The proof of how a hexagon made of 6 equilateral triangles is explained below .
What is a Regular Hexagon ?
A hexagon is figure that is two dimensional and closed and made up of six equal line segments .
We know that the equilateral triangle is a regular polygon that 3 equal sides where each angle is 60° .
We also know that ; sum of interior angles of a hexagon is 720 degree .
So , each interior angle of a hexagon is = 120°
because [tex]\frac{720}{6}[/tex] = 120 degree .
When the lines are connected by using the two opposite vertices, then the internal angles are bisected, and each angle is 60° in measure.
In hexagon , the angle at center is 360° which is being divided into 6 equal parts.
So , the value of each angle at center of hexagon is equal to 60°.
We see that all 3 angles of six triangles formed in given hexagon are equal to 60°.
Therefore , a hexagon made of 6 equilateral triangles .
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Should i use the cosine law? If yes, show me the steps to solve this
The measure of the angle B is 55 degrees
How to determine the measure of the angle BFrom the question, we have the following parameters that can be used in our computation:
A triangle
On the triangle, we have the following readings:
Angle A = 53 degrees
Side AC = 13 units
Side AB = 15 units
To calculate the angle B, we start by calculating the measure of the length BC
This is represented using the following cosine law
BC = √(AC² + AB² - 2 * AC * AB * cos(A))
Substitute the known values in the above equation, so, we have the following representation
BC = √(13² + 15² - 2 * 13 * 15 * cos(53 degrees))
Evaluate
BC = 12.6
Using the sine law, we have
AC/sin(B) = BC/sin(A)
This gives
sin(B) = AC * sin(A)/BC
Substitute the known values in the above equation, so, we have the following representation
sin(B) = 13 * sin(53)/12.6
Evaluate
sin(B) = 0.8239890183
Take the arc sin
B = 55 degrees
Hence, the angle is 55 degrees
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geometry i need help
Answer: [tex]\sqrt{11}[/tex]
Step-by-step explanation:
Using the Pythagorean theroem we can solve this right triangle. We have 3 sides lets call them "a" "b" and "c"
side "a" will be 5
side "b" is the side we don't know
side "c" will be 6
the formula says that [tex]a^2+b^2=c^2[/tex] so that also means [tex]5^2+b^2=6^2[/tex]
then we can just solve with algebra
[tex]5^2+b^2=6^2[/tex]
[tex]25+b^2=36[/tex]
[tex]b^2=11[/tex]
so take the square root of both sides
b = [tex]\sqrt{11}[/tex]
hope that helps ciao
You lift a 45 n bag of mulch 1. 2 meters and carry it a distance of 10 meters to the garden. How much work was done.
The work done in lifting a bag of mulch was 504 Joules.
To find the amount of work done in this scenario, you can use the formula for work, which is work = force x distance x cos(theta), where force is measured in newtons (N), distance is measured in meters (m), and theta is the angle between the force and the displacement.
In this case, first, you lifted the bag of mulch 1.2 meters against gravity and the force applied is 45N and the displacement is 1.2m, the formula becomes:
work = force x distance x cos(theta) = 45 N x 1.2 m = 54 J
After, you carry the bag of mulch 10 meters, and the force applied is still 45N and the displacement is 10m, so the formula becomes:
work = force x distance x cos(theta) = 45 N x 10 m = 450 J
Therefore, the total amount of work done in lifting the bag of mulch 1.2 meters and carrying it at a distance of 10 meters is 54 J + 450 J = 504 J.
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How to factor 75x^2-3
Answer: 75x^2-3 can be factored as (25x)^2 - 3 . The expression can be factored by taking the square root of the constant term and then using difference of squares.
In this case, the square root of -3 is not a real number, so it's not possible to factor it further.
So the final factored form of 75x^2-3 is (25x)^2 - 3.
Answer:
Step-by-step explanation:
75x^2-3 cannot be factored using integer numbers since it's a difference of squares. The expression 75x^2-3 is a binomial, not a trinomial. The difference of squares is a factoring pattern where you have a squared binomial subtracted from a constant.
75x^2-3 = 75x^2 -3x^2 = 72x^2 -3x^2 = (75-3)x^2 = 72x^2
So the factorization of 75x^2-3 is just 72x^2
6. Over time the value of a car decreases. If the value of a car purchased for 25,000 decreases to 20,000 throughout a year, what is the percent of decrease in the price?
The percent of the decrease in the price is 20%.
What is the percent decrease?
Percentage is the fraction of an amount expressed as a number out of hundred. The sign that is used to represent percentage is %.
The first step is to determine the total decrease in the value of the car.
Total decrease = value of the car when purchased - value of the car now
Total decrease = 25,000 - 20,000 = 5,000
Percent decrease = (5,000 / 25,000) x 100 = 20%
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Which postulate proves these two triangles are congruent? A. ASA C. HL B. None, not congruent D. SSA
Answer:
A
Step-by-step explanation:
They have the same side, one side is congruent to itself.
alternate interor angle are the same, which is:
Top left of the triangle on the left + botton right of the triangle on the right,
and top left on the triangle on the right + botton right of of the triangle on the left.
A company can choose to package 12 cans into 3 rows of 4 or 6 rows of 2 which packaging uses more material?
Why would a company choose to package 12 cans one way instead of another?
The packaging that uses more material is the packaging 2
The company's decision to package 12 cans one way instead of another is to save costHow to determine the packaging that uses more materialThe given parameters that can be used in our computation are:
Package = 12 cans Material 1 = 3 rows of 4 Material 2 = 6 rows of 2For a packaging to use more material, it must have a higher perimeter value
The perimeter is then calculated as
Perimeter = 2 * (Rows + Column)
When the values are substituted, we have the following equations
Material 1 Perimeter = 2 * (3 + 4)
Material 1 Perimeter = 14
Material 2 Perimeter = 2 * (6 + 2)
Material 2 Perimeter = 16
This implies that the packaging 2 uses more material
This is so because 16 is greater than 14
Also, the company can choose to package 12 cans one way instead of another because one package can use more material than the other and they need to save cost
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Find the z value such that 86% of the standard normal curve lies between -z and z
The z-score is 1.0803.
Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.
First, we need to find the α of the area we don't want, which would be:
α = 1 - 0.86 = 0.14
We know that the Standard Normal Distribution is symmetric, so we would divide our area we don't want to be on either side of our area, so we solve for:
[tex]\frac{\alpha }{2} = \frac{0.14}{2} = 0.07[/tex]
Now, it becomes easy to solve using the z-table.
The -z value is -1.0803 and the z value is 1.0803.
Hence, the z-score is 1.0803.
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Can someone help me find the range of this please?
the range of the graph is simply the region that it covers vertically, well, from the picture we can see the graph goes down down down to -2 vertically, makes an U-turn and goes back up, the arrowheads mean it keeps on going to infinity, so vertically the graph never goes below -2, so its range is just from -2 up to infinity, or in interval notation [ -2 , +∞ ).
A cube is painted so that one face is blue, two faces are red, and three faces are green. How many different such cubes can be painted
There is only one way to paint such a cube, as each face must be a different color. So, the answer is one.
The Importance of Color Variety in Art: A Look at the Possibility of Painting a CubeWhen it comes to creating art, there is no denying the importance of color. It is one of the most powerful tools an artist has at their disposal, as it can be used to convey a wide range of emotions, ideas, and messages. Even a simple object such as a cube can be transformed into a work of art with the right colors. This essay will explore the potential of painting a cube with a variety of colors, and why it's important to use a variety of colors in artwork.
When it comes to painting a cube, one must choose colors that will create a harmonious yet interesting look. The colors should be chosen carefully because they will be the focus of the piece. A cube painted with only one color would be too dull and boring, while a cube painted with an array of colors will make it more visually appealing. To create a successful painting of a cube, one should use colors that contrast and complement each other. For example, a cube can be painted so that one face is blue, two faces are red, and three faces are green.
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From the set of whole numbers from 1 to 9, what is the ratio of prime numbers to composite numbers in the lowest term?
The ratio of prime numbers to composite numbers in the lowest term is 4:5.
A number with precisely two factors, "1" and the number itself, is referred to as a prime number. A composite number can be divided by at least one positive integer in addition to being divisible by 1 and the number itself since it contains more than two elements. The number 1 is neither a prime nor a composite. In addition to these two, coprime numbers fall into a similar category of numbers.
From the set of whole numbers from 1 to 9, there are 4 prime numbers (2, 3, 5, 7) and 5 composite numbers (4, 6, 8, 9). The ratio of prime numbers to composite numbers in the lowest term is 4:5, which can also be expressed as 4/5.
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When the Preimage and image are congruent the transformation is called an isometry?
Yes, this is correct. An isometry is a transformation that preserves the sample size and shape of an object, meaning that the preimage and image are congruent.
An isometry is a transformation that preserves the size and shape of an object. This means that the preimage and image are congruent, meaning that they have the same size and shape. In order to determine if a transformation is an isometry, one must first identify the preimage and image. Once this has been done, the lengths of the corresponding sides must be compared in order to determine if they are congruent. If the lengths match, then the transformation is an isometry. Additionally, the angles of the preimage and image should also be compared to ensure that they are the same. If all the sides and angles match, then the transformation is an isometry.
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Examine the system of equations. −3x y = 4, −9x 5y = −1 what is the solution?
The solution to the given system of equations (x,y) is
(-3.5,-6.5)
Linear equation is an equation in which the highest power of the variable(s) is 1.Linear equations can have one or more variables, and can be written in the form “ax + by = c,” where a, b, and c are constants and x and y are variables. They always produce a straight line when plotted on a graph, hence the name “linear.”
To solve this substitution method can be used
In the first equation -3x+y=4
y=4+3x
substituting the value of y in second equation -9x+5y=-1
-9x+5(4+3x)=-1
-9x+20+15x=-1
6x=-1-20
x=(-21)/6=-3.5
y=4+3(-3.5)=4-10.5=-6.5
(-3.5,-6.5) is the solution to the given system of equations.
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Write the solution set of the equation:
x = [tex]\frac{-7}{2}[/tex]
y = [tex]\frac{-13}{2}[/tex]
Now, According to the question:
Given the system of equations:
−3x + y = 4 ----1
−9x + 5y = −1-----2
Multiply both sides of the equation by a coefficient:
3( −3x + y) = 4 × 3
−9x + 5y = −1
Apply Multiplicative Distribution Law:
-9x + 3y = 12
-9x + 5y = -1
Subtract the two equations:
-9x + 3y -(-9x + 5y) = 12 -(-1)
Remove parentheses = -9x + 3y + 9x - 5y = 12 + 1
Cancel the unknown variables:
3y - 5y = 12 + 1
Combine like terms:
-2y = 12+1
-2y = 13
Divide both sides of the equation by the coefficient of variable :
y = 13 ÷ (-2)
y = -6.5
Express the number in fractions: y = -13/2
Substitute one unknown quantity into the elimination:
-9x + 3 × ([tex]\frac{-13}{2}[/tex]) = 12
Write as a single fraction:
-9x - [tex]\frac{1}{2}[/tex](3 × 13)= 12
Calculate the product or quotient:
-9x - [tex]\frac{39}{2}[/tex] = 12
Rearrange the unknown terms to the left side of the equation:
-9x = 12 + [tex]\frac{39}{2}[/tex]
Find common denominator and write the numerator above common denominator :
-9x = [tex]\frac{24+39}{2}[/tex]
= -9x = [tex]\frac{63}{2}[/tex]
x = [tex]\frac{63}{2}[/tex]÷( -9)
x = -[tex]\frac{63}{2}[/tex] × 9
x = [tex]\frac{-7}{2}[/tex]
Write the solution set of the equation:
x = [tex]\frac{-7}{2}[/tex]
y = [tex]\frac{-13}{2}[/tex]
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Solve the inequality
4x + 1 > 17
X > ?
Step-by-step explanation:
4x > 17
4x > 17 -1
4x > 16
x > 4
A deadline is approaching for a project at work and you are asked to put in more than the normal 40 hours of work for the first week of january to complete the project on time. your hourly wage is $10.00 per hour and you get time and a half for anything over 40 hours. what was your pay for the first week of january, given that you worked 10 hours of overtime? a. $550 b. $650 c. $600 d. $700
Your pay for the first week of January, given that you worked 10 hours of overtime is option a. $550
To solve this problem, we need to do the calculation for your total pay for the first week of January.
We will multiply the normal working hour by hourly wages:
For the first 40 hours, you would earn a total of
40 * $10.00 = $400=400.
For the 10 hours of overtime, you would earn a total of
10 * $10.00 * 1.5 = $100*1.5=150,
since you get the time and a half for anything over 40 hours. Therefore, your pay for the first week of January would be
$400 + $150 = $400+150=550.
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For the first week of January your pay was $550
The correct answer is an option a. $550
In this question we have been given that hourly wage is $10.00 per hour.
And you get time and a half for anything over 40 hours.
Since the deadline is approaching for a project at work and you are asked to put in more than the normal 40 hours of work for the first week of January.
We need to find the total pay for the first week of January.
Given that, you get time and a half for anything over 40 hours.
This means, for overtime pay:
per hour regular pay + half of regular pay
= 10 + 5
= $15
So, the overtime wage is $15.00 per hour.
Your hourly wage is $10.00 per
Using unitary method, for the first 40 hours, you would earn a total of:
40 * $10.00
= $400
For the 10 hours of overtime, you would earn a total of
10 * $15
= $150
So, your pay for the first week of January would be
$400 + $150
= $550.
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In which number is the value of the digit 4 equal to 40 ? A. 34,589 B. 17,524 C. 23,421 D. 95,247
The value of a digit in a number depends on its place value. The digit 4 will have a value of 40 if it is located in the tens place. The correct answer is option B: 17,524.
Explanation:In the context of place value in mathematics, the value of a digit depends on its position in the number. The digit 4 would have a value of 40 if it is located in the tens place. Therefore, the correct answer to this question would be option B: 17,524, where the digit 4 is in the tens place, giving it a value of 40.
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hi everyone help my math please activity 1 and 2
Answer:
Here you go. I hope this helps. Don't forget that when graphing, the x-axis (horizontal) number is written before the y-axis (vertical).
GEOMETRY PLEASE HELP
Answer:
[tex]\sqrt[2]{45}[/tex]
Step-by-step explanation:
Pythagorean Theorom
a^2+b^2=c^2
a^2+36=81
81-36=45
square root everything
sqaure root 45
Please solve!! just give answetr
Answer:
4π-8
Step-by-step explanation:
area of top semicircle - area of triangle = answer
triangle is a 45 45 90 triangle, so the hypotenuse = one leg * √2 = 4 * √2
the hypotenuse (side opposite right angle) = the diameter
area of top semicircle = πr² (area of whole circle) /2
radius = diameter / 2 = 2√2
area of top semicircle = 8π /2 = 4π
area of triangle = one leg ² /2 = 4²/2 = 8
thus, final area = 4π-8
What are the three types of horizontal asymptotes?
There are 3 cases to consider when determining horizontal asymptotes:
1) Case 1: if: degree of numerator < degree of denominator. then: horizontal asymptote: y = 0 (x-axis)
2) Case 2: if: degree of numerator = degree of denominator.
3) Case 3: if: degree of numerator > degree of denominator.
10x-9<-29 or 9x + 9 > 36
[tex]10x-9 < -29[/tex]
Add 9 to both sides:
[tex]10x-9+9 < -29+9[/tex]
[tex]10x < -20[/tex]
Divide both sides by 10:
[tex]\dfrac{10x}{10} < \dfrac{-20}{10}[/tex]
[tex]x < -2[/tex]
__________________________________________________________
[tex]9x + 9 > 36[/tex]
Subtract 9 from both sides:
[tex]9x+9-9 > 36-9[/tex]
[tex]9x > 27[/tex]
Divide both sides by 9:
[tex]\dfrac{9x}{9} > \dfrac{27}{9}[/tex]
[tex]x > 3[/tex]
__________________________________________________________
[tex]x < -2[/tex] or [tex]x > 3[/tex]
10x - 9 < -29
Add 9 to both sides:
10x - 9 + 9 < -29 + 9
10x < -20
Divide both sides by 10:
10x/10 < -20/10
x < -2
9x + 9 > 36
Subtract 9 from both sides:
9x + 9 - 9 > 36 - 9
9x > 27
Divide both sides by 9:
9x/9 > 27/9
x > 3
x < -2 or x > 3 would be your answer.
Hope this helps!
what is 365x56 divided by 8
Answer:
The answer to your question is 2555
Step-by-step explanation:
365 x 56 = 20440
20440 ÷ 8 = 2555
I hope this helps and have a wonderful day!
Andre has $12.30 in pennies, nickels, dimes, and quarters. If he has the same number of each coin, how many of each does he have?
Answer:
Step-by-step explanation:
0 886 pennies no np
Solve for p in the equation p − 15 = − 48
Answer:
[tex]\huge\boxed{\sf p = -33}[/tex]
Step-by-step explanation:
Given equation:p - 15 = -48
Add 15 to both sidesp = -48 + 15
p = -33[tex]\rule[225]{225}{2}[/tex]
Write the standard form of the quadratic function whose graph is a parabola with vertex (2,-1) and that passes through (5,2).
The standard form of the quadratic function whose graph is a parabola will be;
⇒ y = 1/3 (x² - 4x + 1)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
Vertex coordinate = (-3, 4)
And, A point on the graph = (0, 13)
Since, We know that;
The vertex form of a quadratic equation is given by;
⇒ y = a(x - h)² + k
Where h, k are the coordinates of the vertex.
Hence, At point (5, 2) at the vertex of (2, -1), we have;
⇒ 2 = a (5 - 2)² + (-1)
⇒ 2 = a × 9 - 1
⇒ 2 + 1 = 9a
⇒ 9a = 3
⇒ a = 3/9
⇒ a = 1/3
Since, The equation y = a(x - h)² + k is the vertex form,
Let us put the vertex values for h and k as well as the value of a to get the quadratic equation;
⇒ y = 1/3(x - 2)² - 1
⇒ y = 1/3 (x² + 4 - 4x) - 1
⇒ y = 1/3x² + 4/3 - 4/3x - 1
⇒ y = 1/3x² - 4/3x + 1/3
⇒ y = 1/3 (x² - 4x + 1)
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Which scenario is modeled by the equation (x) (0.65) = 36 dollars and 48 cents?
A pair of boots is on sale for 65 percent of the original cost. The sale price of the boots is x, $56.12.
A pair of boots is on sale for 35 percent of the original cost. The sale price of the boots is x, $56.12.
A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is x, $56.12
A pair of boots is on sale for 35 percent of the original cost. The original price of the boots is x, $56.12.
The answer choice which correctly represents a scenario modelled by the given equation as required is; A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is x, $56.12.
Which scenario is best modelled by the given equation?As evident in the task content; the given equation is; (x) (0.65) = 36 dollars and 48 cents which can be written algebraically as;
0.65x = 36.48
x = 36.48 / 0.65
x = $56.12.
On this note, by observation; it follows that 0.65 is equivalent to 65% and hence, it can be inferred that;
The original price of the boots is; x which is equal to $56.12 and whose 65% equivalent is; $36.48.
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Answer:
c on edge
Step-by-step explanation:
i hate edge
A number of squares are connected in a row to form a rectangle. The table shows the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form. Select all the true statements about this relation.
The true statements are the equation of the function is y=4x+4, the relation is a function, the graph is linear.
The equation of the function start by calculating the slope (m)
The slope formula is used to calculate the inclination or steepness of a line. It finds application in determining the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis. The slope of a line is defined as the change in the "y" coordinate with respect to the change in the "x" coordinate of that line.
The formula to calculate slope is given as,
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]where, m is the slope of the line, x1, x2 are the coordinates of the x-axis, and y1, y2 are the coordinates of the y-axis.
m=[tex]\frac{12-8}{2-1}=4[/tex]
m=4
The equation is then calculated as:
y=m[tex](x-x_{1})+y_{1}[/tex]So, we have
y=4(x-1)+8
y=4x-4+8
y=4x+4
Therefore, the equation is 4x+4. Hence the statement is true.
(b) The graph is nonlinear.
A linear function forms a straight line when it is plotted on a graph. A nonlinear function does not form a straight line (it is curved in some way). The slope of a linear function is constant, whereas the slope of a nonlinear function is continuously changingBecause of (a) above, the graph is linear.
(c) The relation is a function
A linear relation is a relationship or connection between two variables that will produce a straight line when graphed. There will be times when the data points are scattered and do not form an absolutely straight line. When it appears that the scattered points resemble a straight line,
Hence, the given relation is function then the statement is true.
Therefore, the equation of the function is y=4x+4, the relation is a function, the graph is linear.
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Number of squares(x) Perimeter(y)
1 8
2 12
3 16
4 20
Complete Question: What is the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form?
Answer: The relationship between the number of squares, x, and the perimeter of the rectangles can be expressed as a y = 5.1%x. This equation states that for every one square, the perimeter will increase by 5.1%.
To calculate the perimeter of a rectangle with x number of squares, the following calculation can be used: y = 5.1%x = 0.051x. This equation can be rearranged to solve for x: x = y/0.051.
For example, if the perimeter of the rectangle is 10, the number of squares, x, can be calculated as follows: x = 10/0.051 = 196.08. This indicates that the rectangle will have 196 squares.
Therefore, the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form can be expressed as y = 5.1%x, or x = y/0.051.
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HELP ME PLSSS IF YOU DO THANK YOU SO MUCH
Answer:
Step-by-step explanation:
part A Is 1600 because 80x20 is 1600
part b. Yes rick has enough because each bag covers 1000ft so 8 bags is enough.
Hope this helped.
The length of a rectangle is 3 more than its width. The perimeter of the rectangle is
58 cm. What are the rectangle's dimensions?
Answer:
The perimeter of a rectangle is equal to the sum of all four sides. If the length of the rectangle is 3 more than the width, we can express the perimeter as 2width + 2(width+3). This simplifies to 2width + 2width + 6, which is equal to 58. This can be simplified to 4width + 6 = 58, or 4width = 52. Dividing both sides by 4 gives us width = 13.
Since the width of the rectangle is 13 cm, the length is 3 more than this, or 13+3 = 16 cm. So the dimensions of the rectangle are 13 cm by 16 cm.
Step-by-step explanation:
How many types of fraction write with example?
A proper fraction is a fraction where the numerator is less than the denominator. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. A mixed fraction is a combination of a whole number and a fraction.
There are three main types of fractions: proper fractions, improper fractions, and mixed fractions.
1. Proper fraction: A proper fraction is a fraction where the numerator is less than the denominator. An example of a proper fraction is 2/3.
2. Improper fraction: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. An example of an improper fraction is 5/4.
3. Mixed fraction: A mixed fraction is a combination of a whole number and a fraction. An example of a mixed fraction is 3 1/2.
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The three primary categories of fractions are proper fractions, improper fractions, and mixed fractions.
The fraction is deemed accurate when the numerator is less than the denominator. It is considered unacceptable to use a fraction where the numerator is more than or equal to the denominator. A mixed fraction is produced by combining a whole number and a fraction.
The three primary categories of fractions are proper fractions, improper fractions, and mixed fractions.
1. Proper Fraction: A fraction that has a larger numerator than denominator is said to be inappropriate. Somewhere about 2/3 would be a reasonable fraction.
2. Improper fraction: A fraction that has a numerator that is more than or equal to the denominator is referred to as being improper. A bad fraction is demonstrated with the number 5/4.
3. Mixed Fraction: Mixture of a whole number and a fraction: A mixture fraction is one that combines the two. 3 1/2 is an illustration of a mixed fraction.
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