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patriot [66]
2 years ago
13

5. Heathcliff found a road map showing the driving route to a resort that he knows Gertrude enjoys. The map shows a roadway, sta

rting from Heathcliff's position, that goes 8 miles north, 5 miles east, 7 miles north and finally 3 miles east. How many miles will be saved if Heathcliff and Gertrude fly directly to the resort?
Mathematics
2 answers:
tigry1 [53]2 years ago
8 0
\sqrt{ (8+7)^{2} +(5+3)^{2} } =17.
the answer is 17 miles
Kipish [7]2 years ago
4 0

Answer: 6 miles will be saved.

Step-by-step explanation:

The total distance that he traveled is: 8 miles + 7 miles =15 miles to north.

And 5 miles + 3 miles = 8 miles to east.

Then the total distance is 15 miles + 8miles = 23 miles

If they did the direct path, the hipotenuse of a triangle with sides of 15miles and 8 miles, the distance would be:

D = √(15^2 + 8^2) = 17 miles

And the difference is equal to 23 miles - 17 miles  = 6 miles

So they will save 6 miles if they use a direct path.

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Deondra has $12 to spend on a mixture of green and red grapes. What equation can she use to graph a line showing the different a
Sonbull [250]

Answer:

It depends on the cost of grapes.

Step-by-step explanation:

Half of 12 is 6, so if each pack of grapes cost 6 or less, she can buy a pack of green and red grapes.

6 0
2 years ago
Seth’s father is thinking of buying his son a six-month movie pass for $40. With the pass, matinees cost $1.00. If matinees are
Ymorist [56]

Answer:

In order for it to benefit his father to buy the pass Seth have to attend the movies for 11 times.

Step-by-step explanation:

Given:

Cost of movie pass = $40

Cost per matinees with pass = $1.00

Cost per matinees without pass = $3.50

To Find:

Number of times must Seth attend in order for it to benefit his father to buy the pass = ?

Solution:

Let x be the number of times he wants to visit

To profit his father

The number of visits without pass =  the number of visits with passin the cost  of $3.50

Then, without pass if he visits for x times then the cost will be  = 3.50x

Also with pass, the number of times he can visit the pass  =  \frac{40}{3.50}

then

\frac{350 x}{3.50} = \frac{40}{3.50}

3.50x = 40

x = \frac{40}{3.50}

x =  11.42

x = 11 (approx)

3 0
2 years ago
A professor wants to determine information about the Internet usage of middle school students in one state. A sample of 500 boys
zlopas [31]
The answer is A because a sample of 500 boys and girls from middle schools across the state represents the population.
4 0
2 years ago
Read 2 more answers
A person is standing exactly 36 ft from a telephone pole. There is a 30° angle of elevation from the ground to the top of the po
nika2105 [10]

Answer:

20.78feet

Step-by-step explanation:

The question made us to understand that the man is standing and also there is angle of elevation, then we need to draw a right triangle having a base equal to 36 feet with an angle from the base to the top of the pole which is 30 degrees.

tan= opposite side / adjacent side

Let height of the pole =h

Tan(30)= h/36

But tan 30degree= 1/√3

h= 36 × 1/√3

h= 20.78feet

Therefore, the height of the pole= 20.78feet

CHECK THE ATTACHMENT FOR DETAILED FIGURE

7 0
2 years ago
Read 2 more answers
. Given f(x) = e 2x e 2x + 3e x + 2 : (a) Make the substitution u = e x to convert Z f(x) dx into an integral in u (HINT: The ea
MrRa [10]

Answer:

Step-by-step explanation:

Given;

f(x)=\frac{e^{2x}}{e^{2x}+3e^x+2}

a)

substitute u=e^x\\du=e^x dx\\\\\int\frac{e^{2x}}{e^{2x}+3e^x+2}dx=\int\frac{e^x\dot e^x}{e^x^{2x}+3e^x+2}dx\\\\=\int\frac{udu}{u^2+3u+2}

b)

Apply partial fraction in (a), we get;

\frac{u}{u^2+3u+2}=\frac{2}{u+2}-\frac{1}{u+1}\\\\\therefore u^2+3u+2\\=u^2+2u+u+2\\=u(u+2)+1(u+1)\\=(u+2)(u+1)\\\\Now\,\int\frac{u}{u^2+3u+2}\,du=\int\frac{2}{u+2}du-\int\frac{1}{u+1}du\\\\=2ln|u+2|-ln|u+1|+c\\=2ln|e^x+2|-lm|e^x+1|+c

where C is an arbitrary constant

8 0
2 years ago
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