The area of the parallelogram is 32 square units.
What is a parallelogram?Parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
First, we can plot the points on the coordinate plane to get a better visual understanding of the parallelogram:
| (3,6) (11,6)
| *-----------*
| / /
| / /
| / /
| / /
| *-----------*
| (0,2) (8,2)
|
Now,
We can see that the base of the parallelogram is the line segment connecting (0,2) and (8,2), which has a length of 8 units.
To find the height of the parallelogram, we can observe that the line segment connecting (0,2) and (3,6) is perpendicular to the base, and has a length of 4 units.
Therefore,
The height of the parallelogram is 4 units.
Now,
The area of a parallelogram is given by the formula:
Area = base x height
Plugging in the values we found, we get:
Area = 8 x 4
Area = 32
Therefore,
The area of the parallelogram is 32 square units.
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A map of Scotland is drawn to scale of 1:325,000.
how many CM on the map would show 65KM?
On a map of Scotland, drawn to the scale of 1:325,000, 65 KM of real-world distance will be represented by 20 cm on the map.
Explanation:The question pertains to the scale existing on a map. A map scale enables us to convert the measurements on the map into the corresponding real-world distances. Here, we have a map of Scotland that is drawn to the scale of 1:325,000. This signifies that 1 cm on the map equates to 325,000 cm in reality.
To ascertain how many cm on the map would represent 65 KM, we first need to convert 65 KM into cm. As we know, 1 KM is equal to 100,000 cm. Therefore, 65 KM will be equivalent to 65 * 100,000 = 6,500,000 cm.
Now, we divide the real-world cm (6,500,000 cm) by the scale (325,000), which gives us the cm on the map. Thus, 6,500,000 cm / 325,000 = 20 cm
So, on this map, 65 KM will be denoted by 20 cm.
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What is the sum of the arithmetic series below? Use the formula for the sum of an arithmetic series.
Answer: The required sum is 504.
Step-by-step explanation: We are given to find the sum of the following arithmetic series using the formula for the sum of an arithmetic series :
[tex]\sum_{i=1}^{18}(2i+9).[/tex]
The given arithmetic series can be written, in expanded form, as follows :
[tex]11+13+15+17+~.~.~.~+43+45.[/tex]
We know that
the sum of first n terms of an arithmetic series with first term a and common difference d is given by
[tex]S=\dfrac{n}{2}\{2a+(n-1)d\}.[/tex]
In the given series, a = 11 and d = 13 - 11 = 15 - 13 = . . . =2.
Therefore, the sum up to 18 terms will be
[tex]S_{18}=\dfrac{18}{2}\{2\times 11+(18-1)\times2\}=9(22+34)=9\times56=504.[/tex]
Thus, the required sum is 504.
The sum of the arithmetic series ∑₁¹⁸(2i + 9) using the arithmetic series formula is 504.
To find what is the sum of the arithmetic series ∑₁¹⁸(2i + 9) below using the formula for the sum of an arithmetic series, we proceed as follows
The formula for the sum of therms of an arithmetic series is given by
Sₙ = n/2(a + Tₙ) where
n = number of termsa = first term and Tₙ = last termNow, since we have that arithmetic series, ∑₁¹⁸(2i + 9), the nth terms is U = 2i + 9
Now, the first term is when i = 1.
So, U₁ = a = 2(1) + 9
= 2 + 9
= 11
Also, the last term is when i = 18
So, U₁₈ = T₁₈ = 2(18) + 9
= 36 + 9
= 45
So, the sum of terms Sₙ is when n = 18
S₁₈ = 18/2(11 + 45)
= 9(56)
= 504
The current area of the city park is represented by the expression 11x2 + 4x + 6. The city will expand the park this summer by a factor of 5x − 3. If one-fourth of the new park is to be wooded, which expression represents the new area of the park that is not wooded?
The new area of the park that will not be wooded after expansion is represented by the expression 41.25x³ - 24.75x² + 15x - 13.5.
Explanation:The current area of the park is given by the polynomial 11x² + 4x + 6. If the city expands the park by a factor of 5x - 3, the total new area of the park becomes (11x² + 4x + 6) * (5x - 3), which represents the expansion of the park.
However, the question asks for the part of the park that will not be wooded, which we know is three-fourths of the total park. So, we multiply our expanded park equation by 3/4 (or 0.75) to find this area:
(3/4) * [(11x² + 4x + 6) * (5x - 3)]
Using distributive property, we can further expand the expression:
=(3/4) * [(55x³ - 33x² + 20x - 18)]
So the area that will not be wooded after expansion is expressed as 41.25x³ - 24.75x² + 15x - 13.5.
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Given that the current area of the park is represented by a second degree equation, the expansion of the park will proportionally increase its area. The new area after expansion will be the product of the current area and the expansion factor, so we will need to multiply our current area, which is given by 11x^2 + 4x + 6, by the expansion factor, which is 5x - 3.
This will yield: (5x - 3)*(11x^2 + 4x + 6) as the total new area of the park.
Now that we've calculate the total new area of the park, we need to find out the area of the park that will be wooded and the area that will not be. We know that the wooded area will be one-fourth of the total area, so we can find this by dividing our total area by 4.
This yields: (5x - 3)*(11x^2 + 4x + 6) / 4 as the wooded area of the park.
After discovering the area that will be wooded, we can find the non-wooded area by subtracting the wooded area from the total area of the park.
Therefore, the new area of the park that is not wooded is given by:
3*(5x - 3)*(11x^2 + 4x + 6) / 4
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Paysly is studying a mosquito with a mass of 2.5×10−62.5×10-6 kilograms and a housefly with a mass of 2×10−52×10-5 kilograms. Which statement is true?
The mosquito is 88 times the mass of the housefly.
The housefly is 88 times the mass of the mosquito.
The housefly is 1010 times the mass of the mosquito.
The mosquito is 1010 times the mass of the housefly.
Answer: The house fly is 8 times the mass of the mosquitio
Which of the following has a value between 10/3 and 11/3 ? A- 3 1/2 B-3 1/4 C- 3 3/4 D- 3 1/8
Answer:
A IS CORRECT
Step-by-step explanation:
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In order to survive, organisms must maintain stable conditions in their bodies, even though their external environments are always changing.
For example, humans need to maintain an internal temperature around 37°C. Blood needs to have a pH around 7.4 and an oxygen saturation close to 100%.
What needs to happen in order to maintain these conditions?
A) Organ systems must interact with one another.
B) Organisms must be at rest.
C) Genes must be altered each time cells replicate.
D) All of these.
Organ systems must interact with one another.
Write two equivalent fractions for 2/3
Which metric unit of measurement is best to use to describe the height of a tree
A kilometers
B millimeters
C liters
D meters
contractor A estimated a job would cost $54,000 to complete in 90 days. contractor B estimated he could complete the same job for $49,500 in 120 days. how much per day does each contractor charge
Contractor A estimated a job would cost $54,000 to complete in 90 days.
Per day charge of Contractor A = $54,000 / 90 = $ 600 / day
Contractor B estimated he could complete the same job for $49,500 in 120 days.
Per day charge of Contractor A = $49,500 / 90 = $ 412.50 / day
Therefore, Contractor A charges $ 600 per day and contractor B charges $412.50 per day.
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What is the median of the following set?
28, 45, 12, 34, 36, 45, 19, 20
28
34
31
35
Answer:
Median = 31
Step-by-step explanation:
The median is the middle number which comes after arranging the set in ascending order.
Here, the given data is: 28, 45, 12, 34, 36, 45, 19, 20
The data arranged in the ascending order is as follows:
12, 19, 20, 28, 34, 36, 45, 45
Since the number of terms is even, we have two middle numbers, viz.,
28 and 34
The median would be the average of these two.
Therefore, Median = [tex]$ \frac{28 + 34}{2} $[/tex]
= 31
The answer is 31.
The median of the set 28, 45, 12, 34, 36, 45, 19, 20 is 31.
To find the median of a set of numbers, you should first arrange the numbers in ascending order and then locate the middle number.
If there is an even number of terms, the median is the average of the two middle numbers. Let's do that with the given set: 28, 45, 12, 34, 36, 45, 19, 20.
Sort the numbers: 12, 19, 20, 28, 34, 36, 45, 45.Find the middle: Since there are 8 numbers (an even amount), the median will be the average of the 4th and 5th numbers.Calculate the median: (28 + 34) / 2 = 31.Therefore, the median of the given set is 31.
Steve opened a bank account.he plans to deposit $35 every month.write an equation that models the total amount of money,t,deposited after m months
make w the subject of the formula y-aw=2w-1
Answer:
(y+1)\div (a+2)
Step-by-step explanation:
y-aw=2w-1
y+1=2w+aw
y+1=w(2+a)
(y+1)/(a+2)=w
Answer: w= (y+1)\div (a+2)
Solve the equation. 9 = –d + 17
Answer:
d = 8
Step-by-step explanation:
Since the variable appears on only one side of the equation, all terms not containing the variable can be eliminated from that side by adding their opposite to both sides of the equation. That is, add -17 to both sides of the equation:
9 -17 = -d + 17 - 17
-8 = -d . . . . . simplify
Now, the equation can be multiplied by a number that will give "d" on one side of the equation. Here, that number is -1. Multiply both sides of the equation by -1:
(-1)(-8) = (-1)(-d)
8 = d . . . . . simplify
The solution is d = 8.
Answer:
8
Step-by-step explanation:
[tex]9= -d +17\\9-17= -d +17- 17 \\-8/-1 = -d/-1\\8 = d[/tex]
What is the quotient? n+3/2n-6 divide n+3 /3n-9
Round 6 4/9 to nearest whole number
What is the expression of one less than the quotient of four and a number x
you have a large container of olive oil. You have used 22 1/2 quarts of oil. Twenty-five percent of the olive oil remains. How many quarts of olive oil remain?
Solution:
we are given that
You have a large container of olive oil. You have used [tex]22 \frac{1}{2}[/tex] quarts of oil.
Twenty-five percent of the olive oil remains.
we have been asked to find how many quarts of olive oil remain?
Let there were x quarts of olive oil.
It mean , we can write
[tex]x-22 \frac{1}{2}=\frac{1}{4}*x[/tex]
[tex]x-\frac{1}{4}*x=22 \frac{1}{2}[/tex]
[tex] \frac{3x}{4}=22 \frac{1}{2}[/tex]
[tex] 3x=4*22 \frac{1}{2}[/tex]
[tex] x=\frac{4}{3}* \frac{45}{2}[/tex]
[tex] x=30[/tex]
Hence quarts of olive oil remain [tex] =30-\frac{45}{2}=\frac{15}{2}=7\frac{1}{2}[/tex]
Of the 180 days of school last year, Grace was absent 15 days. What percent of the day was she absent?
Round 14.376 to the nearest dollar
determine the range of possible side lengths of the third side AB of triangle ABC from gretaest to least
What words can you use to read 14.895
each day last week, Ms. wilson walked3/4 mile. what is the total distance, in miles, that Ms. Wilson walked in 4 days?
Taking into account the rule of three, the total distance that Ms. Wilson walked in 4 days is 3 miles.
Rule of threeIn first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
Total distance that Ms. Wilson walkedYou can applied the following rule of three: if each day last week, Ms. Wilson walked [tex]\frac{3}{4}[/tex] mile, in 4 days what is the total distance that Ms. Wilson walked?
[tex]total distance=\frac{4 daysx\frac{3}{4} miles }{1 day}[/tex]
total distance= 3 miles
Finally, the total distance that Ms. Wilson walked in 4 days is 3 miles.
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Is 2 miles greater too 3,333 yards or is 3,333 yards greater than 2 miles?
Luca has a box of dog toys. There are 3 bones, 5 balls, and a stuffed animal. What is the ratio of balls to stuffed animals?
Answer:
5.1
Step-by-step explanation:
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The endpoints of sa020-1.jpg are A(9, 4) and B(5, – 4). The endpoints of its image after a dilation are sa020-2.jpg and sa020-3.jpg. Find the scale factor.
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A school sold small and large boxes of fruit for a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Their sales can be represented in two equations where x represents the price of the small boxes and y represents the price of the large boxes. Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? Check all that apply.
1 The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
2 The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.
3 The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.
4 The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.
5 The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.
6 The first equation can be multiplied by 7 and the second equation by 13 to eliminate y.
Answer:
A,C,D,E
Step-by-step explanation:
An equation is formed of two equal expressions. The correct options are 1, 3, 4, and 5.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Also, x represents the price of the small boxes and y represents the price of the large boxes. Therefore,
The equation for the first student can be written as,
5x + 13y = 232
The equation for the second student can be written as,
12x + 7y = 218
Now, the multiplication that can be done to eliminate the variables are,
1.) The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
3.) The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.
4.) The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.
5.) The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.
Hence, the correct options are 1, 3, 4, and 5.
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6 surfaces 2 small stand tall what shape
Divide 49 in the ratio 4:2:1
To divide 49 in the ratio of 4:2:1, find the total quotient of the ratio parts, divide 49 by this total, and then multiply each part of the ratio by the result.
The ratio of the coefficients is 4:2:1, which can be simplified to 2:1:1. To divide 49 in this ratio, follow these steps:
Find the total quotient of the ratio parts: 4 + 2 + 1 = 7.Divide 49 by the total parts: 49 ÷ 7 = 7.Multiply each part of the ratio by 7 to get the divided amounts: 2 x 7 = 14, 1 x 7 = 7.Which sum is equal to 7/12?
A. 1/12 + 1/12 + 1/12 +1/12 + 1/12 + 1/12 +1/12
B. 1/7 + 1/7 + 1/7 +1/7 +1/7 + 1/7 + 1/7
C. 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12
D. 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 +
Answer:
The answer is A.
Step-by-step explanation:
There are 7 1/12ths, so it is equal to 7/12