HELPPPP

lan is on a hiking trail that goes north to south . If Ian hikes miles north, elevation, in feet, can be found using the function f(x) = (x + 2) ^ 2 + 150 . Negative values would find the elevation if Ian hiked south. Find and interpret the given function values and determine an appropriate domain for the function.

The value of length BC is 18.9

Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Therefore,

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

Therefore, the length of BC is 18.9

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In the triangle, the value of the side BC is 18.9cm to 1 decimal place

The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The cosine formula states that

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

In conclusion, the value of  the length of BC is 18.9cm

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69 ÷ 7 = 9 r6

hope it helps.

In the given function H(p) = p/5 + 15, the independent variable is "p" ,

The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.

It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.

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Answer:

y=-2/7x+1/7

Step-by-step explanation:

Find the slope first

-1-1/4+3

-2/7

m=-2/7

y=-2/7x+b

1=-2/7(-3)+b

b=1/7

First we have to do the summation in the parenthesis 7+1= Then we multiply 8 with 1 8x1=

Finally we have to sump up 8 with 12 =20

Answer:

y=2x -1

Step-by-step explanation:

Finding x-intercepts and y-intercepts

1-To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y.

2-To find the x-intercept, set y = 0 \displaystyle y=0 y=0.

3-To find the y-intercept, set x = 0 \displaystyle x=0 x=0.

Answer:

2x^2+x-10=0

Step-by-step explanation:

Answer:

Hi Amy it's don sorry about du mb ronny

Step-by-step explanation:

just bored without you :-'( see ya buttercup

Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

Answer:

Choice A. Draw a single line through the entry and write "error," including the date, time, and initials of the person correcting.

Step-by-step explanation:

Not sure why this is posted under mathematics but here is the answer:

According to the American Health Information Management Association(AHIMA), the proper method to correct a medical record is as follows:

The closest option to the above procedure is

A. Draw a single line through the entry and write "error," including the date, time, and initials of the person correcting.

This includes both date-time stamp and initials of person correcting for follow-up if necessary

Answer:

The answer is choice A. Draw a single line through the entry and write "error," including the date, time, and initials of the person correcting.

Answer:

80 in.²

Step-by-step explanation:

The total surface area of the pyramid is the sum of the area of the base and the areas of the 4 triangular sides.

Square: area = s²

Square: side = 4 in.

Triangular side: area = bh/2

Triangular side: base = 4 in.; height = 8 in.

Area of the base: s² = (4 in.)² = 16 in.²

Total area of the 4 triangular sides: 4 × bh/2 = 2bh = 2 × 4 in. × 8 in. = 64 in.²

Surface area = 16 in.² + 64 in.² = 80 in.²

Answer:

Below.

Step-by-step explanation:

Part A No. That's not the most specific shape.

Quadrilaterals  can be many shapes regular and irregular.

Part B. A rectangle and a rhombus are both types of parallelogram which has 2 pairs of parallel sides.  A rectangle and a rhombus are 2 specific types of parallelogram.

In the case of a rectangle it is a parallelogram with 4 right angles and a rhombus is a parallelogram with all sides equal in length,

The Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞) and Range: (-∞, 0) ∪ (0, ∞).

What is domain?

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

According to question:

In this case, the denominator of the function is a quadratic expression, and we know that dividing by zero is undefined. Therefore, we need to find the values of x that make the denominator equal to zero, and exclude those values from the domain.

To find the values that make the denominator equal to zero, we can factor it as follows:

x² - 3x - 18 = 0

(x - 6)(x + 3) = 0

So, the denominator is equal to zero when x = 6 or x = -3. Therefore, the domain of the function is all real numbers except x = 6 and x = -3.

Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞)

The range of a function consists of all possible output values of the function, given the domain of the function.

To find the range of this function, we need to analyze the behavior of the function as x approaches positive or negative infinity.

As x approaches positive infinity, both the numerator and denominator of the function approach positive infinity. Therefore, the function approaches zero.

As x approaches negative infinity, both the numerator and denominator of the function approach negative infinity. Therefore, the function approaches zero.

Since the function approaches zero as x approaches positive or negative infinity, we can say that the range of the function is all real numbers except zero.

Range: (-∞, 0) ∪ (0, ∞).

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Here, we want to use long division to find the result

We have this as follows;

We start by dividing 99 by 12

This gives 8 remainder 3

Now, as we all know, 3 cannot divide 12

So, what we do now is add zero at the back of 3 while we put a decimal point at the back of 8

Then we divide 30 by 12

This gives 2 remainder 6

Then finally, we add zero to the back of the 60 to leave us with 5

Thus, our answer is 8.25

Answer:

b

Step-by-step explanation:

Hannon's maximum allowable production cost for the All-Body swimsuit is $80 if it wants to make a profit of $20 per unit.

Given data ,

a)

Using cost-plus pricing, the selling price is set 20% above the costs.

Selling price=Costs+(Costs x Markup)

Selling price=$100 + ($100x0.20)

Selling price=$100+$20

On simplifying the equation , we get

Selling price=$120

The price charged for the All-Body swimsuit would be$120.

Hannon might consider manufacturing the All-Body swimsuit under the cost-plus pricing approach if the market demand is strong enough to justify the selling price of $120 and if Hannon can efficiently produce and sell the swimsuit to generate profits.

(b)

Using target costing, the price charged by Hannon to the retailer is determined by subtracting the desired profit per unit from the target selling price.

Target selling price=$100 (given)

Desired profit per unit=$20 (given)

Price charged to retailer=Target selling price - Desired profit per unit

Price charged to retailer=$100-$20

On simplifying the equation , we get

Price charged to retailer=$80

The price that Hannon would charge the retailer for the All-Body swimsuit under target costing is$80.

(c)

To determine the highest acceptable manufacturing cost for the All-Body swimsuit under target costing, we subtract the desired profit per unit from the target selling price.

Target selling price=$100 (given)

Desired profit per unit=$20 (given)

Highest acceptable manufacturing cost=Target selling price-Desired profit per unit

Highest acceptable manufacturing cost=$100-$20

Highest acceptable manufacturing cost=$80

Hannon would be ready to spend up to $80 in manufacturing costs to develop the All-Body swimsuit if it wanted to make $20 each unit.

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Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

Answer:

4, 3 is your answer according to the formula

Step-by-step explanation:

9514 1404 393

Answer:

  (c)  x = -7

Step-by-step explanation:

An angle is equal to the sum of the angles into which it is divided.

  ∠MLK = ∠MLP + ∠PLK

  164° = (x +31)° +(x +147)°

  164 = 2x +178 . . . . . . collect terms

  -14 = 2x . . . . . . . . . . . subtract 178

  -7 = x . . . . . . . . . . . . . divide by 2

The value of x in the secant intersection is 4.

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Therefore, let's find the value of x using the secant intersection theorem as follows;

4(4+x + 2) = 5(5 + x - 1)

4(6 + x) = 5(4 + x)

24 + 4x = 20 + 5x

24 - 20 = 5x - 4x

x = 4

Therefore,

x = 4

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Answer:

A right triangle is always an isosceles triangle.An equilateral triangle is never an obtuse triangle.

Answer:

A right triangle is always an isosceles triangle.

Step-by-step explanation:

After 2 hours, the second rescue worker finds the injured hiker and radios the first worker for help. The first worker arrives in approximately 28.5 minutes after jogging directly to the second worker at 6 mph.

We can start by finding the distances each worker covers in 2 hours.

For the first worker:

Distance = rate × time

Distance = 3.5 × 2 = 7 miles

For the second worker:

Distance = rate × time

Distance = 2.5 × 2 = 5 miles

Now we can use trigonometry to find the horizontal and vertical components of the first worker's displacement while walking:

Horizontal component = 7 × sin(25°) ≈ 3.01 miles

Vertical component = 7 × cos(25°) ≈ 6.30 miles

Similarly, we can find the horizontal and vertical components of the second worker's displacement:

Horizontal component = 5 × sin(54°) ≈ 4.07 miles

Vertical component = 5 × cos(54°) ≈ 3.62 miles

We can now find the horizontal and vertical components of the distance between the two workers:

Horizontal component = 3.01 - 4.07 ≈ -1.06 miles

Vertical component = 6.30 - 3.62 ≈ 2.68 miles

The distance between the two workers is the hypotenuse of a right triangle with these components as its legs:

Distance = √((-1.06)² + (2.68)²) ≈ 2.85 miles

Finally, we can find the time it takes for the first worker to cover this distance at 6 mi/h:

Time = Distance ÷ rate

Time = 2.85 ÷ 6 ≈ 0.475 hours or 28.5 minutes

Therefore, it will take the first worker about 28.5 minutes to arrive.

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Hello there. To solve this question, we'll need to remember some properties about polynomial functions.

Say we have f(x) = ax² + bx + c and g(x) = dx² + ex + h, for a, b, c, d, e, h constants and a, d not equal to zero.

Defining the sum (f + g)(x) = f(x) + g(x), we'll have to analyze each following case:

A) Degree of the sum

There are two possibilities. First, a and d have different absolute values, so for example they cannot cancel each other, getting rid of the second degree term of the function.

If a + d is not equal to zero, then the function will still be of degree two.

If a + d is equal to zero, the function can either be of the first or zero degree (a constant)

B) How many zero roots

We'll need to actually sum the functions to analyze the case:

(f + g)(x) = (a + d)x² + (b + e)x + (c + h)

The roots of this polynomial can be found by using the quadratic formula

(f + g)(x) = 0 for x = (-(b + e) + - sqrt((b + e)² - 4 (a + d) (c + h)))/(2(a + d))

If the expression in the square root is greater than zero, the function will have two distinct real roots.

If it is equal to zero, the function will have two equal real roots.

If it is less than zero, the function will not have real roots (they'll be two conjugate complex roots)

C) Let's say we have the functions f(x) = x² + x + 1 and g(x) = 2x² + 3x + 4

The sum function is (f + g)(x) = 3x² + 4x + 5

Plugging in those coefficients on the expression in the square root, we'll have:

4² - 4*3*5

16 - 60

- 44

As you can see, in this case, the expression will give us a negative number, which means that the sum function will have no real roots.

Answer:

B. -3(4x + 1) (x - 4)

Step-by-step explanation:

Out of the other answer choices, "B," is the only that factorizes correctly and ends up with the correct factorization (It already gives you the break-down of the trinomial).

However, if you're unsure about the answer, you can always take the end result: -3(4x + 1) (x - 4), and multiply it together to see if you can end up with the original trinomial: \(-12x^2 + 45x + 12\)

Answer:

Step-by-step explanation:

The Answer will be D hope this helps ya :)

The function representing the number of bacteria present each day is

\(\rm f(t) = 2032(0.85)^{t}\) .

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

The set X is called the domain of the function and the set Y is called the codomain of the function

A bacteria population starts at 2032 and decrease by 15% everyday.

a function representing the number of bacteria present each day

\(\rm f(t) = 2032(1-.15)^{t}\)

\(\rm f(t) = 2032(0.85)^{t}\)

Therefore \(\rm f(t) = 2032(0.85)^{t}\) is the correct answer .

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Let

\(\displaystyle f(x) = \sum_{n=2}^\infty \frac{x^n}{n^2(n^2-1) \binom{2n}n}\)

Differentiate and multiply by \(x\).

\(\displaystyle xf'(x) = \sum_{n=2}^\infty \frac{x^n}{n(n^2-1) \binom{2n}n}\)

Now differentiate twice.

\(\displaystyle x f''(x) + f'(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{(n^2-1)\binom{2n}n}\)

\(\displaystyle xf'''(x) + 2f''(x) = \sum_{n=2}^\infty \frac{x^{n-2}}{(n+1)\binom{2n}n}\)

Multiply by \(x^3\).

\(\displaystyle x^4 f'''(x) + 2x^3 f''(x) = \sum_{n=2}^\infty \frac{x^{n+1}}{(n+1)\binom{2n}n}\)

Differentiate one last time and multiply by \(\frac1x\).

\(\displaystyle x^3 f^{(4)}(x) + 6x^2 f'''(x) + 6x f''(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{\binom{2n}n}\)

Now integrate with the fundamental theorem of calculus, noting that \(f(0)=f'(0)=0\) follows from our series definition. We do this twice and make use of the recurrence

\(I_n = \displaystyle \int_0^x y^n f^{(n+1)}(y) \, dy = x^n f^{(n)}(x) - n I_{n-1}\)

Integrating once yields

\(\displaystyle x^3 f'''(x) + 3x^2 f''(x) = \sum_{n=2}^\infty \frac{x^n}{n \binom{2n}n}\)

Multiply by \(\frac1x\).

\(\displaystyle x^2 f'''(x) + 3x f''(x) = \sum_{n=2}^\infty \frac{x^{n-1}}{n \binom{2n}n}\)

Integrating once more yields the ordinary differential equation

\(\displaystyle x^2 f''(x) + x f'(x) - f(x) = \sum_{n=2}^\infty \frac{x^n}{n^2 \binom{2n}n}\)

and we recognize the right side as the series

\(\displaystyle \sum_{n=2}^\infty \frac{x^n}{n^2 \binom{2n}n} = 2\arcsin^2\left(\frac{\sqrt x}2\right) - \frac x2\)

Solving the differential equation is quite doable with the variation of parameters method; we ultimately find

\(\displaystyle f(x) = \frac12 + \frac{7x}8 - \left(\frac1x+\frac12\right) \sqrt x \sqrt{4-x} \, \arcsin\left(\frac{\sqrt x}2\right) + 2 \left(\frac1x-1\right) \arcsin^2\left(\frac{\sqrt x}2\right)\)

Recover the sum we want by letting \(x=-1\). Recall that

\(\arcsin(iz) = i \,\mathrm{arsinh}(z) = i\ln(z + \sqrt{1+z^2})\)

Then we have the following equivalent results involving our old friend \(\phi\).

\(\displaystyle f(-1) = -\frac38 - \frac{\sqrt5}2\, \mathrm{arsinh}\left(\frac12\right) + 4 \,\mathrm{arsinh}^2\left(\frac12\right) \\\\ f(-1) = -\frac38 - \frac{\sqrt5}2 \ln\left(\frac{1+\sqrt5}2\right) + 4 \ln^2\left(\frac{1+\sqrt5}2\right) \\\\ f(-1) = \boxed{-\frac38 - \left(\frac12 - \phi\right) \ln(\phi) + 4 \ln^2(\phi)}\)

Hi! Your answer is 11. When multiplying terms with exponents, the exponents add up.

Step-by-step explanation:

You want to multiply the terms with the exponents. You should get 3 and 8, add those up and you will get 11.

Hope this helps! Have a good day :)

Answer:

C

Step-by-step explanation:

Answer:

b=4

Step-by-step explanation:

\(a^{2}+b^{2}=c^{2}\)

\(3^{2}+b^{2}=5^{2}\)

\(9+b^{2}=25\)

\(b^{2}=16\)

\(\sqrt{b^{2}} = \sqrt{16}\)

b=4