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Brilliant_brown [7]

3 years ago

11

Deborah hikes due south for 3 miles. She then turns due west and hikes 4 miles. What is the shortest distance between the starti

ng point and the ending point? 1 mile 2 miles 5 miles 6 miles

1 answer:

Cerrena [4.2K]3 years ago

8 0

Answer:

5 miles

Step-by-step explanation:

The two legs of Deborah's hike form the right-angle legs of a right triangle. The shortest distance is then the hypotenuse of that triangle, found using the Pythagorean theorem.

d^2 = 3^2 + 4^2 = 9 +16 = 25

d = √25 = 5

Deborah ends 5 miles from her start.

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ohaa [14]

Answer: The correct option is (B) $2y^2-y-6=0.$

Step-by-step explanation: We are given the following system of equations :

$x=y^2-1~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-y=4~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We are to find the equation that could be the result of using substitution to solve the above system.

Substituting the value of x from equation (i) in equation (ii), we get

$2x-y=4\\\\\Rightarrow 2(y^2-1)-y=4\\\\\Rightarrow 2y^2-2-y=4\\\\\Rightarrow 2y^2-y-2-4=0\\\\\Rightarrow 2y^2-y-6=0.$

Thus, the required equation is $2y^2-y-6=0.$

Option (B) is CORRECT.

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3 years ago

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Answer:

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Step-by-step explanation:

You can simplify it to (-4+24)^3a

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Ulleksa [173]

$80.00 is what her total is

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3 years ago

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7 0

3 years ago

Read 2 more answers

There are 8 rows and 8 columns, or 64 squares

lawyer [7]

Complete Question:

There are 8 rows and 8 columns, or 64 squares on a chessboard.

Suppose you place 1 penny on Row 1 Column A,

2 pennies on Row 1 Column B,

4 pennies on Row 1 Column C, and so on …

Determine the number of pennies in Row 1

Determine the number of pennies on the entire chessboard?

Answer:

255 in the first row

18,446,744,073,709,551,615 in the entire board

Step-by-step explanation:

Given

$Rows = 8$

$Columns = 8$

Solving (a): Number of pennies in first row

The question is an illustration of geometric sequence which follows

$1,2,4....$

Where

$a =1$ --- The first term

Calculate the common ratio, r

$r = \frac{T_2}{T_1} = \frac{4}{2} = 2$

The number of pennies in the first row will be calculated using sum of n terms of a GP.

$S_n = \frac{a(r^n - 1)}{n - 1}$

Since, the first row has 8 columns, then

$n = 8$

Substitute 8 for n, 2 for r and 1 for a in $S_n = \frac{a(r^n - 1)}{r - 1}$

$S_8 = \frac{1 * (2^8 - 1)}{2 - 1}$

$S_8 = \frac{1 * (256 - 1)}{1}$

$S_8 = \frac{1 * 255}{1}$

$S_8 = 255$

Solving (b): The entire board has 64 cells.

So:

$n = 64$

Substitute 64 for n, 2 for r and 1 for a in $S_n = \frac{a(r^n - 1)}{r - 1}$

$S_{64} = \frac{1 * (2^{64} - 1)}{2 -1}$

$S_{64} = \frac{(2^{64} - 1)}{1}$

$S_{64} = \frac{(18,446,744,073,709,551,616 - 1)}{1}$

$S_{64} = \frac{18,446,744,073,709,551,615}{1}$

$S_{64} = 18,446,744,073,709,551,615$

5 0

3 years ago