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2 years ago

F(x)=4x^2+2x-6.find the range of function f(x).

Mathematics

1 answer:

Triss [41]2 years ago

4 0

Answer:

y ≥ 6.25

Step-by-step explanation:

f(x)=4x²+2x-6

positive (4) leading coefficient, curve is left up and right up

x coordinate of vertex: x = - b/2a = - 2/2*4 = - 1/4 (-0.25)

y = 4*(-1/4)² + 2*(-1/4) - 6 = -6 1/4 (-6.25) ... extreme

range: y ≥ - 6.25 [-6.25,∞)

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Right triangles abc and dbc with right angle c are given below. If cos(a)=15,ab=12 and cd=2, find the length of bd.

dmitriy555 [2]

see the attached figure to better understand the problem

we have that

$cos(A)=\frac{1}{5} \\ AB=12\ units\\ CD=2\ units$

Step 1

Find the value of AC

we know that

in the right triangle ABC

$cos (A)=(AC/AB)\\AC=AB*cos(A)$

substitute the values in the formula

$AC=12*(1/5)\\ AC=2.4\ units$

Step 2

Find the value of BC

we know that

in the right triangle ABC

Applying the Pythagorean Theorem

$AB^{2} =AC^{2}+BC^{2}\\ BC^{2}=AB^{2} -AC^{2}$

substitute the values

$BC^{2}=12^{2} -2.4^{2}\\BC^{2}= 138.24\\ BC=11.76\ units$

Step 3

Find the value of BD

we know that

in the right triangle BCD

Applying the Pythagorean Theorem

$BD^{2} =DC^{2}+BC^{2}$

substitute the values

$BD^{2} =2^{2}+11.76^{2}$

$BD=11.93\ units$

therefore

the answer is

the length of BD is 11.93 units

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2 years ago

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Please help it’s irritating when I keep having to post this and no ones bothering to even help me. Like I need to turn this is A

sukhopar [10]

Measure of E is congruent to K, so E is 50 degrees.

Measure of G is congruent to L, so G is 105 degrees.

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The proof I am using is the Corresponding Angles Postulate.

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