1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sveticcg [70]
3 years ago
13

If the interval (a, ∞) describes all values of x for which the graph of 4/x^2-6x+9 is decreasing, what is the value of a?

Mathematics
2 answers:
qaws [65]3 years ago
8 0

Answer:

Just did this. The answer is 3

Step-by-step explanation:

harkovskaia [24]3 years ago
5 0

Answer:

a = - 1.1

Step-by-step explanation:

Condition for a single variable function f(x) to be decreasing is f'(x) < 0.

So, in our case, f(x) = \frac{4}{x^{2}} - 6x + 9.

Then, differentiating with respect to x on both sides we get,

f'(x) = 4(- 2)\frac{1}{x^{3}} - 6 < 0

⇒ - \frac{8}{x^{3}} - 6 < 0

⇒ \frac{8}{x^{3}} + 6 > 0

{Dividing both sides with - 1 and hence the inequality sign changes}

⇒ \frac{8}{x^{3}} > - 6

⇒ 8 > - 6x³ {Multiplying both sides with x³}

⇒ 6x³ > - 8 {Interchanging the sides}

⇒ x^{3} > - \frac{8}{6}

⇒ x > - 1.1

Therefore, a = - 1.1. (Answer)

You might be interested in
Suppose that E and F are two events and that P(E)=0.3 and P(F|E)=0.5. What is P(E and F)?
Sergio [31]

E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15


Bayes' theorem is transforming preceding probabilities into succeeding probabilities. It is based on the principle of conditional probability. Conditional probability is the possibility that an event will occur because it is dependent on another event.

P(F|E)=P(E and F)÷P(E)

It is given that P(E)=0.3,P(F|E)=0.5

Using Bayes' formula,

P(F|E)=P(E and F)÷P(E)

Rearranging the formula,

⇒P(E and F)=P(F|E)×P(E)

Substituting the given values in the formula, we get

⇒P(E and F)=0.5×0.3

⇒P(E and F)=0.15

∴The correct answer is 0.15.

If, E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15.

Learn more about Bayes' theorem on

brainly.com/question/17010130

#SPJ1

4 0
2 years ago
4. To draw graph of 4x+ 5y = 19, Find y<br>when a=1<br>(A) 4<br>(B 3<br>62<br>D2-3​
babymother [125]
There’s no a in the the equation
6 0
3 years ago
Find k so that the distance from (–1, 1) to (2, k) is 5 units. k= k= *there are two solutions for 2*
dalvyx [7]

Answer:

k = -3

k =5

Step-by-step explanation:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d = 5\\(-1,1) =(x_1,y_1)\\(2,k)=(x_2,y_2)\\

5=\sqrt{\left(2-\left(-1\right)\right)^2+\left(k-1\right)^2}\\\\\mathrm{Square\:both\:sides}:\quad 25=k^2-2k+10\\25=k^2-2k+10\\\\\mathrm{Solve\:}\:25=k^2-2k+10:\\k^2-2k+10=25\\\\\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}\\k^2-2k+10-25=25-25\\k^2-2k-15=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}k^2-2k-15:\quad \left(k+3\right)\left(k-5\right)\\\mathrm{Solve\:}\:k+3=0:\quad k=-3\\

\mathrm{Solve\:}\:k-5=0:\quad k=5\\\\k =5 , k=-3

7 0
3 years ago
Read 2 more answers
Which expression simplifies to 4 √13<br><br><br> √208<br><br> √17<br><br> √29<br><br> √52
arsen [322]

Answer:

√208

Step-by-step explanation:

Step 1: Convert 4 to √

4² = 16

4 = √16

Step 2: Multiply radicals

√16(√13) = √208

7 0
2 years ago
Read 2 more answers
Y = 3/2x + 5/4 −2x + 8y = −25
Andreyy89

Answer:

<h2>x = -347 1/2</h2>

Step-by-step explanation:

When solving algebra, it is important the we follow the steps in correct order and check our answer at the end.

Step 1: Simplify by combining like terms

y = -x/2 + 5/4 + 8y = -25

Step 2: Substitute

y = -25

-25 = -x/2 + 5/4 + 8(-25)

-25 = -x/2 + 5/4 + -200

-25 = -x/2 - 198 3/4

Step 3: Answer

x = -347 1/2

Step 4: Check

y = 3/2x + 5/4 −2x + 8y = −25

-25 = 3/2(-347 1/2) + 5/4 −2(-347 1/2) + 8(-25)

-25 = -25✔️

Step 5: Verified Answer

x = -347 1/2

I'm always happy to help :)

3 0
3 years ago
Other questions:
  • 1. x=1/(root3-root2). find rootx-(1/rootx) 2. if x=[root(a+2b)+root(a-2b)]/[root(a+2b)-root(a-2b]. show that bx^2-ax+b=0
    14·2 answers
  • drako found an emarald in a cave at a depth between negative 1\2 and negative 1 2\3 meters. Which number could represent the dep
    6·1 answer
  • -6*4/2*3-15 help please
    6·2 answers
  • Which two values of x are roots of the polynomial below? x^2-3x+5
    10·1 answer
  • Communicative property
    10·1 answer
  • Find all of the zeros of f(x) = 5x2 + 40x - 100.
    14·2 answers
  • An ice sculpture measures 65 inches and melts continuously by 3% per minute. Find the height of a sculpture after 15 minutes. Ro
    12·1 answer
  • Consider the statement: "The president of the United States is a United States citizen."
    15·2 answers
  • Robert bought 3 toys for $12.6 and Ahmed bought 5 toys for $20.5. Who got a better buy?
    7·2 answers
  • A piece of metal with a length of 2.83 cm was measured using four different devices. Which of the following measurements is the
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!