The polynomial f(x) of degree 5 that has the following zeros is
f(x) = (x+2) (x-3) (x-7)(x-0) (x-4).
What is meant by polynomial?Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents. In many branches of mathematics and science, polynomials are used. For instance, they are used to define polynomial functions, which show up in settings ranging from basic chemistry and physics to economics and social science. They are also used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to form these functions.
The function's zeros are expressed as follows:
f(x) = (x-a)(x-b)..... where the a, b are the zeros
f(x) = (x-(-2)) (x-3) (x -7)(x-0) ( x-4)
f(x) = (x+2) (x-3) (x-7)(x-0) (x-4)
Therefore, the polynomial f(x) of degree 5 that has the following zeros is
f(x) = (x+2) (x-3) (x-7)(x-0) (x-4)
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There is a store that is having a 25% sale off of everything.Lin is buying a jacket that costs $40. What is the cost of the jacket after the discount?
Answer:
30
Step-by-step explanation:
what multiples to 48 and adds to -12
Effectively what you're asking is to solve this equation
x^2 - 12x + 48 = 0
Compare that to this form
ax^2 + bx + c = 0
to find that
a = 1b = -12c = 48Let's compute the discriminant (aka the stuff under the square root in the quadratic formula).
d = b^2 - 4ac
d = (-12)^2 - 4(1)(48)
d = 144 - 192
d = -48
The discriminant is negative, which tells us that there aren't any real numbered solutions to x^2 - 12x + 48 = 0
Therefore, we have no way to factor x^2 - 12x + 48 over the real numbers. Going back at the problem at hand: there aren't any real numbers that (a) multiply to 48 and (b) add to -12.
The two mystery numbers would be complex numbers in the form a+bi, where i = sqrt(-1). If your teacher hasn't covered these types of numbers yet, then you simply would say "no solution".
Solve the equation cos 2 θ = -5 cos θ - 3 on the interval 0 ≤ θ < 2π
Answers must be exact.
Answer:
[tex]\theta =\dfrac{2}{3} \pi ,\;\; \theta =\dfrac{4}{3} \pi[/tex]
Step-by-step explanation:
Given:
[tex]\cos 2\theta=-5 \cos \theta-3, \quad \quad 0 \leq \theta < 2 \pi[/tex]
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Cos Double Angle Identity}\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\\end{minipage}}[/tex]
Use the cos double angle identity to create a quadratic:
[tex]\begin{aligned}\cos 2\theta &=-5 \cos \theta-3\\\cos^2\theta - \sin^2 \theta &=-5 \cos \theta-3\\\cos^2\theta - (1-\cos^2 \theta) &=-5 \cos \theta-3\\2\cos^2\theta - 1 &=-5 \cos \theta-3\\2\cos^2\theta+5 \cos \theta +2 &=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}2\cos^2\theta+5 \cos \theta +2 &=0\\2\cos^2\theta+4 \cos \theta +\cos \theta +2 &=0\\2\cos \theta(\cos \theta +2)+1(\cos \theta +2) &=0\\(2\cos \theta+1)(\cos \theta +2)&=0\end{aligned}[/tex]
Apply the zero-product property:
[tex]2 \cos \theta + 1 = 0 \implies \cos \theta =-\dfrac{1}{2}[/tex]
[tex]\cos \theta + 2= 0 \implies \cos \theta =-2[/tex]
As -1 ≤ cos θ ≤ 1, cos θ = -2 is undefined.
Therefore, the only valid solution is cos θ = -¹/₂
Therefore:
[tex]\implies \cos \theta =-\dfrac{1}{2}[/tex]
[tex]\implies \theta =\cos^{-1}\left(-\dfrac{1}{2}\right)[/tex]
[tex]\implies \theta =\dfrac{2}{3} \pi +2\pi n,\;\; \dfrac{4}{3} \pi+2\pi n[/tex]
Solutions in the given interval 0 ≤ θ < 2π :
[tex]\theta =\dfrac{2}{3} \pi ,\;\; \theta =\dfrac{4}{3} \pi[/tex]
Which inequality is represented by the number line?
A.
|2x + 1| ≥ 7
B.
2|x + 1| ≤ 8
C.
|2x − 1| ≥ 9
D.
2|x − 1| ≤ 10
The inequality represented by the graph is |2x − 1| ≥ 9
How to determine the inequality represented by the graph?The number line represents the given parameter
On the number line, we have the following endpoints
x = -4 and x = 5
So, we test the above solutions in the list of options (representing them as an equation)
So, we have
|2x + 1| = 7
When x = -4
|2(-4) + 1| = 7 ⇒ 7 = 7 --- true
When x = 5
|2(5) + 1| = 7 ⇒ 11 = 7 --- false
2|x + 1| ≤ 8
When x = -4
2|(-4) + 1| = 8 ⇒ 6 = 8 --- false
|2x − 1| ≥ 9
When x = -4
|2(-4) - 1| = 9 ⇒ 9 = 9 --- true
When x = 5
|2(5) - 1| = 9 ⇒ 9 = 9 --- true
Hence, the inequality is (c) |2x − 1| ≥ 9
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My brain has gone blank and I forgot how to do these
Answer:
Step-by-step explanation:
x= 80 degrees
I think that's the answer
113-33= 80
Answer:
133+33+x=180
X=180-133-33
X=14
Use the distributive property to simplify: 5(4x - 7)
Group of answer choices
20x-35
5x-5
35-20x
4x-35
Answer:
the answer is 20x -35
Step-by-step explanation:
5 x 4x = 20x
5 x -7 = -35
The answer options for exercise 5(4x-7) are:
A) 20x-35
B) 5x-5
C) 35-20x
D) 4x-35
To solve this exercise 5(4x-7), we organize the expression with the distributive law.
The distributive law is: a(b+c)=ab+ac.
5(4x - 7) = 5 × 4x - 5 × 720x - 35Therefore, the correct option is alternative "A".
The following are prices for various cars: $22,000, $28,000, $90,000, 22,000, $26,000. What is the median price?
The required median of the prices of the various cars is $26,000.
What is the median?When a dataset is ordered, the median is the value that is exactly in the middle. It is a measure of central tendency that distinguishes between the lowest and top half of data.
here,
Arrange the data set in order,
$22,000, $22,000, $26,000, $28,000, $90,000,
Total number = 5 [ odd numbers ]
Median is given as = n + 1 / 2 th term
= 5 + 1 / 2 th term
= 3 rd term
Thus, as of the given condition, the median of the prices is $26,000.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee
Answer:
51.85g
Step-by-step explanation:
At t = 25 years,
A(t) = 200e^-0.054t
A(25) = 200(e^-0.054(25))
= 200(e^-1.35)
= 200(0.2592)
= 51.85
NO LINKS!! Please help me with this problem.
Answers:
Min cost = $464.76
Dimensions = 11.619 feet by 5.164 feet
Each value mentioned above is approximate.
========================================================
Explanation:
x = horizontal dimension
y = vertical dimension
xy = 60
y = 60/x
The amount of outer fencing needed is 2x+2y feet, aka the perimeter of the largest rectangle.
There are 5 vertical inner fences, so we need 5y feet of inner fencing.
Let's set up the cost function.
Cost = 10*(amount of outer fencing) + 5*(amount of inner fencing)
C = 10*(2x+2y) + 5*(5y)
C = 20x+20y+25y
C = 20x+45y
Plug y = 60/x into the cost function.
C = 20x+45y
C = 20x+45(60/x)
C = 20x + (2700/x)
Then use either calculus or a graphing calculator to find the lowest point on the cost curve is roughly located at (11.619, 464.758)
Use the x value x = 11.619 to find its paired y value
y = 60/x
y = 60/11.619
y = 5.16395558998192
y = 5.164
The entire enclosure should be roughly 11.619 feet by 5.164 feet
The total cost is minimized at approximately $464.76
Answer:
11.619 by 5.164 feet$464.76 minimum costStep-by-step explanation:
You want the dimensions and cost of a rectangular enclosure with an area of 60 square feet and 5 internal partitions. The cost of outside fence is $10 per foot, and the cost of partition fence is $5 per foot.
SetupLet x represent the length of the enclosure, and y the width (and the partition length). Then we have ...
xy = 60
10(2x) = cost fencing for length
10(2y) +5(5y) = cost of fencing for width
We know the cost will be minimized when the cost of fence for the length is equal to the cost of fence for the width.
20x = 45(60/x)
Solutionx² = 135 . . . . . . . . . . . multiply by x/20
x = 3√15 ≈ 11.619 . . . .square root
y = 60/(3√15) = (4/3)√15 ≈ 5.164 . . . . . find y
Then the cost is ...
2(10(2x)) = 120√15 ≈ 464.76 . . . . minimum cost
The enclosure is 11.619 by 5.164 feet, for a cost of $464.76.
Select the locations on the number line to plot the points -7/3, 14/3
Answer:
-7/13 is equivalent to -2 1/3, so plot it 1/3 of a unit to the left of -2.
14/3 is equivalent to 4 2/3, so plot it 2/3 of a unit to the right of 4.
The function g is defined by g(x) = 5+2x/2+x
Find g (4x)
[tex]g(x)=\frac{5+2x}{2+x} \\ \\ \implies g(4x)=\frac{5+2(4x)}{2+4x}=\boxed{\frac{5+8x}{2+4x}}[/tex]
Since 2009 the number of smartphones shipped from manufacturers to stores around the world has increased exponentially. The growth from 2009 through 2015 can be modeled using the function G (t) = 174 . 1.67^t where t is the number of years singe 2009 and G (t) is measured in millions of smartphones.
Use this information and your knowledge of exponential and logistic growth to explore the mathematical concepts in the questions below.
The y-intercept indicates that 174 million smartphones were shipped to stores in 2009. This implies that after two years, in 2011, smartphone manufacturers shipped 500 million smartphones to stores worldwide.
Since 2009 the number of smartphones shipped from manufacturers to stores around the world has increased exponentially.
What is the exponential function?
The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
The growth from 2009 through 2015 can be modeled using the function G(t) = 174 * 1.67^t where t is the number of years since 2009 and G(t) is measured in millions of smartphones.
The required graph of the exponential function G(t) has been attached below
Now, finding the y-intercept
G(t) = 174· 1.67^t...(i)
Substitute the value of t = 0 in the above function,
G(t) = 174* 1.67⁰
G(t) = 174(1)
G(t) = 174
The meaning of the y-intercept is that 174 million smartphones are being shipped to stores in years 2009.
Substitute the value of G(t) =500 in the exponential function(i),
500 = 174 * 1.67^t
500/174 = 1.67^t
2.8735 = 1.67^t
In(2.8735 ) = t In (1.67)
t = In (2.8735 ) / In (1.67
t = 2.05827 ≈ 2
Hence, This means after 2 years i.e. in 2011, smartphone manufacturers were shipping 500 million smartphones to stores around the world.
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What 3 parts are needed to show a number in scientific notation?
1. A whole number and a decimal, a multiplication symbol, a power of 10
2. An exponent to the 2nd power, a multiplication symbol, a whole number from 1 to 10
3. A decimal or whole number, a multiplication symbol, a power of 10
4. A decimal between 1 and 10, a multiplication symbol, a power of 10
Hugo is a veterinarian. he knows the following information about his 41 patrons:
• 20 patrons in total do not have a dog.
• 17 patrons in total have a cat.
• 7 patrons have neither a dog nor a cat
The number of persons who own a dog but no cat is 24 - 7 = 17, while the total number of people who own a dog is 17 + 4 = 21.
What exactly does "patron" mean?formal a customer of a specific eatery, lodging facility, or other establishment. Only customers may use this parking lot. synonyms and words that are similar. a hotel or guest house stay.
Since there are a total of 41 customers, the number of those without cats is calculated as follows: 41 – 17 = 24.
13 people(20 - 7) do not own dogs but do own cats.
There are 4 persons who own both a dog and a cat (17 - 13).
The people who have a dog, and do not have a cat is 24 - 7 = 17, and the total of the people who have a dog is 17+4 = 21.
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23a = 391 A. a = 16 B. a = 17 C. a = 8,939 D. a = 8,993
Answer:
Step-by-step explanation:
it is 17 i did the quiz hope it helps
A clothing store buys a sweater for $15 before marking it up by 1/5 before selling it for a profit. What is the markup on the sweater?
The markup amount on the sweater of cost price $15 is $3.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, A clothing store buys a sweater for $15 before marking it up by 1/5.
So, the markup amount can be obtained if we multiply the cost price by the fraction of mark up which is,
= 15×(1/5).
= 3.
The markup price is $3.
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6. A chemist needs to create 100mL of 38% acid solution. On hand she has a 20% acid solution and
a 50% acid solution. How many mL of each solution should she use?
Solution: 20% acid =
50% acid =
Answer:
40 cc of A and 60 cc of B
Step-by-step explanation:
A+B = 100
0.5A + 0.8B = 100 * 0.68 = 68
0.5A + 0.8 ( 100 - A) = 68
0.5A + 80 - 0.8A = 68
-0.3A = -12
3A = 120
A=40
40 cc of A and 60 cc of B
120 students are signing up for classes. 80 of them are signing up for a Math class (M) and 50 of them are signing up for a Biology
class (B). If 35 of them are signing up for both Math and Biology, how many are signing up for neither Math nor Biology. Hint:
It may help to draw the Venn diagram.
The number of students signing up for neither Math nor Biology is 25.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Given, 120 students are signing up for classes. 80 of them are signing up for a Math class (M) and 50 of them are signing up for a Biology.
We know N(A∪B) = N(A) + N(B) - N(A∩B).
∴ N(M∪B) = 80 + 50 - 35.
N(M∪B) = 95.
So, the number of students signing up for neither Math nor Biology are
(120 - 95) = 25
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Kylie makes $8.50 an hour at a local restaurant. Her paycheck shows she worked 20.88 hours last week. how much money did Kylie make?
If Kylie's hourly wage at a nearby restaurant is $8.50. She worked 20.88 hours last week, according to her paycheck. Kylie's salary is $177.48.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Kylie makes $8.50 an hour at a local restaurant. Her paycheck shows she worked 20.88 hours last week.
We have to find the money did Kylie make,
We can utilize multiplication for a number of common tasks, such as figuring out how much it will cost to buy several identical things, calculating sales tax, and figuring out area and other geometric measurements.
Suppose the money did Kylie make is x,
x = 8.50 × 20.88
x=$ 177.48
Thus, if Kylie's hourly wage at a nearby restaurant is $8.50. She worked 20.88 hours last week, according to her paycheck. Kylie's salary is $177.48.
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Carla's uncle owns a pizzeria. Her uncle has 4 pounds of mozzarella cheese. He uses pound of the mozzarella to make a large pizza.
How many large pizzas could Carla's uncle make before running out of mozzarella cheese?
O 3 pizzas
4 pizzas
O 5 pizzas
O 6 pizzas
Maddy is making banana bread. She has 11 bananas. If she uses 3 bananas for each loaf of bread, how many loaves of banana bread can she make?
Answer: She can make 3 full loaves
Step-by-step explanation: 3 x 3 = 9 3 x 4 = 12 you dont have 12 you only have 11
technically you can make 3 [tex]\frac{1}{3}[/tex] loaves but if you are looking for full loaves you can only make 3
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Kiran invested $1,500 in an account paying an interest rate of 81% compounded
continuously. Isaac invested $1,500 in an account paying an interest rate of 7%
compounded daily. After 6 years, how much more money would Kiran have in his
account than Isaac, to the nearest dollar?
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
Kiran has $191254 more amount than Isaac.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
Kiran:
P = $1500
r = 81%
n = continuously
t = 6 years
A = P [tex]e^{rt}[/tex]
[ e = 2.71828 }
A = 1,500.00 x [tex]2.71828^{0.81\times6}[/tex]
A = $193,536.30
Isaac:
P = $1,500
r = 7%
n = 360
t = 6 years
A = 1500 [tex](1 + 0.07/360)^{360\times6}[/tex]
A = $2,282.85
Now,
The difference between Kiran's and Isaac's amount.
= $193,536.30 - $2,282.85
= $191253.45
= $191254
Thus,
Kiran has $191254 more amount than Isaac.
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Please answer for brainly and 5 star thanks
Using the graph given, the rate of change from hour 4 to hour 7 is: -20.
How to Find the Rate of Change of a Graph?The rate of change of a relationship that is represented on a graph is determined using the formula below:
Rate of change = f(b) - f(a) / b - a.
Given the graph above, we are asked to find the rate of change between the interval x = 4 to x = 7:
a = 4
f(a) = f(4) = 120
b = 7
f(b) = f(7) = 60
Plug in the values:
Rate of change = f(b) - f(a) / b - a = (60 - 120) / (7 - 4)
= -60/3
Rate of change = -20.
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Christopher has $780 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $446.45.
He buys 2 bicycle reflectors for $16.82 each and a pair of bike gloves for $24.60.
He plans to spend some or all of the money he has left to buy new biking outfits for $43.70 each.
Write and solve an inequality which can be used to determine oo, the number of outfits Christopher can purchase while staying within his budget.
The required inequality for number of outfit is n ≤ 6.3 and Christopher can purchase 6 biking outfits.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
Given that,
Maximum amount that Christopher can spend = $780.
The price of new bicycle = $446.45.
Also, Christopher buys 2 bicycle reflectors for $16.82 each.
And a pair of bike gloves for $24.60.
Let Christopher buys n outfits.
The price of 1 outfit is $43.70.
The price of n outfits = $43.70n
Since, Price of 1 bicycle reflectors = $16.82
Price of 2 reflectors = $16.82 x 2 = $33.64
The inequality to determine the number of outfits can be written as,
43.70n + 446.45 + 24.60 + 33.64 ≤ 780.
43.70n + 504.69 ≤ 780.
43.70n ≤ 780 - 504.69
43.70n ≤ 275.31
n ≤ 6.3
The maximum number of outfit Christopher can purchase is 6.
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HELPPPPP!!!!!!!! 30 POINTSSSS!!!!!
What is the correlation of the data shown?
A. -1
B. -0.5
C. 1
D. 0
The correlation of the data shown on the graph is 1
How to determine the correlation?In this question, the graph represents the given parameter
From the graph, we have the following observations
The x values is on the horizontal axisThe y values is on the vertical axisAs the x values increase, the y values increase (approximately)When the change (increase) in the x values causes a change (increment) in the y values, then the correlation is positive
From the list of options, we have
-1, -0.5 and 0 are not positive values
This means that the correlation is (c) 1
Hence, the correlation of the data is 1
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3. Find the x-intercept of y = 3.
(3,0)
(0,3)
(3,3)
O no x-intercept
Answer:
3
Step-by-step explanation:
x-y =3
To find the x intercept, set y=0
x-0 =3
x=3
Step-by-step explanation:
Answer:
x=(3,0)
Step-by-step explanation:
hope this helps
Suppose that x and y vary inversely, and x = 30 when y = 2. Find y when x=5.
Answer:
Step-by-step explanation:
1. x is inversely proportional to y
x=k/y
k is the constant of proportionality
x =60/y
2. x=60/y
x=60/12
x=5
Solve the application using polynomials
find the paramater 1/2x-7 x
Answer:
-13/2x
Step-by-step explanation:
1/2x +(−7x)
Combine Like Terms:
12x +(−7x)
(1/2x +−7x)
−13/2x
Consider a function f(x) = x^ 2.
A second function h(x) is the result of reflecting f(x) across the x-axis and translating it 3 units in the positive y-direction (upward). Write the equation of h(x).
Please Help will mark brainliest :)
Answer:
h(x) = - x² + 3
Step-by-step explanation:
Given f(x) reflected in the x- axis , then
h(x) = - x²
Given h(x) then h(x) + c is a vertical translation
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here h(x) is shifted 3 units up , then
h(x) = - x² + 3
i gotchu