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3 years ago

What multiplies to 6 but adds to 17

Mathematics

2 answers:

MAVERICK [17]3 years ago

5 0

The answer is -4 and 21

I am glad to help!

vladimir1956 [14]3 years ago

5 0

You can write this line as the system:

x + y = 17
xy = 6

To solve it, you first need to get the proper value of either x or y. In this case i choose to get the value of x:

x + y = 17
x = 17-y

With this, i an input the value into the second line:

(17-y)y = 6

17y-y^2=6

-y^2+17y-6=0
can be solved with the quadratic formula.

y = (-17 +/- sqrt(-17^2 - 4*-1*-6))/2*-1
y = (-17 +/- sqrt(289 - 24)/-2
The square root is 16.28
y = (-17 +/- 16,28)/-2
y_1 = (-17 + 16.28)/-2 = 0,36
y_2 = (-17 - 16.28)/-2 = 16,64

To skip the work ahead of us, x_1 and x_2 will end up with the exact same numbers, as we could multiply both ways.

The numbers are ca. 0,36 and 16,64

0,36+16,64 = 17

0,36*16,64 = 5,999997 = ca. 6

Sorry for the small amount of rounding, but i hope this works.

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A circle in the XY-plane has center (5, 7) and radius 2. Which of the following is an equation of the circle?

MAXImum [283]

Answer: A, because the equation of a circle is $(x-h)^2+(y-k)^2=r^2$ . So, if the point of the center is $(5,7)$ and the radius $2$ , then on the equation should be changed as negative and the radius should be multiplied as $4$ , which is $(x-5)^2+(y-7)^2=4$

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3 years ago

In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 specta

Maksim231197 [3]

Answer:

See explanation

Step-by-step explanation:

Let $x,\ x\ge 0$ be the number of students and $y,\ y\ge 0$ be the number of adults on the show.

1. Tickets cost $15 for students, so x student tickets cost $15x.

Tickets cost $25 for adults, so y adult tickets cost $25y.

Total cost of all tickets is $(15x + 25y).

The charity show is conducted in order to raise at least $3,750, thus

$15x+25y\ge 3,750$

2. The auditorium can accommodate up to 180 spectators, hence

$x+y\le 180$

3. We get the system of inequalities:

$\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 180\\15x+25y\ge 3,750\end{array}\right.$

Plot all solutions sets to each inequality and the common region is the solution set to the system of inequalities. This region is not empty, so the charity will reach its goal. For example, if they sell 50 students tickets and 125 adult tickets, they will raise $\$(15\cdot 50+25\cdot 125)=\$3,875$

8 0

3 years ago

What is the volume of the box pictured below?

SpyIntel [72]

Answer:

The volume of the box is 3/4 cubic meters.

Step-by-step explanation:

We know that volume = length * width * height. We have length, width, and height already, so all we have to do is multiply.

5/6 * 1 1/8 * 4/5. First we convert 1 1/8 from a mixed fraction, to give us 9/8, as 8/8 = 1.

5/6 * 9/8 * 4/5. 5 * 9 = 45, and 6 * 8 = 48. 45/48 reduces to 15/16.

15/16 * 4/5. 15 * 4 = 60, and 16 * 5 = 80. 60/80 reduces to 6/8, which reduces to 3/4.

8 0

3 years ago

Read 2 more answers

Gianna is going to throw a ball from the top floor of her middle school. When she throws the hall from 48 feet above the ground,

vazorg [7]

Answer:

So, the times the ball will be 48 feet above the ground are t = 0 and t = 2.

Step-by-step explanation:

The height h of the ball is modeled by the following equation

$h(t)=-16t^2+32t+48$

The problem want you to find the times the ball will be 48 feet above the ground.

It is going to be when:

$h(t) = 48$

$h(t)=-16t^{2}+32t+48$

$48=-16t^{2}+32t+48$

$0=-16t^{2}+32t+48 - 48$

$16t^{2} - 32t = 0$

We can simplify by 16t. So

$16t(t-2)= 0$

It means that

16t = 0

t = 0

t - 2 = 0

t = 2

So, the times the ball will be 48 feet above the ground are t = 0 and t = 2.

6 0

3 years ago

Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x

valkas [14]

$\mathbf f(x,y,z)=x^4\,\mathbf i-x^3z^2\,\mathbf j+4xy^2z\,\mathbf k$
$\mathrm{div}(\mathbf f)=\dfrac{\partial(x^4)}{\partial x}+\dfrac{\partial(-x^3z^2)}{\partial y}+\dfrac{\partial(4xy^2z)}{\partial z}=4x^3+0+4xy^2=4x(x^2+y^2)$

Let $\mathcal D$ be the region whose boundary is $\mathcal S$ . Then by the divergence theorem,

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV$

Convert to cylindrical coordinates, setting

$x=r\cos\theta$
$y=r\sin\theta$

and keeping $z$ as is. Then the volume element becomes

$\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$

and the integral is

$\displaystyle\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=0}^{z=r\cos\theta+7}4r\cos\theta\cdot r^2\cdot r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle4\iiint_{\mathcal D}r^4\cos\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\dfrac{2\pi}3$

4 0

3 years ago