What is the area of this polygon?
units²
5-sided polygon on a coordinate plane with vertices F, N, S, C, W. Point f is at (negative 4, negative 2), point N is at (2, 4), point s is at (5, negative 2), point c is at (5, negative 4), and point w is at (negative 4, negative 4)
Answers
Step 2) Find the area of this rectangle. The area is 18 square units because it is 2 units high and 9 units across (9*2 = 18). You can count out the spaces or you can note how we go from x = -4 to x = 5 so subtracting the values gives -4-5 = -9 which has an absolute value of 9.
Step 3) Find the area of triangle FSN. The base is 9 units and the height is 6 units (count out the spaces or subtract y values). So the area is A = b*h/2 = 9*6/2 = 54/2 = 27
Step 4) Add up the area of the rectangle to the area of the triangle: 18+27 = 45
Final Answer: 45 square units
note: another way to find the answer is to find the area of rectangle WABC where point A is at (-4,4) and point B is at (5,4). Then subtract off the triangular areas of AFN and BNS
In this exercise we have to use the knowledge of polygon area to calculate the area of a trapezoid, in this way we find that:
[tex]45 units[/tex]
So find the area of this rectangle, this area will be:
[tex]9*2 = 18[/tex]
Find the area of triangle FSN, this area will be:
[tex]A = b*h/2 = 9*6/2 = 54/2 = 27[/tex]
Sum all the areas will be:
[tex] 18+27 = 45[/tex]
See more about area at brainly.com/question/1631786
Related Questions
Solve the system of equations using the substitution method.
{2x+8y=4 x=−3y+5
Enter your answers in the boxes.
Answers
I believe the answer is (14,-3)
have a great day & good luck!
Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5
Answers
This is the complete question as I found in internet:
Use substitution to determine which of the following points is a solution to the standard form equation below 5x-2y = 10
these are the points:
-1,5
1,5
0,-5
0,5
Answer: (0, -5)
Explanation:
point x y 5x - 2y = 10 ?
-1,5 -1 5 5(-1) - 2(5) = - 5 - 10 = - 15 ≠ 10 ⇒ not a solution
1,5 1 5 5(1) - 2(5) = 5 - 10 = 5 ≠ 10 ⇒ not a solution
0,-5 0 -5 0 -2(-5) = 10 ⇒ a solution
0,5 0 5 0 - 2(5) = - 10 ≠ 10 ⇒ not a solution
Answer:
(10,5/2) answer is A
Step-by-step explanation:
just took test.
Help! Thanks in advance!
Screenshotted question!
Answers
Find the sum of the summation of 2 i minus 12, from i equals 7 to 16.
22
110
220
440
Answers
S=[2(7)-12]+[2(8)-12]+[2(9)-12]+[2(10)-12]+[2(11)-12]+[2(12)-12]+[2(13)-12]+[2(14)-12]+[2(15)-12]+[2(16)-12]
S=2(7+8+9+10+11+12+13+14+15+16)-10(12)
S=2(115)-120
S=230-120
S=110
Answer: Second option 110
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
[tex]\sum_{7}^{16}(2i-12)\\\\=\sum_{7}^{16}2(i-6)\\\\=2\sum_{7}^{16}(i-6)\\\\=2[(16-6)+(15-6)+(14-6)+(13-6)+(12-6)+(11-6)+(10-6)+(9-6)+(8-6)+(7-6)]\\\\=2[10+9+8+7+6+5+4+3+2+1]\\\\\text{Sum of n natural numbers }\\\\=2(\frac{10\times (10+1)}{2})\\\\\=\frac{n(n+1)}{2}\\\\=2\times \frac{10\times 11}{2}\\\\=10\times 11\\\\=110[/tex]
Hence, the value of summation is 110.
Therefore, Second option is correct.
Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency.
2r
r²
r√2
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.......................
When the polynomial is written in standard form, what are the values of the leading coefficient and the constant? 5x + 2 - 3x^2
Answers
Constant = 2
When you order them in standard form, you need to put them in ascending order of the exponents. Therefore the -3x^2 would come first, which makes the number attached (-3) the lead coefficient.
Also, since the number (2) without an x attached would be last (due to the power of x technically being 0), than that is the constant.
Jason was hired to mow a lawn that covers an area of acres 2 3/4. It took him 4 1/8 hours to complete the job. What was his unit rate in hours per acre?
I understand the steps where I am stuck is how did you get 2/3/
Answers
Divide 2 3/4 acres by 4 1/8 hours:
Divide 2.75 acres by 4.125 hours:
2.75 acres
--------------- = 2.667 acres/hour, or 2 2/3 acres / hour.
4.125 hrs
If this is not entirely clear to you, please share the work you've done yourself and I will respond.
find the greatest common factor 6x^2a + 6xa^2
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If you multiply 6xa with a and x ----> 6xa(x+a), you'll get 6x^2a + 6xa^2
The trapezoids are similar. the area of the smaller trapezoid is 131 m2. find the area of the larger trapezoid to the nearest whole number. (1 point)
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The expression 8x + 2y
Answers
Find the slope of the line on the graph
Answers
1st point ( -4,0)
2nd point (0,3)
slope = change in y over change in x
change in y = 3-0 = 3
change in x = 0 - -4 = 0+4 = 4
slope = 3/4
Sophia and Tyler are running around a 400-meter track. They start running from the same place, at the same time. Sophia runs at a speed of 5 m/s and Tyler runs at a speed of 4 m/s. How long will it take Sophia to lap Tyler?
Answers
S: Runner Sophia.
T: Runner Tyler.
At the beginning the distance between both runners is 400m
At t = 1s Sophia runs 5m and Tyler 4m
At t = 2s Sophia runs 10m and Tyler 8m
and so on.
So, for example at t = 1s, the distance between both runner is:
D = 400m - 5m(the advantage of Sophia) + 4m(what Tyler recovers)
So, we can find a general equation for this matter. Knowing that the distance, velocity and time are related by this equation:
[tex]d=vt[/tex]
Then, the distance between both runners, at any time, is given by:
[tex]D = 400-5t+4t[/tex]
So we need to find the how long it will take Sophia to lap Tyler. This happens when D = 0:
[tex]0 = 400 - 5t+4t[/tex]
∴ [tex]400-t = 0[/tex]
∴ [tex]t = 400s[/tex]
Answer: 400 seconds
Step-by-step explanation:
5x = 400 + y
4x = y
take 4x and add it to the top so it looks like this:
5x = 400 + 4x
cancel 4x if you don't know how to do it you do it like this you take +4x and instead you do -4x to cancel.
and you do it to 5x so you cancel 4x and 5x - 4x = x so x = 400
x = 400
This is probably easy but I'm not smart and don't know what else to do I know this is the correct formula it's just confusing to me because there're three numbers and I'm just really dumb.
Answers
Right side rectangle = 4 × 1 = 4
Left side rectangle = 4 × 1 = 4
Both triangles = 4 × 3 = 12
Both triangles = 6
3 + 4 + 4 + 12 = 23
I think the answer is 23 cm
Hope this helped☺☺
Area of a right triangular prism = 1/2(2B) + Ph
The 1/2 and 2 cancel each other out: B + Ph.
Base of the triangular prism: 3 × 4 = 12 cm²
Perimeter of the base (use the Pythagorean Theorem →a² + b² = c²← to figure out the missing side; hypotenuse): 3² + 4² = c²
9 + 16 = c²
√25 = 5
3 + 4 + 5 = 12 cm
Height of triangular prism: 1 cm
Plug these numbers into the formula (B + Ph):
(12 + 12×1) = 24 cm²
The area of the right triangular prism is 24 cm².
Can anyone help me with this problem?
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Use Pythagorean theorem:
[tex]|AB|^2=|BC|^2+|CA|^2\\\\9^2=6^2+|CA|^2\\\\81=36+|CA|^2\ \ \ \ |-36\\\\|CA|^2=45\to|CA|=\sqrt{45}\\\\|CA|=\sqrt{9\cdot5}\\\\|CA|=\sqrt9\cdot\sqrt5\\\\|CA|=3\sqrt5[/tex]
[tex]\tan\Theta=\dfrac{6}{3\sqrt5}=\dfrac{2}{\sqrt5}\cdot\dfrac{\sqrt5}{\sqrt5}=\dfrac{2\sqrt5}{5}[/tex]
PLEASE ANSWER ASAP Becky purchased a home entertainment center for $2,254 using an 18-month deferred payment plan with an interest rate of 22.48%. She did not make any payments during the deferment period. What will Becky's monthly payment be if she must pay off the home entertainment center within three years after the deferment period?
$121.01
$87.45
$62.61
$113.72
Answers
Answer:
$62.61
Step-by-step explanation:
Data:
The price of home entertainment = $ 2 254
Time to pay = 18 months
interest rate = 22.48 %
monthly payment = $ 2254/ 18
= $ 125. 22
= - 22.48 (2254)/18
= $ 62.61
If x varies directly as y, and x = 48 when y = 16, find x when y = 5.
A) 5/3
B) 153.6
C) 15
Answers
48 = k* 16
k = 3
x=3*5
x=15
Answer:
15
Step-by-step explanation:
x =ky
48 = k16
divide by 16
k = 3
plug k into x=ky
x=3*5
x=15
Consider this system of linear equations:
22x − y = -23 (equation 1)
11x + 12y = 1 (equation 2)
Answers
1. You have the folllowing system of equations given in the problem above:
22x − y = -23 (equation 1)
11x + 12y = 1 (equation 2)
2. If you multiply the equation 2 by -2, and then sum the equation 1+equation 2, you obtain:
-25y=-25
y=1
3. Then, you must substitute y=1 into the equation 1, then you have:
x=-1
4. As you can see, when you solve it, the solutions are:
x=-1
y=1
22x − y = -23
-
(11x + 12y = 1) *2
22x − y = -23
-
22x + 24y = 2
0 -25y = -25
y = 1
22x - 1 = -23
x = 1
Line RS is tangent to circle Q at point R.
What is the measure of ∠SQR ?
Enter your answer in the box.
Answers
Now that we know 2 angles, we can find the 3rd:
180 - 90 - 32 = 58
Using the tangent and radius theorem, the measure of ∠SQR is 58°.
What is Circle Geometry??From the question, we are to determine the measure of ∠SQR
In the given diagram, QR is a radius
By the tangent and radius theorem,
If a tangent and a radius meet at the point of tangency, then they are perpendicular to one another
∴ ∠QRS = 90°
∠SQR + ∠RSQ + ∠QRS = 180° (Sum of angles in a triangle)
∠SQR + 32° + 90° = 180°
∠SQR + 122° = 180°
∠SQR = 180° - 122°
∠SQR = 58°
Hence, the measure of ∠SQR is 58°.
Learn more on Circle geometry here: https://brainly.com/question/21872415
#SPJ 2
Identify a counterexample to disprove 6n>n^2/6,where n is a real number.
Answers
A counterexample to disprove the inequality [tex]6n > n^2/6[/tex] is n = 12, because when plugged into the inequality, it results in 72 > 24, which is false.
The question is asking for a counterexample to disprove the inequality [tex]6n > n^2/6[/tex], where n is a real number. To find a counterexample, let's test an arbitrary positive number, such as n = 7, to see if the inequality holds.
Substituting 7 for n, we get:
6 x 7 > 72/6
42 > 49/6
42 > 8.167
This is indeed true, so 7 is not a counterexample. However, we can think of a larger value of n. Let's try n = 12:
6 x 12 > 122/6
72 > 144/6
72 > 24
This is false. Hence, n = 12 serves as a counterexample to disprove the given inequality. So, the inequality does not hold for all real numbers.
A bakery has 49 donuts and 28 muffins for sale. What is the ratio of muffins to donuts? Please answer ASAP 99 Points :V
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In a ratio, the first thing or item mentioned is first in the ratio. Let the muffins stand for x, and the donuts stand for y. It asks for the ratio of muffins to donuts.
x:y
Plug in the numbers.
28:49
Both numbers are divisible by 7.
28/7= 4 49/7=7
4:7 <=== simplified ratio
I hope this helps!
~kaikers
Donuts: 49
Muffins to donuts: 28/49
Answer = 28/49 = 4/8 = 1/2
~Hope this helped~
Sarah is hiking on a trail near her home. She traveled 5 miles before stopping for a break. After the break, Sarah plans on increasing her speed to 3 miles per hour. Which equation models the total distance, D, Sarah travels after hiking for an additional h hours?
A. D = 3h + 5
B. D = 3(h - 5)
C. D = 3h - 5
D. D = 5h + 3
Answers
Answer: A. [tex]D=3h+5[/tex]
Step-by-step explanation:
Given: The rate of increasing speed = 3 miles per hour
The distance she traveled before stopping = 5 miles
Let h represents the number of additional hours for hiking.
Then the equation that models the total distance 'D' Sarah travels after hiking for an additional h hours is given by :-
[tex]D=3h+5[/tex]
_________________ lines are lines that never intersect and are not coplanar. A) Parallel B) Perpendicular C) Skew D) Transversal
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Skew lines are lines that never intersect and are not coplanar.
So the answer would be C. ^-^
A ball is rolling in a circular path that has a radius of 10 inches as shown in
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we know that
[circumference]=2*pi*r
for r=10 in
[circumference]=2*pi*10-----> 62.8 in
if 360° (full circle) has a length of --------> 62.8 in
54°------------------------------> X
x=54*62.8/360-----> x=9.42 in
the answer is 9.42 in
The square root of 136 is between which two whole numbers?
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Hope this helps!
Four girls and eight boys are running for president or vice president of the student council. find each probability: find the prbability that two girls are elected
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The probability that a girl is elected for one office is 4/12, since there are 4 girls out of 12 students.
The probability that a girl is elected for the second office is 3/11. This is because after one girl is elected, there are 3 girls left out of 11 students left.
Together, this gives us
4/12(3/11) = 12/132 = 1/11
The probability that two girls are elected president and vice president from a group of 4 girls and 8 boys is calculated using a hypergeometric distribution, resulting in a probability of 1/11.
The question is asking for the probability that two girls are elected president and vice president of the student council when there are four girls and eight boys running for these positions. This is an example of a hypergeometric distribution problem, as we are selecting without replacement from a finite population divided into two groups.
To find the probability, we need to determine the number of successful outcomes divided by the total number of possible outcomes. The successful outcome is that the two elected individuals are both girls. Since there are 4 girls, there are 4 choose 2 ways to select 2 girls, which equates to 6 possible successful outcomes. The total number of ways to choose 2 individuals from 12 candidates (4 girls + 8 boys) is 12 choose 2, resulting in 66 possible outcomes.
The probability can be calculated by dividing the number of successful outcomes by the total number of possible outcomes.
Probability = Successful outcomes / Total outcomes = 6 / 66 = 1 / 11
12q^2-17q-7
A. (3q+1)(4q-7)
B. (3q-1)(4q+7)
C. (3q+7)(4q-1)
D. (3q-7)(4q+1)
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PLS HELP ME ASAP WITH 3, 4, AND 5! PLS! (Read directions carefully :)
(BRAINLIEST WILL BE GIVEN HOPEFULLY!)
(Random answers gets moderated!)
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a. d(0) = 20
b. d(2) = 18
c. d(4) = 12
d. d(6) = 10
e. d(9) = 15
f. d(3) = 15, or d(9) = 15
4) The domain is the horizontal extent: 0 to 12.
The range is the vertical extent: 10 to 20.
5)
a. f(7) = -2*7 +5 = -9
b. f(-3) = -2(-3) +5 = 11
c. -2x +5 = 17; -2x = 12; x = -6, so f(-6) = 17
x2+y2-4+2y-11=0 what are the center and radius of the circle?
Answers
You need to complete the square for both x and y.
[tex] x^2 - 4x + y^2 + 2y = 11 [/tex]
[tex] x^2 - 4x + 4 + y^2 + 2y + 1 = 11 + 4 + 1 [/tex]
[tex] (x - 2)^2 + (y + 1)^2 = 16 [/tex]
[tex] (x - 2)^2 + (y + 1)^2 = 4^2 [/tex]
The center is (2, -1).
The radius is 4.
The Freshman class has 27 more boys than girls. If there are 283 freshman, how many are girls?
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283 = x + (x + 27)
Here, we are adding the number of girls with 27 more people than this amount of girls. This will allow us to add the number of girls, x, with the number of boys, x + 27, to get a total of 283.
This equation can be simplified if we add the like terms together: the x's.
So,
283 = 2x + 27.
Since this is a multi-step equation, we must use the reversed order of operations; undo addition first.
283 - 27 = 2x + 27 - 27
256 = 2x + 0
256 = 2x
Now, we must undo multiplication by dividing.
256/2 = 2x/2
128 = 1x
So, x, the number of girls, is equal to 128.
Hope this helps you! :)
triangle XYZ is obtuse which list could represent the angle measures of triangle XYZ?
A. 20 60 100
B. 30 60 90
C. 50 50 80
D. 60 60 60