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Vesna [10]
2 years ago
7

Which function has the greater maximum value: f(x) = -2x2 + 4x+3, or g(x),

Mathematics
1 answer:
Zepler [3.9K]2 years ago
5 0

Answer:

B

Step-by-step explanation:

f(x) maxmum value is

\frac{ - 4}{ - 4}  = 1

- 2( {1}^{2} ) + 4(1) + 3 =  5

G(x) minimum value is 6.

B is the answer.

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A circle passes through points A(7,4), B(10,6), C(12,3). Show that AC must be the diameter of the circle.
Artist 52 [7]

so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}

6 0
3 years ago
Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
MrMuchimi

Answer:

The function h(x) is decreasing on the interval (3, ∞).

Step-by-step explanation:

Please take a look at the attached image.

You will see a graph of the given function h(x) = -2\sqrt{x-3}. The function is decreasing.

The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).

3 0
2 years ago
What's 6+89 .help me pls I'm going to kermit sewer side
NARA [144]

Answer:

95

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Pre-calc<br> Evaluate f(2) using substitution:<br> f(x) = 2x^3 – 3x^2– 18x-8
krek1111 [17]

Answer:

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Step-by-step explanation:

Just substitute x=2 into the function:

f(x) = 2x³ - 3x² - 18x - 8

f(2) = 2(2)³ - 3(2)² - 18(2) - 8

f(2) = 2(8) - 3(4) - 36 - 8

f(2) = 16 - 12 - 44

f(2) = 4 - 44

f(2) = -40

8 0
2 years ago
Solve the equation. 4x2 – 8 = 56<br><br><br> 2, –2<br> 16, –16<br> 8, –8<br> 4, –4
Marta_Voda [28]

Answer:

8,-8

Step-by-step explanation:

6 0
2 years ago
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