The quadrilateral is a parallelogram because the pairs of opposite sides of the quadrilateral are parallel, ABCD is a parallelogram.
Given:- A quadrilateral ABCD in which AB=CD and AD=BC.
To prove:- AB∥CD and AD∥BC
Construction:- Joi A and C.
Proof:-
In △ABC and △CDA,
AB=CD(Given)
AD=BC(Given)
AC=AC(Common)
∴△ABC≅△CDA(By SSS)
Therefore, by CPCTC,
∠ACD=∠BAC
∠DAC=∠ACB
Since alternate angles are equal, thus the lines are parallel.
Therefore,
AB∥CD and AD∥BC
Since both the pairs of opposite sides of the quadrilateral are parallel, ABCD is a parallelogram.
Hence proved.
A quadrilateral in geometry may be a four-sided polygon with four sides and four corners (vertices). The Latin words Quadri, a variation of 4, and latus, meaning "side," are the source of the name. In regard to other polygons, it's also known as a tetragon, from the Greek "tetra" for "four" and "gon" for "corner" or "angle" (e.g. pentagon). Since "gon" is an anagram for "angle," it's also known as a quadrilaterals or 4-angle.
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Michael wants to borrow $12000 for a car loan. Which option would allow him to pay the least amount of interest?
A. A 12-month loan with a 7.25% annual simple interest rate
B. A 18-month loan with a 3.50% annual simple interest rate
C. A 24month loan with a 3.75% annual simple interest rate
D. A 36-month loan with a 2.75% annual simple interest rate
Based on the interest rates available to Michael, the option that would allow him to pay the least interest is B. 18-month loan with a 3.50% annual simple interest rate
How much interest will Michael pay?The interest on the first option is:
= (7.25% x 12,000) x 12/12months in year
= $870
Interest on second loan:
= (3.5% x 12,000) x 18 / 12 months in year
= $630
Interest on third loan:
= (3.75% x 12,000) x 24/12 months in year
= $900
Interest on fourth loan:
= (2.75% x 12,000) x 36/12 months in year
= $990
In conclusion, the 18-month loan with a 3.50% annual simple interest rate gives the lowest rate.
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Find the eighth term of each sequence. 1/2, 1/4, 1/8, 1/16, 1/32, ............
The eighth term of the given sequence 1/2, 1/4, 1/8, 1/16, 1/32 will be 1/256.
According to the give question.
We have a sequence 1/2, 1/4, 1/8, 1/6, 1/32
Since, the first term of the given sequence is 1/2.
The second term of the given sequence is 1/4.
The third term of the given sequence is 1/8.
Here, we can see that the numerator of each term is same i.e. 1. But the denominator is changing by power or 2. For the first term it is 2^1, for the second term it is 2^2, for the third term it is 2^3 and so on.
Therefore, the gneral formula for finding the nth term of the given sequence is given by
[tex]T_{n} = \frac{1}{2^{n} }[/tex]
So, the eighth term of the given sequence is 1/2^8 = 1/256.
Hence, the eighth term of the given sequence 1/2, 1/4, 1/8, 1/16, 1/32 will be 1/256.
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Suppose y varies directly with x , and y-15 when x-3 . What is y when x=12 ?
If y varies directly with x , and y-15 when x-3, y is 60 when x is equal to 12.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
y = kx (Where k is the constant)
Here, we have given
15 = k3
k = 15/3
= 5
So, y = 5x
When x = 12,
y = 5(12)
= 60
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Correct question
Suppose y varies directly with x, and y = 15 when x = 3. What is y when x = 12?
Help please
10 points
Answer: A number is divisible by 3 if the sum of the digits is divisible by 3.
If the last two digits of a number are divisible by 4, the whole number is. For example, in 1,012, 12 is divisible by 4.
A large number is divisible by 8 if the last three digits are also divisible by 8 or are 000.
Three polynomials are factor below but some coefficients and constants are missing all of the missing values of a,b,c, and d are intergers
1. The coefficients of the factored polynomial x² - 8x + 15 are
a = 1,b = -5,c = 1 andd = -32. The coefficients of the factored polynomial 2x³ - 8x² + 24x are
a = 1, b = -2, c = 1 and d = 63. The coefficients of the factored polynomial 6x² + 14x + 4 are
a = 2, b = -4, c = 3 and d = 1How to factor the polynomials?1. How to factor the polynomial x² - 8x + 15Sincw we want to factor the polynomial x² - 8x + 15 in the form (ax + b)(cx + d), we have that
x² - 8x + 15 = x² - 3x - 5x + 15
= x(x - 3) - 5(x - 3)
= (x - 5)(x - 3)
comparing (x - 5)(x - 3) with (ax + b)(cx + d), we see that the coefficients of the polynomial are
a = 1, b = -5, c = 1 and d = -32. How to factor the polynomial 2x³ - 8x² + 24xSincw we want to factor the polynomial 2x³ - 8x² + 24x in the form 2x(ax + b)(cx + d), we have that
2x³ - 8x² - 24x = 2x(x² - 4x - 12)
Factorizing the expression inthe bracket, we have
= 2x(x² - 2x + 6x - 12)
= 2x[x(x - 2) + 6(x - 2)
= 2x(x - 2)(x + 6)
comparing 2x(x - 2)(x + 6) with 2x(ax + b)(cx + d), we see that the coefficients of the polynomial are
a = 1, b = -2, c = 1 and d = 63. How to factor the polynomial 6x² + 14x + 4Sincw we want to factor the polynomial 6x² + 14x + 4 in the form (ax + b)(cx + d), we have that
6x² + 14x + 4 = 6x² + 2x + 12x + 4
= 2x(3x + 1) - 4(3x + 1)
= (2x - 4)(3x + 1)
comparing (2x - 4)(3x + 1) with (ax + b)(cx + d), we see that the coefficients of the polynomial are
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Prove the following.
If VZ ≅ VY and WY ≅ XZ , then VW ≅ VX .
The expression of the segment as the sum of the parts, gives VW = VX
How can the segment parts be used to prove that VW = VX?The given parameters are;
VZ = VY, WY = XZ, then VW = VX
From the given drawing obtained from a similar question, we have;
VZ = VW + WY (Segment Addition Postulate)
VY = VX + XZ, by segment addition
Therefore;
By substitution property, we have;
VW + WY = VX + XZ
Which gives;
VW + WY = VX + WY (substitution)
VW + WY - WY = VX + WY - WY
VW = VX by subtraction property
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help me....................................................................................................,,....
Answer:
f. 4+3=7
g. 23+8+4=35
h. 53+3+28=84
i. 11+17+92=120
j. 24+8+3=35
Step-by-step explanation:
Answer:
F = 4 + 4 = 8
G = 23 + 8 + 4 = 35
H = 53 + 3 + 27 = 83
I = 11 + 17 + 93 = 121
J = 24 + 8 + 3 = 35
Step-by-step explanation:
Henry had a piece of rope that was 23 1/2 inches long. Henry cut the rope into two pieces so that one pieces was 8 1/4 inches long. what was the length of the other piece of rope(also hello again! :)
Answer:
15 1/4 inches
Step-by-step explanation:
Length of the other piece
= 23 1/2 - 8 1/4
= 47/2 - 33/4
= 94/4 - 33/4
= 61/4
= 15 1/4 inches.
Write an explicit and a recursive formula for each sequence. 0, 1/8, 1/4, 3/8 . . . . . .
an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?
See the pattern
1/8-0 =1/8
1/4-1/8 = 1/8
3/8-1/4 = 1/8
the explicit and a recursive formula for each sequence is an=a1+d(n−1).
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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Polygon B C D E ≅ polygon R S T U . Find each value.
To ensure that sailboat races are fair, the boats and their sails are required to be the same size and shape.
c. Name six pairs of congruent angles.
Six pairs of congruent angles are:
∠B≅∠R∠C≅∠S∠D≅∠T∠E≅∠U∠CBD≅∠SRT∠EDB≅∠UTRWhat is a Polygon?A polygon is a plane figure described by a fixed amount of straight-line segments connected to form a closed polygonal chain in geometry. A polygon is defined as a bounded plane region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.To name six pairs of congruent angles:
Given: BCDE ≅ RSTU
Then,
∠B≅∠R∠C≅∠S∠D≅∠T∠E≅∠UNow, connect diagonals BD and RT.
So,
∠CBD≅∠SRT∠EDB≅∠UTRTherefore, six pairs of congruent angles are:
∠B≅∠R∠C≅∠S∠D≅∠T∠E≅∠U∠CBD≅∠SRT∠EDB≅∠UTRKnow more about Polygons here:
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Compare √180 and 102/8 using <, >, or =.
HELP ASAP
Answer:
√180 > 102/8
Step-by-step explanation:
√180 = 13.416407865
102/8 = 12.75
Answer:
Yes
Step-by-step explanation:
Because 180 is greater than 102
_____
8
Compare the two numbers. Use > or < .
√75, 9
As the value of Square root √75 is equals to 8.66, and the number 9 is larger than the number 8.66.
What exactly is a square root?The square root of a number x is a number y whose square (the result of multiplying the number by itself, or y y), equals x in mathematics.The term "radicand" refers to the expression (or quantity) whose square root is being considered.The term or number under the radical sign in this instance is referred to as the radicand, and it is 9.Square roots of negative integers can be discussed in the context of complex numbers.In any circumstance where the idea of an object's "square" is established, square roots can be considered more generally.These include square matrices and function spaces, among other mathematical constructs.The value of Square root √75 is equals to 8.66, and the number 9 is larger than the number 8.66.
So, √75 < 9
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f(x)=x²-3x + 20
Find f(5)
[tex]f(x)=x^2-3x+20\\\\f(5)=(5)^2-3(5)+20\\\\f(5) = 25-15+20\\\\f(5)=\boxed{30}[/tex]
[ Brainliest ]
Apply it! The measure of each central angle of a regular 40-sided polygon is ___ degrees.
Answer:
9 degrees
Step-by-step explanation:
Cindy is deciding between a striped red-and-purple lunch box and a polka-dotted blue lunch box to buy for school. Each lunch box is shaped like a rectangular prism with a volume of 300 cubic inches. The red-and-purple lunch box is 7.5 inches wide and 4 inches tall. The blue lunch box is 8 inches wide and 3 inches tall.
How much longer is the blue lunch box than the red-and-purple lunch box?
============================================
Explanation:
x = length of the red and purple lunch box
y = length of the blue lunch box
volume = length*width*height
The volume expression for the red and purple lunch box is x*7.5*4 = 30x
Set this equal to the stated volume 300 cubic inches, and solve for x.
30x = 300
x = 300/30
x = 10
The red and purple lunch box has length of 10 inches.
-----------------
The blue lunch box has volume of
length*width*height = y*8*3 = 24y
Set this equal to 300 and solve for y
24y = 300
y = 300/24
y = 12.5
The blue lunch box has length of 12.5 inches
Therefore the blue lunch box is longer and is longer by 12.5-10 = 2.5 inches.
line 1: 3x+2y=6 line 2: y= -3/2x+5 is it parallel, perpendicular, or neither, show evidence
the two lines have the same slope and different y-intercept, which means that the lines are parallel.
The lines are parallel, perpendicular, or neither?
Two linear equations:
y = a*x + b
y = c*x + d
Are parallel only if both have the same slope, which means that c = d, and the y-intercepts are different.
And are perpendicular if the slope of one of the lines is equal to the opposite of the inverse of the other slope, so:
a = -1/c
Now, our linear equations are:
3x + 2y = 6
y = (-3/2)*x + 5
We can write both of these in the slope intercept form:
3x + 2y = 6
2y = 6 - 3x
y = (6 - 3x)/2 = 3 - (3/2)*x
y = -(3/2)*x + 3
So the two lines have the same slope and different y-intercept, which means that the lines are parallel.
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raise the difference of r and s to the 9th power
Answer:
(r-s)⁹
Step-by-step explanation:
The difference means to subtract, so we have r-s.
Raising this to the 9th power gives (r-s)⁹.
Determine whether set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 13,15,16
Given set of numbers 13, 15, 16 represent an acute triangle.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
Since the sum of the lengths of any two sides is greater than that of the third side, the set of numbers are the measures of a triangle.
Now we find the type of triangle.
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
The sum of the squares of the two smaller sides is,
= 13² + 15²
= 169 + 225
= 394
And 16² = 256
Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.
Therefore, given set of numbers 13, 15, 16 represents an acute triangle.
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Determine whether each sequence is geometric. If so, find the common ratio. 10,15,22.5,33.75, . . . . .
The given sequence is geometric, with common ratio = 1.5
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 10, 15, 22.5, 33.75,....
Here, 15/10 = 22.5/15 = 33.75/22.5 = 1.5
Since the given sequence follows the required condition for a sequence to be geometric, it is the one.
Hence, The given sequence is geometric, with common ratio = 1.5
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Sue is fishing. she catches a bass weighing 5_ 1/4 lb. then she catches three more weighing 3_ 1/2 lb, 1_3/4 lb, and 2 lb. she releases the smallest fish. what is the total weight of the fish sue keeps?
Answer:
10 3/4 lb
Step-by-step explanation:
she releases the 1 3/4 lb fish and keeps the 5 1/4lb, 3 1/2lb, and 2lb
The total weight of these three fish are
5 1/4lb
+
3 1/2lb
+
2lb
which equals 10 3/4lb
F(x)=x^2-6x , what value of x is f(x) at its minimium
The function value at the minimum is -9
How to determine the function value at the minimum?The function is given as:
f(x) = x^2 - 6x
Differentiate the function
So, we have
f'(x) = 2x - 6
Set the function to 0
So, we have
2x - 6 = 0
This gives
2x = 6
Divide by 2
x = 3
Substitute x = 3 in f(x) = x^2 - 6x
f(3) = 3^2 - 6(3)
Evaluate
f(3) = -9
Hence, the function value at the minimum is -9
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Janet works for the road commission as a flag holder. She has a gross weekly income of $570. How
much is deducted from her paychecks Annually for Social Security? How much Annually for Medicare?
Using proportions, it is found that the deducted amounts each year are given as follows:
Social Security: $1,837.68.Medicare: $429.78.What is the missing information?The tax rates are missing, and they are given as follows:
Social Security: 6.20% = 0.0620.Medicare: 1.45% = 0.0145.What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
Considering that a year has 52 weeks, her yearly salary is given as follows:
52 x 570 = $29,640.
Considering the tax rate, the deducted amount for Social Security is given by:
0.0620 x 29640 = $1,837.68.
Considering the tax rate, the deducted amount for Medicare is given by:
0.0145 x 29640 = $429.78.
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Describe a pair of events that are mutually exclusive and a pair of events that are not mutually exclusive.
The two events are mutually exclusive if they cannot occur at the same time. A triangle is equiangular if it is equilateral. Never can one preclude the other. The two events are mutually exclusive if they cannot occur at the same time.
What pairs of occurrences can never coexist?
Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously. A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.What are some examples of mutually exclusive events?
Several instances of occurrences that can never occur simultaneously include: The outcomes of receiving head or tail while flipping a coin are mutually exclusive.Learn more about probability
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PQ= 6x+25 and QR=16-3z
Solve each formula for the indicated variable. V = lwh , for w
The solution of the given formula V = lwh for the variable w is V/lh.
According to the given question.
We have a formula.
V = lwh
Since, we have to solve this given formula V = lwh for the variable w.
Which means we have to write separate variable w to one side from the other variables which are in the given formua V = lwh .
Thereofre, the solution of the given formula V = lwh for the variable w is given by
V = lwh
⇒ V/l = wh (dividing both the sides by l)
⇒ V/lh = w (dividing both the side by h)
or w = V/lh
Hence, the solution of the given formula V = lwh for the variable w is V/lh.
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For each function, find the y -intercept
y = -(2/3)(x-9)².
Answer:
(0, -54)
Step-by-step explanation:
The y-intercept is when x=0.
[tex]y=-(2/3)(0-9)^2 \\ \\ =-(2/3)(81) \\ \\ =-54[/tex]
Find the slope of the line through each pair of points. (0,0) and (5,-3)
The slope of the line passing through the pair of points, (0 , 0) and (5 , -3), is -3/5.
The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. The formula for solving the slope is:
m = (y2 - y1)/(x2 - x1)
where m is the slope
x1 and y1 are the coordinates of one point
x2 and y2 are the coordinates of the 2nd point
Given two points in the line, (0 , 0) and (5 , -3), plug in the values to the formula for the slope.
m = (y2 - y1)/(x2 - x1)
m = (-3 - 0)/(5 - 0)
m = -3/5
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Chemistry The time required for a certain chemical reaction is related to the amount of catalyst present during the reaction. The domain of the relation is the number of grains of catalyst, and the range is the number of seconds required for a fixed amount of the chemical to react. The table shows the data from several reactions.
b. If the domain and range were interchanged, would the relation be a function? Explain.
x= 6, y = 3 are the domain and range were interchanged, would the relation be a function.
What is domain ?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.If the terms in range and domain were interchanged, one term 6 of domain relates with two different values of range,
x = 6, y = 2.5
x= 6, y = 3
Since, a term of domain can't have two different values in range,
Therefore, interchanged relation will not be a function.
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Jorge is training for a 20 -mile race. Jorge runs 7 miles on Monday, Tuesday, and Friday, and 12 miles on Wednesday and Saturday. After 6 weeks of training, Jorge will have run the equivalent of how many races?
After 6 weeks of training, Jorge will have run the equivalent of 13.5 races.
What does the term equivalent mean?When two quantities, expressions, or numbers have the same value, they are said to be equal. An equivalent quantity can be expressed in a variety of ways, such as by a bar or an equivalent symbol. Because they can relate to it in their everyday lives, children find this topic to be particularly engaging for a variety of reasons.
A common or logical equivalency between several values or quantities can also be referred to as the equivalent. Equivalence is comparable to equality but distinct from it.
1 race = 20 miles
Lets assume he doesn't runs on Sunday and Thursday, thus
Miles he runs a week = (Monday + Tuesday + Friday) + ( Wednesday +Saturday)
1 week = (7 + 7 + 7) + (12 + 12)
= 45 miles
If he runs for 6 weeks then
6 week's run = 6 × 45
= 270 miles
If 1 race is of 20 miles then in 6 weeks he would have ran
= 270/20
= 13.5 races
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When she came to work the next day, she was delighted because four hundred sixteen hundred, nine hundred forty-three containers had been delivered. How many things (Problem 3) would fill them all?
Answer:
When she came to work the next day, she was delighted because four hundred sixteen hundred, nine hundred forty-three containers had been delivered. How many things (Problem 3) would fill them all?
https://www.louisianabelieves.com/docs/default-source/assessment/grade-7-answer-key.pdf
Step-by-step explanation:
