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3 years ago

What is the range of the function f(x) = 3x2 + 6x – 8?

Mathematics

2 answers:

ikadub [295]3 years ago

8 0

The range of the function f(x) = 3x^2 + 6x - 8 is {y|y ≥ –11}

guajiro [1.7K]3 years ago

7 0

Answer:

The range of the function f(x)=3x²+6x-8 is:

{y|y ≥ –11}

Step-by-step explanation:

The function f(x)=3x²+6x-8 could also be written as:

f(x)=3x²+6x+3-11

f(x)=3(x²+2x+1)-11

f(x)=3(x+1)²-11

as we know that the value of 3(x+1)²≥0

Then, the value of 3(x+1)²-11≥-11

i.e. f(x)≥-11

Hence, the range of the function f(x)=3x²+6x-8 is:

{y|y ≥ –11}

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What's the answer to this 94<-2(1+6b)

tigry1 [53]

Answer:

-8 > b

Step-by-step explanation:

94<-2(1+6b)

Distribute

94<-2-12b

Add 2 to each side

94+2<-2-12b +2

96 < -12b

Divide each side by -12, remembering to flip the inequality since we divide by a negative

96/-12 > -12b/-12

-8 > b

5 0

3 years ago

Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC . What is the leng

Thepotemich [5.8K]

Answer:

Length of side of rhombus is $x=\frac{ab}{a+b}$

Step-by-step explanation:

Given Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC. We have to find the length of side of rhombus.

It is also given that AB=a and AC=b

Let side of rhombus is x.

In ΔCEF and ΔCBA

∠CEF=∠CBA (∵Corresponding angles)

∠CFE=∠CAB (∵Corresponding angles)

By AA similarity rule, ΔCEF~ΔCBA

∴ their sides are in proportion

$\frac{EF}{AB}=\frac{CF}{AC}$

⇒ $\frac{x}{a}=\frac{b-x}{b}$

⇒ $xb=ab-ax$

⇒ $x(a+b)=ab$

⇒ $x=\frac{ab}{a+b}$

Hence, length of side of rhombus is $x=\frac{ab}{a+b}$

6 0

3 years ago

12/39 in simplest form is 4/13 what are two ways to get there

arlik [135]

Divide 3 on the numerator and denominator.

Hoped this helped.

~Bob Ross®

7 0

3 years ago

Read 2 more answers

Evaluate the integral. (Assume a ≠ b. Remember to use absolute values where appropriate. Use C for the constant of integration.)

Bess [88]

Answer:

F(x)= 5*[ $\frac{x^{3} }{3}$ + (a*b)* $\frac{x^{2} }{2}$ + a*b*x + C.

Step-by-step explanation:

First step we aplicate distributive property to the function.

5*(x+a)*(x+b)= 5*[ $x^{2}$ +x*b+a*x+a*b]

5*[ $x^{2}$ +x*(b+a)+a*b]= f(x), where a, b are constant and a≠b

integrating we find ⇒∫f(x)*dx= F(x) + C, where C= integration´s constant

∫^5*[ $x^{2}$ +x*(a+b)+a*b]*dx, apply integral´s property

5*[∫ $x^{2}$ dx+∫(a*b)*x*dx + ∫a*b*dx], resolving the integrals

5*[ $\frac{x^{3} }{3}$ + (a*b)* $\frac{x^{2} }{2}$ + a*b*x

Finally we can write the function F(x)

F(x)= 5*[ $\frac{x^{3} }{3}$ + (a*b)* $\frac{x^{2} }{2}$ + a*b*x ]+ C.

4 0

3 years ago

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taurus [48]

Answer:

Step-by-step explanation:

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5 0

3 years ago