The number of images formed by two mirrors kept at an angle of 72° are;
5 images, If the object is positioned symmetrically between the mirrors
4 images if the object is placed asymmetrically between the mirrors
How can the number of images formed by two mirrors placed at an angle be found?The formula that can be used to find the number of images formed, n, when two mirrors are placed at a specified angle, θ, to each other is presented as follows;
If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an even number, the number of images formed is obtained using the formula;
[tex]n = \dfrac{360^{\circ}}{\theta} -1[/tex]If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an odd number, the number of images formed is obtained using the formula;
[tex]n = \dfrac{360^{\circ}}{\theta} -1[/tex]If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an odd number, and the position of the object is asymmetric, the number of images formed is obtained using the formula;
[tex]n = \dfrac{360^{\circ}}{\theta}[/tex]When θ = 72°, we get;
[tex]n = \dfrac{360^{\circ}}{72^{\circ}} = 5[/tex], which is an odd number, therefore;
If the object is placed symmetrically between the two mirrors, the number of images formed is therefore;
[tex]n = \dfrac{360^{\circ}}{72^{\circ}}-1 = 4[/tex]
If the object is placed asymmetrically between the two mirrors, the number of images formed is [tex]n = \dfrac{360^{\circ}}{72^{\circ}} = 5[/tex]
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Question 4 of 10
What can you say about the end behavior of the function f(x)--4x+6x²-52?
A. The leading coefficient is positive so the left end of the graph
goes down.
B. f(x) is an even function so both ends of the graph go in the same
direction.
C. The leading coefficient is positive so the left end of the graph
goes up.
D. f(x) is an even function so both ends of the graph go in opposite
directions.
The end behavior of the Polynomial f(x) = -4x⁶ + 6x² - 52 is;
B. f(x) is an even function so both ends of the graph go in the same
direction
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
Now, we are given the polynomial;
f(x) = -4x⁶ + 6x² - 52
Let us first test if the polynomial is even;
f(1) = -4(1)⁶ + 6(1)² - 52
f(1) = -50
Similarly;
f(-1) = -4(-1)⁶ + 6(-1)² - 52
f(-1) = -50
Since f(1) = f(-1), we can say that both ends of the graph go in opposite
directions.
Lastly, the leading coefficient is negative because it is -4 and as such it means that the left end goes down.
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PLEASE HELP I GIVE 95 POINTS
Find the area of the rhombus.
9 m
9 m
9 m
9 m
Select the correct answer.
A container is made by cutting off the bottom of a cone. The container has a diameter of 30 centimeters and a height of 20 centimeters. The
small cone that was removed has a diameter of 10 centimeters and a height of 6 centimeters.
What is the volume of the container, to the nearest cubic centimeter?
A. 6,126 cm³
B. 6,283 cm³
C. 5,812 cm³
D. 5,969 cm³
The volume of the container is 5969 cm³. The correct option is D. 5,969 cm³
Calculating VolumeFrom the question, we are to determine the volume of the container
Volume of the container = Volume of the cone - Volume of the small cone
The volume of a cone is given by the formula,
V = 1/3πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
For the small cone,
Diameter = 10 cm
∴ Radius, r = 10cm/ 2 = 5 cm
h = 6 cm
For the big cone
diameter = diameter of the container = 30 cm
∴ Radius = 30cm/ 2
Radius = 15cm
h = height of small cone + height of container
h = 6 cm + 20 cm
h = 26 cm
Putting the parameters into
Volume of the container = Volume of the cone - Volume of the small cone
We get,
Volume of the container = 1/3π × 15² ×26 - 1/3π × 5² × 6
Volume of the container = 1/3π (15² ×26 - 5² × 6)
Volume of the container = 1/3π (5850 - 150)
Volume of the container = 1/3π (5700)
Volume of the container = 1/3 × π × 5700
Volume of the container = 5969.026 cm³
Volume of the container ≈ 5969 cm³
Hence, the volume of the container is 5969 cm³. The correct option is D. 5,969 cm³
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What is the equation of the translated function, g(x), if f(x) = x2?
a.) g(x) = (x – 4)2 + 6
b.) g(x) = (x + 6)2 – 4
c.) g(x) = (x – 6)2 – 4
d.) g(x) = (x + 4)2 + 6
Answer: dfghj
Step-by-step explanation: xcfvghj
Answer: It's D
Step-by-step explanation:
Right on edge 2022
What are the answers to quick check for 13-2 equivalence with customary units of capacity in savvas
Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.
According to the question,
The customary units of capacity in Sava's are 1 fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.
Customary units and its equivalent
1 Fluid ounce = 2 Tablespoons
1 Cup = 8 fluid ounces
1 Pint = 2 cups
1 Quart = 2 pints
1 Gallon = 4 quarts
Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.
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Consider the equations y= |x-1 | and y = 3x + 2. The approxirate solution of this system of equations is
Answer:
Point Form: (- 1/4, 5/4)
Equation Form: x = - 1/4, y = 5/4
Step-by-step explanation:
A pizzeria has a choice of 15 toppings. How many ways could someone choose 3?
Select one:
a. 15
b. 455
c. 2,730
d. 3,375
Answer:
the answer is b 455
Step-by-step explanation:
15/(4×12)=455
describe fully the single transformation which maps triangle A onto triangle B.
The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)
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find the value for the following
[tex]\sqrt{3-2\sqrt{2} }[/tex] = 0.06
(2x)ˣ = 25√5
How to solve an expression?[tex]\sqrt{3-2\sqrt{2} }[/tex] = [tex]\sqrt{3}-\sqrt{2\sqrt{2} }[/tex] = 1.73205080757 - 1.67428223427 = 0.06
4ˣ . 4ˣ⁻¹ = 24
4ˣ . 4ˣ / 4 = 24
4ˣ(1 - 1 / 4) = 24
4ˣ(3 / 4) = 24
multiply both sides by 4 / 3
4ˣ = 32
2²ˣ = 2⁵
2x = 5
x = 5 / 2 = 2.5
Therefore,
(2x)ˣ = 25√5
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Solve the following:
-5² + 10²
(2 × (-5) × 3) + 3³
Give your answer in simplest form.
pls HELP Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles?
5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side
6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side
5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side
5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answer:
The first choice
Step-by-step explanation:
You are setting up as you read it. The left side has 5 x and 6 units, so you would set up 5 positive x times and 6 positive unit tiles. On the the right you are setting up 4 positive x tiles and 3 negative unit tiles. It is not asking you to solve with the algebra tiles, just to set it up.
Question down below about linear equations.
The system of equations is -x + y = 4 and -2x + y = 0
How to create the system of linear equations?To do this, we make use of the following ordered pairs
(4, 8)
The above point represents April 2008.
Let the system of equations be
mx + ny = 4
2mx + ny = 0
Substitute (4, 8) for x and y in the above equations.
4m + 8n = 4
8m + 8n = 0
Subtract both equations
4m - 8m = 4
This gives
-4m = 4
Divide by 4
m = -1
Substitute m = -1 in 8m + 8n = 0
-8 + 8n = 0
This gives
8n = 8
Divide by 8
n = 1
So, the system of equations is -x + y = 4 and -2x + y = 0
The graph of the system of equationsThe system of equations is -x + y = 4 and -2x + y = 0
See attachment for the graph of the system
Prove that the solution is (4, 8)The above is represented in the (a) part of this solution
Verify that the solution is (4, 8)We have:
-x + y = 4 and -2x + y = 0
Substitute (4, 8) for x and y in the above equations.
-4 + 8 = 4 --- true
-2*4 + 8 = 0 --- true
Both equations are true
Hence, the system of equations have been verified
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Noah has a summer tree-trimming business. Based on experience, Noah knows that his profit, P, in dollars, can be modelled by = −3^2 + 150 − 1200, where x is the amount he charges per tree.
1. How much does he need to charge if he wants to break even?
2. How much does he need to charge if he wants to make a profit of $600?
Solving quadratic equations, it is found that he needs to charge:
1. He needs to charge $40 to break even.
2. He needs to charge $30 for a profit of $600.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
The profit equation in this problem is:
P(x) = -3x² + 150x - 1200.
He breaks even when P(x) = 0, hence:
-3x² + 150x - 1200 = 0.
The coefficients are a = -3, b = 150, c = -1200, hence:
[tex]\Delta = 150^2 - 4(-3)(-1200) = 8100[/tex][tex]x_1 = \frac{-150 + \sqrt{8100}}{-6}[/tex][tex]x_2 = \frac{-150 - \sqrt{8100}}{-6} = 40[/tex]He needs to charge $40 to break even.
For a profit of $600, we have that P(x) = 600, hence:
-3x² + 150x - 1200 = 600.
-3x² + 150x - 1800 = 0.
The coefficients are a = -3, b = 150, c = -1800, hence:
[tex]\Delta = 150^2 - 4(-3)(-1800) = 900[/tex][tex]x_1 = \frac{-150 + \sqrt{900}}{-6}[/tex][tex]x_2 = \frac{-150 - \sqrt{900}}{-6} = 30[/tex]He needs to charge $30 for a profit of $600.
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The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as
1
L-10log where lo-10-12
and is the least intense sound a human ear can hear. What is the approximate loudness
of a dinner conversation with a sound intensity of 10-7?
[tex]\\ \rm\dashrightarrow B=10log\dfrac{I}{I_o}[/tex]
[tex]\\ \rm\dashrightarrow B=10\log\dfrac{10^{-7}}{10^{-12}}[/tex]
[tex]\\ \rm\dashrightarrow B=10log10^5[/tex]
[tex]\\ \rm\dashrightarrow B=10\times 5log10[/tex]
[tex]\\ \rm\dashrightarrow B=10(5)[/tex]
[tex]\\ \rm\dashrightarrow B=50dB[/tex]
Answer:
50 Db
Step-by-step explanation:
Given:
[tex]L=10 \log \dfrac{I}{I_0}[/tex]
[tex]I_0=10^{-12}[/tex]
where:
L is the loudness measured in decibels (Db)I is the sound intensity measured in w/m²To find the approximate loudness of a dinner conversation with a sound intensity of [tex]I=10^{-7}[/tex], substitute the values of I and I₀ into the given equation and solve for L:
[tex]\implies L=10 \log \dfrac{10^{-7}}{10^{-12}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies L=10 \log 10^{-7-(-12)[/tex]
[tex]\implies L=10 \log 10^5[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies L=5 \cdot 10 \log 10[/tex]
[tex]\implies L=50 \log 10[/tex]
As the given log does not have a specified base, assume the base is 10.
[tex]\implies L=50 \log_{10} 10[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies L=50 (1)[/tex]
[tex]\implies L=50\:\:\sf Db[/tex]
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Let a and b be positive integers such that the product of all positive divisors of a equals the product of all positive divisors of b. Prove that a
The property A*B = (A' + A") * ( B'+B") is equal to each other.
According to the statement
We have given that the a and b is the positive integers and we have to prove that the product of all positive divisors of a equals the product of all positive divisors of b.
And in this statement
Now we use Distributive property
Here A and B is the positive integer and
A' and A" are the divisors of A and B' and B" are the divisors of B.
Now,
A = A' + A" and B = B'+B"
Now, Multiply both with each other then
A*B = (A' + A") * ( B'+B")
then
A*B = (A' B'+ A'B") + ( A"B'+A'B")
by this way it is equal to each other
Hence proved.
So, The property A*B = (A' + A") * ( B'+B") is equal to each other.
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x =x=x, equals
^\circ
∘
Answer:
x = 25°
Step-by-step explanation:
Hello!
25° and x° are vertical angles, therefore they are equal to each other.
Vertical angles are angles formed by two intersecting lines that are non-adjacent.
The angle to the right of 80° would be 55°, because the sum of angles on a line is 180°.
Angle x would be 25° because the other straight line contains angles 80°, 50° and x°.
2. (01.01)
Evaluate 32+(5-2)-4-
O 19
O 16
O 46
24
3
. (1 point)
What is the volume of the space filled with tissue paper in the packaging box? 81.84 cubic centimeters 105.84 cubic centimeters 198.264 cubic centimeters 222.264 cubic centimeters
The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters
Let l,b,h be the dimensions of small gift box V1 = Volume = l*b*h
= 24cm^3
Dimension of Large box are 2.1l , 2.1b,2.1h
Volume of large box = 2.1 l*2.1b*2.1h
= (2.1)^3*lbh
= (2.1)^3*24
V2 =222.264
Volume filled with tissue paper is V2-V1
222.264 - 24
= 198.264cm^3
Hence The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters
The complete question is shown below
Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters.What is the volume of the tissue paper in the packaging box?
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22. What is the area of minor sector DFE?
79.3 square cm
15.2 square cm
37.9 square cm
66.1 square cm
The area of the minor sector DFE is gotten as; D: 66.1 square cm
How to find area of sector?
Formula for area of sector is;
A = (θ/360) * πr²
We are given;
minor angle; θ = 100°
radius; r = 8.7 cm
Thus;
A = (100/360) * π(8.7²)
A = 66.1 square cm
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Which of the following best describes the slope of the line below?
A. Positive
B. Zero
C. Negative
D. Undefined
Answer:
Zero
Step-by-step explanation:
Since the line is a horizontal line, the slope does not change. The slope is zero.
Answer:
Zero
Step-by-step explanation:
A zero slope is when the line is horizontal and when the slope equals to zero
I hope it helps! Have a great day!
bren~
can someone please help me
Answer:
[tex]\frac{13\pi }{9}[/tex] radians
Step-by-step explanation:
to convert degrees to radians
degrees × [tex]\frac{\pi }{180}[/tex]
= 260 × [tex]\frac{\pi }{180}[/tex]
= 26 × [tex]\frac{\pi }{18}[/tex]
= 13 × [tex]\frac{\pi }{9}[/tex]
= [tex]\frac{13\pi }{9}[/tex]
b. Shawn has 42 points on his computer game. He loses the
next round though which takes away 50 points. How
many total points does Shawn now have?
Answer: -8 points
Step-by-step explanation: because he lost 50, and he originally had 42, a smaller number, the answer will go into the negatives.
42-50= -8, which is how you get the answer!
Answer:
-8
Step-by-step explanation:
42-50 is the same as 50-42, except the answer is negative
The table below lists the tallest waterfalls in the world, in feet.
Name/Location Height (ft.) Mutarazi - Zimbabwe 24.99 x 102 Gocta Cataracts - Peru 2.532 x 103 Utigord - Norway 2,625 x 100 Angel - Venezuela .3212 x 104 Espelands - Norway 2.307 x 103 Yosemite - California (USA) 2,425 Monge - Norway 25.4 x 102 Tugela - South Africa 3.11 x 103 **Heights are approximations** [Part 1] List the waterfalls from tallest to shortest.. Show all of your work and/or explain your reasoning. [Part 2] What is the difference between the tallest and shortest heights? Show your work.
The difference between the tallest and shortest heights is 0.787 × 10
StatisticsMutarazi - Zimbabwe 24.99 x 10²Gocta Cataracts - Peru 2.532 x 10³Utigord - Norway 2,625 x 10^0Angel - Venezuela .3212 x 10⁴Espelands - Norway 2.307 x 10⁴Yosemite - California (USA) 2,425Monge - Norway 25.4 x 10²ugela - South Africa 3.11 x 10³From tallest to shortest:
Angel - Venezuela 3.212 x 10⁴Espelands - Norway 2.307 x 10⁴ugela - South Africa 3.11 x 10³Utigord - Norway 2,625 x 10^0Monge - Norway 25.4 x 10²Gocta Cataracts - Peru 2.532 x 10³Mutarazi - Zimbabwe 24.99 x 10²Yosemite - California (USA) 2,425Difference between tallest and shortest heights =
3.212 x 10⁴ - 2,425
= 3.212 x 10⁴ - 2.425 × 10³
= (3.212 - 2.425) × 10^4 - 3
= 0.787 × 10
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9. Construct Arguments Write a two-column
proof for the Angle Bisector Theorem. MP.3
The angle bisector theorems is proved below.
What is the angle bisector theorems?It should be noted that the angle bisector theorem simply states that an angle bisector of a triangle divides the opposite side into two segments which are proportional to the other sides of the triangle.
The way to proof the theorem is illustrated:
Draw a ray CX parallel to AD and then extend BA to intersect this ray at E.
In triangle CBE, DA is parallel to CE.
BD/DC == BA/AE ......... i
Now we want to prove that AE = AC
Since DA is parallel to CE, we have:
DAB = CEA (corresponding angles) ....... ii
DAC = ACE (alternate interior angles) ...... iii
Since AD is the bisector of BAC, we've DAB = DAC.
From the above, ACE makes and isosceles triangle and since the opposite sides are equal, we've AC = CE.
Substitute AC for AE in equation i
BD/DC = BA/AC
Therefore, the angle bisector theorems is proved.
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A salesman is carrying a big bag for selling a machine. In addition to the machine that the salesman wants to sell, there is some personal stuff. The weight of his machine is three kilogram and half a machine. In addition to the machine, there is a repair tool for the machine that weighs half kilogram and one-fourth of the machine. The personal stuff weighs four kilogram minus a fourth of the weight of the machine. Finally, the salesman has some supplies that weigh two-fifth of the machine and personal stuff combined. What is the total weight in the bag of salesman
The total weight of the bag that the salesman is carrying for selling a machine including some personal stuff is 13.9 Kg.
What is a fraction?A fraction is a rational number that consists of a numerator and a denominator, used to represent a part of the whole thing.
Calculation:It is given that,
A salesman is carrying a big bag for selling a machine.
Consider the weight of the machine = w
So,
The weight of his machine is three kilograms and half a machine. I.e.,
w = 3kg +w/2
⇒ w/2 = 3kg
∴ w = 6kg
Thus, the weight of the machine is 6 Kg.
So, the weight of the repair tool for the machine = a half kilogram and one-fourth of the machine
⇒ 1/2Kg + 1/4w
⇒ 1/2 + 6/4
⇒ 2 Kg
The personal stuff weighs - four kilograms minus a fourth of the weight of the machine.
⇒ 4Kg - w/4
⇒ 4 - 6/4
⇒ 2.5 Kg
He has some supplies that weigh two-fifth of the machine and personal stuff combined.
⇒ 2/5(w + 2.5)
⇒ 2/5 × 8.5
⇒ 3.4 Kg
Thus, the total weight of the bag = 6 Kg + 2 Kg + 2.5 Kg + 3.4Kg = 13.9Kg.
Therefore, the total weight of the salesman's bag is 13.9 Kg.
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The sum of the reciprocals of three consecutive integers is 47/60. What is the sum of the three integers
Answer:
56
Step-by-step explanation:
small brain :(
The following table shows each of Haruka's final exam scores last semester. Final exam Score on a 100100100-point scale Astronomy 727272 Biology 858585 Physics 929292 Chemistry \large
The mean calculated shows that the Chemistry score will be 87.
How to calculate the score?From the information given, the total scores will be:
= 84 × 4
= 336
The addition of the scores given will be:
= 72 + 85 + 92
= 249
The Chemistry score will be:
= 336 - 249
= 87
Complete question:
If the mean of the data set is 84 points, find Harukas final exam score in Chemistry.
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Clue 1
The number has three digits.
Clue 2 The number is less than 140.
Clue 3 The number has 7 as a factor.
Clue 4 The number is even.
Clue 5 The sum of the digits of the number is less than 9.
Fill in the table using this function rule.
The complete table is
x y
-1 -2
0 3
1 8
2 13
How to complete the table?
The function is given as:
y = 5x + 3
On the table, we have
x = -1, 0, 1 and 2
Using the above values, we have:
y = 5(-1) + 3 = -2
y = 5(0) + 3 = 3
y = 5(1) + 3 = 8
y = 5(2) + 3 = 13
So, the complete table is
x y
-1 -2
0 3
1 8
2 13
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