The function, y=-16x^2+32x+48, represents the height, in feet, of a firework x seconds after it is launched.

After how many seconds does the firework hit the ground
x=___seconds

Answer:

C. 2

Step-by-step explanation:

A polynomial function has one or more real numbers as roots or zeros. These roots correspond to the values of x for which the function takes on the value of zero.

In this case, y = (x-2)(x+3)², we can factor the equation to find its zeros. The expression (x-2)(x+3)² can be factored into two terms: (x-2) and (x+3)².

The first term, (x-2), is equal to zero when x = 2, meaning that x = 2 is a root of the function.

The second term, (x+3)², is equal to zero when x = -3, meaning that x = -3 is another root of the function.

So, the function y = (x-2)(x+3)² has two roots, or zeros, at x = 2 and x = -3.

Answer: Function

Step-by-step explanation:

Answer is B. 
y= 2x -3 y= -2x + 1

step by step

First I found the y intercepts at (red line) -3 and (green line) +1.

There is only one answer that shows these two y intercept values.

 To double check this answer, I checked the slope of each line. The red line has a slope of 2 and the green line has a slope of -2.

Slope was found on the graph finding rise over run and compared to the number next to x in the equations.

See attached graph.

The 8.4% compounded quarterly is the better investment because it gives a good return.

(i)

S = P

S = P(1.0854) (1.0854)

AP(1) = 1.0846 - 1

AP(1)= 0.08546 or 8.546%

(ii)

r = 0.084/4

AP(2) = (1 + 0.084/4)⁴ -1

AP(2) = 1.08688 - 1

AP(2) = 8.668%

The 8.4% quarterly investment is therefore preferable.

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The domain of the real valued function as required is; [3, infinity).

The range of the function as required is; (-infinity, -3].

By observation of the given function; the domain is the set of all real numbers except those for which;

4x - 12 < 0

4x < 12

x < 3.

Hence, the domain of the function is; [3, infinity).

The range as observed in the task content has a maximum value of; -3. Hence, the range of the function as required is; (-infinity, -3].

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Answer:

Step-by-step explanation:

200-14=186

Frank still needs to give 186

In order to infuse 0.5 grams of magnesium sulfate, 6.25ml must be administered in 1 hour.

A magnesium salt with the counterion sulfate is known as magnesium sulfate. It functions as a medication called, anaesthetic, tocolytic, anti-arrhythmia, analgesic, fertilizer, anticonvulsant, cardiovascular medication, analgesic, and all of the above. Drug is used to treat constipation temporarily.

Additionally, it is employed as a soaking solution to treat minor sprains, bruises, muscular aches, joint stiffness, and fatigued feet. A cleanse and soaking solution, this medication Magnesium sulfate, also known as Bath, is a natural compound used for a variety of therapeutic and physiological benefits.

xml = 0.5*50     (cross multiplication)

               4

So xml = 6.25ml

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Answer:Steve

Step-by-step explanation:

Given,

y=55cm
w=73 cm

Using Pythagoras Theorem,

[tex]w^{2}[/tex] = [tex]y^{2} + x^{2}[/tex]

73² = 55² + x²

x= √3025

x = 48cm

Answer= 48cm

The answer is 0.360, or approximately 36/100.

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.

The probability of matching four out of six numbers in a single ticket can be calculated as follows:

There are C(23, 6) = 8,145 possible combinations of six numbers from 1 through 23.

There are C(23, 4) = 1,531 possible combinations of four numbers from 1 through 23.

So, the probability of matching four out of six numbers in a single ticket is 1,531/8,145 = 19/102.

If you buy five tickets, the probability of matching four out of six numbers in at least one of them is 1 - (1 - 19/102)⁵ , which can be calculated as:

1 - (1 - 19/102)⁵ = 1 - 0.848⁵ = 1 - 0.640 = 0.360

Therefore, The answer is 0.360, or approximately 36/100.

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Answer:

60

Step-by-step explanation:

10,000 * 2 = 20,000, so multiply 30 by 2:

30 * 2 = 60

Answer:

A 60 square meter pond is needed to accommodate 20,000 catfish.

Step-by-step explanation:

We know that 30 square meters is needed per 10,000 catfish.

How large a pond is needed for 20,000 catfish?

We can create an equation like this

[tex]\frac{30}{10000} =\frac{x}{20000}[/tex]

let [tex]x[/tex] represent the number of square meters needed for 20,000 catfish

Lets solve for [tex]x[/tex].

Cross multiply.

[tex]30*20000=x*10000[/tex]

Evaluate [tex]30*20000[/tex]

[tex]600000=10000x[/tex]

Divide both sides by [tex]10000[/tex].

[tex]60=x[/tex]

Answer: The momentum of the truck before the collision is given by the formula:

p_i = m_i * v_i, where m_i is the mass of the object and v_i is its velocity.

The momentum of the truck before the collision is:

p_i (truck) = 3000 kg * 10 m/s = 30000 kg m/s

The momentum of the car before the collision is:

p_i (car) = 1000 kg * 0 m/s = 0 kg m/s

The total initial momentum of the system is the sum of the initial momenta of the truck and car:

p_i (total) = p_i (truck) + p_i (car) = 30000 kg m/s + 0 kg m/s = 30000 kg m/s

After the collision, the final momentum of the system is the sum of the final momenta of the truck and car:

p_f (total) = p_f (truck) + p_f (car)

Let's call the velocity of the truck after the collision v_f (truck). The final momentum of the truck is:

p_f (truck) = 3000 kg * v_f (truck)

The final momentum of the car is:

p_f (car) = 1000 kg * 15 m/s = 15000 kg m/s

Using the conservation of momentum, we can write an equation:

p_f (total) = p_i (total)

30000 kg m/s = p_f (truck) + p_f (car)

30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s

30000 kg m/s = 3000 kg * v_f (truck) + 15000 kg m/s

v_f (truck) = (30000 kg m/s - 15000 kg m/s) / 3000 kg = 7.5 m/s

So, the velocity of the truck immediately after the collision is 7.5 m/s.

Step-by-step explanation:

Answer: 83%

Step-by-step explanation: Take 250 and divide it by 300

Answer:

approximately 0.567088608.

Step-by-step explanation:

The division of 1.28 by 2.26 can be done as follows:

The same shape and similar are relationship between ΔXYZ and ΔUVW options (A) and (D) are correct.

What is the similarity law for triangles?

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the complementary angles are congruent.

We have given two triangles with dimensions.

Take the ratio of the corresponding sides:

12/24 = 5/10 = 13/26 = 1/2

The ratios of the corresponding sides are same which means the triangle are similar and having same shape.

Hence, the same shape and similar are relationship between ΔXYZ and ΔUVW option (A) and (D) are correct.

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The complete question is in the attached image.

The longest border of the Mann's park is 228.6 meter.

The Triangle Inequality It is a basic principle of geometry that the lengths of any two sides of a triangle must add up to more than the length of the third side. In other words, the longest side of any triangle must be shorter than the total length of the other two sides.

In this case, the shortest side of Mann Park measures 5 inches, and the two longer sides measure 7 inches and 9 inches.

So, the sum of the lengths of the two longer sides is:

' 7 inches + 9 inches = 16 inches.

Since 5 inches is less than 16 inches, we know that the 5-inch side is the shortest side, and the 9-inch side is the longest side.

One inch is approximately equal to 0.0254 meters, so we have:

= 9 inches x 0.0254 meters/inch

= 0.2286 meters

Since the shortest side is 1000 meters long, the longest side is:

= 1000 meters x 0.2286 meters/inch

= 228.6 meters long.

Therefore, the longest border of Mann Park is approximately 228.6 meters long.

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Answer:

32/13

Step-by-step explanation:

To evaluate the expression Z₂ * Z3 / Z₁, we first need to find the complex numbers Z₂ * Z3 and Z₁.

Z₂ * Z3 = -2 + 3i * 4 + 2i = (-8 + 14i) + (-6 + 6i) = -8 + 8i

Z₁ = 3 - 2i

So, Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i)

We can simplify this expression by multiplying the numerator and denominator by the complex conjugate of the denominator, which is (3 + 2i).

Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i) * (3 + 2i) / (3 + 2i) = (-8 + 8i) * (3 + 2i) / (3 - 2i) * (3 + 2i)

Z₂ * Z3 / Z₁ = ((-8 * 3 + 8 * 2i) + (8 * 3 + 8 * 2i)) / (3^2 + (-2i)^2) = (16 + 16i) / 13

Therefore, Z₂ * Z3 / Z₁ = (16 + 16i) / 13.

The number of dots will be in each pattern in 4th step:

1. In pattern A: 16 dost

2. In pattern B: 18 dots

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

two patterns,

Pattern A:

number of dots,

step 0:  0

step 1: 4

step 2:  8

step 3:  12

So here it can be seen that,

4 dots are more in each step in compare with previous step,

So generalized expression can be written as:

Number of dots in nth step =  0 + 4n

In 4th step, there will be- 16 dots

Similarly, in Pattern B:

Number of dots in nth step = 2 + n²

In 4th step, there will be- 18 dots

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Answer: The amount of alcohol the woman consumed can be calculated as follows:

Two glasses of wine * 22 grams of alcohol per glass = 44 grams of alcohol

To convert this amount to milliliters, we need to know the concentration of the alcohol, which is typically around 12% for wine. So, 44 grams of alcohol is equivalent to 44 grams / 0.12 g/mL = 367 mL.

Next, we can calculate the woman's blood alcohol content (BAC) using the following formula:

BAC = (Alcohol consumed in mL) / (Blood volume in mL) * 100%

The blood volume for a 103-pound woman with approximately 6 liters of blood can be estimated as follows:

6 liters * 1000 mL/liter = 6000 mL

So, the BAC can be calculated as follows:

BAC = (367 mL) / (6000 mL) * 100% = 0.0612 * 100% = 6.12%

Therefore, the woman's blood alcohol content would be 6.12% if all the alcohol were immediately absorbed into her bloodstream.

Step-by-step explanation:

Answer: 65

Step-by-step explanation:

17 + 48

Answer:

Step-by-step explanation:

ΔABC transformed by 5/2 to A'B'C':

A' = -10, 15

B' = -15, 10

C' = 5, -5

Answer:

Step-by-step explanation:

Yes, the ratios 4:6 and 2:3 are equivalent.

To see why, we can compare the proportions of the two ratios by dividing each term by the smaller term in each ratio.

In the ratio 4:6, if we divide both terms by 4, we get:

4/4 : 6/4 = 1 : 3/2

In the ratio 2:3, if we divide both terms by 2, we get:

2/2 : 3/2 = 1 : 3/2

Since both ratios reduce to the same proportion of 1 : 3/2, we can conclude that the ratios 4:6 and 2:3 are equivalent.

Ratios are mathematical expressions that compare two or more quantities. When two ratios are equivalent, it means that they represent the same proportion, even if the numbers in the ratios are different.

To compare the ratios 4:6 and 2:3, we divided each term in each ratio by the smallest term. This is because dividing each term by the same number will keep the proportion of the ratio the same.

For example, in the ratio 4:6, dividing both terms by 4 gave us the proportion of 1 : 3/2, which is the same as the proportion of 2:3 when divided by 2. This means that, even though the numbers in the two ratios are different, they represent the same proportion, and therefore the ratios are equivalent.

It's important to note that when comparing ratios, it's best to reduce the ratios to their simplest form so that the proportions are more easily compared.

The relation is a direct variation

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

10 inches in 6 hours

80 inches in 2 days

Convert 2 days to hours

So, we have the following representation

10 inches in 6 hours

80 inches in 72 hours

For the relation to be a direct variation, the following must be equal

6/10 = 72/80

Evaluate

0.6 = 0.6

Hence, the relation is a direct variation

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Complete question

Determine if the following relation represents a direct variation

10 inches in 6 hours

80 inches in 2 days

The solution is Option D.

The median of the data is A = 20 and the mean of the data is M = 22.7

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the mean of the data be represented as M

Let the median of the data be represented as A

Now , the equation will be

The list of donations is represented as set D

Set D = { 10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55 }

Now , the mean M is = 10 + 10 + 10 + 10 + 15 + 15 + 15 + 19 + 20 + 20 + 20 + 25 + 25 + 25 + 30 + 30 + 55 + 55 / 18

The mean M = 409 / 18

On simplifying the equation , we get

The mean M = 22.722

Now , the median of the data is A = 20

Hence , the mean is 22.7

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The median of 20 is the most accurate to use, since the data is skewed.

The most accurate measure of center to use in this case is the median of 20. This is because the data is skewed, with a few high-value donations (such as the two donations of 55 dollars) that pull the mean up. However, most of the donations are clustered around 10 to 20 dollars. As a result, the median, which is the middle value when the data is sorted in order, is a better representation of the "typical" donation amount.

In this case, the median is 20, which means that half of the donations were less than 20 dollars and half were more. This is a more accurate representation of the central tendency of the data than the mean of 22.7, which is influenced by the high-value donations. Therefore, the charity should use the median of 20 to accurately represent the typical donations received.

Answer:

Below

Step-by-step explanation:

Instead of x , I assume you want the angle.    

  For RIGHT triangles, remember

cos (angle ) = adjacent leg / hypotenuse

cos ( angle ) = 5 /12    

     angle = arccos( 5/12) = 65 °

You could also use pythagorean theorem to calculate the misssing side....then use cos law to calculate the angle.

Answer:

D

Step-by-step explanation:

We can see that we are not increasing by the same amount.

[tex]\frac{1}{25}= \frac{2}{50} \neq \frac{3}{70} \neq \frac{5}{168}[/tex]

In total, the number of greetings will be 1159.

Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.

The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.

The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.

The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.

In total, the number of greetings will be 38 + 760 + 361 = 1159.

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The APY for the account would be 3.045%.

What is continuous compounding?

The formula for continuous compounding is given by:

A = P[tex]e^{(rt)}[/tex]

where:

A = final amount

P = principal amount

e = the mathematical constant e (approximately 2.71828)

r = annual interest rate

t = time in years

In this case, P = $1000, r = 0.03 (since APR is given), and t = 1 year.

Using the formula, we have:

A = 1000[tex]e^{(0.03*1)}[/tex]

A ≈ $1030.45

So the balance in the account after 1 year is approximately $1030.45.

To find the balance after 5 and 20 years, we simply need to plug in the corresponding values for t:

For t = 5:

A = 1000[tex]e^{(0.03*5)}[/tex]

A ≈ $1160.92

For t = 20:

A = 1000[tex]e^{(0.03*20)}[/tex]

A ≈ $1806.11

To find the APY, we use the formula:

APY = (1 + r/n)ⁿ- 1

where:

n = number of compounding periods per year

Since this is continuous compounding, we take the limit as n approaches infinity:

APY = eʳ - 1

APY = [tex]e^{0.03}[/tex] - 1

APY ≈ 0.03045 or 3.045%

Hence, the APY for the account would be 3.045%.

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Answer:

40 meters per hour.

Step-by-step explanation:

How many seconds are in an hour? 3600. Divide 3600 by 90 to get 40.

Answer:

x = -4°

Step-by-step explanation:

We know that,

→ Sum of angles of straight line is 180°.

Now we have to,

→ Find the required value of x.

Forming the equation,

→ (54°) + (7x + 154°) = 180°

Then the value of x will be,

→ 7x + 154° + 54° = 180°

→ 7x + 208° = 180°

→ 7x = 180° - 208°

→ 7x = -28°

→ x = -28° ÷ 7

→ [ x = -4° ]

Hence, the value of x is -4°.

Answer: I think x = -4

Step-by-step explanation: I used a calculator.