Answer: Domain: (-∞, 0) U (0, ∞)
Step-by-step explanation:
[tex]\frac{12}{x} *-8x^{3}[/tex]
[tex]=-96x^2[/tex]
Domain: (-∞, 0) U (0, ∞)
Mr Abdul made tuna and curry potato filling for some puffs.3/5 of the filling he made was tuna and the rest was curry potato.
After he used 1/8kg of the tuna filling and made another 3/4
kg of curry potato filling, he then had equal amounts of tuna filling
and curry potato filling left. How much tuna filling did he make at first?
Give your answer as a mixed number in its simplest form
At first, he made [tex]2\frac{5}{8}[/tex] kg of tuna filling.
Mr Abdul made tuna and curry potato filling for some puffs.
3/5 of the filling he made was tuna and the rest was curry potato.
So, amount of curry potato = 1- 3/5 = 2/5
Ratio of tuna & curry potato = tuna : curry potato
= 3/5 : 2/5 = 3 : 2
Let amount of tuna = 3x & amount of curry potato = 2x
After he used 1/8kg of the tuna filling and made another 3/4 kg of curry potato filling.
According to the question, he then had equal amounts of tuna filling and curry potato filling left.
So, 3x - 1/8 = 2x + 3/4
Multiplying 8 in both sides we get,
⇒ 24x - 1 = 16x +6
⇒ 24x - 16x = 7
⇒ 8x = 7
⇒ x = 7/8
So, 3x = (3×7/8) = 21/8 kg = [tex]2\frac{5}{8}[/tex] tuna filling at first.
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Please help! Simplify the following expression by combining like-terms.
Step-by-step explanation:
[tex] = 4x - 8y + 6 {x}^{2} + 3x - 5y[/tex]
[tex] = 6 {x}^{2} + (4x + 3x) + ( - 8y - 5y)[/tex]
[tex] = 6 {x}^{2} + 7x - 13y[/tex]
The answer is B.
Answer:
b.) 6x² + 7x - 13y
Explanation:
Given Expression
= 4x - 8y + 6x² + 3x - 5y
collect like terms
= 6x² + 4x + 3x -8y - 5y
combine similar terms
= 6x² + 7x - 13y
State true or false. (i) Cube of any odd number is even. F (ii) A perfect cube does not end with two zeros.T (iii) If square of a number ends with 5, then its cube ends with 25. F (iv) There is no perfect cube which ends with 8. F (v) The cube of a two digit number may be a three digit number. F (vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number. T
Give reasons why
i. Cube of any odd number is even. False
ii. A perfect cube does not end with two zeros. True
iii. If square of a number ends with 5, then its cube ends with 25. False
iv. There is no perfect cube which ends with 8. False
v. The cube of a two digit number may be a three digit number. False
vi. The cube of a two digit number may have seven or more digits. False
vii. The cube of a single digit number may be a single digit number. True
Reasons
i. Cube of any odd number is even. This statement is false because the cube of odd numbers are also odd
ii. A perfect cube does not end with two zeros. This statement is True because the cube of a two digit number cannot be a 3 digit number and therefore cannot end with two zeros.
iii. If square of a number ends with 5, then its cube ends with 25. This statement is False
Using the illustration
35^2 = 35 x 35= 1225 , its square ends with 5
35^3= 35 x 35 x 35= 42875 which ends with 75
iv. There is no perfect cube which ends with 8. This statement is False.
Using the illustration, the cube of 2 is given thus
2 * 2 * 2 = 8
The cube of 2 ends with 8
v. The cube of a two digit number may be a three digit number. This statement is False.
Using the illustration, 10 is a two digit number
10 * 10 * 10 = 1000
The cube of 10 which is a two digit number is not a three digit number and same applies to all two digit numbers
vi The cube of a two digit number may have seven or more digits. This statement is False because the cube of a two digit number can only be a four digit number.
vii. The cube of a single digit number may be a single digit number. This statement is True because the cube of a single digit number can be a single, two or three digit number.
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Find the equivalent exponential expression. [(-4)^5]^3
Answer:
[tex]-4^{15}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left[(-4)^5\right]^3[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies (-4)^{(5 \times 3)}[/tex]
[tex]\implies (-4)^{15}[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}:[/tex]
[tex]\implies -4^{15}[/tex]
Divya is solving the following equation for w. 3w -√20-5w = 2 Her first few steps are given below. 3w = √20-5w+2 3w-2= √/20 - 5w (3w - 2)² =(√20 – 5w) 9w² - 12w + 4 = 20 - 5w Is it necessary for Divya to check her answers for extraneous solutions?
Divya should not check her answers for extraneous solution as it's not required in this case.
What is an extraneous solution?It should be noted that an extraneous solution simply means is the transformed equation that's isn't the root of the original equation.
Based on the information given, Divya had already solved the equation and it's not necessary to check the answers for extraneous solution.
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Answer:
No, she shouldn't.
If log_2(3) = a and log_2(10) = b then an expression for log_2(90) is
[tex]\log_290=\log_2(3^2\cdot10)=\log_23^2+\log_210=2\log_23+b=2a+b[/tex]
Solve the following equation, and check your solution. Be sure to show all work in order to receive full credit.
Solve -17 + n/5 = 33.
Answer:
n = 250
See solution and check blow.
Step-by-step explanation:
Solution:
-17 + n/5 = 33
Add 17 to both sides.
-17 + 17 + n/5 = 33 + 17
n/5 = 50
Multiply both sides by 5.
n/5 × 5 = 50 × 5
n = 250
Check:
-17 + n/5 = 33
Since we found out that n = 250, substitute 250 for n in the equation.
-17 + 250/5 = 33
Simplify the left side. Divide 250 by 5.
-17 + 50 = 33
Add on the left side.
33 = 33
Since 33 = 33 is a true statement, the solution n = 250 is correct.
At a gymnastics meet, twenty gymnasts compete for first, second, and third place.
How many ways can first, second, and third place be assigned
There 6840 ways can first, second, and third place be assigned.
What is Permutation?A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
We will use the concept of permutation
[tex]^{20}P_3[/tex]= 20!/ (20-3)!
= 20*19*18*17!/ 17!
= 6840 ways.
Hence, there are 6840 ways.
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A table of data is given.
x f(x)
-2 71
-1 13
0 3
1 0.6
2 0.1
Which exponential model best represents the data?
Of(x) = 3(1.2)^x
Of(x) = 2(0.3)^x
Of(x) = 2(3)^x
Of(x)=3(0.2)^x
Answer:
The choice D.
[tex]f(x) = 3 {(0.2)}^{x} [/tex]
Answer:
D
Step-by-step explanation:
Order of elimination:
1. the graph is going down exponentially. This means that the base is less than 1.
A and C are eliminated.
2. When x is equal to 0, f(x) = 3.
Substitute x for 0, and you'll find out that the only one possible is D.
Factor this expression completely 9x^2 - 72x + 8
The solution for the given equation will be x=7.8873 and x=0.112699.
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
Find the Solution for
9x²−72x+8=0
using the Quadratic Formula where
a = 9, b = -72, and c = 8
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{(-72)\pm\sqrt{(-72)^2-4(9)(8)}}{2(9)}[/tex]
x= [tex]\dfrac{72\pm4896}{\sqrt{18}}[/tex]
The discriminant b2−4ac>0
so, there are two real roots. After solving for plus and then minus we will get two values as follows.
x=7.8873
x=0.112699
Therefore the solution for the given equation will be x=7.8873 and x=0.112699.
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Genesis is going to see a movie and is taking her 3 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $3 each. How much total money would Genesis have to pay for her family if she were to buy 6 snacks for everybody to share? How much would Genesis have to pay if she bought x snacks for everybody to share?
Total cost with 6 snacks:
Total cost with x snacks:.
need answer quickly as possibly!
Answer #1:
The total cost with 6 snacks is $78.
Answer #2:
The total cost with x snacks is represented by the expression 60 + 3x.
Step-by-step explanation for answer #1:
Starting off with what we know:
Genesis has 3 kids, so there are 4 people total including Genesis.Each movie ticket is $15.Each snack is $3.To answer the question of how much money Genesis would have to pay for her family if she bought 6 snacks for everybody, first consider the total cost of the movie tickets.
Multiply the total number of people by the cost of each movie ticket:
[tex]4* 15=60[/tex]
Genesis will be paying $60 total only to see the movie with her 3 kids. To find the total cost of both seeing the movie and buying 6 snacks, simply multiply the number of snacks by the cost of each snack:
[tex]6 * 3=18[/tex]
Then, add the total cost of the movie tickets by the total cost of the snacks to achieve your first answer:
[tex]60+18=78[/tex]
The total cost with 6 snacks is $78.
Step-by-step explanation for answer #2:
To find the total cost of "x" snacks (x is being used as a variable term to represent a quantity subject to change), we can create an algebraic expression.
Let "t" represent the total cost.
Since we've established that finding the total cost is just a matter of adding the total cost of movie tickets (60) and the total cost of snacks (3 multiplied by the number of snacks), let "x" represent the number of snacks in the equation to find the total cost with x snacks:
[tex]60+3x=t[/tex]
The total cost with x snacks is represented by the expression 60 + 3x.
Based on the given data, the total cost of 6 snacks: $78. total cost with x snacks: $60 + (3x).
Use the concept of multiplication defined as:
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that,
Genesis is going to see a movie with her 3 kids.
Each movie ticket costs $15.
There are snacks available for purchase at $3 each.
Genesis wants to buy 6 snacks for everybody to share.
To calculate the total cost for Genesis and her 3 kids,
Consider the movie tickets and the snacks.
The cost of the movie tickets can be calculated by multiplying the number of people (4 in this case) by the cost of each ticket ($15).
So, Genesis would have to pay 4 x $15 = $60 for the movie tickets.
Now, let's calculate the total cost if Genesis were to buy 6 snacks for everybody to share.
Each snack costs $3, so 6 snacks would cost 6 x $3 = $18.
Therefore, the total cost for Genesis would be,
$60 (movie tickets) + $18 (snacks) = $78.
If we consider x snacks for everybody to share,
The total cost for snacks would be x $3.
So, the final cost would be $60 (movie tickets) + (3x) (snacks).
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Sonam says that the 20th figure in this pattern has 400 small triangles. do you agree? explain your thinking.
Answer:
No. There should be 210 small triangles
Step-by-step explanation:
The number of small triangles in these figures forms a sequence
Fig No Small Triangles
1 1
2 3 (1+2)
3 6 (1+2+3)
So the nth figure should have 1+2+3+.....+(n-1)+ n
1+2+3+.....+(n-1)+ n = [tex]\frac{n (n-1)}{2}[/tex]
So for 20th figure, n = 20 and number of small triangles = 20 x 21 /2 = 420/2 = 210
A local mechanic on average services 14 cars a week. How many cars does he service in 4 years
What are the slope and the y-intercept of the linear function that is represented by the graph?
answer C is “The slope is Negative three-fourths, and the y-intercept is 3.”
answer D is “The slope is Negative three-fourths, and the y-intercept is 4”
Answer:
“The slope is Negative three-fourths, and the y-intercept is 3.”
Step-by-step explanation:
the graph passes through the points (0 , 3) and (4 , 0)
Then
The slope is :
[tex]=\frac{0-3}{4-0}[/tex]
[tex]=-\frac{3}{4}[/tex]
Since , the graph passes through (0 , 3)
THen the y-intercept is 3.
Graph the system of inequalities presented here on your own paper; then use your graph to answer the following questions:
Y > -4x-1
y<3/2x-1
Part A:
Describe the graph of the system; including shading and the types of lines graphed Provide a description of the solution area: (6 points)
Part B: Is the point (-1,1) included in the solution area for the system? Justify your answer mathematically
It is to be noted that the Graph of the indicated inequalities is herewith attached.
What is the graph of the system?As indicated above, this is a graph of a system of inequalities, where:
Y > -4x-1 and
y <3/2x-1
Is the point (-1,1) included in the solution area for the system?No. the point (-1, 1) is not included in the solution area for the system.
Step 1 - Plug in (-1, 1) in to the first equation. where y = -1 and x = 1.
Hence,
-1 > -4(1) -1
4 +1 < -1
4 < 0 (This is False)
Step 2 - Plug in (-1, 1) in to the second equation. where y = -1 and x = 1.
-1 < (3/2)(1) - 1
-1 < 1/2 (This is true).
Thus (-1, 1) is only partially included in the solution area.)
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what is
f(-1)=-3x^{2}+7x+4
Step-by-step explanation:
please mark me as brainlest
What is the solution to the equation startfraction 3 over m 3 endfraction minus startfraction m over 3 minus m endfraction = startfraction m squared 9 over m squared minus 9 endfraction?
The provided equation has no solution because the square of any number cannon is negative.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is:
Find a solution to the given equation
Please refer to the attached picture for the expression.
We have an expression:
[tex]\rm \dfrac{3}{\left(m+3\right)}-\dfrac{3}{\left(m-3\right)}=\dfrac{m^2+9}{\left(m^2-9\right)}[/tex]
3(m - 3) - 3(m + 3) = m² + 9
3m - 9 - 3m - 9 = m² + 9
m² ≠ -27
As the square of any number cannot is negative, so no solution to the provided equation.
Thus, the provided equation has no solution because the square of any number cannon is negative.
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Answer:
D = No Solution
Step-by-step explanation:
5(2x - 12) + 21 = 2x + 41
05
08
O 10
072
Answer:
x = 10
Step-by-step explanation:
5(2x - 12) + 21 = 2x + 41 ← distribute parenthesis and simplify left side
10x - 60 + 21 = 2x + 41
10x - 39 = 2x + 41 ( subtract 2x from both sides )
8x - 39 = 41 ( add 39 to both sides )
8x = 80 ( divide both sides by 8 )
x = 10
Find the value of the lettered angle b
Answer:
60°Step-by-step explanation:
30 is an opposite angle (2 angles of 30°)
sum of all angles = 360°
360 - 90 -30 - 150 - 30 = 60°
check
60 + 30 + 150 + 30 + 90 = 360°
the answer is good
Answer:
b = 60
Step-by-step explanation:
A straight line is 180 degrees
30+90+b = 180
Combine like terms
120 +b = 180
b =180-120
b = 60
write √a^8a^3 as an algebraic expression using a rational exponent
Answer:
A
Step-by-step explanation:
I assume that the whole expression a⁸a³ is under the square root.
then remember 2 things :
1. when multiplying the same base variable (or constant) the result is that single base variable (or constant) to the power of the sum of the exponents.
e.g. x³x² = x⁵ because
x×x×x × x×x = x×x×x×x×x = x⁵
2. a square root as exponent is 1/2.
a cubic root is 1/3 and so on.
therefore
sqrt(a⁸a³) = sqrt(a¹¹) = a^11/2
if sin25=p write the following term of p
cos65
tan205
Answer:
cos65 = sin25 = p
tan205 = tan25 = p/√(1-√p)
Step-by-step explanation:
trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec)
some Trigonometric identities used in the question:
cos(90-θ) = sinθsin²θ + cos²θ = 1tan(π±θ) = tanθtanθ = sinθ/cosθin the question it is given,
sin25 = p
using above mentioned identity:-
cos 65 = cos(90-25) = sin25 = p
hence value of cos65 is p.
for, tan205 we have to first find the cos25
so to find cos25 we use above mentioned identity,
cos²25 + sin²25 = 1
cos²25 + √p = 1
cos²25 = 1-√p
cos25 = √(1-√p)
now to find out tan205 use third identity mentioned above,
tan205 = tan(π+25) = tan25
tan25 = sin25/cos25
tan25 = p/√(1-√p)
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a 48 gram sample of a substance that’s used for drug research has a k value of 0.1325
Using an exponential function, it is found that the half-life of the substance is of 5.23 units of time.
What is the exponential function for the amount of a substance?The function is given by:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which:
A(0) is the initial value.k is the exponential decay rate.The parameters are given by:
A(0) = 48, k = 0.1325.
Hence the equation is:
[tex]A(t) = 48e^{-0.1325t}[/tex]
The half-life is the amount of time for which A(t) = 0.5A(0) = 24, hence:
[tex]A(t) = 48e^{-0.1325t}[/tex]
[tex]24 = 48e^{-0.1325t}[/tex]
[tex]e^{-0.1325t} = 0.5[/tex]
[tex]\ln{e^{-0.1325t}} = \ln{0.5}[/tex]
[tex]0.1325t = -\ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{0.1325}[/tex]
t = 5.23.
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The table and the graph below each show a different relationship between the same two variables, x and y.
How much more would the value of y be on the graph than its value in the table when x = 12?
Answer:
240
Step-by-step explanation:
Using the straight line formula; y=mx+c, take two points, for example, (4, 80) and (5, 100)
m=change in y/change in x, so;
m=(100-80)/(5-4)= 20
Take point (4, 80)
80=20×4 + c
80-80=c=0
so y=20x
y=20×12=240
A website sells a dress at £20 and shoes at £25. The website has an offer: Buy a dress and shoes together and get 1 3 off the price. There is also a shipping and handling charge of £4 added at the end, after any discount. If Ruth buys both a dress and shoes, how much will she actually pay?
£36
20+25=45 Take away 13 and it's 32. 32+4 (the shipping charge) is 36. So Ruth pays 36 pounds.
b) Another sequence is defined using this term-to-term rule, Un+1 = kun + r where k and rare constants. Given that u₁ = 37, U₂= 188 and u3 = 943, find the value of k and the value of r. b ) Another sequence is defined using this term - to - term rule , Un + 1 = kun + r where k and rare constants . Given that u₁ = 37 , U₂ = 188 and u3 = 943 , find the value of k and the value of r .
The values of k and r are given by 5 and 3 respectively.
Here in this problem it is given that,
General formula for the sequence is given by,
[tex]U_{n+1}=kU_n+r[/tex]
First term of the sequence, [tex]U_1=37[/tex]
Second term,
[tex]U_2=188[/tex]
[tex]U_{1+1}=188[/tex], rearranging
[tex]kU_1+r=188[/tex], applying general formula
[tex]37k+r=188[/tex]..........(1)
Third term,
[tex]U_3=943[/tex]
[tex]U_{2+1}=943[/tex], rearranging
[tex]kU_2+r=943[/tex], applying general formula
[tex]188k+r=943[/tex]..........(2)
Now (2) - (1) we get,
188k+r-37k-r = 943-188
151k = 755
k = 755/151 = 5
Hence the value of k is 5.
Substituting the value of k in (1) we get,
37*5+r = 188
185+r = 188
r = 188-185 = 3
Thus the value of r is 3.
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Ella has a collection of vintage action figures that is worth $430. If the collection
appreciates at a rate of 4% per year, which equation represents the value of the
collection after 7 years?
The equation representing the value of the collection after 7 years is value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4
What is an Equation ?An equation is a mathematical statement , where the algebraic expression is equated to another algebraic expression.
It is given that
Ella has a collection of vintage action figures that is worth $430.
collection
appreciates at a rate of 4% per year
equation representing the value of the collection after 7 years is
value of collection = 430 + (0.04 * 430 )* t
value of collection = 430 + (0.04 * 430 )* 7
= $550.4
Therefore the equation representing the value of the collection after 7 years is value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4
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Use separation of variables to solve the differential equation with initial condition y(1)=-2
Answer: A
Step-by-step explanation:
[tex]\frac{dy}{dx}=\frac{1+x}{xy} \\ \\ y \text{ } dy=\frac{1+x}{x} \text{ } dx \\ \\ y \text{ } dy= \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \int y \text{ } dy=\int \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \frac{y^{2}}{2}=\ln \left| x \right|+x+C[/tex]
Substituting in the initial condition,
[tex]\frac{(-2)^{2}}{2}=\ln \left|1 \right|+1+C\\\\2=1+C\\\\C=1[/tex]
So,
[tex]\boxed{\frac{1}{2}y^{2}=\ln \left|x \right|+x+1}[/tex]
Answer:
[tex]\textsf{A.} \quad \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]
Step-by-step explanation:
To solve the differential equation:
Rearrange the given equation to get all the terms containing y on the left side, and all the terms containing x on the right side:
[tex]\dfrac{dy}{dx}=\dfrac{1+x}{xy}[/tex]
[tex]\implies y\dfrac{dy}{dx}=\dfrac{1+x}{x}[/tex]
[tex]\implies y\:dy=\dfrac{1+x}{x}\:dx[/tex]
[tex]\implies y\:dy=\dfrac{1}{x}+\dfrac{x}{x}\:dx[/tex]
[tex]\implies y\:dy=\left(\dfrac{1}{x}+1\right)\:dx[/tex]
Integrate both sides:
[tex]\displaystyle \implies \int y\:dy=\int \left(\dfrac{1}{x}+1\right)\:dx[/tex]
[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+C[/tex]
Find the value of C using the given values of x and y:
when x = 1, y = -2
[tex]\implies \dfrac{1}{2}(-2)^2=\ln|1|+1+C[/tex]
[tex]\implies 2=0+1+C[/tex]
[tex]\implies C=1[/tex]
Substitute the found value of C:
[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]
Find the solution:
3x + 2y = 12
-2x + 3y = 5
Answer:
x = 3
y = 2
Step-by-step explanation:
3x + 2y = 12
-2x + 3y = 5 to find the solution we will use elimination method and for that, multiply second equation with 3 and the first equation with 2
2 * 3x + 2y = 12
6x + 4y = 24
3 * -2x + 3y = 5
-6x + 9y = 15 now find the sum of both equation:
6x + 4y -6x + 9y = 24 + 15 add like terms
13y = 39 divide both sides by 13
y = 3 now that we found the value of y we can use this to calculate the value of x
3x + 2y = 12 replace y with 3
3x + 2*2 = 12
3x + 4 = 12 subtract 4 from both sides
3x = 9 divide both sides by 3
x = 3
f(x)=|3x +5| +6
g(x) = 7
Find (f + g)(x).
Answer:
(f+g)(x)
= |3x+5| + 13
Step-by-step explanation:
(f+g)(x) means
f(x) + g(x)
so you add the functions together.
|3x+5| + 6 + 7
And simplify.
|3x+5| + 13
Which points can be connected to draw a line of symmetry through this diamond?
Drag and drop an answer to the box to complete the statement. please answer asap!
The line is drawn at point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.
What is a line of symmetry?It is defined as the line which will make exactly two halves with similar shape and size in geometry. For a two-dimensional shape, there is a line of symmetry, and for three-dimensional shapes, there is a plane of symmetry. In other words, if we make a mirror image of the shape around the line of symmetry, we will get exactly the same half portion.
We have given a figure in the picture.
The figure is a quadrilateral(a kite)
As we know, lines of symmetry make exactly two halves with similar shapes and sizes.
IF we draw a line from Point A to Point C we will get two similar and figures in size and shape.
Thus, the line is drawn point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.
Learn more about the line of symmetry here:
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Answer:
point C
Here is a step-by-step explanation of the statement:
1. Draw a point B and a point C on a piece of paper or a computer screen.
2. Draw a straight line that goes through both point B and point C.
3. Fold the paper along the line you just drew, so that the line is the fold line.
4. Notice that if you were to fold the paper exactly in half along the line, point B would match up with its reflection on the other side of the line, and point C would match up with its reflection on the other side of the line.
5. This means that the line you drew is a line of symmetry, because it divides the paper into two identical halves that can be folded together.
6. Therefore, the statement "A line drawn through point B and point C is a line of symmetry" is true.
