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Alecsey [184]
3 years ago
10

Mary walks 4 miles north and then turns and walks 5 miles west. How far is she from her original starting point?

Mathematics
1 answer:
dusya [7]3 years ago
5 0
Answer:  6.403 miles; or, write as:  6.403 mi.  .
__________________________________________________
Explanation:
_________________________________________________





                                5
--------------------------------------------
`                             right angle   |_ |
   `          (right triangle )                 |
         `                                               |    4 
             `                                           |
                      `    
       "c"                        `                  \        
 (hypotenuse)                          Starting point
                     
__________________________________________________
Since we have a "right triangle, we solve for "c"; using the 
"Pythagorean theorem" ; 
_______________________________________________________
→  a² + b² = c² ; Solve for "c" ; our answer (in "miles"; or, "mi.") ;
__________________________________________________
Given : a = 4; b = 5 ; 
____________________________
Plug these known values into our equation:
________________________________________
 → 4² + 5² = c² ; 
____________________________
 → 16 + 25 = c² ;  ↔  c² = 16 + 25 ;
______________________________
 → c² = 41 ; 
_______________________________
 → Take the positive square root of each side of the equation (since the side of a "triangle" cannot be "negative"; 
__________________________________
 → √(c²) = √(41) ; 
_____________________________
 → c =  √41 ; Use calculator;
________________________________
 → c =  6.40312423743 ; Round to:  

 → c = 6.403 miles; or, 6.403 mi. 
__________________________________________

 

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3 years ago
Victoria had $200 in her account at the end of one year. At the first of each subsequent year she deposits $15 into the account
telo118 [61]

Answer:

A(t) = 200+15t(1+0.02)^{t}

Step-by-step explanation:

Since the interest is calculated on the new balance every year.

Hence the formula used for compound interest is:

A = P(1+\frac{r}{n}^{nt}

where, A =Amount after t years

P =Principal amount

200 is the initial balance and Since, here the $15 is added to the balance each year. Therefore, P = 200+15t

r = rate each year (0.02)

t = time (in years) (t)

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Therefore, the recursive formula is:

A(t) = 200+15t(1+0.02)^{t}

6 0
3 years ago
Read 2 more answers
Which points are the verticles of the ellipse? Equations of ellipse
Mashutka [201]

Answer:

This question is solved in detail below. Please refer to the attachment for better understanding of an Ellipse.

Step-by-step explanation:

In this question, there is a spelling mistake. This is vertices not verticles.

So, I have attached a diagram of an ellipse in which it is clearly mentioned where are the vertices of an ellipse.

Vertices of an Ellipse: There are two axes in any ellipse, one is called major axis and other is called minor axis. Where, minor is the shorter axis and major axis is the longer one. The places or points where major axis and minor axis ends are called the vertices of an ellipse. Please refer to the attachment for further clarification.

Equations of an ellipse in its standard form:

\frac{x^{2} }{a^{2} }  + \frac{y^{2} }{b^{2} } = 1

This is the case when major axis the longer one is on the x-axis centered at an origin.

\frac{x^{2} }{b^{2} } + \frac{y^{2} }{a^{2} }  = 1

This is the case when major axis the longer one is on the y-axis centered at an origin.

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3 0
3 years ago
Find 4ab when (a+b)=15 and (a-b)=12
Volgvan
A + b = 15 ..... eq 1
a – b = 12 ...... eq 2

So a = 15 – b
Substitute in eq 2 :

15 – b – b = 12
15 – 2b = 12
–2b = 12 – 15
b = 1.5

So a = 15 – 3/2 = 13.5

4ab = 4 x 13.5 x 1.5 = 81
4 0
3 years ago
Read 2 more answers
What are the solution to the equation -3
umka21 [38]

Answer:

38.5

Step-by-step explanation:

Lets say, first number = x


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Total = 49



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4x = 42


x = 42/4


x= 10.5



x= 10.5


3x+7 = 3(10.5)+7 = 38.5



Hope this helps!!

3 0
3 years ago
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