The polynomial function which has a leading coefficient 1 is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))
Given that a polynomial function has leading coefficient 1 and roots (7+i) and (5-i) with multiplicity 1.
We want to find the polynomial function.
As we know that the complex conjugate properties of the roots of a polynomial states that if a+bi is a root of a polynomial then their complex conjugate a-bi is also a root.
So, according to this property (7-i) and (5+i) with multiplicity 1 is also a root of polynomial.
Thus, all the roots are x=7+i, x=7-i, x=5+i and x=5-i
So, the polynomial is f(x)=(x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))
Hence, the polynomial function which has a leading coefficient 1 and roots (7+i) and (5-i) is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i)).
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Sascha owns stock in Lewis Corp, and she bought a $1,000 corporate bond. The bond pays 6.34% annual interest.
How much will Sascha receive in annual interest?
The amount that Sascha will receive in annual interest based on the information is $63.40.
How to calculate the interest?From the information, Sascha owns stock in Lewis Corp, and she bought a $1,000 corporate bond and the bond pays 6.34% annual interest.
In this case, it should be noted that the simple interest is calculated as:
Principal × Rate × Time
Principal = $1000
Time = 1 year
Rate = 6.34%
The interest will be:
= Principal × Rate × Time
= 1000 × 0.0634 × 1
= $63.40
The interest is $63.40.
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Charlie wants to solve the equation -1/4(x-1) =2/3 x +2. Which step would not be an appropriate first step for Charlie to take to solve for x?
The first step Charlie should use to solve the equation will be to open the bracket on the left side of the equation.
How to solve an equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
The equation Charlie wants to solve can be calculated as follows:
-1/4(x - 1) =2/3 x +2
The first step would be to open the parenthesis on the left side of the equation as follows:
-1/4(x - 1) =2/3 x +2
- 1 / 4 x + 1 / 4 = 2 / 3 x + 2
Let's subtract 1 / 4 from both sides of the equation
- 1 / 4 x + 1 / 4 = 2 / 3 x + 2
- 1 / 4 x + 1 / 4 - 1 / 4 = 2 / 3 x + 2 - 1 / 4
- 1 / 4 x = 2 / 3 x + 7 /4
subtract 2 / 3 x from both sides of the equation.
- 1 / 4 x = 2 / 3 x + 7 /4
- 1 / 4 x - 2 / 3 x = 2 / 3 x - 2 / 3 x + 7 /4
- 11 / 12 x = 7 / 4
cross multiply
-44x = 84
divide both sides by - 44
x = 84 / -44
x = - 21 / 11
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I need help like asap !!!
only numbers and decimal points
Answer:
b = 10.06 in
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (10.5)² = b² + (3)²
→ 110.25 = b² + 9
→ b² = 110.25 - 9
→ b = √101.25
→ [ b = 10.06 in ]
Hence, value of b is 10.06 in.
what is the sum between 6/9 and 3/6
Answer:
21/18 or 1 and 3/18
Step-by-step explanation:
6/9 = 12/18
3/6 = 9/18
12/18 + 9/18 = 21/18 or 1 3/18
Answer:
[tex] \frac{6}{9} + \frac{3}{6} \\ \\ = \frac{2 \times 6 + 3 \times 3}{18} = \frac{12 + 9}{18} = \frac{21}{18} = \frac{7}{6} = 1 \frac{1}{6} [/tex]write the equation that has a vertex at (-2,3) and a vertical stretch of 3
Vertex form
f(x)= 3(x+2)^2+4
Which of these strategies would eliminate a variable in the system of equations?
The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 6 ,multiply the bottom equation by -5 then add the equation and is denoted as option B.
What is Equation?This is a mathematical term which is made up of two expressions and is connected by an equal sign.
In the example given below:
8x + 5y = -7
-7x + 6y = -4
We can multiply the top by 6 and the bottom by -5 which will result in:
48x + 30y = -42
35x - 30y = 20
They are then added to each other to give:
48x + 35x + 30y - 30y = -42 + 20
83x = - 22
x = -22/83
From this we can notice that the variable y was eliminated which is why option B is the correct choice.
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Which equation has the solution x = 5?
Select each correct answer.
x/5+5=6
18−2x=9
3x + 1 = 9
32−4x=12
25/x+4=9
11 + 6x = 22
a tank contains 200 liters of fluid in which 30 grams of salt is dissolved. brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 l/min, the well mixed solution is pumped out at a rate of 6 l/min. find the number a(t) of grams of salt in the tank at time t.
The number of grams of salt in the tank at time t is given by the differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].
What is rate?The rate is basically a measurement of something's number, amount, or degree in relation to another item. Its the ratio of some quantity to some other quantity.
An equation with a function and one or more of its derivatives is referred to as a differential equation:
At the start, the tank contains A(0) = 30 g of salt.
Salt flows in at a rate of
(1 g/L) * (4 L/min) = 4 g/min
and flows out at a rate of
(A(t)/200 g/L) * (6 L/min) = 3A(t)/100 g/min
so that the amount of salt in the tank at time t changes according to
A'(t) = 4 - A(t)/50
So,
[tex]A'(t) = 4 - \frac{A(t)}{50}[/tex]
The solution of linear differential equation y' + ay = g(x) is in the form,
[tex]e^{ax}y=\int {e^{ax}g(x)} \, dx +c[/tex]
Now, putting the values,
[tex]a=\frac{1}{50} \\g(x)=4[/tex]
[tex]e^{\frac{1}{50}t}A(t)=\int {e^{\frac{1}{50}t}4} \, dt +c\\=4\int {e^{\frac{1}{50}t}} \, dt +c\\=4\times50e^{\frac{1}{50}t}+c\\=200e^{\frac{1}{50}t}+c\\[/tex]
Now,
[tex]A(t)=200+Ce^{-\frac{1}{50}t}\\[/tex]
Putting the initial value,
[tex]30=200+Ce^{-\frac{1}{50}(0)}\\\\200+C=30\\C=-170[/tex]
So, the function will be [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].
Therefore, the number of grams of salt in tank at time t is given by differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].
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(14x - 2) - (11x-21)
Answer:
3x+19
Step-by-step explanation:
Distribute:
14 x − 2 − ( 11 x − 21 ) 1 4 − 2 − ( 1 1 − 2 1 )
14 x − 2 − 11 x + 21 1 4 − 2 − 1 1 + 2 1
Add the numbers:
14x−2−11x+21
14−2−11+2
Combine like terms:
14x+19−11x
14 +19−113x+193+19
Solution: 3x+19
Answer:
3x + 19
Example:
None.
use the figure to complete the following statements
Step-by-step explanation:
I don't see the options and how they are written, but I can tell you the right answer in numbers :
sin(F) = 3/5 = 0.6
cos(F) = 4/5 = 0.8
sin(G) = 4/5 = 0.8
cos(G) = 3/5 = 0.6
why ?
remember the norm circle (radius 1) with ask the trigonometric functions.
the sine of an angle is the vertical height from that point in the circle arc down to x-axis.
the cosine of an angle is the length on the x-axis from the center of the circle to the point, where the sine touches the x-axis.
in any case, sine and cosine enclose the right angle (90°).
each function is now defined for the norm circle with radius = 1.
for angles in larger circles we need to divide the find lengths by the actual radius (we formality do this in the norm circle too, but a division by 1 does not change anything).
for the angles at F and G the radius is the side with the length 5.
Y=1/2x+5
Y= -5/2x-1 ???
Answer:
It's correct
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point Form: (-2, 4) Equation Form : X= -2, Y = 4.
Amelia need to buy ome cat food. At the nearet tore, 3 bag of cat food cot $13. 50. How much would Amelia pend on 5 bag of cat food?
Amelia would pend $ on 5 bag of cat food. PLEASEE HELPPP QUICK
The amount of money that Amelia would spend on five bags of cat food is $22.5.
Amelia needs to buy some cat food. At the nearest store, three bags of cat food cost $13.50. We need to find out the amount of money that Amelia would spend on five bags of cat food.
Let the amount of money that Amelia would spend on 5 bags of cat food be represented by the variable M. We will use the unitary method. First of all, we will calculate the cost of one bag of cat food.
C = $13.50/3
C = $4.5
Now we need to find out the cost of five bags of cat food.
M = $4.5×5
M = $22.5
Hence, the amount of money that Amelia would spend on five bags of cat food is $22.5.
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Find the solution of the system of equations.
−10x+2y=−32
-2x-2y=−16
The solution of the system of equations are x = 4 and y = 4.
What are the solutions?The system of equations would be solved using the elimination method.
−10x+2y=−32 equation 1
-2x-2y=−16 equation 2
In order to determine the value of x, take the following steps:
Add equation 2 and equation 1 together
-12x = - 48
Divide both sides of the equation by -12
x = -48 / - 12
x = 4
In order to determine the value of y, substitute for x in equation 1:
-(10 x 4) + 2y = -32
-40 + 2y = -32
Combine similar terms:
2y = -32 + 40
Add similar terms:
2y = 8
Divide both sides of the equation by 2
y = 8 / 2
y = 4
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Find the value of x. Then find the measure of each angle and write the answers in ascending order.
The measured interior angles of the triangle are 40°, 60°, and 80° in ascending order.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
The triangle has interior angles are:
(2x)°, (3x)° and (4x)°
As we know that the sum of interior angles is 180 degrees in the triangle.
According to the given figure,
(2x)° + (3x)° + (4x)° = 180°
Apply the addition operation in the above equation,
9x = 180
x = 180/9
x = 20°
Thus, The triangle has interior angles are:
(2x)° = 2 × 20° = 40°
(3x)° = 3 × 20° = 60°
(4x)° = 4 × 20° = 80°
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Jumpin' Dolphin Boat Tours takes tourists into the Gulf of Mexico to see dolphins. Tourists buy tickets and pay extra for tour pictures. The total price for t tickets and p pictures is 10t+5p dollars. The Kelley family went on a tour this afternoon. They bought 4 tickets and 3 pictures.
What was the total cost of the Kelley family's tour?
If Kelley family went on a tour this afternoon and they bought 4 tickets and 3 pictures. The total cost of the Kelley family's tour is $55.
How to find the total cost?Given data
Total price = 10t+5p dollars
Where:
t = tickets =4
p = pictures = 3
Now let find the total cost
Total cost = 10t+5p
Total cost = 10(4) + 5(3)
Total cost =40 +15
Total cost =$55
Therefore we can conclude that the total cost is the amount of $55.
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Ms. Patel purchased some pliers, wrenches, and chisel sets for her shop. She bought twice as many pliers that cost $17. 50 each as wrenches that cost $21. 50 each. She bought 3 fewer chisel sets than pliers. How many of each tool did Ms. Patel buy if she paid a total of $141 and each chisel set costs $28?
NEED ASAP!
This comes to $141, indicating that Ms. Patel spent that money on four sets of pliers, two wrench sets, and a chisel set.
Define the meaning of the term ratios?A ratio is the relationship and comparison involving two numbers belonging to the same unit in order to determine how much larger one number is than the other.The given condition states that;
For her shop, Ms. Patel bought some sets of chisels, wrenches, and pliers. She purchased twice as many wrenches, which were $21.50 each, as she did pliers, which were $17.50 each. She purchased 3 fewer sets of chisels than pliers.Make a ratio first.
This ratio might be expressed as 4:2:1 (in pliers, wrenches, and chisels).
Then, multiply every one of these sums by their respective prices before adding them all up.
Pliers : 4 times 17.50 equals $70
Wrenches : $2 x $21.5 = $43
Chisels : 1 x 28 equals $28
Thus,
Sum = $70 + $43 + $28
Sum = $141
This amounts to $141, proving that she purchased a chisel set, two wrench sets, and four pairs of pliers.
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola is f(x) = 7(x-3)^2+5.
Given:
The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.
If the parabola has same shape then its a values are same.
so f(x) = 7x^2
here a = 7
so the equation with vertex (3,5) also has a value is 7.
(h,k) = (3,5)
f(x) = a(x-h)^2+k
= 7(x-3)^2 + 5.
Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.
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Provide all the necessary calculations to complete the following task.
Suppose AB has endpoints A(1,7) and B(5, 4) and DE has
endpoints D(-6, -2) and E(-2,-5). Use these coordinates to
show that DE is the result of a translation of AB.
Have at least 3 complete sentences.
AB has endpoints A (1, 7) and B (5, 4) and DE has endpoints D (-6, -2) and E (-2,-5). The translation is by the rule (x - 7, y - 9), is used to transform AB to DE
How to get the translation ruleTranslation is a type of transformation that involve a linear movement.
The translation rule is gotten by comparing the points as below
preimage point A (1, 7) and B (5, 4)
image points D(-6, -2) and E(-2,-5)
x coordinate
using point A and D = -6 - 1 = -7
using point B and E = -2 - 5 = -7
y coordinate
using point A and D = -2 - 7 = -9
using point B and E = -5 - = -9
Therefore the translation rule is (x - 7, y - 9) that got the image, point D and E from the preimage , point A and B
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3* + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
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Work out 3^8 =9root3
2– 1 8 y=11+ 7 8 y solve the y
Answer:
y=-3/32
Step-by-step explanation:
2-18y=11+78y
-18y-78y=11-2
-96y=9
y=-3/32
Mila bought stock in a company
two years ago that was worth z
dollars. During the first year that she owned the stock, it decreased by
35%. During the second year the value of the stock decreased
by 32%.
Write an expression in terms of z that represents the value of the stoc
after the two years have passed.
The expression is 2z+0.67
From the question, we have
During the first year that she owned the stock, it decreased by 35%. During the second year the value of the stock decreased by 32%.
z-35%+z-32%
=z-7/20+z-8/25
=2z+0.67
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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How do I solve this and what's the answer please?
The value of the expression when z = -19 is 25.
How to evaluate the expression?
Here we have the expression:
(33 + 2z)²
And we want to evaluate this on z = -19
Evaluating just means that we need to replace the variable in the expression by the given number.
By doing that we will get:
(33 + 2*(-19))^2
(33 - 38)^2
(-5)^2 = 25
The expression is equal to 25.
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Why is Mathematics called the queen of science (1 paragraph response please)
The sum of five times a number and three is between -7 and 23.
The number of the given statement will be inequality -2 < x < 4.
We have been given the statement "the sum of five times a number and three is between -7 and 23".
Let the number would be x
As per the given statement, we can represent this algebraic form with inequality as:
⇒ -7 < 5x + 3 < 23
Subtract 3 on both sides of the above inequality
⇒ -7 - 3 < 5x < 23 - 3
⇒ -10 < 5x < 20
Divided by 5 into both sides of the above inequality
⇒ -2 < x < 4
Thus, the number of the given statement will be inequality -2 < x < 4.
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The question seems to be incomplete the correct question would be
Find the number if the sum of five times a number and three is between -7 and 23.
which expressions are equivalet to the one below check all that apply (7^3) * (7^x)
A. 49^3x
B. (7 * x)^3
C. 343 * 7^x
D. 7^(3+x)
E. 7^(3x)
F. 7^(3-x)
For given expression (7^3) * (7^x) equivalent expressions are:
343 * 7^x and 7^(3+x)
The correct options are option (C) and option (D)
In this question, we have been given an expression (7^3) * (7^x)
We need to find expressions that are equivalent to given expression.
Consider given expression (7^3) * (7^x)
We know that 7^3 = 343
So given expression becomes, (7^3) * (7^x) = 343 * (7^x)
For given expression, the bases of the exponents are equal.
so, by the properties of exponents
(7^3) * (7^x) = 7^(3 + x)
Therefore, for given expression (7^3) * (7^x) equivalent expressions are:
343 * 7^x and 7^(3+x)
The correct options are option (C) and option (D)
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Games at the carnival costs $9 each. The prizes awarded to the winners costs the owner $207.35. How many games must be played for the owner to make more than $100.
Write and solve an inequality. Show your work using 3 or 4 steps. Use g as your variable. Round your initial answer to the nearest hundredth.
The inequality used to represent games at carnival is 9g - 207.35 > 100
The solution is g > 34.15
How to determine the inequality used to represent games at carnivalInformation gotten from the question include
Games at the carnival costs $9 each
The prizes awarded to the winners costs the owner $207.35
How many games must be played for the owner to make more than $100 = ?
Using g as variable which is the number of games to be played we have
total amount gotten from games = 9 * g
prizes of winners = 207.35
The inequality equation as described in the problem is represented using linear function as as follows
9g - 207.35 > 100
for the owner to make more than 100 we have the equation
total amount gotten from games - prizes of winners > 100
9g - 207.35 > 100
100 + 207.35 < 9g
9g > 307.35
g > 34.15
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I need help with these problems in Geometry (Similar Triangles)
Looking at the triangles, the values of x in the figures are
14. x = 1715. x = 3What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
figure in 14)
The solution for x
8 / (x + 5) = (x - 9) / 21
21 * 8 = (x + 5)(x - 9)
168 = x^2 - 4x - 45
x^2 - 4x - 213
x = 16.73 or -12.73
using the positive value
x = 17
figure in 15)
The solution for x
(x + 3) / 15 = 4 / (3x + 1)
cross multiplying
(x + 3)(3x + 1) = 15 * 4
3x^2 + 10x + 3 = 60
3x^2 + 10x - 57 = 0
x = 3 OR -6.333
taking the positive value
x = 3
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Bell Work
You Do
Camspite A is 5 miles north and 2 miles east of a ranger station.
Campsite B is 8 miles north and 6 miles east of the ranger station.
How far is Campsite A from Campsite B?
A 1 mi
B 5 mi
7 mi
25 mi
7 i do not feel like explaining tbh
exponential smoothing is meant to be used with time-series data when the data are made up of some or all of the basic components of level, trend, seasonalitiy, and error. if the data series only fluctuates about an average with no trend and no serasonalitiy, which form of smoothing wouldyou employ? if the data include all of these components, which form of smoothing would you employ? how should the smoothing constants be chosen?
Based on the information provided, ETS is an abbreviation for these three terms (Error, Trend, and Season). Following that, Exponential Smoothing Methods for an ETS system can be described, with the details specified in a smoothing style.
=> As should be obvious, combining Error, Trend, and Season on any occasion in three distinct ways yields a plethora of combinations.
=> The trend depicts the overall layout of the time. It communicates with the data's drawn-out model — its tendency.
=> The seasonal section displays the types associated with anticipated events. Finally, the error component explains what the season and trend components do not. The error is due to the disparity between the first data and the combination of trend and seasonality. As a result, if we crystallize all three parts, we will have the first data back.
=> It has a counted substance conduct when the period of seasonal swings remains constant.
=> We can label our model as ETS (M,A,M).
-> Multiplicative Mistake
-> Added substance Trend
-> Multiplicative Seasonality.
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