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
erastova [34]
3 years ago
7

Write the square of the binomial as a polynomial: (-1 1/3p + 6q)^2

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
5 0

Answer:

\frac{16}{9}p² -16pq + 36q²

Step-by-step explanation:

Given

(- \frac{4}{3}p + 6q)²

= (- \frac{4}{3}p + 6q)(- \frac{4}{3}p + 6q)

Each term in the second factor is multiplied by each term in the first factor, that is

- \frac{4}{3}p(- \frac{4}{3}p + 6q) + 6q(- \frac{4}{3}p + 6q)

= \frac{16}{9}p² - 8pq - 8pq + 36q² ← collect like terms

= \frac{16}{9}p² - 16pq + 36q²

You might be interested in
For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va
Black_prince [1.1K]

Answer:

3 solutions:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is tan(\frac{\theta}{2}) so let's focus on that part of the equation first.

We know that:

tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}

therefore:

cos(\frac{\theta}{2})\neq0

so we need to find the angles that will make the cos function equal to zero. So we get:

cos(\frac{\theta}{2})=0

\frac{\theta}{2}=cos^{-1}(0)

\frac{\theta}{2}=\frac{\pi}{2}+\pi n

or

\theta=\pi+2\pi n

we can now start plugging values in for n:

\theta=\pi+2\pi (0)=\pi

if we plugged any value greater than 0, we would end up with an angle that is greater than 2\pi so,  that's the only angle we cannot include in our answer set, so:

\theta\neq \pi

having said this, we can now start solving the equation:

tan(\frac{\theta}{2})=sin(\theta)

we can start solving this equation by using the half angle formula, such a formula tells us the following:

tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}

so we can substitute it into our equation:

\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)

we can now multiply both sides of the equation by sin(\theta)

so we get:

1-cos(\theta)=sin^{2}(\theta)

we can use the pythagorean identity to rewrite sin^{2}(\theta) in terms of cos:

sin^{2}(\theta)=1-cos^{2}(\theta)

so we get:

1-cos(\theta)=1-cos^{2}(\theta)

we can subtract a 1 from both sides of the equation so we end up with:

-cos(\theta)=-cos^{2}(\theta)

and we can now add cos^{2}(\theta)

to both sides of the equation so we get:

cos^{2}(\theta)-cos(\theta)=0

and we can solve this equation by factoring. We can factor cos(\theta) to get:

cos(\theta)(cos(\theta)-1)=0

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

cos(\theta)=0

\theta=cos^{-1}(0)

\theta={\frac{\pi}{2}, \frac{3\pi}{2}}

Equation 2:

cos(\theta)-1=0

we add a 1 to both sides of the equation so we get:

cos(\theta)=1

\theta=cos^{-1}(1)

\theta=0

so we end up with three answers to this equation:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

7 0
2 years ago
A farmer sells 8.5 kilograms of apples and pears at the farmer's market. 4 5 of this weight is apples, and the rest is pears. Ho
slavikrds [6]

Answer:

your answer gonna be $13 dollars

6 0
2 years ago
Any portion of the circumference of a circle is called a(n)
Alex777 [14]
Any portion of the circumference of a circle is called a radius
5 0
3 years ago
2x+2y= 24 <br> x=3y <br> What is the value of x+y?
natita [175]

Answer:

x = 9

y = 3

Step-by-step explanation:

2x + 2y = 24 is the same as x + y = 12

using substitution, x = 12-y

12 - y = 3y

12 = 4y

y = 3

x = 3(3)

x = 9

5 0
3 years ago
Which of these is a binomial? O A. x + 2y2 - 7 O B. ab O C. 5xy O D. 2x3 - 7y3​
Lemur [1.5K]

Answer:

D

Step-by-step explanation:

2 terms

8 0
2 years ago
Other questions:
  • What do I do about the variables
    10·1 answer
  • If M is the midpoint of PQ and X is the midpoint of PM then PX = a PQ
    9·1 answer
  • Write the equation of the line in slope-intercept form containing the point (2,4) and with a slope of
    14·1 answer
  • 51) Simplify: 4x + 6(3x - 2)
    13·2 answers
  • Complete the point-slope equation of the line through (2,3 and (7,4). Use exact numbers.
    10·1 answer
  • You buy halibut at $31 per pound. One portion of seared halibut requires 6 ounces of halibut. How much does the halibut for one
    14·1 answer
  • Drag the items to complete the sentences about the end behavior of the exponential function graphed.
    13·1 answer
  • According to a survey, 60% of adults believe that all college stu- dents should be required to perform a specified number of hou
    6·1 answer
  • Each bag of rocks for an aquarium costs $12.35. Which equation best represents y, the total cost of x bags of rocks?
    9·1 answer
  • Miles is buying a new computer for $1,150. He is considering two credit options. Option A Offers a 3 year loan with a 10% simple
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!