The provided statements are either given information, interpretations from the given diagram or applying rules of geometry such as the definitions of supplementary angles and the Same-Side Interior Angles Theorem.
Explanation:The missing reasons in this geometric proof are as follows:
a. Given: The fact that angle 5 = 40 is simply provided, it's the given information in the question.
b. Given: Similarly, the measurement of angle 2 being 140 is given information.
c. Definition of supplementary angles: Angle 5 and angle 2 are supplementary because the sum of their measure equals 180 (40+140).
d. Interpretation of the diagram: Without a diagram, it's difficult to be precise, but if angle 5 and angle 2 are indicated as same-side interior angles, then this inference comes from interpreting the diagram.
e. Same-Side Interior Angles Theorem: Lastly, if the same-side interior angles are supplementary, then the lines are parallel. This is a rule encapsulated by the same-side interior angles theorem.
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This is a number that can be divided out of each term in an expression.
Answer:
Hello!
Great question!
The correct answer would be "Common Factor."
Step-by-step explanation:
It is a common factor when it is a factor of two (or more) numbers.
The number which can be divided out of each term in an expression is called the GCF or greatest common factor of that number.
What is GCF (greatest common factor)?GCF or greatest common factor is the common number which all the term has in a group of terms. It is the number which can divide each number of the group.
For example, let a group of number as,
[tex]\{1,2,4,8,16\}[/tex]
The number which can be divided out of each term in this data is 16 which is the greater common factor of this data set.
Thus, the number which can be divided out of each term in an expression is called the GCF or greatest common factor of that number.
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(50 POINTS) Hi, I really need help on this first part of my portfolio it was due last week but I don't really get this part so if someone could explain it to me I could get the other four parts done on my own.
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Use the City Populations table found on the message board and select a city that is experiencing population growth. Determine the percentage growth and use that to write an exponential function to represent the city’s population, y, based on the number of years that pass, x from 2010 (i.e. 2011 means that x = 1)
City: Portland, Oregon 585,256 593,939 603,026 609,456 619,334 630621 639863
This was deleted once and idk why there is plenty of information :(
Ik this is a lot to ask of someone but I haven't had any luck with any function sites.
The distance d in feet that dropped object falls in t seconds is givin by the equation d divided 16 = tsquared how long does it take a dropped object to fall 64 feet
A line goes through the points (8,9) and (2,4).
What is the slope of the line?
Write the equation of the line in point-slope form?
Write the equation of the line in slope-intercept form?
What is the value of x in the figure below? In this diagram, ΔABD ~ ΔCAD.
The value of x in the figure given is E. √70.
The answer is E. √70.
The two triangles are similar by the AAA Similarity Theorem, since they have two pairs of congruent angles, namely ∠ABD and ∠CAD, and ∠BAD and ∠CDA.
Since the triangles are similar, the ratio of corresponding sides is constant. In particular, the ratio of AD to CD is the same as the ratio of BD to AD.
We are given that AD = 14 and CD = 20, so the ratio of AD to CD is 14/20. We are also given that BD = x, so the ratio of BD to AD is x/14.
Setting these two ratios equal to each other, we get x/14 = 14/20, which simplifies to x = √70.
Here is a proof that shows why the two triangles are similar:
AAA Similarity: Triangles ABD and CAD have two pairs of congruent angles, namely <ADB> and <CAD>, because they are both right angles.
SSS Similarity: Triangles ABD and CAD have three pairs of corresponding sides that are proportional, namely AD/CD = 14/20, BD/AD = x/14, and AB/CD = √70/20. Therefore, the two triangles are similar by the SSS Similarity Theorem.
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Multiplying by a conjugate gives a rational number because (a + b)(a -
b.= _____.
Which of the binomials below is a factor of this trinomial?
x2 + 13x + 42
A. x - 7
B. x + 7
C. x + 84
D. x2 + 12
The trinomial x^2 + 13x + 42 factors into (x + 7)(x + 6), making x + 7, which is option B, the correct binomial factor of the trinomial.
To determine which binomial is a factor of the trinomial x2 + 13x + 42, we need to factor the trinomial. To factor the trinomial, we are looking for two numbers that multiply to give us the constant term (42) and add to give us the linear coefficient (13). These two numbers are 7 and 6 because 7 * 6 = 42 and 7 + 6 = 13.
So, we can factor the trinomial as (x + 7)(x + 6). Thus, the binomial that is a factor of x2 + 13x + 42 is x + 7, which is option B.
The formula for the area a of a triangle is a equals 1 half b where is the base and h is the height. solve the formula for h and then find the height of a triangle whose area is 1768 square inches and whose base is 52 inches. round to the nearest tenth if necessary. height = inches
Area of triangle is given as:
A = (1/2) b * h
where b is base and h is height
So given that:
A = 1768 inches^2
b = 52 inches
Rearranging the equation to find for h:
h = 2 A / b
h = 2 * 1768 inches^2 / 52 inches
h = 68 inches
The sum of four consecutive even integers is 180. what is the smallest integer?
The equation is 4x + 12 = 180. Then the value of the smallest integer will be 42.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The sum of four consecutive even integers is 180.
Let x be the smallest integer. Then the other three consecutive even integers will be x + 2, x + 4, and x + 6. Then the equation is given as,
x + x + 2 + x + 4 + x + 6 = 180
4x + 12 = 180
4x = 168
x = 42
The value of the smallest integer will be 42.
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Auto insurance options offered by AA Auto Insurance are outlined in the table below. What monthly payment would you expect for an insurance policy through AA Auto Insurance with the following options? Bodily Injury: $25/50,000 Property Damage: $25,000 Collision: $250 deductible Comprehensive: $100 deductible
a.
$43.23
b.
$46.10
c.
$54.85
d.
$64.44
In this exercise we have to use the knowledge of finance to calculate the monthly amount of insurance, so the best alternative that represents this amount is:
Option C
In this exercise we want to calculate the monthly insurance payment amount, so from the given values we find:
[tex]Payment= (Bodily Injury)+ (Property Damage)+ (Collision)+(Comprehensive)[/tex]
Substituting the values in the formula given above we find that:
[tex]Payment= 22.5 + 120.5 + 415.25 + 100 \\= 658.25\\658.25/12 = 54.854[/tex]
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A pair of vertical angles may also form a linear pair true or false
Simplify using long division
Evaluate.
12⋅(4^−2/4^−4)
a) 14
b) 34
c) 16
d) 192
Answer:
d) 192
Step-by-step explanation:
Your calculator can do this for you.
Or, you can simplify to
[tex]12\cdot\dfrac{4^{-2}}{4^{-4}}=12(4^{-2+4})=12(4^2)=192[/tex]
Answer:
d
Step-by-step explanation:192
If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is ___.
The coming head in the fourth time is independent of the coming head in the first three times thus the probability of coming head in the fourth time is 1/2.
What is probability?Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
In our daily time, there are several instances in the everyday world where we may need to draw conclusions about how everything will turn out.
As per the given,
In the first three attempts coming head in the first three times.
In the fourth attempt, the probability will be independent of the first three events.
Thus, the probability of coming ahead in the fourth time will be as,
Number of desire output/number of total output
=> 1 / 2
Hence "The coming head in the fourth time is independent of the coming head in the first three times thus the probability of coming head in the fourth time is 1/2".
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Out of 100 lottery tickets, each having 50% chance of winning, 2 tickets are bought at random. what is the probability that at least one ticket will win?
For f(x)=3x+1 and g(x)=x squared - 6 find (f- g)(x)
5. The dimensions, in inches, of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and height 3x - 1. The volume is about 7.6 f3. Find the dimensions of the box in inches. Round to the nearest inch. (Hint: 1 f 1,728 in.3)
To find the dimensions of the shipping box, calculate the volume in cubic inches, then set up and solve the volume equation x(x + 5)(3x - 1), substituting the given volume after conversion from cubic feet. Solve for x, then use it to find and round the box's dimensions.
Explanation:To find the dimensions of the shipping box, we need to calculate the volume using the given dimensions in inches and compare it to the provided volume in cubic feet. Recall that the conversion factor between cubic feet and cubic inches is 1 cubic foot equals 1,728 cubic inches. Firstly, convert the volume of the box from cubic feet to cubic inches: 7.6 cubic feet are 7.6 x 1,728 cubic inches.
Next, we can set up the volume equation for the box using the given dimensional expressions: volume = width x length x height, which for this box is x x (x + 5) x (3x - 1). Now we solve the equation for x given that the volume in cubic inches is equal to 7.6 x 1,728 inches.
Once x is found, we can determine the width, length, and height by plugging x back into the expressions x, x + 5, and 3x - 1, respectively, and rounding each to the nearest inch.
Find the resultant of these two vectors: 2.00 x 102 units due east and 4.00 x 102 units 30.0° north of west.
If two vectors are represented both in magnitude and direction by the two adjacent sides of a triangle taken in an order, then their resultant is given by the third side taken in the reverse order.
Resultant vector :
R = sqrt of A^2 + B^2 + 2ABcosθ
given :
A = 200 units
B = 300 units
θ = 30 degrees
∴ R = sqrt of 200^2 + 300^2 + 2(200)(300)cos35
the answer is 477.805656
If two vectors are represented both in magnitude and direction by the two adjacent sides of a triangle taken in an order, then their resultant is given by the third side taken in the reverse order.
Resultant vector :
R = sqrt of A^2 + B^2 + 2ABcosθ
given :
A = 200 units
B = 300 units
θ = 30 degrees
∴ R = sqrt of 200^2 + 300^2 + 2(200)(300)cos35
the answer is 477.805656
Solve the following equation.75 = –5(–3 – 4x)
x = 3
x = –4
x = –3
x = 5
The perimeter of a rectangular concrete patio is 34 meters. the area is 70 square meters. what are the dimensions of the patio?
To find the dimensions of the rectangular patio, use the equations for perimeter and area and solve for length and width.
Explanation:To find the dimensions of the rectangular patio, we can use the given information about its perimeter and area. Let's assume the length of the patio is L and the width is W.
The perimeter is given as 34 meters, which is equal to 2L + 2W. So, we have the equation 2L + 2W = 34.
The area is given as 70 square meters, which is equal to L * W. So, we have the equation L * W = 70.
We can use these equations to solve for L and W using substitution or elimination method.
Simplify 5 - 2 · 3 + 4. 13 -5 3 21
The expression 2/+2w is used to find the perimeter of a rectangle with length / and width w.
What is the perimeter of a rectangle with length 14cm and width 4cm?
9cm
18cm
28cm
36cm
THANKS IN ADVANCE, I MARK BRAINLIEST!!!
Answer: 36 cm
Step-by-step explanation:
Given : The expression 2l+2w is used to find the perimeter of a rectangle with length l and width w.
To find : The perimeter of a rectangle with length 14cm and width 4cm.
Substitute l=14 and w=4 in the given expression , we get
Perimeter= [tex]2(14)+2(4) =28+8=36\ cm[/tex]
Hence, the perimeter of a rectangle with length 14cm and width 4cm= 36 cm
A probability experiment consists of rolling a fair 16-sided die. Find the probability of the event below of rolling a 5.
Answer:
The probability of the event below of rolling a 5 is 0.0625.
Step-by-step explanation:
Given is : A probability experiment consists of rolling a fair 16-sided die. Find the probability of the event below of rolling a 5.
Total number of faces = 16
So, there is only one way for rolling a 5 on a die
And the probability of rolling a 5 on a die = [tex]\frac{1}{16}[/tex]
= 0.0625
If f(x)= 2x+8 and g(x) = x^4, what is (g°f)(-3)?
I only need number 30 answered
What did the doctor say to the guy who thought he was a wigwam one day and teepee the next? math riddle
Answer:
too tenes
This is the correct answer because it is a play on words comparing tents which describes the native american home structure of a wigwam and a teepee and tense, will which describes a physiological response to high anxiety6.
If two angles are congruent and supplementary then each is a right angle true or false
Answer:
The statement is true. Supplementary angles have measures that add up to 180°. Each right angle has a measure of 90°. 90°+ 90° = 180°.
Step-by-step explanation:
whats the answer to the problem
A box of cookies can hold 24 cookies, and a container can hold 75 boxes of cookies. write a program that prompts the user to enter the total number of cookies, the number of cookies in a box, and the number of cookie boxes in a container. the program then outputs the number of boxes and the number of containers to ship the cookies. note that each box must contain the specified number of cookies, and each container must contain the specified number of boxes. if the last box of cookies contains less than the number of specified cookies, you can discard it and output the number of leftover cookies. similarly, if the last container contains less than the number of specified boxes, you can discard it and output the number of leftover boxes.
The provided math problem involves writing a program that helps to calculate the number of cookie boxes and containers required to ship a specific number of cookies considering the capacity of each item. If there are leftover cookies that do not fill a box or if there are leftover boxes that do not fill a container, these are also calculated.
Explanation:This is a programming problem which requires logic to calculate the number of boxes and containers needed to ship a given number of cookies. Assume that 'total_cookies', 'cookies_per_box', and 'boxes_per_container' are user inputs. Initially, you should calculate the total boxes by 'total_boxes = total_cookies / cookies_per_box'. The floored division operator is applied to discard the last box if it contains less than the specified number of cookies. Then, calculate the total containers with 'total_containers = total_boxes / boxes_per_container'. Again, you use the floored division operator to discard the last container if it contains less than the specified number of boxes. Lastly, calculate the leftover cookies and boxes, which is done by applying the modulus operator. 'leftover_cookies = total_cookies % cookies_per_box' and 'leftover_boxes = total_boxes % boxes_per_container'.
The logic of the given program focuses on the calculation of boxes and containers needed to ship the given number of cookies keeping in consideration the capacity of each box and container. Also, the algorithm calculates the leftover cookies and boxes, if not enough to fill a box or container fully.
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Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x − 2, y + 8) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.