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Basile [38]
3 years ago
15

If a point ,located at (3,-2),is rotated clockwise 90 about the origin,what are the coordinates of its image ’?

Mathematics
1 answer:
azamat3 years ago
3 0

Answer:

(-2, -3)

Step-by-step explanation:

90° clockwise rotation:

(x, y) -----> (y, -x)

Let's apply this to our coordinates:

(x, y) -----> (y, -x)

(3, -2) -----> (-2, -3)

Simply make the old y-coordinate the new x-coordinate, and make the old x-coordinate negative and make the new y-coordinate.

Therefore, the coordinate of the new point is (-2, -3).

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Antoine stands on a balcony and throws a ball to his dog, who is at ground level.
sdas [7]

Answer: The ball will hit the ground 4 seconds after being thrown.

Step-by-step explanation:

By definition, the ball hits the grounds when the height is zero.

Then, knowing that the Quadratic function that models that situation is:

h(x)=-2x^2+4x+16

You can make it equal to zero:

0=-2x^2+4x+16

Now you can use the Quadratic formula:

x=\frac{-b\±\sqrt{b^2-4ac} }{2a}

In this case you can identify that:

a=-2\\b=4\\c=16

Therefore, knowing these values, you can substitute them into the Quadratic formula and then evaluate, in order to find the solution:

x=\frac{-4\±\sqrt{4^2-4(-2)(16)} }{2(-2)}\\\\x_1=4\\x_2=-2

Choose the positive solution.

Then, the ball will hit the ground 4 seconds after being thrown.

5 0
4 years ago
Find the measure of the missing angle.<br> 30°<br> a=
Serggg [28]

Answer:

the measurement of a is 60°............

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2 years ago
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Suppose Antonio buys a CD for $500 that earns 3% APR and is compounded monthly. The CD matures in 1 year. How much will Antonio'
Luden [163]

Answer:

$515.21

Step-by-step explanation:

Because you're compounding monthly, use the formula:

A(t)=P(1+\frac{r}n)^{nt}}

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r = .03 (always in decimal form!)

n = 12 (monthly is every month, and there are 12 months in a year) and

t = time in years

Filling in our given info:

A(t)=500(1+\frac{.03}{12})^{(12)(1) which simplifies to

A(t) = 500(1 + .0025)¹² which simplifies to

A(t) = 500(1.0025)¹² which simplifies to

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