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3 years ago

Find all possible values of k so that x^2 + kx - 32 can be factored.

Mathematics

1 answer:

daser333 [38]3 years ago

8 0

Answer:

Step-by-step explanation:

The posssible factors are

x^2 + 4x - 32

(x+8)(x-4)

x^2+ 14x - 32

(x+16)(x-2)

(x+32)(x-1)

x^2+31x-32

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Agustín fabrica artículos de cuero y los vende con un incremento del 8% de su costo. Si en su última campaña utilizó un cuero de

nadezda [96]

Answer:

El aumento del precio de costo único equivalente es un aumento del 20,96% en el precio de costo

Step-by-step explanation:

Los parámetros dados son;

El porcentaje de aumento en el precio de costo que Augustin vende artículos de cuero = 8%

El aumento adicional de Augustin se aplica cuando usó cuero de mayor calidad = 12%

Sea x el precio de costo

Tenemos, el primer precio de venta = 1.08 × x

El precio de venta del cuero de alta calidad = 12% adicional al precio de venta anterior

∴ El precio de venta del cuero de alta calidad = 1,12 × 1,08 × x = 1,2096 × x

Por lo tanto, el precio de venta del cuero de alta calidad = (1.2096 × 100)% de x = 120.96% de x, lo que da;

El aumento del precio de costo único equivalente = (120,96% - 100%) aumento en x = 20,96%

∴ El aumento del precio de costo único equivalente = 20,96% de aumento en el precio de costo.

6 0

2 years ago

Jia is skipping a rock across a pond. The sequence {4.2, 3.57, 3.0345, 2.5793, …} describes the height of the rock on each succe

mylen [45]

Answer:

$u_n=4.2(0.85)^{n-1}$

Step-by-step explanation:

$u_1=4.2\\u_2=3.57\\u_3=3.0345\\u_4=2.5793$

Geometric formula sequence: $u_n=ar^{(n-1)}$

(where $a$ is the first term of the sequence and $r$ is the common ratio)

To find the common ratio, divide one of the terms by the previous term:

$r=\frac{u_2}{u_1} =\frac{3.57}{4.2} =0.85$

From inspection, $a=4.2$

Therefore, $u_n=4.2(0.85)^{n-1}$

8 0

1 year ago

Read 2 more answers

How do you do the number line of this question why do we need to flip the inequality

Phantasy [73]

I don't see an inequality, but I can tell you that the sign of the inequality is flipped whenever you multiply or divide by a negative number.

8 0

3 years ago

( x + 2 )^2 - ( y + 2 )^2

GarryVolchara [31]

The difference of two squares factoring pattern states that a difference of two squares can be factored as follows:

$a^2-b^2 = (a+b)(a-b)$

So, whenever you recognize the two terms of a subtraction to be two squares, you can factor it as the sum of the roots multiplied by the difference of the roots.

In this case, the squares are obvious: $(x+2)^2$ is the square of $x+2$ , and $(y+2)^2$ is the square of $y+2$

So, we can factor the expression as

$(x+2)^2 - (y+2)^2 = [(x+2)+(y+2)] - [(x+2)+(y+2)]$

(the round parenthesis aren't necessary, I used them only to make clear the two terms)

We can simplify the expression summing like terms:

$(x+2)^2 - (y+2)^2 = [(x+2)+(y+2)][(x+2)-(y+2)] = (x+y+4)(x-y)$

3 0

2 years ago

Find values of  that satisfy the equation for 0º    360º and 0  θ  2 . Give answers in degrees and radians.

suter [353]

Answer:

$\theta = 30^\circ, 330^\circ$

$\theta = \frac{\pi}{6}, \frac{11\pi}{6}$

Step-by-step explanation:

Given [Missing from the question]

Equation:

$cos\theta = \frac{\sqrt 3}{2}$

Interval:

$0 \le \theta \le 360$

$0 \le \theta \le 2\pi$

Required

Determine the values of $\theta$

The given expression:

$cos\theta = \frac{\sqrt 3}{2}$

... shows that the value of $\theta$ is positive

The cosine of an angle has positive values in the first and the fourth quadrants.

So, we have:

$cos\theta = \frac{\sqrt 3}{2}$

Take arccos of both sides

$\theta = cos^{-1}(\frac{\sqrt 3}{2})$

$\theta = 30$ --- In the first quadrant

In the fourth quadrant, the value is:

$\theta = 360 -30$

$\theta = 330$

So, the values of $\theta$ in degrees are:

$\theta = 30^\circ, 330^\circ$

Convert to radians (Multiply both angles by $\pi/180$ )

So, we have:

$\theta = \frac{30 * \pi}{180}, \frac{330 * \pi}{180}$

$\theta = \frac{\pi}{6}, \frac{33 * \pi}{18}$

$\theta = \frac{\pi}{6}, \frac{11 * \pi}{6}$

$\theta = \frac{\pi}{6}, \frac{11\pi}{6}$

8 0

2 years ago