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2 years ago

Find the distance between the pair of points.. (-6, -5), (7, -8)

Mathematics

1 answer:

horrorfan [7]2 years ago

6 0

Answer:

$\sqrt{178}$ units

Step-by-step explanation:

Use the distance formula $d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$ where $d$ is the positive distance between $(x_1,y_1)$ and $(x_2,y_2)$ :

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

$d=\sqrt{(-8-(-5))^2+(7-(-6))^2}$

$d=\sqrt{(-8+5)^2+(7+6)^2}$

$d=\sqrt{(-3)^2+(13)^2}$

$d=\sqrt{9+169}$

$d=\sqrt{178}$

Therefore, the distance between $(-6,-5)$ and $(7,-8)$ is $\sqrt{178}$ units.

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A 250-kVA, three-phase, 480-volt transformer requires 75 gallons of insulating oil to keep it properly cooled. How many liters i

Dennis_Churaev [7]

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3 years ago

Can anyone do these problems it’s for my daughter in law

Naya [18.7K]

Classwork:

Given $f(x) = x^2 - 1$ and $g(x)=2x+5$ , we have

(1) $(f\circ g)(x) = f(g(x)) = f(2x+5) = (2x+5)^2 - 1 = \boxed{4x^2+20x+24}$

Using the composition found in (1), we have

(2) $(f\circ g)(-2) = 4\cdot(-2)^2+20\cdot(-2)+24 = \boxed{0}$

(3) $(g\circ f)(x) = g(f(x)) = g(x^2-1) = 2(x^2-1) + 5 = \boxed{2x^2 + 3}$

Using the composition found in (3),

(4) $(g\circ f)(1) = 2\cdot1^2+3 = \boxed{5}$

Homework:

Now if $f(x)=x^2-3x+2$ , we would have

(1) $(f\circ g)(x) = f(2x+5) = (2x+5)^2-3(2x+5)+2 = \boxed{4x^2+14x+12}$

For (2), we could explicitly find $(g\circ f)(x)$ then evaluate it at x = -1 like we did in the classwork section, but we don't need to.

(2) $(g\circ f)(-1) = g(f(-1)) = g((-1)^2-3\cdot(-1)+2) = g(6) = 2\cdot6+5 = \boxed{17}$

(3) We can demonstrate that both methods work here:

• by using the result from (1),

$(f\circ g)(2) = 4\cdot2^2+14\cdot2+12 = \boxed{56}$

• by evaluating the inner function at x = 2 first,

$(f\circ g)(2) = f(g(2)) = f(2\cdot2+5) = f(9) = 9^2-3\cdot9+2 = \boxed{56}$

4 0

2 years ago

Find the midpoint of AB given A (-1,4) and B (7,6)

lutik1710 [3]

Seriously: add the x's divide by 2, add the y's divide by 2, bob's your uncle. you have the midpoint.

8 0

3 years ago

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DiKsa [7]

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Answer:

f^-1(x) = 4+∛((x-6)/5)

Step-by-step explanation:

To find the inverse function, solve ...

x = f(y)

then write the answer in functional form.

$\displaystyle x=f(y)\\\\x=5(y-4)^3+6\\\\x-6=5(y-4)^3\\\\\frac{x-6}{5}=(y-4)^3\\\\\sqrt[3]{\frac{x-6}{5}}=y-4\\\\y=4+\sqrt[3]{\frac{x-6}{5}}\\\\\boxed{f^{-1}(x)=4+\sqrt[3]{\frac{x-6}{5}}}$

The graph shows the function and its inverse to be reflections of each other in the line y=x, as they should be.

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2 years ago

2 is the whole number 4 over 5 + 6 is the whole number 14 over 15 and is has to be a fraction

Nonamiya [84]

Answer:

the answer is 9 11/15 or 26/15 in improper fraction form.

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2 years ago