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
svlad2 [7]
3 years ago
13

Fill in the missing portions of the function to rewrite g(x) = 3a^2 − 42a + 135 to reveal the zeros of the function. What are th

e zeros of g(x)? (show your work!)
Enter your answers in the blanks:


g(x) = 3(_____)(_____)


Zeros: ______ and ______
Mathematics
1 answer:
Nikitich [7]3 years ago
7 0

Answer:

g(x) = 3(x-9)(x-5)

Zeros: x = 9 and x = 5.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

g(x) = 3x^{2} - 42a + 135

So

a = 3, b = -42, c = 135

\bigtriangleup = (-42)^{2} - 4*3*135 = 144

x_{1} = \frac{-(-42) + \sqrt{144}}{2*3} = 9

x_{2} = \frac{-(42) - \sqrt{144}}{2*3} = 5

So

g(x) = 3(x-9)(x-5)

Zeros: x = 9 and x = 5.

You might be interested in
Larry,Moe,and tome at a pizza together. If larry ate 3/8 of the pizza, and tom ate 1/6 of it, how much did moe eat?
mariarad [96]
3/8 + 1/6 is 13/24. 24/24 -13/24 is 11/24.Moe ate 11/24.
6 0
3 years ago
What is 3/5×6 please answer quickly
ludmilkaskok [199]
The answer is 18/5 and simplify that and u get 3 3/5.
7 0
2 years ago
Read 2 more answers
A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. The patient currently has a bone d
kompoz [17]

Answer:

The function f(x) is represented by:

f(x)=1500(0.97)^x

Hence, a=1500 and b=0.97

Step-by-step explanation:

The patient currently has a bone density of 1,500 kg/mg^3.

A doctor estimates that a particular patient is losing bone density at a rate of 3% annually.

This means that the bone density that is remaining is:

100-3=97%

which is also represented as: 97%=97/100=0.97

Hence, the function f(x) that represents the bone density after x years is represented by:

f(x)=a(0.97)^x

where a is the initial bone density which is given to be: 1500 kg/mg^3.

Hence, the function is:

f(x)=1500(0.97)^x

6 0
3 years ago
Read 2 more answers
A manufacturing process is designed to produce bolts with a 0.25-in. diameter. Once each day, a random sample of 36 bolts is sel
Troyanec [42]

Answer:

0.6170

Step-by-step explanation:

Given that a manufacturing process is designed to produce bolts with a 0.25-in. diameter.

i.e. no of bolts which are produced as per standard is X means then

X is normal with mean = 0.250 and std dev = 0.04

No of bolts tested = 36

If this mean falls outside the interval (0.230,0.270) the production would be shut down.

i.e. P(|x-25|>0.20) =production shut down probability

P(|x-25|>0.20)\\=P(|Z|>0.5)\\=2(0.5-0.1915)\\= 0.6170

3 0
3 years ago
Using the Kinetic Molecular Theory, explain Charles's Law of gases. Refer to specific points of the
liubo4ka [24]

Answer:

Kinetic theory explains why the volume of a container must expand when the temperature of the gas inside increases in order for the pressure to remain constant.

Step-by-step explanation:

Charles' law: for a fixed mass of gas at constant pressure the volume is directly proportional to the temperature.

Analysis of a gas when its temperature increases according to kinetic theory:

The temperature has increased therefore the molecules have more kinetic energy, so they move with a greater velocity.¹

If the container's dimensions do not change the molecules will travel across the container between the walls in less time (because they are moving faster and covering the same distance between the container walls). This will increase the rate of collisions, which would increase the pressure.²

But if the dimensions of the container increased then the molecules would cover a larger distance faster thereby maintaining a constant rate of collisions. This would maintain a constant pressure.

6 0
2 years ago
Read 2 more answers
Other questions:
  • Evaluate the expression: a(b – c) if a = -8, b = 12, and c = 4
    10·2 answers
  • Evaluate. ( 2/5 )2 · 52 + 10
    13·1 answer
  • Sandra wants to rent a car to take a trip and has a budget of $90. There is a fixed rental fee of $30 and a daily fee of $10. Wr
    15·1 answer
  • Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solu
    11·1 answer
  • The equation x power 3 - 6x=72 has a solution between 4 and 5.
    12·1 answer
  • Anyone please help!!!​
    13·1 answer
  • What is the probability that I flip a coin three times and they are all heads? (Round to the nearest percent)​
    15·1 answer
  • Which is a logarithmic statement for 10^3.5=3162.28?
    15·1 answer
  • Here is an expression: 4•3^x
    10·1 answer
  • Conrad is making veggie burgers for 18 children with special dietary needs at summer camp. The
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!