Solve: 3x-3y=3
y=-5x-17

The solutions of the given system of equations: y = x2 – 7x + 16 and y = x - 1 is 4 + i and 4 - i.

A quadratic equation in the variable x is an equation of the form

ax² + bx + c= 0, where a, b, c are real numbers, a * 0.

Given equations are:

y= x²-7x+16 and y=x-1

So, x-1= x²-7x+16

or, x²-8x+17=0

or, x²-8x+17  =0

a=1, b=-8, c=17

Using discriminant method,

x= [tex]-b\pm\sqrt{b^{2}-4ac } /2a[/tex]

x= -(-8) ± [√(-8)²- 4*1*17]/2*1

x=8±√(√64-68)/2

x= 8±√(-4)/2

x= 4 ± i

x= 4 + i and x= 4 - i

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Answer is 483,542

Compound Interest:

The formula for compound interest is   [tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]

where P is the principal balance

r is the interest rate

n is the number of times interest is compounded per time period.

t is the number of time periods.

(Given),

P = 320,000

n = 1

t = 12

r = 3.5% = 3.5 / 100 = 0.035

[tex]A = 320,000 (1 + 0.035)^{12}[/tex]

[tex]A = 320000(1.035)^{12}[/tex]

A = 483,541.970 (approx)

A = 483,542 (Rounded to the nearest whole number).

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Various factors cause the disappearance of animals in the wild, including habitat destruction, hunting, disease, and changes in predator-prey relationships.

The disappearance of animals in the wild can be caused by various factors, including habitat destruction, hunting, disease, and changes in predator-prey relationships. One of the main factors is habitat destruction, which occurs when natural habitats are altered or destroyed by human activities such as farming, logging, and construction. This leads to a loss of biodiversity as plant and animal populations are destroyed or displaced.

Hunting is another major cause of animal disappearance. Animals are hunted for various purposes including meat, hides, and horns. Large mammals are particularly vulnerable as they are often targeted for their valuable resources. In addition, diseases can spread among animals due to human activities, such as the introduction of domestic animals, leading to population declines and even extinctions.

Changes in predator-prey relationships can also affect animal populations. For example, the decline of predators like cougars, lions, and leopards can result in an increase in the prey population. This can lead to changes in vegetation, stream paths, and overall biodiversity.

The length of the escalator is approximately 180 feet.

To find the length of the escalator, we can use trigonometry. The vertical distance traveled by the escalator is given as 90 feet and the angle it makes with the ground is 30°.

Using the sine function, we can determine the length of the escalator:

Length of escalator = Vertical distance traveled / sin(angle)

Therefore, the length of the escalator is:

Length of escalator = 90 feet / sin(30°)

Calculating the above expression, the length of the escalator is approximately 180 feet.

Final answer:

The length of the escalator is found using the cosine function for a 30° angle and a vertical height of 90 feet. The calculated length is approximately 77.94 feet.

Explanation:

The question asks how long an escalator is if it covers a vertical distance of 90 feet at a 30° angle with the ground. To find the length of the escalator, we can use trigonometric functions, specifically the cosine function, which relates the adjacent side (the length of the escalator) to the hypotenuse (the vertical height) in a right-angled triangle.

Using the formula:

cos(θ) = adjacent/hypotenuse

Where:

θ is the angle

'Adjacent' is the length of the escalator

'Hypotenuse' is the vertical height, which is 90 feet

To solve for the length (L) of the escalator:

cos(30°) = L / 90 feet

L = 90 feet * cos(30°)

L = 90 feet * (√3/2)

L = 45√3 feet

Or approximately L = 45 * 1.732 = 77.94 feet

Therefore, the length of the escalator is approximately 77.94 feet.

Answer:

Surface area is, 478 square centimeter

Step-by-step explanation:

Surface area (S)of rectangle is given by:

[tex]S = 2(lw+wh+hl)[/tex]                 .....[1]

where,

l is the length

w is the width

h is the height of the rectangle respectively.

As per the statement:

A rectangular solid has sides of 7 cm, 9 cm, and 11 cm

⇒ l = 7 cm , w = 9 cm and h = 11 cm

Substitute in [1] we have;

[tex]S = 2(7 \cdot 9+9 \cdot 11+11 \cdot 7)[/tex]

⇒[tex]S = 2(63+99+77) = 2 \cdot 239 = 478 cm^2[/tex]

Therefore, the surface area is, 478 square centimeter

The more boys than girls are signed up for camp are 22.

We have given that

Summer day camp is about to begin. Today there are 132 boys signed up and 219 total children signed up.

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign

Therefore for the girl

219-132 is the equation because the rest of the 219 comes from the girls who signed up.

219-132= 77.

To find how many more boys than girls signed up you need to subtract 77 from 132.

132-77= 55

Therefore the more boys than girls are signed up for camp are 22.

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The inverse function of f(x) = x^2 - 81 is found by swapping x and y in the original equation and solving for y, resulting in f^-1(x) = ±√(x + 81).

To find the inverse function f-1(x) of the function f(x) = x2 - 81, we need to swap the roles of x and y in the original function and solve for y, which represents f-1(x). Here are the steps:

The correct answer is option 1, ±√(x + 81).

Answer:

the answer is actually 3x - 0.03 = 0.75

Step-by-step explanation:

Since f(x) is an even function, the statement which is true is the graph of f(x) has a line of symmetry about the y-axis.

To answer the question, we need to know what an even function is.

An even function is a function f(x) such that f(x) = f(-x). That is f(x) is single valued for both positive and negative values of x.

Now, for an even function, since f(x) = f(-x), both positive and negative values of x give a single value of f(x).

For this to be true, the graph of f(x) is symmetric about the y-axis.

So, since f(x) is an even function, the statement which must be true is graph of f(x) has a line of symmetry about the y-axis.

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Answer:

The square root of -64 is 8i

Step-by-step explanation:

Given the number -64

we have to find the square root of the above number i.e [tex]\sqrt{-64}[/tex]

As

[tex]\sqrt{-64}=\sqrt{-8\times 8}[/tex]

[tex]=\sqrt{-(8)^2}[/tex]

[tex]=\sqrt{(-1)(8)^2}[/tex]

[tex]=\sqrt{-1}\sqrt{8^2}=8i[/tex]

Hence, the square root of -64 is 8i

To solve for x in the equation 6(x – 1) = 9(x + 2), expand and simplify the equation, combine like terms, isolate the variable x, and solve for x by dividing both sides by 3.

To solve for x in the equation 6(x – 1) = 9(x + 2), we can begin by expanding the equation:

6x - 6 = 9x + 18

Next, we can combine like terms by subtracting 6x from both sides:

-6 = 3x + 18

Then, we can isolate the variable x by subtracting 18 from both sides:

-24 = 3x

Finally, we can solve for x by dividing both sides by 3:

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Daniel can go on 14 rides at the fair.

To find out the greatest number of rides Daniel can go on, we need to calculate the cost of admission and the cost of the rides. The admission to the fair is $4 and each ride costs $1.50. To determine the number of rides, we subtract the cost of the admission from the total amount Daniel has to spend and then divide that by the cost of each ride. So, Daniel can go on (25 - 4) / 1.50 = 14 rides. Therefore, the greatest number of rides Daniel can go on is 14.

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Answer:

A. 50 − 2.5x = y

 40 − 2x = y

Step-by-step explanation:

We know that x represents the number of trips and y represents the amount remaining in each account, then, let's think in an example; after the first trip x = 1, therefore, Kaisorn's account must decrease from $50 to $50 - $2.5 = $47.5 = y, and Thom's account must decrease from $40 to $40 - $2 = $38 = y. Replacing x = 1 in each case gives:

A

50 − 2.5(1) = y

47.5 = y

   40 − 2(1) = y

   38 = y

B

50 + 2.5(1) = y

52.5 = y

 40 + 2(1) = y

 42 = y

C

50 − 2.5y = (1)

y = (1 - 50)/(-2.5)

y = 19.6

 40 − 2y = (1)

  y = (1 - 40)/(-2)

  y = 19.5

D

50 + 2.5y = (1)

y = (1 -50)/2.5

y = -19.6

 40 + 2y = (1)

 y = (1 - 40)/(2)

 y = -19.5

As it can be seen, option A is the correct one.

First, let's write 65% as a decimal. We can do this by moving the decimal point 2 places to the left. When we do this, we will get 0.65.

Next, the word of means "multiply" so we have to multiply 0.65 by 40.

(.65) × (40) = 26.00

To calculate 65 percent of 40, convert 65% to a decimal (0.65) and then multiply by 40 to get the answer, which is 26.

To find what 65 percent of 40 is, you can convert the percentage to a decimal and then multiply by the number. To convert a percentage to a decimal, divide it by 100. In this case, 65% becomes 0.65.

Next, multiply 0.65 by 40 to get the answer.

The calculation process looks like this:
0.65 (converted percentage) × 40 (the number) = 26

Therefore, 65 percent of 40 is 26.

Answer:

16.00

Step-by-step explanation:

80% of 20.00 is 16.00

Final answer:

To evaluate 10⁻⁷, it is understood as 1 divided by 10 to the seventh power, or 0.0000001. This notation is used in scientific measurements, for instance in expressing the hydronium ion concentration based on pH.

Explanation:

To evaluate 10⁻⁷, we must understand the notation of negative exponents.

10 raised to the power of -7 can be written as 1 divided by 10 raised to the power of 7:

10⁻⁷ = 1 / 10⁷

Since 10 raised to any positive power results in a large number, 10 raised to the power of 7 is a very large number (10,000,000). Dividing 1 by this large number is very close to zero:

1 / 10⁷≈ 0.000 000 1

Therefore, 10⁻⁷ is approximately equal to 0.000 000 1. This value is incredibly small, representing one divided by ten million.

This type of notation is commonly used in scientific measurements, such as expressing the concentration of hydrogen ions in a solution with a certain pH level.