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3 years ago

Find the area of the composite shape

Mathematics

1 answer:

Contact [7]3 years ago

4 0

Answer:

Step-by-step explanation:

We can simply subtract the area of the small square from the area of the rectangle

A=8(12)-4(4)

A=96-16

A=80cm^2

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Given the equation of a line y = 5x -16, what is the slope of a line PERPENDICULAR to this line?

Doss [256]

Answer:

$-\frac{1}{5}$

Step-by-step explanation:

Notice that the equation y = 5x - 16 is in slope-intercept form, or $y = mx + b$ format. Whenever an equation is in slope-intercept form, the number in place of the $m$ , or the coefficient of the x-term, represents the slope of that line. So, the slope of the given line is 5.

Slopes that are perpendicular to each other are opposite reciprocals. So, we need to find the opposite reciprocal of 5. To do that, write it as a fraction, making it $\frac{5}{1}$ . Then, switch the sign and flip the numerator and denominator. This means that the opposite reciprocal of 5 is $-\frac{1}{5}$ , so $-\frac{1}{5}$ is the perpendicular slope.

3 0

3 years ago

The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. Management projects that the profit per

Mekhanik [1.2K]

Answer:

850

Step-by-step explanation:

Current profit per year = $ 20

Number of subscribers = 3000

For each additional subscriber over 3000, the profit will increase by 1 cent or by $ 0.01. For example, for 3001 (3000 + 1) subscribers, the profit will be $ 20.01 per year. Similarly, for 3002 (3000 + 2) subscribers, the profit will be $20.02 per year and so on.

So, for x additional subscribers over 3000, the profit will increase by 0.01(x). i.e. for (3000 + x) subscribers, the profit will be $(20 + 0.01x)

Since, profit per each subscriber is $(20 + 0.01x), the profit for (3000 + x) subscribers will be:

Total profit = Number of subscribers x Profit per each subscriber

Total profit = (3000 + x)(20 + 0.01x)

We want to calculate how many subscribers will be needed to bring a profit of $109,725. So, we replace Total profit by $109,725. The equation now becomes:

$109725=(3000+x)(20+0.01x)\\\\ 109725=60000+30x+20x+0.01x^{2}\\\\ 0.01x^{2}+50x+60000-109725=0\\\\ 0.01x^{2}+50x-49725=0\\$

Using quadratic formula, we can solve this equation as:

$\\ x=\frac{-50 \pm \sqrt{50^{2}-4(0.01)(-49725)}}{2(0.01)}\\\\ x=\frac{-50 \pm67}{0.02}\\\\ x=\frac{-50-67}{0.02} , x=\frac{-50+67}{0.02}\\\\ x=-5850, x=850$

x = -5850 is not a possible solution as this would make the total number of subscribers to be negative. So we reject this value.

Therefore, the answer to this question is 850. 850 more subscribers are needed to being a total profit of $109,725

8 0

4 years ago

Solve the equation 2x + 10 = 30.

Morgarella [4.7K]

Answer:

X=10

Step-by-step explanation:

1. Subtract 10 from both sides

2. Simplify

3. Divide both sides by the same factor

4. Simplify

4 0

2 years ago

Read 2 more answers

Work out :32.4(0.2+2.2)0.8<br>

Firdavs [7]

Step-by-step explanation:

hope it is helpful to you

6 0

3 years ago

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Which transformations are needed to change the parent cosine function to the cosine function below?

Otrada [13]

Question:

1. vertical stretch of 2, horizontal stretch to a period of 2 pi, phase shift of StartFraction pi Over 2 EndFraction units to the right, vertical shift of 1 unit up

2. vertical compression of 2, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the left, vertical shift of 2 units down

3. vertical compression of 2, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 3 EndFraction units to the left, vertical shift of 1 unit down

4. vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down

Answer:

The correct option is;

4. Vertical stretch of 2, horizontal compression to a period of π/2, phase shift of π units to the right, vertical shift of 1 unit down

Step-by-step explanation:

Here, we have the parent cosine function given by y = cos(x)

A plot of the above function is attached

By comparison, it is observed that the transformation required to change the parent function includes;

1. Vertical stretch from the parent function of amplitude 1 to amplitude 2

2. A horizontal compression so that the period of one complete revolution is π/2 rather than 2·π in the parent cosine function

3. Phase shift of pi units to the right such that cos(π) = 1 rather than cos(2π) = 1 as it applies to the parent function

4. Shift of the y values from the symmetrical x-axis origin downwards by 1 unit such that the maximum y value of the doubly stretched transformation is 1 rather than 2

5 0

4 years ago

Read 2 more answers