Answer:
p(x) is a function, and a polynomial of degree 3, then
By remainder theorem and factor theorem,
p(0) = p(1) = p (-1) = 0 if and only if
x = 0, 1, -1 are zeroes if and only if
p(x) = k(x - 0)(x - 1)(x + 1) = k(x)(x^2 - 1) = k(x^3 - x) = kx^3 - kx
p(2) = k(2)^3 - k(2) = 6
8k - 2k = 6
6k = 6
k = 1
Thus p(x) = x(x - 1)(x + 1) = x(x^2 - 1) = x^3 - x
p(-x) = (-x)^3 - (-x) = x^3 + x
-p(x) = -(x^3 - x) = -x^3 + x
As you can see, p(x) does not equal to -p(x), unless x = 0, 1, -1,
because p(0) = -p(0) = 0, p(-1) = - p(1) = 0, p(1) = -p(-1) = 0
p(x) = x(x - 1)(x + 1)
If x < -1, then x < 0, x - 1 < 0, x + 1 < 0
That means p(x) < 0
If -1 < x < 0, then x < 0, -2 < x - 1 < -1 < 0, 0 < x + 1 < 1
That means p(x) > 0
If 0 < x < 1, then x > 0, -1 < x - 1 < 0, 0 < 1 < x + 1 < 2
That means p(x) < 0
If x > 1, then x > 0, x - 1 > 0, x + 1 > 2 > 0
That means p(x) > 0
Thus p(x) < 0 if x < -1 or 0 < x < 1
Find the equation of the line and passing through (4,3) with slope= -5
The required equation of the line is 5x + y + 17 = 0.
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. Equations are used to describe geometric shapes in Cartesian geometry. Because the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions, the goal has shifted: instead of directly stating the solutions or counting them, which is impossible, one utilizes equations to investigate the features of figures. This is the fundamental concept of algebraic geometry, a significant branch of mathematics. An equation consists of two expressions joined by an equals sign ("="). The expressions on each side of the equals sign are referred to as the equation's "left-hand side" and "right-hand side."
The equation of the line is given below:
y - 3 = -5(x - 4)
or, y - 3 = -5x - 20
or, 5x + y + 17 = 0
Hence, the required equation of the line is 5x + y + 17 = 0.
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What is the complete factorization of
-12 + 3x + 28?
F. (x-4)(x-7)
G. -(x-4)(x + 7)
H. -(x + 4)(x + 7)
J. -(x-7)(x + 4)
Answer:
J. - (x-7)(x + 4)
Step-by-step explanation:
Travis got a charging fee of 20$.He has an outstanding charge of 7.50 how much will he need to pay to not get feed by the bank
suppose babies born in a large hospital have a mean weight of 3316 grams, and a standard deviation of 324 grams. if 83 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by less than 54 grams? round your answer to four decimal places.
The probability that the mean weight of the sample babies would differ from the population mean by less than 54 grams is 0.4339.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 3316 grams - 54 grams = 3262
μ = mean = 3316 grams
σ = standard deviation = 324 grams
z-score = (3262 - 3316) / 324
z-score = -54 / 324
z-score = -0.1667
Find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = -0.1667
Using interpolation of values,
probability = 0.4339
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NEED DONE ASAP
A bakery prepares boxes of desserts. Each box contains twice as many cookies as brownies. Which line on the graph depicts the number of cookies relative to the number of brownies?
A
Graph shows number of brownies on horizontal axis from 0 to 10 in increments of 2 and number of cookies on vertical axis from 0 to 10 in increments of 2 with the points (0, 0), (10, 5) connected through a line.
B
Graph shows number of brownies on horizontal axis from 0 to 10 in increments of 2 and number of cookies on vertical axis from 0 to 10 in increments of 2 with the points (0, 0), (10, 10) connected through a line.
C
Graph shows number of brownies on horizontal axis from 0 to 10 in increments of 2 and number of cookies on vertical axis from 0 to 10 in increments of 2 with the points (0, 2), (10, 2) connected through a line.
D
Graph shows number of brownies on horizontal axis from 0 to 10 in increments of 2 and number of cookies on vertical axis from 0 to 10 in increments of 2 with the points (0, 0), (5, 10) connected through a line.
Answer:
Answer is the last graph which shows 10 cookies and 5 brownies.
Step-by-step explanation:
There are more cookies (y-axis) than brownies (x-axis), the slope is 2.0 so the line must be > 45 degrees.
Find the circumference of each circle round answer to the nearest tenth
Answer: ask your teacher
Step-by-step explanation:u have to multiply
Using the quadratic formula, find the roots of the equation 3x = 2x² + 1.
A
x = -0.5 and x = −1
B x= 1.5 and x = 0
C
D
x = 2 and x = 1
x = 1 and x = 0.5
Using the quadratic formula we can conclude that the equation 3x = 2x² + 1 has two real roots which are x = 1 and x = 0.5.
What is the quadratic formula?The definition of a quadratic as a second-degree polynomial equation implies that at least one squared term must be present. It also goes by the name quadratic equations. The quadratic equation has the general form ax² + bx + c = 0.The quadratic formula: [tex]x = \frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
Equation is 3x = 2x² + 1.Then, 2x² -3x + 1.Now, a = 2, b = -3 and c = 1.There are two real roots which are x = 1 and x = 0.5.
(Refer to the image attached below for the working)
Therefore, using the quadratic formula we can conclude that the equation 3x = 2x² + 1 has two real roots which are x = 1 and x = 0.5.
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the healthcare provider prescribes propofol (diprivan) at 8 mcg/kg/minute for a client during conscious sedation. the drug is dispensed as a econdary infusion labled, 0.9% normal saline 50 ml with propofol 100 mg/50 ml the client's weight is 198 pounds. the nurse should program the infusion pump to deliver how many ml/hour? (enter numeric value only. if rounding is required, round to the nearest tenth.)
The nurse should program the infusion pump to deliver 21.6ml/hour
Given the following:
Drug propofol prescribed is 8mcg/kg/min
Drug dispensed in 100mg in 50ml NS
Weight of patient is 198 pounds
Converting pounds in Kg:
198 pounds is (1 pound is 0.45Kg)
89.8 equivalent to 90Kg
Converting 8mcg/kg/min into mg/kg/min:
8mcg is 0.008mg so it becomes 0.008mg/kg/min
Patient weight is 90 kg , so required drug is:
90x0.008=0.72 mg/min
Now 50ml has 100mg, so 1ml has 2mg
We want to give 0.72mg, so if there is 2mg in 1 ml how much will be 0.72 mg for, by doing cross multiplication we get as below:
2mg in 1 ml
0.72=?
=0.72x1/2
=0.36ml
Now we have to give 0.36ml/min
Infusion pump has rate in ml/ hour, as 1 hour has 60 min, we multiply 0.36x60=21.6ml/hour
Hence, Infusion pump delivered 21.6ml/hour
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Writing an equation of an ellipse given the foci and major axis length
Given
Major axis of length = 12
Foci at ( 9 ,1 ) and ( -1, 1 )
Find
Equation of an ellipse
Explanation
As we know , major axis = 2a = 12
thus a = 6
the midpoint between the foci is the center , so
[tex]\begin{gathered} C:(\frac{8}{2},\frac{2}{2}) \\ C:(4,2) \end{gathered}[/tex]the distance between the foci is equal to 2c
[tex]\begin{gathered} 2c=\sqrt{\left(9+1\right)^2+0^2} \\ 2c=10 \\ c=5 \end{gathered}[/tex]now,
[tex]\begin{gathered} c^2=a^2-b^2 \\ b^2=a^2-c^2 \\ b^2=36-25 \\ b^2=11 \end{gathered}[/tex]so , the equation of an ellipse is
[tex]\begin{gathered} \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2} \\ \frac{(x-4)^2}{11}+\frac{(y-2)^2}{36} \end{gathered}[/tex]Final Answer
The equation of an ellipse
[tex]\frac{(x-4)^{2}}{11}+\frac{(y-2)^{2}}{36}[/tex]
Please Solve this Algebraic Proof for Geometry!!
2 images attached
The value of x from the given figure is 3. Hence, proved.
Given that, ∠XVW=∠W.
What is vertical angles theorem?When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles. They are also known as "Vertically opposite angles" due to the fact that they are perpendicular to one another.
∠XVW = ∠W (Given)
∠XVW = ∠ZVY (Vertical angles theorem, vertical angles are congruent.)
∠ZVY = ∠W (Transitive property of congruence)
m ∠ZVY = m ∠W (Angle congruence postulate)
8x+13=75x+28 (Substitution property of equality)
5x=15 (Subtraction property of equality)
x=3 (Division property of equality)
The value of x from the given figure is 3. Hence, proved.
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In a school of 2000 students, the ratio of teachers to students is 3:80.
Some teachers join the school and the ratio changes to 1:20.
Find the number of teachers who joined the school.
25 new teachers joined the school such that the new ratio is 1 : 20 .
In mathematics, a ratio illustrates how frequently one number appears in another. For instance, the ratio of oranges to lemons on a fruit platter would be eight to six if there were eight oranges and six lemons.
Ratios can be decreased by dividing each quantity by the sum of all the common components of the numbers (much like fractions are). When the ratio's numbers are the smallest practical integers, the fraction is said to be in its simplest form.The ratio's antecedent and consequent are frequently referred to as A and B, respectively.The total number of students is 2000
The ratio of teachers to students is 3:80 .
Therefore the number of teachers = 3 × 2000 ÷ 80 = 75
Let x teachers joined the school.
Therefore new ratio = (x+75) : 2000
but the new ratio is 1 : 20
Therefore 1 : 20 = (x+75) : 2000
Simplifying we get:
x + 75 = 100
or, x = 25
Therefore the number of teachers who joined the school is 25 .
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a car has a15 gallon gas tank and gets a maximum average mileage of 24 miles per gallon
Answer:
360 miles
Step-by-step explanation:
24*15=360
360 miles can be driven in 15 gallons gas.
what is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For, example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A car has a15 gallon gas tank.
Now, per gallon = 24 miles driven
So, in 15 gallons, the miles driven
= 24 x 15
= 360 miles.
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y/31.25 = 5 solve for y please
Answer:
Step-by-step explanation:
y=652/4
convert decimal to a fraction
46/125=5
multiplying by both sides of the equation by 125/4
y=652/4 = 156 1/4
Expand & simplify
(
x
+
3
)
2
(
2
x
−
5
)
Answer:
4x²+2x-30
Step-by-step explanation:
(x+3) 2(2x-5)
(x+3) (4x-10)
4x²-10x+12x-30
4x²+2x-30
9 Write the double that you would use to solve the problem Then solve it. Write your answers in the blanks. 4+5= ? Use the double 4+5=
how much time has elapsed 2:20 pm to 5:57 pm
Answer:
2:20 pm to 5:57 pm is 3 hours and 37 minutes.
Answer:
3 hours and 37 minutes.
Step-by-step explanation:
5:57
-2:20
= 3:37
the accounting department at weston materials inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the red barn model. assume the assembly times follow the normal distribution. a-1. determine the z values for 29 and 34 hours. (negative amount should be indicated by a minus sign. round z value to 2 decimal places and your final answer to 2 decimal places.) a-2. what percent of the garages take between 32 hours and 34 hours to erect? (round z value to 2 decimal places and your final answer to 2 decimal places.) b. what percent of the garages take between 29 hours and 34 hours to erect? (round z value to 2 decimal places and your final answer to 2 decimal places.) c. what percent of the garages take 28.7 hours or less to erect? (round z value to 2 decimal places and your final answer to 2 decimal places.) d. of the garages, 5% take how many hours or more to erect? (round your answer to 1 decimal place.)
The z-value for 29 and 34 hours is z(32) = 0, the garages take between 32 hours and 34 hours to erect 34%, the garages take between 29 hours and 34 hours to erect 77.45%, and the garages, 5% take 35.29 hours of time.
What is Z -score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
Weston Materials, Inc., a national manufacturer of detached garages, states that erecting the Red Barn type takes two construction workers a mean of 32 hours and a standard variation of 2 hours. Assume that the assembly times are distributed normally.
Calculating the z values for 29 and 34 hours.
z(29) = (29-32)/2 = -3/2
z(34) = (34-32)/2 = 1
z(32) = 0
The percentage of garages take between 32 hours and 34 hours to erect as:
⇒ P(32 < x < 34) = P(0< z < 1) = 0.34
The percentage of garages take between 29 hours and 34 hours to erect as:
⇒ P(29 < x < 34) = P(-1.5 < z < 1) = 0.7745
The percentage of garages take 28.7 hours to erect as:
⇒ z(28.7) = (28.7-32)/2 = -3.3
⇒ P(0 < x < 28.7) = P (-10 < z < -3.3) = 0.00048348...
The z-value corresponds to a 95% left area and only
5% to the right under the curve.
Use z-chart or InvNor(0.95) = 1.645
x-value that corresponds to the z-value.
1.645 = (x-32)/2
x-32 = 2×1.645
x = 35.29 hours
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What is the constant rate of change of the table below?
Help me because i forgot everything :(
The graph that results from placing the coordinates on the graph is shown below.
Consequently, the graph's coordinates are (-1,1), (0,3), and (1,5)
How to solve linear equations on a graph?We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found. The point where the two lines join is (-3, -4), which is where this equation system's solution lies.
There are 3 methods for graphing a linear equation:
1.displaying the graph of a linear equation using two points.
2.Use a linear equation's slope and y-intercept.
3.using a linear equation's x- and y-intercepts.
So we take 3 values to substitute in place of x like
-1,0,1
values of y we get are
1,3,5
Now placing the co ordinates on the graph we get the following graph,
Therefore, the co-ordinates constituting the graph are (-1,1), (0,3), (1,5)
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Tommy deposited $2,000 into a savings account that earns 5% interest per year. What
equation would be used to determine how much money Tommy has after x number of years?
Answer:
7A, 8D
Step-by-step explanation:
The compound interest formula is as followed
[tex]A = P(1+\frac{r}{n} )^{nt}\\[/tex]
A = accumulated amount
P = principle
r = interest rate
n = compounding
t = time
The accumulated amount is represented by f(x).
The principle is the amount of money you start with. In this case Tommy starts with 2000 dollars. P = 2000
The interest rate is 5%. This needs to be converted into a decimal.
5% = 0.05 = r
The money is compounded annually, thus n = 1.
The time is represented by x. x = t.
thus
[tex]f(x) = 2000(1+0.05)^{x}[/tex]
After six years, you simply find f(6), or substitute 6 into x.
f(6) = 2000(1.05)^6 = $2,680.19
It takes 0.5 gallon of cream to make 1 pound of butter.
How much butter could you make with 0.25 gallons of cream?
How much cream would you need to make 2.5 pounds of butter?
What is 955 divided by 36 rounded to the nearest tenth?
The equation of a line is y=4/3x + 4 . Is the point (6, 13) on the line? [ Select ] Is the point (9, 16) on the line?
The point (9, 16) is on the line.
Given,
The equation of the line = y = 4/3x + 4
We have to find whether the given points are on this line or not.
For that substitute the points into the equation.
That is,
Point (6, 13)
x = 6 and y = 13
Equation;
y = 4/3x + 4
13 = 4/3 x 6 + 4
13 = 8 + 4
13 ≠ 12
That is, the point (6, 13) is not in the line.
Next,
Point (9, 16)
x = 9 and y = 16
Equation;
y = 4/3x + 4
16 = 4/3 x 9 + 4
16 = 12 + 4
16 = 16
Therefore, the point (9, 16) is in the line.
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The first three terms of an arithmetic sequence are as follows.-26, -19, -12Find the next two terms of this sequence.-26, – 19, -12,
1) Given that we were told that the first three terms of this Sequence. Let's find the common difference:
[tex]\begin{gathered} -26+7=-19 \\ -19+7=-12 \\ d=7 \end{gathered}[/tex]2) Based on that, we can do the following to find the next two terms:
[tex]\begin{gathered} -26+7=-19 \\ -19+7=-12 \\ -12+7=-5 \\ -5+7=2 \\ \\ -19,-12,-5,2 \\ Or \\ \\ a_4=a_1+d(n-1) \\ a_4=-26+7(4-1) \\ a_4=-26+21 \\ a_4=-5 \\ \\ a_5=-26+7(5-1) \\ a_5=-26+7(4) \\ a_5=-26+28 \\ a_5=2 \end{gathered}[/tex]Thus, the next terms are -5 and 2
Select the equation that has the same solution.
brainiest for the best answer. 100 points.
Answer: 11/4n + 2 = -3 +3/2n
Step-by-step explanation:
1) Solve the given equation
-5n + 31 = -14n -5
9n = -36 (Move like terms)
n = -4
2) Solve every other equation until match
1a)
11/4n + 2 = -3 +3/2n
11/4n = -5 + 6/4n (Change fraction and move like terms)
5/4n = -5 (minus fraction)
n = -4 Correct
The answer to x/-2+1>4
Answer: x < -6
Step-by-step explanation:
1) Bring 1 to the other side
x/-2 > 3
2) Bring -2 to the other side. The sign flips when the number multiplied or divided is negative
x < -6
On a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level. She notices a sea turtle above her and rises 6 ft to take its picture. At what elevation does the diver take the picture?
The elevation at which the diver takes the picture is -14 3/4 feet if, on a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
On a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.
Let x be the elevation at which the diver takes the picture.
The value of x can be found as follows:
x = -20 3/4 + 6
x = -83/4 + 6
x = (-83 + 24)/6
x = -59/6
Or
x = -14 3/4 feet
Thus, the elevation at which the diver takes the picture is -14 3/4 feet if, on a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.
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(8d+4)⁰
(6d+8)°
3. Find d. Show a picture of your work.
d =
pic goes here (or ok to type your steps)
Answer:
d=12
Step-by-step explanation:
8d+4+6d+8 = 180 (Straight angle = 180)
14d+12=180
14d=168
d=12
:]
Answer:
D =12
Step-by-step explanation:
8d+4+6d+8 =180 (being a linear pair)
14d+12=180
14d=180-12
14d=168
d= 168/14
d=12#
Is 1/1 a terminating or repeating decimal
what is the mean of 45,68,77,90,90,95,100,100,86,90,50,55
Answer:
78.8
Step-by-step explanation: