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3 years ago

The point (5, -2) is rotated 90° about the origin. Its image is

Mathematics

1 answer:

Nadya [2.5K]3 years ago

8 0

Answer:

(2,5)

Step-by-step explanation:

The rule to 90 degrees about the origin is (x,y) to (-y,x). You basically switch the values of y and x but remember the value of y is negative. The value of y is -2 so -2 is now 2 since the rule changed the sign (-2×-y=2) and 5 isnt affected except it is the x value. Just know that since they r switched, x is now 2 and y is 5 when rotated 90 degrees about the origin.

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Using this distribution, find the probability

kaheart [24]

Answer:

P = 0.3

Step-by-step explanation:

Here, we are to use the probability distribution in the table to calculate the probability that a children has 4 or more shoes in his or her closet

When we say 4 or more, what we mean by this is that the teenager has 4 shoes or 5 shoes

In probability expressions, when we use the term ‘or’ we are simply talking about adding the terms involved

So what we can do here is to add the probability that the teenager has 4 shoes to the probability that the teenager has five shoes

From the table that would be; 0.1 + 0.2 = 0.3

6 0

3 years ago

Manuela solved the equation 3−2|0.5x 1.5|=2 for one solution. her work is shown below. 3−2|0.5x 1.5|=2 −2|0.5x 1.5|=−1 |0.5x 1.5

irakobra [83]

The other solution to the absolute value equation 3 − 2|0.5x + 1.5| = 2 is x = -4

<h3>How to determine the solution?</h3>

The equation is given as:

3 − 2|0.5x + 1.5| = 2

Subtract 3 from both sides

-2|0.5x + 1.5| = -1

Divide both sides by -2

|0.5x + 1.5| = 0.5

Expand the equation

0.5x + 1.5 = 0.5 or 0.5x + 1.5 = -0.5

Subtract 1.5 from both sides

0.5x = -1 or 0.5x = -2

Divide both sides by 0.5

x = -2 or x = -4

Hence, the other solution to the absolute value equation 3 − 2|0.5x + 1.5| = 2 is x = -4

Read more about absolute value equation at:

brainly.com/question/26954538

#SPJ4

4 0

2 years ago

Ok I'm doing home work and need to show why 1/2 of 60 is not the same as 1/2 of 24 please help! It will give you 24 points.

Tems11 [23]

Simple,

1/2 of 60

re-write it as 0.5 of 60 aka 0.5*60

which is 0.5*60=30

Do the same with 1/2 of 24.

0.5 of 24

0.5*24=12.

Thus, it's not the same because they are different numbers and different number give you different answers.

7 0

3 years ago

A lake polluted by bacteria is treated with an antibacterial chemical. Aftertdays, thenumber N of bacteria per milliliter of wat

jeyben [28]

Answer:

N(1)=50 is a minimum

N(15)=4391.7 is a maximum

Step-by-step explanation:

<u>Extrema values of functions </u>

If the first and second derivative of a function f exists, then f'(a)=0 will produce values for a called critical points. If a is a critical point and f''(a) is negative, then x=a is a local maximum, if f''(a) is positive, then x=a is a local minimum.

We are given a function (corrected)

$N(t) = 20(t^2-lnt^2)+ 30$

$N(t) = 20(t^2-2lnt)+ 30$

(a)

First, we take its derivative

$N'(t) = 20(2t-\frac{2}{t})$

Solve N'(t)=0

$20(2t-\frac{2}{t})=0$

Simplifying

$2t^2-2=0$

Solving for t

$t=1\ ,t=-1$

Only t=1 belongs to the valid interval $1\leqslant t\leqslant 15$

Taking the second derivative

$N''(t) = 20(2+\frac{2}{t^2})$

Which is always positive, so t=1 is a minimum

(b)

$N(1)=20(1^2-2ln1)+ 30$

N(1)=50 is a minimum

(c) Since no local maximum can be found, we test for the endpoints. t=1 was already determined as a minimum, we take t=15

(d)

$N(15)=20(15^2-2ln15)+ 30$

N(15)=4391.7 is a maximum

7 0

3 years ago

Can someone please explain this for me, thank you.

r-ruslan [8.4K]

just divide Atlantic/Mississippi

$\frac{3.1 \times {10}^{17} }{6.3 \times {10}^{11} } = \frac{3.1}{6.3} \times \frac{ {10}^{17} }{ {10}^{11} } \\ = 0.492 \times {10}^{17 - 11} \\ = 0.492 \times {10}^{6} \\ = 4.92 \times {10}^{5}$

7 0

3 years ago