The perimeter of the rectangle below is 166 units. Find the length of side RS.
Write your answer without variables.
S
R
G
4x + 2
P
5x-
Q
⠀
RS
=

Step-by-step explanation:

55x+6=120

55x=120-6

55x=114

X=114/55

The first 5 terms of the sequence is given by A = { -4.8 , 1.92 , -0.768 , 0.3072 , -0.12288 }

Given data ,

Let the geometric sequence be represented as A

Now , the value of A is

A = 12 ( -2/5 )ⁿ

On simplifying , we get

when n = 1

A₁ = 12 ( -2/5 ) = -4.8

A₂ = 12 ( -2/5 )²

A₂ = 12 ( 4/25 ) = 1.92

A₃ = 12 ( -2/5 )³

A₃ = -12 ( 8/125 ) = -0.768

A₄ = 12 ( -2/5 )⁴

A₄ = 12 ( 16 / 625 ) = 0.3072

A₅ = 12 ( -2/5 )⁵

A₅ = -12 ( 32 / 3,125 ) = -0.12288

Hence , the geometric sequence is solved

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Step-by-step explanation:

The number of non square numbers between 12square and 13square are

Step-by-step explanation:

1- 9 + 7z

1-9+7(3)

-8+21

=13

Answer:

Step-by-step explanation:

1-9+7z      z=3

1-9+7(3)

1-9+21

-8+21

13

Answer:

12

742

127.5

Step-by-step explanation:

If it's the area that 6*4=24, but it's not sqaure it's half ,so 24/2=12

742

127.5

Answer:

D. -5 ≤ x ≤5

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

We see from the graph that our x-values span from -5 to 5. Since both are closed dots, they are included in our domain:

[-5, 5]

or

-5 ≤ x ≤ 5

Answer:

x =  6/√3

y = 3/√3

Step-by-step explanation:

For a triangle rectangle with a known angle θ, we have the relations:

Sin(θ) = (opposite cathetus)/(hypotenuse)

Cos(θ) = (adjacent cathetus)/(hypotenuse)

Tan(θ) = (opposite cathetus)/(adjacent cathetus)

For this triangle, we know an angle:

θ = 60°

And the opposite cathetus measures 3 units.

The adjacent cathetus is y.

The hypotenuse is x.

To find the value of x, we can use the Sin equation:

Sin(60°) = 3/x

x = 3/sin(60°) = 3.46 = 3*2/√3 = 6/√3

And we can use the Tan relation to find the value of y.

Tan(60°) = 3/y

y = 3/Tan(60°) = 1.73 = 3/√3

For x he didn't divide by √3, while for y he multiplied by √3 instead of dividing by √3.

Formula for Profit Percentage = (Profit/C.P.) 100Where C.P. denotes the article's cost price, i.e. the price at which the article was originally purchased.

Jane bought a car for £24000

 she sold it for £26000

profit = 2000

profit percentage = 2000/26000 x100 = 7.7%

Here,

Jane bought a car for £24000

 she sold it for £26000

profit = 2000

profit percentage = 2000/26000 x100 = 7.69%

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1) Note that the altitude of the top of the hill is -136 feet above sea level.

2) Note that Checkpoint 1 is 3,558 feet higher than Checkpoint 5.

Altitude or height is a distance measurement between a reference datum and a point or object, generally in the vertical or "up" direction. The precise definition and reference datum vary depending on the circumstance.

1) Checkpoint 4 has an altitude of -202 feet above sea level. The top of the hill rises 66 feet above Checkpoint 4. Therefore, the altitude of the top of the hill is:

-202 + 66 = -136 feet

So, the altitude of the top of the hill is -136 feet above sea level.

2) To find the difference in altitude between Checkpoint 1 and Checkpoint 5, we need to subtract the altitude of Checkpoint 5 from the altitude of Checkpoint 1.

Altitude difference = Altitude of Checkpoint 1 - Altitude of Checkpoint 5

Substituting the values given in the table, we get:

Altitude difference (AD) = 3,459 - (-99)

AD = 3,459 + 99

Thus, AD = 3,558

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Step-by-step explanation:

According phythagorous theorem,

x²=(12)²+(5)²

x²=144+25

x= root of 169

x=13

Answer:

According phythagorous theorem,

x²=(12)²+(5)²

x²=144+25

x= root of 169

x=13

Step-by-step explanation:

By proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

Given:

- Triangle ΔAEB and ΔDFC

- Line ABCD is straight (implies AC and BD are collinear)

- AE is parallel to DF

- EB is parallel to FC

- AC = DB

To prove: ΔEAB ≅ ΔFDC

Recall that:

AE || DF

EB || FC

AC = DB

AE || DF, EB || FC (Parallel lines with transversal line AB)

Corresponding angles are congruent:

  ∠AEB = ∠DFC (Corresponding angles)

  ∠EAB = ∠FDC (Corresponding angles)

Corresponding sides are proportional:

  AE/DF = EB/FC (Corresponding sides)

  AC/DB = BC/DC (Corresponding sides)

  AC = DB

  BC = DC (Equal ratios)

ΔEAB ≅ ΔFDC (By angle-side-angle (ASA) congruence)

∠EAB = ∠FDC

∠AEB = ∠DFC

AC = DB, BC = DC

Therefore, by proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

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Answer:

7.61

Step-by-step explanation:

Sum all of the values

2.22+2.97+2.42=7.61

Answer:

761

Step-by-step explanation:

The zeros and the multiplicities are

from the question, we have the following parameters that can be used in our computation:

f(x) = (x + 6)³(x - 11)²(x - 6)(x + 5)³

The power of each factor are the multiplicities

So, we have

Zero(s) of multiplicity one:

x - 6 = 0

Zero(s) of multiplicity two:

x - 11 = 0

Zero(s) of multiplicity three:

x + 6 = 0 and x + 5 = 0

When evaluated, we have

Zero(s) of multiplicity one:

x = 6

Zero(s) of multiplicity two:

x = 11

Zero(s) of multiplicity three:

x = -6 and x = -5

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Given the value of the original quantity and the value of the new quantity, the percent​age increase is 50%.

Percent​ increase is aimply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.

It is expressed as;

C = ((x₂ - x₁) / x₁)100%

Where x₁ is initial value and x₂ is new value

Given the data in the question;

We substitute the given values into the expression above.

C = ((x₂ - x₁) / x₁)100%

C = ((15 - 10) / 10)100%

C = (5/10)100%

C = 0.5 × 100%

C = 50%

Therefore, given the value of the original quantity and the value of the new quantity, the percent​age increase is 50%.

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Answer:

15.6%

Step-by-step explanation:

Since each day there is a 6% chance that Lisa smiles at him then that means that each day there is a 94% chance that Lisa does not smile at him. To find the probability of Milhouse going longer than a month (30 days) without a smile from Lisa we need to multiply this percentage in decimal form for every day of the month. This can be solved easily by putting 94% to the 30th power which would be the same, but first, we need to turn it into a decimal...

94% / 100 = 0.94

\(0.94^{30}\) = 0.156

Now we can turn this decimal into a percentage by multiplying by 100

0.156 * 100 = 15.6%

Finally, we can see that the probability that Milhouse goes longer than a month without a smile from Lisa is 15.6%

Using the binomial distribution, it is found that there is a 0.1563 = 15.63% probability that Milhouse goes longer than a month without a smile from Lisa.

For each day, there are only two possible outcomes, either Lisa smiles at him, or she does not. The probability that she smiles at him on day is independent of any other day, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that Milhouse goes longer than a month without a smile from Lisa is the probability of no smiles during 30 days, that is, P(X = 0), hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{30,0}.(0.06)^{0}.(0.94)^{30} = 0.1563\)

0.1563 = 15.63% probability that Milhouse goes longer than a month without a smile from Lisa.

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Answer:

The degrees of freedom are:

\(df=n-1=10-1=9\)

The confidence level is 0.95 or 95%, the significance would be \(\alpha=0.05\) and \(\alpha/2 =0.025\), the critical value for this case would be \(t_{\alpha/2}=2.262\)

And replacing we got:

\(54.7-2.262\frac{9.956}{\sqrt{10}}=47.58\)    

\(54.7+2.262\frac{9.956}{\sqrt{10}}=61.82\)    

Step-by-step explanation:

Information given

In order to calculate the mean and the sample deviation we can use the following formulas:  

\(\bar X= \sum_{i=1}^n \frac{x_i}{n}\) (2)  

\(s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}\) (3)  

\(\bar X= 54.7\) represent the sample mean

\(\mu\) population mean  

s=9.956 represent the sample standard deviation

n=10 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\)   (1)

The degrees of freedom are:

\(df=n-1=10-1=9\)

The confidence level is 0.95 or 95%, the significance would be \(\alpha=0.05\) and \(\alpha/2 =0.025\), the critical value for this case would be \(t_{\alpha/2}=2.262\)

And replacing we got:

\(54.7-2.262\frac{9.956}{\sqrt{10}}=47.58\)    

\(54.7+2.262\frac{9.956}{\sqrt{10}}=61.82\)    

An Edge of a polyhedron is the intersection of the Vertex of the polyhedron.

A polyhedron  can be described as the 3-dimensional solid that is been formed through the combination of more than one polygons and they usually have different faces which is been used in knowing them as well as their classification.

It should be noted that this polyhedrons  can be categorized based on the  number of faces that can be found on them, however in this case we can conclude that the Vertex serves as the point of intersection that the edges of  polyhedron has.

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Answer:

edge, vertex

Step-by-step explanation:

Answer:

x = 2.4

Step-by-step explanation:

4x + 5 / x + 7
combine like terms

X + 4x = 5x

5 + 7= 12

12/ 5x

Divide

12 /5= 2.4

X= 2.4

2000 pounds is equal to 1 ton

answer: 2000 pounds = 1 Ton

Answer:

3(-5(-2.9))

=43.5

\(3 \times \frac{1}{4} \div ( - \frac{2}{7} )\)

\( = - 11.375\)

hope it helps you

make me brainliest if u r ok with it

please edit your question man

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:

81 apartments are in the building

Step-by-step explanation:

9 × 9 = 81

If Fran and Jill made a new years resolution to ride bikes.  it will take 3 weeks for Fran and Jill to have ridden the same number of miles..

Let's assume that it takes "x" number of weeks for Fran and Jill to ride the same number of miles.

In the first week, Fran rides 40 miles, and Jill rides 70 miles.

In the "x"th week, Fran will have ridden a total of 40 + 55x miles.

In the "x"th week, Jill will have ridden a total of 70 + 45x miles.

For Fran and Jill to ride the same number of miles in "x" weeks, we need to solve the following equation:

40 + 55x = 70 + 45x

Simplifying this equation, we get:

10x = 30

x = 3

Therefore, it will take 3 weeks for Fran and Jill to have ridden the same number of miles.

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Answer:

6 + 7/10x + 2/y

Step-by-step explanation:

Hope this helps :)

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Answer: b

Step-by-step explanation:

Answer:

-2 11/12 is the answer for me