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2 years ago

Consider 8x2 - 48x = -104. Write the equation so that x2 – 6x + (blank) = –13 + (blank)

Mathematics

2 answers:

Monica [59]2 years ago

5 0

Answer:

That (blank) is 9.

Step-by-step explanation:

Please write 8x^2 - 48x = -104, with " ^ " indicating exponentiation. Thanks.

This sounds like a perfect example of "completing the square."

First, factor 8x^2 - 48x = -104: 8(x^2 - 6x = -13).

If we focus SOLELY on x^2 - 6x = -13, it's just a little easier to "complete the square." Take half of the coefficient of x (which here is -6), and square that result (which here is (-3)^2, or 9. Now add 9 both sides of x^2 - 6x = -13:

x^2 - 6x + 9 = -13 + 9. Note: The "blank" in the problem statement is 9.

We could go ahead and solve this, tho' we weren't asked to do so. Rewrite x^2 - 6x + 9 as (x - 3)^2:

x^2 - 6x = -13 then becomes (x - 3)^2 = 4. To solve for x, take the sqrt of both sides of this latest result, obtaining x - 3 = plus or minus 2. Add 3 to both sides to isolate x: x = 3 plus or minus 2.

Thus, x = 5 or x = 1.

elena-14-01-66 [18.8K]2 years ago

4 0

Write the equation so that:

-6 and -13

Complete the square:

9 and 9

Hope this helps for Edg.

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An art club sells 42 large candles and 56 small candle price of large candle is $10 the cost is $x a small candles cost $5 and c

balandron [24]

Answer:

Profit = $(700 - 42x - 56y)

Step-by-step explanation:

For large candles, the selling price is $10 and its making cost is $x.

So, by selling a large candle the profit is $(10 - x)

Again for small candles, the selling price is $5 and its making cost is $y.

So, by selling a small candle the profit is $(5 - y)

Therefore, in a sell of 42 large candles and 56 small candles the total profit will be, P = 42 (10 - x) + 56 (5 - y)

⇒ P = 420 - 42x + 280 - 56y {Applying distributive property}

⇒ P = $(700 - 42x - 56y) (Answer)

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2 years ago

You are given a graph that models a ball being thrown in the air. The vertical axis is the height of the ball from the ground an

aalyn [17]

The graph is going to be all three, because when you throw the ball it goes higher, then constant, then comes back down. It has a maximum point because you can only throw the ball so high up, then it starts to come back down.

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2 years ago

Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.

Elena-2011 [213]

Given:

The length of the segment of the chord DB is 8.2 units.

The length of the segment AB is 6.9 units.

The length of the radius AC be x units.

We need to determine the value of x.

Length of BC:

Since, we know the property that, "if a radius is perpendicular to the chord, then it bisects the chord".

Thus, applying the above property, we have;

DB ≅ BC

8.2 = BC

Thus, the length of BC is 8.2 units.

Value of x:

Since, ∠B makes 90°, let us apply the Pythagorean theorem to determine the value of x.

Thus, we have;

$AC^2=AB^2+BC^2$

Substituting the values, we have;

$x^2=6.9^2+8.2^2$

$x^2=47.61+67.24$

$x^{2} =114.85$

$x=10.7$

Thus, the value of x is 10.7 units.

Hence, Option A is the correct answer.

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2 years ago

If i leave my house at 6:52 am and run 1 mile at an easy pace (8:15 per mile), then 3 miles at tempo (7:12 per mile) and 1 mile

FinnZ [79.3K]

Running 2 miles at 8:15 per mile takes 16:30 minutes.

Running 3 miles at 7:12 per mile takes 21:36 minutes.

The total running time is 16:30 + 21:36 = 38:06 minutes. That length of time after 6:52 am is 7:30:06 am.

You get home for breakfast at 6 seconds past 7:30 am.

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2 years ago

15) Bob has 12 black pen, 14 red pen, 15 green pens, 24 blue pens and 3 boxes of

cricket20 [7]

Answer:

13, 16, 18

Step-by-step explanation:

Sabemos que podemos calcular el total de plumas amarillos, por medio de la media.

16 = (12 + 14 + 15 + 24 + x + y + z) / 7

16 * 7 = 12 + 14 + 15 + 24 + x + y + z

112 = 65 + x + y + z

x + y + z = 112-65

x + y + z = 47

sabemos que la mediana es el valor medio, y que ese 46 debe dividirse entre 3 valores porque son 3 cajas, entonces debemos buscar los números adecuados para el valor 15 esté en la mitad, es decir de cuarto.

Sin meter los valores nuevos, el ranking sería así:

el 15 esta de tercero, para que quede de cuarto, debe tener dos valores por debajo y un por arriba, así:

Por lo tanto, valores mayores a 15 serían por ejemplo y = 16 y z = 18:

16 + 18 = 34

x = 47-34 = 13

quedaría:

dieciséis

18 años

Si recalculamos la media:

m = (12 + 14 + 15 + 24 + 13 + 16 + 18) / 7 = 16

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2 years ago