All categories

3 years ago

Solve the system and round to the nearest hundredth. Enter the

Mathematics

2 answers:

hram777 [196]3 years ago

6 0

Answer:

Step-by-step explanation:

xy = 300

x + y = 50 Solve for y

y = 50 - x substitute into xy = 300

x(50 - x) = 300 Remove the brackets.

50x - x^2 = 300 Bring the left to the right.

0 = x^2 - 50x + 300

This is a quadratic. It will have 2 solutions.

a=1

b = - 50

c = 300

Put these into the quadratic equation.

It turns out that x has two values -- both plus

x1 = 42.03

x2 = 6.97

x1 + y1 = 50

42.03 + y = 50

y = 50 - 42.03

y = 7,97

(42.03 , 7.97)

====================

x2 + y2 = 50

6.97 + y2 = 50

y2 = 50 - 6.97

y2 = 43.03

(6.97 , 43.03)

tatuchka [14]3 years ago

4 0

Answer:

x ≈ 6.97, y ≈ 43.03; x ≈ 43.03, y ≈ 6.97

Step-by-step explanation:

System: x + y = 50, xy = 300

Alter 1st equation: y = 50 - x

Substitute: x(50 - x) = 300

Distribute: -x² + 50x = 300

Subtract: -x² + 50x - 300 = 0

Quadratic formula: x = (-50 ± √(2500 - 4 * -1 * -300))/(-2)

Simplify: x = (-50 ± √1300)/-2

Distribute: x = 25 ± (10√13)/-2

Simplify: x = 25 - 5√13 --> x ≈ 6.97, x = 25 + 5√13 --> x ≈ 43.03

Substitute: 6.97 + y = 50 --> y ≈ 43.03, 43.04 + y = 50 --> y ≈ 6.97

You might be interested in

The equation of a circle is (x + 3)2 + (y – 5)2 = 81. Determine the coordinates of the center of the circle and the length of th

Nataly_w [17]

Answer:

The center of the circle is (-3 , 5) and the length of the radius is 9 units

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- The center-radius form of the circle equation is in the format

(x – h)² + (y – k)² = r², where the center is the point (h, k) and

the radius is r.

- This form of the equation is helpful, because you can easily find

the center and the radius.

* Now lets solve the problem

- The equation is (x + 3)² + (y - 5)² = 81

- By comparing the two equations

∵ (x – h)² + (y – k)² = r² and (x + 3)² + (y - 5)² = 81

# x - h = x + 3

∴ -h = 3 ⇒ divide both sides by -1

∴ h = -3

# y - k = y - 5

∴ k = 5

# h and k are the coordinates of the center of the circle

∴ The center of the circle is (-3 , 5)

# r² = 81 ⇒ take √ for both sides

∴ r = 9

∴ The length of the radius = 9 units

* The center of the circle is (-3 , 5) and the length of the radius is 9 units

3 0

3 years ago

Let r3 have the euclidean inner product. let u = (-1, 1, 1) and v = (-7, 6, 15). if ||ku + v||= 7, what is k? give the exact ans

amm1812

Ma $k\mathbf u+\mathbf v=k(-1,1,1)+(-7,6,15)=(-k-7,k+6,k+15)$

Recall that for a vector $\mathbf x\in\mathbb R^n$ , we have $\|\mathbf x\|=\sqrt{\mathbf x\cdot\mathbf x}$ . So we have

$\|k\mathbf u+\mathbf v\|=\sqrt{(k\mathbf u+\mathbf v)(k\mathbf u+\mathbf v)}=7$
$\implies k^2\mathbf u\cdot\mathbf u+2k\mathbf u\cdot\mathbf v+\mathbf v\cdot\mathbf v=49$
$\implies3k^2+56k+261=0$
$\implies k=-9,-\dfrac{29}3$

3 0

3 years ago

Given y+6=10(x-9) What is the point used to write the equation?

liubo4ka [24]

Answer:

Point (9, -6)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate
y₁ - y coordinate
m - slope

Step-by-step explanation:

Step 1: Define

y + 6 = 10(x - 9)

Step 2: Break Function

Identify Parts

Slope m = 10

Point (9, -6)

8 0

3 years ago

The midpoint of ab is m(5-2). If the coordinates of a are (6,-5), what are the coordinates of b

Alex

The coordinate of B is (4,1)

7 0

3 years ago

What is the inequality shown here

IgorLugansk [536]

Answer:

$- 3 \leqslant x < 2$

I hope I helped you^_^

5 0

3 years ago