The roots of the Quadratic Equation are
(2 + i√26)/3 and (2 - i√26)/3
Given, a quadratic equation i.e. 3x² + 10 = 4x
On simplifying, we get
3x² - 4x + 10 = 0
while checking the discriminant of the given quadratic equation, we get
D = b² - 4ac
D = (-4)² - 4(3)(10)
D = 16 -120
D = -104
i.e. D < 0.
So, the quadratic equation has imaginary roots
On applying quadratic formula, we get
x = (4 ± √(-104))/6
x = (4 ± i2√26)/6
x = (2 ± i√26)/3
Hence, the roots of the Quadratic Equation are
(2 + i√26)/3 and (2 - i√26)/3
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Please answer both questions:
A container holds 5 pounds of peanuts. How many ounces of peanuts are in the container? (1 pound = 16 ounces)
Ronnie had 64 at-bat opportunities to hit the ball this spring season in baseball. He hit the ball 75% of the time. How many times did Ronnie hit the ball?
Answer:
Ounces of peanuts in the container
= 5 pounds × 16 ounces
= 80 ounces
Number of times Ronnie hit the ball
= 75% × 64 at-bat opportunities
= 48 times
Can someone help me I have to verify the trig identities.
The trigonometric identities are verified that they are true.
What are trigonometric expressions?
Trigonometric identities are, by definition, reciprocal. These formulas show the connections between the sine/cosine functions and tangents.
1. LHS = sec x [ sec x - cos x]+(sin x+ cos x)/sin x- cot x
= sec²x - sec x cos x +(sin x+ cos x)/sin x - cos x/sin x
= sec²x - cos x/cos x +(sin x+ cos x- cos x)/sin x
= sec²x - 1 + sin x /sin x
= sec²x - 1 +1
= sec²x
= RHS
2. LHS = cos (π-Θ)+ sin (π/2 + Θ)
= - cos Θ + cos Θ
= 0
= RHS
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DUE TOMORROW HELP PLEASE :)
Answer:
54°
Step-by-step explanation:
These are supplemental angles. Supplemental angles add to 180
180-126 = 54
What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
The range of this function f(x) = 3x + 9 is: B. {y | y > 9}.
What is a range?In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.
This ultimately implies that, a range simply refers to the set of all possible output numerical values (real numbers), which are shown on the y-coordinate (y-axis) of a graph.
Based on the given function f(x) = 3x + 9, we can reasonably infer and logically deduce that the range of this function in interval notation is given by:
Range = [10, ∞]
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a water droplet has volume of 0.1cubic cm. convert the volume of the droplet to cubic meters. (1m=100cm)
The volume of the droplets in cubic meters would be = 1×10^-7 cubic meters.
What is water droplets?Water droplets can be defined as the formation of small ball like structures with water due to the action of surface tension of liquid.
To convert cubic centimetres to cubic meters the following is carried out;
1 cubic meter = 1,000,000 cubic centimetres.
X cubic meters = 0.1 cubic centimetres
Make X cubic centimetres the subject of formula;
X cubic meters = 0.1× 1/1,000,000
X cubic meters = 1×10^-7.
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ryan paid $133 for 7 pizzas. how much would he have paid for 88 pizzas
Answer: 1672
Step-by-step explanation:
133 divided by 7 = 19
19 x 88 = 1672
The table above shows four numeric expressions. Which expression is an integer when it's evaluated?
Question 9 options:
A)
E
B)
H
C)
G
D)
F
The expression G is an integer when it's evaluated.
What is an integer?
A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8
Negative numbers and all entire numbers are both considered integers. Accordingly, a set of integers can be formed by adding negative numbers as well as whole numbers.
Consider 9+(-3).
9+(-3)
Remove parenthesis
=9-3 = 6
6 is an integer.
So, the expression G is an integer when it's evaluated.
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4x + 5 + 3x - x = 7x - 8
Answer:
x = -1
Step-by-step explanation:
6x +5 = -7x - 8
6x +7x = -8 -5
13x = -13
13/13 x = -13/13
x = -1
subtract the sum of 9t*3-3t+8 and t*2-8t+4 from the sum of 12t+8 and t*2 - 10t +3.
Answer:
[tex]-9t^3+13t-1[/tex]
Step-by-step explanation:
Answer is attached.
in the exponential function g(x)=a(b)^x it is known that g(3)=25 and g(7)=3
By solving a system of equations we will see that the exponential function is:
g(x) = 122.347*(0.589)^x
How to find the exponential function?We know that our function is of the form:
g(x) = a*(b)^x
We also know that g(3)=25 and g(7)=3, then we can write:
a*(b)^3 = 25
a*(b)^7 = 3
So we have a little system of equations.
Taking the quotient between the second and first equations we get:
(a*(b)^7)/(a*(b)^3) = 3/25
b^4 = 3/25
b = (3/25)^(1/4) = 0.589
Replacing that in the first equation we get:
a*(b)^3 = 25
a*(0.589)^3 = 25
a = 25/(0.589)^3 = 122.347
The exponential function is:
g(x) = 122.347*(0.589)^x
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Darbi and Su had sushi for lunch Su's Sushi was $2 more than Darbi sushi. Darbi and Su split the cost of the sushi lunch evenly and each paid at 20% tip if the cost of Su's sushi is represented by s, which of the following expressions represents the amount in dollars that each paid?
a)1.2s-1.2
b)1.8s
c)2.4s-2.4
d)0.2s-0.2
The expression that represents the amount in dollars that each paid is (a) 1.2s - 1.2.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, Su's Sushi is $2 more than Darbi sushi and the cost of Su's sushi is represented by s.
Let the price of Darbi's sushi is $x.
Then, the price of Su's sushi is
s = x + 2
x = s -2
The total cost is:
x + s
= s -2 + s
= 2s -2
Since they divided the total cost evenly, the cost each paid is:
(2s-2)/2
= s -1
Now, the cost after paying a 20% tip is:
(s - 1) + 20% of (s - 1)
= s- 1 + 20(s-1)/100
= s-1 + 0.2s - 0.2
= 1.2s - 1.2
Hence, the expression that represents the amount in dollars that each paid is (a) 1.2s - 1.2.
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what is the reclusive formula
The recursive formula for the given Explicit formula is a₁ = 16 and aₙ = -90aₙ₋₁ , the correct option is (c) .
In the question ,
an explicit formula for the geometric sequence is given
that is aₙ = 16(-90)ⁿ⁻¹ ,
we know that the general explicit formula for the geometric sequence is given by
aₙ = a₁(r)ⁿ⁻¹
where aₙ is the nth term , r is the common ratio, a₁ is the first term of the sequence .
On comparing the given explicit formula with the general formula ,
we get ,
a₁ = 16
r = -90
So , the recursive formula is a₁ = 16 and aₙ = -90aₙ₋₁ .
Therefore, The recursive formula for the given Explicit formula is a₁ = 16 and aₙ = -90aₙ₋₁ , the correct option is (c) .
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Select the correct answer.
What is the completely factored form of this polynomial?
x³+3x² - 6x-18
O A. (x-2)(x − 3)(x+3)
O B. (x²-6)(x+3)
O C. (x²+3)(x-6)
O D. (x+6)(x - 1)(x+3)
(x² - 6 ) ( x + 3 ) is the completely factored form of this polynomial .
What is polynomial in maths?
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable). Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered.= x³+3x² - 6x-18
= x² ( x + 3 ) - 6( x + 3 )
= (x² - 6 ) ( x + 3 )
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Decide whether the experiment is a binomial experiment. If it is not, explain why. Surveying 900 prisoners to see how many crimes in which they were convicted. The random variable represents the number of crimes in which each prisoner was convicted.
The experiment is a binomial experiment as it had two outcomes which are success and failure.
What is a binomial experiment?A binomial experiment is one that has a fixed number of independent trials with only two outcomes. For example, the outcome could be a yes or no response.
A binomial experiment is a statistical test that has the following characteristics: The experiment consists of n trials that are repeated. Each trial has only two possible outcomes. One of these outcomes is referred to as a success, while the other is referred to as a failure. On each trial, the probability of success, denoted by P, is the same.
Tossing a fair coin n times, for example, with success defined as "heads up":
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What is the range of the equation?
5x + 3y = 30
Answer:
Range is all real numbers.
Interval notation:
Range is
(-infinity,infinity)
Step-by-step explanation:
The range is all the y's on a graph of a function or all of the y's allowed to be used in an equation or able to be produced by the equation.
5x + 3y = 30
is a line. Except for a horizontal line, the range of any line is all real numbers. Somewhere on that line every single y value exists somewhere. You may put literally ANY value for y into that equation.
The range is all real numbers.
How many liters each of a 45% acid solution and a 85% acid solution must be used to produce 40 liters of a 80% acid solution? (Round to two decimal places if necessary.)
You need 5 gallon of the 45% acid solution 35 gallon of the 85% solution to get 40 gallon at 80%.
How to find the number of liters?Let x represent the number of liters
0.45x+0.85(40-x) = 0.8(40)
0.45x+34-0.85x = 32
-0.4x = -2
Divide both sides by -0.4
x = -2/-0.4
x = 5
You need 5 gallon of the 45% acid solution
Gallon of the 85% solution to get 40 gallon at 80% = 40-5 = 35 gallon
Therefore 5 gallon and 35 gallon are needed.
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Which equation demonstrates the distributive property?
A 2 (5+7)=2 (7+5)
B 2 (5+7)=2x5+2x7
C7x (2 × 5) = 7 x (5 × 2)
D(2 x 5) x 7 = 2 × (5 × 7)
Answer:B
Step-by-step explanation:
A: Commutative property because the numbers in the parentheses change
B: Distributive property because you multiply the numbers out.
C: Commutative property because you change the numbers in the parentheses.
D: Associative property you move the parentheses to different numbers.
Malik has a compound interest savings account that she initially deposited $7,550. What is the balance in her account after 2 years if the account paid an annual interest rate of 1.95% and the interest was compounded annually.
The balance (future value) in Malik's account after 2 years of investing $7,550 at 1.95% compounded annually is $7,847.32.
What is the future value?The future value is the compounded present value of an investment or periodic deposit.
The future value can be determined using the FV formula, FV table, or an online finance calculator as below.
N (# of periods) = 2 years
I/Y (Interest per year) = 1.95%
PV (Present Value) = $7,550
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $7,847.32
Total Interest = $297.32
Thus, Malik's account balance (future value) after 2 years will be $7,847.32.
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Find the volume of the figure. Round to the nearest hundredth, if necessary. (figure is not to scale)
The volume of the figure is 296 [tex]ft^{3}[/tex].
Volume of a cuboid = Length * breadth * width
Volume of figure = 4*5*2 + 4*5*2 + 4*18*3
= 40 + 40 + 216
= 296
Hence, the volume is 296 [tex]ft^{3}[/tex].
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x² -2(x-y), for x = 7 and y = 4
The value of given expression for x = 7 and y = 4 is 43
In this question, we have been given an expression x² -2(x - y)
We need to find the value of given expression for x = 7 and y = 4
x² -2(x - y)
= 7² -2(7 - 4)
= 49 - 2(3)
= 49 - 6
= 43
Therefore, the value of given expression for x = 7 and y = 4 is 43
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Guys! What is w+2/3=5 1/4
Answer:
Rewrite the equation as w+ 2/5= 3/4
Move all terms not containing w to the right side of the equation.
so if u do that you should get your answer 7/20
Step-by-step explanation:
Solve this using substitution x=-3y+5
x+9=4y
Answer: x=-1 & y=2
Step-by-step explanation:
x = -3y+5
^^^substitute this equation into x in the second equation
(-3y+5)+9 = 4y
-3y+14 = 4y
Add +3y on both sides
14 = 4y+3y
14 = 7y
divide both sides by 7
y = 2
substitute y into either equation (I'm doing the first one)
x = -3(2)+5
x = -6+5
x = -1
Please help me I will Venmo you I’m confused
Give the guy above me a brainliest!!
the graph shows the average number of days of rainfall per month in Rome, Italy.
in which of the following intervals is the relationship between the month and average number of days of rainfall decreasing? Select all that apply.
A. June to August
B. August to October
C. December to February
D. February to April
In the interval June to August and December to February rainfall decreasing.
What is average number of days?
7 days make up a week, there are roughly 365 days in a year, and there are 24 hours in a day. By adding all of your numbers together and dividing by the total amount of numbers, you can arrive at an average. Thus, 132 is the average amount of time periods when joined together.
From the given graph, in the interval June to August and December to February the average number of days of rainfall are decreasing.
Hence, June to August and December to February rainfall decreasing.
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Does the quadratic function
f(x) = 4x² + 5x – 29 have one,
two, or no real zeros? Utilize the
quadratic formula to determine
the answer.
[?] real zero(s)
The given quadratic function has two real zeros.
We are given a function. The function is quadratic in nature. We need to check whether the given quadratic function has one, two, or no real solutions. We will use the quadratic formula to determine the answer. The equation of the quadratic function is given below.
f(x) = 4x² + 5x - 29
The general form of a quadratic equation is ax² + bx + c. The values of the variables a, b, and c for the given equation are 4, 5, and -29, respectively. The quadratic formula is given below.
x = (-b ± √D)/2a
The variable "D" represents the discriminant of the quadratic equation. If the value of D is less than zero, then no real roots exist. If the value of D is equal to zero, then only one real root exists. If the value of D is greater than zero, then two real roots exist. The formula for discriminant is D = b² - 4*a*c. We will calculate the discriminant for the given equation.
D = b² - 4*a*c
D = 5² - 4*(4)*(-29)
D = 25 + 464 = 489
The value of the discriminant is positive, so the function has two real roots.
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Maru makes an initial down payment of \${3000}
$3000
, then repays \${70}
$70
per week.
Calculate how many weeks it takes Maru to fully pay off $43000.
pls help me with this asap
The number of weeks that it'll take Maru to fully pay off $43000 is 571.4 weeks.
How to calculate the value?From the information, Maru makes an initial down payment of $3000 then repays $70 per week and the total amount is $43000.
Let the number of weeks be represented as w.
This will be illustrated as:
3000 + (70 × w) = 43000
3000 + 70w = 43000
Collect like terms
70w = 43000 - 3000
70w = 40000
Divide
w = 40000 / 70
w = 571.4
The number of weeks is 571.4 weeks
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Josh needs to buy plastic spoons. Brand A has a box of 25 spoons for$1.99 . Brand B has a box of 42 spoons for$3.89 .
Find the unit price for each brand. Then state which brand is the better buy based on the unit price.
The units price are:
For brand A: $0.0796For brand B: $0.0926Then brand A is the better option.
How to find the unit price?If you know that a set of N items has a price P, then the unit price is given by the quotient between the price and the number of items that you get, N.
For Brand A, we know that there are 25 spoons for $1.99, then in this case the unit price is:
a = $1.99/25 = $0.0796
For Brand B the set has 42 spoons for $3.89, then the unit price is:
b = $3.89/42 = $0.0926
So we can see that Brand A has a lower unit price, meaning that is a better option.
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Brenda is choosing a car insurance plan. Based on her driving history and traffic where she lives, Brenda estimates that there is a 20% chance she will have a car collision this year. In each plan, the insurance will cover the full cost of the collision after the deductible is paid.
Which of the plans detailed in the table is most likely to save Brenda the most money, based on expected value?
Plan Deductible Collision Comprehensive Premium Total
A $300 $500 $234 $734
B $500 $430 $212 $642
C $1,000 $340 $175 $515
D $2,500 $278 $127 $405
A.
plan A
B.
plan B
C.
plan C
D.
plan D
Answer:
A would save Brenda the most money
Step-by-step explanation:
Use and algebraic equation to find the measure of each angle that is represented in terms of x
The measurement of each angle represented in terms of x is 156°
What is the angle measurement?Here given the two angles : (13x-26)° and (9x+30)°.
We have to find each angle measurement.
From the given figure, it is clear that two angles are just vertically opposite angles.
So , we know that vertically angles are equal
So to find angles , we have to find x.
13x - 26 = 9x + 30
13x - 9x = 30 + 26
4x = 56
x = 56 / 4
x = 14
So the value of x = 14
Then we have to substitute the value of x in any of the given measurement.
By substituting x in (13x - 26)°
13 x 14 - 26
182 - 26
= 156
Similarly by substituting x in (9x + 30) °
9 x 14 + 30
= 126 + 30
= 156°
Therefore, the measurement of each angle is 156°.
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Employees wage please help me!
Answer:
I think it is $10.50 per hour. Hope this helps!!
