.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
Find gradient of y=x^2-4x+6 at (3,3)
Answers
[tex]y=x^2-4x+6\\y'=2x-4[/tex]
To find the slope/gradient of the curve at the specific point, we use the derivative.
Then substitute x = 3 in y' = 2x-4
[tex]y'=2(3)-4\\y'=6-4\\y'=2[/tex]
Therefore, the slope/gradient of y = x²-4x+6 at (3,3) is 2.
A waiter had fifty-seven customers. If twenty-three left, how many customers would the waiter still have?
Answers
Answer:
34
Step-by-step explanation:
Answer:
34 customers.
Step-by-step explanation:
57-23=34
Puteti sa ma ajutati va rog? Vreau solutii cu explicatie elaborata, nu doar raspunsul. Multumesc.
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If I had an iPhone 6 that was 12 by 9 inches and an iPhone X that was 17 by 8 inches, how many feet would they be? If you want a challenge divided by 2 at the end.
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Answer:
$13.41
Step-by-step explanation:
maybe, I'm not that sure :/
btw you can, can you please mark me brainliest :)
r/2+y=11
pleaseeee help!! i need the answer like rn
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Answer:
r=99
Step-by-step explanation:
Solve x in the triangle. Round your answer to the nearest tenth
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Answer:
9.5
Step-by-step explanation:
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ayo if i get this right can i get brainliest, i only need 2 more brainliest to get to the next rank :)
Gino and Milla each open a savings account with an initial deposit of $6,300. Gino's account pays 2% simple interest annually. Milla's account pays 3% simple interest annually. If Gino and Milla make no other deposits or withdrawals, how much more interest will Milla's account earn than Gino's after 1 year?
Answers
Answer:
Milla's account would earn $63 more that Gino's account after 1 year.
Step-by-step explanation:
Both Gino and Milla made an initial deposit of $6300.
Principal = $6300
Gino's rate = 2% = 0.02
Milla's rate = 3% = 0.03
number of years = 1
Interest = Principal x Rate x Time
So that,
for Gino;
Interest = 6300 x 0.02 x 1
= 126
The interest on Gino's savings after a year is $126.
for Milla;
Interest = 6300 x 0.03 x 1
= 189
The interest on Milla's savings after a year is $189.
Milla's interest - Gino's interest = 189 - 126
= 63
Milla's account would earn $63 more that Gino's account after 1 year.
Help pls, almost out of time
Answers
Answer:
angle 1
Step-by-step explanation:
it looks the biggest of all
True or false
It is common for
basic savings accounts
to have interest rates
up to 35%.
Answers
Answer:
TRUE
i think
Step-by-step explanation:
Hope this helps!!
confused :( please help!!!!
angles are confusing aaaaaa
Answers
Answer:
22
Step-by-step explanation:
Angles CBD and ABD are complementary, which means that they have a sum of 90 degrees. Since it tells you that angle ABC is 68 degrees, subtract that from 90.
90-68= 22
Answer:
29
Step-by-step explanation:
matching math game help!
Answers
Answer:
dude your math period is way too long
Answer:
dude your math period is way too long
What is this??????????
Answers
Answer:
A drawing. I guess the sky
Step-by-step explanation:
this is a very hard question
A school district has decided that students in grades 7 through 12 should receive 400 minutes of physical education every 10 school days. A gym teacher at one of the schools believes that his students are not meeting this criterion. She randomly selects 50 students and it is found that her students have a mean of 385 minutes and a standard deviation of 55 minutes. Is this evidence to support her claim?
Answers
Answer:
Yes
Step-by-step explanation:
Based on the information provided we can say that Yes, this is enough evidence to support her claim. Since the 50 students were randomly selected and the physical education criteria applies to all of the students in that grade range then these 50 students perfectly represent the total population. That being the case, the results gathered to show that with a standard deviation of 55 minutes some students are surpassing the requirement by very little but others are falling very far from that requirement. When it is a requirement for all of the students in that grade range. Therefore, it is enough to support her claim.
The linear combination method gives a solution of (–4, 2) for which of these systems of linear equations? 3 x + 13 y = 14. And 6 x + 11 y = -2. 4 x + 5 y = 12. And 8 x + 3 y = -4. 5 x + 4 y = 12. And 7 x + 8 y = 12. 10 x + 3 y = 8. And 17 x + 6 y = 10.
Answers
Answer:
A. [tex]3x + 13y = 14[/tex] and [tex]6x + 11y = -2[/tex]
Step-by-step explanation:
Required
Determine which system of equation satisfy (-4,2)
To do this, we simply substitute -4 for x and 2 for y in the given functions.
A.
[tex]3x + 13y = 14[/tex] and [tex]6x + 11y = -2[/tex]
[tex]3x + 13y = 14[/tex]
[tex]3(-4) + 13(2) = 14[/tex]
[tex]-12 + 26 = 14[/tex]
[tex]14 = 14[/tex]
[tex]6x + 11y = -2[/tex]
[tex]6(-4) + 11(2) = -2[/tex]
[tex]-24 + 22 = -2[/tex]
[tex]-2 = -2[/tex]
The above shows that the given linear combination has a solution of (-4,2).
Hence, this option answers the question and there is no need to check other options
Answer: the answer is A
Step-by-step explanation:
The Point Imperial is the highest point of the Grand Canyon and it is 8,800
- feet tall. A professional hiker climbed to the top of one of the rims of the
Grand Canyon that is 348 feet below Point Imperial. The hiker threw a rock
upward from that rim with an initial velocity of 18 ft per second. How
many seconds will it take the rock to hit the ground? Round your answer
to the nearest tenth of a second.
Answers
Answer:
1222
Step-by-step explanation:
sorry youve been waiting a minute
Eight children sit together at story time. Seven children sit in a circle and one child sits in the middle to tell the story. In how many different ways can the children sit
Answers
Answer: 40320
Step-by-step explanation: I think thats correct because the kids on the outside is 1234567 so then there is a kid in the middle.
The number of ways for the children sit will be 40,320.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Eight children sit together at story time.
And, Seven children sit in a circle and one child sits in the middle to tell the story.
Now,
Since, There are 8 students.
Hence, The number of ways for the children sit = 8!
= 40,320
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
Only right answer please I need help
Answers
convert the word three and five tenths into a fraction
Answers
Your answer would be 3 5/10. (3 and 5/10).
What is the perimeter of the parallelogram?
29 cm
80 cm
58 cm
32 cm 2
Answers
Answer:
199 [tex]cm^{2}[/tex]
Step-by-step explanation:
Answer:
58 CM
Step by Step explanation.
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answers
Answer:
5
Step-by-step explanation:
PLS AWNSER BEST AWNSER GET BRAINLIST.
I need a good grade on this final for my pc lol
Answers
Answer:
D
Step-by-step explanation:
Someone please help me make an equation for the first question! :)
Answers
part b:
22y + 6x
Divide 350rs in 3:4 ratio
plzzz fast
Answers
150 : 200
Explanation:
3 + 4 = 7
350 / 7 = 50
50 x 3 = 150
50 x 4 = 200
Y greater than or less than 1/4 X + 2
Answers
Answer:
y[tex]\geq[/tex]1/4x+2
Step-by-step explanation:
what is the lowest term of 35/63
Answers
Answer:
5/9
Step-by-step explanation:
Martha drew a pair of intersecting non-perpendicular lines, I and m. She numbered one pair of vertical angles <1 and <2, and she labeled the second pair of vertical angles <3 and <4. Martha made the conjecture that <1 =~ <2 to validate this conjecture, which of the following would be appropriate reasoning?
A. M<1+ M<2 +M<3 + m<4 = 360
B. The sum of the measures of angles of a triangle is 180°
C. The measure of all right is 90°
D. Because <1 and <2 are each supplementary to <3, they are therefore congruent
Answers
Answer:
b 3eedeehheheehejwjjhhhejjererj
Which side lengths form a right triangle?
Choose all answers that apply.
A. square root of 2, square root of 3, square root of 4
B. square root of 8, 3, square root of 17
C. 5, 6, 8
Answers
Answer: choice B
Explanation: Go through each answer choice and try the Pythagorean theorem to see if it works. This is because a right triangle’s side lengths are described by the Pythagorean theorem. one side^2 + second side^2 = longest side^2. In a right triangle, this equation will be true. Let me show you what I mean
For answer choice A:
(root 2)^2 + (root 3)^2 = (root 4)^2
2 + 3 = 4
5 = 4
5 does not equal 4. Therefore it cannot be A.
For answer choice B:
(root 8)^2 + (3)^2 = (root 17)^2
8 + 9 = 17
17 = 17
this is true! therefore this is a right triangle and it’s B
Dimensions √17, 3, and √8 are the dimension of the right triangle. Thus, the correct option is B.
What is a Pythagoras theorem?If the dimension satisfies the Pythagorean equation, then the triangle is a right-angle triangle.
The Pythagoras theorem states that the sum of two squares equals the squared of the longest side. The Pythagoras theorem formula is given as,
H² = P² + B²
Let's check the second option, then we have
(√17)² = 3² + (√8)²
17 = 9 + 8
17 = 17
Thus, the correct option is B.
More about the Pythagoras theorem link is given below.
https://brainly.com/question/343682
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Зx +1 <10
What is the answer for this
Answers
Answer:
x < 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Inequality
3x + 1 < 10
Step 2: Solve for x
Subtract 1 on both sides: 3x < 9Divide 3 on both sides: x < 3Here we see that any value x smaller than 3 would work as a solution to the inequality.
A negative correlation has a/an?
positive trend
decreasing trend
stable trend
increasing trend
Answers
Answer:
decreasing trend
►Solve the problems.
I
The tile floor in a restaurant is being replaced. The dimensions of the floor are
shown. What is the total area of the new tile floor in the restaurant?
12 ft
17 ft
15 ft
20 ft
A 64 ft2
B 180 ft2
C 240 ft2
D 300 ft