The perimeter of the figure below is 135.8 in.
Find the length of the missing side.

Step-by-step explanation:

Given (2x + 23), (8x + 2) and (20x - 52) are three consecutive terms of an arithmetic sequence.

(8x + 2) - (2x + 23) = (20x - 52) - (8x + 2)

or, 6x - 21 = 12x - 54

or, 12x - 6x = - 21 + 54 = 33

or, 6x = 33

or, 2x = 11

∴ x = 11/2

∴2x + 23 = 2 × 11/2 + 23 = 34

8x + 2 = 8 × 11/2 + 2 = 46 and

20x - 52 = 20 × 11/2 - 52 = 110 - 52 = 58

34, 46 and 58 are three consecutive terms of an arithmetic sequence.

∴ Common difference(d) = 46 - 34 = 58 - 46 = 12, it is proved.

Hence, the common difference of the sequence is 12.

The length of x is 3√10 units.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation connecting the lengths of the sides a, b, and the hypotenuse c. Pythagoras, a Greek philosopher who was born around 570 BC, is remembered by the theorem's name. The theorem has likely been proved the most times of any mathematical theorem using a variety of techniques.

As per the given data:

Perpendicular = 9 units

Base = 3 units

Using Pythagoras theorem to find x (hypotenuse):

[tex]x^2 = 9^2 + 3^2\\x^2 = 81 + 9\\x^2 = 90\\x = \sqrt{90}\\x = \sqrt{9\times10}\\x = 3\sqrt{10}[/tex]units

Hence, the length of x is 3√10 units.

To learn more about Pythagoras theorem, click:

brainly.com/question/343682

#SPJ7

Since 0 is greater than -4 in the expression 4.1m >-16.4, hence zero is a solution to this inequality

Given the following inequality, we are to check which of them has zero as a solution.

For the expression

4.1m >-16.4

m > -16.4/4.1

m > -4

Since 0 is greater than -4, hence zero is a solution to this inequality

Learn more on inequality here: https://brainly.com/question/24372553

Answer: 22 blue balloons

Step-by-step explanation:

IF 3/10 balloons are red out of 60, we have

[tex]\frac{3}{10} *60[/tex] = 18 red balloons in total

1/3 of the balloons are yellow, 60/3=20 yellow balloons

Blue balloons= 60-18 (red)-20(yellow)=22

Answer:

31781715561888155919761999

Answer:

x = 4

Step-by-step explanation:

3x-4 = 8

3x = 12

x = 4

good luck

Answer:

x = 4

Step-by-step explanation:

3x - 4 = 8

3x = 8 + 4

3x = 12

x = 4

Answer:

Step-by-step explanation:

Answer:

So, yea i cant get you an exact answer but... i can tell you howto solve it.

Step-by-step explanation:

IN this case you would need to rewrite it so it is on the left side!

Bye friend! :)

you have also wasted your time by going down heere so, YOUR FAULT

Answer:

rectangle

Step-by-step explanation:

u can use a graph paper

Answer:A

Step-by-step explanation:i mean that sound logiclity correct

Answer:

hypotenuse Pythagoras property

Answer:

0 ≤  x ≤ 20.

Step-by-step explanation:

-10≤2x – 10 ≤30

2x - 10 ≤ 30

2x ≤  40

x ≤ 20.

2x - 10  ≥ -10

2x ≥  0

x ≥ 0.

For compund inequalities you will have to separate both sides of the inequality into different equations so you can later plug it in.

For Example:

-10 ≤2x-10 Would be 0 ≤x

Add 10 on both sides, end up with 0≤2x then divide by 2 on both sides and end up with 0≤x

2x-10 ≤30 Would be x ≤20

Add 10 on both sides end up with 2x≤40 divide by 2 on both sides and end up with x≤20

So the answer would be 0 ≤ x ≤  20

Answer:

Here you go...

Step-by-step explanation:

You have 4, and you have 5.

You have 4+2 and you have 5+1

So, you take a 1 from the 2 in the first problem, which gives u 4+1 that equals 5.

Therefore, if u put the first equation in a simpler form then you get 5+1 with the other equation. So it would look like 5+1=5+1.

FURTHERMORE, 4+2= 5+1 (because you simplify 2 into a 1).

So. 5+1 equals 5+1. (which is common sense... 5+1= 6.)

Answer:

2:A number is greater than 17.2

Step-by-step explanation:

the ">" in the inequality represents is greater

so the m> means m is greater than... and then the 17.2 means m is greater than 17.2. The way I learnt it was to imagine the ">" sign is like a crocodile, it wants the bigger number. So the ">" being towards the "m" shows that m is the bigger number.

Answer:

2

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

100%-80%=20%

....... .

Answer

Well pi is an irrational number because it can't be simplified into a fraction. And from what I can see neither can the sqaure root of 10/49. So I believe it would be both of them. But if there is only one answer than i'm not sure sorry. But it also says each so maybe there is more than one answer.

Step-by-step explanation:

Answer:jjjjjjjjjjjjjjjjjjjj

jjjjjjjjjjjjjjjjjjjjjjjjjj

jjjjjjjjjjjj

jjjjjjjj

jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj

Answer:

Step-by-step explanation: Ok so the important thing is to figure out how much he makes each month. if he earns 5,600 but the cost are 4,000 he makes 1,600 every month. To figure out how many months it will take we divide 32,000 by 1,600 to get 20. that is when he breaks even, 20 months. To make a profit it will be 21 months.

Answer:

-1 = 1/2*4 + -3 / -1 = 1/2*4 - 3 for slope intercept equations

y + 1 = 1/2(x - 4) for point slope equations

Step-by-step explanation:

Slope intercept formula is y = mx  + b where y is the y point, x is the x point on the graph, m is the slope and b is y intercept. For this we know the slope, the x and the y axis. Now all we need to find is the y intercept, for this we would have have to multiply the x axis by the slope and then find the number to complete the equation in this case its 1/2 (slope) and 4 (x axis),

-1 = 2 + b

for this we'd subtract -2 to both sides

-1 -2 = +2 - 2 + b

Which then we'd get,

-3 = b

So our Y intercept is -3

To complete the equation we'd finish it with putting everything together,

-1 = 1/2*4 + -3 or -1 =1/2*4 -3

If it were a point slope equation (y - y₁ = m(x - x₁)) we have the y₁, x₁ and the slope value 1/2, so we have all we need to fill in the point slope equation and here it is,

y + 1 = 1/2(x - 4)

Hope this helps!

Answer:

A 17, B 19, C 27

Step-by-step explanation:

A + B = 36

A + B + C = 63

63 - 36 = 27, which is C

C - A = 10

27 - A = 10

A = 17

A + B + C = 63

17 + B + 27 = 63

63 - 44 = 19

Answer:

C. [tex]a_n=(9)(\frac{2}{3})^{n-1}[/tex]

Step-by-step explanation:

Iterative geometric sequence:

[tex]a_n=a_1x^{n-1}[/tex]

Recursive geometric sequence:

[tex]a_n=xa_{n-1}[/tex]

The equations are very similar and you only really need to rearrange it. The factor (2/3) and the first term (9) are given, so you can write the iterative equation:

[tex]a_n=(9)(\frac{2}{3})^{n-1}[/tex]

And so the answer is C.

Answer:

slope = -4/5 and y-intercept = -9/5

Step-by-step explanation:

make y the subject of the formula

Answer:

75 degrees

Step-by-step explanation:

all added up is 180 on every triangle. 70+35=105. 180-105=75

Answer:

binomial

Step-by-step explanation:

a monomial has 1 term

a binomial has 2 terms

a trinomial has 3 terms

2x + y has 2 terms and so is a binomial

Answer:

383.5

Step-by-step explanation:

We want to round 383.52 to the nearest tenth.

The tenth would be the 5.

To round we look at the number after the one we want to round ( so 2 )

If the number is greater than 4 so ( 5, 6, 7, 8 or 9 ) then we raise the number that we want to round but if its less than 5 ( 4, 3, 2, 1 , 0 ) we keep the number as it is.

2 is less than 5 so we keep 5 as it is to get 383.5

Based on the boxplots, it can be stated that the interquartile ranges for the two websites are the same.

This is so for the following reasons:

Learn more about maths in https://brainly.com/question/25811665

Answer:

Y = 5x - 10

Step-by-step:

Leave a brainliest if this helped!

Answer:

[tex]i = \sqrt{ \frac{p}{r} } [/tex]