The roots of the function f(x) = [tex]x^2+2x-1[/tex] are
x = [tex]-1+\sqrt{2}[/tex]
x = [tex]-1-\sqrt{2}[/tex]
The function is given f(x)= [tex]x^2+2x-1[/tex]
The roots of given function will be at f(x) = 0
Substitute the value in the equation
[tex]x^2+2x-1[/tex] =0
Here to find the roots of the function, we have to use the quadratic formula in the given function
Roots of the function = [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
From the given function the values of
a = 1
b = 2
c = -1
Substitute the values in the quadratic formula and find the roots of the function
= [tex]\frac{-2+/-\sqrt{2^2-4(1)(-1)} }{2(1)}[/tex]
= [tex]\frac{-2+/-\sqrt{4+4} }{2}[/tex]
= [tex]\frac{-2+/-2\sqrt{2} }{2}[/tex]
The roots of the given functions are
x = [tex]-1+\sqrt{2}[/tex]
x = [tex]-1-\sqrt{2}[/tex]
Hence, the roots of the function f(x) = [tex]x^2+2x-1[/tex] are
x = [tex]-1+\sqrt{2}[/tex]
x = [tex]-1-\sqrt{2}[/tex]
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What is the area of the shaded figure
Answer:
102 squared in.
Step-by-step explanation:
the shaded area is the whole shape minus the unshaded shape.
calculating the whole shape area:
make sure you add all the width together and then all the height together before multiplying
(10+4) x (3+6) = 14 x 9 = 126 squared in.
calculating the unshaded shape area:
6 x 4 = 24 squared in.
based on the logic from my first sentence in this explanation:
126 - 24 = 102 squared in.
DOMAIN AND RANGE, ANSWER ALL
The function is decreasing.
The domain is the set of x-values.
Interval: [tex](-\infty, \infty)[/tex]Inequality: [tex]-\infty < x < \infty[/tex]The range is the set of y-values.
Interval: [tex](0, \infty)[/tex]Inequality: [tex]x > 0[/tex]a number,x,is rounded to 1 decimal place is 12.3 write down the error interval for x.
we know that, a number X, rounded to 1 decimal place is 12.3
so,
X>=12.25
and
X<12.35
The error interval for X is [12.25,12.35)
Two hikers are 33 miles apart and walking toward each other. They meet in 5 hours. Find the rate of each hiker if one hiker walks 2.2 mph faster than the other.
The rate of the slow hike is 2.2 mph and the rate of the faster hiker is 4.4 mph.
Here in this issue, we are managing linear equations which is a condition of one variable regularly composed within the form ax+b=0 , where a and b are real numbers and x is an unknown variable. Solutions to linear equations allude to a linear equation that can have zero, one, or infinitely various solutions. A linear equation with no solutions simplifies to an untrue statement such as 1=0. A linear equation with one solution rearranges to a solution of the form x=n where n may be a real number. A Linear equation with infinitely various solutions simplifies to a true statement without a variable such as 1=1.
Here we considering the rate of the slow hiker to be x, so the rate for the fast hiker will be x+2.2
Since we know that distance = speed * time
therefore, the Distance covered in 5 hours by a slow hiker is 5x , wheras for fast hiker it will be 5(x+2.2)=5x+11 km
As we are given the condition that it i they are 33 miles apart, So
=>5x + 5x+11 = 33
=>10x = 33-11
=>10x = 22
x =22/10 => 2.2
So the rate of a slow hiker is 2.2 mph and the rate of a fast hiker is x+4.4= 4.4 mph.
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equation of the line through (3,5) and parallel to y=2x-2
Answer:
y = 2x - 1
Step-by-step explanation:
y = 2x - 2; (3, 5)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - 5 = 2(x - 3)
y - 5 = 2x - 6
+5 +5
-----------------------
y = 2x - 1
I hope this helps!
The Distributive Property - 5(y - 4)
Answer:
-5y + 20
Step-by-step explanation:
Distributive property: multiply the outside terms with the inside terms
-5(y - 4)
-5 x y = -5y
-5 x 4 = -20
-5y + 20
So -5(y - 4) simplified using distributive property is -5y + 20
Your welcome hope this helps :)
Please help :)))
1. How are rational exponents and radicals related? Explain how to rewrite an expression from rational exponent form into radical form.
2. Explain how equations involving rational exponents or radicals are solved using the rules of exponents.
3. How do extraneous solutions arise from radical equations?
i'll lichuarlly give you so many points
Every radical can be rewritten has an exponent .
Extraneous Solutions occur because squaring both sides of a square root equation results in 2 solutions (the positive and negative number).
1. Exponents that are written as fractions are referred to as rational exponents.
The top of the rational exponent is the new exponent on the radical, and the bottom of the rational exponent is the root, therefore a rational power can be reinterpreted as a radical in this fashion.
2. Separate the radical expression from the equal sign on one side. Put every every clause over there on the other side. Square both sides of the equation if the radical is a square root. Raise both sides of the equation to the third power if it is a cube root. Write an expression as a radical if the expression has a logical exponent. By examining the exponent's numerator, you may determine the power. By examining the exponent's denominator, you can get the root. Raise the radicand to the power while using the base as the radicand, and use the root as the index.
3. Extraneous Solutions appear because there are two solutions when you square the two sides of a square root equation (the positive and negative number). As a result, one of those figures will represent an extra solution, or a solution that is added but does not satisfy the initial equation.
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any number raised to the 2nd power is said to be
Write a real-world problem
that is represented by the division problem 38 ÷ 5 = 7 R3 in which it makes sense to round the quotient up to 8.
Please help me it’s due tmrw
Thanks!!! :)
Answer:
answer is ask to your parents
Question 5 ? Question What does the point (6,0) represent? O the length of time it takes for the height of the plant to reach 72 centimeters O the initial amount of plant food O the amount of plant food used each day O the length of time it takes for Ryan to use all the plant food
The point (6,0) represent the length of time it takes for Ryan to use all the plant food
What is Time ?
Time is a continual and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.
The location and value of x at which the function represented by f(x) equals zero are known as the x-intercept.
The height of the bean sprout and the quantity of plant food added were both measured, per the information given.
Given the observational aspect of the experiment, we know that the function of the variable y = f(x) is the height of the bean sprout, and the variable x, which may be chosen by the researcher, is the amount of the additional plant food.
As a result, the x-intercept, which represents the experiment's starting position (represented by the natural numbers of y = 0), shows how much plant food was initially added to the soil.
Hence, The point (6,0) represent the length of time
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The point (6, 0) represents the initial amount of plant food, which is 0 at this point.
When representing a point in the form (x, y), the x-coordinate typically represents a quantity or value on the horizontal axis, while the y-coordinate represents a quantity or value on the vertical axis.
The point (6,0) means that the x-coordinate is 6, which corresponds to a specific value or measurement along the horizontal axis.
Since the context of the question refers to plant food, the x-coordinate of 6 likely represents a measurement related to the amount of plant food.
The y-coordinate, in this case, is 0, indicating that there is no height or value represented on the vertical axis.
Therefore, (6, 0) represents the initial amount of plant food, which is 0 at this point.
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A quadrilateral is plotted on a coordinate plane. Each of the vertices of the quadrilateral undergoes the same transformation.Which transformation does not preserve the lengths of the sides of the quadrilateral?
Explanations :
(a) (x;y) →(x-3 ; -y+2 ) ; this preserves the lengths of the side, with a reflection across the x -axis .
(b) (x;y) →(2x +1 ; y-5 ); this does not preserve the length of sides, because the 2 multiply by x will change the length by factor of 2 .
(c) (x;y) → (-x+6 ;-y -8 ), preserves the lengths of sides, with reflection of y = -x .
(d) (x;y) →(-x -5 ; y+10 ) preserves the lenghts of the sides , with a reflection in the y -axis .
5(1 − n) + 3n = 3(n − 1) – 5n
Answer:
8 = 0 (this equation is always false)Step-by-step explanation:
5(1 − n) + 3n = 3(n − 1) – 5n
5 - 5n + 3n = 3n - 3 - 5n
5 + 3 = 5n - 3n + 3n - 5n
8 = 0
this equation is always false
A farmer has harvested 26 bushels of
apples and can harvest 24 bushels of
apples each day. In how many days
will she have more than 100 bushels
to sell? Write an inequality represents
this situation. Solve and graph the
inequality on a number line and write
three answers that can represent x.
Write three solutions to the inequality that can be represented by the numbers x 26 + 24 n > 100.
What does maths' inequality mean?A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >,,, or indicate that the two expressions in an inequality are not always equal.
Equations and inequalities are both mathematical sentences formed by relating two expressions to each other
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The equation of inequality is [tex]26+ 24n > 100[/tex] .
What is inequality?Inequality, is a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Make use of the following steps to solve an inequality:
Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator.
Step 2: Simplify the inequality by merging like terms on each side.
Step 3: Add or subtract amounts to get the unknown and the numbers on either side.
In this question it is given that the farmer has 26 bushels of apples
Number of apples he can harvest each day is 24 bushels. This statement indicates that this is not constant.
Thus let us consider a variable say n to represent the inequality.
So we can write it as 24 n.
Also given that she has to sell more than 100 bushels.
The final equation becomes:
Apples present + Number of apples added each day > 100
⇒ 26+ 24n> 100 is the final answer.
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Please help, will give brainliest!
Answer:
Step-by-step explanation:
Outside of Figure A
in preparation for moving into his first apartment after college, Winston goes on a shopping spree and spends $984 on furnishing, decorations, and other home goods. Sales tax in his area is 8.19%, and none of the items he buys are tax exempt. What will Winston’s total bill be at the cash register? Round to the nearest cent
Winston's total bill at the cash register is $1064.59
Sales tax for the items purchased is $80.59
Given,
The price for the items Winston purchased = $984
Sales tax in Winston's area = 8.19%
We have to find Winston's total bill at the cash register:
Total amount = Price of the items + sales tax amount
Sales tax amount = 8.19% of price of items
Sales tax amount = (8.19/100) × 984
Sales tax amount = $80.59
Now,
Total bill amount = Price of the items + sales tax amount
Total bill amount = 984 + 80.59
Total bill amount = 1064.59
Therefore, Winston's total bill at the cash register is $1064.59
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Due in one minute! Help please!!
Answer:
[tex]2x - 25 = 87 \\ 2x = 87 + 25 \\ 2x = 112 \\ \frac{2x}{2} = \frac{112}{2} \\ x = 56[/tex]
I USED THE REASON ALTERNATE ANGLES ARE EQUAL
Solve the problems. The amount in Ebony's bank account B(d) is a function of the number of days d since she opened the account. The graph shows segments representing her day-by-day bank balance. Although there are no labeled tick marks on the graph, you can answer the questions by using the additional given information as well as your general knowledge of graphs of functions.
(b) Give an estimate to the nearest hundreds for B(0). explain how you determined your estimate and tell what B(0) means in the context of the situation.
Since, Domain: 0≤d≤21 and Range: 0≤B(d)≤400, B(0)=200. On Day 0, the day Ebony opened her account, she made initial deposit of $200.
What is a graph?In mathematics, and more specifically in the graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to the mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in the diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are the one of the objects of study in discrete mathematics.
Edges may be directed or undirected. For example, if the vertices represent people at party, and there is an edge between two people if they shake hands, then this graph is undirected because any person A can shake hands with person B only if B also shakes hands with A. In the contrast, if an edge from a person A to a person B means that A owes money to B, then this graph is directed, because owing money is not necessarily reciprocated.
Graphs are basic subject studied by graph theory. J. J. Sylvester was the first to use the word "graph" in this context in 1878 due to the direct relation between mathematics and chemical structure (what he called a chemico-graphical image).
1) Domain: 0≤d≤21
Range: 0≤B(d)≤400
2) B(0)=200
On Day 0, the day Ebony opened her account, she made initial deposit of $200.
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All rational numbers can be written as complex numbers in the form a +bi.
For the number 18, what is the value of a and b?
O a=0 and b = 18
O a=18 and b= 1
O a = 1 and b = 18
O a 18 and b = 0
The correct option a = 18 and b = 0, described the complex number 18.
What is described as the complex number?A complex number is the result of adding a real as well as an imaginary number. A complex number has the formula a + ib and is usually symbolized by the symbol z. Both an as well as b are real numbers in this case. The value 'a' is known as the real part, which is signified by Re(z), and the value 'b' is known as the imaginary part Im (z). ib is also known as an imaginary number.For the given question.
Let R be the rational number.
All rational numbers can be written as complex numbers in the form;
R = a +bi
Where 'a' is the real part and 'ib' is the imaginary part.
The number 18 can be written as;
18 + 0i = 18
As, in number 18 only real part is there.
Thus, a = 18 and b = 0 are correct expression for describing number 18.
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Lesson 1.2.2 Exit Ticket
Brown is making treat bags to give away on Halloween. He has 81 Snickers bars and 54 KitKat bars. He
ants to use all of the candy by making as many identical bags as possible.
a. How many treat bags can he make using all of the candy?
The most appropriate choice for LCM will be given by
He can make 162 treat bags using all the candy.
What is LCM?
Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.
Here,
Number of Snicker bars = 81
Number of kitkat bars = 54
Brown wants to use all of the candy by making as many identical bags as possible.
Number of treat bags he can make using all of the candy = LCM of 81, 54
81 = 3 x 3 x 3 x 3
54 = 2 x 3 x 3 x 3
LCM = 3 x 3 x 3 x 3 x 2
= 162
He can make 162 treat bags using all the candy.
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EASY TRIG MATHEMATICS QUESTION! PLEASE HELP ME SOLVE! THANK YOU!
PLEASE LOOK AT IMAGE!
Based on table shown above, we have that: A. Yes, the table describe a function.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
Based on table shown above, we have the following parameters:
Input value Output value
2001 30
2002 60
2003 30
2004 50
2005 40
In conclusion, we can reasonably infer and logically deduce that this table is a function because it has the different input values (x-values) for different or the same output values (y-values).
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HELPPPPPPPPPPPPPPPPPPPPP
Answer:
the answer to number 2 is: y=-4x-26
The answer to number 3 is y=5/2x+54
Step-by-step explanation:
The formula for the circumference of a circle with diameter d is C = nd.
a. Solve the formula for d.
b. The circumference of a circle is 8 inches. What is the diameter of the circle?
Part (a)
[tex]C=\pi d \implies d=\frac{C}{\pi}[/tex]
Part (b)
[tex]d=\frac{8}{\pi}[/tex]
Can you help me with this math question
Answer:
70
Step-by-step explanation:
Find the number of degrees moved by the minute hand of a clock in the given amount of time of 7/12
Based on the amount of time given, the number of degrees that the minute hand on the clock would have moved is 210 degrees
How to find the number of degrees moved?Based on the fact that the clock is a circle in shape, it means that when the minute hand moves around the clock for an hour, it would have moved 360 degrees.
If the time moved by 7/12 hours, the number of degrees it moved was then:
= Number of degrees x Number of hours
= 360 x 7/12
= 2,520 / 12
= 210 degrees
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11 Amelia has a rectangular table that measures 4 feet wide and 5 feet long. She rotates the table 90° clockwise so that it fits better in the room. What is the length in feet of the table after the rotation?
The only possible answer that would match the simplified inequality is the first answer choice .i.e., -5c + 2 _< _27
What is the mathematical operation?An operation, often known as "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by number of operands.
Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are operations that are most frequently studied. A constant is operation with arity zero, often known as a nullary operation. An example of an operation of arity 3, sometimes known as ternary operation, is the mixed product.
The arity typically assumed to be limited. The "typical" operations of finite dimensionality are referred to finiteary operations when infinitary operations are taken into consideration.
Similar to an operation, but with partial function in place of a function, is the definition of a partial operation.
A closed or filled-in circle represents greater/lesser or equal to symbol (> or with the line at the bottom).
You must flip the inequality sign when multiplying or dividing when one of terms is negative on both sides. In inequality equations, this rule only holds when multiplying or dividing by negative value. This rule is very crucial.
-5c + 2 _< _27
subtract from both sides by 2
-5c _< _ 27
divide both sides by -5
c _< _ 5.4
flip the inequality sign
c _> _5.4
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The surface area of a swimming pool is 395 square feet. Find the
measure of the area in square meters.
one of 55 students is selected at random. written as a fraction, what is the probability that this student passed exactly one of these subjects
The probability that s student will passed exactly one of the subject is 28/55.
How to calculate the probability?It should be noted that probability simply means the likelihood that a particular event will happen.
Based on the Venn diagram that's given, the number if students that passed both subjects is 19.
Therefore, the probability that s student will passed exactly one of the subject will be:
= Fraction of students that passed French + Those that passes German
= 11/55 + 17/55
= 28/55
The probability is 28/55.
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Cruz purchased a large pizza for $12.75. It serves 5 people. What is the cost per serving?
Answer:
2.55 per serving
Step-by-step explanation:
all u have to do is divide 12.75 by 5
.3. Apex Car Share Inc. offers car sharing for a $99 yearly fee plus $19 per hour for the use
of its car share. Write the equation that models the total cost for use of Apex Car Share, if
t represents the total cost and h represents the number of hours the vehicle is used.
The required equation is 99 + 19 h = t .
What is linear equation?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
Given: Total cost = t
and the number of hours the vehicle is used = h hours
Since $99 is supposed to given that is, it is mandatory.
And $19 is supposed to be paid for per hour use.
Thus the equation is ;
99 + 19 h = t ; where t is total cost and h is number of hours the vehicle is used
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(3+√c) (2√c - 3) = 1 + k√c
where c and k are prime numbers.
(a) Find the value of c and the value of k.
Answer:
c = 5
k = 3
Step-by-step explanation:
We have the expression:
(3+√c) (2√c - 3) = 1 + k √c
Expanding the LHS using the FOIL method =>
(3 + √c) (2√c -3)
= (3)(2√c) + 3(-3) + (√c)(2√c) -√c(3)
= 6√c -9 + 2(√c)² -3√c
= 3√c + 2c - 9 [(√c)² = c]
Setting this equal to the RHS of 1 + k√c gives us
3√c + 2c - 9 = 1 + k √c
Since c and k are prime numbers, √c is irrational.
Therefore we match the irrational terms to get
3√c = k√c
=> k = 3 [divide both sides by √c]
Substitute k = 3 into 3√c + 2c - 9 = 1 + k √c
=> 3√c + 2c - 9 = 1 + 3√c
Add 9 to both sides
=> 3√c + 2c - 9 + 9 = 1 + 9 + 3√c
=> 3√c + 2c - 0 = 10 + 3√c
Subtract 3√c from both sides to eliminate this term on both sides
=> 3√c - 3√c + 2c - 0 = 10 + 3√c 3√c
=> 0 + 2c = 10 + 0
=> 2c = 10
Dividing by 2 on both sides gives us
c = 5
Answer: c = 5, k = 3