.Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.
Answers
Answer:
Part 1
The drawing of the quadrilateral is included here
Part 2
The area of the quadrilateral is 60.5 unit²
Step-by-step explanation:
Part 1
Please find attached the given drawing of the quadrilateral created with Microsoft Excel
Part 2
The given quadrilateral ABCD comprises of a trapezium AECD and triangle ABE
The height of the trapezium, h₁ = 4 units
For segment BC, we have;
The slope = (-5 - (-2))/(5 - (-4)) = -1/3
The equation of the line BC in point and slope form is y - (-5) = -1/3×(x - 5)
Which gives;
y = -1/3×(x - 5) - 5 = -x/3 + 5/3 - 5 = -x/3 - 10/3
The y-intercept is (0, -10/3)
The lengths of the opposite parallel sides of the trapezium AECD are;
a = 5 - (-2) = 7 and b = 7 - (-10/3) = 31/3
The area of the trapezium AECD = ((a + b)/2) × h₁ = ((7 + 31/3)/2) × 4 = 104/3 unit²
The height of triangle
The area of ABE, h₂ = 5
The base of triangle ABE = b = 31/3
The area of triangle ABE = 1/2 × b × h₂ = 1/2 × 31/3 × 5 = 155/6 unit²
The area of quadrilateral ABCD = The area of the trapezium AECD + The area of triangle ABE
∴ The area of quadrilateral ABCD = 104/3 unit² + 155/6 unit² = 60.5 unit².
Related Questions
A small town has two local high schools. High School A currently has 500 students and is projected to grow by 80 students each year. High School B currently has 700 students and is projected to grow by 30 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine how many students would be in each high school in the year they are projected to have the same number of students.
Answers
The equation that represent the number of students in High School A at time t is AA = 500 + 80tt.
The equation that represent the number of students in High School B at time t is BB = 700 + 30tt.
The number of students when both schools would have the same number of students is 820.
When would the school have the same number of students?
The equation that represent the number of students in High School A :
current number of students + (number of years x rate of increase)
AA = 500 + 80tt.
The equation that represent the number of students in High School B at time t is:
current number of students + (number of years x rate of increase)
BB = 700 + 30tt.
When the schools would have the same number of students, the two equations would be equal:
700 + 30tt = 500 + 80tt
700 - 500 = 80tt - 30tt
200 = 50tt
tt = 200 / 50
tt = 4
Population = 500 + (80 x 4)
500 + 320 = 820
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What is the number of terms in this expression?
+4.6
Enter your answer in the box.
Answers
Answer:
joe mama
Step-by-step explanation:
Need help on this, please
Answers
Answer: 30 something?
Step-by-step explanation:
if I would have 160$ and was discounted by 75 percent and if used a PROMO CODE and it gave me 10 percent off how much would I have
Answers
Answer:
10 percant off how much would i have
it costs $42 for 7 staplers. what is the unit rate for the stapler?
Answers
Answer:
The answer is 6
Step-by-step explanation:
42 divided by 7=6
Plz help. Will give brainliest to best answer
Answers
Answer:
9
Step-by-step explanation:
11cos35
Answer:
x = 9.0
Step-by-step explanation:
cos(35) = [tex]\frac{x}{11}[/tex]
11cos(35) = x
x = 9.0
jason sees that 2 out of every 5 cars that passes by his house has the windshield wipers on. What is the probability that that of the next 4 cars that pass his house, 2 will have their windshield wipers on?
Answers
Select all the true statements about this graph.
A. The graph is nonlinear
B. The function increases at the same rate.
C. The rate decreases after x=2.
D. The graph is a function
E. The graph is increasing in two intervals.
Answers
Addison is going to invest in an account paying an interest rate of 3.1% compounded continuously. How much would Addison need to invest, to the nearest dollar, for the value of the account to reach $910 in 18 years?
Answers
Answer: $521
Step-by-step explanation:
Find
the
reciprocal
0f
0.65 to three
Significant
figurs
Answers
Answer:
100/ 56
Step-by-step explanation:
100/65 because 0.65 is a decimal number
hope it helps!
Answer:
100/65 because 0.65 is in decimal
Two angles of a triangle measure 55° and 20°.
What is the measure of the third angle of the triangle?
A. 159
B. 90°
O C. 1050
D. 2859
HELP
Answers
Answer:
The three angles of a triangle always add up to 180.
Therefore, we have the equation:
55+20+x=180.
Solving for x, we get x=105.
So the answer is C.
Hope this helps! :D
Which graph shows the solution for d?
Answers
Answer:
is there a picture????
Let the area of a rectangle in square metres is
[tex] {x}^{2} + 13x + 42[/tex]
How much longer is the length than the width of the rectangle?
A. 7m
B. 8m
C. 1m
D. 6m
Answers
Answer:
C)1m
Step-by-step explanation:
So the length and width is
x²-13x+42=0
(x-7)(x-6)=0
x-7=0
x-6=0
x=7 (length)
x=6 (width)
So the difference between length and width is
=7-6
=1m
Answer:
[tex]C.1\ m[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that,\\Area\ of\ the\ rectangle=x^2+13x+42\\Hence\ lets\ factorize\ this\ area\ completely:\\x^2+13x+42\\=x^2+6x+7x+42\\=x(x+6)+7(x+6)\\=(x+7)(x+6)\\Hence,\\Area\ of\ the\ rectangle=(x+7)(x+6)\\As\ we\ know\ that,\\Area\ of\ a\ rectangle=Length*Width\\Area\ of\ a\ rectangle=lw\\Here,\\lw=(x+7)(x+6)\\Hence,\\l=(x+7),w=(x+6)\ or\ l=(x+6),w=(x+7)\\But\ generally\ the\ length\ of\ a\ rectangle\ is\ greater\ than\ it's\ width.\\Hence\ the\ first\ solution\ is\ suitable\ here.\\[/tex]
[tex]Hence,\\l=(x+7),w=(x+6)\\Hence\ in\ order\ to\ find\ the\ difference\ between\ the\ length\ and\ width\\ we\ must\ perform\ the\ operation :l-w\\Hence,\\(x+7)-(x+6)\\=x+7-x-6\\=1\ m[/tex]
What scale factor was used to produce the image?
A. 49
B. 18
C. 7
D. 1
Answers
C. 7
You count the boxes along the green line.
Which congruence theorem can be used to prove angle BDA triangle DBC?
С
B
D
A
OHL
O SAS
O AAS
O SSS
Answers
The answer is actually A. HL
The congruence theorem can be used to prove Δ BDA ≅ Δ DBC is HL.
Option A is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
We see that,
ΔBDA and ΔDBC are both right triangles.
Now,
DC = AB (hypotenuse) (given)
DB = DB ( Common sides )
CB = DA ( Remaining side of the right triangle )
ΔBDA ≅ ΔDBC
Proved by HL.
Thus,
The congruence theorem can be used to prove Δ BDA ≅ Δ DBC is HL.
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5. The price of a new gym bag is $37.00 plus 8% sales tax. What is the sales tax on this gym
bag in dollars and cents?
Answers
Answer:
$25.00 which is $24.50
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): Dot was discarded near "x.s".
(2): "37." was replaced by "(37/1)".
Unauthorized use of the imaginary unit "i" or syntax error in complex arithmetic expression
FIND THE EQUATION OF THE QUADRATIC FUNCTION GIVEN ITS ZEROS. 2.)11/3,-11/3
Answers
Answer:
they will have the same aboulsute value.
Step-by-step explanation:
because the abouslute value can not be negitive
a car was purchased last year for $28,500. now its value is $25,510. at what rate is the car's value depreciating each year?
Answers
Answer:
The car's value is depreciating by $2,990 per year.
Step-by-step explanation:
To solve this problem, we just need to subtract the cars value this year, or $25,510, from the car value of last year, or $28,500.
28,500 - 25,510 = $2,990
Since the car value was $2,990 more just last year, the car's value is depreciating by $2,990 per year.
Hope this helps! :D
–2.5 + (–3.5)
Which number line shows the sum?
A.
B.
C.
D.
Answers
Answer:
The correct answer is C.
Step-by-step explanation:
Because –2.5 + (–3.5) = -6, it means that the red line goes from -6 to -3 1/2 to 0. so that gives us Answer choice C
6th grade math i mark as brainliest
Answers
please help!! i’ll give brainliest!!
Answers
B is 12
hope this helped :)
Answer:
a- 1,100
b- 12
c- the price also increases.
Step-by-step explanation:
If x=−1 and y=−3, then 5(x2−7+y)=
Answers
Answer:
-60
Step-by-step explanation:
5(-1 times 2 -7 -3) = 60
The value of [tex]5(x^2-7+y)[/tex] at [tex]x=-1,y=-3[/tex] is [tex]-45[/tex].
Important information:
The given expression is [tex]5(x^2-7+y)[/tex].The given values are [tex]x=-1,y=-3[/tex].Value of expression:Substitute [tex]x=-1,y=-3[/tex] in the given expression.
[tex]5((-1)^2-7+(-3))=5(1-7-3)[/tex]
[tex]5((-1)^2-7+(-3))=5(-9)[/tex]
[tex]5((-1)^2-7+(-3))=-45[/tex]
Therefore, the value of [tex]5(x^2-7+y)[/tex] at [tex]x=-1,y=-3[/tex] is [tex]-45[/tex].
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5. a) Determine the total surface area of
this tent, including the floor, in order to
estimate the amount of canvas needed
to construct it.
b) What is the volume of the tent?
13m
22 mm
13.5 m
3 m
I
4 m
4 m
Unit 6
Answers
Step-by-step explanation:
Radius of the conical part = radius of cylindrical part r=
2
3
m
Slant height of the cone l=2.8 m
Height of the cylinder, h=2.1 m
Canvas needed to make the tent = Curved surface area of the conical part + curved surface area of the cylindrical part.
Curved surface area of conical part = πrl=
7
22
×
2
3
×2.8=13.2
Curved surface area of cylindrical part =2πrh=2×
7
22
×
2
3
×2.1=19.8
Total surface area = Curved surface area of conical part + Curved surface area of cylindrical part
=13.2+19.8=33 m
2
Cost of 1 m
2
canvas = Rs. 500
Cost of 33 m
2
canvas =33×500=16500
Therefore, it will cost Rs. 16500 for making such a tent.
Write the equation of the line that passes through the points (7,-8) and (2, -8).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answers
Answer:
it has zero slope because it is a horizontil line
Step-by-step explanation:
La Distribuidora Industrial Dulzura va a seleccionar entre dos compañías para transportar su azúcar al mercado. La primera compañía cobra 49,430.00 por alquilar los camiones más 2,480.50 adicionales por cada tonelada de azúcar. La segunda compañía cobra 60,500.00 por alquilar los camiones más 1,927.20 adicionales por cada tonelada de azúcar.
Answers
Answer: La cuenta de Milla ganaría $63 más que la cuenta de Gion después de 1 año.
w/4 + 12.5 - 7z what term has a coefficient
Pls help me.
Answers
This expression contains 3 terms.
7z is the term with a coefficient.
12.5 is the constant term in the expression.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, w/4 + 12.5 - 7z.
There are 3 terms in this expression.
The term that has a coefficient is 7z.
The constant term in the expression is 12.5.
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Please please please help me with this !!!!!!
Answers
Answer:
Measure of angle T is 67.5 and measure of angle V is 22.5
Step-by-step explanation:
Solve for x
All the angles in a triangle equal 180
So,
3x + x +90 is 180.
Subtract 90 from both sides
3x+x = 90
Add like terms
4x = 90
Divide by 4 to solve for x
x = 22.5
Now substitute 22.5 in for 3x and x
Measure of angle T is 3(22.5) = 67.5 and measure of angle V is 22.5
The population of a town is 9,000, and it grows at a rate of 4.6% per year. What will the population be in 10 years ?
Answers
Answer:
13410
Step-by-step explanation:
So, first we find 4.6% of 9000
9000 x .046 = 414
Then we multiply the 414 by 10 because they gain 414 people every year and we need to find how many people after 10 years
414 x 10 = 4140
now add 4140 and 9000
Answer = 13140
A train traveling at a speed of 20mph departs from Manhattan and heads towards New Jersey. At the same time, a train heading to Manhattan from New Jersey is departing at the same time, and will be going 40mph. If the two places are 120 miles apart, how far from New Jersey will the trains meet?
E. 40 miles F. 60 miles G. 80 miles H. 100 miles
PLS ANSWER WITH THE WORK..... THE ANSWER IN THE ANSWER SHEET IS G 80 MILES BUT I NEED THE WORK ON HOW TO GET TO TE ANSWER.
Answers
They will be at exactly 80 miles because the train going from Manhattan to jersey and the train going from Jersey to Manhattan meet at 80 because 60 is the halfway stop and the train going from Jersey is 20 mph more. Therefore, 80 mph is the answer
Hope this helps!
There are 82 candies. 4 candies more are added. How many are there total?
Answers
Answer:
86
Step-by-step explanation:
82+4=86
Answer:
86 candies
Step-by-step explanation:
Just do 82+4= 86 candies