Please help me with this homework

The form that most quickly reveals the zeros of the function is b because it is already factored the zeros are -8 and 2.

We are given that;

Functions f(x) = -1/2(x+3)^2+25/2, f(x)= -1/2(x-2)(x+8) and f(x)= -1/2x^2-3x+8

Now,

The zeros of a quadratic function are the points where the graph of the function intersects the x-axis. At the zeros of the function, the y-coordinate is 0 and the x-coordinate represents the zeros of the quadratic polynomial function1.

To find the zeros of a quadratic function in standard form (ax^2+bx+c), we can use the quadratic formula:

\(x = (-b ± sqrt(b^2-4ac)) / 2a^\\2\\\)

Now, let’s look at the three equivalent forms of f(x) given in your question. a. f(x) = -1/2(x+3)^2+25/2 b. f(x)= -1/2(x-2)(x+8) c. f(x)= -1/2x^2-3x+8

Therefore, by quadratic equations the answer will be -8 and 2.

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Answer:

1211.85

Step-by-step explanation:

3*3.95 = 11.85
11.85+1200 = 1211.85

Answer:

The value of x is 7.

Step-by-step explanation:

First, you have to make the left side into 1 fraction by making the denormintor the same and make it into simplest form :

\( \frac{x}{3} + \frac{x}{6} \)

\( = \frac{x \times 2}{3 \times 2} + \frac{x}{6} \)

\( = \frac{2x}{6} + \frac{x}{6} \)

\( = \frac{2x + x}{6} \)

\( = \frac{3x}{6} \)

\( = \frac{x}{2} \)

Next you have to multiply both sides by 2 in order to make x the subject :

\( \frac{x}{2} = \frac{7}{2} \)

\( \frac{x}{2} \times 2 = \frac{7}{2} \times 2\)

\(x = 7\)

Answer:   x4

Step-by-step explanation:

Answer:

m = 2

Step-by-step explanation:

The gradient ( slope) m is calculated using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (1, 3) ← 2 points on the line

m = \(\frac{3+1}{1+1}\) = \(\frac{4}{2}\) = 2

The gradient (m) of the graph is the slope which is: 2.

Using two points on the line, (0, 1) and (1, 3):

Gradient (m) = (3 - 1)/(1 - 0)

Gradient (m) = 2/1

Gradient (m) = 2

Thus, the gradient (m) of the graph is the slope which is: 2.

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(i) The price elasticity of demand when the price increases from $8 to $10, with an income of $16,000, is approximately -2/9 .ii) The price elasticity of demand when the price increases from $8 to $10, with an income of $20,000, is approximately -0.189.b)

Price Elasticity of Demand = [(Q2 - Q1) / ((Q2 + Q1) / 2)] / [(P2 - P1) / ((P2 + P1) / 2)]

(i) If your income is $16,000:

Price elasticity of demand = [(32 - 40) / ((32 + 40) / 2)] / [(10 - 8) / ((10 + 8) / 2)]

= [-8 / 36] / [2 / 9]

= -2/9

(ii) If your income is $20,000:

Price elasticity of demand = [(45 - 50) / ((45 + 50) / 2)] / [(10 - 8) / ((10 + 8) / 2)]

= [-5 / 47.5] / [2 / 9]

≈ -0.189

b. To calculate the income elasticity of demand, we use the formula:

Income Elasticity of Demand = [(Q2 - Q1) / ((Q2 + Q1) / 2)] / [(I2 - I1) / ((I2 + I1) / 2)]

(i) If the price is $12:

Income elasticity of demand = [(30 - 24) / ((30 + 24) / 2)] / [(20,000 - 16,000) / ((20,000 + 16,000) / 2)]

= [6 / 27] / [4,000 / 18,000]

≈ 0.444

(ii) If the price is $16:

Income elasticity of demand = [(12 - 8) / ((12 + 8) / 2)] / [(20,000 - 16,000) / ((20,000 + 16,000) / 2)]

= [4 / 10] / [4,000 / 18,000]

= 1

b. (i) The income elasticity of demand when income increases from $16,000 to $20,000, with a price of $12, is approximately 0.444. This indicates that pizza is a normal good, as an increase in income leads to a proportionately smaller increase in quantity demanded.

b. (ii) The income elasticity of demand when income increases from $16,000 to $20,000, with a price of $16, is 1. This indicates that pizza is a luxury good, as an increase in income leads to a proportionately larger increase in quantity demanded.

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Gas left after 2 hours is 1.5 gallons and the function that represent the gas which is left in the tank after driving for t hours is 13 - 0.75t gallons.

Zoe is driving on a long road trip.

The amount of gas she has in her car = 13 gallons.

It is given that each hour that she drives,  functions her car uses up 0.75 gallons of gas.

So, Gas used in the car for one hour = 0.75 gallons

Gas used in the car for two hours = 0.75*2 =  1.5 gallons

Hence, Gas left in the tank after driving for 2 hours = 13 - 1.5 = 11.5 gallons.

Now,functions

Gas used in the car for t hours = 0.75*t =  0.75t gallons

Gas left in the tank after driving for t hours = 13 - 0.75t gallons.

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To simplify the expression 3(x + 5) - 2x, let's break it down step by step:

First, apply the distributive property by multiplying 3 with each term inside the parentheses:

3(x + 5) - 2x = 3x + 15 - 2x

Next, combine like terms by grouping the x terms together:

3x - 2x + 15 = (3x - 2x) + 15

Simplifying the x terms, we get:

(3x - 2x) + 15 = x + 15

Therefore, the simplified expression is x + 15.

This means that the original expression, 3(x + 5) - 2x, is equivalent to x + 15.

To further explain, the expression 3(x + 5) - 2x represents three times the quantity of x plus 5, subtracted by two times x. By distributing the 3, we get 3x + 15, and then combining the x terms yields x + 15.

So, the expression x + 15 is equivalent to 3(x + 5) - 2x. It represents the same mathematical relationship and simplifies the original expression by grouping like terms.

It's important to note that this simplification assumes x is a variable and not a specific value. If x has a specific value, then the simplified expression x + 15 will represent a numerical result based on that value.

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Answer:

about $45.71

Step-by-step explanation

32/70%

32 x 100/70

32 x 10/7

320/7

$45.71

The original price would be $41.6.

Let x be the money used in the bank account that pays 4% and let y be the money used for the 10% certificates. We have that 1/3x is the money used to buy the bonds. Since the total investment is $10,000, then we have the following equation:

to find the return of each investment, we change the rate to decimals and multiply it to the amount of the investment:

since the total return of the investment is $885, then we have the following equation:

Now we have the following system of equations:

We can substract the second equation from the first to get the following:

we have that x=1500. This means that the money on the bankn account is $1500. Now we can use this value to find the money for the bonds and the money for the certificates:

finally, we have that the money used for the bonds is $500 and for the certificates is $8000.

Now, suppose that the controller don't buy the bonds. Then the equations would be the following:

Solving the system we get the following:

We can see that the solution changes with an increment on both quantities. Since the investments only were two, the money invested had to go up.

Answer:

<1 = <9 = <4 = <12 = 75

<2 = <3 = <10 = <11 = 105

<5 = <8 = <13 = <16 = 85

<6 = <7 = <14 = <15 = 95

The required two way frequency table is shown below.

We know that a two-way frequency table is nohting but the way to display frequencies for two different categories collected from a single group of people.

While making the two-way frequency tables first we need to identify the two variables of interest. Then we need to determine the possible values of each variable. Select a variable to be represented by the rows and the other to be represented by the columns. And then complete the table with frequencies.

Here we have two variables as:

Time ( practiced for atleast 10,000 hours and did not practiced for atleast 10,000 hours) and the second (won a prize and do not won a major)

Based on the information provided, we can obtain a two way frequency table as shown below:

                                   practiced for atleast          did not practiced for

                                       10,000 hours               atleast 10,000 hours

have won a major                  9                                      1

haven't won a major              1                                       2

Thus the required two-way frequency table is shown in attached figure.

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Find the complete question below.

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

the side "?" is the Adjacent side (Adj)  and we are given the angle and the Hypontenuse ( long side) (Hyp)  of this triangle

so use CAH

cos(75) =  Adj / 8

algebra to solve for the Adj side (which is the "?" for this problem )

8*cos(75) = Adj

2.07055 = Adj

so the "?" is  2.1 ft ( rounded to the nearest 10th )

Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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Answer:

Press down the brake firmly and smoothly. ...

Don't brake and swerve the car at the same time. ...

Avoid using your transmission for quick stops. ...

Focus on where you want to go, not what you want to avoid.

It's important to consider personal financial priorities and budget accordingly.

Location: The cost of living can vary greatly depending on where you live. Movie theaters located in cities or tourist areas may charge more for snacks compared to those located in suburban or rural areas.

Type of movie theater: The type of movie theater can also influence the cost of snacks. Luxury or premium movie theaters may charge more for snacks and offer a wider selection of premium snacks.

Time of day: The time of day can also influence snack prices. Movie theaters may offer discounts for snacks during matinee showings or other off-peak hours.

Personal preferences: The amount spent on snacks can vary depending on individual preferences. Some people may prefer to bring their own snacks from home, while others may prefer to purchase snacks at the movie theater.

Size of snacks: The size of snacks can also affect the cost. Larger sizes of popcorn, candy, or soda may cost more than smaller sizes.

Overall, the amount spent on snacks at the movie theater can vary greatly depending on a variety of factors. It's important to consider personal financial priorities and budget accordingly.

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Answer: False

Step-by-step explanation:

If \(y=0.5\), then \(y^2=0.25\), whereas \(y=0.5\).

Therefore, this is a counterexample. Hence, the statement is false.

The scale factor used to create the dilation is 3

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

comparing the two images it can be seen that dimensions ABCD is a square hence change in one side will equal for all sides

using side BC = 1 unit, B'C' = 3 Units, this shows a maginification of 3 hence the scale factor is 3

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The smallest unit of matter is an atom. The fundamental building block of an element is an atom, which is made up of protons, neutrons, and electrons. This statement is true.

An atom is made up of a nucleus and one or more electrons that are bound to the nucleus. The nucleus is made up of one or more protons, a significant number of neutrons, and other particles. Only the most common form of hydrogen lacks neutrons.

An atom, which is the smallest part of a material, retains all of its properties. A molecule is made up of protons, neutrons, and electrons, which are the building components of matter. Protons and neutrons, which are the only particles in an atom that contribute to its atomic mass, are found in the nucleus of each atom. These early 20th-century discoveries of particles that  a nuclide itself and chemical components are explained by contemporary atomic theory.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

she should mix 6 cups of green paint with 4 cups of white paint

Step-by-step explaination:

you are just multiplying by 2. 2 times 2=4 cups of white paint. So the same thing you do to both sides, 2 times 3=6

so the answer is 6 cups of green paint

It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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Answer:

2nd option

Step-by-step explanation:

8\(x^{4}\) - 4x³ - x + 2 - (2\(x^{4}\) - 8x² - x + 10) ← distribute by - 1

= 8\(x^{4}\) - 4x³ - x + 2 - 2\(x^{4}\) + 8x² + x - 10 ← collect like terms

= 6\(x^{4}\) - 4x³ + 8x² - 8

Answer:

its c

Step-by-step explanation:

Number x = 6 is a solution of proportion ''because if you substitute 6 into the equation for x and cross multiply, you get 1,152 = 1,152''.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The expression of proportion is,

⇒ 192 / 36 = 32 / x

And, x = 6 is the solution of above proportion.

Now,

Since, The expression of proportion is,

⇒ 192 / 36 = 32 / x

⇒  x × 192 = 32 × 36

Substitute x = 6

⇒ 6 × 192 = 1152

⇒ 1152 = 1152

Thus, Number x = 6 is a solution of proportion because if you substitute 6 into the equation for x and cross multiply, you get 1,152 = 1,152

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Answer:

The precipitation for both March and April was 8 7/8 inches below average

Step-by step explanation;

For the month of march, precipitation was 6 1/2 inches less than average

For the month of April, precipitation was 2 3/8 inches left.

Now we want to calculate how many inches less than average was precipitation in both wants

What we simply do here is to add the inches with which they were both left than average in both months

That would be;

6 1/2 + 2 3/8

= 13/2 + 19/8 = (52 + 19)/8 = 71/8 = 8 7/8 inches