1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
svp [43]
3 years ago
11

It will take Adam four hours to drive to Disney Park, and 2.5 times less time if driving 45 mph faster. What is the distance Ada

m should cover to get to the park? Pease and fanks
Mathematics
1 answer:
Butoxors [25]3 years ago
6 0
<h2>Hello!</h2>

The answer is:

The distance that Adam should cover to get to the park is 108 miles.

<h2>Why?</h2>

To solve the problem, we need to write two equations with the given information about the times and his speed.

So,

For the first equation we have: Going to Disney Park

time=4hours

Distance=v*4hours

For the second equation we have: Going back from Disnery Park

time=4hours-2.5hours=1.5hours

Speed=v+45mph

Distance=(v+45mph)*1.5hours

Now, if He covered the same distance going and coming back, we have:

v*4hours=(v+45mph)*1.5hours

v*4hours=v*1.5hours+45mph*1.5hours

v*4hours-v*1.5hours=45mph*1.5hours

v*2.5hours=67.5miles

v=\frac{67.5miles}{2.5hours}=27\frac{miles}{hour}=27mph

We have that the speed when Adam was going to Disney Park was 27 mph.

Therefore, to calculate the distance, we need to substitute the obtained speed in any of the two first equations.

Then, substituting the speed into the first equation, we have:

Distance=v*4hours\\Distance=27mph*4hours=108miles

Hence, we have that the distance that Adam should cover to get to the park is 108 miles.

Havea nice day!

You might be interested in
Which of the following best describes the slope of the line below?
Lina20 [59]

Answer:

I think the answer is A.Negative

Step-by-step explanation:

From x=-5 to x=0 the slope is decreasing and from x=1 to x=6 it keeps decreasing.

4 0
3 years ago
Which event has a probability of 1/2? Select all that apply.
Ymorist [56]
C, E, and F have 50 50 chance
4 0
3 years ago
The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term
Salsk061 [2.6K]

Answer:

The first three terms of the geometry sequence would be 1, 5, and 25.

The sum of the first seven terms of the geometric sequence would be 127.

Step-by-step explanation:

<h3>1.</h3>

Let d denote the common difference of the arithmetic sequence.

Let a_1 denote the first term of the arithmetic sequence. The expression for the nth term of this sequence (where n\! is a positive whole number) would be (a_1 + (n - 1)\, d).

The question states that the first term of this arithmetic sequence is a_1 = 1. Hence:

  • The third term of this arithmetic sequence would be a_1 + (3 - 1)\, d = 1 + 2\, d.
  • The thirteenth term of would be a_1 + (13 - 1)\, d = 1 + 12\, d.

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let r denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d.

Ratio between the third term and the second term of the geometric sequence:

\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}.

Both (1 + 2\, d) and \left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right) are expressions for r, the common ratio of this geometric sequence. Hence, equate these two expressions and solve for d, the common difference of this arithmetic sequence.

\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}.

(1 + 2\, d)^{2} = 1 + 12\, d.

d = 2.

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be 1, (1 + (3 - 1) \times 2) = 5, and (1 + (13 - 1) \times 2) = 25, respectively.

These three terms (1, 5, and 25, respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be r = 25 /5 = 5.

<h3>2.</h3>

Let a_1 and r denote the first term and the common ratio of a geometric sequence. The sum of the first n terms would be:

\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}.

For the geometric sequence in this question, a_1 = 1 and r = 25 / 5 = 5.

Hence, the sum of the first n = 7 terms of this geometric sequence would be:

\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}.

7 0
2 years ago
if there are 2040 seats in a section of a stadium, 20 seats in the first row, and 4 more seats in each row, how many rows are th
Lorico [155]


2040 = n/2(20+(n-1)4)

4080 = n(20+4n-4)

4080= 20n +4n^2 -4n

1020 = 4n + n^2

n^2 +4n -1020 =0

use common formula (can't write out so just look at answers. sorry)

which gives answers of n=-34 and n=30. since n can only be positive, n=30 so there are 30 rows. I liked that challenge

5 0
3 years ago
Read 2 more answers
How did we transform from f(x) =x2 to g(x) = -3x2
Oksi-84 [34.3K]

Answer:

  f(x) is reflected over the x-axis and vertically scaled by a factor of 3

Step-by-step explanation:

If you compare the two functions, you see that ...

  g(x) = -3f(x)

Multiplication by -1 effects a reflection over the x-axis. (All y-values are transformed to their opposite.)

Multiplication by 3 is a vertical scaling by a factor of 3.

Taken together, f(x) is reflected over the x-axis and vertically scaled by a factor of 3.

7 0
3 years ago
Other questions:
  • Original price 65.00; Markdown: 12%
    8·1 answer
  • A restaurant waiter lit the candles on every table. Each candle got 5/8 of an inch shorter over his 5-hour shift. At what rate w
    12·1 answer
  • The elivation of city A is 60 feet above sea level; the elevation of city C is 12 feet above sea level. The elevation of city D
    15·1 answer
  • HELPPPPPPPPPPPPPPPPPPPPPPP I WIL GIVE BRAINLIEST ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    14·1 answer
  • What is the property that allows you move the parentheses in a problem and still get the same answer
    6·1 answer
  • How are the volume formulas of prisms and cylinders similar? How are they<br> different?
    7·1 answer
  • If you get this right I will mark you as a brainliest
    9·1 answer
  • NEED HELP DUE TODAY HELP
    14·1 answer
  • Please help! Correct answer only, please!
    7·2 answers
  • PLEASE I NEED HELP ASAP
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!