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4 years ago

What are two steps are necessary to put this equation into standard form x^2 - 3x + 27 =8x- 3

Mathematics

1 answer:

Wittaler [7]4 years ago

7 0

Answer:

you need to bring the 8x over then the -3

Step-by-step explanation:

X^2-3x+27=8x-3

X^2-11x+27=-3

x^2-11x+24

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Derivative of 4pi(r)^3 = 12pi(r)^2

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3 years ago

Given A = 1 /2 (b1 + b2)h, solve for h.

Tatiana [17]

Answer: b: h=2a/b1+b2

Step-by-step explanation:

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3 years ago

In 25 words or fewer, is this solution reasonable? Why or why not?

Julli [10]

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3 years ago

The hypotenuse of a right triangle is 6 cm and one side is 2 cm longer than the other side. Find the length of each side to one

MA_775_DIABLO [31]

Answer:

The two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

Step-by-step explanation:

Let x be one leg of the right triangle.

Since the other leg is two centimeters longer, it can be represented by the expression:

$x + 2 \text{ cm}$

According to the Pythagorean Theorem, for a right triangle:

$a^2 + b^2 = c^2$

Where c is the hypotenuse and a and b are the two legs.

The hypotenuse is given to be 6 cm and the two legs are x and (x + 2). Hence:

$(x)^2 + (x+2)^2 = 6^2$

Solve for x. Simplify:

$x^2 + (x^2 + 4x + 4) = 36$

Simplify:

$2x^2 + 4x + 4 = 36$

Subtract:

$2x^2 + 4x - 32 =0$

Divide:

$x^2 + 2x - 16 = 0$

The equation is not factorable, so we can consider using the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}$

In this case, a = 1, b = 2, and c = -16. Substitute:

$\displaystyle x= \frac{-(2)\pm\sqrt{(2)^2-4(1)(-16)}}{2(1)}$

And evaluate:

$\displaystyle \begin{aligned}x &= \frac{-2\pm\sqrt{68}}{2} \\ \\ &= \frac{-2\pm\sqrt{4\cdot 17}}{2} \\ \\ &= \frac{-2\pm2\sqrt{17}}{2} \\ \\ &= -1 \pm \sqrt{17} \end{aligned}$

Hence, our two solutions are:

$\displaystyle x = -1 + \sqrt{17} \approx 3.1\text{ or } x = -1 - \sqrt{17} \approx -5.1$

Lengths cannot be negative, so we can ignore the second solution.

Hence, the value of x or the first side length is about 3.1 centimeters.

Since the other side length is two centimeters longer, the other side is about 5.1 centimeters.

In conclusion, the two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

4 0

3 years ago

tavon has a $15 gift card that lose $3 for 30- day period It is not used. he has a $40 that loses $1.50 for each day period it i

Anna11 [10]

The number of 30- period until the value if the give card be equal is 20 30- day period

<h3>How to write and solve equation</h3>

let

Number of 30- day period = x

Card 1:

50 - 2x

Card 2:

40 - 1.50x

50 - 2x = 40 - 1.50x

50 - 40 = -1.50x + 2x

10 = 0.50x

divide both sides by 0.50

x = 10/0.50

x = 20

In conclusion, it will take 20 30- day period until the value of the given card can be equal.

Complete question:

Tavon has a $50 gift card that loses $2 for each 30-day period it is not used. He has a $40 card that loses $1.50 for each 30-day period it is not used.