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3 years ago

The area of a rectangular computer screen is 4x^2+20x+16. The width of the screen is 2x+8. What is the length of the screen?

1 answer:

7 0

So the area of a rectangle is Length x Width.
A = (L)(W)
Substitute the information given:
4x^2 + 20x + 16 = (L)(2x+8)
Isolate L by dividing 2x+8:
(4x^2 + 20x +16)/ (2x + 8) = L
If you divide:
L = 2x + 2.

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Find the equation of the line that passes through point (6, 1) with the x-intercept of 2.

34kurt

Answer:

○ $y = \frac{1}{4}x - \frac{1}{2}$

Step-by-step explanation:

To find the equation of the line, let's first consider the points whose coordinates we have been given:

• (6, 1)

• (2, 0).

The point (2, 0) is what is called the x-intercept, which is the point where the line crosses the x-axis. This means that at this point, the y-coordinate of the line is 0.

Next, let's calculate the slope (gradient) of the line using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

where:

m = gradient,

$(x_2, y_2)$ and $(x_1, x_2)$ = points on the line.

Using the formula:

$m = \frac{1 - 0}{6 - 2}$

⇒ $m =\bf \frac{1}{4}$

Finally, now that we have two points on the line as well as the line's slope, we can use the following formula to find the equation of the line:

$\boxed{y - y_1 = m(x - x_1)}$

You can use any of the points on the line as $y_1$ and $x_1$ .

Using (2, 0):

$y - 0 = \frac{1}{4}( x - 2)$

⇒ $y = \frac{1}{4}x - \frac{1}{2}$

Therefore the equation of the line is $y = \frac{1}{4}x - \frac{1}{2}$ .

Learn more about point-slope form at:

brainly.com/question/15143525

6 0

1 year ago

When a bactericide is added to a nutrient broth in which bacteria are growing, the bacteria population continues to grow for a

baherus [9]

Answer:

a) 1296 bacteria per hour

b) 0 bacteria per hour

c) -1296 bacteria per hour

Step-by-step explanation:

We are given the following information in the question:

The size of the population at time t is given by:

$b(t) = 9^6 + 6^4t-6^3t^2$

We differentiate the given function.

Thus, the growth rate is given by:

$\displaystyle\frac{db(t)}{dt} = \frac{d}{dt}(9^6 + 6^4t-6^3t^2)\\\\= 6^4-2(6^3)t$

a) Growth rates at t = 0 hours

$\displaystyle\frac{db(t)}{dt} \bigg|_{t=0}= 6^4-2(6^3)(0) = 1296\text{ bacteria per hour}$

b) Growth rates at t = 3 hours

$\displaystyle\frac{db(t)}{dt} \bigg|_{t=3}= 6^4-2(6^3)(3) = 0\text{ bacteria per hour}$

c) Growth rates at t = 6 hours

$\displaystyle\frac{db(t)}{dt} \bigg|_{t=6}= 6^4-2(6^3)(6) = -1296\text{ bacteria per hour}$

3 0

3 years ago

Question is in the image, thank you

Alex787 [66]

sin H = Opposite / Hypotenuse

sin H = 5/13

sin H = 0.384615

<H = 22.6198

<H = 23 (nearest degree)

Answer is first one.

6 0

3 years ago

A mountain road drops 5.2 m for every 22.5 m of the road. Calculate the angle at which the road is inclined to the horizontal.

Anastasy [175]

Answer:

13°

Step-by-step explanation:

sin(Ф)= opposite/ hypothenuse

sin(Ф) = 5.2/22.5

Ф= sin∧-1 (5.2/22.5)

Ф= 13.36°

8 0

2 years ago

Attempting to save enough money to buy a car, the summer job will have to come before fun with friends. Which error does the sen

kumpel [21]

The right answer for the question that is being asked and shown above is that: "C. squinting modifier." Attempting to save enough money to buy a car, the summer job will have to come before fun with friends. The error does the sentence above make is that squinting modifier.

6 0

2 years ago