Gavin has $50,000 with which to start a new business. He wants to maintain a cash balance of more than $26,000. If w is the amount Gavin withdraws to pay for expenses, which of the following the inequalities represents this the maximum amount of money that he has to spend on expenses while keeping to his business plan? A. $26,000 > w B. $24,000 w D. $76,000 > w

3. 3 hope this will help you

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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After 18 years, the investment compounded periodically (quarterly) will be worth $1,230.23 more than the investment compounded annually.

Compounded interest refers to the interest system that charges interest on both principal and accumulated interest.

The period of compounding in a year determines the worth of the future value.

The future value can be ascertained using an online finance calculator as follows:

Interest periods: = 4 times yearly (Quarterly)

Principal = $5,000

Annual interest rate = 9%

Number of years: 18

N (# of periods) = 72 quarters (18 years x 4)

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $24,815.83

Total Interest = $19,815.83

Interest periods: = Annually

N (# of periods) = 18 years

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $23,585.60

Total Interest = $18,585.60

Difference in Future Values $1,230.23 ($24,815.83 - $23,585.60)

Thus, an investment compounded periodically earns more than an investment compounded annually.

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Answer: B

Step-by-step explanation:

\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)

\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)

Answer:

The answer to ur question should be, A Object A

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

The solution triangle attached below :

Since we have a right angled triangle, we can make use of Pythagoras rule to obtain the vertical distance, x

Recall :

Hypotenus² = opposite² + adjacent²

Hence,

x² = 61² - 60²

x² = 3721 - 3600

x² = 121

x = √121

x = 11

Vertical distance equals 11 inches

Answer:

\(y = {x}^{2} + 2x + 6 \\ y = {( - 1 + i)}^{2} \)

Answe

y=(x+1)2+5

Step-by-step explanation:

The equation's line that is steeper is y = 3x + 7

From the question, we are to determine which of the given equations' line is steeper

The given equations are

y = 3x + 7

and

y = (1/2)x + 9

First, we will compare the equations to the form of an equation of a straight line

The equation of a straight line is of the form

y = mx + c

Where m is the slope

and c is the y intercept

Thus,

The slope of the equation, y = 3x + 7, is 3

and

The slope of the equation, y = (1/2)x + 9, is 1/2

NOTE: The higher the slope of a line, the steeper the line

Hence, the equation's line that is steeper is y = 3x + 7

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Answer:

None

Step-by-step explanation:

The discriminant of a quadratic equation is \(b^2-4ac\). In this case, that is:

\((-4)^2-4(3)(9)=16-108=-92\)

Since the discriminant is negative, the square root will be a complex number, and this equation must have no real solutions. Hope this helps!

The line represent the amount of money in the line of the account will be x + y = 45.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Alina has $20 in her account she wants to purchase a purse, shoes that cost $45.

If the line makes the purchase, Then the line represent the amount of money in the line of the account will be

x + y = 45

where x be the price of purse and y be the price of shoe.

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Answer:

One bowl has 1 yellow, 1 red, and 2 green apples. The other bowl has 5 each of boysenberries, strawberries, blueberries, and blackberries.

Step-by-step explanation:

Answer:

The answer is described below.

Step-by-step explanation:

What we should do is follow the next four steps

1. Identify the geometric shape of the garden.

2. Consult various mathematical formulas available for the area and perimeter of different types of geometric shapes.

3. Use the formula according to the geometric shape of the garden.

4. Identify in the formula the values of the given dimensions to calculate the perimeter and area.

In this way you could already find the area and the perimeter of the garden.

Answer:

57.3

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\mathsf{10 \dfrac{2}{3}\times 5\dfrac{3}{8}}\)

\(\mathsf{= \dfrac{10\times3 + 2}{3}\times\dfrac{5\times8 + 3}{8}}\)

\(\mathsf{= \dfrac{30 + 2}{3} \times \dfrac{40 + 3}{8}}\)

\(\mathsf{= \dfrac{32}{3}\times \dfrac{43}{8}}\)

\(\mathsf{=\dfrac{32\times43}{3\times 8}}\)

\(\mathsf{= \dfrac{172}{3}}\)

\(\mathsf{= 57\dfrac{1}{3}}\)

\(\huge\text{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{57\dfrac{1}{3}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

The graph with the same end behavior is the one in option C.

The given function has a numerator with a negative leading coefficient and an odd degree, while the denominator is a quadratic polynomial.

It will mean that as x tends to negative infinity, the function tends to infinity, and as x tends to positive infinity, the function tends to negative infinty, that is the end behavior of the given function.

The graph with that end behavior is the same one than in option C.

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2:1 is the simplified ratio

The main answer is that without specific values or elements for sets A and B, we cannot determine the result of A - B and B - A.

To find A - B, we need to subtract the elements in set B from set A. Similarly, to find B - A, we need to subtract the elements in set A from set B.

However, I need the specific values or elements of sets A and B to perform the calculations. Could you please provide the values or elements of the sets?In order to perform set subtraction, we need the specific elements or values of sets A and B. Set subtraction involves removing the common elements between the sets.

Let's say set A is {1, 2, 3} and set B is {2, 3, 4}. To find A - B, we remove the elements in set B from set A. Thus, A - B would be {1}.

To find B - A, we remove the elements in set A from set B. Therefore, B - A would be {4}.

Please provide the values or elements of sets A and B, and I will be able to calculate A - B and B - A accordingly.

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Answer:

cosθ = 4/5

Step-by-step explanation:

The value of Cosθ is 4/5.

Pythagorean identities are identities in trigonometry that are extensions of the Pythagorean theorem.

Given that, the Pythagorean Identity states that: (sin x)² + (cos x)² = 1,

Sinθ = 3/5

We need to find Cosθ,

Put in the identity =

(3/5)² + (cos θ)² = 1

(cos θ)² = 1 - 9/25

(cos θ)² = 25-9 / 25

(cos θ)² = 16/25

cos θ = 4/5

Hence, the value of Cosθ is 4/5.

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Answer:

The formula for density (ρ) is:

Density (ρ) = Mass (m) / Volume (V)

Step-by-step explanation:

Where:

Answer:

Total revenue is the full amount of total sales of goods and services. It is calculated by multiplying the total amount of goods and services sold by their prices. Marginal revenue is the increase in revenue from selling one additional unit of a good or service.

Step-by-step explanation:

Answer:

2979134736

Step-by-step explanation:

Answer: n = 6 or you can do n = -6

Step-by-step explanation:

solve for n and then the left hand side factors

into a product with for terms then multiply both sides by -2  then split into two equations after add 6 to both sides and subtract 6 from both sides.

Answer:

Hope this helps lol !

Step-by-step explanation:

This is how to calculate net price. Start with the list price and add any taxes and other government-mandated charges. Then subtract any discounts, negotiated prices. The result you get will be the net price.

Answer:

0

Step-by-step explanation:

if you slightly change the equation to better fit standard form (without actually changing its meaning) you get

y = 0x + 5

which means the slope is 0

Also, a shortcut:

Answer:

Um, I feel like I don't have enough info to solve this

Step-by-step explanation:

Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90

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