A rhombus is a quadrilateral with all sides of equal length, but its angles are not necessarily equal. The area of the rhombus is √3.
In this case, we are given that one of the angles of the rhombus is 120°. Since opposite angles in a rhombus are congruent, we know that all four angles of the rhombus are 120°.
To find the area of the rhombus, we need to know the length of one of its diagonals. In this case, the shorter diagonal has a length of 2.
The formula for the area of a rhombus is given by the product of the diagonals divided by 2:
Area = (d1 * d2) / 2
Since the rhombus is symmetrical, the diagonals bisect each other at right angles, forming four congruent right-angled triangles. Each of these triangles has a base of 1 (half the length of the shorter diagonal) and a height of √3 (half the length of the longer diagonal).
Therefore, the area of each triangle is (1 * √3) / 2 = √3 / 2.
Since there are four congruent triangles, the total area of the rhombus is 4 * (√3 / 2) = 2√3.
Hence, the area of the rhombus is √3.
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In circle O shown below, diameter DB is perpendicular to chord AC at E.
If DB = 34, AC = 30, and DE > BE, what is the length of
BE?
The length of each segment is: DF=3, FR= 2 2/3, DE=3, GH=4 1/2, EH= 4 5/6.
What is the length of EH ?Length of each segment
16. Length of segment DF
DF=-1-(-4)
DF=3
19. Length of segment FR
FR=-1 1/3-(-4)
FR= 2 2/3
17. Length of segment DE
DE=2 -(-1)
DE=3
20. Length of segment GH
GH= 3 1/2 -(-1)
GH=4 1/2
18. Length of segment FG
FG=3 1/2 -2
FG=1 1/2
21. Length of segment EH
EH=3 1/2-(-1 1/3)
EH= 4 5/6
Therefore the length of each segment is: DF=3, FR= 2 2/3, DE=3, GH=4 1/2, EH= 4 5/6.
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-9 + (-27x) please help
Answer:−
-9−27x
Step-by-step explanation:
What are the 3 types of triangles according to sides describe each?
Three types of triangles according to scalene, isosceles and equilateral triangle.
What is meant by scalene?
Every triangle side in a scalene triangle has a different length.Two triangle sides that are of the same length are called isosceles triangles.All of the sides of a triangle are the same length in an equilateral triangle.An equilateral triangle naturally has three equal internal angles and three equal length sides because, as the triangles above demonstrate, the length and internal angles of a triangle are closely connected.A scalene triangle is a triangle whose three sides are all of various lengths and whose three angles are all of different sizes. Scalene triangle angles always add up to 180 degrees and adhere to the angle sum property.To learn more about scalene refer to
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How do you dilate by a scale factor of 3 4?
16 is a scale factor of 3 4
What is scale factor ?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).The scale factor can be calculated when the new dimensions and the original dimensions are given. The basic formula to find the scale factor of a figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.Scale factor is a number that is used to draw the enlarged or reduced shape of any given figure. It is a number by which the size of any geometrical figure or shape can be changed with respect to its original size. It helps in changing the size of the figure but not its shape.To learn more about scale factor refers to:
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you are standing 10 feet from the base of a tree. the angle of elevation to the top of the tree is 70 degrees. what is the height of the tree
The height of the tree is 17.32 feet.
What is height?Height is the measurement of a person's or object's vertical distance from the ground. It is usually expressed in units of meters or feet. Height is an important factor in determining physical characteristics, such as BMI, or Body Mass Index. Height can also be used to estimate the age of a person, and to measure the effects of a growth-promoting treatment. Height is also used in many sports, as it is often an advantage for athletes.
Using the tangent formula, the height of the tree is approximately 17.32 feet. To calculate this, take the tangent of 70 degrees (which is 1.19175) and multiply it by the 10 feet of distance.
The result is 11.9175 feet, which when rounded to the nearest hundredth is 17.32 feet.
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the first term in this number pattern is 5. 5,10,15,20,25,30...
The first pattern has a difference of 5 while the second is 10 and become by multiplying 2 in pattern 1 so options (A), (B), and (E) will be correct.
What is the pattern?A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint. The hint which is present in a given pattern hides in the pattern only.
Given the two patterns.
In the first pattern, each term become by adding 5 so option (A) is correct.
In the second pattern, each term become by adding 10 so option (B) is correct.
The term in the second pattern becomes by multiplying 2 in pattern 1
For example 5× 2 = 10 and 10 × 2 = 20 so option (E) will be correct.
Hence, "The first pattern has a difference of 5 while the second is 10 and become by multiplying 2 in pattern 1".
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What is the length of the long leg of a 30 60 90 triangle?
The longer leg is the one that faces the 60-degree angle.
Any triangle with a 90-degree angle is considered a right triangle. A unique variety of right triangle with a 30-degree angle and a 60-degree angle in addition to the right angle is known as a 30-60-90 triangle.
Triangle Properties 30-60-90
A triangle with sides of 30-60-90 can be recognized by how they relate to the angles.
The shorter leg is the one that faces the 30-degree angle.
The longer leg is the one that faces the 60-degree angle.
The hypotenuse is the side that faces the right angle of 90 degrees.
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what is the weight of a square if a triangle weighs 4 grams?
Explain your reasoning
HHH
0
8. 2x
C. 4x
D. 2x
E. 4x
Answer: i believe is c or d i not 100% sure
Find and graph the image of quadrilateral PQRS after a dilation centered at the origin with a scale factor of 1/4. What are the coordinates of Q'?
The coordinates of point Q after dilation will be (2,-1). The correct option is B.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the coordinate is Q(8,-4). The point is dilated by a factor of 1/4.
The dilation of the point will be calculated as,
Q(8,-4) = Q'(8/4, -4 / 4)
Q(8,-4) = Q'(2, -1)
Hence the dilated point is Q'(2,-1).
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After allowing a discount of 20% on the marked price then
levying 10% VAT, a radio was sold. If buyer had paid Rs.320 for VAT how much had he got the discount?
Amount of discount allowed = 640 Rs.
What is VAT?VAT meaning value added tax that is attached to an item of product while bought by the buyer and also in each stage of production, distribution level. It is almost similar to a sales tax that is paid within the item price.
What is the value of discount?
given, discount allowed = 20% on the market price.
VAT = 10% on the market price.
Buyer paid as VAT = 320 Rs
Assume, market price of radio = X Rs
now amount of discount = 20/100× X = 0.2X
amount of VAT = 10/100×X = 0.1X
it is said that VAT paid by buyer = 320 Rs
now 320 = 0.1X
X = 320 / 0.1 = 3200 Rs
market price of radio = 3200 Rs
amount of discount = 20/100× 3200 = 640 Rs
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a store pays $68 for a portable dvd player. the markup is 35% what is the sellng price?
Answer:
$91.80 selling price
Step-by-step explanation:
A store pays $68 for a portable DVD player. the markup is 35% what is the selling price?
35% = 0.35
The multiplier for markup of 35% = 1 + 0.35 = 1.35
68 * 1.35 = $91.80 selling price
A vertical number line is given.
A vertical number line starting at negative 2 with tick marks every one half unit up to positive 4. The value 1.25 is labeled.
When scuba diving, a student recorded the value plotted in the image. If 0 represents sea level, which of the following is true about the value?
The student is −1.25 ft above sea level, and the absolute value is 1.25 ft.
The student is −1.25 ft below sea level, and the absolute value is 1.25 ft.
The student is 1.25 ft above sea level, and the absolute value is 1.25 ft.
The student is 1.25 ft below sea level, and the absolute value is 1.25ft.
The true statement regarding the number line and the absolute value is given as follows:
The student is 1.25 ft above sea level, and the absolute value is 1.25 ft.
How to interpret the number line and the absolute value?The number line gives the heights relative to the sea level, and thus their signal are interpreted as follows:
Positive numbers: heights that are above sea level.Negative numbers: heights that are below sea level.The absolute value of a number represents the distance that the number is from the origin. In the context of this problem, it will give the distance of the measure from the sea level of 0 ft.
The height is given as follows:
1.25 ft.
Which is a positive measure, hence the correct option is given by the third option.
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Is it possible to have a triangle with the following sides 6cm 7cm 2cm?
We can form a triangle with sides 6cm, 7cm, and 2cm.
Now, According to the question:
We know that:
What is triangle inequality rule?
The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the third side. The Triangle is a polygon with three line segments as its boundaries.
Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.
We have the sides:
6cm, 7cm, 2cm
Here,
6 + 7 > 2
Hence, we can form a triangle with sides 6cm, 7cm, and 2cm.
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which word does not belong with the other guitar,flute,violin,cello
A alone can do piece of work in 6 day and B alone in 8 day. A and B undertook to do it for $3200. With the help of C, they completed the work in 3 day. How much i to be paid to C?
If A alone can do a piece of work in 6 days and B alone in 8 days, then A and B undertook to do it for $3200 and complete the work in 3 days with the help of C, then C would be paid 400 dollars.
Therefore the answer is $400.
This is a work and time problem that can be solved using the concept of rate of work. Let's call the amount to be paid to C as "x".
A can do 1 piece of work in 6 days. Therefore, his rate of work is 1/6.
B can do 1 piece of work in 8 days. Therefore, his rate of work is 1/8.
Amount of work A and B can do in 3 days is
= 3×(1/6) + 3×(1/8)
= 3×(1/6)×(4/4) + 3×(1/8)×(3/3)
= 12/24 + 9/24
= 21/24
= 7/8
So amount of work C doing is
= 1 - 7/8
= 1/8
As C do 1/8 amount of work, the amount C would receive is
= 3200 × (1/8)
= 400
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What is the area of the trapezoid?
19 cm
30 cm;
31 cm
32 cm
square centimeters
The radius of a circle is increasing at a constant rate of 0. 5 meter per second. What is the rate of increase in the circumference of the circle at the instant when the radius of the circle is 3 meters?.
The rate of increase in the circumference of the circle at the instant when the radius of the circle is 3 meters is 3 phi m/s
From the question, we have the following information :
1. Constant rate of increasing radius with respect of time (t)
= [tex]\frac{dR}{dt}[/tex] = 0.5 m / s
2. Radius of circle is 3 meters ( 3m )
To find constant rate of increasing circumference, we have to know formula of circumference.
We know that circumference = 2 π R
Constant rate of increasing circumference with respect of time (t) can be formulated from contant rate of increasing radius multiply with formula to find circumference
[tex]\frac{dC}{dt}[/tex] = 2πR [tex]\frac{dR}{dt}[/tex]
[tex]\frac{dC}{dt}[/tex] = 2πR ( 0.5 )
= πR
From above equation, we know that the rate of increasing circumference is πR
When R = 3 m, we just simply subtitute πR with R=3
The constant rate will be :
Rate of increasing circumference = πR m/s
= π (3) m/s
= 3π m/s
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You will be writing a short essay on how you can apply the processes you have learned in this unit to solve one of those questions
Calculating Unit Price for Business Owner
A restuarant owner is trying to choose a vendor for their supplies needed for their to-go operation. Since COVID their to-go orders have sky rocketed. Below he has listed how many of each item he has used in the past 6 month. Choose between the two vendors pricing sheets to decide who would be the best option. Give a detailed breakdown of unit prices and amount needed by the particular business to choose between the vendor.
6-month inventory break down:
large to-go boxes: 2,575
small to-go boxes: 1,890
to-go cups w/ lid: 3,010
Vendor 1 pricing:
large to-go boxes: $45.49/case (200 boxes per case)
small to-go boxes: $45.51/case (400 per case)
to-go cups w/ lid: $59.49/case (600/case)
Vendor 2 pricing:
large to-go boxes: $25.49/case (150 boxes per case)
small to-go boxes: $40.51/case (500 per case)
to-go cups w/ lid: $37.50/case (500/case)
Answer:
large to-go boxes: $45.49/case (200 boxes per case)
small to-go boxes: $45.51/case (400 per case)
Step-by-step explanation:
large to-go boxes: $25.49/case (150 boxes per case)
small to-go boxes: $40.51/case (500 per case)
to-go cups w/ lid: $37.50/case (500/case)
A store owner gathered data for several days about the methods customers used to pay for their purchases. The scatter plot shows the data she gathered and the line of best fit. The equation of the line of best fit is y = 0. 755x + 11. 339. Based on the line of best fit, approximately how many customers are predicted to use a card to pay on a day when 90 customers pay by cash? a. 68 b. 79 c. 92 d. 104.
According to the line of best fit, 79 consumers are predicted to use their card to pay during a day when 90 customers pay in cash. The correct answer is C.
The answer is 79. This is because the equation of the line of best fit is:
y = 0.755x + 11.339Which is a linear equation that represents the relationship between the number of customers who pay by cash (x) and the number of customers who pay by card (y).
To use this equation to predict the number of customers who pay by card on a day when 90 customers pay by cash, we can substitute x = 90 into the equation:
y = 0.755x + 11.339y = 0.755(90) + 11.339y = 67.95 + 11.339y = 80.284Y = 79.2879.28 ≈ 79, hence the correct answer is C.
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I need help … please
Check to see if there is a constant rate of change to determine if a table of values represents a linear function. You're looking at a linear function if there is! You can learn how to determine whether a table of values represents a linear function in this tutorial.
Two linear equations are what?If an equation is written in the form axe + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
Which two types of equations are there?Identities and conditional equations are the two types of equations.
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Please help solve this, my last two brain cells aren't working rn
Answer:
dude my brain cells are perishing
-2/3 is your answer my guy
have fun
Step-by-step explanation:
HELP ME On the planet vreel, there are 8 alabers to ever 5 totts. if farmer joogh has 30 totts on his gepsil farm, how many alabers are on the farm? your answer may be exact or accurate to the nearest tenth
Answer:
48
Step-by-step explanation:
[tex]\frac{8}{5}[/tex] = [tex]\frac{x}{30}[/tex]
In the ratio there are 5 totts. The farmer has 30 totts.
5 x 6 = 30, so 8 x 6 = 48
Answer:
Step-by-step explanation: i pretty sure it 240 because there is 8 on every 5 so 8x5 and there is 8 on every 30 8x30=240
A girl answered 38 questions on a reading app named lightsail.
The system indicated that she was 60% complete
How many questions are there in total?
Answer:
its either 63 or 64, im not really sure
Urgent : Need Help will Mark Brainliest
The function a(g)=10-log base 3(g+1) represents the home attendance of a football team in hundreds depending on the number of home games, g.
How many people will attend the second home game?
How many people will attend the eighth home game?
At which game were there 500 attendees? Does this answer seem reasonable based on context of the problem?
The number of people that will attend each game is given as follows:
Second game: 9,000.Either game: 8,000.The number of attendees will be of 500 on the 857th game, which does not make sense in the context of this problem, as a football team plays at most nine home games during a season. (taking the NFL in context).
What is the logarithmic function?The logarithmic function for this problem is defined as follows:
[tex]a(g) = 10 - \log_3{(g + 1)}[/tex]
Hence the number of people that will attend the second home game, when g = 2, is given as follows:
[tex]a(2) = 10 - \log_3{(2 + 1)}[/tex]
a(2) = 10 - 1
a(2) = 9.
Hence 9,000 people, as a(g) is measured in thousands.
The number of people that will attend the eight home game is given as follows:
[tex]a(8) = 10 - \log_3{(8 + 1)}[/tex]
a(8) = 10 - 2
a(8) = 8. (8,000, considering the unit of a(g)).
The game in which 500 people will attend is obtained as follows:
[tex]0.5 = 10 - \log_3{(g + 1)}[/tex]
[tex]\log_3{(g + 1)} = 9.5[/tex]
Applying the cube to both sides, we have that:
g + 1 = 9.5³
g = 857.
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Is root 3x² 2x a polynomial?
The given expression [tex]\sqrt{3}x^{2} -2x[/tex] is a polynomial as the power of x are 2 and 1 which are whole numbers .
What are Polynomials ?
The Polynomials are defined as an expression that are composed of variables, constants and exponents, which are combined using mathematical operators .
For Example : [tex]x^{2} +4x[/tex] .
The Expression can be called as a polynomial if the power of variable present in the expression is a whole number .
The expression is given as : [tex]\sqrt{3}x^{2} -2x[/tex] ,
we can see that , in the first term the power of x is 2 , which is a whole number , and
in the second term the power of x is 1 , which is also a whole number .
Therefore , the expression [tex]\sqrt{3}x^{2} -2x[/tex] is a polynomial .
The given question is incomplete , the complete question is
Is [tex]\sqrt{3}x^{2} -2x[/tex] a polynomial ?
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Find the vale of :
sin 1230°
Answer:
1/2
Step-by-step explanation:
I think it is 1/2 Sorry If i am Wrong
One Kung Pao chicken and two Big Macs provide 2620 calories. Two Kung Pao chickens and one Big Mac provide 3740 calories. Find the caloric content of each item.
One Kung Pao chicken contains 1620 calories. One Big Mac contains 500 calories.
What is an equation?
A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Assume that one Kung Pao chicken content x calories and one Big Mac content y calories.
Given that one Kung Pao chicken and two Big Macs provide 2620 calories.
Two Kung Pao chickens and one Big Mac provide 3740 calories.
Now using the variable finding calories:
One Kung Pao chicken and two Big Macs provide x + 2y calories.
Two Kung Pao chickens and one Big Mac provide 2x + y calories.
The system of equations is:
x + 2y = 2620 ......(i)
2x + y = 3740 .....(ii)
Using the elimination method to solve the given equations.
Multiply equation (i) by 2 and subtract it from equation (ii)
2x + y = 3740
2x + 4y = 5240
(-) (-) (-)
_____________
-3y = -1500
Divide both sides by -3:
y = 500.
Putting y = 500 in equation (i)
x + 2(500) = 2620
x + 1000 = 2620
x = 1620
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The measures of the interior angles of a convex octagon are 45x,40x, 155, 120, 155, 38x, 158x, and 41x. What is the measure of the smallest interior angle
Simon's photo album has 8 photos of his car and some photos of his motorbike
He replaced some of the photos of his motorbike with some more photos of his car.
The number of photos of his car became 12. The ratio of the number of photos of his car to his motorbike became 3:5. How many photos of Simon's bike was there in the album ORGINALLY?
There were 24 photos of Simon's motorbike in the album originally.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Let x be the number of photos of Simon's motorbike in the album originally.
We know that the number of photos of his car became 12, so the number of photos of his car originally was 8.
We also know that the ratio of the number of photos of his car to his motorbike became 3:5.
So the number of photos of his car and his motorbike originally was x-4.
We can set up the following equation:
12/(x-4) = 3:5
We can cross-multiply and simplify to get:
3x - 12 = 60
3x = 60 + 12
3x = 72
x = 72/3
x = 24
Hence, originally there were 24 photos.
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yann just started a new job. for every 5 hours he works yama earns $90. the graph represents yamas earnings for diffrent numbers of hours
Answer:
12
Step-by-step explanation:
2x3 4+5