Answers
Therefore, the angle V in parallelogram WXUV is 100 degrees. Therefore, the angle L in parallelogram LMJK is 98 degrees. Therefore, the length of side SP in parallelogram SRQP is 26 units. Therefore, the length of side FC in parallelogram FCDE is 12.6 units.
What is parallelogram?A parallelogram is a quadrilateral (a four-sided polygon) with two pairs of parallel sides. In other words, the opposite sides of a parallelogram are parallel and congruent (equal in length). The properties of a parallelogram include:
Opposite sides are parallel and congruent
Opposite angles are congruent (equal in measure)
Consecutive angles are supplementary (add up to 180 degrees)
Diagonals bisect each other (divide each other into two equal parts)
Some common examples of parallelograms include rectangles, rhombuses, and squares. A rectangle is a parallelogram with four right angles, a rhombus is a parallelogram with four congruent sides, and a square is a parallelogram with four congruent sides and four right angles.
Here,
1. In a parallelogram, opposite angles are equal. Therefore, if angle U is 80 degrees, then angle W must also be 80 degrees.
We know that the sum of the angles in a quadrilateral is 360 degrees, so the sum of the angles at vertices V and U is 360 - 2*80 = 200 degrees.
Since opposite angles in a parallelogram are equal, the angle at vertex V must also be 100 degrees.
2. In a parallelogram, opposite angles are equal. Therefore, if angle J is 98 degrees, then angle L must also be 98 degrees.
We know that the sum of the angles in a quadrilateral is 360 degrees, so the sum of the angles at vertices J and K is 360 - 2*98 = 164 degrees.
Since opposite angles in a parallelogram are equal, the angle at vertex M must also be 98 degrees.
3. In a parallelogram, opposite sides are equal in length. Therefore, if side RQ is 26 units, then side SP must also be 26 units.
This is because SRQP is a parallelogram, so side SR is equal in length to side PQ, and side RQ is equal in length to side SP.
4. In a parallelogram, opposite sides are equal in length. Therefore, if side DE is 12.6 units, then side FC must also be 12.6 units.
This is because FCDE is a parallelogram, so side FC is equal in length to side DE, and side DE is equal in length to side FC.
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Related Questions
Use the system of inequalities:
y ≥ 0, x ≥ 0, y ≤ -2x + 4
and find the minimum value of f(x,y) = 3x + y
for the feasible region.
a. 6
b. 4
c. 2
d. 0
Answers
Using the system of inequalities y ≥ 0, x ≥ 0, y ≤ -2x + 4 the minimum value of f(x,y) = 3x + y for the feasible region is d) 0.
We need to find the minimum value of the function
f(x,y) = 3x + y
we can use Lagrange multipliers method defining
F(x,y) = f(x,y) - λx g(x,y) , where g(x,y) = x²+36 x y² - 1, such that
Fx(x,y) = fx(x,y) - λx gx(x,y) = 0
Fy(x,y) = fy(x,y) - λx gy(x,y) = 0
g(x,y)=0
where the sub-indices x and y represent the partial derivatives with respect to x and y, then
fx(x,y) - λx gx(x,y) = 3 - λx(2x) = 0 → x =3/(2xλ)
fy(x,y) - λx gy(x,y) = 1 - λx(36x2xy) = 0 → y =1/(72xλ)
x²+36xy² - 1 = 0 → [3/(2xλ)]²+36*[1/(72xλ)]² - 1 = 0
therefore, Using the system of inequalities y ≥ 0, x ≥ 0, y ≤ -2x + 4 the minimum value of f(x,y) = 3x + y for the feasible region is d) 0.
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1000+1000^3 I NEED HELP PLEASE
Answers
To solve this expression, we can use the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (performed left to right), and Addition and Subtraction (performed left to right).
Following this order, we first need to evaluate the exponent, which gives:
1000^3 = 1,000,000,000
Then, we can substitute this value back into the expression:
1000 + 1000^3 = 1000 + 1,000,000,000 = 1,000,000,000 + 1000 = 1,000,001,000
Therefore, 1000 + 1000^3 equals 1,000,001,000.
Answer: 8000000000
Step-by-step explanation:
In analyzing hits by certain bombs in a war, an area was partitioned into 573 regions, each with an area of 0.55 km2. A total of 515 bombs hit the combined area of 573 regions. Assume that we want to find the probability that a randomly selected region had exactly three hits. In applying the Poisson probability distribution formula, P(x)=
μx•e−μ
x!, identify the values of μ, x, and e. Also, briefly describe what each of those symbols represents.
Answers
The probability that a randomly selected region had exactly three hits is approximately 0.139.
How did we get this value?In this problem, we can use the Poisson probability distribution formula to find the probability of a randomly selected region having exactly three hits.
The Poisson probability distribution formula is:
P(x) = (e^(-μ) * μ^x) / x!
Where:
P(x) is the probability of x occurrences of an event.
μ is the mean number of occurrences of the event in a given interval.
x is the number of occurrences of the event.
e is the mathematical constant e, approximately equal to 2.71828.
To apply this formula to the problem at hand, we need to determine the values of μ and x.
Since there were a total of 515 bombs that hit the 573 regions, we can calculate the average number of bombs that hit each region:
μ = total number of bombs / number of regions
μ = 515 bombs / 573 regions
μ = 0.8993
Therefore, the mean number of hits per region is 0.8993.
To find the probability that a randomly selected region had exactly three hits, we can plug in x = 3 into the Poisson probability distribution formula:
P(3) = (e^(-0.8993) * (0.8993)^3) / 3!
P(3) ≈ 0.139
Therefore, the probability that a randomly selected region had exactly three hits is approximately 0.139.
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Which could be the function graphed below?
a. f(x)=√x-2
b. f(x)=√x-3+1
c. f(x)=√2x+4
d. f(x)=√x+1+8
Answers
Answer:A
Step-by-step explanation:
It would have the greatest chance to be the line on the graph
jamilla is building a square sandbox with sides 8 1/2 feet long. she wants to put sand 2 1/2 feet deep in the box. how much sand should jamilla order?
Answers
The amount of sand Jamilla have to order to fill the square sandbox with sides 8 1/2 feet long and 2 1/2 feet deep is 180.625 cubic feet of sand.
To calculate the amount of sand that Jamilla should order, you need to calculate the volume of the sandbox. Given that Jamilla is building a square sandbox with sides 8 1/2 feet long and wants to put sand 2 1/2 feet deep in the box. Thus, the volume of the sandbox is calculated as follows:
Volume of the sandbox = Length * Width * Depth
Volume of the sandbox = (8 1/2 feet) * (8 1/2 feet) * (2 1/2 feet)
Converting each mixed fraction to its corresponding improper fraction, we get:
8 1/2 feet = 17/2 feet
2 1/2 feet = 5/2 feet
On simplifying the above equation we get:
Volume of the sandbox = (17/2 feet)² * (5/2 feet)
Volume of the sandbox = (289/4) * (5/2) cubic feet
Volume of the sandbox = 1445/8 cubic feet
Volume of the sandbox = 180.625 cubic feet
Therefore, Jamilla should order 180.625 cubic feet of sand.
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