Answers
Answer:
x = 2
Step-by-step explanation:
When 2 secants are drawn from an external point to a circle the following theorem applies
outside × whole = outside × whole, that is
(x + 1)(x + 1 + 11) = (x + 4)(x + 4 + 1) ← simplify
(x + 1)(x + 12) = (x + 4)(x + 5) ← expand factors on both sides
x² + 13x + 12 = x² + 9x + 20 ( subtract x² from both sides )
13x + 12 = 9x + 20 ( subtract 9x from both sides )
4x + 12 = 20 ( subtract 12 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
Related Questions
a. 0.98 – 0.053 b. 0.67 – 0.4 c. 0.3 – 0.002 d. 3.2 – .789 e. 6.53 – 4.298 f. 6 – 4.32 g. 7 – 3.574 h. 4.83 – 1.8 i. 3.7 – 1.8 j. 16.17 – 11.632
Answers
a. 0.927
We have:
0.98 – 0.053
We can re-write it as:
0. 9 8 0 -
0. 0 5 3
Moving digits to the right:
0. 9 7 10 -
0. 0 5 3
Digit-per-digit subtraction:
0. 9 2 7
b. 0.27
We have:
0.67 – 0.4
We can re-write it as:
0. 6 7 -
0. 4 0
Digit-per-digit subtraction:
0. 2 7
c. 0.298
We have:
0.3 – 0.002
We can re-write it as:
0. 3 0 0 -
0. 0 0 2
Moving digits to the right:
0. 2 10 0 -
0. 0 0 2
Again:
0. 2 9 10 -
0. 0 0 2
Digit-per-digit subtraction:
0. 2 9 8
d. 2.411
We have:
3.2 – .789
We can re-write it as:
3. 2 0 0 -
0. 7 8 9
We need to rewrite the first term by moving digits to the right several times:
3. 2 0 0 = 2. 12 0 0 = 2. 11 10 0 = 2. 11 9 10
So now we have:
2. 11 9 10 -
0. 7 8 9
Digit-per-digit subtraction:
2. 4 1 1
e. 2.232
We have:
6.53 – 4.298
We can re-write it as:
6. 5 3 0 -
4. 2 9 8
We need to rewrite the first term by moving digits to the right several times:
6. 5 3 0 = 6. 5 2 10 = 6. 4 12 10
So now we have:
6. 4 12 10 -
4. 2 9 8
Digit-per-digit subtraction:
2. 2 3 2
f. 1.68
We have:
6 – 4.32
We can re-write it as:
6. 0 0 -
4. 3 2
We need to rewrite the first term by moving digits to the right several times:
6. 0 0 = 5. 10 0 = 5. 9 10
So now we have:
5. 9 10 -
4. 3 2
Digit-per-digit subtraction:
1. 6 8
g. 4.426
We have:
7 – 3.574
We can re-write it as:
7. 0 0 0 -
3. 5 7 4
We need to rewrite the first term by moving digits to the right several times:
7. 0 0 0 = 6. 10 0 0 = 6. 9 10 0 = 6. 9 9 10
So now we have:
6. 9 9 10 -
3. 5 7 4 =
Digit-per-digit subtraction:
3. 4 2 6
h. 3.03
We have:
4.83 – 1.8
We can re-write it as:
4. 8 3 -
1. 8 0
We can immediately do the digit-per-digit subtraction:
3. 0 3
i. 2.9
We have:
3.7 – 1.8
We can re-write it as:
3. 7 -
1. 8
We need to rewrite the first term by moving digits to the right:
3. 7 = 2. 17
So now we have:
2. 17 -
1. 8 =
Digit-per-digit subtraction:
2. 9
j. 4.538
We have:
16.17 – 11.632
We can re-write it as:
1 6 . 1 7 0 -
1 1 . 6 3 2
We need to rewrite the first term by moving digits to the right:
1 6. 1 7 0 = 1 6. 1 6 10 = 1 5. 11 6 10
So now we have:
1 5. 11 6 10 -
1 1. 6 3 2 =
Digit-per-digit subtraction:
0 4. 5 3 8
1. find the difference 7 1/4 - 3 1/2 =
a. 3 3/4
b. 4 3/4
c. 3 1/2
d. 4 1/2
2. find the product and write it in simplest form 3/8 x 2/3
a. 9/16
b. 6/24
c. 2/8
d. 1/4
3. find the product and write it in simplest form 2 3/8 x 1 2/3
a. 2 6/24
b. 3 23/24
c. 3 3/4
d. 95/8
4. perform the division and write it in simplest form 7/10 ÷ 3/5
a. 35/30
b. 6/7
c. 21/60
d. 1 1/6
Answers
Answer:
1. a
2. d
3. b
4. it would be 7/6 NOT 6/7
Step-by-step explanation:
The cost of a candy bar in a vending machine is $0.95. The cost of a bottle of water in the same machine is $1.25. Jamie has $25.00 to spend on candy bars and bottles of water for her friends. She must buy nine candy bars. If b represents the number of bottles of water, which inequality represents all the possible values of b?
Answers
Final answer:
The inequality representing all possible values of b, the number of bottles of water Jamie can buy, is b ≤ 13, as Jamie has $16.45 left to spend after buying nine candy bars and each bottle costs $1.25.
Explanation:
The student must buy nine candy bars, which cost $0.95 each. The total cost for the candy bars is 9 * $0.95 = $8.55. Jamie has $25.00 to spend, so after buying the candy bars, she will have $25.00 - $8.55 = $16.45 left for bottles of water. Each bottle of water costs $1.25, so the number of bottles she can buy is represented by the inequality $1.25b ≤ $16.45, where b is the number of bottles of water Jamie can purchase.
Now, let's solve this inequality for b. Dividing both sides of the inequality by $1.25 gives us b ≤ 13.16. Since Jamie can't buy a fraction of a bottle, she must buy at most 13 bottles of water.
Therefore, the inequality representing all possible values of b (i.e., the number of bottles of water Jamie can buy) is b ≤ 13.
The Carson’s are on a road trip they paid $62.70 for 16 1/2 gallons of gasoline
Part 1-Find the price of gasoline per gallon show your work
Part 2-Give an example of a cost and amount that would make the gasoline have a rate of $3.49 per gallon
Answers
Answer:
$3.92 per gallon
10 gallons of gas at $3.49 a gallon will cost $34.90
Step-by-step explanation:
To find the price per gallon, we take the total cost, and divide by the number of gallons. I will change 16 1/2 to a decimal for ease of math calculations.
16 1/2 = 16.5
cost/gallons
$62.70/16.5
3.91875
Since we are working with money, we round to the nearest cent
$3.92 per gallon
To find the total cost, we multiply the cost per gallon times the number of gallons. We have a cost per gallon of $3.49. If we multiply by 10 gallons
cost = $3.49 * 10
$34.90
10 gallons of gas at $3.49 a gallon will cost $34.90
sarahs volleyball team won 12 games of their first 18 games. if the continue to win at this rate, how many games will they lose if they play 36 games
Answers
Answer:
They lost 12 games.
Step-by-step explanation:
Set up a proportion.
12/18 = x/36
36 x 12 = 432
432/18 = 24
Because 18 represents how many games they won, the 24 also represents how many games they won. Therefore, you must subtract to find the amount of times that they lost.
36 - 24 = 12
Answer:
they lost 12 games
Step-by-step explanation:
they lost 12 games
A jar contains 133 pennies. A bigger jar contains 1 2/7 times as many pennies. What is 5he value of the pennies in the bigger jar
Answers
133/1×9/7= 171 pennies.
Answer:
The Jar contained 5^67 pennis of nickels and quaters. Making a lot of money in 1/4 of a month. The 5he value of the pennies in the bigger than the amount of the total fitting of itself. The Largest pennies in the jar depended on the nickels and quaers inside. The 133 pennies wer the jar that contained the lesser amount of pennies, therfore the bigger jar standes with a larger value
Step-by-step explanation:
A line passes through (3, -2) and (6, 2). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers
Answers
Answer:
(a)
Given: A line passes through the points (3, -2) and (6, 2)
Point slope form: An equation of line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:
[tex]y -y_1=m(x-x_1`)[/tex] .....[1] where m is the slope of the line.
Calculate first the slope of the line:
Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points;
[tex]m = \frac{2-(-2)}{6-3}=\frac{2+2}{3} =\frac{4}{3}[/tex]
Substitute the value of m in [1] ;
[tex]y - (-2) = \frac{4}{3}(x-3)[/tex]
[tex]y+2=\frac{4}{3}(x-3)[/tex] ......[1]
therefore, the equation of line in point slope form is, [tex]y+2=\frac{4}{3}(x-3)[/tex]
(b)
to find the standard form of the equation [1]
Multiply both sides by 3 in [1] we get;
[tex]3(y+2) = 4(x-3)[/tex]
using distributive property; [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]
3y + 6 = 4x -12
Subtract 3y to both sides we get;
3y + 6 -3y = 4x - 12 - 3y
Simplify:
6 = 4x - 3y -12
Subtract 6 from both sides we get;
0 = 4x - 3y -12-6
Simplify:
4x - 3y - 18 =0
Therefore, the standard form of the equation is; 4x - 3y - 18 =0
Mr. Mateo ordered several copies of a book that weighs 3/5 of a pound each along with some other school supplies for his classroom. If the total weight of the box that contains the supplies was 10 pounds, what is the maximum number of copies of the bookthat Mr. Mateo could have ordered
Answers
Answer:
It's 16 I just did the same question on a quiz
If the total weight of the box that contains the supplies was 10 pound.
The maximum number of copies of the book that Mr. Mateo could have ordered is 16.
Given:
The number of copies of a book = [tex]\frac{3}{5}[/tex] pound
The total weight of the box = 10 pounds
According to question,
[tex]\frac{3}{5} x<10\\3x<50\\x<\frac{50}{3}\\x<16.66[/tex]
let: x = 16
Therefore, the maximum number of copies of the book that Mr. Mateo could have ordered is 16.
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How do you graph square roots
Answers
Answer: Simplify the number in the square root.
Step-by-step explanation: For example, √25 can be simplified to 5 because half of 25 is 5. If x=5, graph this on the x-axis or horizontal line on the graph. Another example, √2 can be simplified to approximately 1.414. To graph this, you can use a graphing tool for accurate representation, or create a graph and place a dot right before 1.5 (in between 1 and 2).
Find the missing lengths of the sides
Answers
If its at a 45 degree angle with a number and square root, the answer is always the number outside of the square root on both sides.
Answer: A
Step-by-step explanation: sin45(9 radical 2)
What monomial do you have to raise to the power of 2 to get the given monomial? What monomial do you have to raise to the power of 3 for this? a x6y12
Answers
When raising a monomial to a power, you multiply the exponents of each variable by that power.
Explanation:When you raise a monomial to the power of 2, you multiply the exponents of each variable by 2. So in the given monomial ax6y12, you would raise each exponent to the power of 2 to get a2x12y24.
Similarly, when you raise a monomial to the power of 3, you multiply the exponents of each variable by 3. So in the given monomial ax6y12, you would raise each exponent to the power of 3 to get a3x18y36.
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What is the total surface area
Answers
We have two right triangles and three different rectangles.
The formula of an area of a right triangle:
[tex]A_T=\dfrac{1}{2}l_1l_2[/tex]
l₁, l₂ - legs
We have l₁ = 20cm and l₂ = 21cm. Substitute:
[tex]A_T=\dfrac{1}{2}(20)(21)=(10)(21)=210\ cm^2[/tex]
The formula of an area of a rectangle:
[tex]A_R=lw[/tex]
l - length
w - width
We have:
rectangle #1: l = 22cm, w = 29cm
[tex]A_{R1}=(22)(29)=638\ cm^2[/tex]
rectangle #2: l = 22cm, w = 21cm
[tex]A_{R2}=(22)(21)=462\ cm^2[/tex]
rectangle #3: l = 22cm, w = 20cm
[tex]A_{R3}=(22)(20)=440\ cm^2[/tex]
The total Surface Area of the triangular prism:
[tex]S.A.=2A_T+A_{R1}+A_{R2}+A_{R3}\\\\S.A.=2\cdot210+638+462+440=1960\ cm^2[/tex]
Need help please help me
Answers
Assuming you have a graphing calculator or a program to lets you graph equations (I use desmos) you simply put in the equetions and note down the coordinates of the point of intersection.
In the graph the first equation is in blue and the second in red.
The point of intersection = the solution = (-6 , -1)
If you dont have access to a graphing calculator you could draw the graphs by hand;
1) Draw a table of values for each equation; you do this by setting three or four values for x and calculating its image in y (you can use any values of x)
y = 0.5 x + 2 (Im writing 0.5 instead of 1/2 because I find its easier in this format)
x | y
-1 | 1.5 * y = 0.5 (-1) + 2 = 1.5
0 | 2 * y = 0.5 (0) + 2 = 2
1 | 2.5 * y = 0.5 (1) + 2 = 2.5
2 | 3 * y = 0.5 (2) + 2 = 3
y = x + 5
x | y
-1 | 4 * y = (-1) + 5 = 4
0 | 5 * y = (0) + 5 = 5
1 | 6 * y = (1) + 5 = 6
2 | 7 * y = (2) + 5 = 7
2) Plot these point on the graph
I suggest to use diffrent colored points or diffrent kinds of point markers (an x or a dot) to avoid confusion about which point belongs to which graph
3) Using a ruler draw a line connection all the dots of one graph and do the same for the other
4) The point of intersection is the solution
y = mx + b - it's the equation of a straight line. We need only two points to the plotting the graph of that function.
Select any two x values and calculate y values:
[tex]y=\dfrac{1}{2}x+2\\\\for\ x=0\to y=\dfrac{1}{2}(0)+2=0+2=0\to(0,\ 2)\\\\for\ x=-4\to y=\dfrac{1}{2}(-4)=-2+2=0\to(-4,\ 0)[/tex]
[tex]y=x+5\\\\for\ x=0\to y=0+5=5\to(0,\ 5)\\\\for\ x=-5\to y=-5+5=0\to(-5,\ 0)[/tex]
Look at the picture.
The solution of the system of equations is the intersection point of the line.
Answer: (-6, -1) → x = -6 and y = -1please help!! Which shape is a continuous line of equal distance from its center?
Answers
Answer: I know it’s a circle but I forget why actually sorry that doesn’t help much
Step-by-step explanation:
combine like terms to simplify the expression. 2x+4y-7x+10y+8
Answers
Answer:
-5x + 14y + 8
Step-by-step explanation:
2x + 4y - 7x + 10y + 8
Combine 2x and -7x because they are both being multiplied by x.
-5x + 4y + 10y + 8
Combine 4y and 10y because they are both being multiplied by y.
-5x + 14y + 8
A proportional relationship between the number of pounds of carrots (x) and the price in dollars (y) is graphed, and the ordered pair (8, 6) is on the graphed line. Part A: What is the price of 1 pound of carrots? Show your work. (8 points)
Answers
Answer:
$0.75
Step-by-step explanation:
We have been given that a proportional relationship between the number of pounds of carrots (x) and the price in dollars (y).
We can represent this information as: [tex]y=kx[/tex].
We are also told that the ordered pair (8, 6) is on the graphed line. Let us substitute x= 8 and y= 6 in our proportional equation to find the constant of proportionality.
[tex]6=k*8[/tex]
[tex]k=\frac{6}{8}[/tex]
[tex]k=\frac{3}{4}[/tex]
Now let us substitute k=3/4 and x=1 in our proportionality equation.
[tex]y=\frac{3}{4}*1[/tex]
[tex]y=\frac{3}{4}[/tex]
[tex]y=0.75[/tex]
Therefore, the price of 1 pound of carrots will be $0.75.
Threeangles of a quadrilateral are equal and its fourth angel is 120° . Find all the angels
Answers
Answer:
80°
Step-by-step explanation:
Three angles are equal
Let the equal angle be x
3x+120=360
3x=240
x=240/3
=80
Hence the three angles are 80∘
Answer:
Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.
Step-by-step explanation:
The sum of the measures of the angles of an n-sided polygon is (n - 2)180.
A quadrilateral has 4 sides, so n = 4 in the formula above.
(n - 2)180 = (4 - 2)180 = 2(180) = 360
The sum of the measures of the angles of a quadrilateral is 360 degrees.
Three angles are congruent. Let the measures of the three congruent angles be x. The sum of the measures of the 3 angles is x + x + x = 3x.
The sum of the measures of the angles is 360 deg.
3x + 120 = 360
Subtract 120 from both sides.
3x = 240
Divide both sides by 3.
x = 80
Answer: Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.
A traveler is walking on a moving walkway in an airport. The traveler must walk back on the walkway to get a bag he forgot. The traveler's ground speed is 1 ft/s against the walkway and 5 ft divided by s with the walkway. What is the traveler's speed off the walkway? What is the speed of the moving walkway?
Answers
Answer: The traveler's speed off the walkway= 3 ft/s
The speed of the moving walkway= 2 ft/s
Step-by-step explanation:
Given: A traveler is walking on a moving walkway in an airport.
Let 't' be the traveler's speed off the walkway and 'w' be the speed of walkway.
Then the traveler's ground speed against the walkway (t-w)= 1 ft/s
And the traveler's ground speed with the walkway (t+w)= 5 ft/s
thus we get the following equations [tex]t-w=1..........(1)\\t+w=5.............(2)[/tex]
Adding (1) and (2), we get
[tex]2t=6\\\Rightarrow\ t=3[/tex]
Subtract (2) from (1), we get
[tex]2w=4\\\Rightarrow\ w=2[/tex]
Therefore, the traveler's speed off the walkway= 3 ft/s
The speed of the moving walkway= 2 ft/s
Item 1 Solve the system of linear equations by graphing. 5x+5y=15 2x−2y=10
Answers
After graphing both lines, we're able to tell the solution by looking at the point where the lines cross. In this case, it's at (4, -1). And so that is the solution set.
what is the ratio of triangles to circle 3 trangle 2 circle
Answers
Answer:
3:2
Step-by-step explanation:
Triangle:circle
3 triangle:2 circle
Identify all the lines on the graph with unit rates that are less than 2 and greater than the unit rate of the relationship in the table.
Answers
recall that the slope, namely the average unit rate of change, is rise/run.
so, what's the slope for the function in the table? well, we can simply pick any two points and get it, or just use the first point rise of 8 and a run of 7, gives us a slope of 8/7 or 1⅐.
now, let's take a peek at the lines, they all have a "rise" of 6, notice they're all lying on the y = 6 line horizontally.
1)
rise = 6, run = 2, slope 6/2 = 3.
well, 3 is more than 2, so no that one.
2)
rise = 6, run = 3, slope = 6/3 = 2.
well 2 = 2, so no that one either.
3)
rise = 6, run = 4, slope 6/4 = 3/2.
3/2 is actually larger than 8/7 and less than 2, you can check. so ✔
4)
rise = 6, run = 5, slope = 6/5.
6/5 or 1⅕ is more than 8/7, and is clearly less than 2, so ✔
5)
rise = 6, run = 6, slope = 6/6 = 1.
well, needless to say 1 is less than 2 but is less than 8/7, recall 8/7 is actually 1⅐.
Answer:
View the picture for your answer!
Have a wonderful day:))
Is 42 and 105 relatively
prime
Answers
Answer:
No.
Step-by-step explanation:
42 has the following prime factors: 2, 3, 7
105 has prime factors: 3, 5, 7
Both prime factors 3 and 7 divide 42 and 105. If 42 and 105 were relatively prime (co-prime), the set of prime factors that divide both would be empty.
which of the following is equal to the fraction below (5/9)^8
Answers
Answer:
the answer is D because both are to the power of 8
Step-by-step explanation:
Answer:
Option D is correct
[tex](\frac{5}{9})^8=\frac{5^8}{9^8}[/tex]
Step-by-step explanation:
[tex]\text{Given the fraction }(\frac{5}{9})^8[/tex]
we have to choose the correct option which is equivalent to above.
As we know
[tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]
Put a=5, b=9, x=8
[tex](\frac{5}{9})^8=\frac{5^8}{9^8}[/tex]
Therefore, option D is correct
What algebraic expression is 5+3(2x-7)=5+6x-21
Answers
Travis is sewing a pillow for his Home Arts class. The pillow will be made from 2 identical rectangles. Each rectangle is 1 1/2 feet wide and 1 3/4 feet long. How many square feet of material is used in the sewing of the pillow?
A.2 3/8 sq. feet
B.2 5/8 sq. feet
C.5 1/4 sq. feet
D.6 1/2 sp. feet
Answers
Answer:
The answer is A.
Step-by-step explanation:
I need help could you please help me
Answers
the sum of two numbers is 17 and their difference is 29 what are the two numbers
Answers
Answer:
According to the question,
Numbers are : 23 and -6
The two numbers are -6 and 23.
To find the two numbers, we can set up a system of equations based on the given information. Let the two numbers be [tex]\( x \) and \( y \), where \( x > y \)[/tex]. According to the problem, we have:
1. The sum of the two numbers is 17:
[tex]\[ x + y = 17 \][/tex]
2. The difference between the two numbers is 29:
[tex]\[ x - y = 29 \][/tex]
Now, we can solve this system of equations. We can add the two equations together to eliminate [tex]\( y \)[/tex] :
[tex]\[ (x + y) + (x - y) = 17 + 29 \] \[ 2x = 46 \] \[ x = \frac{46}{2} \] \[ x = 23 \][/tex]
Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into one of the original equations to find [tex]\( y \)[/tex]. Let's use the first equation:
[tex]\[ 23 + y = 17 \] \[ y = 17 - 23 \] \[ y = -6 \][/tex]
Therefore, the two numbers are 23 and -6.
Which is the simplified form of the expression 3(7/5x+4)-2(3/2-5/4x)
Answers
Simplify 7/5x to 7x/5
3(7x/5 + 4) -2(3/2 - 5/4x)
Simplify 5/4x to 5x/4
3(7x/5 + 4) -2(3/2 - 5x/4)
Expand
21x/5 + 12 - 3 + 5x/2
Collect like terms
(21x/5 + 5x/2) + (12 - 3)
Simplify
67x/10 + 9
The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x) is (67x + 90)/10
What is an Expression ?Expression is a mathematical statement which consists of variables , constant and mathematical operators all together simultaneously.
The given expression is 3(7/5x+4)-2(3/2-5/4x)
[tex]\rm 3 ( \dfrac{7}{5} x+4) -2 ( \dfrac{3}{2}-\dfrac{5}{4}x)[/tex]
(21/5)x +12 - 3 + (5/2)x
((42+25)/10)x + 9
(67x + 90)/10
The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x) is (67x + 90)/10
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Analyze the reflectional symmetry of the regular polygons. The square has -fold reflectional symmetry. The regular octagon has -fold reflectional symmetry.
Answers
Answer:
The square has 4-fold reflectional symmetry. The regular octagon has 8-fold symmetry.
Step-by-step explanation:
For a square,
There are two lines of symmetry along two diagonals and
two lines of symmetry along midpoints of two pairs of opposite sides.
Therefore, there are 4 lines of reflectional symmetry in total.
For a regular octagon,
There are four lines of symmetry along four diagonals and
four lines of symmetry along midpoints of four pairs of opposite sides.
Therefore, there are 8 lines of reflectional symmetry in total.
Final answer:
A square has 4-fold reflectional symmetry, while a regular octagon has 8-fold reflectional symmetry.
Explanation:
Reflectional symmetry refers to a property of a shape where it can be divided into two mirror-image halves. The -fold reflectional symmetry of a regular polygon refers to the number of lines of symmetry it possesses. A line of symmetry is an imaginary line that divides the shape into two equal halves that are mirror images of each other.
For example, a square has 4-fold reflectional symmetry because it has 4 lines of symmetry, dividing it into 4 equal halves. Each line of symmetry passes through the midpoints of opposite sides.
On the other hand, a regular octagon has 8-fold reflectional symmetry because it has 8 lines of symmetry, dividing it into 8 equal halves. Each line of symmetry passes through the midpoints of opposite sides or vertices.
47 POINTS!
PLEASE HELP! (SHOW YOUR WORK)
Answers
Answer:
2. No it is not direction variation
3. This is direct variation with the constant being 2
Step-by-step explanation:
The equation for direct variation is y=kx
2. 8y = 3x+1
Divide each side by 8
8y/8 = 3x/8 + 1/8
y = 3/8 x + 1/8
We are adding 1/8 to each time so it is not direct variation
3. 12y = 24x
Divide each side by 12
12y/12 = 24x/12
y = 2x
This matches y= kx, where k=2
This is direct variation with the constant being 2