I hope someone can help me with 1) & 2). Thank you!!

The initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The initial height of the rocket is given by the value of h when t = 0:

h(t)=-4t² + 16t + 24

h(0)=-4(0)² + 16(0) + 24

h(0)=24

So the initial height of the rocket is 24 metres.

The rocket will hit the ground when its height is 0 metres, so we can set h = 0 in the equation and solve for t:

0 = -4t²+ 16t + 24

-4t² + 16t + 24 = 0

t=-0.88 seconds

So the rocket will hit the ground after approximately 0.88 seconds.

The height of the rocket after 4 seconds is given by:

h(4)== -4(4)²+ 16(4) + 24

=-64+64+24

=24

So the height of the rocket after 4 seconds is 24 metres.

Hence, the initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

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The line PQ of the triangle is an altitude. The correct option is A.

A line segment passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.

The extended base of the altitude is the name given to this line that contains the opposing side. The foot of the altitude is the point at where, the extended base and the height converge.

In the given triangle the line segment PQ is passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.

Therefore, the line PQ of the triangle is an altitude. The correct option is A.

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The length of c is c = 13.3, and the angle measures are A = 17.7 and B = 97.3

From the question, we have the given parameters to be:

b = 10 inches

a = 14 inches

<C = 65 degrees

To calculate the length of c, we use the following equation of law of cosine

c^2 = a^2 + b^2 - 2 * a * b * cos(C)

Substitute the known values in the above equation

c^2 = 14^2 + 10^2 - 2 * 10 * 14 * cos(65 degrees)

Evaluate cos(65 degrees)

c^2 = 14^2 + 10^2 - 2 * 10 * 14 * 0.4226

Evaluate the exponent

c^2 = 196 + 100 - 2 * 10 * 14 * 0.4226

Evaluate the product

c^2 = 196 + 100 - 118.328

Evaluate the sum and the difference

c^2 = 177.672

Take the square root of both sides

c = 13.3

To calculate the angle measure of A, we use the following equation of law of sine

a/sin(A) = c/sin(C)

This gives

14/sin(A) = 13.3/sin(65)

This gives

14/sin(A) = 14.7

Rewrite as:

sin(A)  = 14/14.7

Evaluate the quotient

sin(A)  = 0.9524

Take the arc sin of both sides

A = 17.7

Lastly, we have

B = 180 - A - C

This gives

B = 180 - 17.7 - 65

Evaluate

B = 97.3

Hence, the length of c is c = 13.3, and the angle measures are A = 17.7 and B = 97.3

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The equation of each line that satisfies the given conditions are:

1. y - 2 = 5/2(x - 3)

2. y - 4 = m(x + 3)

3. y = -3x + 5

1. Given the points, (3, 2) and (5, 7), find the slope (m):

Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)

m = 5/2

Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):

y - 2 = 5/2(x - 3)

2. Given:

A point = (-3, 4)

Slope (m) = 2

Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):

y - 4 = m(x + 3) [equation of the line]

3. Given:

Slope (m) = -3

Y-intercept (b) = 5

Substitute m = -3 and b = 5 into the equation y = mx + b:

y = -3x + 5

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We can write k(x) as the composition of g(x) and f(x).

k(x) = g(f(x))

A composition of two functions means that we need to evaluate one function in the other one.

Here we have the functions:

f(x)=  x²

g(x) = √(x - 1)

h(x) = 2x + 3

And we know that:

k(x) = √(x² - 1)

So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:

k(x) = g(f(x))

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Answer: 150 pounds

Step-by-step explanation:

Let her initial weight be represented by x.

Since Shep had lost 16% of his weight, which was 24 pounds. Shep weight before he was put on a diet would be:

16% × x = 24

0.16 × x = 24

0.16x = 24

x = 24/0.16

x = 150 pounds

Answer:

Area = 396 units²

Step-by-step explanation:

Let's assume:

Length = 2c - 5

Width = 5c + 9

Perimeter = 2(L + W) = 106 units

Thus:

2[(2c - 5) + (5c + 9)] = 106

Find the value of c

2[2c - 5 + 5c + 9] = 106

2[7c + 4] = 106

14c + 8 = 106

14c = 106 - 8

14c = 98

Divide both sides by 14

c = 98/14

c = 7

✔️Area of the rectangle = Length × Width

Area = (2c - 5)(5c + 9)

Plug in the value of c

Area = (2×7 - 5)(5×7 + 9)

Area = (14 - 5)(35 + 9)

Area = (9)(44)

Area = 396 units²

Answer:

$2,500 or 25%

Step-by-step explanation:

Let's use the same example:

Cost of Equipment = $10,000

Useful Life = 4 years

Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100

Annual Depreciation = Cost of Equipment / Useful Life

Annual Depreciation = $10,000 / 4 years

Annual Depreciation = $2,500

Depreciation Rate = ($2,500 / $10,000) * 100

Depreciation Rate = 0.25 * 100

Depreciation Rate = 25%

The solutions are: x = ln(2) for 2eˣ = 4,  x = ln(25)/4 for e⁴ˣ = 25, x = ln(72) for eˣ = 72 and x = ln(124)/3 for e³ˣ = 124.

To solve these equations using natural logarithm, we can use the following rules:

Using these rules, we can solve the given equations as follows:

2eˣ = 4

Divide both sides by 2 to get

eˣ = 2.

Take the natural logarithm of both sides to get

ln(eˣ) = ln(2).

Using rule 1 above, we can simplify ln(eˣ) to x, and we get

x = ln(2).

e⁴ˣ = 25

4x = ln(25).

Divide both sides by 4 to get

x = ln(25)/4.

eˣ = 72

Take the natural logarithm of both sides to get

x = ln(72).

e³ˣ = 124

Take the natural logarithm of both sides to get

3x = ln(124).

Divide both sides by 3 to get

x = ln(124)/3.

For the second set of equations, we use the same rule as above

So, we have

ln(x - 3) = 2

x - 3 = e²

x = e² + 3.

x ≈ 10.389.

Therefore, the solution is x ≈ 10.389.

ln(2t) = 4

2t = e⁴

t = 0.5 * e⁴

t ≈ 27.299.

Therefore, the solution is t ≈ 27.299.

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The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

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

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

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Answer:

B. 12

Step-by-step explanation:

Based on the centroid theorem,

\( BP = \frac{2}{3}(BF) \).

BP = 8

Plug in the value of BP into the equation and find the value of BF.

\( 8 = \frac{2}{3}(BF) \)

\( 8 = \frac{2*BF}{3} \)

Cross multiply

\( 8*3 = 2*BF \)

\( 24 = 2*BF \)

Divide both sides by 2

\( \frac{24}{2} = BF \)

\( BF = 12 \)

Answer:

5.4545492e+17

Step-by-step explanation:

aka a really big number

Answer:

Mike made $ 200.63 last Friday.

Step-by-step explanation:

Since Ms. Peralta's friend Mike is a construction worker who gets paid $ 15 an hour, and after working 9 hours he gets paid 1.25 times his hourly rate, and last Friday Mike worked for 5 hours - took an 1 hr and 15 minute break for lunch (does not count toward his work hours) - and worked for an additional 7.5 hours, to determine how much money did Mike make last Friday the following calculation must be performed:

5 + 7.5 = 12.5

12.5 - 9 = 3.5

9 x 15 + (3.5 x (15 x 1.25)) = X

135 + 3.5 x 18.75 = X

135 + 65.625 = X

200.63 = X

Therefore, Mike made $ 200.63 last Friday.

Answer:

\(4(x^4+7)\)

Step-by-step explanation:

Taking out the greatest common factor,\(16x^4+28=4(x^4+7)\).

Answer:

x>125

Step-by-step explanation:

Answer:

x > 125

Step-by-step explanation:

I hope this helps!

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

14000

Step-by-step explanation:

A year he contributes :10/100 × 80000= 8000

Then his employer pays 0.75 × 8000= 6000

The total money contributed to is

401k is = 8000 + 6000 = 14000

Solution

Let x be the number of pennies Ann's bank can hold

So, from the question we have that

The answer is 1000 pennies

Answer:

\(X \sim N(200000,100000)\)  

Where \(\mu=200000\) and \(\sigma=10000\)

From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:

\( Number = 1216*0.16 = 194.56\)

And the answer woud be between 194 and 195 houses

Step-by-step explanation:

Let X the random variable that represent the value of homes in Hampton VA of a population, and for this case we know the distribution for X is given by:

\(X \sim N(200000,100000)\)  

Where \(\mu=200000\) and \(\sigma=10000\)

From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:

\( Number = 1216*0.16 = 194.56\)

And the answer woud be between 194 and 195 houses

The probability that an MP3 player manufactured in Fort Meyers is defective is 0.37%.

To calculate the probability that an MP3 player is defective, we need to consider the manufacturing plants and their respective defect rates.

Given:

Plant at Memphis manufactures 50% of the MP3 players, and 1% of those manufactured at that plant are defective.

Plant at Fort Meyers manufactures 20% of the MP3 players, and 3% of those manufactured at that plant are defective.

No information is provided about the defect rate of the third plant.

To find the overall probability of an MP3 player being defective, we need to consider the probability of selecting a defective player from each plant and then weigh it by the probability of selecting a player from each plant.

Let's calculate the overall probability:

Probability of selecting a defective player from Memphis plant = 50% * 1% = 0.50% or 0.005 (since 50% is equivalent to 0.50 in decimal form)

Probability of selecting a defective player from Fort Meyers plant = 20% * 3% = 0.60% or 0.006 (since 20% is equivalent to 0.20 in decimal form)

To calculate the overall probability, we need to weigh these probabilities by the probability of selecting an MP3 player from each plant:

Probability of selecting from Memphis plant = 50% = 0.50 (decimal form)

Probability of selecting from Fort Meyers plant = 20% = 0.20 (decimal form)

Overall probability of selecting a defective MP3 player is given by:

Overall probability = (Probability from Memphis plant * Probability of selecting a defective player from Memphis) + (Probability from Fort Meyers plant * Probability of selecting a defective player from Fort Meyers)

Overall probability = (0.50 * 0.005) + (0.20 * 0.006) = 0.0025 + 0.0012 = 0.0037 or 0.37%

Therefore, the probability that an MP3 player, manufactured in Fort Meyers, is defective is 0.37%.

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Answer:

\(g'(x) = \frac{x^2}{100} +2\)

Step-by-step explanation:

Given

\(g(x) = 10\sqrt{x - 2\)

Required

Determine the inverse function

\(g(x) = 10\sqrt{x - 2\)

Replace g(x) with y

\(y = 10\sqrt{x -2\)

Swap the positions of x and y

\(x = 10\sqrt{y -2\)

Divide through by 10

\(\frac{x}{10} = \sqrt{y - 2\)

Square of both sides

\(\frac{x^2}{100} = y - 2\)

Make y the subject

\(y = \frac{x^2}{100} +2\)

Replace y with g'(x)

\(g'(x) = \frac{x^2}{100} +2\)

Hence, the inverse function is: \(g'(x) = \frac{x^2}{100} +2\)

Answer:

$406.25

Step-by-step explanation:

Multiply 16.25 by 25:

16.25(25)

= 406.25

So, her gross wages were $406.25

Answer:

406.25

Step-by-step explanation:

The following phrases are used in place of supply chain:

Supply network ; Demand chain ; Extended enterprise ; Supply web.

The supply chain is a networked system of businesses, people, information, and assets created to locate, produce, and transport items from their point of origin to their final destination, which is often from the a supplier to a customer.

Modern supply chains sometimes span several nations and involve numerous processes, making them exceedingly complicated.

The fundamental steps in such a supply chain are as follows:

Thus, the following phrases are used in place of supply chain:

Supply network ; Demand chain ; Extended enterprise ; Supply web.

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Answer:

  2. ASA can be used with the definition of an isosceles triangle

  3. x = 5 5/6

Step-by-step explanation:

Using the given information, the definition of an isosceles triangle tells us, ...

  ∠A = ∠C and ∠A = ∠ABM and ∠C = ∠CBN

By substitution, ∠ABM = ∠CBN. This lets us declare ΔAMB ≅ ΔCNB by ASA, where the sides between the angles are AB and CB.

__

If the angles of interest are the same, then the triangles are similar. That means corresponding sides have the same ratio:

  AB/AD = CB/CE

  x/7 = (10-x)/5

  5x = 7(10 -x) = 70 -7x . . . . . multiply by 35, simplify

  12x = 70 . . . . . . . . . . . add 7x

  x = 70/12 = 35/6

  x = 5 5/6

Answer:

x = 6       y = 7

Step-by-step explanation:

You can isolate y using the first equation and get y = 13 - x.

Plug in for y using the second equation.

4x + (13 - x) = 31       Solve for x

4x - x = 18

3x = 18

x = 6                  Plug in for x using the first equation.

(6) + y = 13         Solve for y

y = 7

I hope this helped and please mark me as brainliest!

Answer:

The solution is (6, 7)

Step-by-step explanation:

Let's solve this system by elimination by addition and subtraction.  To accomplish this, subtract each term of the first equation by the corresponding term beneath it (e. g., subtract x in the first term from 4x in the second term):

3x = 18, which leads to x = 6.

Now substitute 6 for x in the first equation.  We get:  6 + y = 13, so y must be 7.

Substituting 7 for y in the second equation, we get 4x + 7 = 31, or 4x = 24.

Then x must be 6, and so

The solution is (6, 7)

Answer:

7.19%

Step-by-step explanation:

let i be the effective rate

\((1+\frac{.07}{4})^4=(1+i)\\.071859031\)

The annual effective yield will be 7.19% for the investment.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Given that Candace invests $636 in an investment that pays 7% interest compounded quarterly.

The annual effective yield will be calculated as below:-

[ ( 1 + ( 0.07 / 4 )⁴ ] = ( 1 + i)

Solve the equation:-

i = 0.0718

i = 0.0718 x 100 = 7.19%

Therefore, the annual effective yield will be 7.19% for the investment.

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We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

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