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4 years ago

Find the diagonal of the rectangular solid with the given measures part of the answer is provided for you

Mathematics

1 answer:

Svet_ta [14]4 years ago

3 0

Answer: $\sqrt{59}$

Step-by-step explanation:

The diagonal of a rectangular prism can be found with $\sqrt{l^2+w^2+h^2}$

$l^2+w^2+h^2=59$ . Thus, the diagonal is $\sqrt{59}$

Hope it helps <3

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The endpoints of segment RS are R(-4, 3) and S(8, -5). Complete each statement using a fraction.

Ray Of Light [21]

Answer:

a. (-1 , 1) is the point at 1 : 3 of the way from R to S

b. (5 , -3) is the point at 3 : 1 of the way from R to S

Step-by-step explanation:

* Lets explain how to solve the problem

- If point (x , y) divide a line segment whose end points are

$(x_{1},y_{1})$ and $(x_{2},y_{2})$ , at ratio

$m_{1}:m_{2}$ from the first point, then

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

* Lets solve the problem

∵ RS is a line segment whose end points are R (-4 , 3) and S (8 , -5)

∵ Point (-1 , 1) divides it at ratio $m_{1}:m_{2}$ from R

- By using the rule above

∴ $-1=\frac{-4m_{2}+8m_{1}}{m_{1}+m_{2}}$

- By using cross multiplication

∴ $(-1)m_{1}+(-1)m_{2}$ = $-4m_{2}+8m_{1}$

- By collecting $m_{1}$ in one side and $m_{2}$ in the

other side

∴ $3m_{2}=9m_{1}$

- Divide both sides by 3

∴ $m_{2}=3m_{1}$

∴ $m_{1}=\frac{1}{3}m_{2}$

∴ (-1 , 1) is the point at 1 : 3 of the way from R to S

∵ RS is a line segment whose end points are R (-4 , 3) and S (8 , -5)

∵ Point (5 , -3) divides it at ratio $m_{1}:m_{2}$ from R

- By using the rule above

∴ $5=\frac{-4m_{2}+8m_{1}}{m_{1}+m_{2}}$

- By using cross multiplication

∴ $5m_{1}+5m_{2}$ = $-4m_{2}+8m_{1}$

- By collecting $m_{1}$ in one side and $m_{2}$ in the

other side

∴ $9m_{2}=3m_{1}$

- Divide both sides by 3

∴ $3m_{2}=m_{1}$

∴ $\frac{m_{1}}{m_{2}}=3$

∴ (5 , -3) is the point at 3 : 1 of the way from R to S

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4 years ago

What is the LCDof two numbers if one number is a multiple of the other give an example

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3 years ago

Number 10 and number 11 please!.

r-ruslan [8.4K]

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3 years ago

If r = 9, b = 5, and g= −6, what does (r + b − g)(b + g) equal?

r-ruslan [8.4K]

Answer:

-20

Step-by-step explanation:

(r + b − g)(b + g)

we have fom statement:

r = 9

b = 5

g= −6

so we have:

(r + b − g)(b + g)= (9+5-(-6))*(5+(-6))

(r + b − g)(b + g)= (14+6)*(-1)

(r + b − g)(b + g)= -20

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3 years ago

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