Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]
What is an leading coefficient?
The numbers placed in front of the variable with the biggest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like conventional coefficients.
According to fundamental theorem of algebra , if a + bi be a zero of a polynomial with real coefficients then a-bi is also a zero
Now given that f(x) be a polynomial with degree 5 and with zeros -7,-i,-3+i
and f(x) be a polynomial with real coefficients.
therefore by fundamental theorem of algebra
+i and -3-i are also zeros of f(x)
so zeros of f(x) are 7, -i, -3 + i, i, -3 -i
Degree is 5, so there is at most 5 zeros therefore the required polynomial will be
f(x) = a(x + 7)(x + i )(x - i)(x +3- i)(x +3 +i)
= a[(x +7)(x² + 1)(x² +6x + 10)]
[tex]= a\left[x^5+ 13x^4 + 53x^3 +83x^2 + 52x + 70]\right[/tex]
[tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]
Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]
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HELP PLEASE!! Dominique is selling merchandise for a school fundraiser. She is selling calendars for $8 each and coffee mugs for $12 each. She must sell at least $800 of merchandise, including at least 60 calendars, to meet her goals.
If x represents the number of calendars and y represents the number of mugs, which system of inequalities represents this scenario?
8x + 12y ≥ 800 and x ≥ 60
8x + 12y ≥ 800 and y ≥ 60
8x + 12y > 800 and y > 60
8x + 12y > 800 and x > 60
The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.
Given,
The cost for one calendar = $8
The cost for one coffee mug = $12
Dominique must sell at least $800 of merchandise and it should include at least 60 coffee mugs.
Here,
x be the number of calendars and y be the number of coffee mugs;
We have to find an inequality which represents the given situation;
So,
The inequality be;
8x + 12y ≥ 800 and x ≥ 60
That is,
The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.
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Simplify completely. 3x+18 divided 18
solution
3x+18/18
ans4
Solve the equation for all values of x.
2x(x + 7)(x²+49) = 0
Answer:
Step-by-step explanation:
2x(x + 7)(x²+49) = 0
(apply the zero product)
x=0 or x+7 =0 or x² + 49 = 0
x+7 =0
x=-7
x² + 49 = 0
no real solution for this i think
Answer = x=0 or x=-7
3x ≥5 or -3/5x-3>7 solve the compound inequality
By using the concept of linear inequation, the required solution is
[tex]x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
Here the given linear inequation is
[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7[/tex]
Now
[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5} x > 7 + 3\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5}x > 10\\\\x > \frac{5}{3} \ or \ x < \frac{10 \times 5}{-3}\\\\x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]
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helpppp!!
A certain number of quarters, five times as many pennies as quarters and 12 more
dimes than quarters are worth $8.00. How many of each coin are there?
Answer:
Step-by-step explanation:
i think the answer is 10 or 5
Find the measure of the exterior angle. (hint: find x first, then plug it in to the exterior angle)
Answer:
[tex]3x - 10 = 25 + x + 15[/tex]
according to theorem
[tex]3x - x = 40 + 10 \\ 2x = 50 \\ x = 25[/tex]
Hopefully this will help u
help fast plsss bout to turn it in
Answer:
Box A: -2x
Box B: 2/9
Step-by-step explanation:
Multiply 1/3 by each of the expressions above the rectangle.
Box A: 1/3 × (-6x) = -2x
Box B: 1/3 × 2/3 = 2/9
Paula stands on the side of a river and sights the opposite bank at an angle of depression of 7 degrees. if Paula is 5.5 feet tall, approximately how wide is the river, to the nearest foot?
The width of the river to the nearest foot will be 45 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Paula remains on a waterway and sights the contrary bank at a point of the wretchedness of 7 degrees.
If Paula is 5.5 feet tall.
Let 'w' be the width of the river. Then the width of the river will be given as,
tan 7° = 5.5 / w
0.12278 = 5.5 / w
w = 44.79
w ≈ 45 feet
The width of the river to the nearest foot will be 45 feet.
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The operation * is defined as a*b=a+b-2ab
Evaluate 2* (3*5)
(2*3)*5
The value of 2*(3*5) = 68.
The value of (2*3)*5 = 68.
What is multiplication?
A mathematical formula that specifies the objects to be multiplied, known as a factor, produces a product. For instance, the product of 6 and 5 is 30.
Given: The operation * is defined as,
a*b = a + b - 2ab
We have to find the value of 2*(3*5) and (2*3)*5
First to find the value of 2*(3*5).
2*(3*5) = 2*(3 + 5 - 30) = 2*(-22) = 2 + (-22) - 2(-22)(2) = 68.
Now to find the value of (2*3)*5.
(2*3)*5 = (2 + 3 - 12)*5 = -7*5 = (-7) + 5 - 2(-7)(5) = -2 + 70 = 68.
Therefore, 2* (3*5) = 68 and (2*3)*5 = 68.
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Evaluate if xy + 2x if x = 7 and y = 5
Answer:
49
Step-by-step explanation:
35+14=49
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1. Solve the equation (9-6p) =
-11 for p.
Answer:
p=p=10/3
Explanation:
9-6p =-11=p=10/3
The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft. What is the mean height of the low tides? (I need to show work.)
The mean height of the low tides is 1.21 ft
The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft
The mean of a sample is given by the formula =
summation of all observation / number of observation
mean = (x₁ + x₂ + x₃ + x₄)/ 4
mean = -0.22 + 2.64 - 0.22 + 2.64 / 4
mean = 4.48 / 4 = 1.21
Therefore, the mean height of the low tides is 1.21 ft
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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C: Determine the average rate of change between day 2 and day 4. Show your work. (4 points)
A) The data modelling is an exponential function.
B) The explicit funciton that will be used to represent the data is;
f(n) = 2(2)^(n - 1)
C) The average rate of change here is; 7
How to model a function?A) We are given the coordinates as;
(1, 2), (2, 4), (3, 8), (4, 16)
From the given coordinates, we can observe a pattern which is that when x increases by 1, then y is multiplied by 2.
Thus, we can see that as the quotient between consecutive terms is the same, the data is a geometric sequence which is an exponential function.
B) The explicit formula that will be used for a geometric sequence with common ratio r and first term a is given by:
f(n) = ar^(n - 1)
Since first term ; a = 2
and common ratio r = 2, then we can say that;
f(n) = 2(2)^(n - 1)
C) The formula for average rate of change here is;
dy/dx = (y₂ - y₁)/(x₂ - x₁)
The coordinates of the 2nd and 4th day are;
(2, 4) and (4, 16)
Thus;
dy/dx = (16 - 4)/(4 - 2)
dy/dx = 14/2 = 7
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1. Assuming the cost of mortgage is $720,000, and the owner of the house makes a down payment of $60,000, with 7.5% interest rate and 25 years repayment plan. a. Calculate the total amount of loan, monthly rate, number of payment periods, monthly payment, total interest paid, and amount borrowed. b. With the aid of what PMT function in a one variable condition, calculate monthly payment, total amount payable, total interest payable for: 11 yrs, 14 yrs, 18 yrs ,20 yrs, 28 yrs, 31 yrs mortgage.
The total amount he will pay after 25 years is $18,97,500.
His monthly payment will be $6,325.
Given, the cost of mortgage is $720,000, and the owner of the house makes a down payment of $60,000, with 7.5% interest rate and 25 years repayment plan.
Now, the total amount of the loan be,
720000 - 60000 = 660,000
monthly rate = 7.5/12 = 0.625%
Number of payment periods = 25
Total amount he has to pay after 25 years,
660000 + (660000×7.5×25)/100
= $18,97,500
His monthly payment will be
1897500/25×12
= $6,325
Hence, the total amount he will pay after 25 years is $18,97,500
also, his monthly payment will be $6,325.
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Write one quadratic equation that forms a graph through the points (−4,2) and (1,2) and has a
minimum value at the vertex.
Explain it in detail please
Quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.
Graph is attached.
As given in the question,
Quadratic equation passes through the points (-4,2) and (1,2)
(x₁, y₁) =(-4,2)
(x₂ ,y₂) = (1,2)
(y-y₁)/ (x-x₁) = (y₂ -y₁)/(x₂ -x₁)
⇒(y-2)/(x +4) =(2-2)/)1+4)
⇒ (y-2)/(x+4) =0
⇒y -2 =0
⇒y =2
Quadratic equation formed from the given points (-4,2) and (1,2) is y =2.
which represents the horizontal line and does not have any vertex.
Graph of the quadratic equation y =2 is attached.
Therefore, quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.
Graph is attached.
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The graph of a linear function passes through the points ; negative one; negative 1 over 4. and ; one, negative 3 over 4.. Y; X. Which equation represents the function? A Y equals negative one over 2 X. minus one over four. B Y equals 1 over 2 X. plus 1 over 4. C Y equals negative 1 over 4 X. minus 1 over 2. D Y equals 1 over 4 X. plus 1 over 2.
The linear equation that passes through the two given points is:
y = (-1/4)*x - 2/4
Which is the equation of the line?A general linear equation is written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:
m = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (-1, -1/4) and (1, -3/4)
Then the slope is:
m = (-3/4 + 1/4)/(1 + 1)
m = (-2/4)/2 = -2/8 = -1/4
the line is:
y = (-1/4)*x + b
To find the value of v we can replace the point (1, -3/4) so we get:
-3/4 = (-1/4)*1 + b
-3/4 + 1/4 = b
-2/4 = b
The linear equation is:
y = (-1/4)*x - 2/4
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Lacey inherited some money from her grandfather and put it in a bank account that earns 4%
interest compounded monthly. After 2 years, Lacey had $700.00 in the bank account. How
much interest did she earn?
Round your answer to the nearest cent.
The interest eared from the given amount, rate of interest and time period is $426.883.
Given that, amount = $700, rate of interest = 4% and time period = 2 years.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest is [tex]Amount=Principal(1+\frac{r}{100})^{nt}[/tex]
Let the money deposited be x.
So, [tex]700=x(1+\frac{4}{100} )^{2\times12}[/tex]
⇒ [tex]700=x(1+0.04)^{24}[/tex]
⇒ [tex]700=x(1.04)^{24}[/tex]
⇒ 700 = 2.563x
⇒ x=700/2.563
⇒ x=$273.117
So, interest = 700-273.117
= $426.883
Therefore, the interest eared from the given amount, rate of interest and time period is $426.883.
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4. Which expression represents 7 more than the quotient of 12 and 4?
A. (12+4) + 7
B.7 x (12+4)
C.7+(12-4)
D. (7+12) + 4
Answer:
C
Step-by-step explanation:
Even though quotient means divide I instead used the minus symbol since they both mean something negative or taking away. Then, the 7 goes before everything adding onto what was left from the second part.
Salina and Nessa combined like terms using the same expression. Salina’s answer differs from Nessa’s. The table shows both of their solutions.
Salina
Nessa
6 x squared y minus 3 + x squared y + 2 x y squared + 2 x y minus 6 = 7 x squared y minus 9 + x squared y + 2 x y squared + 2 x y
6 x squared y minus 3 + x squared y + 2 x y squared + 2 x y minus 6 = 7 x squared y minus 9 + 2 x y squared + 2 x y
Which statement is correct regarding their solutions?
Salina combined the x squared y terms correctly but then left the Plus x squared y term in her answer.
Salina did not add the constant terms correctly.
Nessa combined the constants correctly but then left the Plus 2 x y squared term in her answer
Nessa did not combine the x squared y terms correctly.
The statement that is correct regarding their solutions is A. Salina combined the x squared y terms correctly but then left the Plus x squared y term in her answer.
How to illustrate the expression?From the information, Salina and Nessa combined like terms using the same expression.
The expression given is illustrated as.
6x²y - 3 + x²y + 2xy² + 2xy - 6
It should be noted that the like terms are:
6x²y and x²y as well as -3 and -6.
Combine the like terms
6x²y + x²y = 7x²y
Also, -3 + (-6) = -9
Therefore, the value will be 7x²y + 2xy² + 2xy - 9
The correct option is A as it illustrated the mistake Salina made.
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Answer:
A is the answer
Step-by-step explanation:
There are 8 kites in the sky, and 5 of those kites are striped. What fraction of
the kites are striped?
A. 6/8
B.5/8
C.5/13
D.4/8
Work out the perimeter of this quarter circle.
Take to be 3.142 and write down all the digits given by your calculator.
4 cm
Step-by-step explanation:
Where's the calculator
This season, the probability that the Yankees will win a game is 0.45 and the probability that the Yankees will score 5 or more runs in a game is 0.6. The probability that the Yankees win and score 5 or more runs is 0.34. What is the probability that the Yankees will win when they score fewer than 5 runs? Round your answer to the nearest thousandth.
The probability that the Yankees will win when they score fewer than 5 runs is; 0.567
How to solve conditional probability?We are given;
Event A which is when Yankees win has a probability of; P(A) = -.45
Thus, Event that the Yankees don't win which is when they lose is;
P(A') = 1 - 0.45 = 0.55
Event B which is the event that the Yankees score 5 or more runs has a probability of; P(B) = 0.6
Event that the Yankees score 4 or less run is given by the probability;
P(B') = 1 - 0.6 = 0.4
The probability that the Yankees win and score 5 or more runs is;
P(A' ∩ B') = 0.34
Thus, the probability that the Yankees will win when they score fewer than 5 runs wanted is given by the chain rule in conditional probability of the formula;
P(A' | B') = P(A' ∩ B')/P(B') = 0.34/0.6
P(A' | B') = 0.567
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The slide at the playground has a height of 9 feet. The base of the slide measured onthe ground is 12 feet. What is the length of the slide?
O 15 feet
O 45 feet
21 feet
36 feet
Step-by-step explanation:
this creates a right-angled triangle, with the length of the slide being the Hypotenuse (the side opposite of the 90° angle), and height and base are the legs.
so, we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse, a and b being the legs.
length² = 9² + 12² = 81 + 144 = 225
length = sqrt(225) = 15 ft
What is the value of x?
Answer:
x = 62
Step-by-step explanation:
40 + (x + 16) + x = 180 (sum of angles in a triangle=180)
2x + 56 = 180
2x = 124
x = 62
Critical thinking questions:
Write a system of equations with the solution (4, -3).
Answer: (4,-3)
Step-by-step explanation:
4x+5y=1 (1)
3x-2y=18 (2)
Multiply both parts of equation (1) by 2 and both parts of equation (2) by 5:
8x+10y=2
15x-10y=90
Sum these equations:
23x=92
Divide both parts of the equation by 23:
x=4
Substitute the value of x=4 into equation (1):
4(4)+5y=1
16+5y=1
16+5y-16=1-16
5y=-15
Divide both parts of the equation by 5:
y=-3
Thus, (4,-3)
Use your calculator to find the angle, to the nearest hundredth of a degree, whose tangent value is
O 0.35
O 18.43
O 0.32
O 71.57
Answer:18.43
Step-by-step explanation:
Differentiate the function with respect to x.
On differentiating the given function with respect to x , we get f'(x) = 10x⁴ - 8x⁻⁵ .
In the question ,
it is given that
the function is f(x) = 2x⁵ + 3 + 2x⁻⁴
the derivative of x⁵ is [tex]=[/tex] 5x⁴ ,
the derivative of 3 is = 0
the derivative of x⁻⁴ = -4x⁻⁵ .
on differentiating the function f(x) = 2x⁵ + 3 + 2x⁻⁴ with respect to x is
f'(x) = 2*d/dx(x⁵) + d/dx(3) + d/dx(x⁻⁴)
Substituting the values of derivative ,
we get
f'(x) = 2*(5x⁴) + 0 + 2(-4x⁻⁵)
f'(x) = 10x⁴ - 8x⁻⁵
Therefore , On differentiating the given function with respect to x , we get f'(x) = 10x⁴ - 8x⁻⁵ .
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Alan has 229 songs on a playlist. He's categorized them in the following manner: 11 rock, 21 Latin American, 46 gospel, 30 country, 39 rap, 25 classical, and 57 pop. If Alan begins listening to his playlist on shuffle, what is the probability that the first song played is a rock song?
=================================================
Work Shown:
11 rock songs
229 total
11/229 is the probability of randomly selecting a rock song. The fraction doesn't reduce since 11 and 229 have no factors in common (other than 1).
If you wanted to convert to decimal form, then 11/229 = 0.04803 approximately. This converts to about 4.803%
Evaluate 4x ÷ y if y = 2 and x = 4
Answer:
18
Step-by-step explanation:
x = 4
4x
= 4 * 4
= 16
y = 2
4x + y
= 16 + 2
= 18
QUEST
Find the median of the numbers in the following list.
Select the correct answer below:
O22
O 21
26
O24
O 14
26, 13, 39, 22, 42, 39, 18, 21, 32, 14
Step-by-step explanation:
first order them from least to greatest
13,14,18,21,22,26,32,39,39,42
then just look for the term in the middle
sunset there are 2 numbers in the middle you will add them both and subtract them by 2
42+39 then / 2 =40.5