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4 years ago

Graph a right triangle with the two points 4,5 and -4,8

Mathematics

1 answer:

Katyanochek1 [597]4 years ago

6 0

Answer:

Step-by-step explanation:

Please write points using parentheses: (4, 5) and (-4, 8}.

(4, 5) is in the 1st quadrant and (-4, 8} is in the 2nd. Reversing the order of these two points yields (-4, 8) and (4, 5). From this we can see that while moving from (-4, 8) to (4, 5) involves following a line with negative slope (because the y-coordinate decreases from 8 to 5 as the x-coordinate increases from -4 to +4). This sloping line is the hypotenuse of a right triangle. Draw a vertical line segment through (-4, 8) and a horizontal line segment through (4, 5). This hypotenuse, the vertical line segment and the horizontal line segment are the boundaries of the desired right triangle.

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If h(x)=(f o g) (x) and h(x)= ∛x+3, find g( x) if f(x)= ∛x+2 (picture attached)

Aleksandr-060686 [28]

Answer:

g(x) = x+1

Step-by-step explanation:

Informally, you can see that the function h(x) takes the root of a value that is 1 more than the value under the same radical in f(x). This suggests that adding 1 to x in f(x) will give you h(x). That is, ...

h(x) = f(x+1) = f(g(x))

g(x) = x+1

_____

More formally, you can apply the inverse of the function f(x) to the equation ...

h(x) = f(g(x))

f^-1(h(x)) = f^-1(f(g(x))) . . . inverse function applied

f^-1(h(x)) = g(x) . . . . . . . . . simplified

Now f^-1(x) can be found by solving for y in ...

x = f(y)

x = ∛(y+2) . . . . . . . . . definition of f(y)

x^3 = y+2 . . . . . . . . . cube both sides

x^3 -2 = y = f^-1(x) . . . subtract 2 from both sides

So, f^-1(h(x)) is ...

f^-1(h(x)) = g(x) = (∛(x+3))^3 -2 = x+3 -2

g(x) = x+1

5 0

3 years ago

X is less than or equal to -5

erma4kov [3.2K]

Answer:

x<=-5

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Work out 1 3/4 x 4 1/6

sattari [20]

Convert mixed number to improper fraction:

$1\dfrac{3}{4}=\dfrac{1\cdot4+3}{4}=\dfrac{4+3}{4}=\dfrac{7}{4}\\\\4\dfrac{1}{6}=\dfrac{4\cdot6+1}{6}=\dfrac{24+1}{6}=\dfrac{25}{6}\\\\1\dfrac{3}{4}\times4\dfrac{1}{6}=\dfrac{7}{4}\times\dfrac{25}{6}=\dfrac{7\times25}{4\times6}=\dfrac{175}{24}=\dfrac{168+7}{24}=7\dfrac{7}{24}$

8 0

4 years ago

What is the answer for number 11

IRINA_888 [86]

No, because you have two y-points that are the same.

6 0

3 years ago

At the start of 2014, tim house was worth £100,000 the value of the house increases by 10%per every year work out the value of h

kotykmax [81]

Answer:

$146410

Step-by-step explanation:

The formula for calculating future value:

FV = P (1 + r)^n

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4 0

3 years ago

Graph a right triangle with the two points 4,5 and -4,8​

Graph a right triangle with the two points 4,5 and -4,8