(a) Find the value of xif 10, x and 30 are in A.P.
(b) If 6,x,y, and 18 are in A.P., find the value of x and y.

it's a optional mathematics Questions please solve him​

Answers

Answer 1

Part A

Answer:  x = 20

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

Explanation:

AP = arithmetic progression, which is another way of saying arithmetic sequence.

Let d = common difference

first term = 10second term = first+d = 10+d = xthird term = second+d = x+d = 30

Apply substitution like so

x+d = 30

10+d+d = 30 ... replaced x with 10+d

10+2d = 30

2d = 30-10

2d = 20

d = 20/2

d = 10 is the common difference

Therefore,

x = 10+d = 10+10 = 20

The AP {10,x,30} updates to {10,20,30}. We see the gap between terms is 10 units. All AP's have the same gap width between adjacent terms.

=============================================================

Part B

Answers:  x = 10 and y = 14

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

Explanation:

We use the same ideas mentioned back in part A.

d = common difference = unknown for now

first term = 6second term = first+d = 6+d = xthird term = second+d = x+d = (6+d)+d = 6+2d = yfourth term = third+d = y+d = (6+2d)+d = 6+3d = 18

Hopefully you can see how each term builds up to form the next one. We'll solve that last equation like so

6+3d = 18

3d = 18-6

3d = 12

d = 12/3

d = 4

So we then can say:

x = 6+d = 6+4 = 10y = 6+2d = 6+2(4) = 6+8 = 14

The arithmetic sequence {6,x,y,18} updates to {6,10,14,18}. There's a gap of 4 between each adjacent term.


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Answer:

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(picture attached)

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If the first term of an A.P is equal to one half of the common difference d, find the eight term of the A. P.

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Step-by-step explanation:

The formula for Arithmatic Series is

[tex]a_n=a_1+(n-1)d[/tex]

where a_1 and a_n are the first and n-th term of the series respectively,

d is the common difference of the series.

Now,

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The temperature at 12:00 p.m. was 8°C. At 7:00 p.m., the temperature was -6°C. What was the change in temperature (in degrees Celsius)?
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Answer: 14 degree decrease

Step-by-step explanation:

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Identify the terms in the expression. (Enter your answers as a comma-separated list.)
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Answers

5y3+y+3

5y4+3

I'm not sure but I think it will help you out

What is the slope of the line represented by the equation y = -1/2x+ 1/4​

Answers

Answer:

y = mx+ b

m=slope

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Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = slopeb = y-intercept

By comparing the formula to the equation given, it is clear the slope of the line is -1/2.

Which of the following demonstrates the distributive property?
A. (r + s)t = (s+r)t
B. (r + s)t=r + (st)
C. (r + s)t = t(r + s)
D. (r + s)t = rt + st

Answers

Answer:

D. (r + s)t = rt + st

Step-by-step explanation:

Distribute means that the term outside gets multiplied to each term on the inside of the parentheses

(r + s)t = rt + st

Jacob conducted a music survey among his friends. He reported that 0.42 prefer pop, 22% prefer rock, and 2/5 prefer hip hop, Explain what's wrong with Jacob's results. ASAP PLS

Answers

Answer:

Step-by-step explanation:

Based on ur graph, in a class of 90 students (20 rock, 40 hip hop, and 30 country...added = 90) , 30 chose country....30/90 reduces to 1/3.....so 1/3 chose country.

In a class of 450 students......1/3 * 450 = 450/3 = 150 chose country

Answer:

The total percentages do not equal 100%, they equal 102%. If all friends answered, his total should equal 100%

Step-by-step explanation:

0.42 is 42%, 22% is 22%, and 2/5 is 0.4 which is 40%. Together that is 102%. If all friends answered, his total should equal 100%

Enter an inequality that represents the graph in the box.

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Answer:

It will be -8≤×≤8

If the function is f(x)=−3x+7, what is f(1/3)=

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Answer:

6 is the answer. Hope this helps you! Stay blessed .

If V(r)=4/3pir³, find V(3/4)

Answers

Answer:

Step-by-step explanation:

r = 3/4

[tex]V(r) =\dfrac{4}{3}\pir^{3}\\\\V(\dfrac{3}{4})=\dfrac{4}{3}*\pi \dfrac{3}{4}*\dfrac{3}{4}*\dfrac{3}{4}\\\\=\dfrac{3*3}{4*4}\pi \\\\=\dfrac{9}{16}*3.14\\\\=1.77[/tex]

Evaluate :
A. [tex]x^{x^3}=3[/tex]
B. [tex]4^x +6^x =9^x[/tex]

Answers

Answer:

A. [tex]x^{x^3} = 3[/tex]log [tex]x^{x^3}[/tex] = log 3x³ log x = log 33x³ log x = 3 log 3x³ log x³ = log 3³[tex]x^3^{x^3}[/tex] = 3³x³ = 3x = [tex]3^{1/3}[/tex]B.4ˣ + 6ˣ = 9ˣ2²ˣ + 2ˣ3ˣ = 3²ˣ

Divide both sides by 2²ˣ

1 + (3/2)ˣ = (3/2)²ˣ

Substitute (3/2)ˣ = t

t² - t - 1 = 0

Solve for t:

t = (1  ± √5)/2

Positive root is considered as (3/2)ˣ can't be negative.

(3/2)ˣ = (1 + √5)/2x = log [(1 + √5)/2] / log (3/2)x = 1.18681439028

If (x - 4) varies inversely as (y + 3) and x = 8 when y = 2, what is x when y = - 1?

Answers

Answer:

[tex]x=14[/tex]

Step-by-step explanation:

If two values are inversely proportional, their product must be maintained. That way, if one value goes up, the other goes down by the same extent.

Therefore, if [tex](x-4)[/tex] and [tex](y+3)[/tex] vary inversely, their product will be the same for all values of [tex]x-4[/tex] and [tex]y+3[/tex].

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Hence, the maintained product is [tex]20[/tex].

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Substitute [tex]y=-1[/tex] to find the value of [tex]x[/tex] when [tex]y=-1[/tex]:

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helppppppppppppppppppp

Answers

Answer to the question is -4

Answer:

x = -4

Step-by-step explanation:

-x+7 = -6x-13

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Answers

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y = -5/7x + 27/7

Step-by-step explanation:

y2 - y1 / x2 - x1

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-5 / 7

= -5/7

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1 = -5/7(4) + b

1 = -20/7 + b

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Answers

Answer:

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Step-by-step explanation:

7 + 11 = 18

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Solve the inequality.
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[?]

Answers

Hi ;-)

-4 ≤ 2x - 6 ≤ 12

2x - 6 ≥ -4  / + 6

2x ≥ 2  / : 2

x ≥ 1

2x - 6 ≤ 12  / + 6

2x ≤ 18  / : 2

x ≤ 9

1 ≤ x ≤ 9
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First add 6 to everything to eliminate the -6 in the middle:
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Then divide everything by 2 to get the 2 off the 2x.

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Answers

Answer:

x = 5

Step-by-step explanation:

The opposite sides of a rectangle are equal , then perimeter

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Step-by-step explanation:

perimeter of a rectangle

2(L+w)

-2x-6(4x+4)

open the bracket

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2(-8x^2-32x-24)

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16=64x

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Answers

Answer:

[tex]\frac{x^{\frac{1}{4} } +2}{x^{\frac{1}{4} } -2}[/tex]

rationalise the denomimator:

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2x² - 5x+1 has roots alpha and beta. Find alpha²+beta².
Please answer fast. I will mark the best answer as brainliest. ​

Answers

Answer:

[tex]\dfrac{21}{4}[/tex]

Hello,

Step-by-step explanation:

[tex]2x^2-5x+1=2(x^2-\frac{5}{2}+\frac{1}{2} )\\\\\alpha+\beta=\dfrac{5}{2} \\\\\alpha*\beta=\frac{1}{2} \\\\(\alpha+\beta)^2=\alpha^2+\beta^2+2\alpha*\beta\\\\\alpha^2+\beta^2\\\\=(\alpha+\beta)^2-2\alpha*\beta\\\\\\=(\dfrac{5}{2} )^2-1\\\\=\dfrac{21}{4} \\[/tex]

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Answers

Answer:

linked below

Step-by-step explanation:

If you use desmos, it show this which is the correct graph :)

Example 5: Writing and Solving an Equation
The circles are identical. What is the area of each circle?
x + 2
4X
Please help…

Answers

Step-by-step explanation:

radius =x+2

diameter=4x

Diameter=2(radius)

4x=2(x+2)

4x=2x+4

4x-2x=4

2x=4

x=4/2

x=2

Subtitute x=2 in radius:

r=2+2=4

Area=πr²

Area=3.14×4²

Area=3.14×16

Area=50.24

Both the circles are identical so area is same.

Note:if you need to ask any question please let me know.

Which best describes the meaning of the statement "If A and B ? i dont understand this
A. If A is false then B must be false
B. If A is true then B must be true
C. If A is false , then B must be false
D. if A is true then B might be true

Answers

Was your original statement “If A, then B”?

If so, this means “if you know A is true, then you know B is true.” (Answer: B)

Example: “If (you’re a dog), then (you’re a mammal).”

Also, answers A and C are the same. Was that a typo?

Can someone explain me this please :)

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Answer:

39) a) [tex]2^{1}[/tex]= 2

     b) [tex]2^{3}[/tex]= 2×2×2=8

     c)[tex]2^{t}[/tex]

40) no

Step-by-step explanation:

40) both point A and B is below the point C. therefore it cannot pass through point c

HELP I'M REWARDING 50 POINTS (YA IKR 50 WOW) IF YALL GET THIS RIGHT..

Answers

Answer:

232

Step-by-step explanation:

Since the polygon is regular, each side of the polygon is equal

[tex]x + 7 = \frac{4}{3} x - \frac{1}{3} [/tex]

[tex]7 = \frac{1}{3} x - \frac{1}{3} [/tex]

[tex] \frac{22}{3} = \frac{1}{3} x[/tex]

[tex]x = 22[/tex]

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[tex]22 + 7 = 29[/tex]

or

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There is 8 sides so the perimeter is

[tex]29 \times 8 = 232[/tex]

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Answers

Step-by-step explanation:

a)6!+12-3

=6!+9

b)-18+3!+4

=3!-14

=3!+(-14)

both are in the form if (+)!+constant.

Note:if you need to know any question about it please let me know.

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O A. 60
O B. 20
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Answers

The answer is 30 I’m sure of it

Mary Lindey wants to purchase pumpkins. She finds different markets advertising pumpkins for sale. What market has the lowest price per pumpkin . 3 for 10.59 , 3.75 per pumpkin , 2 for 7.20

*7th grade*

Answers

Work out the price per pumpkin:
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3p=10.59
p= 3.53

Shop 2
p= 3.75

Shop 3
2p= 7.20
p= 3.60

Therefore the lowest price per pumpkin is 3 for 10.59

Geometry question. “Find the value of x that will make A||B.” Brainliest to whoever is correct

Answers

Answer:

Step-by-step explanation:

The two angles are interior angles on the same side of the transversal. They are supplementary.

2x + 50 + 5x - 80 = 180             Combine like terms

7x - 30 = 180                              Add 30 to both sides

7x = 210                                     Divide by 7 on both sides

x = 210/7

x = 30

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