The cubic polynomial equation which passes through the coordinate (0,-5) and whose zeroes are (2 , 0), (3 , 0), and (5 , 0) is: [tex]y = \dfrac{1}{6}(x-2)(x-3)(x-5)[/tex] and it can be determine by arithmetic operations.
Given :
A cubic polynomial whose zeroes are (2 , 0), (3 , 0), and (5 , 0).Cubic polynomial equation passes through (0 , -5).Arithmetic operations can be used to determine the cubic polynomial equation. The generalised cubic polynomial equation is given by:
[tex]y = K(x-a)(x-b)(x-c)[/tex]
Where, K is constant and a, b, and c are the zeroes of the cubic polynomial equation. Therefore, the value of a, b, and c are 2, 3, and 5 respectively.
[tex]y = K(x-2)(x-3)(x-5)[/tex] ----- (1)
It is given that cubic polynomial equation passes through (0 , -5). So, put x = 0 and y = -5 in equation (1) to evaluate the value of K.
[tex]-5=K(0-2)(0-3)(0-5)[/tex]
[tex]5=30K[/tex]
[tex]K = \dfrac{1}{6}[/tex]
Therefore the cubic polynomial equation is given by:
[tex]y = \dfrac{1}{6}(x-2)(x-3)(x-5)[/tex]
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-22+0.3z=3-0.5z-0.8z
What is the common difference in the arithmetic sequence -4x,-x,2x,5x,8x,... ?
What are the estimated annual wages for a person who earns 10.25 an hour
Which of the following is true regarding the solution to the logarithmic equation below?
Answer:
Option C. is the correct option.
Step-by-step explanation:
The given expression is [tex]log_{2}(x+11)=4[/tex]
We further solve this
[tex](x+11)=2^{4}=16[/tex]
[tex]x = 16-11=5[/tex]
Now we evaluate the options
A). [tex]log_{5}16\neq 2[/tex]
But the expression is given as [tex]log_{2}(x+11)=4[/tex]
Wrong expression so not correct.
B). [tex]log_{5}16\neq 4[/tex]
Wrong expression again so not correct
C). By putting x = 5 in the expression
[tex]log_{2}(x+11)=4[/tex]
[tex]log_{2}(5+11)=log_{2}(16)=log_{2}(2^{4})=4[/tex]
Therefore this option is the correct option.
D). By putting x = 5 in the expression
[tex]log_{4}(5+11)=log_{4}(16)=log_{4}(4^{2})=2[/tex]
But the expression is [tex]log_{2}(x+11)=4[/tex]
So this option is also not correct.
Answer:
c
Step-by-step explanation:
The diameter of your bicycle wheel is 25 inches. How far will you move in two turns of your wheel? Use 3.14 for π.
A) about 39 inches
B) about 78 inches
C) about 157 inches
D) about 314 inches
Answer: D) About 314 inches
Step-by-step explanation:
Since, the radius of the wheel = 25 inches
Also, the angle in one turns of the wheel [tex]= 2\pi[/tex]
⇒ The angle in 2 turn of the wheel [tex]= 4\pi[/tex]
Hence, the distance it will cover in two turns
[tex]= 4\pi\times 25[/tex] ( Arc length = central angle × radius)
[tex]= 4\times 3.14\times 25[/tex]
[tex]=314.159265\approx 314\text{ inches}[/tex]
⇒ Fourth option is correct.
In a "torture test" a light switch is turned on and off until it fails. if the probability that the switch will fail any time it is turned on or off is 0.001, what is the probability that the switch will fail after it has been turned on or off 1,200 times?
Final answer:
The probability of a light switch failing after 1,200 operations can be calculated by first finding the likelihood of it not failing across those operations with the formula [tex]0.999^{1200}[/tex], and then subtracting that result from 1.
Explanation:
The question asks about the probability that a light switch will fail after being turned on or off 1,200 times, given that the probability it will fail on any given operation is 0.001. This can be approached by calculating the probability that the switch does not fail in all 1,200 operations and then subtracting that probability from 1.
To calculate the probability of the switch not failing in a single operation, we subtract the failure probability from 1: 1 - 0.001 = 0.999. The probability of the switch not failing in all 1,200 operations is [tex]0.999^{1200}[/tex].
Finally, the probability of the switch failing at least once in 1,200 operations is [tex]1 - 0.999^{1200}[/tex]. When you calculate this, it gives the probability of failure after 1,200 operations.
Jason can paint a room in 6 hours. Lorissa can paint a room in only 3 hours. Which of the following can be used to determine the amount of time it would take for Jason and Lorissa to paint a room together?
a-1 over 6 plus 1 over 3 equals 1 over x
b-1 over x plus 1 over 3 equals 1 over 6
c-1 over 6 plus 1 over x equals 1 over 3
d-1 over 3 plus 1 over 6 equals x over 9
The feel better spa has two specials for new members. They can receive 3 facials and 5 manicures for $114 or 3 facials and 2 manicures for $78
the gray is a sidewalk and the turquoise is grass. Both are squares. What is the area of the sidewalk?
A) 4 ft2
B) 36 ft2
C) 44 ft2
D) 48 ft2
Answer:
C 44 ft2 i just took the test .
Step-by-step explanation:
A building that is 115 feet tall casts a shadow that is 190 feet long. determine the angle at which the rays of the sun hit the ground to the nearest degree.
The angle at which the rays of the sun hit the ground is equivalent to {β} = 31.22°.
What is the meaning of the angle of depression?Its an angle that is formed with the horizontal line if the line of sight is downward from the horizontal line.
Given is that a building that is 115 feet tall casts a shadow that is 190 feet long
Assume that the angle of elevation or the angle at which the rays of the sun hit the ground is equivalent to {β}. Then, with respect to the question, we can write -
tan{β} = (height of building)/(length of shadow)
tan{β} = (115/190)
tan{β} = 0.606
{β} = tan⁻¹(0.606)
{β} = 31.22°
Therefore, the angle at which the rays of the sun hit the ground is equivalent to {β} = 31.22°.
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y = x – 6
x = –4
What is the solution to the system of equations?
(–8, –4)
(–4, –8)
(–4, 4)
(4, –4)
the answer is (-4 -8)
PLS PLS PLS HELP I rly need help in geometry
Using the definition of even and odd functions explain why y= sin x+ 1 is neither even or odd ?
Can you show how you worked it out cause I'm not sure on how to plug it in exactly
The area of a square is greater than the area of the circle by 12 cm². find the length of the side of a square if the area of the circle is 36 cm².
Final answer:
To find the length of a side of the square, calculate the square root of the sum of the areas of the circle (36 cm²) and the additional 12 cm². This results in a square side length of approximately 6.93 cm.
Explanation:
We are given that the area of the circle is 36 cm², and we know that the area of a square is greater than the area of the circle by 12 cm², which means the area of the square is 36 cm² + 12 cm² = 48 cm².
The area of a square is given by A = a², where a is the length of the side of the square. So, we need to find the value of a that satisfies the equation a² = 48 cm².
By taking the square root of both sides of the equation, we get a = √(48 cm²). Simplifying the square root of 48 gives us a ≈ 6.93 cm. Therefore, the length of a side of the square is approximately 6.93 cm.
create the equation of a quadratic function with a vertex of (5,6) and a y-intercept of -69
Natalie picked 135 berries in 15 minutes if she continues picking at that rate how long will it take her to pick 486 berries? @skullpatrol,
What is the value of n? Enter your answer in the box.
Answer:
n=6
Step-by-step explanation:
Since, we know that when two chords intersect each other inside a circle, the products of their segments are equal. Thus, using this property, we have
[tex](n+8)5=(n+4)7[/tex]
⇒[tex]5n+40=7n+28[/tex]
⇒[tex]40-28=7n-5n[/tex]
⇒[tex]12=2n[/tex]
⇒[tex]n=6[/tex]
Thus, the value of n is 6.
Answer:
[tex]n=6[/tex]
Step-by-step explanation:
We have been given an image of a circle. We are asked to find the value of n.
We can see that two chords of our given circle are intersecting inside it, so we will use intersecting chords theorem to solve for n.
Intersecting chords theorem states that when two chords of a circle intersect inside the circle, then product of the segments of both chords is equal.
Using intersecting chords theorem we can set an equation as:
[tex]5(n+8)=7(n+4)[/tex]
Using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,
[tex]5*n+5*8=7*n+7*4[/tex]
[tex]5n+40=7n+28[/tex]
Subtracting 40 and 7n from both sides we will get,
[tex]5n-7n+40-40=7n-7n+28-40[/tex]
[tex]-2n=-12[/tex]
Dividing both sides by -2 we will get,
[tex]\frac{-2n}{-2}=\frac{-12}{-2}[/tex]
[tex]n=6[/tex]
Therefore, the value of n is 6.
gina is traveling to the beach 20 miles away from her house.On Ginas map her house and the beach are 4 inches apart what is the scale used for Ginas map
Gina is travelling to the beach 20 miles away from her house.
On Ginas map her house and the beach are 4 inches apart
That is a distance of 20 miles is represented by the Ginas map in 4 inches
Therefore, on Ginas map one inch will be = 20/4 miles = 5 miles
So, the scale used for Gina's map is 1 inch = 5 miles
Hope this helps..!!
Thank you :)
WILL GIVE BRAINLIEST FOR CORRECT ANSWER!
How is energy transferred during the water cycle
A. water gains energy during evaporation and condensation
B. water gains energy in condensation and releases it in evaporation
C. water releases energy during evaporation and condensation
D. water gains energy during evaporation and releases it during condensation
The surface area of a box is 160. the length of the box is twice its width as well as 4 less than its height. how many units are in the height of the box? (the surface area of a box is the sum of the areas of all 6 of its rectangular faces.) aops
Final Answer:
The height of the box is 9 units.
Explanation:
Let's denote the width of the box as w, the length as l, and the height as h. According to the problem, we have the following relationships:
l = 2w (the length is twice the width) and
l = h - 4 (the length is also 4 less than the height).
The surface area SA of a rectangular box is calculated by the formula:
SA = 2lw + 2lh + 2wh.
Given that the surface area is 160, we set up our equation:
160 = 2lw + 2lh + 2wh.
Now let's substitute the relations l = 2w and l = h - 4 into the surface area equation:
Since l = 2w, 160 = 2(2w)w + 2(2w)h + 2wh.
Simplifying the equation, we have:
160 = 4w² + 4wh + 2wh
160 = 4w² + 6wh
Now we use the fact that l = h - 4 to substitute for h:
h = l + 4
h = 2w + 4
Now substitute h back into the surface area equation:
160 = 4w² + 6w(2w + 4) ,
Expand the terms:
160 = 4w² + 12w^2 + 24w,
Combine like terms:
160 = 16w² + 24w
Now, we must solve for w. Let's move all terms to one side to solve the quadratic equation:
16w² + 24w - 160 = 0
Divide all terms by 8 to simplify:
2w² + 3w - 20 = 0
We can now attempt to factor the quadratic equation:
(2w - 5)(w + 4) = 0
This gives us two solutions:
2w - 5 = 0 or w + 4 = 0
Solving the first equation for w:
2w = 5,[tex]\( w = \frac{5}{2} \)[/tex]
w = 5/2
We can disregard the second solution w + 4 = 0 for w, as it gives us a negative width, which isn't possible for a box.
Now that we have w, we can find h.
Using our earlier substitute for h:
h = 2w + 4 ,
[tex]h = 2 \cdot \frac{5}{2} + 4[/tex] ,
h = 5 + 4 ,
h = 9 .
Thus, the height of the box is 9 units.
Clark left for school at 7:43 am he git to school 36 minutes later.what time. Did clark get to school???
Patrick is constructing the circumscribed circle for △RST.
Which construction could be his first step?
Construct the perpendicular bisector of ST¯¯¯¯¯ .
Construct the angle bisector of ∠T .
Construct a copy of ∠S that is adjacent to ∠R .
Construct the angle bisector of ∠R .
Two wheels rolled simultaneously. The radius of the smaller wheel is r feet and the radius of the larger wheel is 2r feet If both wheels did a total of 4 rotations, how much farther did the larger wheel travel?
what is the volume of a spear with the radius of 6in.
3, 12, 48, 192, 768, . . .
This sequence has a
A.] common difference of 4
B.] common ratio of 4
C.] common difference of [tex] \frac{1}{4}[/tex]
D.] common ratio of [tex] \frac{1}{4}[/tex]
A cylinder shaped drum is used to store used motor oil. The drum has a height of 3 ft and a radius of 1.5 ft. How many cubic feet of oil does the drum hold? Use 3.14 to approximate pi. Enter your answer as a decimal rounded to the nearest hundredth in the box.
Heidi's hair was 2/3 of a meter long. her grandfather cut off 1/6 of a meter of her hair. how long is heidi's hair now?
Math help!!!!!!!!!!!!!!
Answer:
The answer is E
Step-by-step explanation:
*URGENT ALGEBRA 2* Anyone know these answers? Choices provided. Will award brainliest.
PLEASE HELP!!!!!!
A reflecting telescope is purchased by a library for a new astronomy program. The telescope has a horizontal parabolic frame and contains two mirrors, 3 inches apart from each other- the first in the base and the second at the focal point. The astronomy teacher would like to attach a digital monitoring system on the edge of the telescope, creating a straight line distance above the focal point. Assuming that the telescope is placed on the edge of the roof in such a way that it is parallel to the ground, the position of the monitoring system, in relationship to the distance between the base and the focal point is modeled by the equation, x =[tex] \frac{1}{12} [/tex] y2 (x = the distance between the base and the focal point; y= the height of the monitoring system).
Rewrite the model so that the height of the digital monitoring system is a function of the distance between the base and the focal point of the telescope. How high above the focal point is the digital monitoring system attached to the telescope? Include your function and the height, rounded to the nearest tenth of an inch, in your final answer.
Final answer:
To find the height of the digital monitoring system, we rearrange the given parabolic equation to solve for y, substitute the known distance of 3 inches, and determine that the monitoring system is attached 6 inches above the focal point.
Explanation:
The equation given for the reflecting telescope by the library for their astronomy program is x = \frac{1}{12} y^2. To solve for the height of the digital monitoring system as a function of the distance x, we need to rewrite the equation in terms of y. First, we multiply both sides by 12 to get 12x = y^2. Then, take the square root of both sides to solve for y, which gives us y = \sqrt{12x}. Given that the distance between the base and the focal point is 3 inches, we substitute x with 3 to find the height of the monitoring system. Thus, we have y = \sqrt{12 \cdot 3} which simplifies to y = \sqrt{36} or y = 6 inches. This means the digital monitoring system is attached 6 inches above the focal point of the telescope.