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gregori [183]
4 years ago
8

What is the minimum value of the expression $x^2+y^2-6x+4y+18$ for real $x$ and $y$?

Mathematics
1 answer:
Aleonysh [2.5K]4 years ago
3 0
X^2+y^2-6x+4y+18=0
x^2-6x+y^2+4y+18=0
x^2-6x+9+y^2+4y+4 =-18+9+4
(x-3)^2+(y+2)^2=-5
-5 is the minimum value of the given circle
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What is the measure of
Gnom [1K]

<u>Given</u>:

The measure of \widehat{ADB} is 162°

We need to determine the measure of ∠EAB

<u>Measure of ∠EAB:</u>

Let us determine the measure of ∠EAB

We know that, "If a tangent and chord intersect at a point on a circle, then the measure of each angle formed is half the measure of its intercepted arc".

Applying the above theorem, we get;

\angle EAB=\frac{1}{2} m(\widehat{ADB})

Substituting \widehat{ADB}=162^{\circ}, we get;

\angle EAB=\frac{1}{2}\times 162^{\circ}

Dividing, we get;

\angle EAB=81^{\circ}

Thus, the measure of ∠EAB is 81°

6 0
3 years ago
Find x 10|5x-25|-50=500
diamong [38]

Answer:

x=16

Step-by-step explanation:

10|5x-25|-50=500

+50                     +50

10|5x-25|=550

÷10            ÷10

|5x-25|=55

5x-25=55

+25        +25

5x=80

÷5   ÷5

x=16

8 0
4 years ago
Suppose we are given the following.
Mashutka [201]

Answer:

Slope of line 1 = 3

Slope of line 2 = -3

Slope of line 3 = -1/3

Line 1 and 2 = perpendicular

Line 1 and 3 = perpendicular

Line 2 and 3 = perpendicular

Step-by-step explanation:

trust me its correct

pls mark me as brainliest

6 0
3 years ago
A class consists of 55% boys and 45% girls. It is observed that 25% of the class are boys and scored an A on the test, and 35% o
Julli [10]

Step-by-step explanation:

Probability of event A on the condition of event B is:

P(A|B) = P(A and B) / P(B)

P(scored an A | girl) = P(scored an A and girl) / P(girl)

P(scored an A | girl) = 0.35 / 0.45

P(scored an A | girl) = 0.778

The probability that a randomly selected girl also scored an A is 77.8%.

7 0
3 years ago
Completely factor the given polynomial, if possible. If the polynomial cannot be factored, write NF for your answer.X^3+14x^2+45
vova2212 [387]

Given

x^3+14x^2+45x

Answer

\begin{gathered} x^3+14x^2+45x \\ =x(x^2+14x+45) \\ =x(x^2+5x+9x+45) \\ =x(x+5)(x+9) \end{gathered}

8 0
1 year ago
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