what is a turning point on a quadratic graph?

n=3; We need a third degree polynomials with the following given zero's: 2 and 5i are zeros; f(-1)=156.

Since these are solutions

x = 2 ; x = 5i. Since imaginaries travel in pairs, the other answer is x= -5i.

We have (x-2)(x-5i)(x+5i) = 0

Now,

f(-1) = (-1-2)(-1-5i)(-1+5i) = 156.

f(-1) = (-3)(26) = -78.

But -78 x -2 = 156, so our polynomial becomes

Y= -2x (x - 2 ) x (x to the power of 2 + 25) = 0

Answer:

[tex]f(x)=2x^4-12x^3+50x^2-56x-120[/tex]

Step-by-step explanation:

Complex Conjugate Theorem

For a polynomial p(x) with real coefficients, the complex zeros occur in conjugate pairs.  So if (a + bi) is a zero, then its conjugate (a - bi) is also a zero.

Given zeros:

-1, 3, and (2 + 4i)

As one of the given zeros is a complex number, (2 - 4i) is also a zero.

Write each zero as part of a factor and multiply them together, adding a leading coefficient [tex]a[/tex]:

[tex]\begin{aligned}f(x) & =a(x+1)(x-3)(x-(2+4i))(x-(2-4i))\\& = a(x+1)(x-3)(x-2-4i)(x-2+4i)\\& = a(x+1)(x-3)(x^2-2x+4ix-2x+4-8i-4ix+8i-16i^2)\\& = a(x+1)(x-3)(x^2-4x+4-16i^2)\end{aligned}[/tex]

Remember that [tex]i^2=-1[/tex], therefore:

[tex]\begin{aligned}f(x)&=a(x+1)(x-3)(x^2-4x+4-16(-1))\\&=a(x+1)(x-3)(x^2-4x+4+16)\\&=a(x+1)(x-3)(x^2-4x+20)\end{aligned}[/tex]

To find the value of the leading coefficient (a), use the given [tex]f(1)=-136[/tex] :

[tex]\begin{aligned}f(1) & = -136\\\implies a(1+1)(1-3)(1^2-4(1)+20) & = -136\\a(2)(-2)(17) & = -136\\-68a & = -136\\\implies a & = 2\end{aligned}[/tex]

Therefore, the polynomial in factored form is:

[tex]f(x)=2(x+1)(x-3)(x^2-4x+20)[/tex]

Finally, expand the brackets:

[tex]\begin{aligned}f(x) & =2(x+1)(x-3)(x^2-4x+20)\\& =2(x^2-2x-3)(x^2-4x+20)\\& =2(x^4-4x^3+20x^2-2x^3+8x^2-40x-3x^2+12x-60)\\& =2(x^4-4x^3-2x^3+20x^2+8x^2-3x^2-40x+12x-60)\\& =2(x^4-6x^3+25x^2-28x-60)\\& =2x^4-12x^3+50x^2-56x-120\end{aligned}[/tex]

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Answer: 3/11

The question is just asking you to select three people out of the group of eleven. And because we don't know there ages, the probability they are the oldest three in the group would be 3/11 or 3 out of 11.

Answer:

C.

Step-by-step explanation:

The person who ran farther is Hayley.

Average speed is the total distance travelled per time.

Average speed = total distance / total time

Tyler's average speed =  1 / 8.30 seconds = 0.12 miles per minute

The distance covered by Tyler in 10 minutes = 0.12 x 10 = 1.2 miles

Distance covered by Hayley in 10 minutes : 10 = 8x

x = 10 / 8 = 1.25 miles

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The function that correctly returns grades from 60 percent to a 100 percent is f(x) = [[(x - 50)/10]]

The question tells us that the students do not fail and they do not get a 100 percent score either.

Hence there is no need for worry if the grade is at 5.0 or less than 1.

For example we have

x = 82.976

f(82.976) =[[(82.976-50)/10]

This would then be 3.29

This is then = 3.0

This function is not an odd function and it is not an even function. This is because the domain does not have negative values.

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[tex]x = 12.9[/tex]

Note:

The following is sin formula:

[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]

1) Using the sin formula

[tex]sin(59) = \frac{x}{15} [/tex]

2) Multiply both sides by 15

[tex]15 \sin(59) = \frac{x}{15} \times 15[/tex]

3) Divide both sides by sin(59)

[tex] \frac{15 \sin(59) }{ \sin(59) } = \frac{x}{ \sin(59) } [/tex]

4) Find the value of x

[tex]x = 15 \sin(59) [/tex]

[tex]x = 12.9[/tex]

Answer:

Step-by-step explanation:

n = the number

n = 5m - 3

The algebraic expression is x > 2x + 1 and simplification form of the algebric expression is x < -1

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

The number that is x more than 2x+1

x is the number.

x > 2x + 1

After simplification:

2x - x < -1

x < -1

x ∈ (-∞, -1)

Thus, the algebraic expression is x > 2x + 1 and simplification form of the algebric expression is x < -1

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The numbers are:

What is number system?

A number system is defined as a system of writing to express numbers.

First, the number between 8,500 and 8,800.

So, the thousands place digit is 8.

Second, When multiplied by 8, the result is a whole number.

So, multiplying by 8, the decimal has to end in 5.

Because there is no zeroes in the decimal place..

options are:

8 times 0.5

8 times 0.25

8 times 0.125

Now, The digit in the hundredths place is 200% of the digit in the tenths place

considering digit in the hundreds place is ¾ the digit in the thousands place.

So, choose 0.125.

Now, The digit in the hundreds place is 3/4 the digit in the thousandths place.

Digit in Thousandth Place = 5

Digit in Hundreds place=3/4*2=6

Our number now is:86_ _.125

As, The sum of all the numbers is 26

8+6+1+2+5=22

26-22=4

The possible numbers are:

8,640.125

8,604.125

8,622.125

8,613.12

8,631.125

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Answer:

19/24

Step-by-step explanation:

3/8=36/96

5/12=40/96

36/96+40/96=76/96

76/96=19/24

The interval notation for all real numbers between -3 and 8 is:

[-3, 8].

There are an infinite number of real numbers between a and b, hence we list all them in interval notation, as follows:

In this problem, we include -3 and 8, hence the notation is:

[-3, 8].

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Answer:

The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

Step-by-step explanation:

Let’s assume the speed of the plane =x miles/hr

And let the speed of wind =y miles/hr

So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr

Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr

We know that, distance=speed×time

Then according to the given conditions, we have

3300=(x+y)×(3+(18/60))

here convert 18mins to hour by dividing by 60 and add to 3hrs.

⇒x+y= 3300/3.3

⇒x+y=1000 … (i)

And,

3300=(x-y)×(4+(24/60))

here convert 24mins to hour by dividing by 60 and add to 4hrs.

⇒x-y= 3300/4.4

⇒x-y=750 … (ii)

Adding equation (i) and (ii), we get

2x=1750

⇒x= 1750/2

=875

Substituting the value of x in equation (ii), we get

875−y=750

⇒y=875-750

⇒y=125

Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

Step-by-step explanation:

if I understand your comment correctly, then you need the mean value of the lifetime of these light bulbs.

1. get the midpoint of each interval.

2. multiply each frequency with its midpoint.

3. sum all frequencies.

4. sum all multiplication results if 2. (of frequencies and midpoints).

5. divide 4. by 3.

lifetime midpoints :

(25 + 50)/2 = 75/2 = 37.5

(50 + 100)/2 = 150/2 = 75

(100 + 150)/2 = 250/2 = 125

(150 + 200)/2 = 350/2 = 175

(200 + 250)/2 = 450/2 = 225

(250 + 300)/2 = 550/2 = 275

(300 + 350)/2 = 650/2 = 325

multiply frequencies with their midpoints :

37.5 × 47 = 1762.5

75 × 86 = 6450

125 × 45 = 5625

175 × 36 = 6300

225 × 0 = 0

275 × 37 = 10175

325 × 50 = 16250

sum all frequencies

47+86+45+36+0+37+50 = 301

sum all multiplication results of 2.

1762.5+6450+5625+6300+0+10175+16250 = 46,562.5

divide 4. by 3.

the mean value is

46,562.5 / 301 = 154.692691... hours ≈

≈ 154.69 hours

The total surface area of a cylinder with radius 4 and height 8 is 96π.

It follows from the task content that the total surface area of the cylinder is to be determined. The total surface area of the cylinder is given by the formular;

S=2πr(r+h)

S=2πr(r+h)

= 2 × π × 4(4 + 8)

= 2 × π × 4(12)

= 2π × 48

= 96π

Hence, the total surface area of the cylinder in terms of π is; 96π.

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The notation "t(x)" represents the statement t is a function of x

The notation is given as:

t(x) = ....

The above notation is a function notation, and it used to relate one element  to another

For instance:

f(x) means f is a function of x

Similarly, "t(x)" represents the statement t is a function of x

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The equation of the function is the graph of line.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The function is given below.

f(x) = (3/4)x – 2

The function is an equation of line.

The graph of the function is given below.

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The amount of heavy-duty fencing to be used is 2000 ft for $9000 and the amount of standard fencing to be used is 3000 ft for $9000 in order to make a total cost of $18000.

The area of the rectangular plot is denoted by the length multiplied by the width.

Let us assume that the length = x and the width = y.

Then, for two opposite with heavy fencing for $4.50 a foot and the standard fencing for $3 a foot, we have:

2x (4.50) + 2y(3) = 18000  ---- (1)

⇒ 9x + 6y = 18000

Make (y) the subject, we have:

[tex]\mathbf{y = \dfrac{18000-9x}{6}}[/tex]

Replace the value of y with the area of the rectangle, and we get:

[tex]\mathbf{Area =x(\dfrac{18000 - 9x}{6})}[/tex]

Area = x(3000 - 1.5x)

Area = 3000x - 1.5x²

For the area to be maximum, we take the differentiation of the Area:

dA/dx = 0

dA/dx = 3000 - 3x

x = 3000/3

x = 1000 ft

From equation (1)

2x (4.50) + 2y(3) = 18000  

x (4.50) + y(3) = 9000  

1000(4.50) + 3y = 9000

3y = 9000 -4500

y = 4500/3

y = 1500 ft

So, there are (1000× 2)ft = 2000ft heavy duty fencing for $9000, and (1500 ×2)ft = 3000ft standard fencing for $9000 to make a cost of $18000.

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Answer:

  72 guests

Step-by-step explanation:

We can add up the numbers of bottles per guest, then use that total to find the number of guests from the number of bottles.

Let g represent the number of guests at the party. Then there are ...

The total number of bottles is ...

  g(1/3 +1/6 +1/4) = 54

Multiplying by the inverse of the coefficient of g, we find its value to be ...

  g(4/12 +2/12 +3/12) = g(9/12) = 54

  g = 54(12/9) = 72

There are 72 guests at the party.

Step-by-step explanation:

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Answer:

Height is 40√2 m or 56.57 m

Explanation:

Use Pythagoras theorem: a² + b² = c²

where 'a' and 'b' are the legs and 'c' is the hypotenuse

Here given:

Substitute values:

(20)² + (h)² = 60²

400 + h² = 3600

h² = 3600 - 400

h² = 3200

h = √3200

h = 40√2

h = 56.6 meter

Answer:

Again, this would be 2444.

Step-by-step explanation:

Because of the previous answers 1963 and 481, we can add them together to make 2444.

the astronaut would weigh 1 pound above the Earth.

Given that;

Gravitational force = Gm/r^2

M1 = 196 pounds

M2 = unknown

R1 = 4000 miles

R2 = 300 miles

We can deduce that;

[tex]\frac{m1}{r^21} = \frac{m2}{r^22}[/tex]

Let's substitute the values

[tex]\frac{196}{4000^2} = \frac{x}{300^2}[/tex]

[tex]\frac{196}{1.6 *10^7} = \frac{x}{9 *10^4}[/tex]

Cross multiply

196 × 9 ×10^4 = x × 1.6 ×10^7

1.76 × 10^7 = x × 1.6 ×10^7

Make 'x' the subject of formula

x = [tex]\frac{1.76* 10^7}{1.6*10^7}[/tex]

x = 1.1

x = 1 pound

Thus, the astronaut would weigh 1 pound above the Earth.

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Critical value z_{0.05}=-1.645

Decision Rule, Reject H if z< -1.645

We do not reject the null hypothesis.

Generally, the equation for the hypothesis  is  mathematically given as

H P=0.3

H2:P<0.13

Therefore

[tex]z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n}}}\\\\\\z=\frac{0.11-0.13 }{\sqrt{\frac{0.13(1-0.13)}{76}}}[/tex]

z=-0.52

In conclusion, from the table

Critical value z_{0.05}=-1.645

Decision Rule, Reject H if z< -1.645

In conclusion, we do not reject the null hypothesis.

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Answer:

Graph D (look in the attached picture)

The way you do this is use the quadratic formula to solve for the x intercepts which are [tex](\frac{1+\sqrt{2} }{2} )[/tex] and [tex](\frac{1-\sqrt{2} }{2})[/tex]

The integers are 12,14 and 16

Consecutive even integers are represented as:

x, x + 2 and x + 4

So, the statement is represented as:

7 * (x + x + 2 + x +4) = 140 + 11 * (x + 2)

Evaluate the like terms

7 * (3x + 6) = 140 + 11 * (x + 2)

Open the brackets

21x + 42 = 140 + 11x + 22

Collect the like terms

21x -11x =

Evaluate

10x = 120

Divide by 10

x = 12

So, we have

x + 2 = 14

x + 4 = 16

Hence, the integers are 12,14 and 16

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The value of the equation is A = 12p , where p is the number of packages of batteries

Equations are mathematical statements with two algebraic expressions on either side of the equals (=) sign.

It depicts how the expressions on the left and right sides are linked together.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are all parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of packages be represented as p

Let the number of batteries in one package = 12 batteries

So , the total number of batteries in p packages A = number of packages x number of batteries in one package

The total number of batteries in p packages A = 12p

Hence , the equation is A = 12p

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Answer:

150

Step-by-step explanation:

Mean is average, so adding any number above the original mean would increase the mean.

The amount of interest that the principal in each account had earned is as follows:

Raul Avila = $167.12

Samuel Griffin = $364.91

The compound interest can be calculated using the compound interest formula:

A = P(1 + \frac{r}{n})^{nt}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

It can also be computed using an online finance calculator as follows:

N (# of periods) = 110 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $10,000

PMT (Periodic Payment) = $0

Results:

FV = $10,167.12

Total Interest = $167.12

N (# of periods) = 120 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $20,000

PMT (Periodic Payment) = $0

Results:

FV = $20,364.91

Total Interest = $364.91

Thus, using the online finance calculator, the compound interests for each principal have been computed as $167.12 and $364.91, respectively.

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A triangular prism is a prism which has both of its base sides as a rectangle. The length of side AB is 5/(√2) cm.

Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

The area of AEDC is 25 cm². Therefore,

AEDC = AC²

25 cm² = AC²

AC = 5 cm

In ΔABC,

AB² + BC² = AC²

Since AB=BC,

2(AB²) = AC²

AB² = 25/2

AB = 5/√2 cm

Hence, the length of side AB is 5/(√2) cm.

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False . The equation a= 2√3 ft.;c = 4 ft is: A= 2√3 ft².

Given:

a = 2√3 ft,

c = 4 ft,

Lengths of the sides of a right triangle = a and b

Hypotenuse= c

Hence:

c²=a²+b²

4²=(2√3)²+b²

16=12+b²

4=b²

b=2

Area of triangle

A=1/2×a×b

A=1/2×2√3×2

A=4√3÷2

A=2√3 sq.ft

The Area of the triangle is 2√3 ft².

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