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kvv77 [185]
3 years ago
13

Each week, Rosario drives to an ice-skating rink that is 60 miles away. The round-trip takes 2.75 hours. If he averages 55 miles

per hour on his way to the rink, which equation can be used to find x, the number of miles per hour he averages on his way home?
Mathematics
1 answer:
vazorg [7]3 years ago
3 0

Answer:

The answer to your question is x = 4d/t - S1

Step-by-step explanation:

Data

total time = t = 2.75 hours

Initial speed = S1 = 55 mi/h

Final speed = x

distance = d = 60 mi

Formula

speed = distance / time

Average speed = (Initial speed + final speed)/2  or

                          = (S1 + x)/2

Substitution

                             (S1 + x)/2 = 2(d) / t

Solve for x

                             x = (2d/t)2 - S1

Simplification and result

                              x = 4d/t - S1

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A rectangle has an area of 4 square centimeters. A second rectangle is 3 times as long and 3 times as wide as the first rectangl
vekshin1

Answer:

The area of the second rectangle will be 36 square centimetres

Step-by-step explanation:

Given:

Area of the first rectangle  =  4 square centimetres

A second rectangle is 3 times as long and 3 times as wide as the first rectangle

To Find:

Area of the second rectangle = ?

Solution:

We know that area of the rectangle is  Length X breadth

Length X width = 4

In this case the are 2 possibilities

Case 1:

Length = 2 cm

Width  = 2 cm

2 X 2 = 4

Now According to the question

Length is 3 times  = 2 X 3 = 6cm

width is also 3 times  = 2 X 3 = 6 cm

Now the area of the second rectangle will be

6 X  6 = 36 square centimetres

Case 2:

Length = 4 cm

Width  = 1 cm

4 X 1 = 4

Now According to the question

Length is 3 times  = 4 X 3 = 12 cm

width is also 3 times  = 1 X 3 =3 cm

Now the area of the second rectangle will be

12 X  3 = 36 square centimetres

5 0
3 years ago
If the equation x^2 - 12x - 9 = 0 is converted to the form (x - b)^2 = c and the resulting equation is (x - 6)^2 = c, what is th
Radda [10]

Answer:

Step-by-step explanation:

Identified

7 0
3 years ago
An arithmetic sequence has this recursive formula:
maria [59]

Answer:

C

Step-by-step explanation:

C is the answer because a1=7 , d=-4 and so it's

an=an+(n-1)d

3 0
2 years ago
this week luiz made 80% of what he made last week if he made $72 this week how much did he make last week?
kvv77 [185]

Answer: He made $90 last week.

Assumption :

Let, Luis made $X last week.

He made $72 this week which is 80% of $X that he made last week

⇒ X * 80% = 72

⇒ X * 80/100 = 72

⇒ X = (72 * 100)/80

⇒ X = 90

Therefore, he made $90 last week.

To remember :

While solving this type of problems, be careful to understand which one of last time and current time is not given; just assume that one and input other conditions, the problem will be solved.

8 0
2 years ago
If A is nonsingular, then (AT )-1 =(A-1) T . (a) Verify this theorem for 2 × 2 matrices
kipiarov [429]

Answer:

Verified

Step-by-step explanation:

Let the 2x2 matrix A be in the form of:

\left[\begin{array}{cc}a&b\\c&d\end{array}\right]

Where det(A) = ad - bc # 0 so A is nonsingular:

Then the transposed version of A is

A^T = \left[\begin{array}{cc}a&c\\b&d\end{array}\right]

Then the inverted version of transposed A is

(A^T)^{-1} = \frac{1}{ad - cb} \left[\begin{array}{cc}a&-c\\-b&d\end{array}\right]

The inverted version of A is:

A^{-1} = \frac{1}{ad - bc}\left[\begin{array}{cc}a&-b\\-c&d\end{array}\right]

The transposed version of inverted A is:

(A^{-1})^T = \frac{1}{ad - bc}\left[\begin{array}{cc}a&-c\\-b&d\end{array}\right]

We can see that

(A^T)^{-1} = (A^{-1})^T

So this theorem is true for 2 x 2 matrices

3 0
3 years ago
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