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2 years ago

Solve each equation 3x^2=80

Mathematics

1 answer:

Lapatulllka [165]2 years ago

5 0

Answer:

$x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}$

$x = \frac{\pm4\sqrt{15}}{3}$

Step-by-step explanation:

Hello!

Use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

First, let's convert our equation to standard form of a Quadratic: ax² + bx + c = 0

3x² = 80

3x² - 80 = 0

Note, thats the value of b will be 0, as there is no "bx"

Now, solve:

$x = \frac{-(0) \pm \sqrt{(0)^2 - 4(3)(-80)}}{2(3)}$ Plug in values
$x = \frac{\pm\sqrt{960}}{6}$ Simplify the radical (Discriminant)
$x = \frac{\pm8\sqrt{15}}{6}$ Pull out perfect squares
$x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}$ Reduce factors

The solutions are $x = \frac{4\sqrt{15}}{3}, x = \frac{-4\sqrt{15}}{3}$

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Cidnee is weighing combinations of geometric solids. She found that 4 cylinders and 5 prisms weigh 32 ounces and that 1 cylinder

vitfil [10]

Answer:

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

Step-by-step explanation:

Let be $x$ and $y$ the masses of a cylinder and a prism, measured in ounces, respectively. After a careful reading of the statement we get the following linear equations by interpretation:

i) <em>She found that 4 cylinders and 5 prisms weigh 32 ounces:</em>

$4\cdot x +5\cdot y = 32\,oz$ (Eq. 1)

ii) <em>And that 1 cylinder and 8 prisms weigh 35 ounces:</em>

$x + 8\cdot y = 35\,oz$ (Eq. 2)

Now we solve the system of linear equations algebraically:

From (Eq. 2):

$x = 35 - 8\cdot y$

(Eq. 2) is (Eq. 1):

$4\cdot (35-8\cdot y) + 5\cdot y = 32$

$140-32\cdot y +5\cdot y = 32$

$32\cdot y - 5\cdot y = 140-32$

$27\cdot y = 108$

$y = 4\,oz$

From (Eq. 2):

$x = 35 - 8\cdot (4)$

$x = 35 - 32$

$x = 3\,oz$

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

4 0

2 years ago

Factoring trinomials

Tcecarenko [31]

$c^2$ $2c^2 + 13c +21 \\4c^2 + 13(2)c + 42\\(2c + 6)(2c+7)\\(c+3)(2c+7)$

This is a way to factoring trinomials (there exist different equivalent methods).

Multiply the trinomial but the term accompanying $c^2$ . This is the second line. Then, you could take the square of the $4c^2$ , ant try to create a factor () () that will correspond to the expression in the second line. That is, we want $4c^2 + 13(2) c + 42 = (2c + ?) (2c + ?)$

In ? we put the corresponding numbers that, if we multiply them we will obtain 42, and if we add them we will obtain 13. This numbers are 6 and 7. Then, we have $(2c + 6) (2c +7)$