(a) By expanding, the derivative of the polynomial is f'(x) = 12x² - 6x + 8
(b) Using the product rule, the derivative of the polynomial is f'(x) = 12x² - 6x + 8
(c) The expressions for the derivative in (a) and (b) are the same
Determining the derivative of polynomialsFrom the question, we are to determine the derivative of the given polynomial.
The given polynomial is f(x) = (x² + 2)(4x - 3)
(a) By expanding the polynomial, we get
f(x) = (x² + 2)(4x - 3)
f(x) = x²(4x - 3) +2(4x - 3)
f(x) = 4x³ - 3x² + 8x - 6
∴ f'(x) = 12x² - 6x + 8
(b) By using the product rule
f(x) = (x² + 2)(4x - 3)
g(x) = x² + 2
and
h(x) = 4x - 3
Thus,
g'(x) = 2x
h'(x) = 4
From the product rule
f'(x) = g(x).h'(x) + h(x).g'(x)
f'(x) = (x² + 2)(4) + (4x - 3)(2x)
f'(x) = 4x² + 8 + 8x² - 6x
Collect like terms
f'(x) = 4x² + 8x² - 6x + 8
∴ f'(x) = 12x² - 6x + 8
(c) The expressions are the same
Hence,
The derivative is f'(x) = 12x² - 6x + 8
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Hey guys please help me on this math homework
I need help right now thank you...
Answer:
1 and 3 equal 126 (vertical angle)
2 and 4 equal 54 (supplemental angles 180-126)
Step-by-step explanation:
Answer:
angle 2: 54 degrees
Angle 3: 126 degrees
Angle 4: 54 degrees
Step-by-step explanation:
since angle 1 is 126 degrees we can find angle 2 since it’s right next to it like that the 2 angles added equal 180 degrees so we just subtract from 180
180-126
Angle 2 is 54 degrees
Since angle 3 is across angle 1 they are equivalent so angle 3 is 126 degrees
Since angle 4 is across angle 2 they are equivalent so angle 4 is 54 degrees
Hopes this helps please mark brainliest
In all the cases shown below, the velocity vectors v₁ and v₂ have the same length.
a)
b)
c)
d)
In which case does Δv=v₂-v₁ have the largest absolute value?
A. a
B. b
C. c
D. d
The case of the velocity vectors, v₁ and v₂ that yield the largest absolute value of Δv = v₂ - v₁ is the case of option B. b
What is a velocity vector?A velocity vector provides an indication of s particle's speed and direction of motion.
The vectors in the question can be expressed using vector notation as follows;
a) [tex]\vec{v_1}[/tex] = i + j
[tex]\vec{v_2}[/tex] = i + j
Δv = v₂ - v₁ is therefore;
v₂ - v₁ = i - i + j - j = 0
Δv = 0
b) [tex]\vec{v_1}[/tex] = i + j
[tex]\vec{v_2}[/tex] = -i - j
Δv = v₂ - v₁ is therefore;
v₂ - v₁ = i - (-i) + j - (-j) = 2·i + 2·j
Δv = 2·i + 2·j
c) [tex]\vec{v_1}[/tex] = i + j
[tex]\vec{v_2}[/tex] = i - j
Δv = v₂ - v₁ is therefore;
v₂ - v₁ = i - i + j - (-j) = 2·j
Δv = 2·j
d) [tex]\vec{v_1}[/tex] = i + j
Comparing the vertical and horizontal lengths of the arrows, indicates;
[tex]\vec{v_2}[/tex] ≈ -1.2·i - 0.5·j
Δv = v₂ - v₁ is therefore;
v₂ - v₁ = i - (-1.2·i) + j - (-0.5·j) = 2.2·i + 1.5·j
Δv = 2,2·j + 1,5·j
Option (b) and (d) have the largest values, however, their magnitudes are;
b) |Δv| = √(2² + 2²) = 2·√2 ≈ 2.83
d) |Δv| = √(2.2² + 1.5²) ≈ 2.66
Therefore, option b has the largest absolute value for Δv = v₂ - v₁
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What is the solution to the following inequality?
X/-3≤ 3
O A. x ≤ 1
OB. x ≤-9
OC. x≤-9
D. x ≤ 6
The solution to the x/-3≤ 3 inequality is x ≤ -9.
Define inequality.In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.
Given,
Inequality:
x/-3 ≤ 3
Cross multiplying:
x ≤ 3× -3
x ≤ -9
The solution to the x/-3≤ 3 inequality is x ≤ -9.
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please help asap (math question)
The exponential function for the given graph having points (2, 16) is f(x) = [tex]4^{x}[/tex].
What is an exponential function?The exponential function is a type of mathematical function that can be used to determine whether something is increasing or decreasing exponentially, such as population, money, or price. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base.
Exponents are used in exponential functions, as the name indicates.
The given point on the graph is (2, 16).
The given function is f(x) = [tex]a^{x}[/tex]
From graph, (x, y) = (2, 16)
Put the value of (x, y) = (2, 16) in f(x) = [tex]a^{x}[/tex]
16 = a²
a = √16
a = 4
So, the function is
f(x) = [tex]4^{x}[/tex]
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Between which two benchmark fractions is? How do you know?
I ready classroom mathematics grade 5 volume 1
Answer:
Their Divider
Step-by-step explanation:
1-->1/2+1/2-->1/4+1/4+1/4+1/4-->etc.
The equation of the line that passes through the given points (4,6) and (4.2)
Answer: ___________________________________________________
x = 4
What is the slope of the
function below?
(3, 10)
(0, 1)
Slope = [?]
Simplify your answer.
Answer:
slope is 3
If you need the formula lmk
Answer: 3
Step-by-step explanation:
calculate the slope by subtracting the y coordinates, subtracting the corresponding x coordinates, then dividing y by x.
(10-1)/(3-0)=9/3=3
HELP ME PLS
Kevin needs to read 3 novels each month.
Let N be the number of novels Kevin needs to read in M months.
Write an equation relating N to M . Then use this equation to find the number of novels Kevin needs to read in 19 months.
Kevin needs to read 57 novels in 19 months.
Given,
The number of novels Kevin needs to read in a month = 3
N = Number of novels Kevin needs to read in M months.
Write an equation with M and N.
That is,
Kevin needs to read 3 novels in one month.
So, number of novels, N Kevin reads in M months, 3M = N
The equation is;
3M = N
Now,
The number of months Kevin needs to read the novels = 19
Then,
The number of novels Kevin reads in 19 months;
3M = N
3 × 19 = 57
That is,
Kevin needs to read 57 novels in 19 months.
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y+2=4/5(x+7) in stander form
Answer:
4x - 5y = -18
Step-by-step explanation:
y+2=4/5(x+7)
5(y + 2) = 5 × 4/5(x + 7)
5y + 10 = 4x + 28
5y = 4x + 18
4x - 5y = -18
a company’s stock was selling at 35$ a share a month later it was selling at 14$ a share what is the percent loss
If a company’s stock was selling at 35$ a share a month later it was selling at 14$ a share the percentage loss is 60%
The company's initial share price = $35 per share
The company's new share price = $14 per share
Therefore the share price decreased from $35 to $14, we have to find the percentage loss
The percentage loss = [(The company's initial share price - The company's new share price) / The company's initial share price ] × 100
Substitute the values in the equation
The percentage loss = [(35-14) / 35] × 100
= (21/35)×100
= 0.6 × 100
= 60%
Hence, if a company’s stock was selling at 35$ a share a month later it was selling at 14$ a share the percentage loss is 60%
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A student earns $13 per hour for tutoring and $8 per hour as a teacher's aid. Let x = the number of hours each week spent tutoring and y= the number of hours each week
spent as a teacher's aid.
Complete parts (a) through (e).
a. Write the objective function that describes total weekly earnings.
b. The student is bound by the following
three constraints:
1. To have enough time for studies, the
student can work no more than 23 hours
per week.
2. The tutoring center requires that each
tutor spend at least three hours r week
tutoring.
3. The tutoring center requires that each
tutor spend no more than eight hours per
week tutoring.
Write an inequality for each of
these constraints.
Submit test
...
c. Graph the system of inequalities from part (b). Use only the first quadrant and its boundary, because x and y are nonnegative. Select the correct graph.
OA.
O B.
O C.
O D.
Next
The objective function is z = 13x+8y
From the question, we have
A student earns $13 per hour for tutoring and $8 per hour as a teacher's aid.
x = the number of hours each week spent tutoring and
y= the number of hours each week spent as a teacher's aid.
the objective function is z = 13x+8y
Addition:
Addition is the process of combining two or more things. In mathematics, adding is the process of calculating the sum of two or more numbers. It is a basic mathematical operation that is applied frequently in daily life. We regularly use addition when dealing with money, calculating our food expenses, or calculating the time. However, for larger numbers, we divide the numbers into columns using their respective place values, such as ones, tens, hundreds, thousands, and so on. One-digit numbers can be added simply to solve addition issues.
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Damari needs to paint the circular concrete mural at the
park. The mural has a diameter of 45 feet. A gallon of
paint covers approximately 300 square feet. Each
gallon is $18.99. How much will Damari spend in order
to paint the mural? Use 3.14 to approximate I and
round your answer to two decimal places.
The total spent to paint the mural which is circular with a diameter of 45 feet will be $100.67.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The longest line which can be drawn inside the circle will be the diameter.
The perimeter of the circle = 2πr where r is the radius of the circle.
As per the given,
Diameter = 45 feet so radius 45/2 = 22.5 feet
Area of circle = πr² = π(22.5)² = 1590.43 feet²
Since one gallon covers 300 square feet.
Number of gallons needed to cover the whole area,
1590.43/300 = 5.30
Cost of one gallon = $18.99
Total spend = 5.30 × 18.99 = $100.67
Hence "The total spent to paint the mural which is circular with a diameter of 45 feet will be $100.67".
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Part A
3
A model car is for sale online. Beginning on day one, the owner discounts the price by 5% each day until it sells. On the third day th
If the original price of the model car was $40, how much did the car sell for to the nearest cent?
The car selling price is $34.30
From the question, we have
Selling price = 40* 95/100*95/100*95/100
=$34.30
The car selling price is $34.30
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Express x and y in terms of trigonometric ratios.
In terms of trigonometric ratios, x is 6 sin∅ and y is 6 cos∅.
Define trigonometric ratios.The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others. Circular trigonometric functions are another name for them. The ratios of an angle in a triangle are a straightforward definition of a function. This means that these trig functions provide the relationship between the angles and sides of a triangle.
Given,
Expressing x and y in terms of trigonometric ratios,
Base = 6
x = Opposite
y = Hypotenuse
x = 6 sin∅
y = 6 cos∅
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Which of the j-values satisfy the following nequality?
10 ≥j +5
Choose all answers that apply:
A j = 3
B j=4
C j = 5
Answer:
j=5
10
[tex] 10 \geqslant j + 5[/tex]
10-5=j
j=5
c
If Jeff has 1 Apple and Jessica has 2 apples how many do they have together
answer: 3
simply add 1 apple from Jeff and 2 apples from Jessica
(1+3) = ?
Thus, the answer is 3 apples all together
simplify (8.1)(8.1²)⁴
(8.1)6
(8.1)7
(8.1)8
(8.1)9
The indices (8.1)(8.1²)⁴ simplifies to 8.1⁹
How to simply indices?
Index is the power or exponent which is raised to a number or a variable. For example, in number 3², 2 is the index of 3. The plural form of index is indices
Given: (8.1)(8.1²)⁴
To simplify these indices, we are going to apply one of the indices, which is expressed below: (4³)² = 4³ ˣ ² = 4⁶. We basically multiply the powers
We also need another law which is expressed below:
3⁶ x 3⁴ = 3⁶⁺⁴ = 3¹⁰
If two indices with the same base (in case 3) are being multiplied, you can simplify by taking one of the bases and then add the powers
Thus, to simplify (8.1)(8.1²)⁴:
(8.1)(8.1²)⁴ = (8.1)(8.1)²ˣ⁴
= (8.1)(8.1)⁸
= 8.1¹ × 8.1⁸
= 8.1¹⁺⁸
= 8.1⁹
Therefore, (8.1)(8.1²)⁴ simplifies to 8.1⁹. The 4th option is the answer
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A company that makes hair-care products had 2,000 people try a new shampoo. Of the 2,000 people, 16 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answer:
0.08%
Step-by-step explanation:
A male elephant at the city zoo weighs 8,000 pounds, which is the same as 4 tons. The female elephant weighs 7,000 pounds. How many tons does she weigh?
Answer:
3.5 tons
Step-by-step explanation:
We can use the information we already have to figure out how much 1 ton is. In the equation: 8,000/4 will give us how many pounds per ton. The answer to that is 2,000 pounds per ton. So, if we divide the number of tons the female elephant is by how many pounds a ton is, we use the equation: 7,000/2,000, which equals 3.5 tons.
answer the questions below⬇️⬇️
The perimeter of the given figure is 19 cm and area is 20 cm².
What is perimeter?
A perimeter could be a closed path that encompasses, surrounds, or outlines either a 2 dimensional form or a one-dimensional length. The perimeter of a circle or an oval is termed its circumference.
Main body:
to find the perimeter we need the measurement of each side.
so length of DE side
DE = A F - BC
DE = 6-2
DE = 4 cm
so perimeter = 6+4+2+4+3
= 19 cm
area of figure = area of rectangle ABCG + GDEF
area = 4*3 + 4*2
area of figure = 12+8
Hence area is 20 cm².
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Angela meets with a new couple to determine their needs for a new home and how large a home they can afford. What is Angela’s profession?
A.
financial services sales agent
B.
insurance sales agent
C.
real estate broker
D.
tax accountant
E.
personal finance manager
Angela is a real estate broker option c.
Real Estate Broker;
A real estate broker represents the buyer or seller when looking for the appropriate home. A broker often works for a larger company that helps home sellers and home purchasers select the best and most affordable housing alternative.
A real estate broker is a licenced real estate professional in their own right, as opposed to only being a licenced real estate agent. Like an agent, a real estate broker possesses knowledge that can assist clients with real estate transactions and the sale or acquisition of real estate.
Here,
Angela works as a real estate broker. In order to ascertain the couple's demands for a new home and the size of a property they can afford, Angela meets with them. As a result, choice C is accurate.
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Answer the questions below! Thank you^^
a) The Factor of -4x² + 12x is 4x( -x +3)
b) The multiplication of (4.8x)(4x) is 19.2x²
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
-4x² + 12x
Now, factorizing
4x²= 2 x 2× x × x
12x = 2 ×2× 3 × x
So, the factor can be
-4x² + 12x
= -2 x 2× x × x + 2 ×2× 3 × x
= 4x( -x +3)
and, (4.8x) ×4x
= 4.8 × 4 × x × x
= 19.2x²
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If the required reserve ratio is 10 percent, currency in circulation is $1,200 billion, checkable deposits are $1,600 billion, and excess reserves total $2,500 billion, then the m1 money multiplier is.
If the required reserve ratio is 10 percent, currency in circulation is $1,200 billion, checkable deposits are $1,600 billion, and excess reserves total $2,500 billion
Given that
Reserve ratio is 10 percent
Currency in circulation is $1,200 billion
Checkable deposits are $1,600 billion
Excess reserves total $2,500 billion
Here we are calculating M1 measure of money supply
C: Currency in circulation
D: Checkable Deposits
M1=C+D = 1200+1600= 2800
C: Currency in circulation
D: Checkable Deposits
Currency Deposit Ratio= C/D = 1200/1600 = 0.75
ER: Excess Reserves
CD: Checkable Deposits
Excess Reserve Ratio= ER/CD= 2500/1600 = 1.56
The formula for the M1 money multiplier is:
M1 money multiplier= M1/MB
M1 money multiplier= C+D / R+C
M1 money multiplier= C+D / q∗D+ER+C
M1 money multiplier= (1,200+1,600) / (0.1∗1,600+2,500+1,200)
M1 money multiplier= 0.73
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An airliner passes over an airport at noon traveling 520 mi/hr due east. At 1:00 p.m., another airliner passes over the
same airport at the same elevation traveling due south at 560 mi/hr. Assuming both airliners maintain their (equal)
elevations, how fast is the distance between them changing at 3:00 p.m.?
The distance between the two airlines changing at 3:00 p.m is 374mi/hr
Here, the trajectory of the 2 planes will form a right angle at the airport.
Let 'a' be the distance of the east bound plane travelled past the airport and b be the distance of the south bound plane travelled past the airport and c is the horizontal distance between the two planes
a² + b² = c²
differentiating both sides with respect to time
2a da/dt + 2b db/dt = 2c dc/dt
The speed of both airlines is given,
da/dt = 520mi/hr and db/dt = 560mi/hr
At 12 pm the east bound plane has been flying post airport
at 3 pm, the distance = 3 x da/dt = 2(520) = 1560
At 1 pm the east bound plane has been flying post airport
at 3 pm, the distance = 2 x db/dt = 2(560) = 1120
c = √(a² + b²)
c = √(1560² + 1120²)
c = 1920.41
fast is the distance between them changing dc/dt
dc/dt = (3a da/dt + 2b db/dt)/2c
= (1560 x 520+ 1120x560)/1920
dc/dt = 374
Therefore, the distance between them changing at 3:00 p.m is 374mi/hr
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Write and solve the equation for the following questions:
Leo ordered 4 large popcorn and soda combos. Each combo cost the same amount. With a $5
movie membership fee, the total cost was $68.96. How much did each popcorn and soda combo cost?
Answer:
$15.99
Step-by-step explanation:
Let y = the total cost
Let x = the cost of the combo
4x + 5 = 68.96 Subtract 5 from both sides
4x = 63.96 Divide both sides by 4
x = 15.99
A scientist places 20 mg of bacteria in a culture for an experiment and he finds that the mass of the bacteria triples every day.
a.)Each day that passes, the mass of bacteria in the culture changes by what percent?
Answer: 300%
Step-by-step explanation:
Multiplying something by 3 is the same as 300% of that number
20 x 3 = 60
60 = 300% x 20
Break down 28+5 to make a ten
There is 10.
28+5= 33
10+18+5=33
Subtract the expressions. (9.12n − 4.3) − (8 + 13.6n)
The expression (9.12n 4.3) (8 + 13.6n) are subtracted to yield (12.3 + 4.48n).
What is an algebraic expression?
An algebraic expression is a type of mathematical expression that uses variables and constants.
Algebraic expressions are evaluated by changing the variables to numbers or values.
What in mathematics is a polynomial?
Sums of terms of the form k⋅xⁿ, when k is any variable and n is a positive number, compensate polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video.
Detailed explanation:
We begin by solving the equation = 9.12n - 4.3 - 8 - 13.6n. Next, we remove the comparable terms using the formula = - 12.3 - 4.48n.
Therefore, the simple answer to the formula is -(12.3 + 4.48n).
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Classify the polynomial by its name: 3
A) monomial
B) binomial
C) trinomial
D) other polynomial
