Ask question

Ask question

All categories

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.

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