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3 years ago

Determine the distance between the points (2,7) and (-4,15)

Mathematics

1 answer:

Nikolay [14]3 years ago

4 0

Answer:

option C

Step-by-step explanation:

$distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

$=\sqrt{(-4-2)^2+(15-7)^2} \\\\=\sqrt{(-6)^2 + 8^2}\\\\=\sqrt{36 + 64 }\\\\= \sqrt{100} \\\\= 10$

You might be interested in

What is 2 3/8 as an improper fraction?<br><br> Give answers, please.

m_a_m_a [10]

To convert a mixed fraction into an improper fraction, we must follow some steps.

First, we take the whole part and multiply it by the denominator of the fraction.

In this case, we take 2 and multiply it by 8.

Now we add the numerator:

16+3=19

The denominator stays the same:

$\frac{19}{8}$

Hope it helps! :)

3 0

3 years ago

Find the midpoint of side EF. (4 points)

umka2103 [35]

Answer:

Midpoint of side EF would be (-.5,4.5)

Step-by-step explanation:

We know that the coordinates of a mid-point C(e,f) of a line segment AB with vertices A(a,b) and B(c,d) is given by:

e=a+c/2,f=b+d/2

Here we have to find the mid-point of side EF.

E(-2,3) i.e. (a,b)=(2,3)

and F(1,6) i.e. (c,d)=(1,6)

Hence, the coordinate of midpoint of EF is:

e=-2+1/2, f=3+6/2

e=-1/2, f=9/2

e=.5, f=4.5

SO, the mid-point would be (-0.5,4.5)

3 0

2 years ago

Mr. Fink's economy car can travel 420 miles on a 12-gallon tank of gas. Determine how many miles he can travel on 8 gallons.

Sphinxa [80]

Answer:

280 miles

Step-by-step explanation:

So, 420 miles=12 gallons

That means that for 1 gallon you would be able to go 35 miles.

Just multiply that by 8. 35*8=280

3 0

3 years ago

A group of individuals were surveyed about their plans for vacation. There were 21 individuals who said they were going to the d

Alexeev081 [22]

Answer:

140 individuals were surveyed

42 people are planning on going to the mountains

Step-by-step explanation:

The question is missing the information regarding the percentage of people who said that they were going to each of the possible destinations. After a quick google search I've found that, in the original question, 32% of individuals were going to the beach, 15% to the desert, 23% to major cities, and 30% to the mountains.

If 21 people said they were going to the desert, and that corresponds to 15% of the total number of people surveyed, the number of people surveyed is:

$21=n*0.15\\n=140\ individuals$

140 individuals were surveyed

Since 30% responded "the mountains", the number of people planning on going to the mountains is:

$m = 140*0.30\\m=42\ people$

42 people are planning on going to the mountains

3 0

3 years ago

You need to rent a video camera for your school project. Murphy's Camera charges a $30 rental fee plus $35 per day. Allied Renta

andreev551 [17]

A. If a camera is rented for 1 or 2 days, it would be logical to rent it from Murphy's.

B. If a camera is needed for more than 3 days, it would make sense to rent it from Allied rental.

C. Yes, if a camera is rented for 3 days both rentals charge the same money.

C. If you were need a camera for 3 days, you would have to pay $135 for both stores.

<u>Step-by-step explanation:</u>

Step 1; Murphy's camera costs $30 to rent and an additional $35 for each day of rental. So the equations are

y = $30 + (x × $35), where y is total cost and x is the number of days rented.

So for x = 1, y = $30 + (1 × $35) = $30 + $35 = $65

So for x = 2, y = $30 + (2 × $35) = $30 + $70 = $100

So for x = 3, y = $30 + (3 × $35) = $30 + $105 = $135

So for x = 4, y = $30 + (4 × $35) = $30 + $140 = $170

So for x = 5, y = $30 + (5 × $35) = $30 + $175 = $ 205.

Step 2; Allied rental costs $45 to rent and a $30 for each day of rental. So the equations are as follows

y = $45 + (x × $30), where y is total cost and x is the days rented

So for x = 1, $45 + (1 × $30) = $45 + $30 = $75

So for x = 2, $45 + (2 × $30) = $45 + $60 = $105

So for x = 3, $45 + (3 × $30) = $45 + $90 = $135

So for x = 4, $45 + (4 × $30) = $45 + $120 = $165

So for x = 5, $45 + (5 × $30) = $45 + $150 = $195

Step 3; Comparing both prices over 5 days. Murphy's is cheaper for until 2 days. On day 3 both the rentals cost the same but after day 4, allied rentals is the better option.

3 0

3 years ago