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3 years ago

6. A rectangle has a perimeter of 62 feet. If its length is 9 feet longer than its width, find

Mathematics

1 answer:

Anastaziya [24]3 years ago

8 0

Answer:

length = 20 ft, width = 11 ft

Step-by-step explanation:

let w be width, then length = w + 9

The opposite sides of a rectangle are equal , then

2w + 2(w + 9) = 62

2w + 2w + 18 = 62

4w + 18 = 62 ( subtract 18 from both sides )

4w = 44 ( divide both sides by 4 )

w = 11

and w + 9 = 11 + 9 = 20

then width = 11 ft and length = 20 ft

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Plsss help it also detects if it’s right or wrong

Masteriza [31]

Answer:

3/8

Step-by-step explanation:

Looking at the bottom row, there are 8 possible outcomes

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

There are 3 that have exactly 2 heads HHT, HTH, THH,

That means the probability is

P( exactly 2 heads) = number outcomes with exactly 2 heads/total outcomes

=3/8

7 0

3 years ago

A manager is comparing the cost of buying ball caps with the team emblem from two different companies. Company X charges a $50 f

Nady [450]

Answer:

10 ball caps

Step-by-step explanation:

In this question, we are trying to know the number of caps the manger would buy that would equate the cost at both companies.

How do we get this?

Since we do not know the number of caps, let’s assign a variable. Let the number of caps that is required be x. Let’s now make some costings in terms of x. We proceed;

Company X charges $50 fee plus $7 per cap. Total amount company X will charge on x caps will be; $50 + $7(x) = $50 + $7x

Company Y will charge $30 plus $9 per cap. Total amount company Y will charge on x caps will be $30 + $9(x) = $30 + $9x

We are trying to look at the value of x that will make both costs equal. What we do is to equate both costs.

30 + 9x = 50 + 7x

We simply by taking like terms to the same sides

9x-7x = 50-30

2x = 20

x = 20/2 = 10

X = 10

So what this means is that manger has to buy 10 caps to have the same cost in both companies

3 0

3 years ago

1. Identify a pair of alternate exterior angles.

alisha [4.7K]

First answer is the fourth one, 2 and 6

3 0

3 years ago

A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2

andrey2020 [161]

Answer:

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

Step-by-step explanation:

Consider the provided matrix.

$v_1=\begin{bmatrix}-3\\1 \end{bmatrix}$

$v_2=\begin{bmatrix}-1\\1 \end{bmatrix}$

$\lambda_1=4, \lambda_2=2$

The general solution of the equation $x'=Ax$

$x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}$

Substitute the respective values we get:

$x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}$

Substitute initial condition $x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}$

$\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}$

Reduce matrix to reduced row echelon form.

$\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}$

Therefore, $c_1=2.5,c_2=1.5$

Thus, the general solution of the equation $x'=Ax$

$x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

6 0

3 years ago

Solve: x + 1 < 5<br>Me confused and need help

natita [175]

Answer: x < 4

Step-by-step explanation: You are trying to isolate the variable, x, so you have to subtract 1 on both sides of the inequality. Then, you are left with x < 4.

4 0

3 years ago