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3 years ago

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

1 answer:

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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Answer:

2 quarters and 15 dimes

Step-by-step explanation:

15 dimes = $1.50

2 quarters = $0.50

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3 years ago

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Y=mx+b where m=-6, x=-2, and y=-3. Substituting these values in would result in -3=(-6)(-2)+b, which would simplify to -3=12+b, and further to b=-15. This would mean the y intercept is equal to -15, or (0,-15). To check, (-6)*(-2)-15 is in fact equal to -3, thus allowing easy identification of a graph, which will cross the y axis at -15 and decrease in y-value by 6 with every increase in x-value.

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3 years ago

The diameter of a circle is 23 inches and the circle has two chords of length 14 inches what is the distance from each chord to

Svetradugi [14.3K]

Answer:

9.12 + 9.12 = 18.24 inches

Step-by-step explanation:

Diameter = 23 inches (given)

Radius = 11.5 inches

2 Chords of length = 14 inches ( You didn't specify if the 14 inches is for both chords or for a single cord. I'll assume it's for two cords 14 and 14inches apart.

To clearly solve this, we'll make some mild assumptions.

Let the perpendicular distance of the chords from the center of the circle to represented as " x and y"

Therefore:

x^2 + 7^2 = 11.5 ^ 2

x^2 + 49 = 132.25

x^2 = 132.25 - 49

x^2 = 83.25

x = √ 83.25

x = 9.12 inches

Since the cords have thesame length (Assumed from the way the question was structured, the distance would still be thesame)

y^2 + 7^2 = 11.5 ^ 2

y^2 + 49 = 132.25

y^2 = 132.25 - 49

y^2 = 83.25

y = √ 83.25

y = 9.12 inches

Therefore, the distance will be :

9.12 + 9.12 = 18.24 inches

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4 years ago

Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 16.

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The transformations are

(b) A vertical shift 16 units downward.
(d) A horizontal shift 16 units to the right

<h3>How to determine the transformation?</h3>

The functions are given as:

f(x) = x

g(x)= x - 16

When a function is shifted right, the transformation rule is:

(x, y) = (x - h, y)

This means that the transformation is (d) A horizontal shift 16 units to the right

Since the parent function is a base linear function.

The transformation can also be represented as:

(x, y) = (x, k - h)

This gives

g(x)= x - 16

This means that the transformation is (b) A vertical shift 16 units downward.

Hence, the transformations are (b) and (d)