When dividing the polynomial 3x^2 + 8x -3 by x + 3, we get the quotient as 3x - 1.
The given polynomial is 3x^2 + 8x -3.
First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial:
(x)(3x) = 3x^2
Thus, we multiply the divisor (x+3) by 3x which gives 3x^2 + 9x.
Now we subtract this from the polynomial which gives -x -3.
In the same way we multiply the divisor by -1 which gives -x-3. Subtracting the same from the remaining polynomial -x -3 we get the remainder 0.
Thus, the quotient is 3x - 1.
The question is incomplete, the complete question is:
What is the quotient (3x^2 + 8x -3) ÷ (x + 3)?
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For what values of x:
Is the trinomial x2−11x+31 equal to 1?
Are the values of the polynomials x2−5x−3 and 2x−5 equal?
Is the binomial 7x+1 equal to the trinomial 3x2−2x+1?
Is the trinomial −2x2+5x+6 equal to the binomial 4x2+5x?
a) The values of x for which trinomial x² −11x + 31 equal to 1 are (11 ± 3i)/2.
b) The values of x for which the polynomials x² − 5x− 3 and 2x − 5 are equal are (7 ± √41)/2.
c) The values of x for which the binomial 7x+1 equal to the trinomial 3x² - 2x + 1 are
x = 0, 1/3.
d) The values of x for which the trinomial −2x² + 5x + 6 equal to the binomial 4x² + 5x are ± √3.
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves arithmetic options and non-negative integer exponentiation of variables.
Monomial : is the algebraic expressions with one term or like terms, so “Mono”mial. For example, 2x + 5x + 12x = 19x is a monomial.Binomial: is the algebraic expressions with two like terms, so “Bi”nomial. For example, 2x + 7x² is a monomial.Trinomial: is the algebraic expressions with three like terms, so “Tri”nomial. For example, x + 5x² + 10x³ is a monomial.Now, see the problem, we have to determine the value of x in each case.
a) The trinomial x² - 11x + 31 equal to 1
=> x² - 11x + 31 = 1
Using the quadratic formula,
=> x = ( -(-11)± √121 - 124)/2
=> x = ( 11 ± √-3 )/2 = (11 ± 3i)/2
So, required value of x is (11 ± 3i)/2.
b) The values of the polynomials x² − 5x− 3 and 2x − 5 equal.
=> x² − 5x− 3 = 2x − 5
=>x²− 5x− 3 - 2x + 5 = 0
=> x² - 7x + 2 = 0
=> x = (-(-7) ± √49 - 8)/2
=> x = (7 ± √41)/2
c) The binomial 7x+1 equal to the trinomial 3x² - 2x + 1
=> 7x + 1 = 3x² - 2x + 1
=> 3x² - 2x + 1 - 7x - 1 = 0
=> 3x² - 9x = 0
=> x( 3x - 9 ) = 0
=> x = 0, 1/3
d) The trinomial −2x² + 5x + 6 equal to the binomial 4x² + 5x.
=> 2x² + 5x + 6 = 4x² + 5x
=> 2x² + 5x + 6 - 4x² - 5x = 0
=> - 2x² + 6 = 0
=> 2x² -6 = 0
=> x² = 6/2 = 3
=> x = ± √3
Hence, the required values of x are ±√3.
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Please help! percentage rates
12. The fire department hopes to raise $30,000 to repair a fire house. So far the department has raised $1,750.00. What percent is this of their goal?
14. A TV is advertised on sale. It is 35% off and has a new price of $195. What was the pre-sale price?
16. Store A and Store B both sell bikes, and both buy bikes from the same supplier at the same prices. Store A has a 40% mark-up for their prices, while store B has a 90% mark-up. Store B has a permanent sale and will always sell at 60% off those prices. Which store offers the better deal?
the percent of cash the Fire branch raised is 5.833 and the pre-sale rate of the TV is $300.
What is percentage?A price or ratio that can be said as a fragment of one hundred is called a percent in mathematics. If we want to compute a percent of a number, we need to divide it with the aid of using its complete after which multiply it with the aid of using one hundred. The percentage consequently refers to an issue in keeping with a hundred. Per one hundred is what the time period percentage signifies. The letter "%" stands for it.
Given, The fire department hopes to raise $30,000 to repair a firehouse. So far the department has raised $1,750.00
From the general formula of Percentage, we have to divide the value by the total value and then multiply the resultant by 100.
Percentage = (1750/30,000) * 100 = 5.833%
Also given, A TV is advertised for sale. It is 35% off and has a new price of $195.
Price of TV before Sale = (195 / 65) * 100
Price of TV before Sale = 300$
Therefore, the percentage of money the Fire department raised is 5.833 and the pre-sale price of the TV is $300.
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What is meant by rules of substitution in mathematics?
A principle in logic specifying what expressions may be substituted for one another.
What is a mathematical expression?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division.
Term is defined as a constant, a single variable, or a combination of a variable and a constant combined with multiplication or division. Algebra Expression Example: 3x + 9, 5x + 10
What are an equation and an expression?
In mathematics, an expression is a word or phrase that combines variables, operators, and numbers to represent the value of something. Two expressions are assigned equal to one another in a mathematical statement known as an equation.
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Solve for x.
4(2x − 13) = 4 + x
X = [?]
Hey there!
Answer:
After solving for x, our final solution is [tex]x=8[/tex].
__________________________________
Further Explanation:1. Expand [tex]4(2x-13)[/tex].
[tex]8x-52[/tex]
[tex]8x-52=4+x[/tex]
2. Move 52 to the right side.
[tex]8x=x+56[/tex]
3. Move x to the left side.
[tex]7x=56[/tex]
4. Divide both sides by 7.
[tex]\frac{7x}{7} =\frac{56}{7}[/tex]
5. Simplify.
[tex]x=8[/tex]
________________________________________
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What are the characteristics of an absolute function?
The characteristics of an absolute function are listed below:
An absolute function gives the distance of a number on the number line from 0 irrespective it is on the left or right. An absolute function always gives the positive of a number.Example: | -2 | = 2
The domain of an absolute function is the set of all real numbers. The range of an absolute function is the set of all real numbers greater than or equal to zero.An absolute function is an even function.An absolute function is graphically symmetric about the y-axis.The graph of an absolute function is in the form of a V. The vertex of the absolute function graph is also the maximum or minimum point of the function.To know more absolute value:
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WILL GIVE BRAINLIST!!
In the figure, mGE = 97 and mHF = 43. Since GPEQ is a parallelogram, opposite angles are congruent. Therefore, m<GPE = m<EQG = mGE = 97.
m<GPEQ = 97
What is the frequency of the sinusoidal graph?
Answer:
equal to 1
Step-by-step explanation:
I believe this is the answer. Also I see that ur new. Well welcome to Brainly.
The radius of a quarter circle is 4 feet. What is the quarter circle's perimeter?
r=4 ft. help
The perimeter of the quarter circle is 6.28ft
What is the perimeter of a circle ?The perimeter of a circle is called as the circumference of the circle. The circumference is the external body of a circle.
The perimeter of a circle = 2πr
where r is the radius of the circle.
The perimeter of a quarter circle will be 1/4 ×2πr
= 1/2πr
the radius of a quarter circle is still thesame as the radius of a complete circle.
Therefore the perimeter of the quarter circle = 1/2πr
= 1/2 ×3.14 × 4
= 6.28ft
Therefore the radius of the perimeter of the quarter circle is 6.28ft
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when the product of 10 and 15 is divided by the sum of 10 and 15, what is the quotient?
Answer:
The answer would be 6
Step-by-step explanation:
first multiply 10*15=150 then 10+15=25 150 divided by 150 is 6
What is the value of Z in the diagram below?
Answer:
Step-by-step explanation:180+59 then half the anwser
Deondra is going to invest $90,000 and leave it in an account for 15 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Deondra to end up with $201,000?
Interest is compounded is 4.63%
What is compound interest?Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.Compound interest is calculated by multiplying the initial loan amount, or principal, by the one plus the annual interest rate raised to the number of compound periods minus one. This will leave you with the total sum of the loan including compound interest"12% interest" means that the interest rate is 12% per year, compounded annually. "12% interest compounded monthly" means that the interest rate is 12% per year (not 12% per month), compounded monthly. Thus, the interest rate is 1% (12% / 12) per month. "1% interest per month compounded monthly" is unambiguousTo learn more about compound interest refers to:
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How do you find the range of K in a quadratic equation?
The range of K in a quadratic equation is the set of all possible values that K can take on in order for the equation to remain valid.
What is quadratic equation?A quadratic equation is an algebraic equation that contains a second-degree polynomial with one or more unknown variables. It can be written in the form of ax2 + bx + c = 0, where a, b, and c are just numbers, and x is the unknown variable. The solutions to the equation can be found using the quadratic formula. Quadratic equations are used to model a variety of different problems in mathematics, physics, and engineering.
To find the range of K, we must first understand the quadratic equation. A quadratic equation is an equation in which a variable (K) is raised to the second power and is equal to some other constant. The most common form of a quadratic equation is:
K2 = C
Where K is a variable, and C is a constant. The range of K in a quadratic equation can be found by forming two equations – one equation with K2 = C, and the other equation with K2 = -C.
The first equation (K2 = C) will tell us the maximum value that K can take on. To find this value, we take the square root of C and assign that value to K. The maximum value of K is the square root of C.
The second equation (K2 = -C) will tell us the minimum value that K can take on. To find this value, we take the square root of -C and assign that value to K. The minimum value of K is the negative square root of C.
Therefore, the range of K in a quadratic equation can be found by calculating the square root of C and the negative square root of C. The range of K is the set of all possible values that K can take on in order for the equation to remain valid, which is between the maximum and minimum values found.
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what is the difference of the rational expressions below? 5/2-3/5
The difference of the rational expressions 5/2-3/5 is 19/10.
Rational Number -Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K.
A fraction with polynomials as the numerator, denominator, or both is all that a rational expression is. Any equation with at least one rational expression is said to be rational. If the numerator and denominator of a rational expression do not have any common factors, then the expression is said to be simplified.
Given the expressions is 5/2-3/5
⇒ 25 - 6 / 10
⇒ 19/10
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Last year, 7 people each paid $4,433 for an insurance package. How much did the people pay in total?
Answer:
$31,031
Step-by-step explanation:
Since 7 people each pay $4,433 which means that you would have to do 7 x 4433 which equals 31031. So the answer is $31,031.
a statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 58.0 minutes. find the probability that a given class period runs between and minutes.
The probability that a given class period runs between 50.5 and 51 minutes is 0.05
Understanding that a uniform probability distribution is essentially a rectangle with a surface area of one will help you to find the simplest solution to this problem.
Find a section of this rectangle's area now.
Her classes are uniformly distributed between 48.0 and 58.0 minutes so,
We have to find the probability that a given class period runs between 50.5 and 51 minutes
51−50.5-/58-48
=0.5/10
=0.05
1 X0.05=0.05
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The full question:
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 58.0 minutes. Find the probability that a given class period runs between 50.5 and 51 minutes.
HELP I NEED HELP HELP
Step-by-step explanation:
5. .....................................................
Is this parabola a function?
Yes, a parabola is always a function, specifically a quadratic function.
To determine if a parabola is a function, you will need to check if it passes the vertical line test.
To do this, draw a vertical line through any point on the parabola and see if it intersects the parabola more than once. If it does, then the parabola is not a function. If it only intersects the parabola once, then the parabola is a function. To graph a parabola, you will need to find five points that make up the curve in order to get a better approximation of the general shape. This can be done by using the equation of the parabola in the form y = ax2 + bx + c . First, calculate the x-intercepts by setting y = 0 and solving for x. Then, calculate the y-intercept by setting x = 0 and solving for y. Finally, calculate two more points by solving for x when y is equal to a positive and negative value. Once the five points have been identified, plot them on a graph and draw a smooth curve through them.Learn more about parabola function:
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1/7 x 3/5 what is the Answer !!!!!!
Answer:
3/35 or 0.0857
Answer:
3/35
Step-by-step explanation:
Multiplying fractions
1/7 x 3/5
Multiply the numerators.
1*3 = 3
Multiply the denominators.
7*5 = 35
Put the numerator over the denominator.
3/35
Identify the initial value and rate of change for the graph shown.
A coordinate plane graph is shown. A line is graphed that passes through the y-intercept at 4 and through the point 4 comma 1.
a
Initial value: 5.5, rate of change: negative 3 over 4.
b
Initial value: 4, rate of change: negative 3 over 4.
c
Initial value: negative 3 over 4., rate of change: 4
d
Initial value: negative 3 over 4., rate of change: 5.5
Thanks :')
The solution is Option B.
The equation of line is given by y = ( -3/4 )x + 4 , where the rate of change is the slope m = ( -3/4 ) and the initial value is 4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
A line is graphed that passes through the y-intercept at 4 and through the point P ( 4 , 1 )
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
y = mx + 4 be equation (1)
when y = 1 , x = 4
1 = 4m + 4
Subtracting 4 on both sides of the equation , we get
4m = -3
Divide by 4 on both sides of the equation , we get
m = -3/4
So , the slope of the line is m = -3/4
Therefore , the equation of line is y = ( -3/4 )x + 4
Now , the initial value of the equation is when x = 0
So ,
y = ( -3/4 ) ( 0 ) + 4
y = 4
So , the initial value of f ( 0 ) = y = 4
Hence , the equation of line is y = ( -3/4 )x + 4
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The rectangle shown has a perimeter of 104 cm and the given area. Its length is 8
more than three times its width. Write and solve a system of equations to find the
dimensions of the rectangle.
Therefore , the solution is l=3 w + 8 is the formula to solve for the dimensions of a rectangle.
Rectangle: What is it?
In Euclidean plane geometry, a rectangle is a square with four right angles. You may also refer to it as a quadrilateral that seems to be equiangular, meaning that each of its angles is equal. Another possibility for the parallelogram is a straight angle. Four of the sides of a square are of identical length. Four 90 ° vertices and equal equal sides make up a rectangle-shaped quadrilateral.
Here,
Given that the rectangle's perimeter is 104 cm
W = the rectangle's width
rectangle's length is equal to 3 w + 8.
Rectangle perimeter equals 2 (length + width).
= >104 =2(3 w + 8 + w)
= >104 =2(4 w + 8)
= >104 =8 w + 16
= >8 w = 104- 16
= >8w = 88
= >w = 11
hence the rectangle's length is equal to 3 w plus 8.
= >3 * 11 + 8
=> 33 + 8
=> 41
Consequently, l=3 w + 8 is the formula to solve for the dimensions of a rectangle.
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Noah went into a movie theater and bought 9 drinks and 4 candies‹ costing a total of $6o. Nachelle went into the same movie theater and bought 10 drinks and a candies, costing a total of $57.50. Determine the price of each drink and the price of each candy.
Each drink costs $5.48, and each candy costs $2.67.
What are Systems of equations?
simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given, Noah went into a movie theater and bought 9 drinks and 4 candies‹ costing a total of $6o.
Let "d" be the price of a drink, and "c" be the price of a candy.
So,
9d + 4c = 60
Also given, Nachelle went into the same movie theater and bought 10 drinks and one candy, costing a total of $57.50
So,
10d + c = 57.50
c = 57.50 - 10d
From equation 1
9d + 4(57.50 -10d) = 60
9d + 230 -40d = 60
31d = 170
d = 170/31
d= 5.48
After substituting this value in equation 2
c = 57.50 - 54.83
c = 2.67
Therefore, The price of each drink is 5.48$, and candy cost $2.67.
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on the bus 12/40 of the seats were taken what is the fraction simplest form?
Answer:
Step-by-step explanation:
3/10 you find the GCF of both
It rains an inch and a half in 8 hours. If it rains at the same rate the rest of the day, how much more will it rain? ____inches
(Please explain how you got your answer)
Answer: Yoo
To find out how much more it will rain, we can use the information given to calculate the rate of rain in inches per hour. We know that it rained an inch and a half in 8 hours, so the rate of rain is:
(1.5 inches) / (8 hours) = 0.1875 inches/hour
Now that we know the rate of rain, we can use it to find out how much more it will rain in the rest of the day. We can assume that the rest of the day has 16 hours, so we can use the rate of rain to find out how much more it will rain:
(0.1875 inches/hour) x (16 hours) = 3 inches
So, it will rain 3 inches more the rest of the day.
We can also check this by multiplying the inches per hour (1.5/8) by the number of hours in a day (24) and subtracting the inches of rain fallen (1.5 inches)
(1.5/8)*24-1.5 = 3
This means that it will rain 3 inches more the rest of the day.
Step-by-step explanation:
Why is the addition method of solving a system with two variables also called the elimination method?
Using the Addition Method to Solve Two-Variable Equation Systems The addition approach, often known as the elimination method, is a third strategy for resolving linear equation systems.
What is meant by the elimination method?
The elimination approach involves removing one of the variables from the system of linear equations by adding or subtracting, as well as multiplying or dividing the variable coefficients.
What is the process of elimination's formula?
Utilizing the addition property of equality, the elimination approach is used to solve systems of linear equations. Both sides of an equation can be increased by the same amount.
The first equation can be solved by adding x + y to the left side and 8 to the right side if your system is x - 6 = 6 and x + y = 8.
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In a recent basketball game, the Grizzlies lost by II points
The Palominos beat them with a score of 92 points. How
many points did the Grizzlies score?
What is the unknown number?
Equation:
n =
Answer:
81
Step-by-step explanation:
n = 92 - 11
Therefore,
n = 81
PLEASE HELP I NEED THE STEPS AND ANSWER TO THIS QUESTION
Answer:
x = 12
Step-by-step explanation:
Definition of a point between two points:
Point B is between points A and C if and only if AB + BC = AC.
Now we apply it to this problem.
AB = 3x + 5
BC = 2x + 3
AC = 68
AB + BC = AC
Substitute each segment length with the expression or length above. Then, solve the equation for x.
3x + 5 + 2x + 3 = 68
5x + 8 = 68
5x = 60
x = 12
Which statement could describe the returns from a bond?
Answer:
A bond is a debt security, meaning that it represents a loan made by an investor to a borrower (typically a corporation or government). The bond issuer promises to pay interest to the bondholder, usually at regular intervals, and to repay the principal when the bond matures.
So, a statement that could describe the returns from a bond is:
"Bonds typically provide a steady stream of income in the form of interest payments, but the return on investment is generally lower than that of stocks."
Another statement that could describe the returns from a bond is:
"Bonds are considered to be a relatively safe investment option, but they are not as profitable as stocks in terms of returns."
In general, bonds are considered to be less risky than stocks, but they also typically offer lower returns.
Answer: B
Step-by-step explanation:
Find the value of X in the figure.
The angle of 'x' is 87°
Vertically Opposite Angles:
The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another is always equal.
Here we have
Two lines are intersected at the point and forms four angles
As we can see that given angles are vertically opposite angles
=> x = 82°
Therefore,
The angle of 'x' is 87°
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find the area of shaded regions below. give your answer as a completely simplified exact values in terms of pi
The area of the shaded region in the figure in terms of pi is
81 - 20.25π m²How to find the area of the shaded portionThe shaded portion is a portion of a squared which has two semi circles of diameter equal to the side of the square.
The area of the two semi circle will be subtracted from the area of the square to give the area of the shaded region
Area of a square is solved by the formula
= length * width
= 9 * 9 = 81 m²
Area of the two semi circle
= 0.5πr² * 2
= πr²
and r = 9/2 = 4.5
= 20.25π m²
area of shaded portion
= 81 - 20.25π m²
The area of the shaded region in terms of pi is (81 - 20.25π) m²
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How do you tell if a system of equations has no solution or infinitely many formula?
When the graphs are parallel, a system of linear equations cannot have a solution. endless options. When the graphs are on the exact same line, a system of linear equations has an infinite number of solutions.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
What makes an equation linear?
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.
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