When the root of x²-bx+c = 0 is decreased by 2, the resulting equation is x²-2x+1, then b = 2 and c = 1
What is root of quadratic equation?The values of variables satisfying the given quadratic equation are called its roots.
if the roots of a quadratic equation ax²+bx+c = 0 are alpha and beta
alpha + beta = -b/a and
alpha × beta = c/a
when the roots are reduced by 2
alpha-2+ beta-2 = -b/a
(alpha+beta)-4 = -b/a
alpha+ Bata = -b/a + 4
the resulting equation is x²-2x+1 = 0
a = 1, b = -2 and c = 1
therefore alpha +beta = -b/a = -(-2)/1 = 2
therefore 2 = -b/a+4
a = 1
2 = -b+4
b = 4-2 = 2
alpha×beta = c/a = 1/1
(alpha -2)× ( beta -2) = (alpha)( beta) -2(alpha+beta) + 4 = 1-2(2)+4 = 1
therefore b = 2 , c = 1
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The sunshine rental company rents cars for $17 per day plus $0. 50 per mile driven. The rent me company rents cars for $20 per day plus $0. 36 per mile driven. When will the two companies be equal in cost?
The two companies will be equal in cost when 21.428 miles are driven.
How do you calculate the cost of rent?
The weekly rental amount is divided by 7 to determine the daily rental rate, then multiplied by 365 (days per year) to determine the yearly rate, and finally divided by 12 to determine the monthly rental amount. For example, a property is advertised as $200 per week, ($200 divided by 7) is $28.57 for the daily rate.
We can set up an equation to represent the cost of renting a car from each company in terms of the number of miles driven, and then solve for the number of miles at which the cost is the same for both companies.
Let x be the number of miles driven.
The cost of renting from Sunshine Rental Company is given by:
Cost1 = 17 + 0.5x
The cost of renting from Rent Me company is given by:
Cost2 = 20 + 0.36x
We can set the two equations equal to each other, and solve for x:
17 + 0.5x = 20 + 0.36x
0.14x = 3
x = 21.428 miles
Hence, the two companies will be equal in cost when 21.428 miles are driven.
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A line passes through (8,9) and has a slope of 5/2
Answer:
y = 5/2x - 11
Step-by-step explanation:
y = 5/2x + b
9 = 5/2 (8) + b
9 = 20 + b
-11 = b
y = 5/2x - 11
PLEASE HELP ASAP- What is the value of AB?
Answer:
the answer would be 19 because these are congruent shapes
Hope this helps:)
Step-by-step explanation:
Jon flips a coin and writes down H if heads comes up or T if tails comes up. He does this 3 times. If the order of the results matters, how many possible outcomes are there?
Answer:
There are always two possible outcomes H (heads) and T (tails) but the possible combination outcomes are HH, TT, HT, and TH
Step-by-step explanation:
It is just my common sense~
There is 8 possible outcomes.
Dalis' employer pays $2,150 in health insurance and $86
in life insurance per year. She also gets $3,520 in paid time
off per year. Her monthly gross pay is $4,370. What are
Dalis' total job benefits?
Answer: chiki
Step-by-step explanation:
While Tanya wa hopping, he overheard the aleman at Electronic Mania ay that if they old 30% more computer than they old lat month, they would get a bonu. Lat month they old 27 computer. How many computer mut the ale team ell to receive the bonu? Explain your reaoning
The sales team must sell 8 more computers than they sold last month to receive the bonus.
Last month the sales team of Electronic Mania sold 27 computers.
If they sold 30% more computer than they sold last month, they would get a bonus.
First we find the 30 percent if 27
27 × 30/100
= 8.1
Let m be the total number of computers sold.
So, the total number of computers sold would be,
m = 27 + 8.1
m = 35.1
m ≈ 35
Therefore, they need to sell 35 computers in total.
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Is 4 a perfect square?
Answer:
ye
Step-by-step explanation:
Answer: Yes
Step-by-step explanation:
A perfect square is a number from a number system that can be shown as the square of the number in the given number system. 4 can be written as 2 x 2 Making 4 a perfect square. In other words, if a number can be multiplied by its self and equal the number you are trying to square, then it is a perfect square.
Which word or phrase describes the value of the function over the interval [ -6, 0]
Answer:
C is the correct answer
From the graph we can see that at the given interval [-6,0] the graph decreases from left to right.
Initially the y-values is a little over 3 and then it decreases to about 0.5 at the end of the interval.
Thus, the graph of the function over the interval [-6,0] is decreasing.
What multiplication expression can I use to find 3/8 divided 3/4
Answer: [tex]\frac{3}{8}[/tex]➗[tex]\frac{3}{4}[/tex]
Step-by-step explanation: Are you looking to work out and calculate how to multiply 3/8 by 3/4? In this really simple guide, we'll teach you exactly what 3/8 times 3/4 is and walk you through the step-by-process of how to multiply two fractions together.
567854+98723=?
Let's see who knows the correct answer
Evaluate the following:
c) The height of each cylinder in a set of food-storage containers is 30 cm.
The radius of the largest container is 10 cm.
The volume of the smallest container is one-third the volume of the largest container.
The volume of the middle-sized container is two-thirds the volume of the largest
container. What is the volume of each container?
Answer:
Volume of smallest container = 3141.6 cm³
Volume of middle sized container = 6283.2 cm³
Volume of largest container = 9424.8 cm³
Step-by-step explanation:
The formula to find the volume of a cylinder = πr²h
The height of each cylinder in a set of food-storage containers is 30 cm.
The radius of the largest container is 10 cm.
Step 1
We can find the volume of the largest cylinder
= r = 10cm
h = 30cm
Volume of largest cylinder = π × 10² × 30
= 9424.8 cm³
Step 2
We find the volume of the smallest container
We are told in the question:
The volume of the smallest container is one-third the volume of the largest container.
Hence
Volume of Smallest container = 1/3 (9424.8 cm³)
= 3141.6 cm³
Step 3
The volume of the middle-sized container is two-thirds the volume of the largest container.
Hence,
Volume of the middle sized container =
2/3 (9424.8 cm³)
= 6283.2 cm³
Therefore, the volume of each container is
Volume of smallest container = 3141.6 cm³
Volume of middle sized container = 6283.2 cm³
Volume of largest container = 9424.8 cm³
A salesperson at a jewelry store earns 8% commission each week. Last week, Jarrod sold $720 worth of jewelry. How much
did he make in commission? How much did the jewelry store make from his sales?
Jarrod earned $ in commission.
Is the interval 0 to infinity open?
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers
the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).
Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
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9/10 - 3/10
?????…..
Answer:
Step-by-step explanation:
9 - 3 = 6
6/10 = 3/5
Answer:
6/10 and/or 3/5(this is the answer simplified
Step-by-step explanation:
Subtract: 9/10 - 3/10
= 9 - 3/10
= 6/10
= 2 · 3/ 2 · 5
= 3/5
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 3/5. In other words - nine tenths minus three tenths is three fifths.
6x - 4y = 8 ; x
Solve for indicated value
Solved equation is, x = 4/3 + 2y/3
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here we have,
Write equation
6x - 4y = 8
Then,
Solve for x
Add 4y to both sides: 6x = 8 + 4y
Divide both sides by 6: x = 8/6 + 4y/6
Simplify: x = 4/3 + 2y/3
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Evaluate the expression (-243)1/5
[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ (-243)^{\frac{1}{5}}\implies \sqrt[5]{(-243)^1}\implies \sqrt[5]{(-3)(-3)(-3)(-3)(-3)} \\\\\\ \sqrt[5]{(-3)^5}\implies -3[/tex]
ILL BRAINLIEST YOU PLEASE HELP ME
Answer:
A. 45.7
Step-by-step explanation:
Side a = 8
Side b = 7.8
Side c = 11.17318
Angle ∠A = 45.725° = 45°43'31" = 0.79806 rad
Angle ∠B = 44.275° = 44°16'29" = 0.77274 rad
Angle ∠C = 90° = 1.5708 rad = π/2
=======================================================
Explanation:
Apply the tangent ratio and inverse tangent function (aka arctangent) to get the following
tan(angle) = opposite/adjacent
tan(x) = 8/7.8
x = arctan(8/7.8)
x = 45.7252242990592
x = 45.7
Be sure that your calculator is in degree mode.
Algebra 2
1) What is the multiplicative inverse of 300?
a) 300
b) 0.03
c) 1/300
d) None of the above
e) a and b
f) b and c
g) a and c
Answer:
Step-by-step explanation:
Option C is the correct answer
Answer:
the multiplicative inverse of 300 is 300Step-by-step explanation:
answer 300What is the coefficient of y² in the expression 3y² 4x *?
The coeficient of y² in the expression is the number 3
What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In the given expression we have the following:
3y² + 4x
As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.
3 is the coefficient of y²
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if a+b+c=9 and ab+bc+ca-26 find a²+b²+c²?
Answer:
we have :
(a+b+c)² = a² + b² + c² + 2(ab+bc+ca)
a+b+c= 9
and
ab+bc+ca = 26
Substituting the values in the above formula,
We get,
9² = a² + b² + c² + 2×26
81 = (a² +b² +c²) + 52
(a² +b²+c²) = 81-52
(a²+ b² + c²) = 29 is a required answer.
Guys I'm going to ask a question, Now i know this question i just want to see if u guys know the answer.
The question is The horizontal number line is the ?
u guys have to give me the answer
Answer:
The answers is called the x-axis and the vertical number line is called the y-axis
Step-by-step explanation:
Hope this helps
Answer:
x-axis
Step-by-step explanation:
Please help me with this
Answer:
9) C: x=4, y=2rt3
10) A: XY/YZ
11) A: XY/XZ
Step-by-step explanation:
9 - that is a 30, 60, 90 triangle so the ratios will be a, root3a, 2a
10 - tan = opposite / adjacent
11 - cos = adjacent/hypotenuse
Answer:
9. (c)
10. (a)
11. (a)
................
PLEASE ANSWE ASAP IF YOU’RE AN EXPERT AT MATH !!!
Answer:
13.67
Step-by-step explanation:
Find the equation of the line
Step-by-step explanation:
Use photo math in the AppStore
Answer: y=1/4x-6
Step-by-step explanation:
The slope formula is y=mx+b
M- represents the rise over run.
B- represents where the line crosses over the y-axis.
So once you input the numbers you get 1/4 for m and -6 for b.
1. Karissa is determining the solution to the
equation 14 + 2e = 40.
Which value is the solution to Karissa's
equation?
A. 13
B. 20
C.
26
D. 40
Find the GCF of the monomials 6d3, 27d2
Answer:
3d^2
Step-by-step explanation:
First, find the GCF of 6 and 27, which is 3.
Factors of 6: 1, 2, 3, 6
Factors of 27: 1, 3, 9, 27
Then, find the greatest value of the variable d^3 and d^2, which is d^2. Since this is a variable, we just need to take out the highest degree accompanying the variable.
27(d^2)
6d(d^2)
Combine both of your findings to get 3d^2.
Which ordered pair would form a proportional relationship with the point graphed below? GIVING 30 POINTS FOR CORRECT ANSWER!!!
Answer:
c
Step-by-step explanation:
Which ordered pair would form a proportional relationship with the point graphed below?
[tex]( - 30,10 \: )[/tex]HOPE IT WILL HELP YOU
Casey charges $11 per hour to babysit infants and $9 per hour for toddlers. She babysat infants for 22 hours and toddlers for 18 hours. How much more does she need to earn to buy a $450 bike?
Answer:
46
Step-by-step explanation
11 x 22 and 9 x 18 then add them then do 450 - 404
1.If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?
Answer:
6
Step-by-step explanation:
5 × 24= 120 and 24 - 4 = 20 and 120 ÷ 20 = 6
I hope this helps!!
What are the values for the coefficients and constant term of 0 2 3x² 5x?
The coefficient of the expression 3x² is the number 3 and constant term is 20
What are the coefficients?
The coefficients are the numbers on the left side or before each variable.
What is an algebraic expression?
Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
If the expression of a single term is:. 3x²
Then the only coefficient will be the number that is placed before it and it is:
Number 3
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