The opposite angles of a parallelogram are congruent this can be proved by the fact that;
Opposite sides are congruent Corresponding parts of congruent triangles are congruentTo prove opposite angles in a parallelogram are congruent, it's necessary to recognize that opposite sides are congruent and use the property that corresponding parts of congruent triangles are congruent.
Explanation:To prove that the opposite angles of a parallelogram are congruent, it's not necessary that opposite sides be perpendicular. Instead, let's consider the properties that are relevant to this proof:
Opposite sides are congruent (C)Corresponding parts of congruent triangles are congruent (D)In this case:
Option A is not relevant because a parallelogram does not require opposite sides to be perpendicular; that is a characteristic of a rectangle.Option B refers to similar triangles, which is not necessary for proving the opposite angles are congruent in parallelograms. Similar triangles have proportional sides and identical angles, which is not the focus here.Option C is a defining property of parallelograms and is necessary to help prove that opposite angles are congruent.Option D can be used in the proof if one demonstrates that two triangles within the parallelogram are congruent, therefore their corresponding angles must be congruent; this includes the opposite angles of the parallelogram.The proper proof would rely on establishing congruent triangles within the parallelogram and then using the property that corresponding parts of congruent triangles are congruent to show that the opposite angles are congruent.
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A 2.2 GB game is being downloaded on your laptop. When you have downloaded half a gigabyte, you notice that your computer has been downloading at the rate of .01GB per minute. (A) Write an inequality that represents at least how many minutes it will take to download the game (b) Your computed only has two hours of battery life, will it be enough to download the game?
The game which is 2.2 GB will need 170 minutes to download at a rate of 0.01 GB per minute. But the computer has only 120 minutes of battery life which is insufficient.
Explanation:The total size of the game is 2.2 GB. The part that is already downloaded is 0.5 GB, so the remaining size of the game to be downloaded is 2.2 GB - 0.5 GB = 1.7 GB. Now, since the downloading speed is 0.01 GB/minute, we extrapolate the remaining time as (1.7 GB) / (0.01 GB/min) which equals 170 minutes.
(a) So, the inequality representing at least how many minutes it will take to download the rest of the game is x ≥ 170, where x is the required time in minutes.
(b) Two hours of battery life is equivalent to 2*60 = 120 minutes. Since 170 minutes is required to download the game and the available battery life is only 120 minutes, the battery will not be enough to download the game.
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use multiples to write two fractions equivalent to 7/9
Answer:
[tex]\displaystyle\frac{35}{45}, \frac{49}{63}[/tex] are two equivalent fractions of the given fraction.
Step-by-step explanation:
We are given the following information in the question:
We are given the fraction:
[tex]\displaystyle\frac{7}{9}[/tex]
We have to find an equivalent fraction. This could be done by multiplying both the numerator and the denominator by the same number.
Equivalent fraction:
Multiplying both numerator and denominator by 5
[tex]\displaystyle\frac{7\times 5}{9\times 5} = \frac{35}{45}[/tex]
Multiplying both numerator and denominator by 7
[tex]\displaystyle\frac{7\times 7}{9\times 7} = \frac{49}{63}[/tex]
Hence, [tex]\displaystyle\frac{35}{45}, \frac{49}{63}[/tex] are two equivalent fractions of the given fraction.
You plan to take $450 u.s. on a trip to south africa. how many rands is this if one u.s. dollar equals 3.70 rands?
Which of the following inequalities is equivalent to -6 > x?
Express 275% as a decimal number
The conversion of a percentage to a decimal number, divide the percentage by 100 it means that 275% represents 2.75 times the original quantity.
To convert a percentage to a decimal number,
divide the percentage value by 100.
Here's the step-by-step explanation for converting 275% to a decimal:
Take the percentage value (275%) and divide it by 100.
275 ÷ 100 = 2.75
So, 275% as a decimal is 2.75.
It means that 275% is equal to 2.75 times the whole quantity.
For example, if you have 100 dollars and increase it by 275%, you will end up with 100 + (2.75 × 100) = 375 dollars.
Therefore, the 275% as a decimal number is equal to 2.75.
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Bethany's family can eat (13h + 6) hotdogs. Clark's family can eat (10h + 3) hotdogs. Which expression shows the difference between the number of hotdogs Bethany's family can eat and the number of hot dogs Clark's family can eat?
A.3h - 9
B.3h + 3
C.-3h + 9
D.-3h + 3
Of 50 students surveyed, 19 said they had soda for breakfast. write a portion in fraction, decimal, percent
The Tigers lost 15% of the 60 games that they played this season. How many games did they win?
Determine the x- and y-intercepts of the graph of y = 1/4x - 2
Then plot the intercepts to the graph the equation
Answer:
The y-intecept is [tex](0,-2)[/tex], and the x-intercept is [tex](8,0)[/tex].
Step-by-step explanation:
The interception points with the axes can be foun by making zero one variable.
If you wanna find y-interception, we must make x = 0.
If you wann find x-interception, we must make y = 0.
The given function is
[tex]y=\frac{1}{4}x-2[/tex]
For [tex]x=0[/tex], we have
[tex]y=\frac{1}{4}(0)-2\\y=-2[/tex]
For [tex]y=0[/tex], we have
[tex]y=\frac{1}{4}x-2\\0=\frac{1}{4}x-2\\2=\frac{1}{4}x\\x=8[/tex]
Therefore, the y-intecept is [tex](0,-2)[/tex], and the x-intercept is [tex](8,0)[/tex].
The image attached show this.
What is the minimum value for p=x-2y over the feasibility region defined by the constraints shown above?
x <= 8
y>= 0
y<= 3x+2
y<= -x+10
a. 8
b. -2
c. -16
d. -14
Jason draws a line in the sand at the beach. The line is 78 ft long. He wants to divide the line into sections that are each 1/8 ft long.
How many sections will the line be divided into?
Enter your answer in the box.
Consider the statement 4-3+5=-6+8+4 this mathematically correct sentence is the sentence true or false? Explain how you know
Suppose you traveled 84 in 1.5h moving at the same speed, how many mi would you cover in 3 1/4? & can someone answer number 45 also?
A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman for her to keep. Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose. Are these events independent or dependent?
A) Dependent because the women both received a pink rose.
B) Independent because the women both received a pink rose.
C) Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.
D) Independent because when the first flower is taken, it does not change the ratio of the types of flowers in the vase.
Answer:
Option C - Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.
Step-by-step explanation:
Given : A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations.
One flower is chosen at random and given to a woman for her to keep.
Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose.
To find : Are these events independent or dependent?
Solution :
According to the statements,
The probability that the second woman receives a pink rose is dependent upon what the first woman receives.
Total flowers = 5+4+6=15
If the first woman does not receive a pink rose,
Then, the probability of the second woman receiving one is [tex]\frac{4}{15}[/tex]
If the first woman does receive a pink rose
Then, the probability of the second woman receiving one is [tex]\frac{3}{15}=\frac{1}{5}[/tex]
Therefore, Option C is correct.
Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.
4nm - 4m = 8. Solve for m
Find the value of x so the rectangles have the same area
Using formula:
Area of rectangles = width [tex]\bold{\times}[/tex] length.Using the first image to calculate the area:
[tex]\to \bold{ x\times 12 = 12x }[/tex]
Using the second image to calculate the area:
[tex]\to \bold{16\times (x-2) = 16x -32 }[/tex]
equalling both the area:
[tex]\to \bold{12x = 16x -32}\\\\\to \bold{32 = 16x -12x}\\\\\to \bold{32 = 4x }\\\\\to \bold{4x=32 }\\\\\to \bold{x=\frac{32}{4}}\\\\\to \bold{x=8}\\\\[/tex]
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100 envelopes cost $0.70 how much would it be for 250
If 100 envelopes cost $0.70 then it would cost $1.75 for 250 envelopes.
If 100 envelopes cost $0.70, we can set up a proportion to determine the cost of 250 envelopes:
100 envelopes / $0.70 = 250 envelopes / x
Cross-multiplying:
100 × x = 250 × $0.70
Simplifying:
100x = 175
Dividing both sides by 100:
x = 175 / 100
x = $1.75
Therefore, it would cost $1.75 for 250 envelopes.
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A cab ride from the airport to your home costs $19.50. If you want to tip the cab driver close to 10 percent of the fare, how much should you tip?
$1
$2
$3
The tip for the cab is close to 10 percent is around $2.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A cab ride from the airport to your home costs $19.50.
Now, The tip given is 10% of the fare so,
= (10/100)×19.50.
= 0.1×19.50.
= 1.95.
So, The exact tip would be $1.95 which is approximately $2.
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Can someone please help me
Factor completely
9-6a-24a^2
Answer:
3(3+4a)(1-2a)
Step-by-step explanation:
If m∠APW = 20°, then the measure of ∠WPZ is
20
70
90
160
Answer:
It is 70
Step-by-step explanation:
Both angles have to add up to 90 and I did the lesson ight
Which expression is undefined
A. -8÷(-8)
B. -8÷8
C. 0÷8
D. 8÷0
lisa wants to make at least $300.00 selling candy. Hard candy cost $3.00 per piece and chocolates cost cost $6.00 per piece. How many pieces of each type of candy could Lisa sell in order to make at least $300.00
Lisa can either sell 100 hard candies or 50 chocolate to make $300.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Lisa wants to make at least $300.00 selling candy. Hard candy cost $3.00 per piece and chocolates cost $6.00 per piece.
Establishing the equation for this problem.
Let,
Hard candy = x
Chocolate = y
Therefore,
3x+6y=300
To find y, let x=0
3(0)+6y =300
6y = 300
y = 50
Similarly,
To find x, put y=0
3x+6(0)=300
3x=300
x=100
Hence, Lisa can sell 100 hard candies or 50 chocolate to make $300.
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How many different sums of money can be formed from penny and half a dollar?
Divide: 1,485 ÷ 0.09
If events X and Y are independent, what must be true? Check all that apply.
3. P(Y | X) = P(Y) and 6. P(X | Y) = P(X)
What is the probability that it lands on heads at least 5 times?
Suppose that hot dogs come in packs of 9 and buns come in packs of 12 . kareem bought the same number of hot dogs as buns. it was the least number of each for which this was possible.
36 is least number of each for which this was possible.
what is Least common multiple?The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory.
4 is the LCM of 2 and 4. To get the smallest multiple that is exactly divisible by 2 and 4, i.e. 4, we must first determine the multiples of 2 and 4 (multiples of 2 = 2, 4, 6, 8; multiples of 4 = 4, 8, 12, 16).
Given:
Hot dogs cam in pack of 9.
Buns came in pack of 12.
Now, to find least number of each bought the same number of hot dogs as buns.
So, LCM(9, 12)
9= 3x 3
12= 2 x2 x 3
Thus, LCM(9, 12) = 3 x 3 x 2 x 2 = 36
Hence, 36 is least number of each for which this was possible.
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Suppose a fair coin is flipped and a fair six-sided die is rolled. list the members of the event "the die does not land on 5"
What is 0.72 written as a simplified fraction? (1 point) seventy-two over one hundred one hundred over seventy-two thirty-six over fifty eighteen over twenty-five 4. ms. johnson's class is having a pizza party. if there are 14 students and 7 pizzas cut into 8 slices, what answer choice represents the fraction of one pizza that each student receives? (1 point) one-third one-fourth one-half one-eighth?
what are two decimals that have square root between 3 and 4