What are the solutions of the polynomial 4x^2-4x+10 4 x 2 − 4 x + 10? Write the answer in complex, a+bi a + b i form.
x=____+____i,x=____-____i
The solutions of the polynomial are [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
Step-by-step explanation:
The solutions of a polynomial is the value of x when the polynomial equal to zero
The formula of quadratic polynomial is [tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}[/tex] , where
a is the coefficient of x²b is the coefficient of xc is the numerical term∵ The polynomial is 4x² - 4x + 10
- Equate it by zero to find its solutions
∴ 4x² - 4x + 10 = 0
∵ The coefficient of x² is 4
∴ a = 4
∵ The coefficient of x is -4
∴ b = -4
∵ The numerical term is 10
∴ c = 10
- Use the formula to find the values of x
∵ [tex]x=\frac{(-4)(+/-)\sqrt{(-4)^{2}-4(4)(10)}}{2(4)}[/tex]
∴ [tex]x=\frac{-4(+/-)\sqrt{16-160}}{8}[/tex]
∴ [tex]x=\frac{-4(+/-)\sqrt{-144}}{8}[/tex]
∵ [tex]\sqrt{-144}=12\sqrt{-1}[/tex]
- Substitute [tex]\sqrt{-1}[/tex] by i
∴ [tex]12\sqrt{-1}=12i[/tex]
∴ [tex]x=\frac{-4(+/-)12i}{8}[/tex]
- Divide up and down by 4 to simplify the fraction
∴ [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
The solutions of the polynomial are [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
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On a dell river, a boat will pass the Colby drawbridge and then the wave drawbridge opening times.There are 60 minutes in a hour so use 60 as a common denominator. Then rename each opening time using another common denominator. Explain how you found your answer
45/60 and 10/60 because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10
By finding common denominators, we can express the boat drawbridge opening times in terms of a shared timeframe, such as every 60 minutes or 30 minutes. The common denominator is the smallest number that the opening times can be equally divided into.
Explanation:The question relates to the application of common denominators in the context of timekeeping. Without specific times for the opening of Colby and Wave drawbridge, I will give a hypothetical scenario as an example.
Let's say Colby drawbridge opens every 20 minutes and Wave drawbridge opens every 15 minutes. A common denominator of 20 and 15 is 60, as they both divide evenly into 60. So, you could rename the opening times in terms of 60 minutes: Colby drawbridge opens 3 times every 60 minutes (60/20) and Wave drawbridge opens 4 times every 60 minutes (60/15).
If we want to use another common denominator, you could use 30. Then Colby drawbridge opens 1.5 times every 30 minutes (30/20) and Wave drawbridge opens 2 times every 30 minutes (30/15).
The way to find common denominators involves looking for the smallest number that both of the numbers can divide equally into. In this case, 60 was an obvious choice since there are 60 minutes in an hour, but other common denominators like 30 can also be used.
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Look this is very confusing plz explain
Answer:
Step-by-step explanation:
[tex](\sqrt[3]{2} )^{5}=(2^{\frac{1}{3}})^{5}=2^{\frac{1}{3}*5}=2^{\frac{5}{3}}[/tex]
What is the solution to the following equation?
х+11 = 24
А. x = 13
B.х = 35
C. х = 17
D. x = 29
Answer:
A. x=13
Step-by-step explanation:
[tex]x + 11 = 24 \\ x = 24 - 11 \\ x = 13[/tex]
What is 400 times 1/4
Answer:
100
Step-by-step explanation:
We know that if we convert 1/4 into a decimal it becomes 0.25 so,
0.25
x
400
____________________
100
Hope this helps!
What is the range of f(x) = 1/x?
Answer: f(x)=1x can have any number as an input except for zero.
Step-by-step explanation:
Domain is all the possible x-values that can be plugged in and range is all the possible y-values that can be outputs. f(x)=1x can have any number as an input except for zero.
:
Select all that apply.
40 is what percent of 25.
A
160%
B
62.5%
C
1600%
D
625/1000
E
160/100
F
1600/100
Answer:
The answer is A 160% and E [tex]\frac{160}{100}[/tex].
Step-by-step explanation:
To find what percentage 40 is of 25, you first need to find what 1% of 25 is. To solve you do 25 ÷ 100 which is equal to 0.25. You then need to divide 40 by 0.25, which would be the same as multiplying 40 by 4. 40 ÷ 0.25 = 160. Therefore, 40 is 160% of 25. 160% is the same as saying [tex]\frac{160}{100}[/tex] or 160 out of 100 or you could say 160 ÷ 100 = 1.6, which would mean 25 × 1.6 = 40.
40 as a percentage of 25 can be applied such that the percentage would be:
A. 160%E. 160/100How to find the percentages ?To find what percent 40 is of 25, you would use the formula:
= (Part / Whole) * 100%
So here, 40 is the part and 25 is the whole:
= (40 / 25) * 100%
= 160%
40 is 160 % of 25.
160 / 100 is also 160 %. The rest of the options are incorrect leaving options A and E.
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Find the slope of the line passing through the points (3,4) and (8, -3)
Answer:
1.5
Step-by-step explanation:
y2 - y1 ÷ x2 - x1
(3,4) (8, -3)
(x1,y1) (x2,y2)
The angle of elevation of the top of a house from a point on the horizontal line 45m away from the foot of the house is 30 degree,find the height of house
The height of the house, given the angle of elevation and the distance of the point is 25. 98 meters.
How to find the height ?
You can use the tangent function because it relates the angle of elevation to the opposite side and the adjacent side (the horizontal distance).
The tangent of the angle of elevation is equal to the ratio of the height to the horizontal distance:
tan(30 degrees) = h / 45 meters
Solve for "h" by multiplying both sides by 45 meters:
h = 45 meters x tan(30 degrees)
You can calculate the value of tan(30 degrees):
tan(30 degrees) = 0.5774
Multiply:
h = 45 meters x 0.5774
= 25.98 meters
A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment, and find the probability of the given event. (Enter your answer as a fraction.)
The sum of the numbers is at least 4.
The probability of the sum of the numbers rolled on two dice being at least 4 is 25/36.
Explanation:When rolling two dice, the total number of outcomes is 36 (each die has 6 possible outcomes). To find the probability of the sum being at least 4, we need to determine the number of favorable outcomes. The pairs that satisfy this condition are (1, 3), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6). Therefore, there are 25 favorable outcomes. So, the probability is 25/36.
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Given the line below.
Write the equation of the line, in point-slope form. Identify the point (-2, -2) as (x1, y1). Use the box provided to submit all of your calculations and final answer.
Answer:
[tex]y+2=(x+2)[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(-2,-2) and (2,2)
substitute the values
[tex]m=\frac{2+2}{2+2}=1[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=1\\(x1,y1)=(-2,-2)[/tex]
substitute
[tex]y-(-2)=(1)(x-(-2))[/tex]
[tex]y+2=(x+2)[/tex]
what is the answer?
Answer:
when multiplying polynomials you want to times the coefficients but add the exponents
(-7a^4b^1c^3)(5a^1b^4c^2) (if there isn't an exponent then it is 1)
-7*5=-35
a^4*a^1=a^5
b^1*b^4=b^5
c^3*c^2=c^5
Your answer would be
-35a^5b^5c^5
Hope this helps ;)
The high school tennis team is selling tennis balls to raise $500 for new equipment.They sell the balls for $2 each.
4).How many cases of tennis balls does the tennis team have to sell in order to raise enough money for new equipment.
5).Write and solve the hidden questions you need to answer before finding the answer to exercise 4
There are 24 tennis case and 3 tennis balls in each
Please help me solve this.
Answer:
84 cases
Step-by-step explanation:
The amount of money need to be raised = $ 500
Selling price of each ball = $2
1 Tennis case = 3 balls.
Earnings = Selling Price of each ball x Number of balls sold
Quantity sold = Earnings / Selling Price of each ball
Quantity sold = $ 500 / $ 2 = 250 balls
Using direct proportions
1 case = 3 balls
? cases = 250 balls
No.cases = 250 balls / 3 balls = 83.333
Note: Minimum number of cases required are 83.3333 to earn $ 500; however, we can not sell 0.3333 number of cases, hence, we will sell atleast 84 cases.
Which of the following is an example of a function?
O {(3, 4), (4, 8), (6, 6), (7, 10)}
O {(0, 2), (1, -4), (1, -3), (3, 6)}
O {-1, 4), (0, 3), (0, -2)}
{(5, 7), (6,8), (6,9), (7, 10)}
Answer:
{(3, 4), (4, 8), (6, 6), (7, 10)}
Step-by-step explanation:
Only the first one is a function because the others have repeated x values in some of the ordered pairs.
For example, {-1, 4), (0, 3), (0, -2)} has a repeated x = 0.
How far did you drive if you drove 2 hours at 55 miles per hour and 3 hours at 60 miles per hour?
Answer:
290 miles.
Step-by-step explanation:
To answer this, first multiply the hours by miles. 2 hours at 55 miles per hour means a total of 110 miles. 3 hours at 60 miles per hour means a total of 180 miles. Therefore, 110 + 180 = 290, so you drive 290 miles.
Answer:
Step-by-step explanation:
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION???
A typical traffic signal is programmed on a timer so that it is red 50% of the time, green 42% of the time, and yellow 8% of the time. The bulbs for each color are LED and are designed to last 100,000 hours. How many years does each color light last? Give your answer in years and months (rounded to the nearest month). What is the problem asking? What do we know? How did you solve the problem? Explain your steps.
Please answer this question for me
Answer:
The complete answer is explained below.
Step-by-step explanation:
The problem is demanding to simply determine the number of years each color light would last.
We know the following information from the question:
As it is clear that a red light remains TURNED ON 50% of the time.Green remains TURNED ON 42% of the timeYellow remains TURNED ON 8% of the time.Also the bulbs for each color are LED and are designed to last 100,000 hours. So, each light does last 100,000 hours.
lets make conversions
As
[tex]1\:day\:=\:24\:hours[/tex]
[tex]1\:year\:=\:365\:days[/tex]
Dividing [tex]100,000[/tex] hours by [tex]24[/tex] hours would bring [tex]4166.67[/tex] days
Dividing [tex]4166.67[/tex] days by [tex]365[/tex] days would bring [tex]11.4[/tex] years, meaning 11 years and 4 months.
Keywords: light, conversion, day, hours
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When constructing a graph that compares the land areas of the five largest countries, you choose to depict the five areas with squares of different
sizes. If the squares are drawn so that the areas are in proportion to the areas of the corresponding countries, is the resulting graph valid? Why or why
not?
The resulting graph is valid as it uses the concept of area scaling, where the area of each square accurately represents the relative land sizes of the different countries.
Explanation:Yes, the resulting graph is valid. This is because a proportional representation by different-sized squares aligns with the principle of area scaling. Area scaling is a mathematical concept where each length is scaled by a particular factor and the area will scale by the square of that factor. If the areas of the countries are correctly scaled to the squares, then the graph accurately represents the relative sizes of the land areas of the five largest countries.
For example, if country A is twice as big as country B, the square representing country A should have an area that is four times (2^2) the area of the square representing country B. Vice versa, if country C is half the size of country D, the square for country C should have an area that is a quarter of the square for country D. Therefore, through area scaling, each country will be proportionately represented on the graph.
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A group of students rolled two number cubes 107 times and recorded a sum of seven 10 times. Find the experimental probability of rolling a sum of seven. Write your answer with a % sign without any spaces rounded to the nearest percent. x
Probability is the calculation of = (desired outcomes/total outcomes)
therefore,10/107).
If m varies directly with n.
and m = 20 when n = 5.
what is it m= 18?
The equation d = rt relates distance, rate, and time. A turtle walked 400 feet
in 10 minutes. What was the turtle's speed?
Answer:
Step-by-step explanation:
d = rt....and just so you know, speed is the same as rate
since we are looking for r, I am gonna change the equation
d = rt......r = d / t
d = 400
t = 10
now sub
r = d / t
r = 400/10
r = 40 ft per minute <=====
Answer: 40 per minute
Step-by-step explanation:
A cone has a radius of 1.2 and a height of 2.9 inches. What is the volume, to the nearest tenth of a cubic inch, of the cone?. Explain or show ur work?
A. 3.6
B. 4.4
C. 10.6
D. 13.1
Answer:
4.4 cubic inches
Step-by-step explanation:
From the question;
Radius of the cone is 1.2 inchesHeight of the cone is 2.9 inchesWe are required to determine the volume of a cone;
Volume of a cone is given by the formula;
V=1/3πr²h
Therefore; taking π to be 3.142
Volume =1/3 × 3.142 × 1.2² × 2.9
= 4.373664
= 4.4 cubic inches (to the nearest tenth)
Thus, the volume of a cone is 4.4 cubic inches
Solve each word problem using a system of equations. Use substitution or elimination.
1. One number added to three times another number is 24. Five times the first number added to
three times the other number is 36. Find the numbers.
Answer:
Step-by-step explanation:
x + 3y = 24.....multiply by -1
5x + 3y = 36
------------------
-x - 3y = -24 (result of multiplying by -1)
5x + 3y = 36
------------------add
4x = 12
x = 12/4
x = 3 <=======
x + 3y = 24
3 + 3y = 24
3y = 24 - 3
3y = 21
y = 21/3
y = 7 <========
Final answer:
To solve the system of equations for the given word problem, define two variables and set up two equations. Use the substitution or elimination method to find the solution. The numbers are 3 and 7, and this solution is confirmed by substituting the values back into the original equations.
Explanation:
To solve the given word problem using a system of equations, we can define two variables for the two numbers we are looking for. Let's call the first number x and the second number y. Now we can formulate two equations based on the information provided:
One number added to three times another number is 24: x + 3y = 24
Five times the first number added to three times the other number is 36: 5x + 3y = 36
We can choose substitution or elimination method to solve these simultaneous linear equations. To use the substitution method, we start by solving the first equation for x (x = 24 - 3y) and then substitute this expression into the second equation:
Solve for x in the first equation: x = 24 - 3y
Substitute x into the second equation: 5(24 - 3y) + 3y = 36
Expand and simplify: 120 - 15y + 3y = 36
Solve for y: -12y = -84
Divide by -12: y = 7
Substitute y back into x = 24 - 3y to find x: x = 24 - 3(7)
Calculate x: x = 3
So the two numbers are 3 and 7.
As a check, we can substitute these values back into the original equations to verify that they lead to identities:
3 + 3(7) = 24, which simplifies to 24 = 24
5(3) + 3(7) = 36, which simplifies to 36 = 36
This confirms our solution is correct.
WILL MARK THE CORRECT ANSWER BRAINLIEST!
Select all the correct answers:
Answer:
B, D
Step-by-step explanation:
Solve all equations:
A.
[tex]x-3x=-2x+4\\ \\-2x=-2x+4\\ \\0=4[/tex]
This is false equality, so this equation has no solutions.
B.
[tex]x-\dfrac{1}{3}(3x)=0\\ \\x-x=0\\ \\0=0[/tex]
This equality is true for all values of x, so this equation has infinitely many solutions.
C.
[tex]\dfrac{1}{3}x-3=4+2x\\ \\x-9=12+6x\\ \\x-6x=12+9\\ \\-5x=21\\ \\x=-\dfrac{21}{5}[/tex]
This equation has the unique solution.
D.
[tex]3x+2-\dfrac{1}{3}(3x)=2+2x\\ \\9x+6-3x=6+6x\\ \\6x+6=6+6x\\ \\0=0[/tex]
This equality is true for all values of x, so this equation has infinitely many solutions.
E.
[tex]x-\dfrac{1}{3}x+2=0\\ \\3x-x+6=0\\ \\2x=-6\\ \\x=-3[/tex]
This equation has the unique solution.
three sets of the sum of a number and four are added to the sum of seven times the same number and thirteen
The algebraic expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)
Solution:
Given the statement:
Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen
Let us first understand the given statement,
Let the number be "x"
" sum of a number and four" means x + 4
"Three sets of a sum of a number and four" translated to 3(x + 4)
"sum of seven times the same number and thirteen" means 7x + 13
Thus the algebraic expression for given statement is:
[tex]3(x+4)+(7x + 13)[/tex]
Using distributive property in above expression
[tex]a(b+c) = ab + bc[/tex]
Therefore,
[tex]3(x+4)+(7x + 13) = 3x + 12 + 7x + 13[/tex]
Combine the like terms
[tex]3(x+4)+(7x + 13) = 10x+25[/tex]
Thus the required expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)
Find the sum of these polynomials.
(х2 +х+ 9) + (7х2 + 5) =
А. 7х2+x+ 14
7х2+x+4
оооо
Ос. 8х2 +х+4
OD. 8х2+x+ 14
SUBMIT
[tex]\text{The sum of given polynomials is } 8x^2+x+14[/tex]
Solution:
Given given expression to calculate is:
[tex](x^2+x+9) + (7x^2+5)[/tex]
We have to add both the polynomials
Addition of two polynomials involves combining like terms present in the two polynomials
We have to add like terms
Like terms means "the terms having same variable and same exponent"
And we have to add the constants
[tex]\rightarrow (x^2+x+9) + (7x^2+5)\\\\\text{Remove the parenthesis and simplify }\\\\\rightarrow x^2 + x + 9 + 7x^2 + 5\\\\\text{Combine the like terms }\\\\\rightarrow x^2 + 7x^2 + x + 9 + 5\\\\\text{Add the coefficients of like terms }\\\\\rightarrow 8x^2 + x + 9 + 5\\\\\text{Add the constants 9 and 5 }\\\\\rightarrow 8x^2 + x + 14[/tex]
Thus the polynomials are added
Four times a number decreased by seven
which value of the variable is the solution of the equation a+$5.92=$12.29? a=$5.37,$5.47,$6.37,$6.27
Answer:
Option a=$6.37 is correct
The value of the variable is the solution of the given equation is a=$6.37
Step-by-step explanation:
Given equation is a+$5.92=$12.29
To find the value of the variable is the solution of the given equation :
a+$5.92=$12.29
Subracting the above equation by $12.29 on both sides we get
a+$5.92-$12.29=$12.29-$12.29 ( Subtraction property of equality)
a-$6.37=0
Now add $6.37 on both sides we get
a-$6.37+$6.37=0+$6.37 ( Addition property of equality)
a-0=$6.37
Therefore a=$6.37
Therefore option a=$6.37 is correct
Answer:
3rd answer is correct, $6.37
Step-by-step explanation:
Rewrite m+3n=7 to solve for m
Interest earned: $3250 principal: $5000 Interest rate: ? Time: 10 years Please HELP ME! :0 20 points
Answer: Interest rate = 0.065
Step-by-step explanation:
I=PRT
3250=5000r*10
Divide by 10 on both sides
325=5000r
r=0.065
Could someone help me understand how to solve this?
Answer:
Amount in 4% account: $550
Step-by-step explanation:
Use simple interest formula [tex]I=P\cdot r\cdot t,[/tex] where
I = interest
P = principal
r = rate (as decimal)
t = time.
4% account:
[tex]P_1=x\\ \\r_1=0.04\\ \\t_1=1,[/tex]
then
[tex]I_1=x\cdot 0.04\cdot 1=0.04x[/tex]
5% account:
[tex]P_2=1,500-x\\ \\r_2=0.05\\ \\t_2=1,[/tex]
then
[tex]I_2=(1,500-x)\cdot 0.05\cdot 1=0.05(1,500-x)[/tex]
You have earned $69.50 in total, so
[tex]I_1+I_2=69.50\\ \\0.04x+0.05(1,500-x)=69.50\\ \\4x+5(1,500-x)=6,950\\ \\4x+7,500-5x=6,950\\ \\4x-5x=6,950-7,500\\ \\-x=-550\\ \\x=550\\ \\1,500-x=1,500-550=950[/tex]
Amount in 4% account: $550
Amount in 5% account: $950