-4x + 3y - x - 2y + y

Factor the following equation to find its zeros. y = x² - 36

alukav5142 [94]

Answer:

x = 6, x = - 6

Step-by-step explanation:

Given

y = x² - 36

To find the zeros let y = 0, that is

x² - 36 = 0 ← x² - 36 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 36 = 0

x² - 6² = 0

(x - 6)(x + 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 6 = 0 ⇒ x = - 6

3 0

3 years ago

Algebra 1 CR-8

antiseptic1488 [7]

$\mathrm{Domain\:of\:}\:x^2+2x-15\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

$\mathrm{Range\:of\:}x^2+2x-15:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:-16\:\\ \:\mathrm{Interval\:Notation:}&\:[-16,\:\infty \:)\end{bmatrix}$

$\mathrm{Axis\:interception\:points\:of}\:x^2+2x-15:\quad \mathrm{X\:Intercepts}:\:\left(3,\:0\right),\:\left(-5,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:-15\right)$

$\mathrm{Vertex\:of}\:x^2+2x-15:\quad \mathrm{Minimum}\space\left(-1,\:-16\right)$

4 0

2 years ago

Brass is an alloy of zinc and copper. if 30%of the content is zinc, find the weight of zinc and copper in 300 grams of brass if

Marina86 [1]

Answer:

Socratic app

Step-by-step explanation:

it will help you

8 0

3 years ago

Analysis of an accident scene indicates a car was traveling at a velocity of 69.5 mph (31.1 m/s) along the positive x-axis at th

STatiana [176]

We can find the acceleration via

${v_f}^2-{v_i}^2=2a\Delta x$

We have

$\left(5.20\dfrac{\rm m}{\rm s}\right)^2-\left(31.1\dfrac{\rm m}{\rm s}\right)^2=2a(115\,\mathrm m)$

$\implies\boxed{a=-4.09\dfrac{\rm m}{\mathrm s^2}}$

Then by definition of average acceleration,

$a_{\rm ave}=\dfrac{v_f-v_i}t$

so that

$-4.09\dfrac{\rm m}{\mathrm s^2}=\dfrac{5.20\frac{\rm m}{\rm s}-31.1\frac{\rm m}{\rm s}}t$

$\implies\boxed{t=6.33\,\mathrm s}$

We alternatively could have found the time without knowing the acceleration. Since acceleration is constant, the average velocity is

$v_{\rm ave}=\dfrac{x_f-x_i}t=\dfrac{v_f+v_i}2$

Then

$\dfrac{115\,\rm m}t=\dfrac{5.20\frac{\rm m}{\rm s}+31.1\frac{\rm m}{\rm s}}2$

$\implies\boxed{t=6.33\,\mathrm s}$

7 0

2 years ago

A certain region currently has wind farms capable of generating a total of 2500 megawatts (2.5 gigawatts) of power. Complete p

marishachu [46]

Answer:

The correct answer is A. 7,665'000,000 kilowatt-hours per year and B. 766,500 households.

Step-by-step explanation:

1. Let's review the information provided to us for solving the questions:

Power capacity of the wind farms = 2,500 Megawatts or 2.5 Gigawatts

2. Let's resolve the questions a and b:

Part A

Assuming wind farms typically generate 35% of their capacity, how much energy, in kilowatt-hours, can the region's wind farms generate in one year?

2,500 * 0.35 = 875 Megawatts

875 Megawatts = 875 * 1,000 Kilowatts = 875,000 Kilowatts

Now we calculate the amount of Kilowatts per hour, per day and per year:

875.000 Kw generated by the farms means that are capable of produce 875,000 kw per hour of energy

875,000 * 24 = 21'000,000 kilowatt-hours per day

21'000,000 * 365 = 7,665'000,000 kilowatt-hours per year

Part B

Given that the average household in the region uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by these wind farms?

For calculating the amount of households we divide the total amount of energy the wind farms can generate (7,665'000,000 kilowatt-hours) and we divide it by the average household consumption (10,000 kilowatt-hours)

Amount of households = 7,665'000,000/10,000 = 766,500

4 0

2 years ago