

[tex]B(\stackrel{x_1}{21}~,~\stackrel{y_1}{11})\qquad C(\stackrel{x_2}{26}~,~\stackrel{y_2}{-1}) ~\hfill BC=\sqrt{(~~ 26- 21~~)^2 + (~~ -1- 11 ~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 5)^2 + ( -12)^2}\implies \boxed{BC=13} \\\\\\ C(\stackrel{x_1}{26}~,~\stackrel{y_1}{-1})\qquad D(\stackrel{x_2}{2}~,~\stackrel{y_2}{-8}) ~\hfill CD=\sqrt{(~~ 2- 26~~)^2 + (~~ -8- (-1)~~)^2} \\\\\\ ~\hfill CD=\sqrt{( -24)^2 + ( -7)^2}\implies \boxed{CD=25}[/tex]

[tex]D(\stackrel{x_1}{2}~,~\stackrel{y_1}{-8})\qquad A(\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) ~\hfill DA=\sqrt{(~~ 5- 2~~)^2 + (~~ -1- (-8)~~)^2} \\\\\\ ~\hfill DA=\sqrt{( 3)^2 + ( 7)^2}\implies \boxed{DA=\sqrt{58}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{20~~ + ~~13~~ + ~~25~~ + ~~\sqrt{58} ~~ \approx ~~ \text{\LARGE 65.6}}[/tex]

now, as far as the area goes, let's check the picture below, hmmm, there are two triangles, both have a base of 21, and you can see their heights there, well, let's simply get the area of each triangle and sum them up.

[tex]\cfrac{1}{2}(21)(12)~~ + ~~\cfrac{1}{2}(21)(7)\implies 126~~ + ~~73.5\implies \text{\LARGE 199.5}[/tex]

make a conjecture about the relationship between two intersecting lines that form four congruent angles

Answers

Answer:

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

The following question has two parts. First, answer part A. Then, answer part B. Part A A high school athlete ran the 100 meter sprint in 13.245 seconds. Round the time to the nearest tenth. Enter the answer in the box. seconds Part B Explain how you arrived at the answer. Include any rules that you followed.

Answers

If the sprinter ran the race for 13.245 seconds, if we are to represent it in tenth then it would be written as 13.2

What is tenth in mathematics?

This is the term that is used to refer to the place value that would come immediately after the decimal point that we have in a group of digits that are a decimal.

In the question, the rule I followed is the one that I have explained above. The number that is after the decimal value is given as 2.

Hence we can say that the the answer after it has been rounded to the nearest tenth is  13.2

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If the median of a data set is 760, the third quartile is 950, and the first quartile is 650, what is the interquartile range?

Answers

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.

What is Statistic?

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 4th term of an A.P. is 27. and the sum of the 1st and the fourth term is 42. Find the common difference

Answers

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

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