The function y = 4x² + 9x-2 has______at the vertex.

A:minimum
B:Maximum

"Distance traveled is a function of time." In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

Distance is a fundamental concept in physics and mathematics that measures the extent or length between two points.

It represents the amount of ground covered or space traveled. When we say that distance is a function of various factors, it means that different variables or parameters can influence the distance traveled.

In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

The sentence "Distance traveled is a function of time" expresses this relationship, indicating that the distance traveled can be determined or calculated based on the value of time.

Thus, it implies that as time changes, the corresponding distance traveled also changes, establishing a functional relationship between the two variables.

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when we talk about a proportional relationship is written in the form

Where k is the constant of proportionality and must be fulfilled on all x points.

in this case table D all points have a constant of proportionality of 3.

Table c does not have a constant of proportionality.

Based on the net cashflow over the three year life, the NPV that Sausage Hut will realize is -$17,891.

First find the present value of the increased cashflows. As it is a constant amount of $123,300, we can treat it as an annuity.

Present value = Amount x (Present value of annuity interest factor, 9%, 3 years)

= 123,300 x 2.5313

= $312,109.29

The net present value is:
= Present value of cashflows - Amount invested

= 312,109.29 - 330,000

= -$17,890.71

= -$17,891.

In conclusion, option B is correct.

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Answer:

\(17.5-1.796\frac{3.61}{\sqrt{12}}=15.63\)    

\(17.5+1.796\frac{3.61}{\sqrt{12}}=19.37\)    

Step-by-step explanation:

Data given

20 13 21 18 19 22 19 15 12 12 18 21

We can calculate the sample mean and deviation with the following formulas:

\(\bar X =\frac{\sum_{i=1}^n X_i}{n}\)

\(s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}\)

And we got:

\(\bar X = 17.5\) represent the sample mean

\(\mu\) population mean (variable of interest)

s=3.61 represent the sample standard deviation

n=12 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\)   (1)

The degrees of freedom are given by:

\(df=n-1=12-1=11\)

Since the Confidence is 0.90 or 90%, the significance is \(\alpha=0.1\) and \(\alpha/2 =0.05\), the critical value would be given by \(t_{\alpha/2}=\)

Now we have everything in order to replace into formula (1):

\(17.5-1.796\frac{3.61}{\sqrt{12}}=15.63\)    

\(17.5+1.796\frac{3.61}{\sqrt{12}}=19.37\)    

Answer:

(2x² + 5x + 2) = (2x + 1)(x +2)

Step-by-step explanation:

Given expression is (2x² + 5x + 2).

We have to factorize the given expression.

(2x²+ 5x + 2) = 2x² + 4x + x + 2

                     = 2x(x + 2) + 1(x + 2)

                     = (2x + 1)(x + 2)

So the factored form of the given expression will be (2x + 1)(x + 2).

solution:

V=πr2h

3=π·9.32·18.4

3≈1666.52694

Round off to the nearest tenth: 1666.5

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

Answer:

y = x + 2

Step-by-step explanation:

Given

\(\frac{y}{x-2}\) + 1 = \(\frac{2x}{x-2}\)

Multiply through by x - 2 to clear the fractions

y + x - 2 = 2x ( subtract x - 2 from both sides )

y = x + 2

log₂ 24 can be expressed as 3 + log₂ 3 in terms of prime factors, using the properties of logarithms.

To express log₂ 24 in terms of prime factors, we can use the properties of logarithms and the fact that any positive integer can be expressed as a product of prime factors.

First, let's find the prime factorization of 24.

24 can be divided by 2, so we have 24 = 2 × 12.

12 can be divided by 2, so we have 12 = 2 × 6.

6 can be divided by 2, so we have 6 = 2 × 3.

Therefore, the prime factorization of 24 is 2 × 2 × 2 × 3, or 2³ × 3.

Now, using the properties of logarithms, we can express log₂ 24 as the sum of logarithms of its prime factors.

log₂ 24 = log₂ (2³ × 3)

According to the properties of logarithms, we can separate the factors inside the logarithm as individual terms:

log₂ (2³ × 3) = log₂ 2³ + log₂ 3

Since log₂ 2³ is equal to 3, we can simplify the expression further:

log₂ (2³ × 3) = 3 + log₂ 3

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The perimeter of a shape is the sum of its side lengths

Becca, Lucas, and Christian are correct

The side lengths of the triangle are x, 3x - 4 and 3x - 4

So, the perimeter (P) is:

P = x + 3x - 4 + 3x - 4

The above equation can be rewritten as:

P =2(3x - 4) + x

P = 6x + x - 4

P = (3x - 4) + (3x - 4) + x

P = 7x - 4

Hence, Becca, Lucas, and Christian are correct

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Answer:

c

Step-by-step explanation:

Answer:

these are your answers: a. y = 2.5x + 2000

b. The variable x represents the domain because the domain is the range of the possible x values.

c. x ≥ 0

d. The variable y represents the range because the range is the range of the possible y values.

e. y ≥ 2000

f. y = 2.5(25) + 2000

 y = 62.5 + 2000

 y = $2062.50

g. 2500 = 2.5x + 2000

  2.5x = 500

  x = 200

Step-by-step explanation:

you would have to factor in the different numbers in order to get these answers and try to solve the missing variable. hope this helps :)

The perimeter and area of the given composite shape are respectively;  10a² + 10b and 37a²b

The perimeter of the composite figure here will simply be the sum of the entire boundary lengths and as such we have;'

Perimeter = 2(a² + 3a² + a²) + 2(4b) + b + b

= 10a² + 8b + 2b

= 10a² + 10b

The area of a rectangle is;

Area = Length * width.

Thus;

Area of composite shape = Overall area of rectangle - Area of cut out rectangle

Area = (10a² * 4b) - (3a² * b)

Area = 40a²b - 3a²b

Area = 37a²b

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The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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Answer:

The frequency of the resulting harmonic motion is 0.000219 Hz

Step-by-step explanation:

We are going to calculate the time it takes for one single wave ocillation.

Frequency and the time taken to finish a single wave oscillation are inversely proportional. The formula for calculating frequency when given the time taken to complete a wave cycle is written as: f = 1 / T

In this formula, f represents frequency and T represents the time period or amount of time required to complete a single wave oscillation.

I consider the initial speed to be zero, because it is of no significance compared with the free fall into the earth, through the earth and back again.

Given from Wikipedia:

The diameter of the earth is 1.2742 * 10⁴ km which is 1.27 * 10⁷ m

2 times the radius = diameter, so the radius of the earth = (1.27 * 10⁷ m) /2 = 6.4 * 10⁶ m

radius earth = r

r = 6.4 * 10⁶ m

Now imagine the tunnel and the free fall.

1. Initially the rock has no speed.

2. Due to the gravitational accelleration, the rock will increase it's speed every second by a factor of 9.8.

3. The Rock gains speed untill it reached the centre of the earth. By then it will have reached it's maximum speed and it has travelled the distance r !

4. After this moment, the Rock will be slowed down because of the negative accelleration...

After it has travelled from the centre of the earth to the other end of the earth, it will have stopped completely, and again passing the distance r.

5. Now at the other end of the earth there is the same initial situation as described at point 1, only the Rock has travelled the distance equal to the diameter of the earth, (exactly 2 times r).

So basically, the samething happens once more, only this time it starts exactly from the other end of the earth...

6. Initially the rock has no speed.

7. Due to the gravitational accelleration, the rock will increase it's speed every second by a factor of 9.8.

8. The Rock gains speed untill it reached the centre of the earth. By then it will have reached it's maximum speed.

9. By now the Rock will be slowed down because of the negative accelleration... It is moving towards the initial starting point...

After it has travelled from the centre of the earth to the other end of the earth, it will have stopped completely.

10. Now finally the Rock is exactly at the starting position.

In reality there will have been some loss of speed due to friction, so the Rock will be slightly lower then the 100 m above the ground.

let's calculate the time it takes to free fall for the distance r.

initial speed =0 and after 6.4 * 10⁶ m it's speed will be maximum. We need to find out how much time passes before that distance is passed.

r = v*t + 0.5*a*t²

r = 0 + 0.5*a*t²

0.5*a*t² = r

t² = r / ( 0.5 * a )

t² = 6.4 *10⁶ / ( 0.5 * 9.8 )

t² = 1.306 * 10 ⁶

t = 1142.86 s

Now please confirm that in order for the Rock to move back to the initial starting point it has to travel 4 times as much time. It has to travel r to centre of the earth then another r to travel to to the other side of the earth, and back again. So indeed 4 times r.

The time it will take must be the same as 4 * 1142.86 s

now this is the time of one single wave ocillation.

Since T = 4571.43 s

f = 1 / 4571.43

f = 0.00021874993164 Hz

The frequency of the resulting harmonic motion is 2.19 *10-4

The frequency of the resulting harmonic motion is 0.000219 Hz

Answer:

measure 3 equals 121 degrees

Step-by-step explanation:

Measure 2 and 3 make a 180 angle and you subtract 59 from 180 and you get 121.

Answer:

151200

Step-by-step explanation:

We want to know how many permutations of 6 digits can be chosen from 10 different digits, so we use the formula:

nPr=n!(n−r)!

Here, r=6 and n=10, so we have:

10P6=10!(10−6)!=10!4!=10⋅9⋅8⋅7⋅6⋅5⋅4!4!=151,200

The measure of each inscribed angle at T and S is 72.5 degrees, and the sum of their measures is: 145 degrees

What is inscribed angle ?

An inscribed angle is an angle formed by two chords of a circle that have a common endpoint on the circle. The vertex of the inscribed angle is on the circle, and the sides of the angle intersect the circle at two distinct points.

There are some important properties of inscribed angles:

According to the question:
If the inscribed angles of T and S intercept the same arc, then they must be equal in measure. Let's call the measure of each angle x.

Since the sum of the measures of the angles in a triangle is 180 degrees, we can set up an equation to find the measure of the third angle in triangle TSY:

x + x + measure of angle YTS = 180 degrees

Simplifying the equation, we get:

2x + measure of angle YTS = 180 degrees

But we know that the measure of angle YTS is equal to half the measure of arc YZ, since it is an inscribed angle intercepting the same arc. So:

measure of angle YTS = 1/2 * measure of arc YZ = 1/2 * 70 degrees = 35 degrees

Substituting this value into our equation, we get:

2x + 35 degrees = 180 degrees

Solving for x, we get:

2x = 145 degrees

x = 72.5 degrees

Therefore, the measure of each inscribed angle at T and S is 72.5 degrees, and the sum of their measures is:

72.5 degrees + 72.5 degrees = 145 degrees

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Austin's rate of motion is (1/70)π Radians per second.

To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:

ω = Δθ / Δt

Where:

ω = angular velocity (in radians per second)

Δθ = change in angular displacement (in radians)

Δt = change in time (in seconds)

We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:

s = (3/4) * 2πr

s = (3/2)πr

We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).

So, Δt = 105 seconds

Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:

Δθ = (3/4) * 2π

Δθ = (3/2)π

Therefore, Austin's rate of motion (ω) in radians per second is:

ω = Δθ / Δt

ω = [(3/2)π] / 105

ω = (3/210)π

ω = (1/70)π radians per second

So, Austin's rate of motion is (1/70)π radians per second.

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Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

The perimeter of the rectangle = 2(length + width)

From the given figure

The length of the rectangle = 3x

The width of the rectangle = x

The perimeter = 2(3x + x)

Since the perimeter of the rectangle P = 1000

We will equate the expression of the perimeter above by 1000

2(3x + x) = 1000

Let us simplify the left side

2(3x) + 2(x) = 1000

6x + 2x = 1000

Add the like terms

8x = 1000

Divide both sides by 8

x = 125

To find the length

Substitute x by 125

The length = 3(125) = 375

Equation is 2(3x + x) = 1000

Length = 375

Answer:

B. x is less than or equal to 5

Step-by-step explanation:

The dot is on 5 and is also a solid dot which means it is less than or equal to or greater than or equal to

In this case it is less than or equal to because the line goes to the left

Hope this helped!

The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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Answer:

32 m

Step-by-step explanation:

Height of mast = 96tan30

Distance of second point = 96tan30 / tan60

Distance  = 32 m

Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

Answer:

396 miles

Step-by-step explanation:

he drove enough miles for it to charge $99, and charging 25 cents per mile  you would multiply 99x4 because .25 goes into one 4 times