To compute the area of a parallelogram determined by two vectors U = (4, -1) and V = (-6, -2), we can use the formula that states the area of a parallelogram is equal to the magnitude of the cross product of the two vectors. Therefore, the area of the parallelogram determined by U = (4, -1) and V = (-6, -2) is 28 square units.
The formula to compute the area of a parallelogram determined by two vectors U and V is given by:
Area = |U x V|
To calculate the cross product U x V, we can use the following determinant:
| i j k |
| 4 -1 0 |
|-6 -2 0 |
Expanding the determinant, we get:
i * (0 * -2 - 0 * -2) - j * (4 * -2 - 0 * -6) + k * (4 * -2 - (-1) * -6)
= -12i + 24j + 8k
Taking the magnitude of the cross product, we have:
|U x V| = √((-12)^2 + 24^2 + 8^2) = √(144 + 576 + 64) = √784 = 28
Therefore, the area of the parallelogram determined by U = (4, -1) and V = (-6, -2) is 28 square units.
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If JKLM is a rectangle, solve for x.
Kora and Wallace planted a garden bed the size of the red square. How big is their garden bed? (Finding the area)
Answer: no sol
Step-by-step explanation:
bro there is no pic to do so im just going to say...
Legs are 5ft and 25ft what is the hypotenuse round to the nearest tenth
Answer:
15ft
Step-by-step explanation:
Which of the following best describes the vertical cross-section of the cylinder ?
A.
cone
B.
rectangle
C.
triangle
D.
circle
The shape that best describes the vertical cross-section of the cylinder is given by: Option B: Rectangle.
What is a vertical cross section?When you slice a given object vertically (perpendicular to the ground level), then the sliced surface is called vertical cross section.
For a cylinder, usually it sits on its base and we take a right circular cylinder. When we slice it vertically, we obtain a rectangle, as shown in the figure attached below.
It can be proven that this shape is always going to be rectangular.
Thus, the shape that best describes the vertical cross-section of the cylinder is given by: Option B: Rectangle.
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How can this expression be written another way?
32k + 24
Factor using the distributive property and the greatest common factor to write an equivalent expression
Enter your answer by filling in the boxes
32k + 24 = __ (__)
Mr. Piper's plumbing needed
repairs. The plumber charged
$98 for parts plus $45 per hour
for labor. If the bill totaled $458,
how many hours of labor were
required?
Answer:
8 hours of labor at 45 dollars an hour, plus the 98 dollars for parts equal 458
Solve by completing the square.
x2 - 4x – 20 = 0
A. x = {-2±6√2}
B. x = {2+6√2}
C. x = {2+2√6}
D. x = {-2±2√6}
Show your work.
Step-by-step explanation:
Subtract
20
from both sides of the equation.
x
2
−
4
x
=
−
20
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
.
(
b
2
)
2
=
(
−
2
)
2
Add the term to each side of the equation.
x
2
−
4
x
+
(
−
2
)
2
=
−
20
+
(
−
2
)
2
Simplify the equation.
Tap for more steps...
x
2
−
4
x
+
4
=
−
16
Factor the perfect trinomial square into
(
x
−
2
)
2
.
(
x
−
2
)
2
=
−
16
Solve the equation for
x
.
Tap for more steps...
x
=
2
±
4
i
There are 244 seventh grade students. The number of students enrolled in P.E. Is 8 fewer than three times the number of students enrolled in health
Answer:
No. of students enrolled in Health = 63
No. of students enrolled in P.E. = 181
Step-by-step explanation:
Given,
Total students in grade seven = 244 students
A.T.Q.
Let the number of students enrolled in Health be x
so, The number of students enrolled in P.E. = 3x - 8
As we know,
x + (3x - 8) = 244
4x = 244 + 8
x = 252/4
x = 63
Thus, the number of students enrolled in Health = 63
The number of students enrolled in P.E. = 3x - 8
= 3 * 63 - 8
= 189 - 8
= 181 students
Find the value of $x$ .
A circle with center Q has four points L, M, N, and P lie on the circle. Diameter L N and chord M P intersect perpendicularly. The diameter divides the chord M P into two parts with measures 5 x minus 6 and 2 x plus 9.
Answer:
What
Step-by-step explanation:
I dont understand what you are asking
Please help me, it's due today. I'll give 86 points to someone who answers and writes the problem step by step.
A 14 -in. diameter pizza is cut into 6 equal sides. About how many square inches of pizza are on each slice? Round to the nearest square inch.
Answer:
here go the answer hope it help
Step-by-step explanation:
-12 x (1/3)? what is this equal to!
Answer:
-4
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
-12 times 1/3.
It's pretty much just -12x1, then divided by 3.
-12x1 is equal to -12.
Your equation is now simplified, making it easier to solve.
Your equation is: [tex]\frac{-12}{3}[/tex]
-12 divided by 3 is -4, because when a negative number is divided (or multiplied) by a positive number, the quotient (or product) is negative.
-12 x (1/3) = -12/3 = -4.
Plz help I’ll mark brainliest:$
(1) x = -2 y = -8
(2) x = -1 y = -4
(3) x = 0 y = 0
(4) x = 1 y = 4
(5) x = 2 y = 8
Those are the answers for what y is so now i think you have to plug it in to the right side of the chart
A neighborhood in Shiloh is building a treehouse. It has a rectangle floor of 6 ft by 4 ft. What is the area of the tree house floor?
Answer:
24
Step-by-step explanation:
Shiloh is building a tree house
It's measurement is 6ft by 4ft
Therefore the area can be calculated as follows
= 6×4
= 24
Hence the area of the rectangle is 24
#1 someone help me with this question pls ??
Answer:
58-51
why to have the speed of a cucumber you need a potato on a skateboard at 1000kmh, ok?
Answer: 4 I think
on each side it has 4
Just need the answer thank you
Answer:
The multiplicative rate of change is 3/4
Step-by-step explanation:
Here, we want to get the multiplicative rate of change
In this case, by dividing the succeeding term by the preceding term, we will get the multiplicative rate of change
mathematically, we have this as;
81/128 divided 27/32
= 81/128 * 32/27
= 3/4
Find the area of a circle if the diameter is l6 meters.
PLEASE EXPLAIN AND DO THE PROBLEM IN THE ANSWER!!!!
Answer:
Step-by-step explanation:
the formula for a circle is pi(r^2) where r is the radius. the diameter is 16 so 16/2 =8. substitute 8 for the radius to get pi(8^2). 8^2=64 so you have pi(64).
pi(64)= approximately 201.06
Hila found the data at the left that shows the number of ways that each sum can be obtained when rolling three dice. a) Determine the mean and the standard deviation. b) Draw a frequency polygon to show the data. c) Does the data have a normal distribution? Explain. Rolling 3 Dice Sum Frequency 3 1 4 3 5 0 6 6 10 7 15 8 21 9 25 10 27 11 27 12 25 13 21 14 15 15 10 16 6 17 3 18 1
a) The mean and standard deviation need to be determined for the given data on the number of ways each sum can be obtained when rolling three dice.
b) A frequency polygon can be drawn to represent the data.
c) Whether the data has a normal distribution or not needs to be determined, and an explanation is required.
a) Mean and Standard Deviation: The mean can be calculated by summing up the products of each value and its corresponding frequency, then dividing by the total frequency. The standard deviation can be calculated by finding the square root of the variance, where the variance is the sum of the squared differences between each value and the mean, divided by the total frequency.
b) Frequency Polygon: A frequency polygon can be plotted by taking the sum values on the x-axis and the corresponding frequencies on the y-axis. Points are plotted for each sum value, and then lines are drawn to connect these points to form the polygon.
c) Normal Distribution: To determine if the data follows a normal distribution, one can visually analyze the frequency polygon. If the polygon displays a symmetric, bell-shaped curve, it suggests a normal distribution. However, if the polygon is skewed or does not exhibit a bell shape, the data is unlikely to have a normal distribution.
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John flew a kite. He started flying the cat at 2:20 p.m. and ended at 3:14 p.m. How many minutes did John fly a kite?
A. 47 minutes
B. 50 minutes
C. 54 minutes
D. 55 minutes
Answer:
54 minutes
Step-by-step explanation:
3:14 = 3 × 60 = 180 + 14
= 194
2:20 = 2 × 60 = 120 + 20
= 140
194 - 140
= 54
it is 20 miles from the airport to the hotel. The driver says that there is 1/8 of the total distance left to travel. What distance has already been driven?
Answer:
2.5mi
Step-by-step explanation:
?/20 = 1/8
^ If you turn into a percentage you get 1/8 = 12.5%
so now the question is v
what is 12.5 percent of 20?
which is 2.5
I WOULD CHECK FIRST, NOT 100 PERCENT SURE
Let P(n) be the set of all partitions of the positive integer n. For all (a₁,..., ak), B = (B₁, ...) = P(n), define (a) Show that (P(n), ≤) is a partially ordered sets (b) Draw its Hasse diagram of (P(6),≤). Is (P(n), ) a lattice for all n?
The set of all partitions of a positive integer n, denoted as P(n), forms a partially ordered set (poset) under the relation of set inclusion (≤).
In part (a), we show that (P(n), ≤) satisfies the properties of a poset. In part (b), we draw the Hasse diagram for P(6) to illustrate the partial order. Whether (P(n), ≤) forms a lattice for all n depends on the specific values of n.
a) To show that (P(n), ≤) is a poset, we need to verify three properties:
Reflexivity: Every partition is included in itself, so for any partition A in P(n), A ≤ A.
Antisymmetry: If A ≤ B and B ≤ A, where A and B are partitions in P(n), then A = B.
Transitivity: If A ≤ B and B ≤ C, where A, B, and C are partitions in P(n), then A ≤ C.
These properties hold for the relation of set inclusion, thus establishing that (P(n), ≤) is a poset.
b) The Hasse diagram for P(6) represents the partial order of the partitions of 6. The partitions are depicted as nodes, with an upward-directed edge connecting A to B if A is included in B (A ≤ B). The diagram illustrates the hierarchy of partitions based on the inclusion relation.
Whether (P(n), ≤) forms a lattice for all n depends on whether it has both a least element (bottom element) and a greatest element (top element). For P(n), if n is greater than 1, there is no unique greatest element since there can be multiple ways to partition n. Therefore, (P(n), ≤) is not a lattice for all values of n.
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QUICK! WHOEVER GIVES CORRECT ANSWER GETS BRAINLIEST
I need help thank you
Answer:
A & C
Step-by-step explanation:
If you substitute the first coordinate (which is the x coordinate) for x in the function and set it equal to the y, options A and C should satisfy the function.
The cook at the Elmview School cafeteria made grilled chicken and fried chicken yesterday for lunch. He made 5 pieces of grilled chicken for every 2 pieces of fried chicken.
Pick the diagram that models the ratio in the story.
If the cook made 80 pieces of fried chicken, how many pieces of chicken did he make altogether?
The cook made 280 pieces of chicken altogether.
the diagram is like this :
Grilled chicken: [#####] [#####] [#####] [#####] [#####] ,
Fried chicken: [##] [##]
The ratio of grilled chicken to fried chicken is 5:2, which means for every 5 pieces of grilled chicken, the cook made 2 pieces of fried chicken.
To model this ratio, we can use a bar diagram with five sections for the grilled chicken and two sections for the fried chicken,
If the cook made 80 pieces of fried chicken, we can use this ratio to calculate the number of pieces of grilled chicken.
First, we need to find out how many sets of 5:2 there are in 80. We can do this by dividing 80 by 2 and then multiplying by 5:
80 ÷ 2 = 40
40 × 5 = 200
So the cook made 200 pieces of grilled chicken.
To find the total number of pieces of chicken, we just need to add the grilled and fried chicken together: 200 + 80 = 280 .
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Please awnser correctly! I will mark you as Brainliest!
A coach ordered 20 practice jerseys for her soccer team. Six of the jerseys she ordered arrived late. What decimal represents the fraction of jerseys that arrived late?
Answer: 0.3
Step-by-step explanation:
There are 20 practice jerseys in total.
Six of those 20 jerseys arrived late.
The fraction of jerseys that arrived late is therefore:
= 6 / 20 jerseys
Convert them to decimal form by dividing the numerator with the denominator:
= 6 ÷ 20
= 0.3
Here's a easy one
Not accepting links!
You have two unknown integers. Double the larger integer increased by triple the smaller integer is 46. Squaring the larger number and increasing it by four times itself gives the same result as multiplying the smaller number by 20 and adding 5. Use a system to solve for the integers by graphing
The two unknown integers can be found by graphing the given equations. The larger integer is 10, and the smaller integer is 8.
Let's represent the larger integer as 'x' and the smaller integer as 'y.' According to the given information, we have two equations:
Equation 1: 2x + 3y = 46
Equation 2: x^2 + 4x = 20y + 5
To solve this system of equations, we can graph both equations on the same coordinate plane. The point where the two graphs intersect will give us the values of 'x' and 'y' that satisfy both equations simultaneously.
For equation 1, we rearrange it to y = (46 - 2x)/3. Plotting this equation on the graph, we see a straight line.
For equation 2, we rearrange it to x^2 + 4x - 20y - 5 = 0. Plotting this equation, we get a quadratic curve.
By examining the graph, we can see that the two lines intersect at a point where 'x' is approximately 10 and 'y' is approximately 8. Therefore, the larger integer is 10, and the smaller integer is 8.
By substituting these values back into the original equations, we can verify that they satisfy both equations.
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Find a curve that passes through the point (1,5) and has an arc length on the interval [2,6] given by:
6
S2 V1 + 16x dx.
6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx = 6S²V1 + 16x dx. To solve this equation, we need additional information about the curve, such as a boundary condition or another equation that relates f(x) and f'(x).
To find a curve that passes through the point (1, 5) and has an arc length on the interval [2, 6] defined by the expression 6S²V1 + 16x dx, we can follow these steps:
Step 1: Determine the general form of the curve equation.
Step 2: Use the arc length formula to obtain an equation involving the curve's equation.
Step 3: Solve the resulting equation to find the specific curve.
Let's proceed with each step:
Step 1: Determine the general form of the curve equation.
Let's assume the curve equation is y = f(x), where f(x) represents the unknown function describing the curve.
Step 2: Use the arc length formula to obtain an equation involving the curve's equation.
The arc length formula for a curve defined by y = f(x) is given by:
S = ∫[a,b] √(1 + (f'(x))²) dx
We are given that the arc length on the interval [2, 6] is defined by the expression 6S²V1 + 16x dx. Substituting the formula for arc length, we have:
6∫[2,6] (√(1 + (f'(x))²))²dx + 16∫[2,6] x dx
Simplifying, we get:
6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx
Step 3: Solve the resulting equation to find the specific curve.
Since the expression 6S²V1 + 16x dx represents the arc length on the interval [2, 6], we need to equate it to the arc length formula obtained in Step 2.
6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx = 6S²V1 + 16x dx
To solve this equation, we need additional information about the curve, such as a boundary condition or another equation that relates f(x) and f'(x). Without such information, it is not possible to determine the specific curve. Please provide additional constraints or information if available to proceed further in finding the specific curve.
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What is an equation of the line that passes through the point (3,-1) and is parallel to the line 5.2 + 3y = 6?
Answer: Its y=-1.
Step-by-step explanation:
Find the area of the trapezoids
Answer:
48 square units
Step-by-step explanation:
Each square on the grid is 2 units by 2 units.
Bases: AT = 8; RS = 4
Height: 8
area = (b1 + b2)h/2
area = (8 + 4)(8)/2
area = 48 square units
Answer:
The area of trapezoid is 48 sq units.
Step-by-step explanation:
According to the question,
➻ Trapezoid is consist of many square shapes. Each grid square equals 2 units. We need to find the area of trapezoid.
➻ To find area we need to find the length if base and height of trapezoid.
Calculate the square grids to find base and height. we get.
Base ; SR = 4 units and TA = 8units
Height = 8 units.
Finding the area of trapezoid.
We know that,
Area of trapezoid = ( Base1 + Base2 ) ×Height / 2
plug the values of both base and a height.
Area of trapezoid = ( 4 + 8 ) × 8 / 2
Add the numbers which are in bracket and multiply by 8.
Area of trapezoid = 12 × 8 / 2 = 96/2
Divide 96 by 2.
Area of trapezoid = 48 sq units.
Hence,
The area of trapezoid is 48 sq units.