Form a polynomial whose zeros and degree are given.
Zeros: - 2, 2, 6; degree: 3
Type a polynomial with intéger coefficients and a leading coefficient of 1 in the box below.
f(x)=(Simplify your answer.)
Answer:
[tex]f(x) = (x + 2)(x - 2)(x - 6)[/tex]
[tex]f(x) = ({x}^{2} + 4)(x - 6)[/tex]
[tex]f(x) = {x}^{3} - 6 {x}^{2} + 4x - 24[/tex]
Step-by-step explanation:
Multiply factors.
BRAINLIEST FOR ANSWER
A cylinder of water was holding a volume of 2 mL of water. An irregularly shaped stone was put into the cylinder and the volume rose to 8 mL. If the mass of the stone was 21 g, what was its density?
Answer:
3.5g/ml or 3.5g/cm³
Step-by-step explanation:
1cm³=1ML
Volume of the irregular shaped stone = New Volume of water in cylinder -initial Volume of water in cylinder
Volume of irregular shaped stone = 8ml-2ml
Volume of irregular shaped stone =6ml
Denisty =Mass/Volume
Density = 21g/6ml
Density = 3.5g/ml
Please Help!
What is the locus of the midpoints of all chords that can be drawn from a given point on a circle with a radius of 6.
The locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.
Given: A circle of radius 6 units
To find: The locus of the midpoint of all chords that can be drawn from a given point on the circle.
To find the required locus, we need to know the following:
Locus of a moving point is the trajectory of that point. It is the geometrical figure represented by the equation which is satisfied by the coordinates of the moving point.A chord of a circle is a line segment joining any points of a circle.Equation of a circle with center at origin and radius of [tex]r[/tex] units is [tex]x^{2} +y^{2} =r^{2}[/tex] According to the midpoint formula, the coordinates of the midpoint of the line segment joining the points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )[/tex]Let, without loss of generality, the given circle be centered at the origin. Even if it is not, we can shift the origin to the center of the given circle with coordinate transformation.
Then, the equation of the given circle is [tex]x^{2}+y^{2} =6^{2}[/tex], that is, [tex]x^{2}+y^{2} = 36[/tex]
Let the coordinates of the given fixed point be [tex](a,b)[/tex]
Let the coordinates of any point on the circle be [tex](p,q)[/tex] and let the coordinates of the midpoint of the chord joining the points [tex](a,b)[/tex] and [tex](p,q)[/tex] be [tex](h,k)[/tex]
We have to find the locus of [tex](h,k)[/tex]
Then, using the midpoint formula,
[tex](h,k)=(\frac{a+p}{2} ,\frac{b+q}{2})[/tex]
On solving, we get,
[tex]p=2h-a,q=2k-b[/tex]
Since [tex](a,b)[/tex] and [tex](p,q)[/tex] are both points on the given circle, they satisfy the equation of the circle, [tex]x^{2}+y^{2} = 36[/tex]
Then,
[tex]a^{2} +b^{2} =36[/tex]
[tex]p^{2} +q^{2} =36[/tex]
Substituting [tex]p=2h-a,q=2k-b[/tex] in [tex]p^{2} +q^{2} =36[/tex], we have,
[tex](2h-a)^{2} +(2k-b)^{2} =36[/tex]
[tex](2(h-\frac{a}{2}) )^{2} +(2(k-\frac{b}{2}))^{2} =36[/tex]
[tex]4(h-\frac{a}{2})^{2} +4(k-\frac{b}{2})^{2} =36[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =\frac{36}{4}[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =9[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =3^{2}[/tex]
This is the locus of the point [tex](h,k)[/tex]
Replace [tex](h,k)=(x,y)[/tex] to get,
[tex](x-\frac{a}{2})^{2} +(y-\frac{b}{2})^{2} =3^{2}[/tex]
This is the equation of a circle with center at [tex](\frac{a}{2} ,\frac{b}{2} )[/tex] and radius 3 units.
Thus, we can conclude that the locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.
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Given the following absolute value function find the range.
f(x) = |x + 5| -8
Range: [5,00)
Range: [-5,00)
Range: [-8,00)
Range: [8,00)
Answer:
Range is (-8,00)
Step-by-step explanation:
A California distributor of sporting equipment expects to sell 10,000 cases of tennis balls during the coming year at a steady rate. Yearly carrying costs (to be computed on the average number of cases in stock during the year) are $10 per case, and the cost of placing an order with the manufacturer is $45. Determine the economic order quantity, that is, the order quantity that minimizes the inventory cost.
The economic order quantity is 300 cases of tennis balls.
The economic order quantity (EOQ) is the minimum quantity that the distributor can order per order to minimize inventory costs.
Data and Calculations:
Sales of tennis balls for the coming year = 10,000 units
Carrying (holding) costs per case = $10
Cost of placing orders with the manufacturer = $45 per order
Economic Order Quantity (EOQ) = square root of (2 * Annual Demand/Sales * Ordering cost)/Carrying cost per case
= square root of (2 * 10,000 * $45)/$10
= square root of 90,000
= 300 cases of tennis balls
This implies that the distributor will place about 33 orders (10,000/300) in the coming year. With each order, the quantity placed is 300 units.
Thus, the economic order quantity that will minimize the California distributor's inventory costs for the year is 300 cases of tennis balls.
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PLEASE HELP ASAP!!!!
What is the square of 22?
A.44
B.444
C.844
D.484
If the two lines below are perpendicular and the slope of the red line is
what is the slope of the green line?
A. -2/5
B. 2/5
C. 5/2
D. -5/2
Answer:
B. 2/5
Step-by-step explanation:
what is the uniqueness of comeplex integration from line integaration?
A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,000.
Please help I am in class rn and I need this DONe
pattern. quadrant
(- ,-). III
(+,+). I
(+,-). IV
(-,+). II
Step-by-step explanation:
PLS MARK BRAINLIEST
#4.
Quadrant I - top right: (+, +)
Quadrant II - top left: (-, +)
Quadrant III - bottom left: (-, -)
Quadrant IV - bottom right: (+, -)
#5.
a. (-6, -2) : (-, -) : III
b. (3, 8) : (+, +) : I
c. (1, -4) : (+, -) : IV
d. (-5, 6) : (-, +) : II
Hope this helps!
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18x + 3y = -18
Answer:
y= -6x-6, I think, hope it helped
Step-by-step explanation:
Help with this please!!!!!!!!!!!!!!
Answer:
A is the correct answer :)
Answer:
A
Step-by-step explanation:
checking if A is correct, if we get x as 76 then it is correct
if 5miles = 8 kilometers
47.5 miles= x
that is
5=8
47.5=x
cross multiply
5x=380
x=380/5
x=76
there fore A is correct
checking if B is correct, if we get x as 86 then it is correct
if 5miles = 8 kilometers
52.5 miles= x
that is
5=8
52.5=x
cross multiply
5x=420
x=420/5
x=84
therefore B is incorrect
checking if C is correct, if we get x as 34 then it is correct
if 5miles = 8 kilometers
22.5 miles=x
that is
5=8
22.5=x
Cross multiply
5x=180
x=180/5
x=36
therefore C is incorrect
checking if D is correct, if we get x as 22 then it is correct
if 5miles = 8 kilometers
12.5miles = x
that is
5=8
12.5=x
5x=100
x=100/5
x= 20
C = qt - k
(Make k the subject using transportation)
V = u + at
(Make u the subject using transportation)
Answer:
C - qt = -k
k = - C + qt
V = u + at
V - at = u
u = V - at
Answer:
c=qt-k
c-qt= -k
c-qt/-1=-k/-1
k=c-qt/-1....
v=u+at
v-at=u
u=v-at
I hope this helps
PLEASE HELP URGENT!!!
Janine determines that the total resistance in her circuit is 80 ohms. Using the inverse equation modeling this situation, find the resistance of the second lightbulb.
The resistance of the second lightbulb is ohms.
A. 120
B. 240
C. 300
D. 40
The sum of resistors arranged in parallel is the inverse of the sum of the inverses of the magnitudes of the individual resistances
The correct option for the resistance of the second light bulb in ohms (Ω) is option B;
B. 240
The reason why option B is the correct answer is s follows:
Known parameters:
Based on a online search, the question appears to have some parts missing which can be as follows;
The resistance of the first light bulb = 120 Ω
Janine's model of the total resistance of the circuit, [tex]t = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex]
Where;
r = The resistance of the second light bulb
The unknown parameter:
Resistance of the second light bulb
Method:
Find r using Janine's model of the total resistance, which is the equation of total resistances in parallel arrangement
The inverse relationship modelling the sum, t, of resistances, r, and 120, arranged in parallel, presented as follows;
[tex]\mathbf {\dfrac{1}{t} } =\dfrac{1}{120} + \dfrac{1}{r}[/tex]
∴ [tex]\mathbf {\dfrac{1}{t}} = \dfrac{r + 120 }{120 \cdot r}[/tex]
Therefore, by finding the inverse of both sides of the above equation, we get Janine's model as follows;
[tex]t = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex]
The above equation is the inverse equation modelling the total resistance of the parallel arrangement of the resistances in the lightbulb
The question details include:
The total resistance in her circuit, t = 80 Ω
Solution:
Plugging in t = 80 in [tex]t = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex], gives;
[tex]80 = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex]
Therefore, we get;
80·(r + 120) = 120·r
80·r + 80 × 120 = 120·r
∴ 120·r - 80·r = 80 × 120 = 9,600
120·r - 80·r = 40·r
∴ 40·r = 9,600
r = 9,600/40 = 240
The resistance of the second light bulb, r = 240 Ω
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Answer:240
Step-by-step explanation:
i watched the walk through
An environmentalist wants to find out the fraction of oil tankers that have spills each month.
Suppose a sample of 1036 tankers is drawn. Of these ships, 777 did not have spills. Using the data, estimate the proportion of oil tankers that had spills. Write your answer as a fraction or a decimal number rounded to three decimal places.
Answer:
The estimate of the proportion of oil tankers that had spills is 0.25.
Step-by-step explanation:
Proportion of oil tankers that had spills:
1036 tankers.
777 did not have spills.
So 1036 - 777 = 259 had spills.
The proportion is:
[tex]p = \frac{259}{1036} = 0.25[/tex]
The estimate of the proportion of oil tankers that had spills is 0.25.
Does the graph represent a function?
Answer:
Yes, the graph is a function.
Vertical line test proves so.
Lucinda is writing a coordinate proof to show that a diagonal of a parallelogram partitions the parallelogram into two equal areas.
A parallelogram graphed on a coordinate plane. The vertices of rectangle are labeled as K L M and N. The vertex labeled as K lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as L lies on begin ordered pair x comma 2 y end ordered pair. The coordinate of vertex M is left blank. The vertex labeled as N lies on begin ordered pair 3 x comma 0 end ordered pair. A diagonal is drawn between points K and M.
Enter your answers in the boxes to complete Lucinda's proof.
Since KLMN is a parallelogram and a parallelogram's opposite sides are parallel and congruent, the coordinates for M are (4x, 2y).
In △KMN, the length of the base is and the height is . So an expression for the area of △KMN is .
In △KLM, the length of the base is 3x and the height is 2y. So an expression for the area of △KLM is .
Comparing the area of the two triangles that are formed by a diagonal of the parallelogram shows that a diagonal of a parallelogram partitions the parallelogram into two equal areas.
9514 1404 393
Answer:
ΔKMN: base, 3x; height, 2y; area, 3xyΔKLM: area, 3xyStep-by-step explanation:
ΔKMNThe base length is the length of the horizontal line segment KN. That length is the difference of the x-coordinates: 3x -0 = 3x.
The height is the difference of the y-coordinate of point M and the y-coordinate of horizontal segment KN. That difference is 2y -0 = 2y.
The area is half the product of base and height:
A = (1/2)bh
A = 1/2(3x)(2y) = 3xy
In ΔKMN, the length of the base is 3x and the height is 2y. So an expression for the area of ΔKMN is 3xy.
__
ΔKLMIn ΔKLM, the length of the base is 3x and the height is 2y. So an expression for the area of ΔKLM is 3xy.
Select the correct answer.
As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and hair color among students. The table below contains the results of the survey.
Answer: Choice B) 0.27
=========================================================
Explanation:
There are a lot of data values here, and it's possible to easily get lost in them. However, we're asked only about students with blond hair. So we only focus on the first row. Ignore everything else.
We see that there are 78 of these students total. Of this total, 21 have green eyes.
Therefore, the relative frequency of blonds with green eyes is 21/78 = 0.2692 which rounds to 0.27; so that's why the answer is choice B.
May I get help with this question?
Answer:
C. <F
Step-by-step explanation:
The angle that sees the largest side length has the largest measurement.
Amongst the given side lengths the one that sees <F has the longest length so the answer is C
A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 9. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01.
Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to two decimal places.)
Answer:
The answer is "-3.04"
Step-by-step explanation:
[tex]\to \bar{x_1}-\bar{x_2}=9-11=-2[/tex]
Sample distribution:
[tex]z=\frac{\bar{x_1}-\bar{x_2}- \bar{\mu_1}-\bar{\mu_2}}{\sqrt{\frac{\sigma_{1}^2}{n_1}+\frac{\sigma_{2}^2}{n_2}}}\\\\[/tex]
[tex]=\frac{(-2)-0}{\sqrt{\frac{3^2}{49}+\frac{4^2}{64}}}\\\\=\frac{-2}{\sqrt{\frac{9}{49}+\frac{16}{64}}}\\\\=\frac{-2}{\sqrt{\frac{576+784}{3136}}}\\\\=\frac{-2}{\sqrt{\frac{1360}{3136}}}\\\\=\frac{-2}{\sqrt{0.433}}\\\\=\frac{-2}{0.658}\\\\=-3.039\\\\=-3.04[/tex]
jope works 42 hours in a 6 day week, calculate the number of hours in a week he is not at work
Answer:
the number of hours in a week Jope, who is not at work, is 102 hours
Step-by-step explanation:
call X is the number of hours in a week Jope is not at work.
=> the number of hours in a week = X + the number of work hours in a week
=> 6*24 = X + 42
=> X = 6*24 - 42
=> X = 102 hours
An angle, Theta. is in standard position. The terminal side of the angle passes through the point (6.-5).
Find sin Theta
9514 1404 393
Answer:
sin(θ) = (-5√61)/61
Step-by-step explanation:
The distance from the origin to the given point is ...
d = √(6² +(-5)²) = √61
The sine of the angle is the ratio ...
sin(θ) = y/d = -5/√61
Rationalizing the denominator gives us ...
sin(θ) = (-5√61)/61
Write in standard form (×-3)(x+2)(x-5)
Answer: X - 3 x X + 2 x X - 5
Step-by-step explanation:
X - 3 x X + 2 x X - 5
Answer:
its (x - 3)( x^2-3x-10
Step-by-step explanation:
On their farm, Adam’s family maintains a storage that can hold 19.9 cubic yards (yd3) of grain. Use the fact that 1 yard is approximately equal to 0.9144 m to convert this volume to m3
19.9 cubic yards converted to cubic meters is 15.21 m³.
How do you convert to cubic meters?The volume of the storage is the amount of space inside it. Large volumes are measured in cubic metres.
Given this unit of conversion: 1 yard = 0.9144 m
To convert to cubic meters, find the cube: 0.9144³ = 0.764555
Now, multiply 0.764555 by 19.9 : 0.764555 x 19.9 = 15.21 m³
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Find the solutions of the quadratic equation x2 + 7x + 10 = 0.
Question 13 options:
A)
x = 2, 5
B)
x = –2, –5
C)
x = –7, –3
D)
x = 7, 3
Answer:
Step-by-step explanation:
x² + 7x + 10 = 0
x = [-7 ± √(7² - 4·1·10)]/(2·1) = [-7 ± √9[/2 = [-7 ± 3]/2 = -2, -5
Select the statement that best justifies the conclusion based on the given information.
If a(b + c) = d, then ab + ac = d.
associative
commutative
distributive
closure
Answer:
distributive
Step-by-step explanation:
a(b + c)=ab + ac
it's distributive one
10
8
12
10
14
?
a. 16
b. 10
c. 12
d. 18
Answer:
12
Step-by-step explanation:
10 8 subtract 2
8 12 add 4
12-10 subtract 2
10 14 add 4
Now we subtract 2
14-2 = 12
please help with this on the picture
Answer:
There is not enough information to solve this problem :(
You wish to have $2000 in 3 years to buy a fancy new stereo system. How much
should you deposit each quarter into an account paying 6% compounded quarterly?
Answer:
The correct answer is - $1977.7913.
Step-by-step explanation:
Given:
Maturity value = 2000
time = 3 years
rate = 6% compounded quarterly
Solution:
If A is the Maturity Value, P is the Principal Amount, r is the Rate of Return, n is the Frequency And t is the Time in Year then the Formula for Compound Interest would be -
A = P(1+r/n)^nt
Putting the given values in formula,
2000 = P*(1 + (0.06/4))^(3*4)
P = 2000/(1 + (0.06/4))^(3*4)
Thus,
P = $1977.7913
Oscar has 1/5 of a jar of mustard. He puts equal amounts of the mustard onto 7 sandwiches and uses all of the mustard. What fraction of a jar of mustard does each sandwich have?
Answer:
1/35 jar of mustard yuh yuh
