A committee of five members is to be randomly selectedfrom a group of nine freshman and seven sophomores.Which expression represents the number of different committeesof three freshman and two sophomores that can be chosen?

Real solutions = 4/5 and 3

Imaginary solutions = 3i

The quadratic equation x² + 1 = 0 has a solution in the imaginary unit or unit imaginary number I Although there isn't a real number associated with this attribute, addition and multiplication can be employed to expand real numbers to so-called complex numbers. A real number is the real root of an equation. A complex root is a fictitious root that is represented by complex numbers in an equation. Imaginary numbers are "real" in the sense that they exist and are used in mathematics, even though they are not real numbers because they cannot be defined on a number line. Complex numbers, often known as imaginary numbers, are used in quadratic equations and in real-world applications like electricity.

Given,

Equation

4x³ + 5x² + 36x + 45 = 0

x²(4x + 5) + 9( 4x + 5) = 0

x² + 9 + (4x +5) = 0

(x - 3 ) (x +3) + (4x+5) = 0

x = 3i

x = [tex]\frac{4}{5}[/tex] and 3

Real solutions = 4/5 and 3

Imaginary solutions = 3i

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To find the coordinates of the midpoint of HX, we would apply the midpoint formula which is expressed as

From the information given,

Answer:

4x + 4y ≤ 80

6x + 8y ≤ 100

Explanation:

Let's define x as the number of children and y as the number of adults.

For Matinee tickets, they spend $4 per child and $4 per adult, so if the total is no more than 80, we get:

4x + 4y ≤ 80

In the same way, they spend $6 per child and $8 per adult on the evening tickets, so

6x + 8y ≤ 100

Therefore, the system is

4x + 4y ≤ 80

6x + 8y ≤ 100

The or probability in the context of this problem is represented as follows:

P(A U B).

The or probability between two events A and B is the probability that at least one of the events happen.

The symbol of the or probability is given as follows:

U

In the context of this problem, the events are given as follows:

Hence the probability of selecting a male students or selecting a student who owns a bicycle is represented as follows:

P(A or B) = P(A U B).

The other options are as follows:

The complete problem is given by the image at the end of the answer.

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The number of acres that are not federally owned = 3089.98 million

Land or other assets that are legally owned by the government or a government agency are referred to as government-owned property.

Federal, state, or local governments may be the owners of government-owned land, which may or may not be open to the general public without restriction.

If 14% of the land is federally owned, then 100 -14  = 86% of the land is not federally owned.

(14 *3593 ) / 100

50302 / 100 = 503.02

Federal owned land is 503.02 million acres of land.

3593 - 503.02 = 3089.98 =  (86× 3593) ÷ 100

Land not owned by Federal Government = 3089.98 million acres of land.

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SOLUTION

The figure above consists of a triangle and a semi-circle.

Area of the figure = Area the of triangle + Area of the semi-circle

Area of composite figure = 112.5 + 88.3125 = 200.8125

Therefore the Area of the figure = 200.81 squared feet to the nearest hundredth

Answer: g(f(5)) = 352

Step-by-step explanation:

The question being asked is the same as finding g(f(5)).

What this means is to find f(5), and then plug that value into g(x) as x and solve.

f(5) = 4(5) + 1 = 20 + 1 = 21

g(f(5)) = g(21) = 21^2 - 4(21) - 5 = 441 - 84 - 5 = 357 - 5 = 352

Note: You could also find g(f(x)), and then plug 5 in as x and solve.

Start by plugging f(x) into g(x) such that you get g(x = f(x))

g(f(x)) = (4x + 1)^2 - 4(4x + 1) - 5

Now, replace x with 5 and solve to get g(f(5)).

g(f(5)) = (4(5) + 1)^2 - 4(4(5) + 1) - 5 = 352

The y-intercept is located at the coordinate (0, 4) as shown below. Y-intercept is the point where a line or a graph crosses the y-axis.

If a quadratic equation has solutions

Then

Furthermore, the quadratic can be written as

Therefore,

Given:

Hence,

Simplify

Hence, the quadratic equation is

The given triangles are similar to each other, this means that we can get the length of the sides of the larger triangle by multiplying the corresponding lengths of the smaller one by a scale factor.

We can get the scale factor by dividing the length of one of the sides of the larger triangle by the length of the corresponding side in the smaller triangle, like this:

By taking the left sides

Then, in order to get the length of the base of the larger triangle (6), we just have to multiply the length of the base of the smaller triangle (y) by the scale factor (2), like this:

6 = 2×y

From this equation, we can solve for y to get:

2y = 6

2y/2 = 6/2

y = 3

Then, y equals 3 meters

Answer: 23

Step-by-step explanation:

You have 1 ten and 8 ones + 5 ones. First, add the ones to get 13 ones. Then, split the ones into tens and ones to get 2 tens and 3 ones which is 23.

Answer:

Step-by-step explanation:

find and classify the global extrema of the following function

f(x)=(x-2)^2+5

compute the critical points of (x-2)^2+5

to find all critical points, first compute f(x)

f(x)=2(x-2)

solving 2(x-2)=0 yields x=2

x=2

f(x) exists everyhere

2(x-2) exists everyhere

the only critical point of (x-2)^2+5 is at x=2

x=2

the domain of (x-2)^2+ 5 is R

the endpints of R are x = -∞ and ∞

Evalute (x-2)^2+5 at x = -∞, 2 and ∞

the open endpoints of the domain are marked in gray

x () f(x)

-∞   ∞

2     5

∞     ∞

the largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:

the open endpoints of the domain are marked in gray

x () f(x) extrema type

-∞   ∞  global max

2     5  global min

∞     ∞  global max

remove the points x = -∞ and ∞ from the table

These cannot be  global extrema, as the value of f(x) here is never achieved

x () f(x) () extrema type

2     5     global min

f(x) = (x-2)^2+5 has one global minimum

Answer:

f(x) has a global minimum at x = 2

Answer:

Step-by-step explanation:

we have the points

(-2,6) and (-3,-7)

step 1

Find out the slope

m=(-7-6)/(-3+2)

m=-13/-1

m=13

step 2

Find out the equation in slope-intercept form

y=mx+b

we have

m=13

point (-2,6)

substitute and solve for b

6=13(-2)+b

6=-26+b

b=32

therefore

y=13x+32

step 3

Convert to standard form

AX+By=C

y=13x+32

13x-y=-32 -------> is equivalent to -13x+y=32

therefore

Answer:

my answer i got is y=2x+9

Answer:

5

Step-by-step explanation:

They are asking for the Period. The Period goes from one peak to the next (or from any point to the next matching point). To me it looks like that value is 5 for this graph.

Answer:

53.76

Explanation:

The volume of the triangular prism is given by

where h is the height, b is the base, and l is the length of the prism.

Now in our case h = 3.2 m, b = 4.8 m, and l = 7m; therefore, the above equation gives

which is our answer!

Hence, the volume of the triangular prism is 53.76 cubic meters.

volume of a triangular pyramid = 1/3 * base area (triangle) *height

triange area= 1/2 base * height

triegle area= 1/7 in * 5.5 in = 38.5 in^2

Volume = 1/3 * 38.5 in^2 * 3 in

Volume = 38.5 in^3

___________________

Answer

choice b)

2) If DB = 27 the we can replace that:

and we can solve for x

now we can replace x in the equation for AC:

3) we have that:

So the segment AC will be the sum of the segments:

and we also know that

3) we have that:

Answer:

2pi

Explanation:

By definition, 360 degrees are equal to 2π radians.

This follows from the fact that the circumference of a circle is 2π times the radius. Therefore, if radius = 1, then

circumference = 2π

Since the circumference is the distance around a circle, and degrees are the "angular distance " around the circle, these two quantities can be related.

So if you think of the circle in terms of the circumference, a circle measures 2π. If you think in terms of degrees, a circle measures 360 degrees.

Therefore, we say

360 degrees = 2π (radians)

Let:

Mp = Marked price = $310

r = Rate of discount = 20% = 0.2

D = Discount

Sp = Sale price

The discount will be given by:

And the sale price will be:

first we need to solve X

we need to write the equation on this form

where h=-(b/2a) and k=c- a (b/2a)2

we obtain a,b and c from the equation to solve x

so a=-1/4, b=7/2 and c=-57/4

now lets find h and k

now replace a, h and k on the equation

the evrtex is (h,k)=(7,-2)

The equation of a parabola in standard form is

So, we have the following equations,

For ( 2, -20) , -20 = a(2)^2 + b (2) + c,

For (-2, -4), -4 = a( -2)^2 + b (-2) + c,

For (0.-8), -8 = a (0) + b (0) + c

Then solving,

4a + 2b + c = -20 .............. equ 1

4a - 2b + c = -4 ................... equ 2

c= -8

put c= -8 in equ 1,

we have

4a + 2b -8 = -20 = 4a + 2b = -12 ------equ 3

put c= -8 in equ 2,

4a - 2b -8 = -4 = 4a - 2b = 4................... equ 4

Solving equ 3 and equ 4, a= -1 , b= -4

so a =-1, b= -4, c= -8

Then substituting the values in

So, y= -x^2 -4x-8

Step 1: Let's review the information provided to us to answer the question correctly:

• Option 1: 10 donuts for 13.00

• Option 2: 1 dozen donuts for 12.00​

Step 2: Let's calculate the price of a donut in each option, as follows:

• One donut Option 1 = 13/10 = 1.30, this means the price of an individual donut is $ 1.30

• One donut Option 2 = 12/12 = 1, this means the price of an individual donut is $ 1

Step 3: Twitch Beast 8 will decide what is the cheapest unit rate based on the calculations we did on Step 2

To solve this problem, we can use the compound interest formula

Where A represents the accrued value, P represents the invested value, r represents the interest(in decimals), n represents the amount of times the interest is compounded per unit 't' and t represents the time.

Since the unit of the time 't' is years, and the interest is compounded yearly, n = 1.

To write a percentage as a decimal, we just have to divide the percentage value by 100.

To find the amount of time t, we just have to subtract the year the money was invested from the year we want to know the money accrued.

Then, using those values on the formula, we have

The accrued value in the year 2029 will be $16,073.18.

Answer: 503,000

Step-by-step explanation:

The best way to understand the concept is to look at a round to the nearest thousand example: what is 52437 rounded to the nearest thousand?

As the hundredth digit is 4, which is less than 5, the number should be rounded down to 52000. As for 52678, as the hundredth digit is 6, which is larger than 4, it will be rounded up to 53000.

As given by the question

There are given that the equation:

Now,

Put the value of x into the given equation and find the value of y from all the tables one-by-one and match their value of x and y are equal or not.

Then,

Form the option third,

Put x = -2 to find the value of y, then match the value of y with the given value of y in the table.

So,

Now,

Put x = -1, then:

Then,

Put x = 0, then:

Then,

Put 1 into the given equation instead of x:

So,

And,

Put x = 2, so:

Now,

From option d, all values of x and y are matched also but curve representation is matched in option D.

Hence, the correct option is D.

The equation is formed and solved below

What is an equation?

Algebra is concerned with two types of equations: polynomial equations and the particular case of linear equations. Polynomial equations have the form P(x) = 0, where P is a polynomial, while linear equations have the form ax + b = 0, where a and b are parameters, when there is only one variable. To solve equations from either family, algorithmic or geometric approaches derived from linear algebra or mathematical analysis are used. Algebra also investigates Diophantine equations with integer coefficients and solutions. The approaches employed are unique and derive from number theory. In general, these equations are complex; one frequently searches just for the existence or lack of a solution, and, if they exist, the number of solutions.

Let the price of washer = $x

The cost of dryer = $x+85

The equation is formed as

x + x + 85 = 765

or, 2x = 765 - 85

or, x = 680/2 = 340

Price of dryer = $(340+85) = $425

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This problem is related to the linear equation and the required cost of the dryer is $425.

What is a linear equation?

If a variable's maximum power is always 1, an equation is said to be a linear equation. As a one-degree equation, it also goes by that name.

Let a washer costs be [tex]w[/tex] and a dryer costs be [tex]d[/tex].

Since the total cost of a washer and a dryer is $765, it follows:

[tex]w+d=765[/tex]                ... (1)

Further, it is given that the washer costs $85 less than the dryer, it means that:

[tex]w=d-85[/tex]                 ... (2)

Using the two linear equations (1) and (2), it follows:

[tex]d-85+d=765\\2d-85=765\\2d=765+85\\2d=850\\d=\frac{850}{2}=425[/tex]

Therefore, the cost of a dryer is $425.

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Answer:

Step-by-step explanation:

You want the intercepts of the equation -6x +9y = -18.

There are several ways to find the intercepts. In each case, the x-intercept is the value of x that satisfies the equation when y=0, and vice versa.

For y = 0, we find the x-intercept to be ...

  -6x + 0 = -18

  x = -18/-6 = 3

The x-intercept is 3; the point at that intercept is (3, 0).

For x = 0, we find the y-intercept to be ...

  0 +9y = -18

  y = -18/9 = -2

The y-intercept is -2; the point at that intercept is (0, -2).

The intercept form of the equation for a line is ...

  x/a +y/b = 1

where 'a' is the x-intercept, and 'b' is the y-intercept.

We can get this form by dividing the original equation by -18.

  -6x/-18 +9y/-18 = 1

  x/3 +y/(-2) = 1

The x-intercept is 3; the y-intercept is -2.

__

Additional comment

When asked for the intercepts, it is sometimes not clear whether you are being asked for the value where the curve crosses the axis, or whether you are being asked for the coordinates of the point there.

Your previous "wrong" answer was given as point coordinates. Apparently, just the value at the axis crossing is required.

You have to have some understanding of your answer-entry and answer-checking software to tell the required form of the answer (or you can ask your teacher).

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Given:

There are 43 people who like chocolate 39 people like peanut butter and 29 people like both.

To draw: The ven diagram

Explanation:

Since 29 people like both chocolate and peanut butter.

Therefore,

The number of people who like chocolate only is,

The number of people who like peanut butter only is,

So, the total number of persons is,

The ven diagram is,

Where C represents the chocolate likers, B represents the peanut butter likers and U represents the total number of persons.

Final answer:

• The number of people who like chocolate only is 14.

• The number of people who like peanut butter only is 10.

• The total number of people is 53.

To solve the quotient below;

We simply both the numerator and the denominator as follows;