The values of x that will make x² = 9 are positive 3 and negative 3.
What is a quadratic equation?A quadratic equation is an algebraic equation that has highest degree of 2, therefore, it also has two roots or we can say it has two solutions.
We know sign distributions that negative distributed to a negative is positive and positive distributed to a positive also results in positive.
∴ 9 can be obtained by either multiplying (-3)(-3) or (3)(3).
So, the value of x that will make x² = 9 is
x = ± √9
x = ± 3.
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The product of any integer and –1 is always
Simplify each expression.
√11(4√11)
The expression given tests on indices. The expression can be written in index form as a^m. Thus, b√a = a^(1/b) From the power rule of indices, a^m x a^n = a^(m+n).
√11(4√11)
11^1/2 ( 11^1/4)
11 ^(1/2+1/4)
11^3/4
4√11^3
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can someone help me really quick
Answer:
2 2/4 because i just know the answer
x+2−0.5x=1+.0.5x+1 solve for x
Answer:
x = 0
Step-by-step explanation:
x + 2 - 0.5x = 1 + 0.5x +1
2 - 0.5x = 2 + 0.5x
-0.5 - 0.5x = 2 - 2
-1x = 0
-1x/-1 = 0/-1
x = 0
Answer:
Step-by-step explanation:
Solve X + 2 - 0.5 x = 1 + 0.5 x + 1 : The answer is: X = 2X
the sum of a number and two thirds the number is the same as 4 less than twice the number
12
Step-by-step explanation:
n + (2/3)n = 2n - 4
(5/3)n = 2n - 4
(5/3)n - 2n = -4
(-1/3)n = -4
n = 12
Juan and Houa are reading the same book. At the beginning of the month, Juan was on page 45 and Houa was on page 9. Juan will read 15 pages per day and Houa will read 18 pages per day. Let J represent the page of the book that Juan is on at the end of t days into the month, and let H represent the page of the book that Houa is on at the end of t days into the month. Write an equation for each situation, in terms of t, and determine what page Juan and Houa will be on on the day they are both on the same page.
The page they will be on is 225.
What page will they be on?The page that both Juan and Houa would be on at the end of the month is a function of the page they are at the beginning of the month and the page they read per day.
Pages they are in t days:
J = 45 + 15t
H = 9 + 18t
When they are on the same page, both equations would be equal
45 + 15t = 9 + 18t
45 - 9 = 18t - 15t
36 = 3t
t = 36 / 3
t = 12
Page they would be in 12 days: 45 + 15(12)
45 + 180 = 225
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Giải Phương trình
(x-3)^2+x^4= -y^2+6y-4
Answer:
Solution on screen
Step-by-step explanation:
Don't worry it's okay
dana said that 0.6 divided by 30 = 0.02. is she correct? explain.
Answer:
It can be said that Dana is correct when she says that 0.6 divided by 30 gives 0.02 as a reminder.
Step-by-step explanation:
It is given that we need to rectify whether 0.6 divided by 30 = 0.02 or not.
Firstly, let us understand how does simplification work;
In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.
Now, let us understand what exactly is arithmetic;
According to the assertions, it deals with a number of operations in mathematics. Addition, subtraction, multiplication, and division are the four main arithmetic operators.
Now, let us equate the given condition that is;
=> 0.6 can also be expressed as 6/10
Now, let us divide the above numbers with each other as given in the question;
=> (6/10) ÷ 30
=> 6/300
On dividing both the numbers with each other we get;
=> 0.02 which can be expressed as 2/100
Therefore, it can be said that Dana is correct when she says that 0.6 divided by 30 gives 0.02 as a reminder.
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Answer:
Step-by-step explanation:
The force F of gravity on a rocket varies directly with its mass m and inversely with the square of its distance d from Earth. Write a model for this combined variation. Write an equation to find the mass of the rocket in terms of F and d .
Model for the Combined variation is [tex]F = \frac{km}{d^{2} }[/tex]
Equation to find the mass of the rocket in terms of F and d is :
[tex]m=\frac{F d^{2} }{k}[/tex]
What is Force ?A force is the quantity that change the motion of the object. Force is that influence which can cause any object having some mass, to change it's position or to accelerate from it's original position.
Force (F) and mass (m) of any object are directly proportional to each other. More the mass of the object , more the force will require to accelerate it.
Mathematically, we can write the equation of force as :
F = m . a
where , m = mass of the object
a = constant value
In the statement given,
As, force of gravity varies directly with its mass
Therefore, F= k m , where k is a constant
Also force is inversely varies with square of distance d
Thus, F = k / d²
Combining both equations :
[tex]F = \frac{km}{d^{2} }[/tex]
and the equation of mass in terms of F and d can be written as :
[tex]m=\frac{F d^{2} }{k}[/tex]
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Which method do you think is easier to use to find the gradient of the line joining R(-50, 460) and S(115, 55)? Explain your answer.
The gradient of the line joining R(-50, 460) and S(115, 55) is -2.45
How to find the gradient of the line joining R(-50, 460) and S(115, 55)?The points on the line are given as
R = (-50, 460)
S = (115, 55)
The gradient of the line joining R(-50, 460) and S(115, 55) is calculated using
Gradient = (y2 - y1)/(x2 - x1)
This gives
Gradient = (460 - 55)/(-50 - 115)
Evaluate
Gradient = -2.45
Hence, the gradient of the line joining R(-50, 460) and S(115, 55) is -2.45
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HELP ME PLSSSSSS , MY DEADLINE IS NOW PLS HELPPP
Multiple choice :
A) 0
B) 2
C) -1.5
D) 4
E) 0.5
=======================================================
Explanation:
The given equation is in the form of ax^2+bx+c = 0
The coefficients are
a = 2b = kc = -3According to Vieta's formula, we know that the roots of a quadratic multiply to c/a
In this case, the roots multiply to -3/2
Let p and q be the two roots. We're told that -3 is one of the roots, so p = -3. Let's find q.
pq = c/a
-3q = -3/2
q = (-3/2)*(-3/1)
q = 1/2
q = 0.5
The other root is 0.5
The product of the roots is -3*0.5 = -1.5 = -3/2 to confirm the answer.
-------------
The longer way to solve would be to plug x = -3 into the equation and solve for k. You should get k = 5
Once you know the value of k, use the quadratic formula to find the two roots. You should get -3 and 1/2 = 0.5 as the two roots.
Find the least integer greater than each number. Do not use a calculator.
log₅1/47
The least integer greater than each number for log₅1/47 = -3
All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.
Let y = log₅1/47
We know, logₐ x = y, only if a^y= x
Therefore, 5^y = 1/47
So, we must find an integer y such that 5 > 1/47
5^y > 1/47
5^{-3} > 1/47
(As, 5² = 25; 5³ = 125) (Since, 5² < 47, the answer will be 5³ as 5³ > 47)In this case, y = -3 will be the least integer to satisfy this inequality.
Therefore, the ultimate answer to the equation is log₅1/47 = -3
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An athlete trains for 105 min each day for as many days as possible write an equation that relates the number of days d that the athlete spends training when the athlete trains for 630 min
Write each logarithm as the quotient of two common logarithms. Do not simplify the quotient.
log₅140
The value of logarithm as the quotient of two common logarithms is [tex]\frac{Log 140}{Log5}[/tex]. Because [tex]Log_{a}(b)=Log\frac{b}{a}[/tex]
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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Write each expression in simplest form. (x⁻²/₃ / y⁻¹/₃)¹⁵
The given expression is a fraction raised to a power and will be solved by multiplication of exponents for both numerator and denominator.
When in an expression, the base is a fraction raised to a number (exponent), the exponent is applied to both numerator and denominator.
In this case, the base is x^-2/3/y^-1/3 and the exponent is 15.
Since (x^a)^b=x^ab
Multiplication of exponent applied to both numerator and denominator,
(x^⁻²/₃/y^⁻¹/₃)^¹⁵=x^⁻²/₃*15/y^⁻¹/₃*15
Simplifying,
x^⁻²/₃*15/y^⁻¹/₃*15=x^-10/y^-5
Since both numerator and denominator have negative exponents, it is not yet in the simplest form.
According to negative exponents rule, x^-a=1/x^a
To remove the negative exponent, the fraction should be reversed.
x^-10/y^-5=y^5/x^10
The simplest form of the expression (x^⁻²/₃/y^⁻¹/₃)^¹⁵ is y^5/x^10
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Simplify each expression.
10 ln e
10 (ln (e)) = 10, by the definition of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
By property of logarithm, ln (e) = 1
Thus, in the expression 10 (ln (e)) = 10 (1) = 10.
Hence, 10 (ln (e)) = 10, by the definition of logarithm.
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Jerica sells used motorcycles. she makes $300 per week plus $75 for each bicycle sold. she wants to earn $1059?per week. write an equation to find out how many motorcycles she must sell each week to accomplish this.
Answer: $684
Step-by-step explanation: Add 300 to 75 and you have 375, next subtract the total payment she wants to have per week (which is 1059) so, subtract 1059 to 375 then you have $684. To check your answer, add 684 to 375 and you come up with 1059.
Simplify each number. 100⁴.⁵
The result of simplifying each number 100⁴.⁵ using the exponent rules is
10⁽⁴⁰⁾
To solve this exercise we have to resolve algebraic operations following the exponent rules.
100⁴.⁵
Base= 100 = 10²
The base number 100 is the same that: 10², then we get:
(10²)⁴.⁵
Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
10⁽²*⁴*⁵⁾
10⁽⁸*⁵⁾
10⁽⁴⁰⁾
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Moussa has a collection of vintage action figures that is worth $390. If the collection appreciates at a rate of 3% per year, which equation represents the value of the collection after 3 years?
The equation representing the future value of the collection is given by V=390(1.03)³ as the value appreciates by 3%.
When a value appreciates at a certain percentage means the value of the collection increases by that percentage each year.
The equation that represents such an appreciation is in the form of an exponential equation.
The general equation for calculating future value with appreciation is:
[tex]V = P (1 + r)^n[/tex] where
V = Future value
P = Present value
r = appreciation rate
n = number of years
Given P = $390 , r= 3%=0.03 , n = 3
Now we substitute the given values in the equation to get:
V=390(1+0.03)³
or, V= 390(1.03)³
or, V= 426.16 dollars approximately .
Hence the required equation is V= 390(1.03)³ .
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Tim wants to enclose a 12ft x 8ft plot of land for his garden. How much fencing does he need?
Tim needs 40ft fencing.
For fencing the square garden we need to ascertain perimeter of the square.
Perimeter of plot = 2*(a+b)
Where a = length of the plot
b=width of plot
length =12ft
width=8ft
Perimeter of plot = 2*(a+b) = 2*(12+8)ft=40ft
He needs 40ft fencing.
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work out 7+8 over 5-2
Answer:
[tex]6\frac{3}{5}[/tex]
Step-by-step explanation:
[tex]8 \div 5 = 1\frac{3}{5} \\\\1\frac{3}{5} + 7 = 8\frac{3}{5}\\\\8\frac{3}{5} - 2 = 6\frac{3}{5}[/tex]
The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has
$21 and would like to travel 50 kilometers. She wants to know the largest number of stops she
can afford to buy on a ticket.
Let S represent the number of stops that Julia buys.
1) Which inequality describes this scenario?
Choose 1 answer:
5 + 2.75 . S € 21
5 + 2.75 - 5 > 21
(C
5 + 2.75 - 5 = 50
5 + 2.75. S > 50
Considering the definition of an inequality, the inequality 5 + 2.75×S ≤21 describes the scenario.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has $21 and would like to travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticket.Being "S" the number of stops that Julia buys, the inequality that expresses the previous relationship is
5 + 2.75×S ≤21
Finally, the inequality 5 + 2.75×S ≤21 describes the scenario.
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What is the final version of this supposed to look like?
The graph of the inequality expressions is added as an attachment
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine the graph of the inequality expression?The inequality expressions are given as
y ≥ 2
x + y ≤ 4
y ≤ 2x + 2
Next, we interpret each inequality expression
First expression: y ≥ 2
The inequality symbol in the above inequality expression is ≥
This implies that the inequality expression is a greater than or equal to
When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line
Also, the inequality symbol implies that the upper part is shaded
Second expression: x + y ≤ 4
The inequality symbol in the above inequality expression is ≤
This implies that the inequality expression is a less than or equal to
When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line
Also, the inequality symbol implies that the bottom part is shaded
Third expression: y ≤ 2x + 2
The inequality symbol in the above inequality expression is ≤
This implies that the inequality expression is a less than or equal to and the inequality symbol implies that the bottom part is shaded
See attachment for the graph of the inequality expressions
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rearrange x=3g+2 make g the subject
Answer:
3g=x-2
Step-by-step explanation:
3g+2=x then, move 2 to the other side(nb*change to negative) then it will be 3g=x-2 finally divide both sides by 3 then it will be g=x-2
3
The product of 3 and a number x is 23.
What is the value of x?
x=7/3
x=2/9
x=2
x=2 1/3
Answer:
D.
Step-by-step explanation:
x=2 1/3
That is the answer
The graph of y = f(X) is shown.
b) Find the roots of f(X) = 0
c) Find f(0)
A) The roots of the graph f(x) are; x = -2 and x = -1
B) The value of the function at f(0) is; 2
How to find the roots of a quadratic graph?
a) We want to find f(0) of the graph.
Now, f(0) simply refers to the y-values when x = 0.
This is the point at which the graph crosses the y-axis
From the graph we can see that the value here is 2. Thus;
f(0) = 2
b) To find the roots of f(x) , we simply find the points at which the plot crosses the x-axis.
From the graph, the roots are at x = -2 and x = -1
Thus, the roots of the equation are x = -2 and x = -1
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what is the answer to the problem.
Answer:
0
Step-by-step explanation:
Because there is no question only
solve the equation -27=3/4w
Answer: w = -32
Step-by-step explanation:
Start isolating the variable by getting rid of 3/4. You can do this by multiplying by its reciprocal.
That leaves us with 3/4 times -27
The product is -32.
Hope this helps!
P
=
2
L
+
2
W
to find the length of a rectangle when the width is
4 1/2
inches and the perimeter is
29 2/5
inches.
Answer:
10 2/5 inches
Step-by-step explanation:
Since P=2L+2W, we can flip it to find the length. For example, we could minus 2L from both sides to get P-2L=2W.
We already know that W is 4.5, and P is 29.4.
Plugging that in, we get 29.4-2L=9. Again we can flip the perimeter, and -29.4 on both sides. This would make -2L=-20.4.
For our last flip, we divide the -2 from both sides to finally get L=10.2 (or 10 1/5 if you want) inches.
the graphs of y=-4x and y = -4x + 2 are shown. Use the drop down menus to complete the statements The ratios of y/x are the same for the graph of ________ the ratios of y/x are NOT the same for the graph of ______
The ratios of y/x are the same for the graph of y = -4x and y = -4x + 2 because they both represent parallel lines.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope and it is given by this mathematical expression, slope, m = Δy/Δx.
In this context, we can reasonably infer and logically deduce that the ratios of y/x are the same for the graph of y = -4x and y = -4x + 2 because they both represent parallel lines.
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