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OleMash [197]
3 years ago
8

What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)

Mathematics
1 answer:
lutik1710 [3]3 years ago
7 0

so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).

\bf \stackrel{f(x)}{0}=-(x-3)(x+11)\implies 0=(x-3)(x+11)\implies x= \begin{cases} 3\\ -11 \end{cases} \\\\\\ \boxed{-11}\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}-4\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}\boxed{3}

so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?

\bf f(-4)=-(-4-3)(-4+11)\implies f(-4)=7(7)\implies f(-4)=49 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{(-4~~,~~49)}~\hfill

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Will a truck that is 10 feet wide carrying a load that reaches 12 feet above the ground clear the semielliptical arch on the one
beks73 [17]

Figure is missing, so i have attached it.

Answer:

it will clear the arch because the height of the archway of the bridge 5 feet from the center is approximately 12.76 ft

Step-by-step explanation:

The standard form of equation of an ellipse is;

x²/a² + y²/b² = 1

From the figure in the image attached, we can see that the radius is; a = 52/2 = 26 ft

While the value of b = 13 ft

Thus;

x²/26² + y²/13² = 1

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Thus, we will plug in 5 for x to get;

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The function f(x) is given by the set of ordered pairs.
Lana71 [14]

The equation that is true and one that matches the set of ordered pairs of functions is option C. f (0) = 6

<h3>What is the equation about?</h3>

Note that a function can be made to be a given set of ordered pairs such as the ordered pairs (2,4), (3,5), (4,6)  can have  input functions of ​​(as domain) 2,3,4 and output functions of ​​(as range) of 4,5,6.

So when you see the ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)} one can see that the option that matches to the set of ordered pairs of functions above is f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)

See full question below

The function f (x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)}:Which equation is true?

f(-10)=1

f(2)=-10

f(0)=6

f(1)=-10

The answer choices are :

f (-10) = 1 values ​​x = -10, f (x) = y = 1, ordered pairs (-10,1)

f (2) = - 10 values ​​x = 2, f (x) = y = -10, ordered pairs (2, -10)

f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)

f (1) = - 10 values ​​x = 1, f (x) = y = -10, ordered pairs (1, -10)

Learn more about ordered pairs from

brainly.com/question/6200217

3SPJ1

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