The polynomial 9x^2 + 4 is equivalent to (3x+2i)(3x-2i). The answer is A.
Polynomials are algebraic expressions that consist of variables and coefficients where arithmetic operations can be performed.
A polynomial is expanded if no variable appears within parentheses and all like terms have been combined.
To expand a polynomial, multiply its factors (often by using the distributive property) or perform the indicated operations. Then combine all like terms.
Expanding each of the options provided using FOIL method:
a) (3x+2i)(3x-2i)
= 9x^2 - 2ix + 2ix - 4i^2
= 9x^2 - 4i^2 *(i^2 = -1) note that i is an imaginary number and i squared is equal to -1
= 9x^2 - 4(-1)
= 9x^2 + 4
b) (3x+2)(3x-2)
= 9x^2 + 6x - 6x - 4
= 9x^2 - 4
c) (3x + 2i)^2
= 9x^2 + 6ix + 6ix + 4i^2 *(i^2 = -1)
= 9x^2 + 12ix - 4
d) (3x + 2)^2
= 9x^2 + 6x + 6x + 4
= 9x^2 + 12x + 4
Hence, the polynomial 9x^2 + 4 is equivalent to (3x+2i)(3x-2i). The answer is A.
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Solve this with steps in standard form.
8y - 12 =3x
Answer:
3x - 8y = -12
Step-by-step explanation:
Standard form is:
[tex]Ax + By = C[/tex]
-------------------------------------------
[tex]8y - 12 = 3x\\\rule{150}{0.5}\\8y - 8y -12 =3x - 8y\\\\-12 = 3x-8y\\\\\boxed{3x - 8y = -12}[/tex]
--------------------------------------------
A graph is attached. Hope this helps!
a2- 3x -10 please solve this what will be the factor of it
The factors of the equation is (x - 5) (x + 2).
Given the equation is x²-3x-10
we are asked to factorize the equation.
Factorization is the process of identifying two or more expressions whose product is an algebraic expression. It is often referred to as finding the factors of an expression. Finding two or more expressions whose product is the given expression—known as factorization—is the process of breaking down algebraic expressions. A factor is any number that divides the given number by itself without leaving any remainder. It simply implies representing a number as the product of two other integers.
x²-3x-10
x² - 5x + 2x - 10
x(x - 5) + 2(x - 5)
(x - 5) (x + 2)
Thus, the factorization of the given expression x²-3x-10
= (x - 5) (x + 2)
Hence we get the factors as (x - 5) (x + 2)
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Answer:
To factor the quadratic expression a2 - 3x - 10, we need to find two numbers that multiply to give -10 and add to give -3. These numbers are -5 and 2. Therefore, we can write:
a2 - 3x - 10 = (a - 5)(a + 2)
So the factors of the quadratic expression a2 - 3x - 10 are (a - 5) and (a + 2).
a study concluded that following 7 simple health rules can extend a man's life by 11 years on the average and a woman's life by 7 years. these 7 rules are as follows: no smoking, get regular exercise, use alcohol only in moderation, get 7 to 8 hours of sleep, maintain proper weight, eat breakfast, and do not eat between meals. in how many ways can a person adopt 5 of these rules to follow
There are total 35 such ways in which a person can adopt rules.
What are combinations?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
According to the question, we are Given,
Total rules = 7
No of rules a person can adopt = 5
using combinations,
= ⁷C₅
= 7! / 5! (7 - 5)!
= 7! / 5! 2!
= 35
So a person can choose it in 35 possible ways.
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Ava can clean 6 apartments in 4 hours. At this rate, how long will it take Ava to clean 9
apartments?
Answer: 6 hours
Step-by-step explanation: 6 apartments divided by 2 is 3 apartments and 4 hours divided by 2 is 2 hours. 3 apartments per 2 hours. So, 3/2 x 3/3 is 9/6 which is 9 apartments for 6 hours.
Your friend Alex has won a scholarship to study abroad. (Congratulations!) Alex has only 8 weeks to earn enough money to buy a plane ticket, and he wants to work at an amusement park over the summer to achieve this goal.
Tech intership
Schedule- Part Time (20hours/week)
Wage- 11.50/hour
Amusement park attendant
Schedule- full time (40hours/week)
Wage - 9/hour+ 100 bonus
8 weeks to buy airplane ticket $2200
Please help with the table
The formula for calculating Alex's earnings from his employment at the theme park is 8(40 x 9 + 100) = 8(360 + 100) = 8(460) = $3,680.
Given: that the plane ticket costs $2,200 and that y = 11.5x gives the function that represents the potential earnings Alex may make from the tech internship, the inequality that reflects the maximum number of hours Alex can work at the internship follows.
He puts in 20 hours every week at the internship, which translates to 160 hours of work over the course of 8 weeks.
Given that the internship pays $11.5 an hour for 160 hours, her earnings of 11.5 x 160 = $1,840 will not be sufficient to cover the cost of the plane ticket.
A few of the theme park employment that are available in this sector include costume character work, ride technician, admissions attendant, lifeguard, and gaming attendant. Workers at concession stands must be swift to prevent long queues and receive cash for food and drinks.
Hence, Alex's employment at the internship will not generate enough income to pay for the ticket.
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hi does anyone know whats this?? Or this?? Thank you for helping.
Answer:
1) [tex]\frac{51}{2}[/tex] 2) [tex]\frac{55}{12}[/tex]
Step-by-step explanation:
Answer: I simplify the answer for u my friened 25.5
WORTH 20 POINTS!!!!!!!!! PLEASE HELP SCREENSHOTS ATTACHED DO ALL OF THEM PLEASE
1. The value of x is 14°
2. The value of x is 23°
3. The value of x is 22.5°
Calculating anglesFrom the question, we are to determine the value of x in the given diagrams.
1.
∠ CBA = 180° - 6x (Linear pair theorem)
and
m ∠BAC + m ∠CBA = m ∠FCB (Exterior angle theorem)
Thus,
2x + 180° - 6x = 124°
180° - 4x = 124°
180° - 124° = 4x
56° = 4x
x = 56/4
x = 14°
Hence, the value of x is 14°
2.
m ∠ABE = 4x (Alternate angles theorem)
m ∠ABD + m ∠ABE + m ∠EBF = 180° (Sum of angles on a straight line)
x + 4x + 65° = 180°
x + 4x = 180° - 65°
5x = 115°
x = 115°/5
x = 23°
Hence, the value of x is 23°
3.
m ∠EAB = 2x (Vertical angles theorem)
m ∠AEB = 180° - 4x (Linear pair theorem)
m ∠ABE = 180° - 6x (Linear pair theorem)
m ∠EAB + m ∠AEB + m ∠ABE = 180° (Sum of angles in a triangle)
Thus,
2x + 180° - 4x + 180° - 6x = 180°
180° + 180° - 180° = 6x + 4x -2x
180° = 8x
x = 180°/8
x = 22.5°
Hence, the value of x is 22.5°
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
(Please help)
For the data set {11, 13, 15, 15, 16, 17, 18, 19, 19, 20}, which is greater, the mean or the median?
Answer:
Median
Step-by-step explanation:
Median: (16+17)/2= 16.5
Mean: 11+13+15+15+16+17+18+19+19+20= 163
163/10= 16.3
Median is greater.
Please help me with this question!!
The statement that is true about the segment connecting points B and C is D. The segment has a finite length that can be measured.
What is a segment?It should be noted that ieometry, a line segment is the part of a straight line bounded by two distinct end points, and contains every point on the line that is between its endpoints.
It should be noted that the length of a line segment is given by the Euclidean distance between its endpoints.
Therefore, in this case, the statement that is true about the segment connecting points B and C is that the segment has a finite length that can be measured.
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an envelope contains eight bills: two $ 1 bills, two $ 5 bills, two $ 10 bills, and two $ 20 bills. two bills are drawn at random without replacement. what is the probability that their sum is $ 20 or more? (a) 1 4 (b) 2 5 (c) 3 7 (d) 1 2 (e) 2 3
Probability is nothing but the ratio of favorable cases to all possible cases or in simple terms it is the ratio of sample set to all set
We are required to find all the cases in which sum of any two bills is 20$ or more
The total number of bills are two $ 1 bills, two $ 5 bills, two $ 10 bills, and two $ 20 bills.
The total case of drawing any two bills will be =
2 for $ 1 bill x two for 5$ bill x two for 10$ bill x two 20$ bills
=2 x 2x2x2 =16
Hence 16 ways in which two bills can be drawn at random
Cases in which bill can be greater than 20$= (1,20)(20,1)(5,20)(20,5)(10,10)(20,10)(10,20) (20,20)= 8 cases
Hence, total number of possible outcomes = 8
Hence the probability of bill to be 20$ or more= favorable outcome/total outcome
=8/16 =1/2
Hence the probability is 1/2
Disclaimer: the fraction sign is missing in question options
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Please Answer the question in photo [ Brainliest + points ]
Answer:
72
Step-by-step explanation:
Step-by-step explanation:
QC = Qu + UC
Qu= 22
Uc= 70
QC= 22 + 70
QC = 92
Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until
she is finished. Write and solve a linear equation to find the total number of pages
months.
at 5
Answer:
f(x) = 12x+35
f(5) = 95 pages written at 5 months
Step-by-step explanation:
Step 1: write the slope intercept equation
f(x) = mx+b
f(x) = the value of the equation at month x
m = slope of the linear equation (pages written PER month)
x = the month
b = intercept of the equation (pages already written)
Step 2: relate given information to the variables
m = 12 pages per month
b = 35 pages already written
Step 3: update equation
f(x) = 12x+35
Step 4: solve for x = 5 months
f(5) = 12(5) + 35 = 60 + 35 = 95
Josie took a long multiple-choice, end of the year vocabulary test. The ratio of the number of problems Josie got incorrect to the number of problems she got correct is 2:9. If Josie missed 20 questions, how many did she get correct?
Hence she got 90 correct answer.
How many did she get correct?
Ratio of the number of problems she got incorrect to the number of problems she got correct = 2:9
Number of incorrect answers = 8
Let the number of incorrect answers be 2x
Let the number of correct answers be 9x.
So, According to question, we get that
[tex]2x = 20\\ x =\frac{20}{2} \\ x = 10[/tex]
So, the number of correct answers would be
[tex]9x = 9\times 10\\\\ =90[/tex]
Hence she got 90 correct answer.
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please help with this question, thank you!!
Answer:
2.1 cm (nearest tenth)
Step-by-step explanation:
The radius (r) of a circle is the distance between its center and its circumference. Therefore, from inspection of the given circle:
⇒ r = OX = OY = OA
Given:
AB = 3.5 cmOA = r⇒ AB = OA + OB
⇒ 3.5 = r + OB
⇒ OB = 3.5 - r
As OX = OY and AB is perpendicular to XY then XB = BY.
As XY = 3 cm:
⇒ XB = BY = 1.5 cm
Therefore, for ΔOBX:
Leg a = OB = (3.5 - r) cmLeg b = XB = 1.5 cmHypotenuse = OX = r cmPythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.Use Pythagoras Theorem and the defined sides of ΔOBX to find r:
[tex]\implies OB^2+XB^2=OX^2[/tex]
[tex]\implies (3.5-r)^2+1.5^2=r^2[/tex]
[tex]\implies 12.25-7r+r^2+2.25=r^2[/tex]
[tex]\implies 14.5-7r+r^2=r^2[/tex]
[tex]\implies 14.5-7r+r^2-r^2=r^2-r^2[/tex]
[tex]\implies 14.5-7r=0[/tex]
[tex]\implies 14.5=7r[/tex]
[tex]\implies 7r=14.5[/tex]
[tex]\implies \dfrac{7r}{7}=\dfrac{14.5}{7}[/tex]
[tex]\implies r=2.07142857...\: \sf cm[/tex]
Therefore, the radius of the circle is 2.1 cm (nearest tenth).
What technique do researchers use to reduce the impact of confounding variables?.
The technique researchers use to reduce the impact of confounding variables is randomization.
What are confounding variables?
Confounding variables are variables that affects or influences both the dependent and independent variable.
Some techniques used to reduce this influence are;
Statistical controlRestriction of valuesRandomizationMatchingThe most effective way of reducing the impact of confounding variables is the conduction of random trials.
Thus, the technique researchers use to reduce the impact of confounding variables is randomization.
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does anyone know this? this is 8th grade math. (eureka math squared)
Solutions of given exponents are :
1. [tex]9^{18}[/tex] 2. [tex]16x^4[/tex] 3. [tex]\frac{6561}{y^2}[/tex]
What are exponents ?In, mathematics a exponent or exponential equation or exponential function is inverse of a logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The shows the behavior of something to the power of something. The basic form of the exponential can be written as [tex]a^x[/tex]
where, a = the base of function
x = exponential
Important properties of exponential :
[tex](a^n)^m = a^{nm}[/tex][tex](ab)^n = a^n.b^n[/tex][tex](\frac{a}{b})^n = \frac{a^n}{b^n}[/tex][tex]a^0=1[/tex][tex]a^1=a[/tex]According to the question,
1. given, [tex](9^{3})^6[/tex]
use the property, [tex](a^n)^m = a^{nm}[/tex]
[tex](9^{3})^6[/tex] = [tex]9^{3.6} = 9^{18}[/tex]
2. Given, [tex](2x)^4[/tex]
use the property, [tex](ab)^n = a^n.b^n[/tex]
[tex](2x)^4[/tex] = [tex]2^4.x^4 = 16x^4[/tex]
3. Given , [tex](\frac{3^4}{y}) ^{2}[/tex]
use the property, [tex](\frac{a}{b})^n = \frac{a^n}{b^n}[/tex]
[tex](\frac{3^4}{y}) ^{2}[/tex] = [tex]\frac{(3^4)^2}{y^2}[/tex]
now use , [tex](a^n)^m = a^{nm}[/tex]
= [tex]\frac{3^8}{y^2} = \frac{6561}{y^2}[/tex]
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Please help me as soon as possible major grade due today
Answer:
51/8
Step-by-step explanation:
each bracelet length as a fraction will be 51/8 inches if the artist uses the 51 inches of the string to make 8 bracelets
Express the number 78.263 using ones, tenths, and thousandths.
The number 78.263 using ones, tenths, and thousandths means
8 = ones2 = tenth3 = thousandthsPlace valueThis is the value of each digits based on its position in a number.
It is divided into whole number part and fractional part.
Whole number part:
Hundred thousandTen thousandThousandHundredTensOnesFractional part:
TenthsHundredthThousandthsTen thousandthsHundred thousandths78.263
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City A and City B are 312
miles apart. John leaves City B, driving towards City A at an average rate of 80
miles per hour. Pat leaves City A at the same time, driving towards City B in her antique auto, averaging 24
miles per hour. How long will it take them to meet?
Pat and John will meet in 3 hours.
How to calculate the value?It should be noted that speed = Distance / Time
The appropriate equation will be:
80t + 24t = 312
104t = 312
t = 312/104
t = 3. hours
Therefore, it will take them 3 hours to meet.
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please help me with this 6x^(2)+4x+3*y + 6y + y^(2)
hi
A = 6x^(2)+4x+3*y + 6y + y^(2)
A= 6x²+y²+4x+9y
PLEASE HELP ASAP
R is the midpoint of HS. N is the midpoint of RS and RN=5cm. What is the length of HS
Answer: 20 cm
Step-by-step explanation: if the length of R-N= 5cm therefore you multiply 5 by each dot so H-O is 5 cm, H-R is 10 cm, H-N is 15 cm, and H-S is 20 cm.
can someone help me please
Answer:
1. A, 450 = 2(p+w); 450 = 3(p-w)
2. A, 2 units
3. D, Between step 6 and step 7
Step-by-step explanation:
1. This one is confusing on first glance.
[tex]450 = 2(p+w); 450 = 3(p-w)[/tex] Lets break down this equation.
[tex]2(p+w)[/tex] means, the plane speed, plus the windspeed, will take 2 hours to travel 450 KM. The reason we add the plane speed and the windspeed is because we have a tailwind instead of a headwind, the wind is pushing us forward, adding to the planes speed.
[tex]3(p-w)[/tex] means, the plane speed, minus the windspeed, will take 3 hours to travel 450 KM. We subtract the wind speed from the plan speed because the wind is a headwind, it's pushing us backwards, taking away from the planes speed.
----------------------------------------------------------------------------------------------------------
2. Let set these up as two-sided equations.
[tex](6x+3) + (4x) + (2x + 1) = (5x) + (5x) + (3x+2)[/tex]
Combine like terms
[tex]12x + 4 = 13x + 2[/tex]
Subtract 12x from both sides
[tex]4 = 1x + 2[/tex]
Subtract 2 from both sides
2 = 1x, or x = 2.
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3. Take a look at step 6. You want to get x by itself, to do that, and get rid of the 8, you'd divide both sides by 8 to get [tex]x = -\frac{15}{4}[/tex]
shane made a scale drawing of a hotel. a room in the hotel, which is 18 feet wide in real life, is 51 inches wide in the drawing. what is the scale of the drawing?
The scale of the drawing is 6 feet = 17 inches
Scaling is the process of increasing or reducing the size of a figure by a factor k.
In the given statement is:
Shane made a scale drawing of a hotel. a room in the hotel, which is 18 feet wide in real life, is 51 inches wide in the drawing.
A figure which is 18 feet wide in real life, is 51 inches wide in the drawing, hence the scale is:
Now, According to the question is
18 feet = 51 inches
Divide both sides by 3:
6 feet = 17 inches
Therefore, the scale of the drawing is 6 feet = 17 inches
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Decimal equivalent to 2/5
Answer:
0.4
Step-b0.y-step explanation:
The volume of a cuboid having health is double of the height and length is triple of the height is 1296 cm ³ find the area of base.
The area of the base is 216 cm².
The volume of a cuboid is 1296 cm³.
The breadth of the cuboid is double the height of the cuboid and the length of the cuboid is triple the height of the cuboid.
Let the length, breadth, and height of the cuboid be l, b, and h respectively.
Then,
l = 3(h)
b = 2(h)
The volume of a cuboid is given as:
V = l × b × h
1296 = 3(h) × 2(h) × h
1296 = 6 × h³
h³ = 1296 / 6
h³ = 216
h = ∛216
h = ∛(6)³
h = 6 cm
Therefore, the length of the b is l = 3(h) = 3 × 6 = 18 cm
The breadth of the cuboid will be:
b = 2(h)
b = 2 × 6
b = 18 cm
Now the volume of the cuboid is also given as:
Volume = base area of cuboid × height
1296 = base area × 6
base area = 216 cm²
The base area is 216 cm².
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when 10 candles are sold, the store makes a profit of $7. when 15 candles are sold, the store makes a profit of $12. when 20 candles are sold, the store makes a profit of $17. write an equation to describe the relationship between the profit, y, and the number of candles sold, x.
The equation which describe the relationship between the profit, y, and the number of candles sold, x is x - y = 3.
Given that:-
When 10 candles are sold, the store makes a profit of $7.
When 15 candles are sold, the store makes a profit of $12.
When 20 candles are sold, the store makes a profit of $17.
We have to write an equation which describe the relationship between the profit, y, and the number of candles sold, x.
As we can observe from the given data,
number of candles sold - 3 = profit (in $)
Hence, we can write,
x - 3 = y
x - y = 3.
Where,
x represents the number of candles sold and,
y represents the profit
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a container with 3 1/2 gallons of weed killer can spray 2 1/4 lawns. how many gallons would it take to spray 2 lawns
To spray on 2 lawns is required [tex]3\frac{1}{9}[/tex] gallons.
Mixed fraction A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given ;
A container with [tex]3\frac{1}{2}[/tex] gallons of weed killer can spray = [tex]2\frac{1}{4}[/tex] lawans
∵ in [tex]\frac{9}{4}[/tex] lawn the week killer can spray = [tex]\frac{7}{2}[/tex]gallons
∴ in 1 lawn the weed killer is used = [tex]\frac{7}{2}[/tex] × [tex]\frac{4}{9}[/tex] gallon
∴ in 2 lawns the weed killer can spray =[tex]\frac{7}{2}[/tex] × [tex]\frac{4}{9}[/tex]× 2 =[tex]\frac{28}{9}[/tex] gallon =[tex]3\frac{1}{9}[/tex]gallons
[tex]3\frac{1}{9}[/tex] gallons require to spray 2 lawns.
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Evaluate g(x)=x−13 over the domain {2,4,6,8}. What is the range of g(x)?
The range of the function is {-11, -9, -7, -5}.
The given function is g(x)=x−13.
We need to find the range of g(x).
What is the range and domain of the function?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
Now, put x=2,4,6,8 in the given function and find the range of function.
So, g(2)=2−13=-11
g(4)=4−13=-9
g(6)=6−13=-7
g(8)=8−13=-5
Therefore, the range of the function is {-11, -9, -7, -5}.
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