a rectangle has a perimeter of 46cm and an area of 120cm squared. find its dimensions by writing an equation and using the quadratic formula to solve it. Thanks!

Answers

Answer 1

Answer: Let length = l , width = b
Perimeter = 2 (l +b)
46= 2 (l +b)
(l + b) = 23

l*b = 120

So l + 120/l = 23
l^2 + 120 - 23l = 0
l^2 -15l + 8l + 120 = 0
(l-8) (l - 15) =
l = 8 or 15
i.e if l =8, w=15
and if l = 15, w = 8

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Can someone please help me with Geometry?

Evaluate the polynomial 6x - y for x = 3 and y =4

Answers

6 x 3 is 18. y is equal to 4. 18 minus 4 is 14. The answer is 14.

Use Gauss-Jordan elimination to solve the following linear system.x – 6y – 3z = 4
–2x – 3z = –8
–2x + 2y – 3z = –14

Answers

$\begin{cases}x-6y-3z=4&(1)\n-2x-3z=-8&(2)\n-2x+2y-3z=-14&(3)\end{cases}$

First eliminate $y$ by adding $(1)$ to three times $(3)$ . This gives

$(x-6y-3z)+3(-2x+2y-3z)=4+3(-14)\iff -5x-12z=-38$

This reduces the system of one of two equations and two unknowns:

$\begin{cases}-5x-12z=-38&(1)^*\n-2x-3z=-8&(2)^*\end{cases}$

You can eliminate $z$ by subtracting $(1)^*$ and four times $(2)^*$ to get

$(-5x-12z)-4(-2x-3z)=-38-4(-8)\iff3x=-6\implies x=-2$

Back-substitute to find $z$ and $y$ . You should end up with $(x,y,z)=(-2,-3,4)$ .

Answer:

(-2,-3,4)

Step-by-step explanation:

A quadratic equation is shown below:x2 − 8x + 13 = 0

Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers?
Subtract 5 from both sides of the equation

Add 3 to both sides of the equation

Add 5 to both sides of the equation

Subtract 3 from both sides of the equation

Answers

The given quadratic equation can be represented in the form $(x-p)^2 = q$

by adding 3 to both sides of the equation.

What is a quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation. The equation is given by

$ax^2 + bx + c = 0$

where $a\neq 0$ .

The given quadratic equation is

$x^2 - 8x + 13 = 0$

Case 1: Subtract 5 from both sides of the equation

i.e. $x^2 - 8x + 13 - 5 = 0 - 5$

⇒ $x^2 - 8x + 8 = -5$

The LHS of the above equation can not be expressed in $(x-p)^2$ form. Hence, it is not the correct step.

Case 2: Add 3 to both sides of the equation.

i.e. $x^2 - 8x + 13 +3 = 0 + 3$

⇒ $x^2 - 8x + 16 = 3$

⇒ $x^2 - 2* x * 4 + (4)^2 =3$

⇒ $(x - 4)^2 = 3$

The above equation is expressed in $(x-p)^2 = q$ form where p = 4 and q = 3.

Case 3: Add 5 to both sides of the equation

i.e. $x^2 - 8x + 13 + 5 = 0+5$

⇒ $x^2 - 8x + 18 = 5$

The LHS of the above equation can not be expressed in the $(x-p)^2$ . Hence, it is not the correct step.

Case 4: Subtract 3 from both sides of the equation

i.e. $x^2 - 8x + 13 - 3 = 0-3$

⇒ $x^2 - 8x + 10 = -3$

The LHS of the above equation can not be expressed in the $(x-p)^2$ . Hence, it is not the correct step.

Hence, "Add 3 to both sides of the equation" is the correct step.

Learn more about quadratic equations here:

brainly.com/question/2263981?referrer=searchResults

#SPJ2

Add 3 to both sides, so you will have

x^2 - 8x + 13 + 3 = 3
x^2 -8x + 16 = 3

And now the left side is a perfect square trinolmial: (x-4)^2.

the ratio of the circumferences of two circles is 2:3. If the large circle has a radius of 39 cm, what is the radiusof the small circle?

Answers

Answer:

$r_(1) = 26$ .

Step-by-step explanation:

Given : the ratio of the circumferences of two circles is 2:3. If the large circle has a radius of 39 cm,

To find : what is the radius of the small circle.

Solution : We have given that ratio of the circumferences of two circles is 2:3.

Let $r_(2)$ is radius of larger circle and $r_(1)$ is radius of small circle .

Then circumference = $(2\pi\ r_(1) )/(2\pi\ r_(2))$ = $(2)/(3)$ .

Solving the above equation

$(r_(1))/(r_(2) )$ = $(2)/(3)$ .

We have given radius of larger circle = 39 then

$(r_(1))/(39)$ = $(2)/(3)$ .

On multiplying both sides by 39.

$r_(1) = 39 *(2)/(3)$ .

$r_(1) = 13 * 2$ .

$r_(1) = 26$ .

Therefore, $r_(1) = 26$ .

C1/C2 = 2/3

2pi r1 / 2pi r2 = r1/r2 = 2/3

r1/39 = 2/3

r1 = 39*2/3 = 26

So, your answer is 26cm

The first order was 13 bushes and 4 trees for a total of $487 the second order was 6 bushes and 2 trees for a total of $232 what were the costs of one bush and of one tree