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
Furkat [3]
3 years ago
9

The area of a rectangular garden is given by the trinomial x2 + x – 42. What are the possible dimensions of the rectangle? Use f

actoring.
Mathematics
2 answers:
gizmo_the_mogwai [7]3 years ago
8 0

Answer:

<h3>\boxed{ \boxed{ \bold{ \sf{(x + 7) \: and \: (x - 6)}}}}</h3>

Step-by-step explanation:

\sf{ {x}^{2}  + x - 42}

Here, we have to find two numbers which subtracts to 1 and multiplies to 42

⇒\sf{ {x}^{2}  + (7 - 6)x - 42}

⇒\sf{ {x}^{2}  + 7x - 6x - 42}

Factor out x from the expression

⇒\sf{x(x + 7) - 6x - 42}

Factor out 6 from the expression

⇒\sf{x(x + 7) - 6(x + 7)}

Factor out x + 7 from the expression

⇒\sf{(x + 7)(x - 6)}

So, the possible dimensions of the rectangle are x + 7 and x - 6 .

Hope I helped!

Best regards!

Murrr4er [49]3 years ago
3 0

Answer:

Step-by-step explanation:

Hello, please consider the following.

x^2+x-42\\\\\text{The sum of the zeroes is -1=-7+6 and the product is -42=-7*6.}\\\\\text{So, we can factorise.}\\\\x^2+x-42\\\\=x^2+7x-6x-42\\\\=x(x+7)-6(x+7)\\\\=(x+7)(x-6)

So, the possible dimensions of the rectangle are (x+7) and (x-6).

Thank you.

You might be interested in
El número equivalente de 25/50 por favor
Viefleur [7K]

Answer:

El número equivalente de 25/50 es 1/2

Step-by-step explanation:

3 0
2 years ago
Help!! 50 points and brainliest!
Viktor [21]

Answer:

Second choice:

x=2t

y=4t^2+4t-3

Fifth choice:

x=t+1

y=t^2+4t

Step-by-step explanation:

Let's look at choice 1.

x=t+1

y=t^2+2t

I'm going to subtract 1 on both sides for the first equation giving me x-1=t. I will replace the t in the second equation with this substitution from equation 1.

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

Expand using the distributive property and the identity (u+v)^2=u^2+2uv+v^2:

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

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

y=x^2+0+-1

y=x^2

So this not the desired result.

Let's look at choice 2.

x=2t

y=4t^2+4t-3

Solve the first equation for t by dividing both sides by 2:

t=\frac{x}{2}.

Let's plug this into equation 2:

y=4(\frac{x}{2})^2+4(\frac{x}{2})-3

y=4(\frac{x^2}{4})+2x-3

y=x^2+2x-3

This is the desired result.

Choice 3:

x=t-3

y=t^2+2t

Solve the first equation for t by adding 3 on both sides:

x+3=t.

Plug into second equation:

y=(x+3)^2+2(x+3)

Expanding using the distributive property and the earlier identity mentioned to expand the binomial square:

y=(x^2+6x+9)+(2x+6)

y=(x^2)+(6x+2x)+(9+6)

y=x^2+8x+15

Not the desired result.

Choice 4:

x=t^2

y=2t-3

I'm going to solve the bottom equation for t since I don't want to deal with square roots.

Add 3 on both sides:

y+3=2t

Divide both sides by 2:

\frac{y+3}{2}=t

Plug into equation 1:

x=(\frac{y+3}{2})^2

This is not the desired result because the y variable will be squared now instead of the x variable.

Choice 5:

x=t+1

y=t^2+4t

Solve the first equation for t by subtracting 1 on both sides:

x-1=t.

Plug into equation 2:

y=(x-1)^2+4(x-1)

Distribute and use the binomial square identity used earlier:

y=(x^2-2x+1)+(4x-4)

y=(x^2)+(-2x+4x)+(1-4)

y=x^2+2x+-3

y=x^2+2x-3.

This is the desired result.

3 0
3 years ago
Read 2 more answers
What is 3√20 - 3√45 + 5√12 in simplest radical form? Show all work.
lesya692 [45]

Answer: -3√5 + 10√3

Step 1: Find the prime factorization of the number inside the radical.

Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind.

Step 3: Move each group of numbers or variables from inside the radical to outside the radical. In this case, the pair of 2’s and 3’s moved outside the radical.

Step 4: Simplify the expressions both inside and outside the radical by multiplying.


8 0
3 years ago
Which statement is not necessarily true?<br> Given: DE is the ⊥ bisector of JL
Ket [755]

"DJ= DL" is the one statement among the following choices given in the question that is not necessarily true. The correct option among all the options that are given in the question is the fourth option. I hope that this is the answer that you were looking for and it has actually come to your desired help.

<u>THIS ANSWER IS WRONG EVERYBODY</u>

8 0
3 years ago
Suppose log subscript a x equals 3, log subscript a y equals 7, and log subscript a z equals short dash 2. Find the value of the
enyata [817]

Answer:

<h2>24</h2>

Step-by-step explanation:

Given the following logarithmic expressions log_ax = 3, log_ay = 7, log_az = -2, we are to find the value of log_a(\frac{x^3y}{z^4} )

from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}Substituting x = a³, y = a⁷ and z = a⁻² into the log function log_a(\frac{x^3y}{z^4} ) we will have;

= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24

Hence, the value of the logarithm expression is 24

6 0
3 years ago
Other questions:
  • Which equation gives the number of 1/4 centimeter that are in 7/8 centimeter?
    11·1 answer
  • Item 22 the navy pier ferris wheel in chicago has a circumference that is ​56% of the circumference of the first ferris wheel bu
    7·1 answer
  • What does X equal? 14x+24=18x-32
    6·2 answers
  • Whst is the answer to 1 3/4 - 7/10 = ?
    5·2 answers
  • Solve for 1 divided by x equals 3
    12·2 answers
  • Tyrone had $17,000 to invest. He invested part of that amount at 2.5% annual interest for one year and the other part at 6.5% an
    15·1 answer
  • Help im sister needs help and i can't help her im doing my school work !
    11·1 answer
  • Multiply. Write your answer as a fraction in simplest form 9/10 x 2/3
    7·2 answers
  • Someone please <br> Help me!!!<br> Is due today
    8·1 answer
  • If you can, please tell how you solved
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!