The 2 real solutions are rational and irrational solutions.
Quadratic Formula is the simplest method to find the roots of a quadratic equation. There are particular quadratic equations that cannot be easily factorized, and here we use this quadratic formula to find the roots in the quickest possible way.
Quadratic Formula: The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.
The value b² - 4ac is called the discriminant of a quadratic equation and is represented as 'D'. The nature of the roots of the quadratic equation can be predicted based on the discriminant value.
If D > 0, the roots are real and distinct (two real solutions).
If D = 0, the roots are real and equal (one real solution).
If D < 0, the roots do not exist, or they are imaginary (two imaginary solutions).
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The answer is in the photo for you to answer.
Answer :
HU length = 24
If UVW is Isosceles triangle then UGH is Isosceles
UV=UW = 132
Then,
HU = UG = 24
Please Help Asap...! :)
A) The time in minutes that it would reach 40% charge is; 48 minutes
B) The percent at 1 hr 48 minutes is; 90%
How to solve Linear Equation Word problems?The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
From the given parameters, we can find the slope from the formula;
m = (y2 - y1)/(x2 - x1)
m = (30 - 10)/(36 - 12)
m = 20/24
m = 5/6
Thus, for a 40% charge, we have;
5/6 = (40 - 30)/(t - 36)
Cross multiply to get;
5(t - 36) = 60
t - 36 = 12
t = 48 minutes
B) After 1 hr 48 minutes or 108 minutes, it means that;
Percentage = 5/6 * 108
= 90%
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At the grocery tore 4 pint of ice cream cot $10. 36. How much would 20 pint of ice cream cot?
Answer:$51.08
Step-by-step explanation:
The quotient of a number x and 19 is 10.
An equation is [ ].
In the continental United States the ratio of states the border an ocean to states that do not boarder an ocean is 7:9. How many states are landlocked and do not boarder an ocean.
There are 21 states landlocked and 27 states do not border an ocean.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Since there are 48 states in the continental United States, some of which are on the border of an ocean and some of which are not.
According to the question,
The ratio of the states having the border to the ocean and not having the border to the ocean = 7 : 9
Let the states having the border to the ocean = 7x
The states do not have a border to the ocean = 9x
Thus, 7x + 9x = 48
⇒ 16x = 48
⇒ x = 3
So, the states do not have a border to the ocean = 7 × 3 = 21
And, the states do not have a border to the ocean = 9 × 3 = 27
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in a group of 42 students 17 use pens for writing and 21 use pencils for writing. find the probability that a student picked from this group at random is using a pen or pencil?
(Using addition rule of probability)
The probability that a student picked from this group at random is using a pen or pencil is 19/21
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, in a group of 42 students, 17 use pens for writing and 21 use pencils for writing.
P(A or B) = P(A) + P(B)
P(A) = 17 / 42
P(B) = 21 / 42
P(A or B) = 17 / 42 + 21 / 42
P(A or B) = 38 / 42
P(A or B) = 19/21
Hence, the probability that a student picked from this group at random is using a pen or pencil is 19/21
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What is the difference between mixture and compound Class 9?.
The main difference between a mixture and a compound is that a mixture is a physical combination of substances while a compound is a chemical combination of elements.
In chemistry, a mixture is a combination of two or more substances that are not chemically combined and can be easily separated by physical means. The properties of a mixture depend on the properties of the individual substances that make it up, and the substances retain their original properties. Examples of mixtures include air, salt water, and a bowl of fruit.
A compound, on the other hand, is a substance that is made up of two or more elements chemically combined in a fixed ratio. The properties of a compound are different from those of the individual elements that make it up. The atoms in a compound are chemically bonded together and cannot be easily separated by physical means. Examples of compounds include water (H₂O), table salt (NaCl) and sugar (C₁₁H₂₂O₁₁).
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Alexia needs to add 2/3 cup of sugar for the recipe she is making. She has added 1/2 cup already. How much more sugar does she need to add?
Answer: 1/6
Step-by-step explanation: 2/3 = 4/6
1/2 = 3/6
4/6 - 3/6 = 1/6
Sylvester and Lin go to the amusement park. Sylvester plays 5 rounds of mini golf and takes 4 turns in the batting cages for $60. Lin plays 3 rounds of mini golf and takes 6 turns in the batting cages for $45. Use two equations to find the price for each activity. Enter your answers in the boxes.
Answer:
Mini golf costs: $10.00 per round.
Batting cages cost: $2.50 each turn.
Step-by-step explanation:
Let g= rounds of golf
Let b = batting cage
Sylvester
5g+4b = 60
Lin
3g +6b = 45
We have two equations and two unknowns
5g+4b = 60
3g +6b = 45
Divide the second equation by 3
3/3g +6/3b = 45/3
q+2b = 15
Multiply this equation by -2
-2q -4b= -30
Add this to the first equation
5g+4b = 60
-2q -4b = -30
3q = 30
Divide by 3
3g/3 = 30/3
g = 10
A game of mingolf is 10 dollars
Now we need to find b
q+2b = 15
10 +26 =15
Subtract 10
10-10+2b =15-10
26=5
Divide by 2
2b/2 =5/2
b=25
A turn in the batting cage is 2.50
Which is the correct graph for 3y=2x−3
Answer:
D or the last graph. (I attached it)
Step-by-step explanation:
Rewrite in slope-intercept form:
[tex]y = \frac{2}{3}x - 1[/tex]
Using the slope-intercept form, the slope is [tex]\frac{2}{3}[/tex] or [tex]m = \frac{2}{3}[/tex].
Start on the graph by graphing (0, -1), then graph your slope. Up 2, over 3 & repeat!
What is the y-intercept for the graph of this line 3x 5y 6'6 next question?.
The y-intercept for the graph of this line 3x-5y=6 is -6/5.
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
To determine the intercept of the equation, it would be helpful to write it in its slope-intercept form which is expressed as:
y = mx + b
where m is the slope and b is the y-intercept. Therefore, the value of b would be the correct answer here.
3x-5y=6
5y=3x - 6
y = 3x/5 - 6/5
Thus, the y-intercept is -6/5.
Thus, the y-intercept for the graph of this line 3x-5y=6 is -6/5.
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What is the slope of the line 5y =- 3x 10?.
The slope of the line 5y = -3x + 10 is -3/5.
To find the slope of the line represented by the equation 5y = -3x + 10, we can first put the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
In this case, we can start by dividing both sides of the equation by 5:
y = (-3/5)x + 2
where (-3/5) is the slope of the line, and 2 is the y-intercept. Therefore, the slope of the line 5y = -3x + 10 is -3/5.
Alternatively, you could have directly found the slope by looking at the x and y coefficients, in this case the slope is -3/5
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What are the steps to plotting points on a coordinate plane?.
To plot a point in a coordinate plane, first we have to define the point, then determine the coordinates, both x and y coordinates. Then plot the point in the appropriate plane.
A point is usually in a coordinate plane is described by two axis, X and Y. A point will usually be denoted as (x,y). From these values we have to determine where the point might be lying. If the x value is positive it is towards the right of 0 and negative it will be towards left. Y value become positive upwards and negative downwards.
After determining the coordinates we label as the readings the the X axis and Y-axis. In the figure given below we have plotted some points.
Point A (2,2) with x-coordinate 2 and y coordinate 2 , B(4,-2) with x coordinate 4 and y coordinate -2, C(-3,-1) with x coordinate -3 and y coordinate -1, D(-2,3) with x coordinate -2 and y coordinate 3.
So, for plotting we have to determine the coordinates and plot it.
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1. Find the equation of the line with slope 5 and y-intercept, 6.
2. Find the equation of the line that passes through the point with coordinates(0,5) and a slope of 3.
3. Determine the x-intercept and y-intercept of equation 4x+2y=16
What are the ratios of trigonometry?.
The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).
In arithmetic, the trigonometric functions (also known as circular features, perspective features, or goniometric functions) are actual features that relate an angle of a proper-angled triangle to ratios of side lengths. they may be extensively utilized in all sciences which might be associated with geometry, such as navigation, strong mechanics, celestial mechanics, geodesy, and lots of others. they are a few of the handiest periodic features, and as such are also extensively used for analyzing periodic phenomena through Fourier analysis.
The trigonometric functions most extensively used in cutting-edge mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. each of these six trigonometric capabilities has a corresponding inverse function and an analog most of the hyperbolic features.
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which of the following subtractions is closest to 809-392
a=800-300
b=800-400
c850-400
d=900-300
Can someone show how to do this step by step with a graph?
Plot the lines and shade in the regions on the same x-y plane to find the solution to the system of inequalities 4x+6y ≤ 24 and x + 5y ≤ 10 fall under the mixed shaded region in the graph.
What is the linear inequalities?
Linear inequalities are mathematical expressions that describe a relationship between two variables that is linear in nature. The most common form of a linear inequality is of the form ax + by < c, where a, b, and c are constants and x and y are variables.
Yes, this system of two linear inequalities can be represented graphically on the x-y plane by plotting the solutions to each inequality. The steps are as follows:
Replace the equation with the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. For example, the first equation can be rearranged as:4x + 6y <= 24
=> -6y <= -4x + 24
=> y >= (4/6)x + 4
=> y = (4/6)x + 4
Plot the line corresponding to each equation. You can use the slope-intercept form of each equation to get the slope and y-intercept of each line, and then plot the line using the slope and y-intercept. For example, the line for the first equation is y = (4/6)x + 4, which is the graph of a line with slope 4/6 and y-intercept 4. The line for the second equation is y = (1/5)x + 2, which is the graph of a line with slope 1/5 and y-intercept 2.Determine the side of the line to shade in for each inequality. If the inequality is less than or equal to, shade in the region below the line. If the inequality is greater than or equal to, shade in the region above the line.The solution to the system of inequalities is the intersection of the shaded regions, which is the region where both inequalities are simultaneously satisfied. This represents the set of all possible (x, y) pairs that satisfy both equations.Plot the lines and shade in the regions on the same x-y plane to find the solution to the system of inequalities.To learn more about linear inequalities, Visit
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How to multiply 3 digit numbers by 2 digit numbers without regrouping?.
Multiply the number in the one's place, Multiply the number in the ten's place and multiply the one's and ten's place with the hundred place number, then add them up.
Follow along with example 343 × 32:
Place one number above the other so that the ones' place digits and tens' place digits are lined up. Mark a line just below the bottom number.
3 4 3
×3 2
_______
Multiply the ones' place digits (2 × 3 = 6), one's place of the second number by the ten's place of the first number (2 × 4 = 8), and one's place of the second number by the hundred place of the first number (2 × 3 = 6). Place the 6 below the line in the ones' place column, 8 below the line in the tens' place column and 6 below the line in the hundred place column.
3 4 3
×3 2
________
6 8 6
Multiply the digit in the tens' place column (3) by the digit in the ones' place of the first number (3). The result is 3 × 3 = 9; multiply the digit in the tens' place column (3) by the digit in the tens' place of the first number (4). The outcome is 3 × 4 = 12, and multiply the digit in the tens' place column (3) by the digit in the hundred place of the first number (3). The outcome is 3 × 3 = 9. Now add the numbers and place the answer below the line.
3 4 3
×3 2
__________
6 8 6
10 2 9×
__________
10 976
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What is distributive property of equality?.
The distributive property of equality states that the product of an expression and a sum is equal to the sum of the products of the expression and each term in the sum.
Distributive Property of equality : Distribution in mathematics means multiplying an element by two or more additive elements in parentheses.
Multiplying the set by the sum of two terms is the same as adding the products of the original set and each term. In other words, multiplying a quantity by the sum of two or more terms is the same as adding the product of original quantity and each term. A simpler way of expressing this is that the equality holds after the distribution of the terms. Let a, b, and c be real numbers. Then: a(b + c) = ab + ac. A more general formulation is to let be natural numbers and a, b₁, b₂, b₃,---, bₙ be real numbers. Then, a( b₁+b₂+ b₃ +---+ bₙ) = ab₁ + ab₂ + ab₃ + ----+bₙ.
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Pls help me with this
Answer:
Answers in attached photo.
Step-by-step explanation:
SolutionSteps are in the attached photo, do note that to ensure the inequality sign are always constant throughout the entire working, otherwise one wrong line will result incorrect answers below it.
What is the product 4y − 3 )( 2y 2 3y − 5?.
The product of equation (4y-3)(2y²+3y-5) is 8y³+6y²-29y+15.
According to the question,
The equation is = (4y-3)(2y²+3y-5)
A product is defined as the result of two or more numbers when multiplied together.In mathematics, a product is the result of multiplication or an expression that identifies objects ( variables) to be multiplied, called factors.First, let us start with "4y"
4y×2y² = 8y³
4y×3y = 12y²
4y×(-5 )= -20y
Next, let us multiply by "-3"
(-3)×(2y²) = -6y²
(-3)×3y = -9y
(-3)×(-5) = 15
Now, let us combine all of our values.
The product is = 8y³+12y²-6y²-20y-9y+15
= 8y³+6y²-29y+15 (apply BODMAS rule)
So, the product is 8y³+6y²-29y+15.
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7. Choose a method to solve the following system of equations. Then write 2-3 sentences
to why the system is set up for that method.
y = -2x + 6
y = 5x - 8
Type your 2-3 sentences in
text box below.
On solving the linear equations y = -2x + 6 and y = 5x - 8, the value for x is x = 2 and the value of y is y = 2.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The first linear equation is - y = -2x + 6
The second linear equation is - y = 5x - 8
Subtracting equation (1) from (2) -
y - y = 5x - 8 - (-2x + 6)
0 = 5x - 8 + 2x - 6
0 = 7x - 14
7x = 14
x = 14/7
x = 2
Substituting the value of y in equation (1) -
y = -2x + 6
y = -2(2) + 6
y = -4 + 6
y = 2
The subtraction and substitution method is chosen to solve the system of linear equations. The linear equations are first made equal in order to find the desired variable. Then subtraction is done to find the value of one variable. Next, the found value is substituted into the equation to find the unknown variable. This method is easy to understand and gives accurate value.
Therefore, the value of x and y is 2 and 2 respectively.
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A reflecting telescope's mirror diameter is 76 inches and depth is 42 inches. Where would the focus of the mirror be located? Answer to the nearest hundredth
The focus of 76-inch diameter and the 42-inch deep reflecting telescope is located approximately 87.92 inches or 7.32 feet from the center of the mirror, at the prime focus.
The focus of a reflecting telescope's mirror is the point where incoming light rays converge after being reflected by the mirror. The location of the focus depends on the size and curvature of the mirror. In this case, the mirror has a diameter of 76 inches and a depth of 42 inches.
This information can be used to calculate the location of the focus, which is approximately 87.92 inches or 7.32 feet from the center of the mirror. This distance is also known as the prime focus and is the point where the image is formed. The eyepiece of the telescope, which magnifies the image formed at the prime focus, is typically located a short distance away from the prime focus, often around 0.90 inches.
The secondary mirror is positioned to reflect light from the prime focus to the eyepiece.
Complete question:
A reflecting telescope's mirror diameter is 76 inches and depth is 42 inches. Where would the focus of the mirror be located? Answer to the nearest hundredth.
Primary Mirror
Lighting
Prime Focus
Secondary Mirror
Eyepiece
O1.68 inches
O 87.92 inches
O 512.00 inches
O 8.60 inches
O 0.90 inches
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What are the domain and range of g of x equals the square root of the quantity x minus 3? D: [3, ∞) and R: [0, ∞) D: [–3, ∞) and R: [0, ∞) D: (–3, ∞) and R: (–∞, 0) D: (3, ∞) and R: (–∞, 0)
ASAP
Answer: The domain of g(x) = √(x - 3) is (3, ∞) because the square root function is defined for non-negative numbers, x - 3 must be greater than or equal to 0, which means x must be greater than 3.
The range of g(x) = √(x - 3) is (0, ∞) because the square root function can only output non-negative numbers, and as x increases, the value of √(x - 3) will also increase.
So the correct answer is: D: (3, ∞) and R: (0, ∞)
Step-by-step explanation:
The domain of the given function is Domain: [3,∞),{x|x≥3} and the range is Range: [0,∞),{y|y≥0}. Therefore, the option A is the correct answer.
The given function is g(x)=√(x-3).
We know that, the domain is set of all x-values and the range is set of all y-values.
Substitute x=1, 2, 3, 4,.....in the given function, we get
g(1)=√(1-3) = i√2
g(7)=√(7-3) = 2
g(19)=√(19-3) = 4
So,
Domain: [3,∞),{x|x≥3}
Range: [0,∞),{y|y≥0}
Therefore, the option A is the correct answer.
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What is the value of the digit 3 in 17039 write in words
The digit 3 in the number 17039 represents the value of 3 in the tens place. The place value system is a way to understand the value of each digit in a number. In this case, each digit in the number 17039 has a specific place value, starting from the rightmost digit, which is the ones place, then the tens place, followed by the hundreds place and so on. In the number 17039, the digit 3 is located in the tens place which represent 3 x 10 = 30. To understand the value of any digit in a number, you can multiply the digit by its corresponding place value.
Answer:
The digit 3 in the number 17039 represents the value of 3 in the tens place
Step-by-step explanation:
How do you solve 4 more than 5?.
To write 4 more than 5, we use the mathematical operation of addition and the notation 4 + 5 = 9.
To write 4 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.
In this case, we are given the number 5 and we are asked to find the number that is 4 more than it. To do this, we can use the mathematical notation: 4 + 5 = 9.
This notation means that we are adding 4 to 5, which results in N+4. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+4
Another way to write 4 more than a number is to use the phrase "4 plus 5". This phrase indicates that we are adding 4 to 5 to get 9.
Therefore, In short, to write 4 more than a number, we use the mathematical operation of addition and the notation 4 + Number = N+4. This means that we are adding 10 to a number, resulting in N+4. It can also be written as "4 plus N", indicating the same operation i.e 4 + 5 = 9.
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Part A Determine the magnitude of the resultant force. Express your answer to three significant figures and include the appropriate units. OCH Å ? O Units Fr = Value Submit Request Answer Part B Determine the direction of the resultant force, measured counterclockwise from the positive axis. Express your answer using three significant figures. IVO A ¢ vec ROO? Submit Request Answer Provide Feedback
The angles from an isosceles triangle are simple to calculate. But in order to strengthen the customary methodical approach to vector addition, we note that the angle [tex]$\overrightarrow{\mathrm{b}}$[/tex] makes with the [tex]$+\mathrm{x}$[/tex] axis is
[tex]$30^{\circ}+105^{\circ}=135^{\circ}$[/tex]
What is resultant force?The difference between the forces exerted on an item when a system of forces is at work is known as the resultant force. For instance, a force of 3 N to the left and 10 N to the right results in a force of 7 N to the right. If all of the forces are acting in the same direction, then all of the forces will be acting in the same direction. The three forces that are operating on a body in the same direction are represented by the letters F (1), F (2), and F (3) in the formula above. F(R) = [(F (1) ^2+F (2) ^2)] ^ 1/2.The combined force that two or more forces exert on an item can be calculated by adding up the component forces.It should be noted that using the cosine law for general triangles is an effective technique to solve this vector addition problem (also because
[tex]$\vec{a}[/tex], [tex]\vec{b}[/tex] and [tex]$\vec{r}$[/tex] The angles from an isosceles triangle are simple to calculate. But in order to strengthen the customary methodical approach to vector addition, we note that the angle [tex]$\overrightarrow{\mathrm{b}}$[/tex] makes with the [tex]$+\mathrm{x}$[/tex] axis is
[tex]$30^{\circ}+105^{\circ}=135^{\circ}$[/tex]
(a) The x component of
[tex]$\overrightarrow{\mathrm{r}_{\mathrm{x}}}=(10.0 \mathrm{~m}) \cos 30^{\circ}+(10.0 \mathrm{~m}) \cos 135^{\circ}=1.59 \mathrm{~m}$[/tex]
(b) the y component of
[tex]$\vec{r}$ is $r_y=(10.0 \mathrm{~m}) \sin 30^{\circ}+(10.0 \mathrm{~m}) \sin 135^{\circ}=12.1 \mathrm{~m}$[/tex].
(c) the magnitude of
[tex]\vec{r}$ is $r=|\vec{r}|=\sqrt{(1.59 \mathrm{~m})^2+(12.1 \mathrm{~m})^2}=12.2 \mathrm{~m}[/tex]
(d) The angle between
[tex]\overrightarrow{\mathrm{r}}$ and the $+\mathrm{x}$ direction is $\tan ^{-1}[(12.1 \mathrm{~m}) /(1.59 \mathrm{~m})]=82.5^{\circ}$[/tex]
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A bank account pays 2% annual (yearly) interest. a. If $500 is put in the account, what will the balance be at the end of five years, assuming no additional deposits or withdrawals are made? b. Write an equation that shows how to correctly determine the answer.
The balance at the end of five years is $552.04.
The equation that that represents the balance in the account is $500 x (1.02)^5
What will be the balance of the account?The amount of money in the bank account would grow at an exponential rate.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate N = number of years$500 x (1 + 2/100)^5
$500 x (1.02)^5 = $552.04
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What is the first step in solving this equation 3 2x 6 )- 4x 2 5x 2 )+ 6?.
The correct option is D. Use the distributive property on each side of the equation.
In step with this belongings, multiplying the sum of two or more addends by means of a number will deliver the identical result as multiplying each addend in my view by the quantity after which including the products together. The distributive belongings tell us how to remedy expressions in the form of a(b + c). The distributive belongings are every so often known as the distributive law of multiplication and division.
The Distributive asset is an algebraic asset that states that when an element is improved by means of the sum or difference of terms, it's far essential to multiply every one of the two numbers by means of the element, and subsequently perform the addition or subtraction operation.
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Complete Question:
What is the first step in solving this equation? 3(2x + 6) – 4x = 2(5x – 2) + 6.
A). Use the subtraction property of equality to subtract 6 from both sides. B). Use the addition property of equality to add 4x to both sides.
C). Combine the like terms on each side of the equation.
D). Use the distributive property on each side of the equation.
Ivan has inherited his mother's 1963 Chevrolet Corvette, which hevalues at $45,000. He decides that he might be willing to sell it so heposts it on Craigslist for $55,000. Samantha is interested and willing to pay up to $72,000
Samantha is willing to pay up to $72,000 for the 1963 Chevrolet Corvette, which is $17,000 more than Ivan's asking price of $55,000.
What do you mean by inherit?It means to receive something from a parent or ancestor through genetic transmission. It also means to receive something as a devise or legacy from an ancestor. inherit an enzyme that is flawed.
Ivan inherited the car and valued it at $45,000, therefore he would make a profit of $17,000 if he sells the car to Samantha.
It's important to note that the final price will depend on the negotiation and agreement between Ivan and Samantha.
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