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3 years ago

How do you determine if an ordered pair is a solution to a given equation?

2 answers:

6 0

For this case, we have to: Be an equation of the form $y = f (x)$ , where f (x) represents an expression as a function of the variable "x". To determine if an ordered pair is a solution to that equation, you must replace the pair in the equation and see if equality is met.

Example:

Let $y = 2x$

We want to know if the pair $(x, y) = (2,1)$ is the solution of the equation. If we replace, we have:

$1 = 2 (2)\\1 = 4$

Equality is not met, so the pair is not a solution.

Answer:

Replace the pair in the equation and see if equality is met.

vitfil [10]3 years ago

4 0

Answer:

You have to substitute the x-value into the equation to see whether the solution gives the y-value.

Step-by-step explanation:

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If x+y+z=9, xy+yz+zx =26; find x²+y²+z²

vichka [17]

<em>First, we must expand and simplify :</em>
$x + y+z = 9$

$(x + y+z)^{2} = (9)^{2}$

$x^{2} + y^{2}+z^{2} + 2(xy + yz+zx) = 81$

<em>And Than, Enter the value :</em>
$x^{2} + y^{2}+z^{2} + 2(26) = 81$

$x^{2} + y^{2}+z^{2} + 52 = 81$

$x^{2} + y^{2}+z^{2} = 81- 52$

$\boxed{x^{2} + y^{2}+z^{2} = 29}$

7 0

3 years ago

Read 2 more answers

Write an equation of a line that has a slope of 7/2 and passes through the point (14,-3). Convert it to slope-intercept form.

Simora [160]

Answer:

Step-by-step explanation:

The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:

m = ⁷/₂

(14, -3) ⇒ x₀ = 14, y₀ = -3

So, the point-slope form of the equation:

y + 3 = ⁷/₂(x - 14)

So::

y + 3 = ⁷/₂x - 49 {subtract 3 from both sides}

y = ⁷/₂x - 52 ← the slope-intercept form of the equation

4 0

3 years ago

One of the roots of the equation 5x2−36x+t=0 is five times as big as the other root. Find the value of t.

Bas_tet [7]

Answer:

t = 36

Step-by-step explanation:

If one of the roots is "a", the equation can be factored as ...

(5x -a)(x -a) = 0

5x^2 -6ax +a^2 = 0

Comparing terms to the given equation, we see that ...

-6ax = -36x

a = 6 . . . . . . . . divide by -6

Then ...

a^2 = t

36 = t . . . . . . . substitute 6 for a

_____

The roots are 6 and 6/5.

4 0

3 years ago

The current temperature is 48F. It is expected to drop 1.5F each hour. Determine how many hours the temperature will be 36 F.

Nina [5.8K]

Answer: 6 hours

Step-by-step explanation:

48/6 = 8

36/6 = 6

6 0

3 years ago

A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.

Montano1993 [528]

Answer:

x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

area = xy +2(xz +yz)

volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

L = xy +2(xz +yz) +λ(xyz -8788)

partial with respect to x: 0 = y+2z +λyz

partial with respect to y: 0 = x +2z +λxz

partial with respect to z: 0 = 2x+2y +λxy

partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

λ = (y +2z)/(yz) = 1/z +2/y

λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

1/z +2/y = 1/z +2/x ⇒ x = y

The third equation then tells us ...

λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

1/z +2y = 2/x +2/y ⇒ z = x/2

This is the result we started the answer with:

x = y = 2z = ∛(2·8788 cm³)

7 0

2 years ago