Find the axis of symmetry and the vertex of the graph of the function: y=-1/2x^2+4x-7

Answer:

$7.50

Step-by-step explanation:

Have a good day

Answer:

3.65

rounded to the nearest hundredth

Answer:

3.65

Step-by-step explanation:

5 rounds up. That makes the 4 in the hundredth place a 5 because of the rounding.

Answer:

6 : 11

Step-by-step explanation:

12 : 22

reduce

6 : 11

Answer:

6:11

Step-by-step explanation:

Bunnies: dogs

12           :  22

Divide by 2

12/2      :22/2

6         : 11

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Answer: Here is what you need to solve your problem!

The graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.

If the value of is constant for every value that satisfies a certain condition, it means that the graph is a horizontal line on that interval. The behavior of the graph is constant or unchanging in terms of its vertical position.

When every value of x that satisfies a given condition results in a constant value of y, this tells us that the behavior of the graph of the function on this interval is horizontal. In other words, the graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.

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The parametric equations for the tangent line are:

x = 1 + at

y = -8t

z = 1 - at

To find the parametric equations for the tangent line, we need to determine the slope of the curve at the specified point (1, 0, 1). The slope of the curve can be found by taking the derivative of each component of the parametric equations with respect to t.

Taking the derivatives, we have:

dx/dt = -8e^(-8t)cos(8t) - 8e^(-8t)sin(8t)

dy/dt = -8e^(-8t)sin(8t) + 8e^(-8t)cos(8t)

dz/dt = -8e^(-8t)

Evaluating these derivatives at t = 0 (since the point (1, 0, 1) corresponds to t = 0), we get:

dx/dt = -8cos(0) - 8sin(0) = -8

dy/dt = -8sin(0) + 8cos(0) = 8

dz/dt = -8

The slope of the tangent line at t = 0 is given by the ratios of these derivatives: dx/dt, dy/dt, dz/dt. Therefore, the slope of the tangent line is (-8, 8, -8).

Using the point-slope form of the equation of a line, we can write the parametric equations for the tangent line as:

x = 1 - 8t

y = 8t

z = 1 - 8t

These parametric equations represent the tangent line to the curve at the specified point (1, 0, 1).

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Answer:

k = ±12

Step-by-step explanation:

Equation of the graph is,

y = -2x² + kx - 18

Discriminant of a quadratic equation, y = ax² + bx + c is defined by

Discriminant = √(b²- 4ac)

If √(b²- 4ac) = 0,

Equation will have one real solution.

Discriminant of the the given equation = √[k² - 4(-2)(-18)]

Since, graph of the equation is tangent to the x-axis, there will be one real solution.

Therefore, √[k² - 4(-2)(-18)] = 0

k² - 144 = 0

k = ±√144

k = ±12

Answer:

Shakespeare creates an immediate mood of sadness around Romeo because he said sad hours go by slow. also, he talks to benvolio about how sad he is

Answer:

Step-by-step explanation:

You can add the numbers in different ways but still get the same answer.

1. 3 + 5 + 4.5 = 12.5

2. 5 + 3 + 4.5 = 12.5

3. 3 + 4.5 + 5 = 12.5

4. 5 + 4.5 + 3 = 12.5

5. 4.5 + 5 + 3 = 12.5

6. 4.5 + 3 + 5 = 12.5

These a couple of different ways you can add the numbers to get the same answer. This shows proof of how the associative property is related and gets you the correct answer no matter how the numbers are positioned.

P.S - You can solve this for different numbers.

Hope this helped,

Kavitha

Step-by-step explanation:

f(-6) means we replace every x with the value -6

(-5 × -6) + 3×2

30 + 6 = 36

Answer:

3/4

Step-by-step explanation:

Given two points , we find the slope using the formula

m = (y2-y1)/(x2-x1)

   = ( 5 - -1)/ ( 6 - -2)

   = (5+1)/( 6+2)

   = 6/8

   = 3/4

________________________________

Hey!!

Solution,

P(-2,-1)-------- (X1,y1)

Q(6,5)-----------(x2,y2)

Slope=y2-y1/x2-x1

= 5-(-1)/6-(-2)

= 5+1/6+2

=6/8

= 3/4

The slope is 3/4

Hope it helps

Good luck on your assignment

________________________________

Answer:

v = - 6

Step-by-step explanation:

10 + 3v = - 8 ( subtract 10 from both sides )

3v = - 18 ( divide both sides by 3 )

v = - 6

Answer:

Step-by-step explanation:

10 + 3v = –8

3v=-8-10

3v=-18

v=-18/3

v=-3

Answer:

300 students is the maximum capacity of students the school can hold.

Step-by-step explanation:

The variables of farmer are independent variables and dependent variables.

In this scenario, the farmer is testing the impact of different amounts of nitrogen on corn plant height. Her variables are as follows:

1. Independent variable: The amount of nitrogen infused in the soil (one pot has nitrogen-infused soil and the other has regular soil).

2. Dependent variable: The height of the corn plants (measured in feet).

However, it's important to note that the experimental setup has a potential confounding variable, which is the location of the pots (one is outside and the other is in the bathroom). This might influence the results and make it difficult to solely attribute the differences in height to the nitrogen content in the soil.

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zbzbbzbzbzbzbzbznndn

Step-by-step explanation:

znzbzbBbB BBNNNNNNNNNNBBBBBBBBBBVVVCCFXDDDZSDJ

Answer:

( -3 , ∞)

Step-by-step explanation:

Answer:

dam I'll try to find the. answer 4 u

part a: In order to determine and interpret the least squares regression line (LSRL), you need to have a set of data points and perform regression analysis.

The LSRL is a line that best fits the data points and represents the relationship between two variables. It is commonly used to predict or estimate values based on the given data.

To determine the LSRL, you will need to calculate the slope and the y-intercept of the line. The slope (m) represents the rate of change of the dependent variable for a one-unit increase in the independent variable.

The y-intercept (b) represents the value of the dependent variable when the independent variable is equal to zero.

Once you have determined the LSRL equation in the form of y = mx + b, you can interpret it.

For example, if the LSRL equation is y = 2x + 3, it means that for every one unit increase in the independent variable, the dependent variable is expected to increase by 2 units.

The y-intercept of 3 indicates that when the independent variable is zero, the dependent variable is expected to be 3.

part b: To predict the percent of children living in single-parent homes in 1991 for state 14, we can use the LSRL equation.

First, substitute the known value of the independent variable (1985) into the equation and solve for the dependent variable (percent of children living in single-parent homes). Let's say the LSRL equation is y = 0.5x + 10.

In this case, x represents the year and y represents the percent of children living in single-parent homes. So, when x is 1985, we can substitute it into the equation:

y = 0.5 * 1985 + 10
y = 993.5 + 10
y ≈ 1003.5

Therefore, the predicted percent of children living in single-parent homes in 1991 for state 14 would be approximately 1003.5 percent.

part c: To calculate the residual for state 14, we need to compare the observed percent of children living in single-parent homes in 1991 (21.5 percent) with the predicted value we obtained in part b (1003.5 percent).

The residual is calculated by subtracting the predicted value from the observed value:

Residual = Observed value - Predicted value
Residual = 21.5 - 1003.5
Residual ≈ -982

The negative value of the residual indicates that the observed value is significantly lower than the predicted value.

In other words, the actual percent of children living in single-parent homes in state 14 in 1991 is much lower than what was predicted based on the LSRL equation and the data from 1985.



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Answer:

115.7 km/h

Step-by-step explanation:

velocity = distance/time

velocity = (0.9 km)/(28 s) = 0.032143 km/s

The velocity is 0.032143 k/s. The question is answered, but since km/s is not a common unit of speed, we can convert to a more common unit of speed such as km/h.

velocity = (0.9 km)/(28 s)[(3600 s)/(1 h)] = 115.7 km/h

Answer:

14

put the biggest number in the from and the smallest number in the back then add it

Answer:

Step-by-step explanation:

im asuming you want to find x.

25 + 16 = 41.

the length of the rectangle is sqrt41

64-41 = 23

the width of the rectangle is sqrt23

The perimeter of television is = 100 inches

The study of measuring geometric shapes and their qualities such as length, volume, shape, surface area, lateral surface area, and so on is known as mensuration. Mensuration will be covered in fundamental mathematics.

let the length be 16x and width be 9x

area given = 576 sq. inches

16x * 9 x = 576

144 \(x^{2}\) = 576

x = 24/12

x = 2

length = 32

width = 18

perimeter = (32 + 18)*2  =100 inches

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Answer:

yes

Step-by-step explanation:

The answer to your question is yes. We have calculated all the numbers that 831 is evenly divisible by. The numbers that 831 is divisible by are 1, 3, 277, and 831.

Bending moment curve equation below point A will be:

M = 15x - 3x² for 0 ≤ x ≤ b

Determination of shear and bending moment curves.

For the beam and loading shown, we can do the following:

Equation of shear curve (above point A):V = RA - w.x

For x = a,V = RA - w.a

For x = b,V = RA - w.b

Since the loading is symmetric, RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15 - 6a for a ≤ x ≤ b

Equation of shear curve (below point A):

V = RA - w.x

For x = 0,V = RA - w.0RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15k for 0 ≤ x ≤ a

The shear curve equation becomes;

V = 15k for 0 ≤ x ≤ a

V = 15 - 6a for a ≤ x ≤ b

Equation of bending moment curve (above point A):

M = RAx - ½w.x²For 0 ≤ x ≤ a,

M = 15x - ½(6x²) = 15x - 3x²For a ≤ x ≤ b,

M = 15x - 6a(x - a) - ½(6x²)= 15x - 6ax + 6a² - 3x²

The bending moment curve equation above point A becomes:

M = 15x - 3x² for 0 ≤ x ≤ a

M = 15x - 6ax + 6a² - 3x² for a ≤ x ≤ b

Equation of bending moment curve (below point A):

M = RAx - ½w.x²For 0 ≤ x ≤ b,

M = 15x - ½(6x²) = 15x - 3x²

The bending moment curve equation below point A becomes;

M = 15x - 3x² for 0 ≤ x ≤ b

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