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3 years ago

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A rectangular yard has dimensions 10 meters by 8 meters. In the middle of the yard is a rectangular pond of 8 square meters, lea

ving a uniform walkway around the pond. Write a quadratic equation in standard form to find the width of the walkway.

1 answer:

Nikolay [14]3 years ago

8 0

hahahaha i had this same question in my grade

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5. Enter the answer as a decimal

Hitman42 [59]

Answer:

6.5%

Step-by-step explanation:

I = prt

5616 = 7200 × r × 12

r = 5616/(7200 × 12)

r = 0.065

r = 6.5%

5 0

2 years ago

Which of the following statement is false?

emmainna [20.7K]

Answer:

D.) rational numbers are associative under subtraction

Step-by-step explanation:

rational numbers are closed under subtraction

↳ TRUE

zero is the identity for addition of rational numbers

↳ TRUE

subtraction is the inverse of the addition

↳ TRUE

rational numbers are associative under subtraction

↳ FALSE

5 0

3 years ago

Which real numbers are zeros of the function?

monitta

<h3><u>The roots are -1/2, 0, 2, and 3.</u></h3>

Let's trying factoring this polynomial.

We can factor an x out of each term to start.

x(2x^3 - 9x^2 + 7x + 6)

We now know one of the roots is going to be zero.

Using the rational roots theorem, and the remainder theorem, we can try to find some more roots that way.

Factors of 6: 1, 2, 3, 6.

Factors of 2: 1

Possible rational roots: +/-1/2, +/-1, +/-2, +/-3/2, +/-3, +/-6

Using the remainder theorem, we can plug these values into the polynomial, and if we get a remainder of zero, we know it's a root.

-1/2(2(-1/2)^3 - 9(-1/2)^2 + 7(-1/2) + 6) = 0

Our first root is -1/2.

We can successfully factor a -1/2 out of this polynomial.

After diving the polynomial by -1/2, we're left with: 2x^2 - 10x + 12.

We can now try using the AC method to get our last two roots.

First, we can factor this polynomial to simplify it.

Divide all terms by 2.

2(x^2 - 5x + 6)

Now let's try using the AC method.

The digits -3 and -2 satisfy the criteria.

2(x - 3)(x - 2)

We now have all of our roots: 0, -1/2, 2, and 3.

6 0

4 years ago

A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares from the

Stells [14]

Answer:

$\frac{5}{3}$ in

Step-by-step explanation:

Let x be the side of square.

Length of box=8-2x

Width of box=15-2x

Height of box=x

Volume of box= $L\times B\times H$

Substitute the values then we get

Volume of box=V(x)= $(8-2x)(15-2x)x=(15x-2x^2)(8-2x)$

$V(x)=120x-30x^2-16x^2+4x^3$

$V(x)=4x^3-46x^2+120x$

Differentiate w.r.t x

$V'(x)=12x^2-92x+120$

$V'(x)=0$

$12x^2-92x+120=0$

$3x^2-23x+30=0$

$3x^2-18x-5x+30=0$

$3x(x-6)-5(x-6)=0$

$(x-6)(3x-5)=0$

$x-6=0\implies x=6$

$3x-5=0\implies x=\frac{5}{3}$

Again differentiate w.r.t x

$V''(x)=24x-92$

Substitute x=6

$V''(6)=24(6)-92=52>0$

Substitute x=5/3

$V''(5/3)=24(5/3)-92=-52$

Hence, the volume is maximum at x= $\frac{5}{3}$

Therefore, the side of the square , $x=\frac{5}{3}$ in cutout that gives the box the largest possible volume.

5 0

3 years ago

Evalute 2√72 divided by √8+ √2. I need help asap!!!<br><br><br> :( I will mark brainliest pls!!

Ghella [55]

Answer:

It's 4

Step-by-step explanation:

* / = square root

You simply 2/72 which is 12/2, then simplify /8 which is 2/2.

You combine 2/2 and /2 which is 3/2.

The equation should be 12/2 over 3/2 so you simplify it which will give you 4.

(By simplifying 12/2 over 3/2, you cross out /2 and convert 12 over 3 into a whole number)

6 0

3 years ago