Since the y-intercept of the polynomial must be 3600, then:
[tex]p(0)=3600[/tex]Since the only zeroes of the polynomial must be x=5, -4, -6 and 1, then the factors of the polynomial, are:
[tex]\begin{gathered} (x-5) \\ (x+4) \\ (x+6) \\ (x-1) \end{gathered}[/tex]Let the multiplicity of the factor (x-1) be equal to 3 and let the multiplicity of the rest of the factors to be equal to 1. Then:
[tex]p(x)=a(x-5)(x+4)(x+6)(x-1)^3[/tex]Where a is a constant. Notice that the degree of that polynomial is 6. Evaluate it at x=0 to find the value of a that makes the y-intercept to be equal to 3600:
[tex]\begin{gathered} p(0)=a(0-5)(0+4)(0+6)(0-1) \\ =a(-5)(4)(6)(-1) \\ =120a \end{gathered}[/tex]Since p(0)=3600, then:
[tex]\begin{gathered} 3600=120a \\ \Rightarrow a=\frac{3600}{120} \\ \Rightarrow a=30 \end{gathered}[/tex]Therefore, the following polynomial is a 6th degree polynomial with zeroes at the values of 5, -4, -6 and -1 with a y-intercept equal to 3600:
[tex]p(x)=30(x-5)(x+4)(x+6)(x-1)^3[/tex]2Over the course of 6 days, Tonda ran 17.22 miles. She ran the same distance each day. How far did Tonda run each day? Write an equation to show your work help any smart people here help me plss
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
Need help with a question
It will take Sofia 3 hours to travel 13.5 miles at the same rate.
What is 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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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.
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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Given that A, O & B lie on a straight line segment, evaluate x
Given that the points A, O and B lie on a straight line, then we can say that; x = 11°
What is the value of the missing angle?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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Find two consecutive even integers whose sum is 126
The consecutive even numbers have a value of 62 and 64
How to determine the consecutive even integers?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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3. Smartphones come with an app that keeps track of the amount of time that the phone is being used. For teenagers, the distribution of amount of time they use their phone is approximately normal with mean = 7.75 hours per day and standard deviation = 1.25 hours per day.
(a) What percent of teenagers use their phone less than 5 hours per day?
(b) What percent of teenagers use their phone more than 10 hours per day?
(c) What proportion of teenagers use their phone between 6 to 8 hours per day?
(d) What is the 75th percentile of this distribution?
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.
Normal Probability DistributionThe 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 z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.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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Please help me i don't understand this
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
There are 85 women and 55 men in a school marching band. Find the ratio of women to men.
Answer:
17:11
Step-by-step explanation:
85/5 = 17 and 55/5 = 11
Thus, 85:55 ratio simplified is 17:11
At store a 3 lb of apples cost $12 at store B the cost is given by y = 2x where Y is the cost in dollars and X is the number of pounds of apples the cost of apples at store C is shown in the graph what is the unit price of apples at store a explain how you found this unit price
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
A rock climber completing a two-minute training session climbed 12 meters higher on the wall during the second minute of the session. at the end of the two-minute session, the climber was back to the same spot she was at when the session started. what value represents the climber's change in elevation during the first minute of the training session
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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Pls help Lila's mom is decorating her room and placed acircular rug near her window for story time.How much space does this rug take up if its diametermeasures 25 feet?
Step1: Write the area of the circular Rug
The area of the circle is
[tex]\Pi r^2[/tex]From the question the diameter is 25feet, hence the radius is
[tex]\begin{gathered} \text{radius}=\frac{diameter}{2} \\ =\frac{25}{2} \end{gathered}[/tex]Step2: substitute the value into the formula
[tex]\begin{gathered} \text{area of circular rug=area of a circle=}\Pi r^2 \\ =\frac{22}{7}\times\frac{25}{2}\times\frac{25}{2} \\ =\frac{13750}{28} \\ =491.07ft^2 \end{gathered}[/tex]Hence the area of the circular rug is 491.07 square feet
The will take approximately 491square feetyou
Distance (mi)
Rate (mph)
Time (hr)
Trip to Library
x
6 mph
StartFraction x Over 6 EndFraction
Trip to Home
x
12 mph
StartFraction x Over 12 EndFraction
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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in Mrs raps advisory 20 students saw the action movie and 5 didn't what is the ratio of students who saw the movie to the total students simplify the ratio
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
[tex]\frac{\text{saw the movie}}{\text{total students}}=\frac{20}{25}[/tex]To simplify the ratio, we divide both the numerator and the denominator by 5. This gives
[tex]\frac{20\div5}{25\div5}[/tex][tex]\frac{4}{5}[/tex]Hence, the ratio of the students who saw the movie to the total number is 4 : 5.
13. When feeding, a juvenile whale shark filters about 600 cubic meters of water through its
mouth each hour. About 2.8 kilograms of food are filtered out from the water each hour.
120
a. Graph the function that represents the amount a of water filtered by the whale shark as a
function of the number of minutes.
m
b. The whale shark feeds for 7.5 hours each day. Graph the function that represents the amount f
of food (in pounds) filtered by the whale shark as a function of the number d of days.
Answer:214.29
Step-by-step explanation:600 divided by 2.8
possibly the answer
Danny recipe calls for 3 cups of flour He would like to combine some wheat flour and some white flour to equal 3 cups Write two mixed numbers that have a sum of 3
Answer:
1 1/2 + 1 1/2
Step-by-step explanation:
1 1/2 (or 1.5) plus 1 1/2 equals 3
How many times smaller is 1.9 × 10^3 than 4.085 × 10^5?
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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I need help on this question its due in tomorrow.
The perimeter of the semi circle is 56.54 cm
How to find the perimeter of a semi circle?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
r = radiusperimeter 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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GAME DESIGN A computer software designer is creating a new video game. The designer wants to create a secret passage that is halfwaybetween the castle and the bridge. Where should the secret passage be located?
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
which term number -385 for the sequence: -25, -35, -45, -55
Mrs. Holmes’s physics class uses 3D-printing software to create miniature bridges that can hold at least 5 pounds. Teams will print multiple parts of the bridges and then assemble the parts. One team wants at least 6 inches between the bridge's upper and lower rail. The lower rail of the bridge contains points (2, 10) and (16, 3). Will the bridge meet the team's specifications if the upper rail contains points (5, 1)? If yes, how far apart are the rails? Let every unit represent an inch. Round your answer to the nearest hundredth, if needed.
Answer:
I litteraly have the same problem and no clue how to do I
Step-by-step explanation:
The question is in the photo. Complete C and D.
x = -12
Explanations:Given the following equation
[tex]-\frac{1}{2}x=6[/tex]We are to find the variable x. To do that, we will multiply both sides by -2 as shown:
[tex]\begin{gathered} -\frac{1}{2}x\times-2=6\times-2 \\ x=6\times-2 \\ x=-12 \end{gathered}[/tex]This shows that the value of x for the equation to be true is -12
Check
If x = -12, on substiituting;
[tex]\begin{gathered} =-\frac{1}{2}(-12) \\ =\frac{-12}{-2} \\ =\text{ 6} \end{gathered}[/tex]Since the result is equivalent to 6, this shows that the solution x = -12 is correct.
question in the screenshot
Answer:
4.2
Step-By-Step explanation:
12.5+1.5=14
14 times 3= 42
42/10= 4.2
A turtle and a rabbit are in a race to see who is first to reach a point 100 feet away. The turtle travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continues at a constant speed of 40 feet per minute for the last 50 feet. Determine which animal won the race and by how much time.
The options are relational/irrational and is equal to an integer/has a square root in its denominator
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
[tex]\frac{p}{q}[/tex]hence
for
[tex]\frac{20}{\sqrt{16}}[/tex]we can solve the root in the denominator, so we have
[tex]\begin{gathered} \frac{20}{\sqrt{16}} \\ \frac{20}{\sqrt[]{16}}=\frac{20}{4} \end{gathered}[/tex]so, as the number can be expressed as the ratio of two integers ( 20 and 4) we can conclude
[tex]\text{the quotient }\frac{20}{\sqrt[]{16}}\text{ is a rational number}[/tex]because, the quotient has an integer in its denominator
I hope this helps you
A number, double the number, and 16 are added. The result is 61. What is the original number?
ANSWER
[tex]15[/tex]EXPLANATION
Let the number be x.
If the number is doubled, it becomes:
[tex]2x[/tex]The number, double the number and 16 are added and the result is 61.
This implies that:
[tex]x+2x+16=61[/tex]Solve for x:
[tex]\begin{gathered} 3x+16=61 \\ 3x=61-16=45 \\ x=\frac{45}{3} \\ x=15 \end{gathered}[/tex]That is the number.
Can someone pls help me it would mean a lot
The position where where angle, θ would be located is at: angle F (∠F).
What is a right angle?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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32 Développe et réduis les expressions
suivantes :
A = (x + 4)(x + 3)
B = (y + 3)(2y + 8)
C = (3z + 4)(5 + 6z)
D = (7t+8)(3 + 5f)
a poster of area 15360 cm215360 cm2 has blank margins of 10 cm10 cm wide on the top and bottom and 6 cm6 cm wide on the sides. find the dimensions that maximize the printed area. (use decimal notation. give your answers as whole or exact numbers.)
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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read the attachment.
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
Factor the polynomial function over the complex numbers. f(x)=x4−x3−2x−4
(requesting an explanation as well!)
Using the Factor Theorem, the polynomial is factored as follows:
f(x) = (x - 2)(x + 1)(x² + 2).
What is the Factor Theorem?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:
x = 2.x = -1.x = -1.41i.x = 1.41i.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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