What is the area of a parallelogram whose vertices are A(−1, 12) , B(13, 12) , C(2, −5) , and D(−12, −5) ?
Answers
Answer: The area of the parallelogram with the given vertices=238 square units.
Step-by-step explanation:
Let CD be the base of the parallelogram ABCD is given by distance formula
CD=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} =\sqrt{(-12-2)^2+(-5-(-5))^2} =\sqrt{196} =14[/tex]units[or you can count distance by using graph as ordinates of C and D are same to we can count the distance of x from C to D]
Now consider P a point on CD such that AP become the height of the parallelogram which is given by (from the graph attached)=17 [as abscissa of P and A are same to we can count the distance of y from A to P]
Area of parallelogram = base × height=14×17=238 square units.
Related Questions
I really need help with these questions. What will these word problems look like?
A. The perimeter, P, of a rectangle is the sum of twice the length and twice the width.
1. P = 2(l+w) units
2. P = 2(5)+2(9) units
3. P = 4x units
4. P = (l+l)+(w+w) units
5. P = 2(x+3) units
B. The area, A, of a triangle is one-half the product of the triangle's base and height.
1. A = 1/2 (b+h)
2. A = 1/2(12)(5)
3. A = 1/2(b*h)
4. A = (x + y)/2
5. A = x^2/2
There is more than one answer to each problem. I will award brainliest answer, I really could use some help with this.
Answers
answer
1. P = 2(l+w) units
2. P = 2(5)+2(9) units
4. P = (l+l)+(w+w) units
B. The area, A, of a triangle is one-half the product of the triangle's base and height.
answer
2. A = 1/2(12)(5)
3. A = 1/2(b*h)
Absolute Value equations always have 2 answers.
True
False
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A baker wants to put 3 3/4 pounds of apples in each pie sge makes. She purchased 52 1/2 pounds of apples. How many pies can she make?
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She can make 14 pies.
divide 52 1/2 pounds by 3 3/4 pounds
52 1/2 / 3 3/4 = 14
she can make 14 pies
Find the average value of f over region
d. f(x, y) = 4x sin(y), d is enclosed by the curves y = 0, y = x2, and x = 7.
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The question involves finding the average value of function f(x, y) = 4x sin(y) over a particular region. This is done using a double integral to integrate the function over the region and divide by the area of that region. The area of the region is determined using the given boundaries.
Explanation:The subject of this question is calculus, specifically dealing with a double integral to find the average value of a function over the specified region. The given function is f(x, y) = 4x sin(y), and the region d is enclosed by the curves y = 0, y = x^2, and x = 7.
To find the average value of function f over the region d, you should use the formula for the average value of a function of two variables. This is given by: Avg = (1/Area(D)) ∫∫_D f(x, y) dA
Before we can use this formula, we need to find the area of region D. This can be obtained as a simple integral from the given boundaries: Area(D) = ∫ from 0 to 7 dx ∫ from 0 to x^2 dy = ∫ from 0 to 7 x^2 dx = [x^3/3]_0^7 = 343/3
We can then proceed with the double integration by applying the appropriate limits. This is a more complex process that requires substitutions and careful calculation. After evaluating the average value, you should get a numerical solution.
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To find the average value of a function over a region, calculate the double integral of the function over that region and divide it by the area of the region.
Explanation:To find the average value of a function over a region, we need to calculate the double integral of the function over that region and then divide it by the area of the region. In this case, the region d is enclosed by the curves y = 0, y = x-2, and x = 7. We can set up the integral as follows:
So, the average value of f over region d is 1.12.
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A city has 7204 recycle bins. The city gives half of the recycle bins to it's citizens. The rest of the recycle bins are divided into 23 equal groups for city parks. How many recycle bins are left over?
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7204 : 2= 3602
The number of recycle bins is left:
7204 - 3602= 3602
The largest number of bins that can be given in each group:
3602 : 23 = 156 (residual: 14)
=> There are 14 bins left over.
Robert climbed 775 steps in 12 1/2minutes. how many steps did he average per minute?
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What happens when you multiply a fraction by its reciprocal?
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(1/2)/(3/4)=(1/2)*(4/3)=4/6=2/3
How do you verify that a hexagon formed by A=(0,0), B=(2,1), C=(3,3), D=(2,5), E=(0,4) and F=(-1,2) is equiangular? (I already know that it is equilateral)
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To verify that the hexagon is equiangular, calculate the slopes and angles of all sides using the coordinates of the vertices.
Explanation:To verify that a hexagon is equiangular, we need to show that all interior angles of the hexagon are congruent. We can calculate the angles using the coordinates of the vertices A, B, C, D, E, and F.
Calculate the slope of each side of the hexagon. For example, for side AB with points A(0,0) and B(2,1), the slope is (1-0)/(2-0) = 1/2.Use the slope to find the angle using the formula arctan(slope). For side AB, the angle is arctan(1/2) = 26.57 degrees.Repeat steps 1 and 2 for all sides of the hexagon.If all six angles are equal, then the hexagon is equiangular.Learn more about Equiangular Hexagon here:https://brainly.com/question/31803879
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Convert 7 4/7 to a mixed decimal and rounded to the nearest thousandth.
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The endpoints of a diameter of a circle a(-1,1) and b(3,3). what is the length of the radius
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If we determine the distance from one point to the second point, we get the length of the diameter. This is calculated through the equation,
D= sqrt ((x2 – x1)^2 + (y2 – y1)^2)
Substituting the known values,
D = sqrt ((-1 – 3)^2 + (1 – 3)^2)
D = 4.47
The length of the radius is half that of the diameter. Hence, the radius is,
R = 4.47 /2 = 2.236
Answer: r = 2.24
An air cargo plane can transport as many as 15 regular shipping containers. One supersize container takes up the space of 3 regular containers.
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Let the number of regular containers the plane can transport be x and the number of super-size containers the plane can transport be y, then
Given that one super-size container takes up the space of 3 regular containers, i.e. y = 3x and that the capacity of the plane is 15 regular containers.
When the ship is not carrying any super-sized container, it can carry up to 15 regular containers and when the ship is not carrying any regular containers it can carry up to 5 super-sized containers.
Therefore, the inequality to model the number of regular and super-size containers the plane can transport is given by
x + 3y ≤ 15
(a) A certain solution has a hydrogen ion concentration of 0.00000914 moles per liter. Write this number in scientific notation.
(b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.
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(b) As to this one, the equation seems incomplete. What's the exponent of 10, if it says there's any exponent?
The hydrogen ion concentration can be written in scientific notation as 9.14 x 10-6 M. The weight of a humpback whale can be written in standard notation as 11,105 pounds.
Explanation:(a) The given hydrogen ion concentration of 0.00000914 moles per liter can be written in scientific notation as 9.14 x 10-6 M. To convert the number to scientific notation, we move the decimal point to the left until there is one non-zero digit to the left of the decimal point and multiply by the corresponding power of 10.
(b) The weight of a humpback whale, which is given as ×1.1105 pounds, can be written in standard notation as 11,105 pounds. To convert from scientific notation to standard notation, we move the decimal point to the right or left by the power of 10 indicated by the exponent.
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To take a taxi , it cost $3.00 plus an additional $2.00 mile traveled. you spent exactly $20 on a taxi, which includes the $1tip you left. how many miles did you travel?
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You spent $20. Plus the $1 tip.
20 - 1 = 19
$19 is how much you spent without the tip
The cost for the taxi ride itself is $3
19 - 3 = 16
$16 is how much you spent without the ride cost + tip
You spent $2 for every mile traveled.
16/2=8
You traveled 8 miles
A jet travels 510 miles in 2 hours. At this rate, how far could the jet fly in 15 hours? What is the rate of the speed of the jet?
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510/2 = 255.
Multiply 1 hour distance covered by 15
255*15=3825 miles
Hope I helped :)
Evaluate the function f(x)=−4x−3 f(x)=−4x−3 for x=−6x=−6.
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round 999.999 to the nearest tenth
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to the left of the point you start with tenths then hundredths and so on
Reasoning:
For the number 999.999, the 0.9 is the tenth's digit.
Since the next number is 5 or greater, we round the 0.9 up. Now 0.9 rounded up is 1, so that takes away the decimals and adds one to the ones place value.
Since we are adding 1 to 9, it becomes 10, meaning the following 9 becomes a ten as well.
All said and done, it becomes 1000 from the rounding.
Write a decimal number that, then round to the nearest tenth, is 0.3.
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Simplify. y^-3 pls help me i need this very bad
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In this case, the base is y, the power is -3
y^(-3)=1/(y^3)
Each digit in the division example has been replaced with the same letter throughout (r stands for remainder) the digits used were 1, 2, 3, 4, 5, 7, and 9 find the numbers clue u is 5
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This is a cryptarithm problem where every unique letter represents a unique digit. Given that 'u' equals 5, we would navigate the problem by dividing numbers out front and subtracting the exponents.
Explanation:This question is about a form of a cryptarithm. Cryptarithms are mathematical puzzles where the digits are replaced by letters of the alphabet or other symbols. If the same letter appears more than once, it represents the same digit each time. Your question implies that each letter corresponds to a unique digit and that division is involved. Therefore, we need to figure out which numbers are represented by the remaining letters. You've already been given that 'u' represents 5. Since there isn't a complete problem provided, I can't offer a step by step guide on how to solve it. However, I can suggest to you to start the cryptarithm solution by dividing numbers out front and subtracting the exponents.
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The question involves substituting the given number for a letter in a division problem and then solving it. It's a step-by-step process of trial and error.
Explanation:In this problem, you are asked to find the numbers that replace the same letter throughout a division problem. Given that 'u' is 5, you know that wherever 'u' appears in your division equation, you can replace it with 5. Solve the division problem accordingly. Do not forget, each distinct letter represents a distinct number. It is a process of trial and error until you come up with the right numbers that fit the equation and abides by the division rules.
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Read the following conjecture.
Any number that is divisible by 2 is also divisible by 8.
Find a counterexample to show that the conjecture is false
A: 16
B: 24
C: 28
D: 32
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16/2 =8, 16/8 = 2
24/2 = 12, 24/8 = 3
28/2 = 14, 28/8 = 3.5
32/2 = 16, 32/8 = 4
28 isn't divisible by 8
Answer is C
A rectangular swimming pool with a flat bottom is 20 feet by 12 feet. How long will it take to fill the swimming pool to 5 feet if water is being pumped into the pool at 30 cubic feet per minute?
A) 8 minutes
B) 40 minutes
C) 67 minutes
D) 120 minutes
Answers
The answer to this question is going to be
20 feet * 12 feet * 5 feet
= 20 * 12 * 5 feet ^3
= 1200 feet^3
1200 feet^3 / (30 feet^3 / minute)
= (1200 / 30) minutes
= (120 / 3) minutes
= 40 minutes
Hoped I Helped
Will give brainliest if correct.
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Given that f(a+b)= f(a) + f(b) and f(x) is always positive, what os the value of f(0)?
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[1] We know that f(a+b) = f(a) + f(b). Therefore, f(0+0) = f(0) + f(0). In other words, f(0) = f(0) + f(0). Subtracting, we see, f(0) - f(0) = f(0) or 0 = f(0).
[2] So, what's the problem? We found the answer, f(0) = 0, right? Maybe, but the second rule says that f(x) is always positive. However, f(0) = 0 is not positive!
Since there is a contradiction, we must either conclude that the single value f(0) does not exist, or that the entire function f(x) does not exist.
To fix this, we could instead say that "f(x) is always nonnegative" and then we would be safe.
Describe the end behavior of the function:
y = x3 + 3x2 - 2x + 4
a)left - rises, right - falls
b)left - rises, right - rises
c)left - falls, right - falls
d)left - falls, right - rises
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See the picture I added.
Therefore, the answer must be D.
Hope this helps
Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.
Alexander thought the equivalent quarterly interest rate would be 2%. Is Alexander correct? If he is, explain
why. If he is not correct, state what the equivalent quarterly interest rate is and show how you got your
answer. i need to show my work and everything
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If the length of the rectangle is twice the width and the perimeter of the rectangle is 30 cm find its area
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Length is twice the width, twice meaning two times and we know that the width is x so length = 2x.
The perimeter is the sum of all the sides or width + width + length + length which is equal to x + x + 2x + 2x by substituting x for width and 2x for length. We know that x is really 1x since 1 times anything is that anything.
So the perimeter can be written as 1x + 1x + 2x + 2x which we are told is equally 42 meters. We reduce the equation by collecting all terms that have the same variables so we get (1 + 1 + 2 + 2 )x = 42. Adding the collected terms together we get 6x = 42. Now we solve for x by dividing both sides of the equation by six. Whatever we do to one side we have to do to the other so the equation remains balanced. So 6x divide by 6 is 1x or we can just say x, and 42 is divided 6 giving us 7. So x = 7. Going back to our original stated facts width = x = 7 and length = twice the width or 2x = 2 (7) =14. So
width = 7 meters
legth = 14 meters
We can double check this since we know the formular for the perimeter = width + width + length + length = 7 + 7 + 14 + 14 = 42.
What’s the reciprocal of 7/2a
2a/7
-2a/7
7/2a
-7/2a
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So, to get the reciprocal of 7/2a, you need to divide 1 by this number as follows:
reciprocal = 1 / (7/2a) = 2a/7
The answer is : 2a/7
PLEASE HELP ASAP!! Will give brainliest!
Answers
2n + 3n = 2
5n = 2
n = 2/5
So... n = 2/5
I hope this helped! : )
Please rate and thank!
How to solve the second equation
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[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} y = &{{ -0.01}}x^2&{{ +0.7}}x&{{ +6}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( -\cfrac{0.7^2}{2(-0.01)}~~,~~6-\cfrac{0.7^2}{4(-0.01)} \right) \\\\\\ (\stackrel{\textit{how far ahead it went}}{24\frac{1}{2}}~,~\stackrel{\textit{how high it went}}{18\frac{1}{2}})[/tex]
what transformation has changed the parent function f(x) =log3x to its new appearance shown in the graph below
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log_3(1) asks "3^? = 1," which we know is 0. So, log_3(1) = 0, which means (1,0) is a point on the graph for the parent function.
log_3(3) asks "3^? = 3" which we know is 1. So, log_3(3) = 1, which means (3,1) is a point on the graph for the parent function.
Now, we look at the graph they gave us and we see that our two points have moved upward 2 units. Now, (1,2) and (3,3). The transformation appears to be f(x) + 2, as you have selected.
Answer:
"f(x) + 2" You were correct