Answer:
3x^2 + 3xz
Step-by-step explanation:
Under the assumption that I need to distribute,
(x + z)(x + 2x)
(x + 2x) is (3x)
3x(x + z) becomes 3x*x and 3x*z
3x*x = 3x^2
3x*z = 3xz
combine, 3x^2 + 3xz
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On December 1, Jasmin Ernst organized Ernst Consulting. On December 3, the owner contributed $85,360 in assets in exchange for its common stock to launch the business. On December 31, the company’s records show the following items and amounts. Cash $ 7,010 Cash dividends $ 3,390 Accounts receivable 18,350 Consulting revenue 18,350 Office supplies 4,480 Rent expense 4,820 Office equipment 19,360 Salaries expense 8,370 Land 46,040 Telephone expense 910 Accounts payable 9,740 Miscellaneous expenses 720 Common stock 85,360
The income statement illustrates that the net income will be $3530.
How to calculate the income statement?The income statement will be:
Revenue
Consulting revenue 18350
Expenses
Miscellaneous expenses 720
Rent expense 4820
Salaries expense 8370
Telephone expenses 910
Total expenses 14820
Net income = 18350 - 14820 = 3530
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How can triangles be proven similar by the SAS similarity theorem?
Answer: Option (2)
Step-by-step explanation:
We need the angle to be included between the two mentioned sides.
This eliminates the first and fourth options.Also, the sides need to be corresponding for the ratio, and both sides of the triangle need to be in either the numerators or the denominators.
This eliminates the third option.3y-12x=24 and goes through point (2,-6) . write your answer in y=mx+b
Answer:
y= 4x+8
Step-by-step explanation:
Add 12x to both sides.
3y=24+12x
The equation is in standard form.
3y=12x+24
Divide both sides by 3.
3
3y
=
3
12x+24
Dividing by 3 undoes the multiplication by 3.
y=
3
12x+24
Divide 24+12x by 3.
y=4x+8
Write the equation of the line with a slope of 3/4 and a y'-intercept of -7 in Slope-Intercept and Poin Slope Form.
A company is considering producing some new products. Based on past records, management believes that there is a 70% chance that each of these will be successful, and a 30% chance of products were predicted to be successful based on market research 90% of the time. However, failure. Market research may be used to revise these probabilities. In the past, the successful for products that failed, the market research predicted these would be successes 20% of the time.
The probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful is P=0.77.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Events:
S: success
F: failure
MS: market research forecast a success
MF: market research forecast a failure
The information we have is:
P(S)=0.70
P(F)=0.30
P(S|MS)=0.90
P(F|MS)=0.20
If P(F|MS)=0.20, we can derive that P(F|MF)=0.80. That is, the failed products were predicted to be a failure based on market research 80 per cent of the time.
We also can conclude that P(S|MF)=0.10.
We can calculate the probability of having a forecast of a failure, given that the product is actually unsuccessful as:
[tex]P(MF|F) = \dfrac{P(F|MF)\times P(F)}{P(F|MF)\times P(F)+P(S|MF)\times P(S)}[/tex]
[tex]P(MF|F) =\frac{(0.8\times 0.3)}{0.8\times 0.3)+(0.1\times 0.7}[/tex]
[tex]P(MF|F) =\dfrac{0.24}{0.31}=0.77[/tex]
The probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful is P=0.77.
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Each team is required to bring 24 baseballs to each game. If there are 3
baseballs in a pack, how many total packs do the teams bring to each game?
The total packs the teams bring to each game is 8 packs.
How many packs do the team bring to each game?
Division is the process of dividing a number into equal parts using another number. The sign used to denote division is ÷.
Number of packs = 24 ÷ 3 = 8
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Let's say that the turkey sat on the counter for an additional hour (beyond the 390 minutes) and its temperature cooled to 80 degrees. Write that value in function notation
The value of the temperature in function notation is gotten as; f(x) = 91 - 11x
How to write a function Notation?Let us first find the relationship between temperature and how long the turkey sits out.
The temperature after the normal 390 minutes is equal to approximately 6.5 hours.
Let us create a ratio and solve for x, which represents the temperature change during that extra hour after the "normal time sitting out".
Thus;
(7.5/6.5) = (80/80+ x)
Solving for x gives x = -10.7.
This means that for every extra hour it sits out, the turkey cools approximately 11°. When we add that to 80°, we have 91° which is the expected temperature after 390 minutes (6.5 hours) of sitting out.
Thus, the motion as a function of time is;
f(x) = 91 - 11x
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Evaluate.
-|a+bl
2-c
when a = 1, b = -2, and c = -7
Enter your answer as a simplified fraction in the box.
Answer:
-9
Step-by-step explanation:
-|1-2|2+7
-|-1|9
-9×1
-9
For a fair coin, suppose you toss the coin 100 times.
What is the probability of getting more than 66 heads?
Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].For the binomial distribution, the parameters are given as follows:
n = 100, p = 0.5.
Hence the mean and the standard deviation of the approximation are given as follows:
[tex]\mu = np = 100(0.5) = 50[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5[/tex]Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is one subtracted by the p-value of Z when X = 66.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66.5 - 50}{5}[/tex]
Z = 3.3
Z = 3.3 has a p-value of 0.9995.
1 - 0.9995 = 0.0005.
0.0005 = 0.05%
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pls solve this question
Answer:
[tex] {( \sqrt{ {x}^{ - 3} }) }^{5} = ({( {x}^{ - 3}) }^{ \frac{1}{2} } ) ^{5} \\ \\ = {x}^{ - 3 \times \frac{1}{2} \times 5} = {x}^{ - \frac{15}{2} } = \frac{1}{ {x}^{ \frac{15}{2} } } [/tex]
Or ;
[tex] {( \sqrt{ {x}^{ - 3} } )}^{5} = {( \sqrt{ \frac{1}{ {x}^{3} }} })^{5} = ( { \frac{ \sqrt{1} }{ \sqrt{ {x}^{3} } } })^{5} \\ \\ = ( { \frac{1}{ \sqrt{x} \sqrt{ {x}^{2} } } })^{5} = ({ \frac{1}{ x\sqrt{x} }})^{5} \\ \\ = ( \frac{ {(1)}^{5} }{ {x}^{5} ( \sqrt{x} )^{5} } ) = \frac{1}{ {x}^{5} \times {x}^{ \frac{1}{2} \times 5 } } \\ \\ = \frac{1}{ {x}^{5} \times {x}^{ \frac{5}{2} } } = \frac{1}{ {x}^{5} \sqrt{ {x}^{5} } } \\ \\ = \frac{1}{ {x}^{5} \sqrt{ {x}^{4} {x}^{1} } } = \frac{1}{ {x}^{5} \sqrt{x} \sqrt{( { {x}^{2} })^{2} } } \\ \\ = \frac{1}{ {x}^{5} {x}^{2} \sqrt{x} } = \frac{1}{ {x}^{7} \sqrt{x} } = \frac{ \sqrt{x} }{ {x}^{8} } [/tex]
(X+p)(x+q) what part of the trinomial will equal the product of p and q?
The part of the trinomial that will equal the product of p and q is the constant part
How to determine the part?The expression is given as:
(x + p)(x + q)
From the expression, p and q are both constants.
When a constant is multiplied to another, the result is a constant
This means that:
pq = constant
Hence, the part of the trinomial that will equal the product of p and q is the constant part
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A farmer raises only cows and Sheep. He wants to raise no more than 16 animals, including no more than 12 sheep. He spends birr 5 to raise a cow and Br 2 to raise a sheep. He has Br 50 available for this purpose. Cows sell birr 100 and sheep birr 50. Required: How many of each animal should he raise to maximize profit? What is the maximum profit?
The maximum profit will be 956 birrs for both cows and sheep.
What is profit?The amount of money earned by any seller on the cost price is called the profit.
Given that:-
A farmer raises only cows and Sheep. He wants to raise no more than 16 animals, including no more than 12 sheep. He spends birr 5 to raise a cow and Br 2 to raise a sheep. He has Br 50 available for this purpose. Cows sell birr 100 and sheep birr 50.From the given data we can see that the total number of animals cows and sheep is 16.
C + S = 16
To raise a cow need 2 Br
To raise Sheep need 5 Br
The number of sheep is 12 and cows 4.
So the amount required to raise sheep and cows is:-
Sheeps = 12 x 2 = 24 Br
Cows = 4 x 5 = 20 Br
Total = 44 Br
The selling price of cows and sheep are 100 and 50 Br.
Cows = 100 x 4 = 400Br
Sheeps = 50 x 12 = 600 Br
Total = 1000 Br
So the profit will be calculated as follows:-
P = 1000 - 44 = 956 Br
Therefore the maximum profit will be 956 birrs for both cows and sheep.
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Drainpipe comes in lengths of 2.5 metres. A man wants to buy drainpipe to fit down
one side of his house from the ground to the gutter.
Estimate how many lengths he will need.
lengths
The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that the distance from the man side of the house to the gutter is 15 m, since the drainpipe comes in lengths of 2.5 m, hence:
Number of drainpipe needed = 15 m / 2.5 m = 6
The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.
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The required quantity of drainpipe is mathematically given as six.
L=6
What is the lengths he will need?Generally, Let's say the distance from the male side of the house to the gutter is 15 meters. Since the length of the drainpipe typically comes in increments of 2.5 meters, we may reason as follows:
In conclusion, The required quantity of drainpipe is equal to 15 meters divided by 2.5 meters, which is equal to six.
L=15/2.5
L=6
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Below what price level would the firm go out of business in the long run?
A firm should go out of business in the long run when its price level is less than the average total cost.
When should a firm go out of business in the long run?The long run is a period where all factors of production are varied. It is known as the planning time of a firm. In the long run, if the if the average total cost is greater than the price, the firm should exit the market.
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Chef Fabio does beginning inventory on Thursday night and finds that he has $1456 in food products in the restaurant. Throughout the week he purchases:
$457 produce,
$632 protein,
$356 dry goods, and
$147 dairy.
The following Thursday he does ending inventory and finds that he has $1643 in food. He looks at his sales and finds that he made $5546 over the same 7 day period. What is his food cost as a percentage of sales (food cost percentage)?
Using it's concept, it is found that the percentage of his sales that area food costs is of 29.62%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, he has $1643 out of $5546 in food, hence the percentage is given by:
[tex]P = \frac{1643}{5546} \times 100\% = 29.62%[/tex]
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If the center of a circle is at (5,-7)
and its radius is 6, complete its
equation:
Answer:
(x-5)²+(y+7)²=36
or
x²+y²-10x+14y+38=0
First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded above first and second line. Part B shaded below first line and above second line. Part C shaded below first and second lines. Part D shaded above first line and below second line. Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ −1? Part A Part B Part C Part D Question 3(Multiple Choice Worth 5 points) (05.05 MC) Two systems of equations are shown below: System A System B 2x + y = 5 −10x + 19y = −1 −4x + 6y = −2 −4x + 6y = −2 Which of the following statements is correct about the two systems of equations? They will have the same solutions because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A. They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A. The value of x for System B will be −5 times the value of x for System A because the coefficient of x in the first equation of System B is −5 times the coefficient of x in the first equation of System A. The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −12 to the first equation of System A and the second equations are identical. Question 4(Multiple Choice Worth 5 points) (05.06 LC) To which graph does the point (−1, −4) belong? y ≤ −x + 4 y ≤ −x − 6 y ≤ 2x − 3 y ≤ 5x − 1 Question 5(Multiple Choice Worth 5 points) (06.04 MC) What is the equation of the graph below? A graph shows a parabola that opens up and crosses the x axis at negative two and negative four. y = − (x − 3)2 + 1 y = − (x + 3)2 + 1 y = (x − 3)2 − 1 y = (x + 3)2 − 1 Question 6 (Fill-In-The-Blank Worth 5 points) (06.04 MC) A ball is thrown upward from the top of a building. The function below
The part that represents the solution to the inequality will be Part B shaded below first line and above second line.
How to depict the inequality?From the information given, the equation of the first line will be:
y - 3 = (-3 - 3/2 + 4)(x + 4)
y - 3 = -1(x + 4)
y + x = -4 + 3
x + y = -1
The equation of the second line will be:
y + 3 = -1(x + 4)
y = x + 4 - 3
y = x + 1
This is plotted on the graph attached.
From the systems of equations, the statement that is correct about the two systems of equations is that They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A.
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2/5 X -3/4
i need help on this
Answer:
[tex]-\frac{3}{10}[/tex]
Step-by-step explanation:
[tex]\frac{2}{5} *-\frac{3}{4} \\=-\frac{6}{20} \\=-\frac{3}{10}[/tex] (Reduced to simplest form.)
A kitchen measures 20 feet long and 10 feet wide. A scale drawing is made using a scale factor of 124.
What is the length of the kitchen in the scale drawing?
5/12
5/6
5/4
Drag and drop a number to correctly complete the statement.
The length of the kitchen in the scale drawing is Response area ft.
The length of the kitchen in the drawing using the scale factor is: B. 5/6.
How to Find Length Using Scale Factor?We are given a scale factor of 1:24.
Let the length of the kitchen in the drawing = x
Actual length of kitchen = 20 ft.
Using the scale factor, we have:
1/24(20) = 20/24
= 5/6
The length of the kitchen in the drawing is: B. 5/6.
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(3x+7)(x+7)=0
What are the two possible values?
For the given equation, either 3x + 7 = 0 or x + 7 = 0
Now,
3x + 7 = 03x = -7 x = -7/3or
x + 7 = 0x = -7So, possible values of x is : -7 and -7/3
[tex](3x + 7)(x + 7) = 0 \\ \\ \\3x + 7 = 0 \\ \\ 3x = - 7 \\ \\ x = \frac{ - 7}{3} . \\ \\ \\ x + 7 = 0 \\ \\ x = - 7.[/tex]
A function, h(x), is defined as shown.
h(x) = StartLayout Enlarged left-brace 1st row 1st column one-fourth x minus 4, 2nd column x less-than-or-equal-to 0 2nd row 1st column one-third x minus 3, 2nd column 0 less-than x less-than-or-equal-to 3, 3rd row 1st column one-half x minus 2, 2nd column x greater-than-or-equal-to 4
Which graph represents h(x)?
On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, 0) and goes up to a closed circle at (0, 1). The second line starts at (0, negative 3) and goes up to a closed circle at (3, negative 2). The third line has a closed circle at (4, negative 2) and goes up to (6, negative 1).
On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). The second line starts at (0, negative 3) and goes up to a closed circle at (3, negative 2). The third line has a closed circle at (4, 0) and goes up to (6, 1).
On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, 3) and goes up to a closed circle at (0, 4). The second line starts at (0, 3) and goes up to a closed circle at (3, 4). The third line has a closed circle at (4, 4) and goes up to (6, 5).
On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, 0) and goes up to a closed circle at (0, 1). The second line starts at (0, negative 1) and goes up to a closed circle at (3, 0). The third line has a closed circle at (4, negative 2) and goes up to (6, negative 1).
The graph that represents h(x) is option B: On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). ....
What is the graph about?Using the piecewise function, one can see that;
In x ≤ 0, the slope of the graph of h(x) = 1/4
In 0 < x ≤ 3, the slope of the graph of h(x) = 1/3
In x ≥ 4, the slope of the graph of h(x) = 1/2
Note that the movement is left to right and the slope of h(x) often increases and the slope of the graph is said to become steeper.
Option B shows the graph of h(x) as it best tells the exact point of various aspect of the function.
Therefore, The graph that represents h(x) is option B: On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). The second line starts at (0, negative 3) and goes up to a closed circle at (3, negative 2). The third line has a closed circle at (4, 0) and goes up to (6, 1).
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On a coordinate plane, a dashed solid line has an equation of y less-than five-thirds x + 1. It has a positive slope and goes through (negative 3, negative 4) and (0, 1). Everything to the right of the line is shaded.
Which linear inequality will not have a shared solution set with the graphed linear inequality?
y < Five-thirdsx – 2
y < Negative five-thirdsx + 1
y > Five-thirdsx + 2
y > Negative five-thirdsx + 2
The inequality is represented by y < 5/3(x+1)
Use the information about the straight line and find the equation of the line.
Given coordinates (-3,-4) and (0,1), we can find the slope
Slope,
Change in y = y2 – y1 = 1-(-4) = 5
Change in x = x2 – x1 = 0-(-3) = 3
Therefore, Slope (m) = Change in y / Change in x = 5/3
Equation of line using m = 5/3 and points (0,1) and (x, y) in form of y = mx + c
Y – 1/ X – 0 =5/3
3(Y-1) = 5(X)
3Y -3 = 5X
3Y = 5X + 3
Y = 5X + 3/3
Y = 5/3(X + 1)
To find the inequality take a point in the shaded region and check it in the above equation.
Given Options
a. y < Five-thirds x – 2
b. y < Negative five-thirds x + 1
c. y > Five-thirds x + 2
d. y > Negative five-thirds x + 2
Let’s take points (-3,-4) for verification
Option a: y < 5/3 (x-2)
-4 < 5/3(-3-2)
--4 < -3.33
-4 is less than -3.33
Thus option a is in the shaded region
Option b: y < -5/3 (x+1)
-4 < -5/3(-3+1)
--4 < 3.33
-4 is less than 3.33
Thus option a is in the shaded region
Option c: y > 5/3 (x+2)
-4 > 5/3(-3+2)
--4 > -1.67
-4 is NOT GREATER than -1.67
Thus option c is NOT in the shaded region
Option d: y > -5/3 (x+2)
-4 > - 5/3(-3+2)
--4 > 1.67
-4 is NOT GREATER than 1.67
Thus option d is NOT in the shaded region
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Answer:
y > Five-thirdsx + 2
Step-by-step explanation:
Find the inverse of the function.
y=x+8
Answer:
y^-1= x +8
Step-by-step explanation:
this may be helpful for you
find the area for this pls
Answer:
3,36 in^2
Step-by-step explanation:
The geometric shape shown in image is called a trapezoid
to calculate the area of a trapezoid we use the following formula:
1/2*(a+b)*h (a and b are bases, h: height)
bases are 1.3 and 3.5 and height is 1.4
1/2(1.3 + 3.5)*(1.4) = 3,36 the area is stated in square units so the answer is
3,36 in^2
Which absolute value functions will be narrower than the parent function, f(x) = |x|? Check all that apply.
f(x) = |x|
f(x) = |x – 2|
f(x) = |x| + 3
f(x) = 2.9|x|
f(x) = 1.2|x + 8|
f(x) = 0.7|x| – 3.2
The correct answer is option 4 which is f(x) = 2.9|x| is narrower than the parent function f(x) = |x|
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
Given parent function is f(x)=|x|
Now we have to find which function from given choices will be narrower than the parent function.
Notice that adding or subtracting some number from the parent function only shifts the graph up, down, and left of the right side.
But that will not make the function narrower or broader.
So f(x) = |x – 2| and f(x) = |x| + 3, can't be the answer.
Multiplying by some positive real number which is more than 1, makes the function narrower.
Only f(x) = 2.9|x| from remaining choices fits that case.
Hence correct answer is option 4 which is f(x) = 2.9|x| is narrower than the parent function f(x) = |x|
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Answer:
D,E
Step-by-step explanation:
Which graph represents y=12+2x
or
What is (fg)(x)?
f(x)=
–
3x+1
g(x)=x2
Write your answer as a polynomial or a rational function in simplest form.
The value of (fg)(x)= 3x³+ x²
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
f(x) = -3x+1
g(x) = [tex]x^{2}[/tex]
Now, (fg)(x)
=f(x) * g(x)
= (-3x+1) * ([tex]x^{2}[/tex])
=-3x³+ x²
Hence, (fg)(x)= 3x³+ x²
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Consider the set S of bit strings defined recursively by:
The correct option regarding the recursively defined strings is given by:
c) Both i) and ii).
Which of the strings belong to alphabet S?First we start with string 101, we have that:
101 -> 1w -> 10w -> 101
Which belongs to alphabet S.
For string 001, we have that:
001 -> 0w -> 00w -> 001.
Which belongs to alphabet S.
Hence statement c is correct.
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find the zeros of following quadratic polynomial and verify the relationship between the zeros and the coefficient of the polynomial f(x)=5x-4√3+2√3x²
Answer:
[tex]\textsf{Zeros}: \quad x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Rewrite the given polynomial in the form ax² + bx + c:
[tex]f(x)=2 \sqrt{3}x^2+5x-4 \sqrt{3}[/tex]
To find the zeros, set the function to zero and solve for x using the quadratic formula.
[tex]\implies 2 \sqrt{3}x^2+5x-4 \sqrt{3}=0[/tex]
Quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore,
a = 2√3b = 5c = - 4√3Substituting the values into the quadratic formula:
[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2\sqrt{3})(-4\sqrt{3})} }{2(2\sqrt{3})}[/tex]
[tex]\implies x=\dfrac {-5 \pm \sqrt {121}}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {-5 \pm 11}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {6}{4\sqrt{3}}, \:\:x=\dfrac {-16}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {3}{2\sqrt{3}}, \:\:x=-\dfrac {4}{\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]
The sum of the roots of a polynomial is -b/a:
[tex]\implies -\dfrac{b}{a}=-\dfrac{5}{2 \sqrt{3}}=-\dfrac{5\sqrt{3}}{6}[/tex]
The sum of the found roots is:
[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)+\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{5\sqrt{3}}{6}[/tex]
Hence proving the sum of the roots is -b/a
The product of the roots of a polynomial is: c/a
[tex]\implies \dfrac{c}{a}=\dfrac{-4\sqrt{3}}{2\sqrt{3}}=-2[/tex]
The product of the found roots is:
[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{12}{6}=-2[/tex]
Hence proving the product of the roots is c/a
Therefore, the relationship between the roots and the coefficients is verified.
Answer:
Step-by-step explanation:
Rewrite the given polynomial in the form ax² + bx + c:
To find the zeros, set the function to zero and solve for x using the quadratic formula.
Quadratic formula:
Therefore,
a = 2√3
b = 5
c = - 4√3
Substituting the values into the quadratic formula:
The sum of the roots of a polynomial is -b/a:
The sum of the found roots is:
Hence proving the sum of the roots is -b/a
The product of the roots of a polynomial is: c/a
The product of the found roots is:
Hence proving the product of the roots is c/a
Therefore, the relationship between the roots and the coefficients is verified.
(x^4) (3x^3-2) (4x^2+5x)
Answer:
12x^7+15x^6
Step-by-step explanation:
Change 3x^3-2 to 3x
(x^4)(3x)(4x^2+5x)
Multiply your single terms
(3x^5)(4x^2+5x)
Then distribute
12x^7+15x^6
