For the polynomial p(x) = -3x² - 4x + 10, the degree is 2 and the leading coefficient is -3
What is an polynomial?Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction.
Polynomial is an expression composed of variables, constants and exponents combined using mathematical operations such as addition, subtraction, multiplication
Given the polynomial:
p(x) = -3x² + 10 - 4x
Rewriting the polynomial in standard form is done by rearranging based on exponents. Hence:
p(x) = -3x² - 4x + 10
The degree is 2 (x²) and the leading coefficient is -3(-3x²)
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The depth of water in a tank oscillates sinusoidally once every
8 hours. If the smallest depth is 6. 6 feet and the largest
depth is 9. 4 feet, find a possible formula for the depth in terms
of time t in hours. Assume that at t=0 the water level is at
the average of the depth and is rising.
.
The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.
Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D
where, A --> amplitude
B--> period in form of pi
C--> phase or horizontal shift
D --> vertical shift
We have, the depth of water in a tank oscillates sinusoidally.
The smallest depth of water in tank = 6.6 feet
The largest depth of water in tank = 9.4 feet
We have to determine the formula of depth of water in tank as a function of time in hours .
For sinusoidal function,
Amplitude , A = average depth
= ( largest depth + smallest depth)/2
= (6.6 + 9.4)/2
= 16.0/2 = 8
Now, The period of 8 hours so, B = 2π/8
=> B = 45° = π/4
Also, upward shift , D is 9.4 - 6.6 = 2.8
Horizontal shift, C = 0
So, required function is D = 2.8 + 8 sin(π t/4) .
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3 divided by 3/4 IN FRACTION FORM! HELP ASAP
i need help with this pleasee
Answer:
25%
Step-by-step explanation:
1 out of 4 chance = 25% chance to get 2
What is the additive inverse of 6 /- 5 of Class 8?
The additive inverse of 6 /- 5 is 6/5
We know that for any real number 'a' an additive inverse is a number 'b' such that a + b = 0
i.e., b = -a
An additive inverse of 'a' is -a.
The means, an additive inverse is nothing but changing sign + to - OR - to +
Here we have been given a rational number 6/(-5)
Let m be the additive inverse of number 6/(-5)
From the definition of additive inverse,
6/(-5) + m = 0
[6/(-5) + m] - 6/(-5) = -6/(-5)
[6/(-5) - 6/(-5)] + m= -6/(-5) ...........(associative property of addition)
0 + m = 6/5
m = 6/5
Hence, the additive inverse is 6/5
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The lateral urface area of cone A i equal to the lateral urface area of cylinder b
A statement 'The lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.' is True.
We know that the formula for the lateral surface area of cone:
Area = π × radius × slant height
and the formula for the lateral surface area of cylinder:
Area = 2π × (radius) × (height)
Here we have been given a cone A with radius r and slant height 2h.
Using the above formula, the lateral surface area of cone A would be:
A1 = π × r × 2h
A1 = 2π × r × h ..................(1)
Also, we have been given a cylinder B with radius r and height h.
Using the above formula, the lateral surface area of cylinder A would be:
A2 = 2π × r × h ..............(2)
From (1) and (2) we can observe that,
A1 = A2
Therefore, the lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.
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A triangle has the sides of 7 in, 14 in, and 25 in. Is it a right triangle?
Answer:
No it does not equal a right triangle.
Find the length of the diagonal of the rectangle.
Round your answer to the nearest tenth. The height of the rectangle is 7 meters. The length is 9 meters
Answer:
≈ 11.4 m
Step-by-step explanation:
The diagonal splits the rectangle into 2 right triangles , with legs 7 and 9 and the diagonal the hypotenuse.
Using Pythagoras' identity with h as the diagonal, then
h² = 7² + 9² = 49 + 81 = 130 ( take the square root of both sides )
h = [tex]\sqrt{130}[/tex] ≈ 11.4 m ( to the nearest tenth )
A company manufactures industrial laminates (thin nylon-based sheets) of thickness 0.016 in., with a tolerance of 0.004 in.
0.016 in.
(a) Find an inequality involving absolute values that describes the range of possible thickness for the laminate. (Use h for
the thickness.)
(b) Solve the inequality that you found in part (a). (Enter your answer using interval notation.)
An inequality involving absolute values that describes the range of possible thickness for the laminate.
|h - 0.016| <= 0.004The range of possible thickness for the laminate is given by the interval (0.012, 0.02).What is inequality?(a) The range of possible thickness for the laminate is given by the tolerance of 0.004 in., so we can write an inequality involving absolute values as:
|h - 0.016| <= 0.004
(b) To solve the inequality, we need to consider two cases:
Case 1: h - 0.016 <= 0.004
h <= 0.02
Case 2: h - 0.016 >= -0.004
h >= 0.012
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Kendrick is planting a circular flower garden with a low fence around the border. He has 38 feet of fence. What is the radius of the largest garden he can make?
Answer: [tex]6.04\ ft[/tex]
Step-by-step explanation:
Given
The fence has a length of 38 ft i.e. it is the circumference of the circular flower
The circumference of the circle is [tex]2\pi r[/tex]
Insert the values
[tex]\Rightarrow 2\pir=38\\\\\Rightarrow 2\times \dfrac{22}{7}\times r=38\\\\\Rightarrow r=\dfrac{38\times 7}{2\times 22}\\\\\Rightarrow r=\dfrac{266}{44}\\\\\Rightarrow r=6.04\ ft[/tex]
The largest radius of the garden is [tex]6.04\ ft[/tex]
What is the volume of this rectangular prism?
Answer:
40
Step-by-step explanation:
5 x 4 x 2 = 40
length x width x height = volume
What are the domain and range of the function fix) = x* - 2x2 - 4?
Answer: domain(-oo,oo). range= f(x) >-5
Step-by-step explanation:
Kayla had 20 candie. Kayla have 1/5 of the candie to her iter. Of the amount left , he gave 3/8 of her friend. How many candie doe Kayla have left for herelf ?
The candies left for Kyla were 10 based on the amount given to her sister and friend from total 20 candies.
Firstly we will calculate the remaining candies from twenty after giving to her sister. Next calculation will be the final answer representing candies left for Kyla herself.
Remaining candies = total number of candies - 1/5×total candies
Keep the values in formula
Remaining candies = 20 - 1/5×20
Remaining candies = 20 - 4
Remaining candies = 16
Total candies for Kyla = remaining candies - 3/8×remaining candies
Candies for Kyla = 16 - 3/8×16
Candies for Kyla = 16 - 3×2
Candies for Kyla = 16 - 6
Candies for Kyla = 10
Thus, Kyla received 10 candies.
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Solve |x| + 7 < 4.
{x | x < -11 or x > -3}
Ø
{x | -3 < x < 3}
The solution of equation is ∅.
What is linear inequality?According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols.
Given equation |x| + 7 < 4
subtract 7 from both sides
|x| + 7 - 7 < 4 - 7
|x| < -3
but |x| ≥ 0, for all real values,
so solution is ∅.
Hence the solution of equation is ∅.
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round 34.171875 to the nearest 100th
The rounding off of 34.171875 to the nearest 100th gives us= 34.17
The nearest hundredth should be the second digit after the decimal point. To round off any decimal figures, we need to see if the digit after the hundredth is greater than or equal to 5. If such is the case, then add 1 to the hundredth, or else remove the digits.
Here, the nearest hundredth digit is 7, and the digit after it (i.e, the third place after decimal) is smaller than 5. So, there is no need of adding an extra 1 to the hundredth. Now, after casting off the remaining digits, we get 34.17.
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A total of 4 pennies are put into 4 piles so that each pile has a different number of pennies. What is the smallest possible number of pennies that could be in the largest pile
Answer:
Step-by-step explanation:
iF THERE MUST BE 4 PILES, and you have only 4 pennies, then there must be 1 penny in each pile.
In the Himalaya Mountains along the border of Tibet and Nepal, Mount Everest reaches a record height of 29,035 feet. How high is Mt. Everest in miles
The height of the mt. Everest in miles exists 5.499 miles.
What is meant by unit conversion?By changing the unit of measurement, a quality can be expressed differently. In contrast to distance, which can be stated in miles, kilometers, feet, or any other unit of length, time can also be expressed in minutes rather than hours.
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. The right conversion factor to an equal value must be used when a conversion is required. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.
The height of the mt. Everest is : 29035 feet.
The unit conversion is given as :
5280 feet = 1 mile
1 feet = 1/5280 mile
So, 29035 feet =29035 × 1/5280 miles
29035 feet = 29035/5280 miles
29035 feet = 5.499 miles
So, the height of the mt. Everest in miles is 5.499 miles.
The complete question is:
In the Himalaya mountains along the border of Tibet and Nepal, mount Everest reaches a record height of 29,035 feet. how high is mt. Everest in miles? use the conversion equivalency of 1 mile = 5280 feet.
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Answer: The height of the Mount Everest in miles is 5.499 miles
Step-by-step explanation:
1 miles = 5,280 feet
For feet to miles conversion, you should multiply your length value by 0.0001894: mi = ft × 0.0001894 .For miles to feet conversion, you should multiply your length value by 5,280: ft = mi × 5,280 .1 feet = 1/5280 mileso So, 29035 feet = 29035×1/528029035 feet = 29035/5280in the given question, 29035 feet = 5.499 milesSo, the height of the mt. Everest in miles is 5.499 mileTo learn more about it refer to:
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Gary, Mary, and Rory have the same number of candies. If Gary gives Mary half of all his candies, then Mary gives Rory half of all the candies she has at the moment, and then Rory gives Gary half of all the candies he (Rory) has at the moment, Gary would have 12 more candies than he had originally. How many candies do Gary, Mary, and Rory have altogether
Gary, Mary, and Rory have 96 candies altogether.
Let's assume that the original number of candies that Gary, Mary, and Rory had is "x".
After Gary gives Mary half of all his candies, he would have x/2 candies.
Then, after Mary gives Rory half of all the candies she has at the moment, she would have x/4 candies.
And then, after Rory gives Gary half of all the candies he (Rory) has at the moment, he would have x/8 candies.
Now, we know that Gary would have 12 more candies than he had originally, which means:
x/2 + x/8 = x/2 + x/4 - 12
We can combine like terms and simplify the equation:
x/2 + x/8 = x/4 + x/4 - 12
x/8 = 12
x = 8 * 12
x = 96
Thus, Gary, Mary, and Rory have 96 candies altogether.
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Approximately how tall is the streetlight? Round your answer to the nearest tenth.
Note: your teacher may not want you to enter "feet" and instead may just want the number only.
===================================================
Work Shown:
tan(angle) = opposite/adjacent
tan(40) = h/20
20*tan(40) = h
h = 20*tan(40)
h = 16.7819926 which is approximate
h = 16.8
The streetlamp is approximately 16.8 ft tall.
When using your calculator, make sure it's in degree mode. One way to check is to compute something like tan(45) and you should get 1 as a result.
Solve for x. Solve for x.
Answer:
23
Step-by-step explanation:
7(x+1) = 8(x-2)
7x+7 = 8x-16
x = 23
How to simplify an equation?
The process of simplify the equation is explained below.
The term equation is known as a mathematical statement that defines the equality between two expressions.
Here we have to define the process of simplifying the equation.
The first and foremost step is to remove parentheses and brackets by multiplying factors.
And then we have to use the exponent rule to remove grouping if the terms contain exponents.
Then we have to combine like terms by adding or subtracting coefficients.
Finally, we have to Combine the constants.
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The function w (t) = 29 + 0.0674t gives the estimated weight, in pounds, of a beaver t days
after June 1, where t < 90. Which of the following is the best interpretation of 29 in this context?
1)The estimated weight, in pounds, of the beaver 90 days after June 1
2)The estimated weight, in pounds, of the beaver on June 1
3)The estimated number of pounds by which the beaver's weight increased each day after June 1
4)The estimated number of pounds by which the beaver's weight increased in the 90 days after
June 1
Answer:
2) The estimated weight, in pounds, of the beaver on June 1.
Step-by-step explanation:
Given function:
[tex]w(t) = 29 + 0.0674t \quad t < 90[/tex]
where:
w = weight of a beaver (in pounds)t = time after June 1 (in days)When t = 0:
[tex]\begin{aligned}\implies w(0)&=29+0.0674(0)\\&=29+0\\&=29\end{aligned}[/tex]
Therefore, the constant of the equation (29) is the estimated weight of the beaver, in pounds, when t = 0.
As t = 0 is June 1:
29 is the estimated weight, in pounds, of the beaver on June 1.Of the 50 members of a staff, 40 percent worked the day shift and the remaining 60 percent worked the night shift in a given week. Of the staff members, 80 percent prefer working the day shift and the remaining 20 percent prefer working the night shift. What is the minimum number of staff members who failed to receive his or her preference of shift that week
The minimal number of employees who did not get their preferred shift that week was 20.
Out of 50, 40% are on the day shift = 0.4*50 = 20 & 60% are on the night shift = 30.
But, 80% of 50 prefer day shift = 0.8*50 = 20 & 20% of 50 prefer night shift = 10.
We need to find the minimum no. of people who did not get their desired shift. Since slots for the night shift(30) are greater than the people who desired it (10). We can assume that among those 30-night shift slots, 10 were occupied by the ones who wanted the night shift. So, whoever wanted the night shift got the night shift.
But, for the day shifts the no. of slots (20) is less than the number of people who desired it (40). So, there are going to be 20 people who did not get what they desired.
Thus, 20 is the minimum number of staff members who failed to receive her preference of shift that week.
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A line is drawn so that is passed through the points (2, -1) and (0, 5). What is the slope of the line
If a line is drawn so that it passes through the point [tex](2,-1)[/tex] and [tex](0,5)[/tex] , then slope of line is -3 .
What is Slope ?
The slope of a line is defined as measure of steepness and direction of line. The slope of line in a plane help in predicting whether lines are parallel, perpendicular, or none without using a compass.
The slope of line passes through points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is calculated by formula ⇒ [tex]Slope = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] ;
the points are given as [tex](2,-1)[/tex] and [tex](0,5)[/tex] ;
So , on substituting the values in the slope formula ,
we get ;
[tex]Slope = \frac{5 -(-1) }{0 -2 }[/tex] ;
= [tex]\frac{6}{-2}[/tex]
= -3 .
Therefore , the required slope of the line is -3 .
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PLEASE HELP?
Rewrite the function in factored form (show your work)
Standard form for the function is:
p(x)=-5x^+120x-315
Answer:
-5(x-21)(x-3)
Step-by-step explanation:
-5[tex]x^{2}[/tex] + 120x - 315 = -5([tex]x^{2}[/tex] - 24x + 63)
= -5([tex]x^{2}[/tex] - 3x - 21x + 63)
= -5[x(x-3) - 21(x-3)]
= -5[(x-21)(x-3)]
hi, I need mo ney for food anything helps its been such a struggle since co vid hit.
Answer:
get a job....
Write the ratio of the first measurement to the second measurement. Compare in inches.
Answer:
when the ratio of the first measurment is already there, get the pot, put it in place and chec the correct ratio, the slope should help the gaurdian. so in that case, the answer is 75inch
Blue's Berry Farm charges Percy a total of $24.75 for entrance and 2.5 kilograms of strawberries. The entrance fee is $6, and the price for each kilogram of strawberries is constant.
Answer:
$7.50 if the question is how much in a kilogram of strawberries you did not specify.
Step-by-step explanation:
24.75-6=2.5*x
18.75=2.5*x
7.5=x
Answer:
7.5 for 1 kg of strawberries
Step-by-step explanation:
I'm not sure what to solve, but I assumed that you wanted to know the unit price.
Melissa made pancakes using a circle
mold. The circumference of the mold
is 8 centimeters. Which measurement
is closest to the area of the mold in
centimeters?
A 50.24 cm
B 200.96 cm
C 25.12 cm
D 100.48 cm
Answer:
c
Step-by-step explanation:
The circumference should equal c = 2π × 8 cm = 50.265 cm . The area should equal A = π × (8 cm)² = 201.06 cm² . To check your results, input the 8 cm diameter in the calculator. The results should also be 50.265 cm and 201.06 cm². which is closest to c
jonn has a total of 50 coins in her purse The are either nickles or quarters The value of the ccoins is $7.10 Which system of equations can be used to determine the number of nickles ,n and quarters ,q, that jonna has in her purse .
Answer:
n + q = 50
.05n + .25q = 7.10
Step-by-step explanation:
total of 50 coins .... are either nickles or quarters
n + q = 50
value of the coins is $7.10
The value of each coin times the quantity is the value
.05n + .25q = 7.10
You earn $35 for washing 7 cars. How much do you earn for washing 4 cars?
You earn $
for washing 4 cars.