A hot-air balloon is tied to the ground with two taut ropes. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50º with the ground. What is the height x, to the nearest foot, of the balloon? A) 85 feet B) 96 feet C) 115 feet D) 128 feet
I know the setup is like this,
Sin(50) =(x/150)
(but I don't have a calculator and the online ones aren't working - plz help)
Answers
Answer:
C) 115 feet
Step-by-step explanation:
Assuming your setup is correct and the question is asking the height, given that the length of the slant rope is 150 ft, you find x by multiplying the equation by 150:
... 150*sin(50°) = x ≈ 115 ft
Almost any on-line calculator will compute this value. If you don't specifiy the angle is degrees, you will need to verify that it is properly interpreted. (It may be interpreted as radians. Different calculators make different assumptions.)
The Google or Bing search boxes are pretty reliable calculators. Usually * is suitable as the multiplication indicator, and / works for division. They follow the order of operations rigorously, so parentheses are needed for numerators, denominators, and exponents when more than a single number is involved.
_____
There are on-line equation solvers, too. I've found them to be more fussy and less useful. One likes to give irrational results as the ratio of two (large) integers, for example.
Answer:
115 feet
Step-by-step explanation:
Given : A hot-air balloon is tied to the ground with two taut ropes. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50º with the ground.
To Find: What is the height x, to the nearest foot, of the balloon?
Solution:
We are given a set up :
[tex]sin 50 ^{\circ}=\frac{x}{150}[/tex]
Using scientific calculator find the value of sin 50
0.76604
[tex]0.76604=\frac{x}{150}[/tex]
[tex]0.76604 \times 150=x[/tex]
[tex]114.906=x[/tex]
Hence the height of the balloon is 115 feet.
Option C is correct.
Related Questions
Help! will give points for brainliest
This table shows the input and output values for an exponential function f(x) .
What is the ratio of outputs for any two inputs that are three values apart?
Enter your answer, as a simplified fraction, in the boxes.
table:
x −3 −2 −1 0 1 2 3
f(x) 827 89 83 8 24 72 216
Answers
Answer:
27
Step-by-step explanation:
Choose two outputs that are 3 values apart and find their ratio:
... f(3)/f(0) = 216/8 = 27
Jamie owns a sailboat rental company, which has a large variety of sailboats of different sizes. He observed that the speed of the sailboat (with the wind) largely depends on the length of the sailboat, and is approximately one and a half times the square root of its length. Which of the following options represents the relationship between length and speed of a sailboat?
Answers
Answer:C
Step-by-step explanation:
Formula must be S(x) = (1+1/2)√x = 1.5√x, eliminating A and D. Diagram must show that a zero length boat doesn't move, and that boat length four feet goes 1.5×2 = 3 knots. That eliminates B. Check: C says zero feet goes zero knows and 4 feet goes 3 knots.
Answer:
Graph C
Step-by-step explanation:
We know the speed is equal to one and a half times the square root of the length. This means that speed is the dependent variable (y), and length is the independent variable (x).
Since the speed, S(x), is 1.5 times the square root of the length (x), we get the function
S(x) = 1.5√x.
When x = 0, S(x) = 1.5√0 = 1.5(0) = 0. This makes it graph C.
Two consecutive integers have a sum of 61 . Find the integers.
Answers
Answer:
The integers are, 30 and 31
Step-by-step explanation:
Given the statement: Two consecutive integers have a sum of 61 .
Let x and x+ 1 are the two consecutive integers.
then;
as per the given condition we have;
[tex]x +(x+1) = 61[/tex]
Combine like terms;
[tex]2x+1 = 61[/tex]
Subtract 1 from both sides ;
[tex]2x + 1-1 = 61 -1[/tex]
Simplify:
2x = 60
Divide both sides by 2 we get;
x = 30
and
value of x+1 = 30+1 = 31
Therefore, the integers are, 30 and 31.
during a sale at the grocery store Mrs.reynolds bought 4.2 pounds of green beans for $5.25 is each of the following proportion to the sale price of green beans? select yes or no
(A)6 pounds for $7.50 .......(yes) or (no)
(B)3.4 pounds for $4.25 ....(yes) or (no)
(C)3.5 pounds for $4.20.....(yes) or (no)\
(D)5.8 pounds for $8.70....(yes) or (no)
(E) 2 pounds for $2.50.......(yes) or (no)
plz....HELP
Answers
You can go at this in different ways. In the attached, we multiplied the number of pounds by the sale price per pound ($5.25/4.2). You can also figure the price per pound of each proposed purchase and compare with the sale price.
... sale price = $5.25/(4.2 lb) = $1.25/lb
(A) $7.60/(6 lb) = $1.25/lb (yes)
(B) $4.25/(3.4 lb) = $1.25/lb (yes)
(C) $4.20/(3.5 lb) = $1.20/lb (no)
(D) $8.70/(5.8 lb) = $1.50/lb (no)
(E) $2.50/(2 lb) = $1.25/lb (yes)
Options A (6 pounds for $7.50), B (3.4 pounds for $4.25), and E (2 pounds for $2.50) are proportional to the sale price as their unit prices match, whereas options C (3.5 pounds for $4.20) and D (5.8 pounds for $8.70) do not match the unit price and are thus not proportional.
To determine if the proportions are equivalent to the sale price of green beans, we need to calculate the unit price for each scenario and compare it to the unit price that Mrs. Reynolds paid during the sale. Mrs. Reynolds bought 4.2 pounds of green beans for $5.25. The unit price is found by dividing the total cost by the total weight in pounds:
Unit price = $5.25 / 4.2 pounds = $1.25 per pound.
Now, let's calculate the unit price for each of the given scenarios and see if they match the unit price Mrs. Reynolds paid:
6 pounds for $7.50: $7.50 / 6 pounds = $1.25 per pound (yes)3.4 pounds for $4.25: $4.25 / 3.4 pounds = $1.25 per pound (yes)3.5 pounds for $4.20: $4.20 / 3.5 pounds = $1.20 per pound (no)5.8 pounds for $8.70: $8.70 / 5.8 pounds = $1.50 per pound (no)2 pounds for $2.50: $2.50 / 2 pounds = $1.25 per pound (yes)Based on these calculations, options A, B, and E are proportional to the sale price Mrs. Reynolds paid, while options C and D are not.
Please help: this is due in 15 minutes and showing the work is needed
Answers
Answer:
4 people
Step-by-step explanation:
You Know that 1/3 of an hour is 20 min, and u find out that 1/4 of an hour is 15 min. So then it takes 45 min for 1 person. 3 1/3 hour= 3 hr 20 min= 200 min. 200/45=4.44...= 4 people
Prove without solving that the solution of the equation 7(2x+1)=13 is not a whole number.
Answers
Assume x is a whole number. Then 2x+1 is a whole number, and 7(2x+1) is a whole number that is a multiple of 7.
13 is not a multiple of 7, so we have reached a contradiction, and our assumption must be false.
x cannot be a whole number.
What is the factorization of the polynomial below?
4x2 - 25
A. (2x + 5)(2x - 5)
B. (4x - 5)(x - 5)
C. (2x - 5)(2x - 5)
D. (4x + 5)(x - 5)
Answers
Answer:
A. (2x + 5)(2x - 5)
Step-by-step explanation:
Factor out the polynomial given.
(4x² - 25) = (2x - 5)(2x + 5)
Check: Use the FOIL method.
(2x)(2x) = 4x²
(2x)(5) = 10x
(2x)(-5) = -10x
(-5)(5) = -25
Simplify. Combine like terms: 4x² + 10x - 10x - 25 = 4x² - 25
A. (2x + 5)(2x - 5) is your answer
~
So for this, we will be applying the difference of squares rule, which is [tex]x^2-y^2=(x+y)(x-y)[/tex] . In this case:
[tex]\sqrt{4x^2}=2x\\\sqrt{25}=5\\\\4x^2-25=(2x+5)(2x-5)[/tex]
Answer:In short, your answer is A. (2x + 5)(2x - 5).
Please help me if you can
Answers
Answer:
y = .025x +20
The y intercept is the value when x = o, or the starting value. In this case, it is the temperature in degrees F at a depth of 0 meters.
Step-by-step explanation:
We have a point a (0,20) and a point at (2 , 20.05)
We can find the slope from
m = (y2-y1)/(x2-x1)
= (20.05-20)/(2-0)
= .05/2
=.025
One of the points (0,20) is the y intercept since x=0
We can use the slope intercept form of the equation
y= mx+b
y = .025x +20
The y intercept is the value when x = o, or the starting value. In this case, it is the temperature in degrees F at a depth of 0 meters.
Answer:
.
Step-by-step explanation:
how do i find a median?
Answers
First you have to rearrange the numbers from greatest to least.
If there are any odd numbers then the median is in the center term.
If there is an even number of terms, you add the two middle terms and divide them by 2.
Final answer:
The median is found by arranging a data set in ascending order and locating the middle value for an odd number of values or averaging the two middle values for an even number. Quartiles divide the data into sections and are related to the median. The median offers a measure of the center that is not skewed by outliers.
Explanation:
To find the median of a data set, start by arranging the data in ascending order. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, calculate the median by taking the average of the two middle values.
For example, for the ordered data set 3, 4, 8, 8, ... 44, 44, 47, which has 40 values, the median is between the 20th value (24) and the 21st value (24). In this case, since they are the same number, the median is 24. However, if the two numbers were different, you would add them together and divide by two to find the median.
When considering a data set like 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5, with an even number of values (14), the median is the average of the 7th and 8th values, in this case, (6.8+7.2)/2 = 7. The quartiles can also be determined: Q1 is the median of the lower half, and Q3 is the median of the upper half of the data set.
Measures of the center of the data, like mean, median, and mode, offer different ways to represent the data set's central tendency. The median is particularly useful in data sets with outliers, as it is not as affected by extreme values as the mean.
what are the domain and range of the function below?
A) Domain: (-∞, -5)
Range: (5, ∞)
B) Domain: (-5, -10)
Range: (5, 10)
C). Domain: (-5, 10)
Range: (-10, 5)
D) Domain: (-∞, ∞)
Range: (-∞, ∞)
Answers
The domain and range is all real numbers.
Answer: D) Domain: (-∞, ∞); Range: (-∞, ∞)Answer:
D) Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
The domain is the input values, or the x values.
We can put in any x values for this function.
Domain : (-∞, ∞)
The range is the output values or the y values.
We can get any output values for this function
Range: (-∞, ∞)
Write the equation of the line that passes through (2,3) and (4, 1) in point-slope form. Use (2,3) for (x1, y1).
Answers
Answer:
y-2 = -(x-2)
Step-by-step explanation:
To find the slope
m = (y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are two points on the line
= (1-3)/(4-2)
=-2/2
=-1
The point slope form is
y-y1 = m(x-x1) wher m is the slope and (x1,y1) is a point on the line
y-3 = -1(x-2)
y-2 = -(x-2)
Identify negative angle measure. Select all angles that have a negative measure.
Answers
see attachments below
Step-by-step explanation:In Algebra, angles are measured counterclockwise (CCW), generally using the +x axis as a reference. Thus any angle with an arrow shown in the CW direction will have a negative measure.
Know that clockwise measured angles are negative and anticlockwise measured angles are positive in sign.
Thus,
In first figure first angle is positive, second is negative.In second figure first angle is negative, second is positive.In third figure, first angle is positive, second angle is negative, third angle is positive.How does rotation measure specifies sign of angles?
It is a standard convention used in mathematics that if you measure an angle clockwise(like the clock's hand moves), then the measured angle will be written with negative sign.
If the angle is measured anticlockwise, then the measured angle is written with positive sign.
Thus, by these conclusions, we have:
Thus, In first figure first angle is positive, second is negative.In second figure first angle is negative, second is positive.In third figure, first angle is positive, second angle is negative, third angle is positive.Learn more about sign of angles here:
https://brainly.com/question/11043027
Nathan just bought a car. He models the value, V, in dollars, of the car after t years as V(t)=21,000(0.861)^t. Based on this model, by what percent does the value of Nathan car decrease each year?
Answers
Answer:
Value of the car is decreasing by 13.9% each year.
Step-by-step explanation:
This equation tells us V(t) is the value of the car after a certain time in years, $21,000 is the initial value of the car. What we need to focus on is on the 0.861 part of this equation. This means that the price of the car is worth 0.861 or 86.1% of what it was worth the year prior, this means that the price of the car is decreasing over time. By how much is it decreasing? Well if we consider 1 to mean 100% (since 100 / 100 =1) then we have 100%-86.1%=13.9%. This means that the value of the car is decreasing 13.9% each year.
what is the solution to the following equation x2 - 10x + 24 =0
Answers
Answer:
x=6 x=4
Step-by-step explanation:
x^2 - 10x + 24 =0
We need to factor this equation
What numbers multiply together to give us 24 and add together to give us -10
-6* -4 = 24 and -6+-4 = -10
(x-6) (x-4) = 0
Using the zero product property
x-6 = 0 x-4=0
x=6 x=4
Answer:
1.)C
2.)A
3.)B
Step-by-step explanation:
edge 2024
What is the slope of a line that is parallel to a line with slope of m=-6/5.What is the slope of the line that is perpendicular to a line with a slope of m=6/5.Explain how you know
Answers
Answer:
a) m = -6/5
b) m = -5/6
Step-by-step explanation:
The slopes of parallel lines are the same. The parallel line will have a slope equal to that of the line it is parallel to, -6/5.
__
The slopes of perpendicular lines are the opposite of the reciprocal of one another. The perpendicular line will have a slope that is the negative reciprocal of the slope of the one it is perpendicular to: -1/m = -1/(6/5) = -5/6.
The polar form of this is?
Answers
Answer:
2, 120 degrees
Step-by-step explanation:
The first step in finding the polar form is finding the modulus, r
r= sqrt( x^2 + y^2)
r = sqrt( (-1)^2 + sqrt(3)^2)
r = sqrt(1+3)
r= sqrt(4)
r =2
The next step is finding the angle
theta = arctan (y/x)
theta = arctan (sqrt(3)/-1))
theta = arctan (-sqrt(3))
theta = -60
The point (-1, sqrt(3)) is in the 2nd quadrant, but our angle is in the 4th quadrant, so we add 180 degrees
theta = -60 + 180 = 120
theta = 120 degrees
What is the equation of a line with an intercept of -3 and a slope of 5?
(Please provide step by step process, I will also give brainliest answer)
Answers
Answer:
y= 5x-3
Step-by-step explanation:
We have an intercept of -3 and a slope of 5
We can use the slope intercept form of the equation
y= mx+b where m is the slope and b is the y intercept
Substituting in the known values.
y= 5x-3
One integer is 9 less than 5 times another. Their product is 18. Find the integers.
Answers
Answer:
x = 3 and x=-6/5
Step-by-step explanation:
x = one integer
y = other integer
One integer is 9 less than 5 times another
x= 5y-9
product is 18
xy = 18
Substitute in for x
(5y-9) *y = 18
Distribute
5y*y -9y = 18
5y^2 - 9y = 18
Subtract 18 from each side.
5y^2 - 9y -18= 18-18
5y^2 - 9y -18 = 0
Using the quadratic formula
-b ± sqrt(b^2 -4ac)
-----------------------
2a
-(-9) ±sqrt(9^2 -4*5*(-18))
--------------------------------------
2(5)
9 ±sqrt(81 +360))
--------------------------------------
10
9 ±sqrt(441)
--------------------------------------
10
9±21
----------
10
x = (9+21)/10 and x = (9-21)/10
x = 30/10 and x = (-12)/10
x = 3 and x=-6/5
Final answer:
The two integers in question are 21 and 6, with 21 being 9 less than 5 times 6, and their product equating to 18.
Explanation:
Finding the Two Integers
The problem states that one integer is 9 less than 5 times another integer, and their product is 18. Let's call the first integer x and the second integer y.
From the problem, we can write two equations:
x = 5y - 9 (One integer is 9 less than 5 times the other)
xy = 18 (The product of the two integers is 18)
Using substitution from the first equation, in the second equation, we replace x with 5y - 9 and solve for y:
(5y - 9)y = 18
This equation leads to a quadratic equation: 5y^2 - 9y - 18 = 0. Factoring the quadratic equation, we find two pairs of numbers that multiply to give -18 and add up to -9: (-6) and 3.
The factors of the equation are (5y + 3)(y - 6) = 0, giving us y = 6 or y = -³/₅. However, since we are looking for integers, we disregard the fraction and only consider y = 6. Plugging y = 6 back into x = 5y - 9, we get x = 5(6) - 9 which simplifies to x = 21.
Therefore, the two integers are 21 and 6.
what are the apparent zeros of the function graphed above. (-0.7, -2,7)
Answers
Answer:
x ∈ {-2, 1, 4}
Step-by-step explanation:
The graph shows y = 0 when x = -2 or 1 or 4. Hence these values of x are the zeros of the function.
For the given central angle, determine the distance traveled along the unit circle from the point (1, 0).
180 degrees to units
How do i figure this out ?
Answers
Answer:
The length of a 180° arc of a unit circle is π ≈ 3.14 units.
Step-by-step explanation:
Use your knowledge of the circumference of a circle (the length full around) and the fact that there are 360° in the central angle of a full circle. The distance around is proportional to the angle, so an arc of measure 180° will have a length equal to
... (180°/360°) × circumference = (1/2)×circumference
For a unit circle, the circumference is 2π (= π×diameter = 2π×radius). Half that length is π units.
Answer:
A central angle of 180 degrees corresponds to half of the unit circle, and the circumference of the unit circle is 2π units. So, the distance traveled along the unit circle from the point (1, 0) is half of the circumference, which is 1/2 * 2π = π units. Thus, the answer is 3.14 units (approximately).
please help me asap!
Answers
Answer:
D) [tex](x-5)^2 + (y-2)^2 = 49[/tex]
Step-by-step explanation:
Center is (5,2) and radius = 7
We use center - radius form of equation of circle
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h,k) represents the center
and r is the radius of the circle
We know center is (5,2) so h= 5 and k =2
r= 7
Plug in all the values
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
[tex](x-5)^2 + (y-2)^2 = 7^2[/tex]
[tex](x-5)^2 + (y-2)^2 = 49[/tex]
A gumball machine has 420 red gumballs. If the red gumballs are 75% of the total number of gumballs, how many gumballs are in the gumball machine?
Answers
Answer:
The answer is 560
Step-by-step explanation:
multiply 420 by .75 for 75%
(420).75=560
Find the length of AC. Round answer to the nearest tenth.
Answers
16.0
Step-by-step explanation:The mnemonic SOH CAH TOA reminds you of the relationship ...
... Tan = Opposite/Adjacent
... tan(32°) = 10/AC
Multiply by AC and divide by tan(32°) to get ...
... AC = 10/tan(32°) ≈ 16.0033 ≈ 16.0
The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 ln (9t + 4), where y is the number of mowers sold. How many mowers will be sold 6 years after a model is introduced?
Answers
Answer:
22,332
Step-by-step explanation:
Put 6 where t is in the equation and do the arithmetic.
... y = 5500 ln(9·6 +4) = 5500 ln(58) ≈ 22,332
Answer:
The answer is: 22,332 mowers will be sold 6 years after a model is introduced.
Step-by-step explanation:
Given that y = 5500 ln (9t + 4)
In order to calculate the number of mowers (y) that will be sold after 6 years, substitute t = 6 (years):
y = 5500 ln (9 × 6 + 4) = 5500 In 58
In 58 = natural logarithm of 58 = 4.0604
Therefore, y = 5500 In 58 = 5500 × 4.0604 = 22,332.44 = 22,332 mowers.
how many radians is -135°? -1/4pie 3/4pie -3/4pie -4/3pie
Answers
Answer:
hello :
- 3π/4 = (-3×180°)/4 = - 540°/4 = - 135°
Step-by-step explanation:
Answer: [tex]\bold{-\dfrac{3}{4}\pi}[/tex]
Step-by-step explanation:
Set up a proportion using π = 180° → [tex]\dfrac{\pi}{180} = \dfrac{x}{-135}[/tex]
Multiply both sides by -135 to solve for x → [tex]\dfrac{-135\pi}{180} = x[/tex]
Simply the fraction by dividing by [tex]\dfrac{45}{45}[/tex] → [tex]-\dfrac{3}{4}\pi = x[/tex]
Select the correct answer. Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets represent their answers. Class A: {2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5} Class B: {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6} Which statement is true for the data sets?
A: The mean study time of students in Class A is less than students in Class B.
B: The mean study time of students in Class B is less than students in Class A.
C: The median study time of students in Class B is greater than students in Class A.
D: The range of study time of students in Class A is less than students in Class B. E: The mean and median study time of students in Class A and Class B is equal.
Answers
Answer:
B: The mean study time of students in Class B is less than students in Class A.
Step-by-step explanation:
To find out why answer B is the right answer, I will give you facts from each option.
Option A is false. The mean study time in Class A is 4.8. Meanwhile in Class B it is 4. For Class A, sum up the 20 study times which is 96 and divide them by 20, you will get 4.8 hours of mean study time. For Class B, the sum of the 20 study times is 80, which divided by 20 will be 4.
Option B is True. See previous explanation.
Option C is False. The median study time in Class B is 4. The median study time in Class A is 4.8,
Option D is False. The range in Class A is from 2 to 8. The range in Class B is from 2 to 7.
Option E is False: The mean and median study time of these classes is different.
Answer:
B: The mean study time of students in Class B is less than students in Class A.
Step-by-step explanation:
Alex, Bob, and Claudia split 126 cm wire evenly among themselves. They then proceeded to cut their pieces of wire into smaller, equal parts. Alex cut his wire 18 times, and kept 7 pieces. Bob cut his wire 2 times more than Alex did, and kept 9 pieces. While Claudia divided her wire into 13 equal parts, and kept only one piece. Who kept the longest part of the original wire and what was the length of that part?
Answers
If Alex cut his wire 18 times, he ended up with 19 equal pieces. He kept 7, so has 7/19 of his 1/3 of the wire.
Bob cut his wire 20 times, so ended up with 21 pieces, of which he kept 9. So he has 9/21 = 3/7 of his 1/3 of the wire.
Claudia kept 1/13 of her 1/3 of the wire, so has the smallest piece.
Bob kept (3/7)·(1/3)·126 cm = 18 cm.
Alex kept (7/19)·(1/3)·126 cm ≈ 15.47 cm.
Bob kept the longest part of the original wire.
if u=(1+i√3) and v=(1-i√3), what is uv?
Answers
Answer:
4
Step-by-step explanation:
You may recognize these as factors of the difference of two squares:
... a² -b² = (a+b)(a-b)
where a=1 and b=i√3.
Then the product is ...
... 1² -(i√3)² = 1 - 3i² = 1 +3 = 4
_____
Of course, i = √-1, so i² = -1.
Answer: 4
Step-by-step explanation:
u=(1+i√3) =2 v=(1-i√3)=2 Uv = (2)(2)=4
kAITLIN EANRS $6.50 FOR EACH HOUR SHE WORKS. ON FRIDAY SHE WORKED FOR 3 HOURS. SHE ALSO WORKED ON SATURDAY. IF SHE EARNED A TOTAL OF $52.00 FOR TWO DAYS OF WORK, HOW MANY HOURS DID SHE WORK ON SATURDAY
Answers
Answer:
5 hours
Explanation:
$
6.50
(
3
)
+
$
6.50
x
=
$
52.00
$
19.50
+
$
6.50
x
=
$
52.00
$
6.50
x
=
$
32.50
x
=
5
Glad i could help! Sorry if i came out kinda weird lol
Answer:
Answer:
5 hours
Explanation:
$
6.50
(
3
)
+
$
6.50
x
=
$
52.00
$
19.50
+
$
6.50
x
=
$
52.00
$
6.50
x
=
$
32.50
x
=
5
Glad i could help! Sorry if i came out kinda weird lol
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Third-degree, with zeros of −4, −3, and 1, and a y-intercept of −11.
Answers
Given zeros -4, -3, and 1, and a y-intercept of -11, the corresponding third-degree polynomial function can be formulated as y = (11/12)(x + 4)(x + 3)(x - 1).
Explanation:To construct a third-degree polynomial function, we first need to define the polynomial based on its zeros. Given that the zeros are -4, -3, and 1, we can write the polynomial function in the form [y = a(x + 4)(x + 3)(x - 1)], where 'a' is the coefficient that affects the y-intercept. Because the y-intercept is -11, we set the value of y to -11 when x equals 0 to solve for 'a'. Thus the equation becomes [ -11 = a * 4 * 3 * -1], which simplifies to [a = -11/(-12) = 11/12]. Therefore, the polynomial function with the stated properties is [y = (11/12)(x + 4)(x + 3)(x - 1)] .
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The third-degree polynomial with zeros at -4, -3, and 1 and a y-intercept of -11 can be written as P(x) = 0.917(x+4)(x+3)(x-1).
Explanation:To construct a third-degree polynomial with zeros at -4, -3, and 1, we write the factored form of a polynomial P(x), with the zeros plugged into the factors: P(x) = a(x+4)(x+3)(x-1). The term 'a' is a coefficient that we can find using the provided y-intercept of -11.
Because the y-intercept happens when x = 0, we substitute x = 0 and y = -11 into the polynomial: -11 =a(0+4)(0+3)(0-1). Solving for 'a' gives a = 11/12 or 0.917.
Thus, the resulting third-degree polynomial in lowest terms is P(x) = 0.917(x+4)(x+3)(x-1).
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