I am thinking of six different odd numbers, the mean of the numbers is 16, the median is 15, the range is 26, the greatest number is 31, what is the greatest number value for the 2nd number?

The number of solutions possible to a system of equations that include a conic section depends on the type of equations involved

A system of equation that has a conic section may or may not have solutions.

It would have a solution if the equations intersect, when plotted on a graph and it would not, if otherwise

A conic section can be any of:

Example 1: No solution

Consider the following system of equations

The above system of equations has no solution because they do not intersect when plotted on a graph (see graph 1)

Example 2: One solution

Consider the following system of equations

The above system of equations has one solution because they intersect at one point (see graph 2)

Example 3: One solution

Consider the following system of equations

The above system of equations has two solutions because they intersect at two points (see graph 3)

The above examples imply that a system of equations that involves conic section can have as many solutions as possible.

The number of solutions depends on the type of equations involved

The attached graphs illustrate how a system of equations can have 0 to 4 solutions

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Answer:

c is the right answer

Step-by-step explanation:

okk how are u ?

The statement (C) "While long-term bonds have more risks associated with them, they have the potential to bring in higher returns for the initial investment" is correct.

Long-term bonds keep an investor's money locked up for a longer period than a short-term bond, giving the bond's price more time to be impacted by changes in interest rates and inflation.

As we know,

The fact that short-term bonds offer lower interest rates than long-term bonds is a drawback.

Long-term bonds have a larger chance of receiving higher rates since there is a bigger likelihood that interest rates will rise over time.

Bonds with a long term are often those that investors hold for almost ten years.

Thus, the statement (C) "While long-term bonds have more risks associated with them, they have the potential to bring in higher returns for the initial investment" is correct.

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Answer:

B.) y= 5/4x - 4

Step-by-step explanation:

Slope intercept form

y = 1.25x +-4

Equation of a straight line:

y = mx + b ------(i)

Step by Step Solution:

Step 1: Calculating Slope (m).

m = y2-y1x2-x1

m = -4-10-4

m = -5-4

m = 1.25

Now putting value of m in equation (i)

y = 1.25x + b -----(ii)

Step 2: Calculating Y-intercept (b).

Lets choose the first point, (4,1) for calculating y-intercept:

y = mx + b

1 = 1.25(4) + b

1 = 5 + b

-4 = b

b = -4

Now putting value of b in equation (ii)

y = 1.25x + -4

The domain is the set of inputs (x) and the range is the set of outputs (y).

Answer:

Step-by-step explanation:

Area of the rectangle = 33 inches sq

Area of a rectangle (formula) = l*b

let the width be x

length = 2 inches + 3x = 2+3x

Area of the rectangle = l*b = 2+3x + x

33 inches sq = 2+3x + x

33 in sq = 2+4x

33/2 = 4x

16.5/4 = x

x = 4.125

width= 4.125 inches

length = 2+3x = 2+3(4.125) = 14.375

(unless your poster is 32 sq inches and you made a mistake, just replace 33 with 32 and solve it)

The dimensions of the given rectangle are 11 in and 3 in.

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.

Given that the length of a rectangular poster is 2 more in than three times its width. The area of the poster is 33 square in.

Let the length of the rectangle be l and the width be w then,

Area = length*width

(3w+2)w = 33

3w² + 2w -33 = 0

On factorizing, we get,

w = 3 or -11/3

Considering w = 3 in because width can't be negative.

Therefore, width = 3 in

Length = 3*3+2 = 9 in

Hence, The dimensions of the given rectangle are 11 in and 3 in.

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Answer:

6720

Step-by-step explanation:

8 Permute 5

8 x7 x6 x5 x4

Answer: 6 large frames and 12 small frames

Step-by-step explanation:

We define the following:

x = number of large frames

y =  number of small frames

Make the following equations:

x + y = 18

19x + 9y = 222

Use system of equations to solve. We find the value of x first.

y = 18 - x

⇒ 19x + 9(18 - x) = 222

⇒ 19x + 162 - 9x = 222

⇒ 10x + 162 = 222

⇒ 10x = 60

⇒ x = 6

Find value of y:

6 + y = 18

y = 12

∴ 6 large frames and 12 small frames were purchased.

The system of equations is 5x - y - 5 = -7, -6x + 6y + 3z = 8 and -6x - 8y - 2z = 2

The matrix is given as:

[tex]\left[\begin{array}{ccc}5&-1&-5\\-6&6&3\\-6&-8&-9\end{array}\right] \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}-7&8&2\end{array}\right][/tex]

Next, we multiply the matrices

[tex]\left[\begin{array}{c}5x - y - 5&-6x + 6y + 3z&-6x -8y -2z\end{array}\right] = \left[\begin{array}{c}-7&8&2\end{array}\right][/tex]

By comparing the position of the cells, we have

5x - y - 5 = -7

-6x + 6y + 3z = 8

-6x - 8y - 2z = 2

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The system of equations is 5x - y - 5z = -7, -6x + 6y + 3z = 8, and -6x -8y -2z = 2 which is represented by the matrix in the provided picture.

It is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.

We have given matrices in the picture that represents the system of the equation.

[tex]\rm \left[\begin{array}{ccc}5&-1&-5\\-6&6&3\\-6&-8&-2\end{array}\right] \rm \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-7\\8\\2\end{array}\right][/tex]

After the multiplication of two matrices:

[tex]\rm \left[\begin{array}{ccc}5x-y-5z\\-6x+6y+3z\\-6x-8y-2z\end{array}\right] = \left[\begin{array}{ccc}-7\\8\\2\end{array}\right][/tex]

On comparing:

5x - y - 5z = -7

-6x + 6y + 3z = 8

-6x -8y -2z = 2

Thus, the system of equations are 5x - y - 5z = -7, -6x + 6y + 3z = 8, and -6x -8y -2z = 2 which is represented by the matrix in the provided picture.

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Answer:

$450,000

Step-by-step explanation:

$150,000 times 3 because he made 1/3 of the profits

Hi student, let me help you out!

...................................................................................................

Let's substitute the value of x for x: [tex]\mathrm{2(3)+y=7}[/tex].

Upon simplifying, we get: [tex]\mathrm{6+y=7}[/tex].

Now we solve for y by subtracting 6 from both sides: [tex]\mathrm{1=y}[/tex]

Thus, the solution is [tex]\bigstar~\underline{\boxed{\mathrm{y=1}}}[/tex]

Hope it helped you out, ask in comments if any queries arise.

The values of sin (x/2) = 4/√17,   cos (x/2) = 1/√17 and  tan (x/2) = 4.

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

Here, cos x = -15/17  (given)

we know, cos x = 2cos²x/2 - 1

                cos²(x/2) = (cos x + 1)/2

                  cos²(x/2) = (-15/17 + 1)/2

                 cos²(x/2) = 1/17

                 cos (x/2) = 1/√17

then, sin (x/2) = √(1- cos²(x/2))  

          sin (x/2) = √(1 - 1/17)

          sin (x/2) = √16/17

          sin (x/2) = 4/√17

and tan (x/2) = sin (x/2) / cos (x/2)  

       tan (x/2) = [tex]\frac{4/\sqrt{17} }{1/\sqrt{17} }[/tex]

       tan (x/2) = 4

Thus, the values of sin (x/2) = 4/√17,   cos (x/2) = 1/√17 and  tan (x/2) = 4.

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The rate of change would be 300 bacteria per minute at 0.1 minutes past 1 PM

The given parameters are:

Initial, a = 20

At 30 minutes, Value = 500

An exponential function is represented as:

y = ab^t

Where a is the initial value.

So, we have:

y = 20b^t

After 30 minutes, we have:

20b^30 = 500

Divide both sides by 20

b^30 = 25

Take the 30th root of both sides

b = 1.11

Substitute b = 1.11 in y = 20b^t

y = 20(1.11)^t

Hence, the exponential model is y = 20(1.11)^t

This means that:

y = 11,000

So, we have:

20(1.11)^t = 11000

Divide both sides by 20

1.11^t = 550

Take the logarithm of both sides

tlog(1.1) = log(550)

Divide both sides by log(1.1)

t = 66

Hence, the population would reach 11,000 after 66 minutes

This means that:

t = 60 i.e. 60 minutes after 1PM

So, we have:

y = 20(1.11)^60

Evaluate

y = 10481

Hence, the population at 2PM is 10481

In (c), we have:

y = 10481 ------ population at 2PM is 10481

t = 60

The rate of change is calculated as:

Rate = 10481/60

Evaluate

Rate = 174.68

Hence, the rate of change at 2PM is 174.68 bacteria per minute.

The rate of change is calculated as:

Rate = Population/Time

So, we have:

y/t = 300

This gives

y = 300t

Substitute y = 300t in y = 20(1.11)^t

300t = 20(1.11)^t

Divide both sides by 20

15t = (1.11)^t

Using a graphing calculator, we have:

t = 0.1

Hence, the rate would be 300 bacteria per minute at 0.1 minutes past 1 PM

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Answer:

B

Step-by-step explanation:

just do 2x + 1 - (x^2 - 7) = -x^2 +2x + 8 = B

The three strength training exercises that can be performed by adults at an average fitness level are:

The health benefits of strength training include:

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The time it takes to cover 279 miles is 4.5 hours.

Rate is a measure of one quantity against another.

Analysis:

If it takes 6 hours to cover 279 miles, then it takes 6/372 hours to cover 1 mile.

Therefore 279 miles = 6/3472 x 279 = 4.5 hours

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The equation in point slope form is y - 6 = -8/5(x + 2)

The points are given as:

(-2, 6) and (3, -2)

Start by calculating the slope (m) using:

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

This gives

m = (-2 - 6)/(3 + 2)

Evaluate

m = -8/5

The linear equation is then calculated using:

y - y1 = m(x - x1)

This gives

y - 6 = -8/5(x + 2)

Hence, the equation in point slope form is y - 6 = -8/5(x + 2)

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Answer:

D. 64

Step-by-step explanation:

-2(square root of x) + 4 = -12

-2(square root of x) = -12 - 4

-2(square root of x) = -16

divide by negative 2 both sides

square root of x = 8

the we square both sides

(square root of x)^2 = (8)^2

therefore x = 64

Answer:

Step-by-step explanation:

Converting [tex]\theta[/tex] to degrees,

[tex]\theta=\left(\frac{11\pi}{6} \right) \left(\frac{180}{\pi} \right)=330^{\circ}[/tex]

This means [tex]\theta[/tex] lies in Quadrant 4, and thus its reference angle is [tex]360^{\circ}-330^{\circ}=\boxed{30^{\circ}}[/tex]

Since [tex]\theta[/tex] lies in the fourth quadrant, [tex]\sin \theta[/tex] and [tex]\tan \theta[/tex] are negative.

Since [tex]\theta[/tex] lies in the fourth quadrant, [tex]\cos \theta[/tex] is positive, and is equal to [tex]\cos (30^{\circ})=\boxed{\frac{\sqrt{3}}{2}}[/tex]

By applying the change of scale, we will see that the drawing has a length of 0.83ft and a width of 0.42ft.

When we apply a scale factor, we just need to multiply all the dimensions by the scale factor.

Here we know that the real length of the kitchen is 20ft, and the scale factor is K = 1/24.

Then the length of the kitchen in the drawing will be:

L = 20ft*(1/24) = (5/6) ft = 0.83 ft.

And the original width is 10ft, so the width on the scale drawing is:

W = 10ft*(1/24) = (5/12) ft = 0.42ft

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The change of scale, we will see that the drawing has a length of 0.83ft and a width of 0.42ft.

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

Here,  we know that the real length of the kitchen is 20ft, and the scale factor is k = 1/24.

Length = 20ft*(1/24) = (5/6) ft = 0.83 ft.

and, Width = 10 X (1/24) = (5/12) ft = 0.42ft

Thus, the change of scale, we will see that the drawing has a length of 0.83ft and a width of 0.42ft.

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Part A

The x intercepts always occur when y = 0.

The two x intercepts are at the locations (-2, 0) and (2, 0)

We can shorten that to p = -2 and q = 2

The intercept form of a quadratic is y = a(x-p)(x-q)

So we have y = a(x-(-2))(x-2) which turns into y = a(x+2)(x-2)

Plug in x = 0 and y = -4 from the y intercept and solve for 'a'

y = a(x+2)(x-2)

-4 = a(0+2)(0-2)

-4 = a(2)(-2)

-4 = -4a

a = -4/(-4)

a = 1

We go from y = a(x+2)(x-2) to y = (x+2)(x-2) which is one possible answer.

Let's expand that out using the FOIL rule

y = (x+2)(x-2)

y = x*x - 2*x + 2*x + 2(-2)

y = x^2 - 2x + 2x - 4

y = x^2 - 4 is another possible answer

-----------------------

The two possible answers are:

y = (x+2)(x-2)

y = x^2 - 4

=============================================================

Part B

We have p = -7 and q = -1 as the x intercepts. They occur when y = 0.

y = a(x-p)(x-q)

y = a(x-(-7))(x-(-1))

y = a(x+7)(x+1)

Plug in x = 0 and y = 7. Solve for 'a'

y = a(x+7)(x+1)

7 = a(0+7)(0+1)

7 = a(7)(1)

7 = 7a

a = 7/7

a = 1

We go from y = a(x+7)(x+1) to  y = (x+7)(x+1)

Expanding that out gets us

y = (x+7)(x+1)

y = x*x + 1x + 7x + 7*1

y = x^2 + 8x + 7

-----------------------

The two possible answers are:

y = (x+7)(x+1)

y = x^2 + 8x + 7

Answer:

a.

• In standard form : x² - 4 = 0

• In factored form : (x - 2)(x + 2) = 0

b.

• In factored form : (x + 7)(x + 1) = 0

• In standard form :  x² + 8x + 7 = 0

Step-by-step explanation:

a)  Consider the quadratic expression:

P(x) = ax² + bx + c

• (0 , -4) ∈ Table ⇒ P(0) = -4 ⇒ a(0)² + b(0) + c = -4

⇒ c = -4

• (-1 , -3) ∈ Table ⇒ P(-1) = -3 ⇒ a(-1)² + b(-1) - 4 = -3

⇒ a - b = 1

• (1 , -3) ∈ Table ⇒ P(1) = -3 ⇒ a(1)² + b(1) - 4 = -3

⇒ a + b = 1

Solving the system for a and b :

a - b = 1

a + b = 1

⇒ 2a = 2 and 2b = 0

⇒ a = 1 and b = 0

Conclusion:

The quadratic equation P = 0 for the table is :

• In standard form : x² - 4 = 0

• In factored form : (x - 2)(x + 2) = 0

………………………………………………………………………

b)  Consider the quadratic expression:

Q(x) = a'x² + b'x + c'

Factored form :

Q(x) can be written in the form Q(x) = m(x - p)(x + q)

• (-7 , 0) ∈ Table ⇒ Q(x) = m(x − -7)(x - q) = m(x + 7)(x - q)

• (-1 , 0) ∈ Table ⇒ Q(x) = m(x + 7)(x − -1) = m(x + 7)(x + 1)

• (0 , 7) ∈ Table ⇒ Q(0) = 7 ⇒ m(0 + 7)(0 + 1) = 7

⇒ 7m = 7 ⇒ m = 1

Therefore ,

Q(x) = (x + 7)(x + 1)

Equation of the table :  (x + 7)(x + 1) = 0

Q in Standard form :

Just factor  (x + 7)(x + 1)

⇒ x² + x + 7x + 7 = x² + 8x + 7

Equation of the table :  x² + 8x + 7 = 0

Answer:

dehydration

Step-by-step explanation:

Answer:

Centroid of the triangle is (4, 1).

Step-by-step explanation:

Centroid Formula (for a triangle)

[tex]\text{centroid} = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3})[/tex]
x₁, x₂, x₃ ... x-coordinates of the vertices

y₁, y₂, y₃ ... y-coordinates of the vertices

Given:

A(6, 2)

B(-1, 6)

C(7, -5)

Insert coordinates in the formula. Points are in form (x, y).

[tex](\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3})[/tex]

[tex](\frac{6 - 1 + 7}{3}, \frac{2 + 6 - 5}{3})[/tex]

[tex](\frac{12}{3}, \frac{3}{3})[/tex]

[tex](4, 1)[/tex]

1. Drawn a straight line AB =7 cm with the help of ruler.

2. With the help of compass drawn an arc from A and at the point where it cuts AB from that point made another arc drawn an arc cutting the previous arc.

3. From A drawn a straight line joining the arc and extend it to M.

4. With the help of ruler measured 5 cm and mark it as AC.

5. Joined BC and we get the required triangle.

6. From C drawn an arc and make it cut on AC and BC and from the point it cuts AC and BC drawn arc cutting each other and extend a line from point C extend a line to the point point of intersection of two arc.

7. Similarly we do for A and the point where the two line intersect denoted as O.

8. Made a perpendicular from O on AB this perpendicular will be radius and taking O as centre we draw a circle this is our incircle.

9. And AN is our locus of points equidistant from two lines AB and AC.

We need to construct a circle inscribed in triangle that is incircle it can be done by making angle bisector of two sides the point where it intersect will be incentre. The centre of required circle.

The angle bisector is the locus where points are equidistant from two sides.

In the interval (-2, 0) the function f(x) and g(x) will be negative, the correct choice would be (2, 0)

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have functions:

f(x) = x² + 2x

g(x) = log(2x + 1)

The domain of the function f(x) will be all real values of x

The domain of the function g(x) will be x ∈ (-0.5, ∞)

After plotting the graph of functions f(x) and g(x) we see:

f(x) will be negative in the interval of (-2, 0)

g(x) will be negative in the interval of (-0.5, 0)

Thus, in the interval (-2, 0) the function f(x) and g(x) will be negative the correct choice would be (2, 0)

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Using a proportional function, it is found that there are 60 pieces of gum in 4 packages.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

The constant is given by:

k = 15/1 = 30/2 = 45/3 = 15.

Hence the number of pieces of gums in x packages is given by:

y = 15x.

In 4 packages:

y = 15 x 4 = 60 pieces of gum.

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The option that represents a quadratic function is: (c) x^2 = 125

The attached image completes the question

A quadratic function is represented as:

y = ax^2 + bx + c

Using the above format, the option that represents a quadratic function is: (c) x^2 = 125

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Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

[tex]~~~~~~4x-12 = 24\\\\\implies 4(x-3) = 24\\\\\implies x -3 = \dfrac{24}4\\\\\implies x-3 = 6\\\\\implies x = 6+3\\\\\implies x = 9[/tex]