All categories

3 years ago

Factor z2 + 17z + 72.

1 answer:

3 0

Hello!

It looks like you meant,
$z^2+17z+72$
Break the expression into two groups, that would imply splitting the 17.
$=\left(z^2+8z\right)+\left(9z+72\right)$
Let's start factoring.
First, factor the $z$ from $z^2+8z$
Then, factor the $9$ from $9z+72$
We would be left with,
$=z\left(z+8\right)+9\left(z+8\right)$
Factor out the common term, which is $(z+8)$
$=\left(z+8\right)\left(z+9\right)$

Our final answer would be,
$=\left(z+8\right)\left(z+9\right)$

You can feel free to let me know if you have any questions regarding this!
Thanks!

- TetraFish

You might be interested in

Hurry I’ll give 10pts

balandron [24]

The answer to the question is a

4 0

3 years ago

The area of a rectangular city park is 25/54 square miles. The length of the park is 5/9 miles what is the width in the miles of

kotykmax [81]

Note that $A=lw$ , where $A$ is the area, $l$ is the length, and $w$ is the width. Substituting our values in, we have:

$\frac{5w}{9} = \frac{25}{54}$

Multiplying by $\frac{9}{5}$ gives:

$w=\frac{5}{6}$

So the width is $\frac{5}{6}$ miles.

7 0

3 years ago

The temperature function (in degrees Fahrenheit) in a three dimensional space is given by T(x, y, z) = 3x + 6y - 6z + 1. A bee i

madam [21]

You're looking for the extreme values of $T(x,y,z)=3x+6y-6z+1$ subject to $x^2+y^2+z^2=9$ . The Lagrangian is

$L(x,y,z,\lambda)=3x+6y-6z+1+\lambda(x^2+y^2+z^2-9)$

with critical wherever the partial derivatives vanish:

$L_x=3+2\lambda x=0\implies x=-\dfrac3{2\lambda}$

$L_y=6+2\lambda y=0\implies y=-\dfrac3\lambda$

$L_z=-6+2\lambda z=0\implies z=\dfrac3\lambda$

$L_\lambda=x^2+y^2+z^2-9=0$

Substituting the first three solutions into the last equation gives

$\dfrac9{4\lambda^2}+\dfrac9{\lambda^2}+\dfrac9{\lambda^2}=9$

$\implies\lambda=\pm\dfrac32$

$\implies x=1,y=2,z=-2\text{ or }x=-1,y=-2,z=2$

At these points, we have

$T(1,2,-2)=28$

$T(-1,-2,2)=-26$

so the highest temperature the bee can experience is 28º F at the point (1, 2, -2), and the lowest is -26º F at the point (-1, -2, 2).

6 0

3 years ago

210,704 in equivalent Form

Verizon [17]

Answer:

<h2><em>210= 2×3×5×7 (4 distinct prime factors)</em></h2><h2><em>2×2x2x2x2x2x11 or 2^6×11 (7 prime factors, 2 distinct)</em></h2><h2><em>please mark me as braini</em><em>est </em></h2>

4 0

3 years ago

A dog's leash is 8 feet long. The owner estimates that their hand is 3 feet off the ground. The leash is not parallel to the gro

Elza [17]

Answer: 24 feet

Step-by-step explanation:

5 0

4 years ago