Vertex A in quadrilateral ABCD lies at (-3, 2). If you rotate ABCD 180° clockwise about the origin, what will be the coordinates of A′ of the rotated quadrilateral A′B′C′D′?

Let us say that:

x = width of walkway

So the area is:

(12 + 2x) (15 + 2x) = 238

2x because we must add x on both sides of length and width

Expanding:

180 + 24x + 30x + 4x^2 = 238

4x^2 + 54x = 58

By completing the square:

x^2 + 13.5x + 45.5625 = 60.0625

(x + 6.75)^2 = 60.0625

x + 6.75 = ±7.75

x = -14.5, 1

Since dimension cannot be negative, therefore:

width = 1 ft

Final answer:

The width of the walkway around the garden is 3.87 ft.

Explanation:

The width of the walkway around the garden can be found by subtracting the area of the garden from the total area of the garden with the walkway.

To find the length (l) of a rectangle in terms of the perimeter (p) and width (w), use the formula l = (p - 2w) / 2.

To find the length (l) of a rectangle in terms of the perimeter (p) and width (w), we can use the formula for the perimeter of a rectangle, which is given by:

p = 2l + 2w

Now, solve the equation for l by subtracting 2w from both sides:

p - 2w = 2l

Finally, divide both sides by 2:

l = (p - 2w) / 2

area of a circle = PI x r^2

r = 8.4/2 = 4.2

using 3.14 for PI

 area = 3.14 x 4.2^2 = 55.3896 square cm

 round answer as needed

divide 72.9 by 2.7

72.9 / 2.7 = 27 miles per gallon

Answer:

27 mi/gal

Step-by-step explanation:

The car mileage refers to the number of miles that a vehicle can run per gallon of fuel. A higher car mileage is desirable because it means that the vehicle has a better performance (travels more distance per gallon of fuel.) A driver uses 2.7 gallons of gasoline to drive her car 72.9 miles. The car mileage is:

72.9 miles / 2.7 gallon = 27 miles/gallon

The car can travel 27 miles per gallon of gasoline.

The area of the enlarged figure will be 327.68 square units

The scale factor will be the ratio of the similar sides of a rectangle.

For the given triangles, the required scale factors will be expressed as:

[tex]\frac{4}{8} =\frac{a}{25.6}\\\frac{1}{2} =\frac{a}{25.6}\\2a = 25.6\\a=\frac{25.6}{2} \\a=12.8[/tex]

Next is to get the area of the bigger rectangle:

[tex]Area = Length \times Width\\Area=a\times 25.6\\Area=12.8\times 25.6\\Area=327.68 units^2[/tex]

Hence the area of the enlarged figure will be 327.68 square units

Learn more here: https://brainly.com/question/21067938

the answer is x=9

i'm not good at showing my work, but I'm positive in my answer I'm an honors student.

Answer: The answer is [tex]\cos \theta=\dfrac{\sqrt{7}}{4}.[/tex]

Step-by-step explanation:  Given that

[tex]\sin \theta=\dfrac{3}{4}[/tex] and [tex]\theta[/tex] is in Quadrant I.

We are to find the value of [tex]\cos \theta.[/tex]

We have the following trigonometric identity :

[tex]\sin^2\theta+\cos^2\theta=1\\\\\Rightarrow \cos^2\theta=1-\sin^2\theta\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\sin^2\theta}\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)^2}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\dfrac{9}{16}}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{\dfrac{7}{16}}\\\\\\\Rightarrow \cos \theta=\pm\dfrac{\sqrt{7}}{4}.[/tex]

Since [tex]\theta[/tex] lies in the first quadrant, so cosine of [tex]\theta[/tex] will be positive.

Thus,

[tex]\cos \theta=\dfrac{\sqrt{7}}{4}.[/tex]

1/5(15x-20) = 1/3(12x-9)

multiply the 15 and 20 on the left by 1/5 to get

3x-4

 now multiply 12 and 9 by 1/3 to get

4x-3

 now you have 3x-4 =4x-3

now solve for x

3x-4 =4x-3

subtract 3 x from each side:

-4 = x-3

 add 3 to each side

-1 = x

x = -1

Probability of an event is the measure of its chance of occurrence. The probability that of 5 delivered chips, exactly 2 will fail is 0.003764768 or approx 0.0004

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

For the given case, as failing or working of chips usually doesn't depend on other chips' working condition, so they're independent(assuming). There are two cases for each chip's working(random experiment) that it is either working or failed.

If we take Success of the considered binomial experiment(working status of chip) = Chip working fine

Then, as per given data, we have

P(chip working fine ) = 1  - P(chip not working) = 1 - 0.02 = 0.98 = Probability of success in Bernoulli experiment (chip's working status).

There are n = 5 chips, p = probability of success = 0.98, q = 1-p = 0.02

If we take X = number of chips of of 5 chips working, then:

[tex]X \sim B(n = 5, p = 0.98)[/tex]

Then, the needed probability is P(Exactly two chips fail) = P(Exactly 5-2 = 3 chips work) = P(X  = 3)

And thus,  the needed probability is calculated as:

[tex]P(X = 3) = \: ^5C_3(0.98)^3(0.02)^2 = \dfrac{5.4.3}{3.2.1} \times 0.941192 \times 0.0004 = 0.003764768[/tex]

(using the probability mass function of binomial distribution).

Thus, the probability that of 5 delivered chips, exactly 2 will fail is 0.003764768 or approx 0.0004

Learn more about binomial distribution here:

https://brainly.com/question/13609688