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Furkat [3]
2 years ago
12

A triangle has side lengths of (1.3k+3.5m)(1.3k+3.5m) centimeters, (4.1k-1.6n)(4.1k−1.6n) centimeters, and (9.7n+4.4m)(9.7n+4.4m

) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Mathematics
1 answer:
Scorpion4ik [409]2 years ago
5 0

Answer:

(5.4k+7.9m+8.1n) centimeters

Step-by-step explanation:

Given the side length of a triangle;

S1 = (1.3k+3.5m) cm

S2 = (4.1k-1.6n) cm

S3 = (9.7n+4.4m) cm

Perimeter of the triangle = S1+S2 + S3

Perimeter of the triangle = (1.3k+3.5m) + (4.1k-1.6n) + (9.7n+4.4m)

Collect the like terms;

Perimeter of the triangle = 1.3k+4.1k+3.5m+4.4m-1.6n+9.7n

Perimeter of the triangle = 5.4k+7.9m+8.1n

Hence the expression that represents the perimeter of the triangle is (5.4k+7.9m+8.1n) centimeters

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The correlation coefficient for the ages of drivers in a driver safety class and the number of traffic violations they have rece
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A correlation coefficient is always a value in between -1 and 1
The closest a coefficient to -1, the correlation is a strong negative correlation
The closest a coefficient to 1, the correlation is a strong positive correlation
The closest a coefficient to 0, there is no correlation at all

The coefficient -0.61 shows a strong negative correlation
This means that the relationship between the age and the violation is an inverse relationship; as age increases, violation decreases

Answer: option C
7 0
2 years ago
A rectangular exercise mat has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to
Karo-lina-s [1.5K]
<h2>Hello!</h2>

The answers are:

- Length

length=2width=12feet

- Width

width=6feet

- Area

Area=72feet^{2}

<h2>Why?</h2>

We are given the perimeter of a rectangular mat, and we are asked to find the area, and write an equation to determine the length, if feet, of the mat. To solve this problem we need to remember the equation of the perimeter of a rectangle, which is:

Perimeter=2length+2width

Using the given information we have,

36feet=2length+2width

Also, we know that the length is twice the width, so:

length=2width

Then, substituting the second equation into the first equation, we can find the width of the mat.

Substituting, we have:

36feet=2(2width)+2width

36feet=4width+2width

36feet=6width

[tex]\frac{36feet}{6} =width\\width=\frac{36feet}{6} =6feet[/tex]

Then, substituting the width into the second equation, we can find the length of the mat,

Substituting, we have:

length=2width

length=2(6feet)=12feet

Then, finding the area, we have:

A=length*width=12feet*6feet=72feet^{2}

Have a nice day!

7 0
2 years ago
A flu epidemic is spreading through a town of 48,000 people. It is found that if x and y denote the numbers of people sick and w
Liula [17]

Answer:

a) The simultaneous equation represented in matrix form, is

[1/3 1/4] [x] = [s]

[2/3 3/4] [y] = [w]

Ax = B

[1/3 1/4] = matrix A (matrix of coefficients)

[2/3 3/4]

[x] = matrix x (matrix of unknowns)

[y]

[s] = matrix B (matrix of answers)

[w]

b) Number of sick people the preceding week = 12005

Step-by-step explanation:

x = Number of sick people in a week

y = Number of people that are well in a week

s = Number of sick people the following week

w = Number of people that are well the following week.

The relationship between these is given as

(1/3)x + (1/4)y = s

(2/3)x + (3/4)y = w

In matrix form, this is simply presented as

[1/3 1/4] [x] = [s]

[2/3 3/4] [y] = [w]

which is more appropriately written as

Ax = B

where

[1/3 1/4] = matrix A (matrix of coefficients)

[2/3 3/4]

[x] = matrix x (matrix of unknowns)

[y]

[s] = matrix B (matrix of answers)

[w]

b) Taking the current conditions as s and w, then the preceding week will be x and y

The number of sick people in this week, s = 13000

The number of people well in this week, w = total population - Number of sick people.

w = 48000 - 13000 = 35000

So, the simultaneous equation becomes

(1/3)x + (1/4)y = 13000

(2/3)x + (3/4)y = 35000

Then we can solve for the number of sick and well people the preceding week.

We can solve normally or use matrix solution.

Ax = B

x, the matrix of unknowns is given by product of the inverse of A (inverse of the matrix of coefficients) and B (matrix of answers)

x = (A⁻¹)B

But, solving normally,

(1/3)x + (1/4)y = 13000

(2/3)x + (3/4)y = 35000

x = 12004.8 = 12005

y = 35995.2 = 35995

Number of sick people the preceding week = x = 12005

8 0
2 years ago
In a right triangle, angle a measures 20. The side opposite angle a is 10 centimeters long. Approximately how long is the hypote
AleksAgata [21]

<span>sin(angle)=<span><span>opposite leg/</span><span>hypotenuse</span></span></span>

<span><span><span>
</span></span></span>

<span><span><span> sin(20) = 10/ hypotenuse</span></span></span>

<span><span><span>hypotenuse = 10/sin(20) = 29.238 ( round off as necessary)</span></span></span>

<span><span><span>
</span></span></span>


6 0
2 years ago
Read 2 more answers
A stereo speaker in the shape of a triangular pyramid has a height of 6 inches. The area of the base of the speaker is 11 square
Jet001 [13]

Answer:

<u>The correct answer is A. 22 inches ³</u>

Step-by-step explanation:

Let's recall that the formula of the volume of a triangular pyramid:

Volume = 1/3 * Area of the base * height

Replacing with the values we have:

Volume = 1/3 * 11 inches² * 6 inches

Volume = 66/3

Volume = 22 inches ³

<u>The correct answer is A. 22 inches ³</u>

5 0
2 years ago
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