-1= -3r+2r please i need it

The perimeter of a triangle is 16 to the square root of 7 feet. If the two sides measure the square root of 343 feet and the squ

Taya2010 [7]

Answer:the length of the third side is 4√7

Step-by-step explanation:

The perimeter of a triangle is 16 to the square root of 7 feet. This is expressed as

Perimeter = 16√7 feet

The perimeter of a triangle is the sum of the length of the three sides of the triangle.

If the two sides measure the square root of 343 feet and the square root of 175, which are expressed as √343 and √175, the third length would be

16√7 - (√343 + √175)

Expressing √343 as a radical, it becomes 7√7

Expressing √175 as a radical, it becomes 5√7

7√7 + 5√7 = 12√7

Therefore, the third length would be

16√7 - 12√7 = 4√7 feet

5 0

4 years ago

(NEED HELP FAST , WILL GIVE BRAINLIEST!!!)

Kryger [21]

Answer:

Explained below.

Step-by-step explanation:

The data from the scatter plot is as follows:

Arm Span Height

19.5 25

35.5 35

37.0 39

40.5 40

44.5 45

45.5 50

49.0 49

51.0 55

52.5 47

59.0 60

61.0 58

(1)

Compute the value of slope and intercept as follows:

$\sum{X} = 495 ~,~ \sum{Y} = 503 ~,~ \sum{X \cdot Y} = 23822 ~,~ \sum{X^2} = 23660.5$

$\begin{aligned} b &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 503 \cdot 23660.5 - 495 \cdot 23822}{ 11 \cdot 23660.5 - 495^2} \approx 7.174 \\ \\m &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 11 \cdot 23822 - 495 \cdot 503 }{ 11 \cdot 23660.5 - \left( 495 \right)^2} \approx 0.857\end{aligned}$

The equation of the line of best fit is, y = 0.857·x + 7.174.

(2)

The slope of the line represent the rate of change in y caused by one unit change in x.

In this case the slope of m = 0.857 indicates that as the arm span increases by 1 unit the height increases by 0.857 units.

(3)

To perform the Residual Test, simply take two values from the table and interchange the x and y values.

Consider the values: (37, 39) and (51, 55)

Compute the value of y if x = 39:

$y = 0.857\cdot x + 7.174\\=0.857\times 39+7.174\\=40.597\\\approx 40.6$

The new value of y (40.6) is close to the original value (39.0)

Compute the value of y if x = 55:

$y = 0.857\cdot x + 7.174\\=0.857\times 55+7.174\\=54.309\\\approx 54.0$

The new value of y (54) is close to the original value (55)

Thus, it can be said that the line of best fit models the data provided.

(4)

The line of best fit is:

y = 0.857·x + 7.174

The slope of the line is positive.

This implies that there is a positive relationship between the two variables.

The formula of slope in terms of correlation coefficient is:

$\text{Slope}=r\times\sqrt{\frac{Var(x)}{Var(x)}}$

The correlation coefficient is directly proportional to the slope.

This implies that the correlation coefficient is also positive.

Thus, the variables Arm span and Height are positively correlated.

4 0

3 years ago

A circle with area 9pi has a sector with a central angle of 60 degrees What is the area of the sector ?

belka [17]

Area of the sector is 4.71 sq units

Step-by-step explanation:

Step 1: Area of the sector = Area of the circle × (C/360) where C is the central angle.

Area of the sector = πr²(C/360) = 9π × 60/360

= 9 × 3.14 × 1/6

= 28.26/6 = 4.71 sq units

4 0

4 years ago

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Create your own real-world problem which uses either an arithmetic or geometric sequence to solve it. Include the solution, with

yanalaym [24]

Let's say that you're in your room and you find that the current temperature of 72 degrees is too cold, so slowly you increase the temperature of the room by two degrees.

We know that the explicit formula is
a^n=a^1+ (n-1)d

and so by substituting the given information in

a^n= 72 + (n-1)2

a^1=Initial temp
d= rate of change

by substitution a value of n (the term we are looking for) into this equation, you can then calculate the temperature that you just set the room too.

6 0

4 years ago

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The function below represents the annual interest Alexander earns on a savings account. Identify the term that represents the am

lisabon 2012 [21]

Answer:

Option 4

The term that represents the amount of time that the money is accruing interest is 'x'.

Step-by-step explanation:

Given : The function below represents the annual interest Alexander earns on a savings account.

$f(x)=500(1+0.02)^x$

To find : Identify the term that represents the amount of time that the money is accruing interest ?

Solution :

The general annual interest formula is $A=P(1+r)^t$

Where, A is the amount

P is the principal

r is the interest rate

t is the time

The annual interest Alexander earns on a savings account is

$f(x)=500(1+0.02)^x$

Comparing with general formula,

t=x

The term that represents the amount of time that the money is accruing interest is 'x'.

Therefore, Option 4 is correct.

4 0

4 years ago

Read 2 more answers