Polygon ABCD has the following vertices:
A(−4, 2), B(3, 2), C(3, −5), and D(−4, −2)
Calculate the area of the polygon.
Answers
To be able to solve clearly this problem, the best thing to do is to plot the graph (see attached pic). From the graph we can see that the points form a trapezoid.
The base is formed by the segment connecting point A and point B.
While the two heights: shorter one by the segment connecting points A and D, and the longer one by the segment connecting points B and C.
The formula for area of trapezoid is given as:
A = b (h1 + h2) / 2
Where,
b = base of the trapezoid = 3 – (-4) = 7
h1 = shorter height = 2 – (-2) = 4
h2 = longer height = 2 – (-5) = 7
Therefore the area is:
A = 7 (4 + 7) / 2
A = 77 / 2
A = 38.5
The answer is 38.5. I took this exam and I chose 38.5 and got it right, I hope this helps!
Related Questions
What does interior angle A of the polygon in the figure equal? A. 110 B. 150 C. 230 D. 100
Answers
(n-2) × 180° = 4 x 180 = 720
A = 720 - (50+100-120-110 - 230)
A = 110
answer is A. 110
Which statement is true about the solutions for the equation 3y + 4 = −2?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
Answers
Answer:
B, One solution
Step-by-step explanation:
Which best describes the range of the function f(x) = 2(1/4) after it has been reflected over the y-axis? all real numbers all real numbers less than 0 all real numbers greater than 0 all real numbers less than or equal to 0
Answers
all numbers greater than 0
Answer:
All real numbers greater than 0.
Step-by-step explanation:
We have the function, [tex]f(x) = 2(\frac{1}{4})^{x}[/tex].
'Reflection over y-axis means to flip the graph over y-axis', which changes the function by f(x) becomes f(-x).
So, after reflection, the given function transforms into,
[tex]g(x)=f(-x)[/tex]
i.e. [tex]g(x)=2(\frac{1}{4})^{-x}[/tex]
According to the graph of the function g(x), we see that,
Range of [tex]g(x)=2(\frac{1}{4})^{-x}[/tex] is the 'Set of all real non-negative numbers' i.e. {x | x > 0} i.e. [tex](0,\infty)[/tex]
The number 6√3 is between what two integers and is closer to which integer on the number line.
Between 6 & 7 & is closer to 6
Between 10 & 11 & is closer to 10
Between 6 & 7 & is closer to 7
Between 63 & 64 & is closer to 63
Answers
Answer: integer on the number line. Between 6 & 7 & is closer to 6 Between 10 & 11 & is closer to 10 Between 6 & 7 & is closer to 7 Between 63 & 64 & is closer to 63.
Step-by-step explanation:
If the population of Town B is 50% greater than the population of Town A and the populations of Town C is 20% greater than the population of Town A, then what percent greater is the population of Town B tan the population of Town C
Answers
A = population of town A,
B = population of town B,
C = population of town C.
Because the population of town B is 50% greater than that of town A,
B = 1.5A (1)
Because the population of town C is 20% greater than that of town A,
C = 1.2A (2)
From (1), obtain
A = B/1.5 = (2/3)B (3)
Substitute (3) into (2).
C = 1.2*(2/3)*B = 0.8B
Divide each side by 0.8.
1.25C = B
This result means that B is 25% greater than C.
Answer: 25%
How many times does 6 go into 22
Answers
3.
Why?
6 X 3 = 18.
Glad I Could Help, And Good Luck!
My Brainly Name: AnonymousGiantsFan
We can use long division to solve this,
Let's write it.
[tex]6\overline{|\smallspace22}\space\space\space\space[/tex]
Then, divide [tex]22[/tex] by [tex]6[/tex] to get [tex]3[/tex].
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace22}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Multiply the quotient by the divisor...
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace22}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace8}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Subtract [tex]18[/tex] from [tex]22[/tex].
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace22}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace8}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\space\space\emptyspace4\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
As you can see, our answer using long division would be 3 with a remainder of 4.
Thanks!
-TetraFish
Melissa and Emily are playing at the pool.They have three different measuring jars for; liters, cups, and pints. They find that 7 cups of water and 3 liters of water filled 9.8 pints. Later, they find that if they start with 5 liters of water and remove 9 cups of water, they end up with 6 pints of water. Model the given two situations as a system of linear equations. Based on your equations, determine the relationship between;
●cups and liters,
●cups and pints,
●and pints and liters.
Show all your work and submit your work along with the resulting relationships.
Answers
[tex]7c+3l=9.8p[/tex] ⇒ Equation 1
5 litres - 9 cups = 6 pints
[tex]5l-9c=6p[/tex] ⇒ Equation 2
Relationship between cups and litres
Rearranging equation 1 to make pints the subject
[tex]7c+3l=9.8p[/tex]
[tex]p= \frac{7c+3l}{9.8} [/tex] ⇒ substitute this into Equation 2
[tex]5l-9c= \frac{7c+3l}{9.8} [/tex]
[tex]49l-88.2c=7c+3l[/tex]
[tex]49l-3l=7c+88.2c[/tex]
[tex]46l=95.2c[/tex]
[tex]l=2.1c[/tex]
Hence, 1 litre = 2.1 cups
Relationship between cups and pints
Rearrange equation 1 to make litres the subject
[tex]7c+3l=9.8p[/tex]
[tex]3l=9.8p-7c[/tex]
[tex]l= \frac{9.8p-7c}{3} [/tex] ⇒ Substituting this into Equation 2
[tex]5( \frac{9.8p-7c}{3})-9c=6p [/tex]
[tex] \frac{49p-35c}{3}-9c=6p [/tex]
[tex] \frac{49}{3}p- \frac{35}{3}c-9c=6p [/tex]
[tex] \frac{49p}{3}-6p= \frac{35}{3}+9c [/tex]
[tex] \frac{31}{3}p= \frac{62}{3}c [/tex]
[tex]p=2c[/tex]
Hence, 1 pint = 2 cups
Relationship between pints and litres
Rearranging equation 1 to make cup the subject
[tex]7c=9.8p-3l[/tex]
[tex]c= \frac{9.8p-3l}{7} [/tex] ⇒ subsitute this into equation 2
[tex]5l-9( \frac{9.8p-3l}{7})=6p [/tex]
[tex]5l- \frac{63}{5}p+ \frac{27}{7}l=6p [/tex]
[tex]5l+ \frac{27}{7}l=6p+ \frac{63}{5}p [/tex]
[tex] \frac{62}{7}l= \frac{93}{5}p [/tex]
[tex]l=2.1p[/tex]
Hence, 1 litre = 2.1 pints
Here's work you can copy and paste:
7 cups + 3 liters = 9.8 pints
7c+3l=9.8p
5 liters - 9 cups = 6 pints
5l+9c=6p
Cups and Liters
7c+3l=9.8p
p= 7c+3l/9.8 (put in equation 2)
5l-9c= 7c+3l/9.8
49l-88.2c=7c+3l
49l-3l=7c-88.2c
46l=45.2c
1Liter = 2.1 Cups
Cups and Pints
7c+3l=9.8p
3l=9.8p-7c
l=9.8p-7c/3 (put in equation 2)
5(9.8p-7c/3)-9c=6p
(49p-35c/3)-9c=6p
49/3p-35/3c-9c=6p
49/3p-6p=35/3c+9c
31/3p=62/3c
1 Pint = 2 Cups
Pints and Liters
7c=9.8p-3l
c=9.8p-3l/7 (put in equation 2)
5l-9(9.8p-3l/7)=6p
5l-63/5p+27/7l=6p
5l+27/7l=6p+63/5p
62/7l=93/5p
1 Liter = 2.1 Pints
a polynomial of degree zero is constant term. true or false
Answers
Find the circumference of a circle whose area is 24pi ft^2
Answers
This gives r = root24
Circumference = 2pi * r
= 2pi * root24
= 4pi * root6
Hope I'm able to help you.
Answer:
30.76 [tex]ft^{2}[/tex]
Step-by-step explanation:
To calculate the circumference of a circle you just have to multiply the diameter by pi.
C= D*[tex]\pi[/tex]
And in order to calculate the value of the diameter you have to clear the formula for the area.
A= [tex]r^{2} *\pi[/tex]
r=[tex]\sqrt{\frac{24 \pi }{\pi } }[/tex]
r=[tex]\sqrt{24}[/tex]
r=4,89
Once we get the radius, we only have to calculate the diameter:
D=2r=9,79
now we just calculate the circumference:
C=D*[tex]\pi[/tex]= (9.79)(3.14)= 30.76
classify the following triangle . check all that apply
Answers
Two equal sides ⇒ Isosceles
Answer:
Option (a) and (d) is correct.
The given triangle is obtuse and isosceles.
Step-by-step explanation:
Given : A triangle with measure of one angle is 120° and two legs of the triangle are given equal in length.
We will have to choose the correct classification for the given triangle.
For a triangle if the measure of one the angles is
1) less than 90 then it is acute triangle ,
2) equal to 90 then right triangle
3) greater to 90 then obtuse triangle
Since the measure of one angle of the triangle is 120° > 90° Thus, the given triangle is obtuse.
For a triangle if all the three sides are equal then it is equilateral triangle, if two sides are equal then it is isosceles and if no side is equal then it is scalene.
Since, for the given triangle, the two legs of the triangle are given equal in length so it is an isosceles triangle.
Thus, the given triangle is obtuse and isosceles.
is √2/3 a rational or irrational
Answers
sqrt(2/3) = 0.816496
since it is a decimal with no repeating numbers it would be irrational
What is 2.33 written as a mixed number in simplest form?
Answers
ur mixed number is 2 33/100...and this does not reduce
Is 7/2 the same thing as 3.5
Answers
3.5 as a fraction is 7/2 but in mixed numbers it's 3 1/2
1/5 [4(x+2)-(3-x)]=4
Answers
Hope you wanted this answer ^.^
A quadratic equation is shown below: 2x2 − 10x − 8 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 4x2 − 12x + 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answers
The given quadratic equation is 2x²-10x-8=0
The radicand is given by b²-4ac where a, b, and c are the constants in a quadratic form ax²+bx+c
From the given equation, we have
a = 2
b = -10
c = -8
Radicand b²-4ac = (-10)² - 4(2)(-8) = 100 + 64 = 164
The radicand is >0 hence the quadratic equation has two distinct roots
PART B:
4x²-12x+5 = 0
We can use the factorization method to solve the equation
Firstly, we multiply 4 by 5 to get 20
Then we find the pair of numbers that multiply gives 20 and sum gives -12
The pair of number is -2 and -10
Rewriting the equation
4x²-2x-10x+5 = 0
2x(2x-1)-5(2x-1) = 0
(2x-1)(2x-5) = 0
2x-1 = 0 and 2x-5 = 0
x = 1/2 and x = 5/2
Which list has the numbers in order from least to greatest
Answers
x/9=4/y=y/36 solve for x
Answers
Lauren describes a parabola where the focus has a positive, nonzero x coordinate. Which parabola(s) could Lauren be describing? Check all that apply.
x2 = 4y
x2 = –6y
y2 = x
y2 = 10x
y2 = –3x
y2 = 5x
Answers
it answer is c ,d and f
The correct equations are [tex]y^2 = x[/tex], [tex]y^2 = 10x[/tex] and [tex]y^2 = 5x[/tex] respectively
What is a Parabola?A parabola is symmetrical open plane curve that is created by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.
In the given question, Lauren describes a parabola that has positive non zero coordinate value on
focusThe equation of focus of a parabola is given as
[tex]y = a(x - h)^2 + k[/tex]
In the options given,
[tex]y^2 = x[/tex] is correct
[tex]y^2 = 10x[/tex] is also correct and
[tex]y^2 = 5x[/tex] is correct
This shows that only option c, d and f are the right answers.
The correct equations are [tex]y^2 = x[/tex], [tex]y^2 = 10x[/tex] and [tex]y^2 = 5x[/tex] respectively
Learn more on focus of a parabola here;
https://brainly.com/question/4061870
a student scores 71 out of 100 on a test, if the maximum score on the tests is also 100, what score does the student need to maintain at least an average of 78?
Answers
71+x=156
x=85
Th student needs to score a min of 85
Twice a number decreased by 15 is equal to -27 . What is the number ?
Answers
2x = -27 + 15
2x = - 12
x = -12/2
x = -6 <==
If f(x)=2x-4, find f(q+1)
please show your work!
Answers
If the function f(x) = 2x-4, the function f(q + 1) = 2q - 2
What is a function?A function is a mathematical equation that shows the relationship between two variables.
Since if f(x)=2x-4, to find f(q+1), we proceed as follows.
Since we have the function f(x) = 2x - 4, and we want to find f(q + 1). To find the function f(q + 1), we substitute x = q + 1 into the equation. so, we have that
f(x) = 2x - 4
When x = q + 1, we have that
f(x) = 2x - 4
f(q + 1) = 2(q + 1) - 4
Expanding the brackets, we have that
f(q + 1) = 2q + 2 - 4
= 2q - 2
So, f(q + 1) = 2q - 2
Learn more about function here:
https://brainly.com/question/29631554
#SPJ3
A juice company did a survey among 100 customers to find their juice preferences. The customers were asked about their preferences for apple or orange juices. Out of the total 35 people who liked apple juice, eight liked orange juice also. There were 20 people who liked orange juice. Part A: Summarize the data by writing the values that the alphabets A to I in the table below represent. (5 points) Like apple juice Do not like apple juice Total Like orange juice A B C Do not like orange juice D E F Total G H I Part B: What percentage of the total people did not like either apple or orange juice? (3 points) Part C: Do the people surveyed have more dislike for apple juice than orange juice? Justify your answer. (2 points)A juice company did a survey among 100 customers to find their juice preferences. The customers were asked about their preferences for apple or orange juices. Out of the total 35 people who liked apple juice, eight liked orange juice also. There were 20 people who liked orange juice. Part A: Summarize the data by writing the values that the alphabets A to I in the table below represent. (5 points) Like apple juice Do not like apple juice Total Like orange juice A B C Do not like orange juice D E F Total G H I Part B: What percentage of the total people did not like either apple or orange juice? (3 points) Part C: Do the people surveyed have more dislike for apple juice than orange juice? Justify your answer. (2 points)
Answers
Part A:(This table is a three by three table, with the first top two sections being liked apple juice and didn't like apple juice, and the first left two sections being liked orange juice and didn't like orange juice. The end sections are totals.)
No 27 45 72
Total 35 55 100
Part B:(What percentage of the total people did not like either apple or orange juice?)
25 people did not like either apple or orange juice so 25/100 is 25%.
Part C:(Do the people surveyed have more dislike for apple juice than orange juice? Justify your answer.)
There were a total of 28 people that liked orange juice against a total of 35 people that liked apple juice, so it is safe to say that out of the 100 surveyed there was more dislike for orange juice than apple juice.
Answer:
Part A: A = 8
B = 20
C = 28
D = 35
E = 37
F = 72
G = 43
H = 57
I = 200
Part B: 18.5%
Part C:
D = People who do not like Orange Juice
B = People who do not like Apple Juice
I use the values of B and D because these are the values that represent dislike for that juice, and also because adding them together creates a value for not liking either juice.
D = 35
B = 20
So there is a greater dislike for Orange Juice.
Step-by-step explanation:
If 3a+4b = 4a-4b = 21 find the value of a
Answers
a=8b
Plug it in:
24b+4b=21
28b=21
b=21/28
a=8b=6.
4a-4b=21
4a=21+4b
a=(21+4b)/4
now using 1st and 2nd
3(21+4b)/4+4b=4(21+4b)/4-4b
(63+12b+16b)/4=(84+16b-16b)/4
63+28b=84
28b=21
b=21/28
b=3/4
.... now using 4a-4b=21 we have
4a-4(3/4)=21
4a=3=21
4a=24
a=6
What is the value of x?
Answers
=>5x-20=180
=>5x=200
=>x=40
ANSWER FOR 15 POINTS!!
Which number(s) below belong to the solution set of the inequality? Check all that apply. (Meaning tell me all the ones that apply.)
x + 16 > 51
A. 16
B. 35
C. 80
D. 38
E. 55
F. 34
Answers
x+16>51
minus 16 both sides
x>35
so any number greater than 35 will work
A doesn't work
B doesn't work
C works
D works
E works
E works
F doesn't work
answers are C,D, E
A dogs weight increased by 50% in 3 years . By the end of the 3years , the dog weighed 45 pounds . How much did the dog weigh 3 years ago
Answers
Then, it would be: x * 150/100 = 45
x * 1.5 = 45
x = 45/1.5
x = 30
So, your final answer is 30 Pounds
Goodluck
Final answer:
To calculate the dog's weight from three years ago, we take the current weight and divide it by 1.50 since the weight increased by 50%. The equation 1.50 * x = 45 pounds results in x = 30 pounds, indicating the dog weighed 30 pounds three years ago.
Explanation:
The question concerns the original weight of a dog whose weight increased by 50% over a period of three years, bringing its weight to 45 pounds at the end of that period. To determine the dog's weight from three years ago, we use the following steps:
Understand that a 50% increase implies that the final weight is 150% of the original weight (100% + 50%).
Represent the original weight as 'x'.
Set up the equation: 1.50 * x = 45 pounds.
Divide both sides by 1.50 to solve for 'x': x = 45 / 1.50.
Calculate 'x' to find that 'x' equals 30 pounds.
Therefore, the dog weighed 30 pounds three years ago.
The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 2 units, the value of k is ________. Numerical Answers Expected!
Answers
Answer: The value of k is 2.
Step-by-step explanation:
Given : The graph of [tex]f(x)=(0.5)x[/tex] is replaced by the graph of [tex]g(x)=0.5)x-k.[/tex]
If g(x) is obtained by shifting f(x) down by 2 units, then [tex]g(x)=(0.5)-2[/tex]
[since f(x)shifted down down by 2 , so only the value of dependent variable effect]
When we compare both functions of g(x), we found that k=2.
Hence, the value of k is 2.
The value of [tex]k[/tex] is 2.
The following information should be considered:
when [tex]g(x)[/tex] is obtained by shifting f(x) fall by 2 units so [tex]g(x) = (0.5) - 2.[/tex]Since [tex]f(x)[/tex] shifted down by 2 so there is the effect on the dependent variable. Now at the time of comparing both functions of g(x) the k should be 2.Learn more: brainly.com/question/17429689
The lines y = 2x + 1 and y = -5x - 6 intersect at?
Answers
so intersect at (-1,-2)
Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have?
6 ounces
12 ounces
18 ounces
27 ounces
Answers
Answer:
The answer is C. 18 ounces
Step-by-step explanation:
Answer:
c on egde
Step-by-step explanation:
answer both questions to get brain ( if u cant see all the answers its fine all u need is the question)
Answers
Answer:
a and c
Step-by-step explanation: