What is the area of the composite figure whose vertices have the following coordinates?
(−4, 3) , (2, 3) , (4, −1) , (0, −3) , (−2, −1)
Answers
Answer:
30 square units
Step-by-step explanation:
There are several ways to determine the area of the figure from its coordinates. A straightforward method is to plot the coordinates on a graph and decompose the resulting figure into simple shapes whose area formulas are known
Area from simpler shapesA plot reveals the figure to be a parallelogram with a base length 6 and a height of 4, together with a triangle of base 6 and height 2.
The area of the parallelogram is given by the formula ...
A = bh
The area of the triangle is given by the formula ...
A = 1/2bh
In each case, 'b' represents the base of the figure, and 'h' represents its height.
Parallelogram area
A = bh = (6)(4) = 24
Triangle area
A = 1/2bh = 1/2(6)(2) = 6
Total area
The composite area will be the sum of the parallelogram and triangle areas:
A = 24 +6 = 30 . . . . square units
The area of the composite figure is 30 square units.
__
Area from coordinatesThe area can also be figured directly from the coordinates. The formula for that can be written ...
[tex]\displaystyle A=\dfrac{1}{2}\left|\sum_{k=1}^n (x_k(y_{k+1}-y_{k-1}))\right|\qquad\text{where $y_0=y_n$ and $y_{n+1}=y_1$}[/tex]
Using this formula, we find the area to be ...
A = 1/2|(-4(3-(-1)) +2(-1-3) +4(-3-3) +0(-1-(-1)) -2(3-(-3))|
= 1/2|-16 -8 -24 +0 -12| = 1/2|-60| = 30
The area of the figure is 30 square units.
Related Questions
How do you solve this inequality: 7 ≤ x+11
Answers
7 ≤ x + 11
subtract 11 from both sides
-4 ≤ x
From there on, any number greater than or equal to -4 will be a solution to the inequality
Hope this helps
[tex] 7 \leq x+11 \\ \\ 7 -11\leq x \\ \\ -4 \leq x\qquad\to\qquad x\in \left[-4; +\infty) [/tex]
.can you please help me thank you you will be given brainley
Answers
Find the smallest value of k if 264k is a perfect square
Answers
264k = 132*2k = 11*12*k = 11*3*2*2*k
To get a perfect square, you are going to have to have an even number of prime factors.
You have one 11 and one 3. You are going to have to do something about those two.
k = 11 * 3 <<<<< ======= answer.
Now put that into 264k and you get 11 * 3 * 2 * 2 * 11 * 3 which is a perfect square. 11^2 * 3^2 * 2^2 = 4356
The square root of 4356 = 66
4356 is a perfect square when 33 = k.
Select the correct factor from the presentation and calculate how many calories used. (Round to the hundredths.) A person weighing 165 lbs. jogs 1 mile in 8 minutes. How many calories used?
A. 102.30
B. 107.25
C. 253.85
D. 266.13
Answers
Answer:
the answer is 107.25
Step-by-step explanation:
Answer:
B. 107.25
Step-by-step explanation:
Let x be the calories burnt by the man,
Since, when a person runs 1 miles in 8 minutes,
Then,
[tex]\frac{\text{Calories used by him}}{\text{His weight in lb}}=65\%[/tex],
Given,
Weight of the person = 165 lb,
Thus,
[tex]\frac{x}{165}=\frac{65}{100}[/tex],
[tex]x = \frac{165\times 65}{100}[/tex]
[tex]x=\frac{10725}{100}[/tex]
[tex]\implies x=107.25[/tex]
Hence, 107.25 calories will be used.
Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles?
∠M ≅ ∠A
∠M ≅ ∠D
∠M ≅ ∠C
Answers
Answer:
It is M = C
Step-by-step explanation:
The measure of the angle ∠WMT is congruent to the measure of the angle ∠DCA. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ∆MTW is congruent to the triangle ∆CAD. Then we have
∠MTW ≅ ∠CAD
∠TWM ≅ ∠ADC
∠WMT ≅ ∠DCA
The proportion of the point ∠WMT is harmonious with the proportion of the point ∠DCA. Then, at that point, the right choice is C.
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Which equation has the graph that is a parabola with a vertex at 5,3
Answers
[tex]y=a(x-h)^2+k[/tex]
In our case h=5 and k=3, these are coordinates of our vertex point.
There is no way to find a without knowing any other coefficients.
When you start solving some equations to get the parameters you always end up with identity (example 25=25). This means that your equation has an infinite number of solutions. In other words, any a will give you a parabola with vertex at the specified point.
The final answer would:
[tex]y=a(x-5)^2+3[/tex]
Where a is any real number.
Which graph shows the equation y = x + 2?
Answers
Write an expression to represent: four more than the product of three and a number xxx.
Answers
product of 3 and the x = 3x
four more = 3x + 4
Answer:
x-4
Step-by-step explanation:
What is the answer to this problem?
Answers
To start, an isosceles triangle is any triangle with two sides of the same length.
In this case, you are given two measurements: 20 and 30.
This means that the third side of the triangle can either be 20 or 30, since two of the sides must equal one another.
Because the question is asking for the greatest possible perimeter of the triangle, it would only make sense that the third side would have to be 30 units in length to make the greatest possible perimeter since it is the possible length that is greatest in value (20 < 30).
Therefore, knowing that the sides of the triangle are now 20, 30, and 30, add the lengths up to find the perimeter:
20+30+30
=80
Therefore, the largest possible value of the perimeter would be 80 units.
Hope this helps and I hope you have a marvelous day! :)
Match the corresponding function formula with each function when h(x) = 3x + 2 and g(x) = 2 x .
1. k(x) = 2x + 3x + 2 k(x) = g(x) ∘ h(x)
2. k(x) = 2x - 3x - 2 k(x) = g(x) + h(x)
3. k(x) = (3x)2-x + 2-x + 1 k(x) = h(x) ÷ g(x)
4. k(x) = 23x + 2 k(x) = g(x) - h(x)
5. k(x) = 2x(3x + 2) k(x) = g(x) × h(x)
6. k(x) = 3(2x) + 2 k(x) = h(x) ∘ g(x)
Answers
h(x) = 3x + 2
g(x) = 2^x
I proceed to calculate the different values of K (x)
case 1) k(x) = g(x) ∘ h(x)
g(x) ∘ h(x)=g(h(x))
k(x) = [2]^[3x + 2]-----------> is the option 4. k(x) = 2^(3x + 2 )
case 2) k(x) = g(x) + h(x)
k(x) = [2^x]+[3x + 2]=2^x+3x+2--------> is the option 1.) k(x) = 2^x + 3x + 2
case 3)k(x) = h(x) ÷ g(x)
k(x) = [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)
is the option 3.) k(x) = (3x)2^(-x) + 2^(-x + 1 )
case 4)k(x) = g(x) - h(x)
k(x) = [2^x]-[3x + 2]=2^x-3x-2--------> is the option 2.) k(x) = 2^x - 3x - 2
case 5) k(x) = g(x) × h(x)
k(x) = [2^x]*[3x + 2]-----------> is the option 5.) k(x) = 2^x(3x + 2)
case 6)k(x) = h(x) ∘ g(x)
h(x) ∘ g(x)=h(g(x))
k(x)=3*[2^x]+2---------------> is the option 6. k(x) = 3(2^x) + 2
To simplify the other user's answer (which is correct):
1 = B
2 = D
3 = C
4 = A
5 = E
6 = F
Alternatively, your right boxes should look like:
4
1
3
2
5
6
How could the relationship of the data be classified? (1 point)
scatter plot with points loosely scattered going down to the right
Answers
A 10-foot ladder is leaning against a tree. The bottom of the ladder is 4 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?
A.2.4
B.6.0
C. 9.2
D. 10.8
Answers
Can someone please help me with 4?? I’m really struggling.
Answers
m<DAC=y
m<BAC=3x
ABCD is a square so m<DAB = 90° because each angle in a square is a right angle so 3x+y=90° (1) ;
AC is a diagonal in the square so m<DAC=m<BAC so 3x=y (2);
Find x by substituting y to 3x from (2) into (1)
3x+3x=90
6x=90
x=90/6=15°
Answer x=15°
Fiecare dintre cei 25 de elevi ai clasei a |||-a a realizat un jurnal al luni . Stiind ca pentru fiecare zi s-a folosit o pagina si ca luna are 31 de zile,afla cate pagini au jurnalele tuturor elevilor.
Answers
Each of the 25 students in the class has made a journal on Monday. Knowing that every day a page was used and that the month is 31 days, find out how many pages the logs of all students.
Let
x--------------> total students
y--------------> total days in a month
z--------------> total page used per one student in 1 day
T--------------> total page used per total students in 1 month
we know that
x=25 students
y=31 pages
z=1 page
T=[x]*[y]*[z]------------> T=[25]*[31]*[1]------------> T=775 pages
the answer is 775 pages
the answer in Romanian
lăsa
x--------------> numărul total de elevi
y--------------> total zile într-o lună
z--------------> pagina totală utilizată pentru un student în 1 zi
T--------------> pagina totală utilizată pentru toți elevii în 1 lună
noi stim aia
x=25 elevi
y=31pagini
z=1 pagină
T=[x]*[y]*[z]------------> T=[25]*[31]*[1]------------> T=775 pagini
răspunsul este de 775 de pagini
Find all real values of $v$ that satisfy the equation $(v+6)^2 = 324$. If you find more than one, then list your values in increasing order, separated by commas.
Answers
(v+6)^2 = 324-----> I raise to 1/2 both members----> [(v+6)^2]^(1/2)=(324)^(1/2)[(v+6)]=(324)^(1/2)-------------> v+6=√324
v=√324-6---------> 18-6=12
v=12
the answer is v=12
Answer:
The values of v in increasing order are, -24, 12
Step-by-step explanation:
Given equation is,
[tex](v+6)^2=324[/tex]
[tex]v+6=\pm 18[/tex]
[tex]v=-6\pm 18[/tex]
[tex]\implies v=-6-18\text{ or }v=-6+18[/tex]
[tex]\implies v = -24\text{ or }v=12[/tex]
Since, -24 < 12
Thus, the values of v in increasing order are,
-24, 12
the elevation in denver colorado is 13 times greater than that of waikapu, hawaii. the sum of their elevations is 5600 feet. find the elevation of each city
Answers
h2 = denver height
A) 13 h1 = h2
B) h1 + h2 = 5,600
B) h1 + 13h1 = 5,600
B) 14h1 = 5,600
h1 = Waikapu height = 400 feet
h2 = 5,600 - h1
h2 = 5,600 -400
h2 = Denver height = 5,200
Marie earns $96 in interest each year on an investment what is the rate of simple interest if her principal was $800
Answers
The rate of simple interest that Marie earns on her $800 investment is 12% per year, calculated by dividing the annual interest earned ($96) by the principal amount ($800).
To find the rate of simple interest, we can use the formula Interest = Principal * rate * time. Given that Marie earns $96 in interest each year on an investment and her principal was $800, we can rearrange the formula to solve for the rate.
The formula for simple interest is:
Interest = Principal * rate * time
Assuming the interest earned is for one year, we have:
$96 = $800 * rate * 1 year
To find the rate, we divide both sides by $800:
rate = $96 / $800
rate = 0.12
Converting into a percentage, the simple interest rate is 12% per year.
Select all of the following expressions that are equal to 2.5.
5 ÷ 2
-2(-1.25)
(-0.5)^2
-1 + (-1.5)
Answers
a) 5/2 = 2.5
b) -2(-1.25)
What is the denominator of the fraction 1/9?
Answers
any number below the bar is the denominator, any number above the bar is the numerator
this is a physics question that requires a lot of math. Hoping on of you genius could help me.
Q: You're driving down the highway late one night at 16m/s when a deer steps onto the road 44m in front of you. Your reaction time before stepping on the brakes is 0.50s , and the maximum deceleration of your car is 10m/s2 .
How much distance is between you and the deer. I solved this =23m
What is the maximum speed you could have and still not hit the deer?
The answer is 25 m/s. A lot of people had stated to use the quadratic formula. I just don't know where to begin.
Answers
If it takes 0.5 seconds before stepping on the breaks while going 16 m/s, then you travel 8 meters before anything happens. That means you are 44-8 = 36 meters away from the deer now.
v^2 = v_initial^2 + 2(acceleration)(distance)
0 = (16 m/s)^2 + 2(-10m/s^2)(distance)
256 m^2/s^2 / (2(10 m/s^2) = distance = 12.8 meters (13 meters after significant figures are taken into account).
The maximum speed would be:
0 = v_initial^2 + 2(-10m/s^2)(36m)
v_initial^2 = 720m^2/s^2
v_initial = 27 mph
Anybody have the proper answer to this
Answers
A = π * 5.5 * 5.5
A = 30.25 π
3025 / 100 π mm^2
.. r = d/2
.. r = (11 mm)/2 = (11/2) mm
The area is given by
.. A = π*r^2
.. = π(11/2 mm)^2
.. A = (121/4)π mm^2
X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5) work out the coordinates of point X
Answers
x = 2/5(Q) + 3/5(P)
= 2/5(12.5,7.5) + 3/5(2,1)
= 2( 2.5, 1.5) + 3( 0.4, 0.2)
= (5,3) + (1.2,0.6)
= (6.2, 3.6)
The Coordinates of X will be;
=(6.2, 3.6)
Answer: (6.2, 3.6)
Step-by-step explanation:
We know that if a point M (x,y) divide a line segment having endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in ratio m:n , then the coordiantes of M is given by :-
[tex]x=\dfrac{mx_2+nx_1}{m+n}\ ;\ y=\dfrac{my_2+ny_1}{m+n}[/tex]
Given : X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5).
Then, coordinate of X is given by :-
[tex]x=\dfrac{2(12.5)+3(2)}{2+3}\ ;\ y=\dfrac{2(7.5)+3(1)}{2+3}\\\\\Rightarrow\ x=\dfrac{31}{5}\ ;\ y=\dfrac{18}{5}\\\\\Rightarrow\ x=6.2\ ;\ y=3.6[/tex]
Hence, the coordinate of X = (6.2, 3.6)
Find the 200th term, given the first term and the common difference. A1=34 and d=15
Answers
1. it is arithmetic progression, where a₁=34 and d=15. Formula for aₓ is aₓ=a₁+d(x-1);
2. a₂₀₀=34+15*(200-1)=3019.
answer: 3019.
P.S. if it is possible check the arithmetic part.
Number of security staff = a over 100 if a audience, is 10500, how many security staff are needed for the event
Answers
.. Number of security staff = 10500/100 = 105
Ava bought a rectangular rug for her hallway. The rug is 2\3 yards wide and 2 3\4 yards long. What is the area of the rug as a mixed number in simplest form?
Answers
Answer:
1 5/6
Step-by-step explanation:
A ladder is leaning against the side of a building. The building and the ground form a right angle. How high on the building will the ladder touch if the ladder is 10 ft long and the base of the ladder is 6 ft from the base of the building?
Answers
The given question describes a right triangle with the hypotenuse as 10 ft and one of the legs as 6 ft.
We can make use of Pythagoras theorem to evaluate the length of the other side.
We know that by Pythagoras theorem, the square root of the sum of the squares of the legs of a right triangle gives the hypotenuse. Let the length of the required leg be x, then
[tex] x^2+6^2=10^2\\ \\ \Rightarrow x^2=100-36=64\\ \\ \Rightarrow x=\sqrt{64}=8. [/tex]
Therefore, the ladder reached 8 ft high on the building.
what do all similar circles have in common
a) congruent circumference value
b) congruent diameters
c) π
Answers
All the similar circles have π in common.
Thus, option (c) is correct.
When two circles are similar, it means they have the same shape but possibly different sizes.
However, the ratio of their corresponding lengths, including the circumference, remains constant.
Second, the ratio of the diameter will be constant but not congruent.
Third, the value of π is the universal constant whose value is 22/7 or 3.14.....
which is the same for every similar circle.
Thus, π has a common value.
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13) Suppose a coffee cup has a diameter of 8 cm and a height of 9 cm. What is the volume of the cup? (to nearest whole number)
Answers
Radius is 4 cm (half of diameter)
Height = 9 cm
Volume of cylinder = pi x r^2 x h
The answer is 452.16 or can be rounded to 452 cubic cm
Answer:
[tex]452\ cm^{3}[/tex]
Step-by-step explanation:
we know that
the volume of a cylinder (coffe cup) is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=8/2=4\ cm[/tex] -----> the radius is half the diameter
[tex]h=9\ cm[/tex]
substitute
[tex]V=\pi (4^{2})(9)=452.4\ cm^{3}[/tex]
Round to the nearest whole number
[tex]452.4\ cm^{3}=452\ cm^{3}[/tex]
Can someone help me?
Answers
There are 4+3+2 = 9 people who scored exactly 85 points (look at column 2)
So there are 4+9 = 13 people who are from brazil or scored exactly 85 points. Subtract out those who fit both criteria. So we'll subtract off 3 people
13-3 = 10
There are 10 people who fit the criteria out of 19 total. The 19 is from adding up all the values in the table.
Divide the two values to get 10/19
Answer: 10/19
A employer, who started a new business, has promised his employees a minimum starting wage of $3, with an increase of $2 every 4 years. Sketch a graph of wage as a function of time for 16 years. Assume the wages take effect at the beginning of the year where the change is made. (HINT: use a step function to represent the function.)
Answers
To sketch the graph, use a step function to represent the wage as a function of time over 16 years. The minimum starting wage is $3, and it increases by $2 every 4 years.
Explanation:
To sketch a graph of wage as a function of time for 16 years, we can use a step function to represent the function.
The minimum starting wage is $3 and it increases by $2 every 4 years. For the first 4 years, the wage will be $3. At the start of the 5th year, the wage will increase to $5. This pattern continues, with the wage increasing by $2 every 4 years.So, the graph will have flat lines representing each 4-year interval, with a step up at the start of each interval.
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