A three-course meal will contain 1 pizza, 1 salad, and 1 dessert.
The question tells us that there are 4 different salads, 5 different pizzas, and 3 different desserts.
Therefore, the total number of possible ways a three-course meal can be served is calculated as the product of all the numbers. This is shown below:
[tex]\Rightarrow4\times5\times3=60[/tex]60 different meals can be ordered.
Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. Theamounts she spent in each category are pictured here.Food$333Rent$417Other$500Fun$250What percent of her total spending did she spend on Fun? Answer to the nearest whole percent.
In this problem we have to calculate the total spences so we add all the costs so:
[tex]\begin{gathered} T=333+417+500+250 \\ T=1500 \end{gathered}[/tex]So 1500 is the 100% so now we can calculate which percentage correspount to 250 so:
[tex]\begin{gathered} 1500\to100 \\ 250\to x \end{gathered}[/tex]so the equation is:
[tex]\begin{gathered} x=\frac{250\cdot100}{1500} \\ x=16.66 \end{gathered}[/tex]So she spend 16.66% in fun
Find the volume of the given solid.Round to the nearest 10th, If necessary. In cubic inches
ANSWER
33.5 cubic inches
EXPLANATION
This is a cone with radius r = 2 in and height h = 8 in. The volume of a cone is,
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]Replace the known values and solve,
[tex]V=\frac{1}{3}\cdot\pi\cdot2^2in^2\cdot8in=\frac{32}{3}\pi\text{ }in^3\approx33.5\text{ }in^3[/tex]Hence, the volume of the cone is 33.5 in³, rounded to the nearest tenth.
The figure shows rectangle PQRS in the first quadrant of the coordinate plane?
The quadrants of a coordinate plane are:
Then, we can say that the rectangle PQRS is in the first quadrant.
10) f(x) = x5 - 10x4 + 42x3 -124 x2 + 297x - 306; zero: 3i ? A) 2, -3i, -4 - i, -4 + i C) 2, -3i, 4 - i, 4 + i B) -2, -3i, -4 -i, -4 + i D) -2, -3i, 4-i, 4 + i
Answer
Option C is correct.
The roots of the given function include
2, -3i, (4 + i), (4 - i)
Explanation
To solve this, we would put the given roots of the solution into the place of x. The ones that give 0 are the roots of the expression
The expression is
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
Starting with 2
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(2) = 2⁵ - 10(2)⁴ + 42(2)³ - 124(2)² + 297(2) - 306
= 32 - 160 + 336 - 496 + 594 - 306
= 0
So, 2 is a root
-3i
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(-3i) = (-3i)⁵ - 10(-3i)⁴ + 42(-3i)³ - 124(-3i)² + 297(-3i) - 306
= -243i - 810 + 1134i - 1116 - 891i - 306
= 0
So, -3i is also a root
4 + i
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(4 + i) = (4 + i)⁵ - 10(4 + i)⁴ + 42(4 + i)³ - 124(4 + i)² + 297(4 + i) - 306
= 0
So, we know that the right root, when inserted and expanded will reduce the expression to 0.
4 - i
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(4 - i) = (4 - i)⁵ - 10(4 - i)⁴ + 42(4 - i)³ - 124(4 - i)² + 297(4 - i) - 306
= 0
Inserting any of the other answers will result in answers other than 0 and show that they aren't roots/zeros for this expression.
Hope this Helps!!!
HELP ASPAPP The general form of an equation is x2+y2−25x+3y+1=0.
What is the equation of the circle in standard form?
Answer:
the first (top) answer option. ... = 129/100
Step-by-step explanation:
the for me qualifying or disqualifying term is the constant term as the product and sum of all the constant parts.
the general form has the constant parts
... + 1 = 0
so, all the constant terms from the squares on the left side minus the constant term on the right side must be 1.
let's start from the bottom : the 4th answer option.
the constant parts are
... + (-1/5)² + ... + (3/2)² = 121/100
... + 1/25 + ... + 9/4 = 121/100
... + 0.04 + ... + 2.25 = 1.21
... + 2.29 - 1.21 = ... + 1.08
and NOT 1. so, this is wrong.
the 3rd answer option.
... + (-1/3)² + ... + (-3/2)² = 221/100
... + 1/9 + ... + 9/4 = 221/100
... + 0.111111... + ... + 2.25 = 2.21
... + 0.111111... + ... + 2.25 - 2.21 = 0
... + 0.111111... + ... + 0.04 = 0
... + 0.111111 + 0.04 = 0.15111111...
and NOT 1. so, this is wrong.
the 2nd answer option.
... + (-1/5)² + ... + (3/2)² = 229/100
... + 1/25 + ... + 9/4 = 229/100
... + 0.04 + ... + 2.25 = 2.29
... + 2.29 - 2.28 = ... + 0
and NOT 1. so, this is wrong.
the first answer option.
... + (-1/5)² + ... + (3/2)² = 129/100
... + 1/25 + ... + 9/4 = 129/100
... + 0.04 + ... + 2.25 = 1.29
... + 2.29 - 1.29 = ... + 1
this IS 1. so, this is correct.
this corresponds now to the original
... + 1 = 0
Answer: Choice A (May vary from test to test)
Step-by-step explanation:
(x-1/5)^2 + (y+3/2)^2 = 129/100
Just an FYI:
I can't stress this enough... Add equation symbols when applicable, for example: √,^,/, etc. You can't expect to have someone give the correct answer when you literally typed the equation out incorrectly.Complete the square for each expression. Write the resulting expression as a binomial. x^2+14x+____
To complete the square is take the second term in the expression, divided it by 2 and then squared it. This will be the number that we have to add to the original expression.
(14/2)^2=49
so, completing the expression:
x^2+14x+49
Then, the new expression can be factored into a single term squared:
x^2+14x+49= (x+7)^2
is 2÷2 4 or am I wrong
2/2 = 1
The answer would be 1
Position Value of Term 1 1 2 3 -18 1-24 5 -30 What expression shows the relationship between the value of any term and n, its position in the sequence?
basically they are the negative multiples of 6, so:
[tex]a_n=-6n[/tex]7(x+2)=
4(x+4)=
9(x+6)=
Bao is mixing flour and water to make dough the graph shows how much water he uses for different amounts of flour .How many liters of water does Bao use per liter or flour?------ liters for this one your answer should be a simplified proper fraction like 3/5.How many liters of flour does Bao use per liter of water?------ liters.
To know how many liters of water Bao use per liter of flour we have to divide the liters or flour so:
[tex]\frac{1}{3}=0.33[/tex]So Bao uses 0.33 or 1/3 of water per liter or flour
and to know hoy manu liters of flour Bao use per liter of water we have to made the oposite division so:
[tex]\frac{3}{1}=3[/tex]She use 3 liters of flour per liter of water
Find a degree 3 polynomial that has zeros -2,3 and 6 and in which the coefficient of x^2 is -14. The polynomial is: _____
Given:
The zeros of degree 3 polynomial are -2, 3 , 6.
The coefficient of x² is -14.
Let the degree 3 polynomial be,
[tex]\begin{gathered} p(x)=(x-x_1)(x-x_2)(x-x_3) \\ =(x-(-2))(x-3)(x-6) \\ =\mleft(x+2\mright)\mleft(x-3\mright)\mleft(x-6\mright) \\ =\mleft(x^2-x-6\mright)\mleft(x-6\mright) \\ =x^3-x^2-6x-6x^2+6x+36 \\ =x^3-7x^2+36 \end{gathered}[/tex]But given that, coefficient of x² is -14 so, multiply the above polynomial by 2.
[tex]\begin{gathered} p(x)=x^3-7x^2+36 \\ 2p(x)=2(x^3-7x^2+36) \\ =2x^3-14x^2+72 \end{gathered}[/tex]Answer: The polynomial is,
[tex]p(x)=2x^3-14x^2+72[/tex]I solved for Part A and the correct graph was answer A I just need Part B to be solved (at the bottom)
In Part (b) of this problem, we want to determine which function is the bes representation for the graph and table.
We are given:
To determine which function matches best, we can look at the parent function of a linear, logarithmic, and exponential function.
(see comparisons below):
Notice that our graph most closely resembles that of the exponential function. Therefore, the best model for the data would be an exponential function.
A museum curator counted the number of paintings in each exhibit at the art museum. Number of paintings Number of exhibits 9 2 21 1 40 1 1 46 3 52 1 67 2 X is the number of paintings that a randomly chosen exhibit has. What is the expected value of x Write your answer as a decimal.
Answer
Expected number of paintings that a randomly chosen exhibit has = 40.3
Explanation
The expected value of any distribution is calculated as the mean of that distribution.
The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
Σx = (9 × 2) + (21 × 1) + (40 × 1) + (46 × 3) + (52 × 1) + (67 × 2)
Σx = 18 + 21 + 40 + 138 + 52 + 134
Σx = 403
N = 2 + 1 + 1 + 3 + 1 + 2 = 10
Mean = (Σx)/N
Mean = (403/10) = 40.3
Hope this Helps!!!
Given the following absolute value function sketch the graph of the function and find the domain and range.
ƒ(x) = |x + 3| - 1
pls show how did u solve it
In order to sketch the graph we need to find the vertex and two more points to connect with the vertex.
To do so set the inside of absolute value to zero:
x + 3 = 0x = - 3The y-coordinate of same is:
f(-3) = 0 - 1 = - 1.So the vertex is (- 3, - 1).
Since the coefficient of the absolute value is positive, the graph opens up, and the vertex is below the x-axis as we found above.
Find the x-intercepts by setting the function equal to zero:
|x + 3| - 1 = 0x + 3 - 1 = 0 or - x - 3 - 1 = 0x + 2 = 0 or - x - 4 = 0x = - 2 or x = - 4We have two x-intercepts (-4, 0) and (-2, 0).
Now plot all three points and connect the vertex with both x-intercepts.
Now, from the graph we see there is no domain restrictions but the range is restricted to y-coordinate of the vertex.
It can be shown as:
Domain: x ∈ ( - ∞, + ∞),Range: y ∈ [ - 1, + ∞)Answer:
Vertex = (-3, -1).y-intercept = (0, 2).x-intercepts = (-2, 0) and (-4, 0).Domain = (-∞, ∞).Range = [-1, ∞).Step-by-step explanation:
Given absolute value function:
[tex]f(x)=|x+3|-1[/tex]
The parent function of the given function is:
[tex]f(x)=|x|[/tex]
Graph of the parent absolute function:
Line |y| = -x where x ≤ 0Line |y| = x where x ≥ 0Vertex at (0, 0)Translations
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
Therefore, the given function is the parent function translated 3 units left and 1 unit down.
If the vertex of the parent function is (0, 0) then the vertex of the given function is:
⇒ Vertex = (0 - 3, 0 - 1) = (-3, -1)
To find the y-intercept, substitute x = 0 into the given function:
[tex]\implies \textsf{$y$-intercept}=|0+3|-1=2[/tex]
To find the x-intercepts, set the function to zero and solve for x:
[tex]\implies |x+3|-1=0[/tex]
[tex]\implies |x+3|=1[/tex]
Therefore:
[tex]\implies x+3=1 \implies x=-2[/tex]
[tex]\implies x+3=-1 \implies x=-4[/tex]
Therefore, the x-intercepts are (-2, 0) and (-4, 0).
To sketch the graph:
Plot the found vertex, y-intercept and x-intercepts.Draw a straight line from the vertex through (-2, 0) and the y-intercept.Draw a straight line from the vertex through (-4, 0).Ensure the graph is symmetrical about x = -3.Note: When sketching a graph, be sure to label all points where the line crosses the axes.
The domain of a function is the set of all possible input values (x-values).
The domain of the given function is unrestricted and therefore (-∞, ∞).
The range of a function is the set of all possible output values (y-values).
The minimum of the function is the y-value of the vertex: y = -1.
Therefore, the range of the given function is: [-1, ∞).
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it
So we need to solve the following equation for x:
[tex]\sqrt[]{x-2}+8=x[/tex]The first step would be substracting 8 from each side of the equation:
[tex]\begin{gathered} \sqrt[]{x-2}+8-8=x-8 \\ \sqrt[]{x-2}=x-8 \end{gathered}[/tex]The next step is to square
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Jimmy ran 20 meters west
from home and then turned
north to jog 25 meters. Jimmy
ran 45 meters, but could have
arrived at the same point by in
a straight line. How many
meters could he have using a
line distance?
A. 3.5 meters
B7 meters
C. 32 meters
D. 45 meters
Answer:
32m
Step-by-step explanation:
The distance he would've covered is 32m if he ran through a straight line.
What is Pythagoras's Theorem?
In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.
Mathematically, the theorem can be expressed as
Let's substitute the values into the equation and solve.
Jimmy would've jogged 32m if he ran through a straight line.
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what does -1 3/4+4.7=
-1 3/4 + 4.7 = -1.75 + 4.7 = 2.95
3/4 = 0.75, so -1 3/4 is -1.75
-1.75 + 4.7 = 2.95
Answer: 2.95
Give the slope and the y-intercept of the line y=– 8x+7. Make sure the y-intercept is written as a coordinate.
Solution
We have the following function given:
y =-8x+7
If we compare this with the general formula for a slope given by:
y= mx+b
We can see that the slope m is:
m =-8
And the y-intercept would be: (0,7)
Solve each system of equations "-x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3
show your work please so i can understand how to do it!
x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given three equations are
-x+y+2z=-5.....(1)
5x+4y-4z=4....(2)
x-3y-2z=3....(3)
Add equations (1) and (3)
-x+y+2z+x-3y-2z=-5+3
Add the like terms
-2y=-2
y=1
Now put value of y in equations (1) and (2)
-x+2z=-6..(4)
5x-4z=0...(5)
Multiply with 5 on equation 4 and add with equation 5
-5x+10z+5x-4z=-30
6z=-30
z=-5
Now put y and z values in equation (1)
-x+1+2(-5)=-5
-x+1-10=-5
-x-9=-5
-x=4
x=-4
Hence x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3
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1. Ms. Oates is going to plant grass in her backyard. It is 14feet wide and 20.5 feet long. What is the area of thebackyard that will need to be covered with grass?
Area of a rectangle is given by the expression:
[tex]A=\text{base}\times height[/tex]Then:
[tex]\begin{gathered} A=20.5\times14 \\ A=287\text{ square f}eet \end{gathered}[/tex]The area that will need to be covered is 287 square feet.
Simplify this equation −(4x−4)+4x−4
The equation -(4x - 4) + 4x - 4 is simplified as: -8.
How to Simplify an Equation?An equation can be simplified using the necessary properties of equalities where possible to give an expression that is simplified compared to the original equation.
Given the equation, -(4x - 4) + 4x - 4, to simplify, start by applying the distributive property of equality to open the parentheses:
-(4x - 4) + 4x - 4 = -(4x) -(+4) + 4x - 4 [distribution property of equality]
-(4x - 4) + 4x - 4 = -4x - 4 + 4x - 4
Combine like terms
-(4x - 4) + 4x - 4 = -4x + 4x - 4 - 4
Simplify the equation
-(4x - 4) + 4x - 4 = 0 - 8
= -8
Therefore, -(4x - 4) + 4x - 4 = -8.
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a museum wants to use equal rows to arrange the African baskets. which list shows all the different possible arrangements so that all the rows have the same number. Assume that an arrangement such as 4 x 20 is the same as 20 x 4.
Answer:
(B)1 x 80,2x 40,4 x 20,5 x 16,8 x 10
Explanation:
The number of African Baskets = 80
The list of all possible arrangements so that all the rows have the same number will be a list that contains all the positive product of factors of 80.
Factors of 80 are: 1,2,4,5,8, 10, 16,20,40,80
The list is, therefore:
[tex]1\times80,2\times40,4\times20,5\times16,8\times10[/tex]The correct choice is B.
In an art classroom, 8 students can sit around 1 table, and 48 students can sit around 6 tables. What is the relationship between the number of students to tables? (Do not reduce the ratios to their lowest terms.)
Answer: 8/1 = 6/48
Step-by-step explanation: um thats the answer bye
The relationship between the number of students to tables or the ratio of students to number of tables is 8 to 1.
According to question,
We have the following information:
In an art classroom, 8 students can sit around 1 table, and 48 students can sit around 6 tables.
Now, we will find the relationship between the number of students and the number of tables or in simple words, ratio.
So, we have:
8 students = 1 table
48 students = 6 tables
It can be rewritten by dividing both the sides by 6 as 8 students to 1 table.
It means that there are 8 students for 1 table.
Hence, the relationship between the number of students to the number of tables is 8 to 1.
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How do I do this ? I need to find the solution for it
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equations
[tex]\begin{gathered} y=-\frac{4}{3}x \\ y=\frac{3}{2}x \end{gathered}[/tex]STEP 2: Define the point that is the solution for the given functions on the graph
The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
STEP 3: Determine the solution for the system of equations
It can be seen from the image below that the two lines intersect at the origin and hence they are given as the solutions to the given system of equations.
Hence, the solutions are:
[tex]x=0,y=0[/tex]I need help on this calculus practice problem, I’m having trouble on it.
From the question
We are given
[tex]\lim _{x\to-7}g(x)[/tex]We are to determine if the table below is appropriate for approximating the limit
From the table
The value of the limit as x tends to -7
Can be found using
[tex]x=-7.001\text{ and x = 7.001}[/tex]Hence, from the values given in the table
The table is appropriate
Ninas math classroom is 6 and 4/5 meters long and 1 and 3/8 meters wide. What is the area of the classroom?
The most appropriate choice for area of rectangle will be given by -
Area of classroom = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]
What is area of rectangle?
Rectangle is a four sided figure whose parallel sides are equal and whose every angle is 90°
The total space taken by the rectangle is called area of the rectangle.
If the length of the rectangle be l and the breadth of the rectangle be b, then area of the rectangle is given by
Area = [tex]l \times b[/tex]
Here,
Length of classroom = [tex]6\frac{4}{5}[/tex] m = [tex]\frac{34}{5}[/tex] m
Width of classroom = [tex]1\frac{3}{8}[/tex] m = [tex]\frac{11}{8}[/tex] m
Area of classroom = [tex]\frac{34}{5} \times \frac{11}{8}[/tex]
= [tex]\frac{187}{40}[/tex]
= [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]
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helpppppp plssssssssssssssssssss
Answer:
No.
Step-by-step explanation:
Pre-SolvingWe are given the following inequality:
[tex]76 < 5-\frac{136}{s}[/tex]
And we want to know if s=2 is a solution, meaning if s is 2, will the inequality still be true?
SolvingWe can substitute 2 for s in the inequality to test it.
Replace s with 2.
[tex]76 < 5-\frac{136}{2}[/tex]
First, let's divide 136 by 2.
136/2 = 68
The inequality is now:
76 < 5 - 68
Subtract 68 from 5.
76 < -63
The inequality reads "76 is less than -63", which is a false statement (76 is positive, -63 is negative, and positive numbers are greater than negative numbers).
Ergo, s = 2 is not a solution to the inequality.
Suppose Yolanda places $9000 in an account that pays 8% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. $ (b) Find the amount in the account at the end of 2 years. $0 X S
Compound interest - The amount in the account at the end of 1st year is $9720 and The amount in the account at the end of 2nd years is $10497.6
What is compound interest?
The interest earned on savings that is calculated using both the initial principal and the interest accrued over time is known as compound interest. It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a sum more quickly than simple interest, which is only calculated on the principal sum. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
We are given that the principal amount is $9000
An the interest is 8%
Hence after 1 year the amount will be
[tex]A=9000(1+0.08)\\A=9000(1.08)\\A=9720\\[/tex]
After 1 year the amount becomes $9720
Now After 2 years we will get interest on $9720
Hence the amount after 2 years will be
[tex]B=9720(1+0.08)\\B=9720(1.08)\\B=10497.6[/tex]
Therefore the amount after 2 years is $10497.6
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The height, in feet, of a particle from the ground is given by the function s(t) = 1.512 + 20r, where 0 ≤ ≤ 17.
Find the velocity of the particle at t = 4.
Answer
feet per second
The velocity is v= 30.6 ft/ sec.
What is a velocity?Velocity defines the direction of the movement of the body or the object. Speed is primarily a scalar quantity. Velocity is essentially a vector quantity. It is the rate of change of distance. It is the rate of change of displacement.
Given that,
We have given the height
s(t) = 0.2[tex]t^{3}[/tex] + 21t, where 0 ≤ [tex]x[/tex] ≤ 17.
To find the velocity we have to differentiate s(t) wrt to t.
s(t) = 0.2[tex]t^{3}[/tex] + 21t
= 0.6[tex]t^{2}[/tex]+21
velocity of the particle at t = 4
s(4) = 0.6*[tex]4^{2}[/tex]+21
= 9.6+21
= 30.6
v= 30.6 ft/ sec
Hence, The velocity is v= 30.6 ft/ sec.
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Complete each equation so that it has infinitely many solutions. 12x - x + 8 + 3x = __x + __ (__ are blanks)
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
What are a definition and an example of a linear equation?Linear formula first-degree algebraic equation with the variables y = 4x + 3 or similar (that is, raised only to the first power). Such an equation has a straight line for its graph.
-12-x=8-3x
Add what is to the right of the equal sign to both sides of the equation, then rewrite the equation as follows:-12-x-(8-3*x)=0
Take like variables away:-20 + 2x = 2 • (x - 10)
Solve: 2 = 0There is no answer to this equation.A constant that is not zero can never equal zero.x-10 = 0
On both sides of the equation, add 10:x = 10.
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