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leonid [27]
2 years ago
9

Factor the following perfect square trinomials

Mathematics
1 answer:
Lorico [155]2 years ago
3 0

Answer:

1) (m+3)2

2) (b+6)2

3) (3n−2)^2

Step-by-step explanation:

You might be interested in
The expression 2.5 + 2t gives the cost, in dollars, of t tulips at a flower store. Joanna has $14.00.
Elena-2011 [213]

Answer:

5 tulips.

Step-by-step explanation:

Given:

The expression for the cost of the tulips is Cost=2.5+2t

Where, t is the number of tulips.

Now, Joanna has \$ 14.00.

So, number of tulips that can be bought with the above amount can be obtained by substituting \$ 14.00 for cost. This gives,

Cost=2.5+2t\\14=2.5+2t\\2t=14-2.5\\2t=11.5\\t=\frac{11.5}{2}=5.75 \approx 5.

As the number of tulips cannot be in decimals or fractions, so the maximum number of tulips that can be bought will be 5.

6 0
3 years ago
Interest rate fixed at 6%, n = 26 payments per year, for payment
sergiy2304 [10]

Answer:

hi the anser might be 600$

Step-by-step explanation:

8 0
3 years ago
What is the answer to this question I am really having trouble ??
masya89 [10]
<h3>Answer: Choice B</h3><h3>y = x^2 + 7x + 1</h3>

======================================

Proof:

A quick way to confirm that choice B is the only answer is to eliminate the other non-answers.

If you plugged x = 1 into the equation for choice A, you would get

y = -x^2 + 7x + 1

y = -1^2 + 7(1) + 1

y = -1 + 7 + 1

y = 7

We get a result of 7, but we want 9 to be the actual output. So choice A is out.

-----------

Repeat for choice C. Plug in x = 1

y = x^2 - 7x + 1

y = 1^2 - 7(1) + 1

y = 1 - 7 + 1

y = -5

We can eliminate choice C (since again we want a result of y = 9)

-----------

Finally let's check choice D

y = x^2 - 7x - 1

y = 1^2 - 7(1) - 1

y = 1 - 7 - 1

y= -7

so choice D is off the list as well

-----------

The only thing left is choice B, so it must be the answer. It turns out that plugging x = 1 into this equation leads to y = 9 as shown below

y = x^2 + 7x + 1

y = 1^2 + 7(1) + 1

y = 1 + 7 + 1

y = 9

And the same applies to any other x value in the table (eg: plugging in x = 3 leads to y = 31, etc etc).

3 0
3 years ago
Josiah skateboards from his house to school 3 miles away. It takes him 36 minutes.
nikdorinn [45]

Using the speed - distance relationship, the number of minutes it will take Josiah to cover a distance of 2.5 miles is 30 minutes.

<u>Calculating Josiah's speed</u> :

  • <em>Speed = (distance ÷ time) </em>

Speed = (3 ÷ 36) = 0.08333 miles per minute.

<u>Time taken to cover a distance of 2.5 miles</u> :

  • <em>Time taken = (Distance ÷ Speed) </em>

Time taken = (2.5 ÷ 0.08333) = 30 minutes

Therefore, it will take 30 minutes for Josiah to cover a distance of 2.5 Miles

Learn more : brainly.com/question/18112348

4 0
2 years ago
Given two points P(sinθ+2, tanθ-2) and Q(4sin²θ+4sinθcosθ+2acosθ, 3sinθ-2cosθ+a). Find constant "a" and the corresponding value
vodomira [7]

Answer:

\rm\displaystyle \displaystyle \displaystyle θ=    {60}^{ \circ} , {300}^{ \circ}

\rm \displaystyle a =    - \frac{   \sqrt{3} }{2}    - 1, \frac{\sqrt{3}}{2}  - 1

Step-by-step explanation:

we are given two <u>coincident</u><u> points</u>

\displaystyle  P( \sin(θ)+2,  \tan(θ)-2)   \: \text{and } \\  \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)

since they are coincident points

\rm \displaystyle  P( \sin(θ)+2,  \tan(θ)-2)    = \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ )\cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)

By order pair we obtain:

\begin{cases}  \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ) =  \sin( \theta)   + 2 \\   \\  \displaystyle 3 \sin( \theta)  - 2  \cos( \theta)  + a =  \tan( \theta)  - 2\end{cases}

now we end up with a simultaneous equation as we have two variables

to figure out the simultaneous equation we can consider using <u>substitution</u><u> method</u>

to do so, make a the subject of the equation.therefore from the second equation we acquire:

\begin{cases}  \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sinθ \cos(θ)+2a \cos(θ )=  \sin( \theta)   + 2 \\   \\  \boxed{\displaystyle  a =  \tan( \theta)  - 2 - 3 \sin( \theta)   +  2  \cos( \theta) } \end{cases}

now substitute:

\rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2 \cos(θ) \{\tan( \theta)  - 2 - 3 \sin( \theta)   +  2  \cos( \theta)   \}=  \sin( \theta)   + 2

distribute:

\rm\displaystyle \displaystyle 4 \sin ^{2}( θ)+4 \sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta)  - 6 \sin( \theta) \cos( \theta)    + 4  \cos ^{2} ( \theta)   =  \sin( \theta)   + 2

collect like terms:

\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta)     + 4  \cos ^{2} ( \theta)   =  \sin( \theta)   + 2

rearrange:

\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) + 4 \cos ^{2} ( \theta)  - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + =  \sin( \theta)   + 2

by <em>Pythagorean</em><em> theorem</em> we obtain:

\rm\displaystyle \displaystyle 4  - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta)  =  \sin( \theta)   + 2

cancel 4 from both sides:

\rm\displaystyle \displaystyle   - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta)  =  \sin( \theta)    - 2

move right hand side expression to left hand side and change its sign:

\rm\displaystyle \displaystyle   - 2\sin(θ) \cos(θ)+\sin(θ ) - 4\cos( \theta) + 2  =  0

factor out sin:

\rm\displaystyle \displaystyle  \sin (θ) (- 2 \cos(θ)+1) - 4\cos( \theta) + 2  =  0

factor out 2:

\rm\displaystyle \displaystyle  \sin (θ) (- 2 \cos(θ)+1)  + 2(- 2\cos( \theta) + 1 ) =  0

group:

\rm\displaystyle \displaystyle ( \sin (θ)   + 2)(- 2 \cos(θ)+1)  =  0

factor out -1:

\rm\displaystyle \displaystyle -  ( \sin (θ)   + 2)(2 \cos(θ) - 1)  =  0

divide both sides by -1:

\rm\displaystyle \displaystyle   ( \sin (θ)   + 2)(2 \cos(θ) - 1)  =  0

by <em>Zero</em><em> product</em><em> </em><em>property</em> we acquire:

\begin{cases}\rm\displaystyle \displaystyle   \sin (θ)   + 2 = 0 \\ \displaystyle2 \cos(θ) - 1=  0 \end{cases}

cancel 2 from the first equation and add 1 to the second equation since -1≤sinθ≤1 the first equation is false for any value of theta

\begin{cases}\rm\displaystyle \displaystyle   \sin (θ)     \neq  - 2 \\ \displaystyle2 \cos(θ) =  1\end{cases}

divide both sides by 2:

\rm\displaystyle \displaystyle \displaystyle \cos(θ) =   \frac{1}{2}

by unit circle we get:

\rm\displaystyle \displaystyle \displaystyle θ=    {60}^{ \circ} , {300}^{ \circ}

so when θ is 60° a is:

\rm \displaystyle a =  \tan(  {60}^{ \circ} )  - 2 - 3 \sin(  {60}^{ \circ} )   +  2  \cos(  {60}^{ \circ} )

recall unit circle:

\rm \displaystyle a =   \sqrt{3}  - 2 -  \frac{ 3\sqrt{3} }{2}   +  2   \cdot  \frac{1}{2}

simplify which yields:

\rm \displaystyle a =    - \frac{   \sqrt{3} }{2}    - 1

when θ is 300°

\rm \displaystyle a =  \tan(  {300}^{ \circ} )  - 2 - 3 \sin(  {300}^{ \circ} )   +  2  \cos(  {300}^{ \circ} )

remember unit circle:

\rm \displaystyle a =  -  \sqrt{3}   - 2  +   \frac{3\sqrt{ 3} }{2}  +  2   \cdot  \frac{1}{2}

simplify which yields:

\rm \displaystyle a = \frac{ \sqrt{3} }{2} - 1

and we are done!

disclaimer: also refer the attachment I did it first before answering the question

5 0
3 years ago
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