The theorem simply states that diagonals of a parallelogram bisect each other is proven as OA = OC.
How to proof the parallelogram?From the information, OA = OC and OB = OD. In both triangles AOD and BOC, AD = BC since opposite angles are equal.
Also, ADO = CBO since alternate interior angles are equal. Also, DAO = BCO.
Therefore, OA = OC
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Which statements must be true according to the histogram? check all that apply. the data is qualitative. the data is skewed right. there were 31 people at the party. there were children at the party. the most common age of the attendees was 13 years old. the majority of the people at the party were less than 61 years old.
The statements that must be true according to the data presented by the considered histogram are:
Option 2: the data is skewed right. Option 3: there were 31 people at the party.Option 6: the majority of the people at the party were less than 61 years old.How to identify skewed graph?A skewed distribution is a distribution having bias on one of the two sides (either left or right).
It is like leaning mountain on one side (left or right).
A left skewed graph have elongated tail on the left side of the main mountain like figure. The mountain like figure is after that elongated tail. It is also called negatively skewed graph.A right skewed graph has elongated tail on the right side of the main mountain like figure. The mountain like figure is before that elongated tail. It is also called positively skewed graph.The missing image of the considered histogram is attached below.
Checking all the options:
Option 1: the data is qualitative.It is wrong. The data is numeric, and therefore, not describing qualities, so its not a qualitative data.
Option 2: the data is skewed right.The histogram has long tail on the right side, so its right skewed. Thus, this option is correct.
Option 3: there were 31 people at the party.Age group Frequency (number of people of that age group in party)
0-20 5
21-40 13
41-60 8
61-80 3
81-100 2
total 5+13+8+3+2 =31
So yes, there were total 31 people at the party as a person can be at max in one age group, so no repeated counting.
Option 4: there were children at the party.From 0 to 20 age group, there were 5 people. But it isn't known if they were < 18 or ≥ 18 (this is the side effect of grouped data, the loss of some information). So this option is not necessarily correct.
Option 5: the most common age of the attendees was 13 years old.It is false. The most common age was from the group 21-40 years old. And 13 is < 20, so it doesn't lie in this group.
Option 6: the majority of the people at the party were less than 61 years old.
Total number of people < 61 = 5+13+8 = 26
26 is more than half of 31 people. So yes, this option is correct.
Thus, the statements that must be true according to the data presented by the considered histogram are:
Option 2: the data is skewed right. Option 3: there were 31 people at the party.Option 6: the majority of the people at the party were less than 61 years old.Learn more about skewed distribution here;
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The area of a rectangular field is 4526 m².
If the width of the field is 62 m, what is its length?
Answer:
73 m
Step-by-step explanation:
The formula for the area of a rectangle is a = w(l). Using this, we can plug in the given values and solve for l, the length.
4526 = 62(l)
[tex]\frac{4526}{62} =\frac{62l}{62}[/tex]
l = 73
hope this helps!
Answer: 73 meters
Step-by-step explanation:
The simple formula to calculate the area of a regular rectangle is (Length x Width)
Given the area is 4526, and the width 62, we can use "y" to represent the unknown length.
So, '
62(y)=4526
Divide both sides by 62
1/2[62(y)]=4526/62
Y= 73 meters.
To check, 73x62= 4526, which follows the formula
Do number 12 pleasee
Answer:
114
Step-by-step explanation:
25% = 25/100 = 0.25
152 × 0.25 = 38
152 - 38 = 114
Answer:
$114
Step-by-step explanation:
152x0.75 = 114
Find the surface area of the cylinder. Round your answer to the nearest tenth.
6 ft
7 ft
Answer:
490.1 (If the radius is 6ft and height is 7ft)
571.8 (If the radius is 7ft and height is 6ft)
Step-by-step explanation:
A=2πrh+2πr2
Plug in the value for the radius and height. Then solve.
What is the mean absolute deviation (mad) of the data set? 2, 5, 6, 12, 15 enter your answer as a decimal in the box.
Answer: 4.4
To find the mad you have to first find the mean of the data set then you have to find the sum of the data values and divide the sum by the number of data values.
13. If ZA and ZB are supplementary angles and ZA
is three times as large as ZB, find the measures
of ZA and ZB.
Answer:
A. ZA+ZB =180
B. ZA is 135 and ZB is 45
Step-by-step explanation:
Step-by-step explanation:since ZA and ZB are supplementary
ZA+Zb =180°
But ZA=3ZB
∴ 3ZB+ZB=180° ⇒4ZB=180°
∴ZB =45
Which equation results from taking the square root of both sides of (x 9)2 = 25?
Answer:
[tex]x^{9}[/tex] = ± 5
Step-by-step explanation:
([tex]x^{9}[/tex] )² = 25 ( take square root of both sides )
[tex]\sqrt{(x^{9})^2 }[/tex] = ± [tex]\sqrt{25}[/tex]
[tex]x^{9}[/tex] = ± 5
5x – 5 = 7x + 1 what is this question
Answer:
x = - 3
Step-by-step explanation:
5x - 5 = 7x + 1 ( subtract 7x from both sides )
- 2x - 5 = 1 ( add 5 to both sides )
- 2x = 6 ( divide both sides by - 2 )
x = - 3
Answer: x = -3
Step-by-step explanation: Here is my explanation...
Step 1: Take away 5x from both sides 5x - 5x - 5 = 7x - 5x + 1.
Step 2: You should then get -5 = 2x + 1, then take away 1 from both sides -5 - 1 = 2x + 1 - 1
Step 3: -6 = 2x, divide 2x on both sides -6/2 = 2x/2
x = -3
Work Check:
5 (-3) - 5 = 7 (-3) + 1
-15 - 5 = -21 + 1
-20 = -20
If the -20 = -20 then this proves that x = -3. I hope this helped!
Based only on the information given in the diagram, it is guaranteed that ABC ~ XYZ.
Check the picture below.
please help me i need help
Answer:
Step-by-step explanation:
a c d are the answer
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. she then solves this equation for y. which statement explains karina’s solution? the cost of natural gas is $0.17 per unit. the cost of natural gas is $0.20 per unit. the cost of natural gas is $0.72 per unit. the cost of natural gas is $0.83 per unit.
The correct option is D. The cost of natural gas is $0.83 per unit.
What is a linear equation?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation
Consider the provided equation.
116y=96.28
We need to solve the above equation for y.
Divide both sides by 116.
[tex]\dfrac{116y}{116}=\dfrac{96.28}{116}[/tex]
[tex]y=0.83[/tex]
Now consider the provided options.
Hence, the correct option is D. The cost of natural gas is $0.83 per unit.
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Q. Find the area 41.5in2 430in2 215in2 1.5in2
Answer:
430 in^2
Step-by-step explanation:
Area of parallelogram = base * height = 20 * 21.5 = 430 in^2
A pizza shop sells 6 pizza rolls for 10.74. At this rate, in dollars and cents, how much would 9 pizza rolls cost?
Answer:
$16.11
Step-by-step explanation:
10.74÷6
times the number you get by 3
add that number to 10.74
If x > 0, what is the difference of
[tex]6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } [/tex]in simplest radical form?
Answer:
[tex]\longmapsto \sf \: \: - 14x \cdot\sqrt{14x}[/tex]
Step-by-step explanation:
[tex] \sf \: if \: x > 0 [/tex]
[tex] \sf 6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } [/tex]
[tex] \sf Let's \: solve \: for \sqrt{56 {x}^{3} } \: first, \\\longmapsto \sf \sqrt{56 {x}^{3} } = \sqrt{14 \times 4 {x}^{2} \times x } \\ \sf \longmapsto \sqrt{56 {x}^{3} } = 4x \sqrt{14x} [/tex]
Substituting above value in given equation,
[tex]\longmapsto \sf 6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } \\ \longmapsto\sf 6x \sqrt{14x} - 5 \times 4x \sqrt{14x} \\ \longmapsto \sf \: 6x \sqrt{14x} - 20x \sqrt{14x} \\\longmapsto \sf \: \sqrt{14x}(6x - 20x) \\ \longmapsto \sf \: \: - 14x \cdot\sqrt{14x}[/tex]
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The local volleyball team hosts a concession stand to raise money. They spend $120 to purchase popcorn, candy, and drinks. They buy 95 bags of popcorn at $0. 75 each and 35 bags of candy at $1. 20 each. How much money does the volleyball team have left to spend on drinks
Answer: $6.75
Step-by-step explanation:
Popcorn95 × 0.75 = 71.25
Candy35 × 1.20 =42
Totally 113.25
Deduct from 120
Drinks6.75
Which is the completely factored form of 4x2 28x 49? (x 7)(4x 7) 4(x 7)(x 7) (2x 7)(2x 7) 2(x 7)(x 7)
The completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)
How to find the factors of a quadratic expression?If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:
[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]
Then writing b in terms of alpha and beta would help us getting common factors out.
Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any trial and error.
For this case, the given quadratic expression is:
[tex]4x^2 + 28x + 49[/tex]
So we've to find two numbers such that:
Their sum = b = 28
Their product = [tex]ac = 4\times 49 = 196[/tex]
We can see that 196 is square of 14, and that 14 added twice forms 28, thus:
14 + 14 = 28
14×14 = 196
Writing b = 28 as sum of 14 twice, we get:
[tex]4x^2 + 28x + 49 = 4x^2 + 14x + 14x +49 \\4x^2 + 28x + 49 = 2x(2x+7) + 7(2x + 7)\\4x^2 + 28x + 49 = (2x+7)(2x+7)[/tex]
Thus, the completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)
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which of the following expressions is equivalent to 7(x+ 3)?
Answer:
7x+21
Step-by-step explanation:
Answer:
7x + 21
Step-by-step explanation:
Given
7(x + 3)Solving
Use the Distributive Property ⇒ x(a + b) = xa + xb7(x) + 7(3)7x + 21Find the slope of the line represented by the
equation below. Give your answer as a
Fraction in simplest form.
6x - 8y = 2
answer
7
Step-by-step explanation:
cause I said so
Answer:
m=3/4
Step-by-step explanation:
Explanation:
The slope of a line parallel to a line L has the same slope as line L.
6x−8y=−2
6x+2=8y
y=6/8x+2/8
Simplfied= y=3/4x+1/4
Therefore the answer is 3/4.
what is the area of the figure
Step-by-step explanation:
make the figure into 1 rectangle with dimensions 25 and w,and rite triangle with hypotenuse = 18 and h = 8
applying Pythagoras theorem
18^2 = 8^2 + b^2
b^2 = 260
b = 2√65ft
area of rectangle = 2√65 * 25= 50√65
area of triangle = 1/2 * 2√65*8 = 8√65
total area = 58√65 ft^2
What is the area of the composite figure? 262 cm2 264 cm2 266 cm2 268 cm2
The Area is a two-dimensional scalar quantity. The area of the composite figure is 264 cm².
What is the area?The area of a two-dimensional region, form, or planar lamina in the plane is the quantity that represents its extent. On the two-dimensional surface of a three-dimensional object, the surface area is its counterpart.
The composite figure can be broken down into four parts a square(A), a triangle(B) and two rectangles(C and D).
Now, if the area of the composite figure is taken out it will be,
[tex]\text{Area of composite}=\text{Area of Square A} + \text{Area of triangle B} + \text{Area of Rectangle C} + \text{Area of Rectangle D}\\[/tex]
[tex]\text{Area of Composte}=(10^2)+(\dfrac12 \times 6 \times 4)+(8 \times 4)+(20 \times 6)\\\\\text{Area of Composte}= 100+ 12 + 32 + 120 =264\rm\ cm^2[/tex]
Thus, the area of the composite figure is 264 cm².
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7th grade math and serface area
Answer:
108 square yards
Step-by-step explanation:
l = 6 yd
w = 4 yd
h = 3 yd
Surface area of rectangular prism = 2*(lw +wh + hl)
= 2*(6*4 + 4*3 + 3*6)
= 2* ( 24 + 12 + 18)
= 2 *54
= 108 square yards
Which sentence is true?
A. 4/5 > 3/4
B. 4/5< 3/4
C. 4/5=3/4
D. 3/4> 4/5
Answer:
A.
Step-by-step explanation:
4/5 = 0.8
3/4 = 0.75
0.75 < 0.8
the club sells 144 cans of lemonade what is the least number of bottles of water that must be sold to cover the cost of rending costumes
Answer:
A total of 142 units of water bottles must be sold to recover the costs of renting costumes.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
There are some dogs cats and rabbits in a pet farm the number of dogs is 3/5of the total number of cats and rabbits .
Let the number of cats in a farm be [tex]x[/tex] and the number of rabbits be [tex]y[/tex]. The total number of cats and rabbits would be be [tex]x + y[/tex]. As the number of dogs in the farm are [tex]\frac{3}{5}^{th}[/tex] the total number of cats and rabbits, so:
Number of dogs in the farm = [tex]\frac{3}{5} (x + y)[/tex]
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What should be done to x^2 - 12x to create a perfect square?
A) add 36
B)subtract 6
C)add 6
D)subtract 36
Answer:
A.) add 36To find the last term, divide the coefficient of the middle term by 2 then raise to the power of 2,that will be :
[tex]( \frac{ - 12}{2} )^{2} = { - 6}^{2} = 36 [/tex]
Answer:
add 36
Step-by-step explanation:
briwilljohn
16 minutes ago
Mathematics
High School
GIVE A DETAILED AND GOOD ANSWER FOR BRAINLIEST
Question 2(Multiple Choice Worth 5 points)
(06.08A LC)
Look at the triangle ABC.
Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 2, 1, and C at ordered pair 4, 1.
What is the length of the side AB of the triangle?
2
Square root of 20
6
Square root of 38
Answer:
Square root of 20 :)
Step-by-step explanation:
Pythagorean theorem: a^2 + b^2 = c^2
Now lets solve!!
2^2 + 4^2 = c^2
4 + 16 = c^2
20 = c^2
Now lets find the square root if any :)
[tex]\sqrt{20}[/tex] = no square root
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
im answering so you can give other guy brainliest :)
necesito saber el área de un cilindro de 10 cm de ancho y 4 de alto
Answer:
40 cm
Step-by-step explanation:
10cm*4cm=40cm
the sum of two consecutive integers is 23. what are the numbers?
Answer:
23
Step-by-step explanation:
the 1st number is x
because they are consecutive:
2nd number is (x+1)
now,
x+(x+1)= 23
2x=23–1
2x=22
x=22/2= 11
so two consecutive numbers are 11 & (11+1)=12
now 11+12=23
Answer:
11 and 12
Step-by-step explanation:
Let the integers be x and x + 1.
Sum of two consecutive integers is 23.
x + x + 1 = 23
2x + 1 = 23
2x = 23 - 1
2x = 22
x = 22 / 2
x = 11
x + 1
= 11 + 1
= 12
The numbers are 11 and 12.
two times a number less 4 is greater than the same number plus 6. for what number or numbers is true?
Answer:
n > 10 meaning, n is greater than 10
Step-by-step explanation:
Two times a number : 2n
Less 4 : -4
2n-4
Greater than the same number : >n
Plus 6 : +6
> n+6
2n-4 > n+6
To find n, we have to get n alone and equal to a single number. To do this, we first subtract 6 from both sides.
2n-10 > n
Then, subtract 2n from both sides
-10 > -n
Now, divide by -1
10 < n
So, n is greater than 10
Give ten (10) symbols of logic mathematics or logic in computer science.
Answer:
Step-by-step explanation:
open the page below
Answer:
please read through the ten symbols of logic mathematics