4. Create an equation for a 6th degree polynomial that only has the zeros of x=5, -4, -6, 1 with a y-intercept of 3600. Explain how you found your equation.

Answer:

8.5 and 10.5

Step-by-step explanation:

add your x1 and x2 coordinate and divide them by 2 to get your x.

and for the y add your y1 and y2 coordinate and divide them by 2 to get your y.

The x1, x2, y1, and y2 in this situation would be (5,14) (being the bridge)

and (12,7) being the castle.

x1 = 5

x2 = 12

y1 = 14

y2 = 7

Step1: Write the area of the circular Rug

The area of the circle is

From the question the diameter is 25feet, hence the radius is

Step2: substitute the value into the formula

Hence the area of the circular rug is 491.07 square feet

The will take approximately 491square feetyou

Answer:

4 : 5

Explanation:

We are told that 20 students saw the movie and 5 didn't, meaning there were in total 20 + 5 = 25 students; therefore, the ratio is

To simplify the ratio, we divide both the numerator and the denominator by 5. This gives

Hence, the ratio of the students who saw the movie to the total number is 4 : 5.

I am sorry if this is incorrect but the elevator started at floor 8 and

between 7 and 6 seconds it started to rise, it stopped moving at 19 seconds and 23

when it descended it stopped at floor 20

the floor rate is, 4 floors second

Answer:

I litteraly have the same problem and no clue how to do I

Step-by-step explanation:

x = -12

Given the following equation

We are to find the variable x. To do that, we will multiply both sides by -2 as shown:

This shows that the value of x for the equation to be true is -12

Check

If x = -12, on substiituting;

Since the result is equivalent to 6, this shows that the solution x = -12 is correct.

Answer:214.29

Step-by-step explanation:600 divided by 2.8

possibly the answer

It will take Sofia 3 hours to travel 13.5 miles at the same rate.

A rate is a ratio which compares two different quantities with different units.

For rate, the quantity at the denominator is usually expressed as a single unit to ascertain the extent of change of the other quantity

Sofia travelled 9miles for 2 hours so that her rate is 4.5 miles per hour

If she travels with the same speed and covered 13.5 miles,

Then the time she took to cover 13.5 miles is  = 13.5/4.5 = 3

In conclusion, It took Sofia 3 hours to cover 13.5 miles at the rate of 4.5 miles per hour.

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Answer:

17:11

Step-by-step explanation:
85/5 = 17 and 55/5 = 11

Thus, 85:55 ratio simplified is 17:11

The most appropriate choice for equation of line in slope intercept form will be given by

Unit price of apple in store A  = $4

Unit price of apple in store A  = $2

Unit price of apple in store A  = $3

What is equation of line in slope intercept form?

Equation of line in slope intercept form is given by y = mx + c

Where, m is the slope of the line and c is the y intercept of the line

The distance from the origin to the point where the line cuts the x axis is called x intercept

The distance from the origin to the point where the line cuts the y axis is called y intercept

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by [tex]tan\theta[/tex]

If the line passes through ([tex]x_1,y_1[/tex]) and ([tex]x_2, y_2[/tex])

slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Unit price of apple in store A = [tex]\frac{12}{3}[/tex] = $4

For store B

Putting x = 1

y = [tex]2 \times 1[/tex]

y = 2

Unit price of apple in store B = $2

For  store C

From the graph,

At x= 1, y = 3

Unit price of apple in store C = $3

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Complete Question

The graph has been attached

Over the course of 6 days, Tonda ran 17.22 miles. She ran the same distance each day. How far did Tonda run each day?

___________________________________________________________

17.22 miles / 6 days = 2.87 miles/ day

___________________________________________________

Answer

Ronda run each day 2.87 miles

Given that the points A, O and B lie on a straight line, then we can say that; x = 11°

We are told that the points A, O and B lie on a straight line.

Now, according to angle postulates, we know that the sum of all angles on a straight line sums up to 180 degrees. Thus, it means that;

∠AOC + ∠COD + ∠BOD = 180°

Plugging in the relevant values gives us;

3x + 88 + x + 36 + 2x - 10 = 180

6x + 114 = 180

6x = 180 - 114

6x = 66

x = 66/6

x = 11

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1.9 × 10^3  is 215 times smaller than 4.085 × 10^5.

The basic formula for the area of ​​a rectangle is length x width, but the basic formula for volume is length x width x height. The calculation does not change depending on how you refer to different measurements. For example, you can use depth instead of height.

Every 3D object occupies a certain space. This space is measured by its volume. Volume is defined as the space occupied within the bounds of an object in three-dimensional space. Also called the capacity of the object. The volume of an object is the amount of space it fills. Large capacity is measured in cubic meters m3. Smaller volumes are measured in cubic centimeters cm3 or cubic millimeters mm3.

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ANSWER

EXPLANATION

Let the number be x.

If the number is doubled, it becomes:

The number, double the number and 16 are added and the result is 61.

This implies that:

Solve for x:

That is the number.

Answer:

4.2

Step-By-Step explanation:

12.5+1.5=14

14 times 3= 42

42/10= 4.2

The consecutive even numbers have a value of 62 and 64

The sum of the consecutive even integers is given as

Sum = 126

Let the consecutive even integers be x and y

Where

y = x + 2

This means that the variable y has a smaller value

The sum of the consecutive even integers can be represented as

Sum = x + y

So, we have

Sum = x + x + 2

Evaluate the sum

Sum = 2x +2

This gives

2x + 2 = 126

Subract 2

2x = 124

Divide by 2

x = 62

Substitute x = 62 in y = x + 2

y = 62 + 2

Evaluate

y = 64

Hence, the even numbers are 62 and 64

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Answer:

1 1/2 + 1 1/2

Step-by-step explanation:

1 1/2 (or 1.5) plus 1 1/2 equals 3

Using the normal distribution, it is found that:

a) 1.39% of teenagers use their phone less than 5 hours per day.

b) 3.59% of teenagers use their phone more than 10 hours per day.

c) 49.85% of teenagers use their phone between 6 to 8 hours per day.

d) The 75th percentile of the distribution is of 8.59 hours.

The z-score of a measure X of a variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the fraction presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the daily amounts they use their phone are given as follows:

[tex]\mu = 7.75, \sigma = 1.25[/tex]

The proportion that use their phone for less than 5 hours a day is given by the p-value of Z when X = 5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (5 - 7.75)/1.25

Z = -2.2

Z = -2.2 has a p-value of 0.0139.

Thus the percentage is of 1.39%.

The proportion that use their phone for more than 10 hours a day is one subtracted by the p-value of Z when X = 10, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (10 - 7.75)/1.25

Z = 1.8

Z = 1.8 has a p-value of 0.9641.

1 - 0.9641 = 0.0359 = 3.59% (percentage).

The proportion between 6 and 8 hours a day  is the p-value of Z when X = 8 subtracted by the p-value of Z when X = 6, hence:

X = 8:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (8 - 7.75)/1.25

Z = 0.2

Z = 0.2 has a p-value of 0.5793.

X = 6:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (6 - 7.75)/1.25

Z = -1.4

Z = -1.4 has a p-value of 0.0808.

0.5793 - 0.0808 = 0.4985 = 49.85% (percentage).

The 75th percentile is X when Z = 0.675, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

0.675 = (X - 7.75)/1.25

X - 7.75 = 0.675 x 1.25

X = 8.59 hours.

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She travels at a speed of 6 miles per hour to the library. She travels at a speed of 12 miles per hour on her way home. The residence and library are eight miles apart.

Given that,

Bree's journey from her house to the library and return is shown in the table below. She travels at a speed of 6 miles per hour to the library. She travels at a speed of 12 miles per hour on her way home. The journey takes two hours in total.

We have to find which equation can be used to calculate the mileage between Bree's home and the library in miles.

Two or more equations that can be solved to get a singular result are referred to as a system of equations. The equation's power must be in one degree.

From home to the library, it takes d/6 hours.

The journey from the library to home takes d/12 hours.

The equation is

d/6+d/12=2 hours

2d+d=24

3d=24

d=24/3

d=8

Therefore, The residence and library are eight miles apart.

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The value represents the climber's change in elevation during the first minute of the training session is  1/5.

Given,

During the second minute of a two-minute training session, a rock climber completed a 12-meter ascent up the wall. The climber returned to the identical location she had been in at the beginning of the two-minute session.

Let x be the distance climbed by the climber is x m

During the first minutes(60 seconds): distance climbed =[tex]\frac{x}{60}[/tex]

In the 2nd minute, they climbed 12 m higher than in the 1st minute.

Now, the distance climbed by the climbed in the Second minute = [tex]\frac{x+12}{60}[/tex]

Now, the change in the elevation during the first minute of the training session= [tex]\frac{x+12}{60}-\frac{x}{60} = \frac{12}{60}=\frac{2}{10}=\frac{1}{5}[/tex]

Hence, the value represents the climber's change in elevation during the first minute of the training session is [tex]\frac{1}{5}[/tex]

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The determinant of a is the product of the pivots in any echelon form u of​ a, multiplied by ​(​1)r​, where r is the number of row interchanges made during row reduction from a to u is False.

Given:

The determinant of a is the product of the pivots in any echelon form u of​ a, multiplied by ​(​1)r​, where r is the number of row interchanges made during row reduction from a to u.

Definition of det A:

det A = (-1)^r * (product of pivots in echelon form) if A is invertible or 0 when A is not invertible.

From definition of det A we can simply say the given statement is false - This can only hold if A is an invertible matrix, but the problem does not state this.

Reduction to an echelon form may also include scaling a row by a nonzero constant, which can change the value of the determinant.

Therefore the determinant of a is the product of the pivots in any echelon form u of​ a, multiplied by ​(​1)r​, where r is the number of row interchanges made during row reduction from a to u is False.

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Answer: C, D

Step-by-step explanation:

Answer C is correct because 2/5 is 0.4 and 0.55 is greater than 0.4.

Answer D is correct because 2/5 is 0.4 and 3/4 is 0.75 therefore 0.75 is greater than 0.4.

Answer:

C and D

Step-by-step explanation:

On the number line, the first point is 2/5. 2 divided by 5 gets you .4, so that's why it's at .4. .55 is the next point. .55 is a bigger number than .4, so it would be an answer.

3 divided by 4 gets you .75. 3/4=.75. 2/5=.4. .75 is greater than .4. 3/4 is greater than 2/5

The dimensions that maximize the area are, 96cm and 84cm.

What is area?

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Let the height of poster be h and breadth be b,

bh = 15630cm square........(1)

Height of the printed area=h-10-10 = h - 20

(decrement of 10 from top and bottom)

the breadth of the printed area b-6-6 = b-12

(decrement of 9 from both sides)

for maximum printed area:

A=(h-20)(b-12) should be maximum

[tex]A = (h - 20)(\frac{15360 }{h}-12)[/tex]

From equation (1)  

[tex]A = 15360-12h-\frac{307200}{h} +240[/tex]

A = 15600 - 12h - (307200/h)

differentiate with respect to h (it should be=0)

[tex]\frac{dA}{dh}= 0-12 + \frac{307200}{h^2}[/tex]

[tex]12 = \frac{307200}{h} \\h = 160 cm[/tex]

from equation (1),

[tex]bh = 15630cm^2\\b = 96cm[/tex]

dimension of printed area,

= h - 20

= 160 - 20

= 140 cm

= b - 12

= 96 - 12

= 84 cm

Therefore, the dimensions that maximize the area are, 96cm and 84cm.

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The position where where angle, θ would be located is at: angle F (∠F).

A right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angle has a measure of 90 degrees.

Additionally, all right angles are are formed as a linear pair and they are marked with a right angle symbol.

In conclusion, the measure of the angle in this right angle triangle would be calculated by using the tangent function as follows:

Tanθ = Opposite side/Adjacent side

Tanθ = 6/4

Angle, θ = tan⁻¹(6/4)

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Using the Factor Theorem, the polynomial is factored as follows:

f(x) = (x - 2)(x + 1)(x² + 2).

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the following rule.

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

In this problem, the polynomial is given by:

f(x) = x^4 - x³ - 2x - 4.

This polynomial is factored applying the inverse factor theorem, finding the roots of the polynomial, which are given as follows:

For the complex roots, we have that 1.41² = 2, hence the term corresponding to the two complex roots is:

x² + 2.

Then the complete factored polynomial is:

f(x) = (x - 2)(x + 1)(x² + 2).

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The perimeter of the semi circle is 56.54 cm

The perimeter of a figure is the sum of the whole sides of the figure.

The perimeter of  the semi circle is the sum of the whole sides of the semi circle.

Therefore,

perimeter of the semi circle = 2πr / 2 + 2r

perimeter of the semi circle = πr + 2r

where

perimeter of the semi circle = 3.14 × 11 + 2r

perimeter of the semi circle = 34.54 + 2(11)

perimeter of the semi circle = 34.54 + 22

Therefore,

perimeter of the semi circle = 56.54 cm

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because, the quotient has an integer in its denominator

Explanation

A rational number is a number that is expressed as the ratio of two integers

hence

for

we can solve the root in the denominator, so we have

so, as the number can be expressed as the ratio of two integers ( 20 and 4) we can conclude

because, the quotient has an integer in its denominator

I hope this helps you