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
astra-53 [7]
3 years ago
7

For any perfect square trinomial (quadratic), the constant term (last term) must be positive.

Mathematics
1 answer:
Ronch [10]3 years ago
5 0

Answer:

For the perfect square trinomial (quadratic) i.e. \left(x\:+\:3\right)^2, the constant term (last term) is positive.

Step-by-step explanation:

"Perfect square trinomials" are termed as the quadratics that are the outcomes of squaring binomials.

For example:

\left(x\:+\:3\right)^2

\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2

a=x,\:\:b=3

=x^2+2x\cdot \:3+3^2

=x^2+6x+9

Therefore, for the perfect square trinomial (quadratic) i.e. \left(x\:+\:3\right)^2, the constant term (last term) is positive.

You might be interested in
Which shows all the names that apply to the figure?
saul85 [17]
The answer is A


A Parallelogram is a shape with 4 sides that has two pairs of parallel sides. The opposite sides must have equal length.  This is accurate for this shape.

A Rectangle is a shape with 4 sides that has four right angles.  This is accurate for this shape.

A rhombus is a shape with 4 sides of equal length.  This is not accurate for this shape.

A square is a shape with 4 sides of equal length and four right angles.  This is not accurate for this shape.
4 0
3 years ago
A man climbing a banana tree. Which sentence achieves the purpose of telling the man that what he is doing is dangerous? How do
hichkok12 [17]

Answer:

Be careful!

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
What is the value of x????
inysia [295]

If QR is a median, then:

\dfrac{NO+MP}{2}=QR

We have NO = 30, MP = 9x - 42 and QR = x + 15. Substitute:

\dfrac{30+9x-42}{2}=x+15\qquad\text{multiply both sides by 2}\\\\9x-12=2x+30\qquad\text{add 12 to both sides}\\\\9x=2x+42\qquad\text{subtract 2x from both sides}\\\\7x=42\qquad\text{divide both sides by 7}\\\\\boxed{x=6}

<h3>Answer: A. 6</h3>
3 0
3 years ago
A metal beam was brought from the outside cold into a machine shop where the temperature was held at 65degreesF. After 5 ​min, t
ivolga24 [154]

Answer:

The beam initial temperature is 5 °F.

Step-by-step explanation:

If T(t) is the temperature of the beam after t minutes, then we know, by Newton’s Law of Cooling, that

T(t)=T_a+(T_0-T_a)e^{-kt}

where T_a is the ambient temperature, T_0 is the initial temperature, t is the time and k is a constant yet to be determined.

The goal is to determine the initial temperature of the beam, which is to say T_0

We know that the ambient temperature is T_a=65, so

T(t)=65+(T_0-65)e^{-kt}

We also know that when t=5 \:min the temperature is T(5)=35 and when t=10 \:min the temperature is T(10)=50 which gives:

T(5)=65+(T_0-65)e^{k5}\\35=65+(T_0-65)e^{-k5}

T(10)=65+(T_0-65)e^{k10}\\50=65+(T_0-65)e^{-k10}

Rearranging,

35=65+(T_0-65)e^{-k5}\\35-65=(T_0-65)e^{-k5}\\-30=(T_0-65)e^{-k5}

50=65+(T_0-65)e^{-k10}\\50-65=(T_0-65)e^{-k10}\\-15=(T_0-65)e^{-k10}

If we divide these two equations we get

\frac{-30}{-15}=\frac{(T_0-65)e^{-k5}}{(T_0-65)e^{-k10}}

\frac{-30}{-15}=\frac{e^{-k5}}{e^{-k10}}\\2=e^{5k}\\\ln \left(2\right)=\ln \left(e^{5k}\right)\\\ln \left(2\right)=5k\ln \left(e\right)\\\ln \left(2\right)=5k\\k=\frac{\ln \left(2\right)}{5}

Now, that we know the value of k we can use it to find the initial temperature of the beam,

35=65+(T_0-65)e^{-(\frac{\ln \left(2\right)}{5})5}\\\\65+\left(T_0-65\right)e^{-\left(\frac{\ln \left(2\right)}{5}\right)\cdot \:5}=35\\\\65+\frac{T_0-65}{e^{\ln \left(2\right)}}=35\\\\\frac{T_0-65}{e^{\ln \left(2\right)}}=-30\\\\\frac{\left(T_0-65\right)e^{\ln \left(2\right)}}{e^{\ln \left(2\right)}}=\left(-30\right)e^{\ln \left(2\right)}\\\\T_0=5

so the beam started out at 5 °F.

6 0
3 years ago
The bill for a group of eight people at a restaurant came to $196. Because they are a large party, the restaurant also adds an 1
Iteru [2.4K]
I did the multiplications and I think it is 1,568
8 0
2 years ago
Other questions:
  • What is the probability of picking a vowel from the word invite?
    8·2 answers
  • What does 20% off the regular price mean
    6·2 answers
  • What fraction is equal to 2/5 4/7,4/10,6/9
    15·1 answer
  • Six less than seven times a number is equal to-12
    11·1 answer
  • What’s the value of [-1.1]
    9·2 answers
  • About 42% of a paint mix is white. A painter orders 18 gallons of paint mix. How much of it is white
    9·1 answer
  • 3x + 8y - 36 = 0
    13·2 answers
  • What is the volume of a rectangular prism 11 inches long, 6 inches wide and 3 inches high
    10·1 answer
  • What am I supposed to do here? I could use some help.
    5·1 answer
  • I will mark brianliest
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!