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Anuta_ua [19.1K]
3 years ago
15

The length of EF in the right triangle

Mathematics
2 answers:
LiRa [457]3 years ago
3 0

In order to find the sides of a right triangle, you can use the pythagorean theorem. (a^2 + b^2 = c^2)

The pythagorean theorem basically means that the square of two sides is equal to the square of the hypotenuse (the longest side of a triangle)

In this case, we already have 'a' and 'c', but not 'b'.

12^2 + b^2 = 19^2

Mutliply everything:

144 + b^2 = 361

Isolate b into one side by subtracting both sides by 144:

b^2 = 217

Square root both sides in order to completely isolate b:

b = \sqrt{217}

The answer is Option F

Good luck!

Mashutka [201]3 years ago
3 0

Answer:

F.

\sqrt{217}

Step-by-step explanation:

Use the Pythagorean Theorem, which is a^2 + b^2 = c^2.

c represents the hypotenuse, or the longest side of the right triangle. c in this case would be 19.

Side a can be represented as 12 since it is the other side that has a given value.

Substitute in the values to get the equation: (12)^2 + b^2 = (19)^2

12 squared is 144 and 19 squared is 361. To figure out what b^2 is subtract 361 - 144 to isolate the variable. We will be left with b^2 = 217.

In order to find what b is, find the square root of 217, which is Choice F.

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1. f(x)=x²+10x+16

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(As, a>0 the parabola is open upward), b=10. by putting the values.

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Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

Now find x-intercept put y=0 in the above equation. 0= x²+10x+16

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2. f(x)=−(x−3)(x+1)

By multiplying the factors, the general form is f(x)= -x²+2x+3.

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

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So, Vertex = (1, 4)

Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

Now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.

3. f(x)= −x²+4

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

So, Vertex = (0, 4)

Now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

Now find x-intercept put y=0 in the above equation. 0= −x²+4

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Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(As, a>0 the parabola is open upward), b=16. by putting the values.

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if a>0 parabola is opened upward.

if a<0 parabola is opened downward.

Compare the given equation with general form of parabola.

-h=2 ⇒h=-2

k=4

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As, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.

The graph is attached below.

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