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The polygon has a rectangle and a triangle
Area of triangle FSCW
= Length × width
= 9 × 2
= 18 square units
area of triangle FNS
= 1/2 × base× height
= 1/2 × 9 × 6
= 27 square units
Therefore the area of the polygon is
= 27 + 18
= 45 square units
Related Questions
The function f(x)= 2 x 5^x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function ?
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because to get the y coordinate of (2,50) we multiply the y coordinate of (1,10) by 5, similarly to get the y coordinate of (3,250) we multiply that of (2,50) by 5
i really need help please :)
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The basic idea is that you set your compass to have a distance somewhat greater than half the distance between the points you want to bisect. (Setting it to approximately their distance apart works pretty well.) Then you make arcs on either side of the line between the points.
Use the same compass setting to make arcs from both the points you want to bisect. The arcs should be drawn so they have points of intersection. The line between those intersection points is the bisector of the segment (and figure) between the given points.
That process of drawing the arcs and using a straightedge to connect their points of intersection constitutes the construction you are asked to do.
In (3), the point S is where your bisector crosses the given curve.
In (4), the two bisectors of AB and BC will be expected to cross each other at approximately the midpoint between A and C.
The volume of a rectangular box is found by multiplying its length, width, and height: V = lwh. A certain box has a volume of b 3 + 3b 2 - 4b - 12. Factor the four-term polynomial to find the dimensions of the box. Hint: Use factoring by grouping to factor the four term polynomial first.
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Answer:
The dimensions of the box are (b+3), (b-2) and (b+2).
Step-by-step explanation:
The volume of a rectangular box is
[tex]V=l\times w\times h[/tex]
The volume of a certain box is
[tex]V=b^3+3b^2-4b-12[/tex]
First of all find the factors of above expression by grouping method.
[tex]V=b^2(b+3)-4(b+3)[/tex]
[tex]V=(b+3)(b^2-4)[/tex]
[tex]V=(b+3)(b^2-2^2)[/tex]
[tex]V=(b+3)(b-2)(b+2)[/tex] [tex][\because a^2-b^2=(a+b)(a-b)][/tex]
Volume of a rectangle is the product of its dimensions, therefore the dimensions of the box are (b+3), (b-2) and (b+2).
Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5).
Write the equation of this cubic polynomial function.
Recall that the zeroes are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?
-5
The linear factors of the cubic are
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f(x) = k(x-2)(x-3)(x-5)
Use the y-intercept (0,-5) to solve for k.
-5 = k(0-2)(0-3)(0-5)
-5 = -30k
-5/-30 = k
1/6 = k
The cubic polynomial function is then ..
f(x) = (1/6)(x-2)(x-3)(x-5)
Linear factors are the linear (line) expressions you can factor out of the polynomial. They are (x-2), (x-3) and (x-5).
The cubic polynomial equation which passes through the coordinate (0,-5) and whose zeroes are (2 , 0), (3 , 0), and (5 , 0) is: [tex]y = \dfrac{1}{6}(x-2)(x-3)(x-5)[/tex] and it can be determine by arithmetic operations.
Given :
A cubic polynomial whose zeroes are (2 , 0), (3 , 0), and (5 , 0).Cubic polynomial equation passes through (0 , -5).Arithmetic operations can be used to determine the cubic polynomial equation. The generalised cubic polynomial equation is given by:
[tex]y = K(x-a)(x-b)(x-c)[/tex]
Where, K is constant and a, b, and c are the zeroes of the cubic polynomial equation. Therefore, the value of a, b, and c are 2, 3, and 5 respectively.
[tex]y = K(x-2)(x-3)(x-5)[/tex] ----- (1)
It is given that cubic polynomial equation passes through (0 , -5). So, put x = 0 and y = -5 in equation (1) to evaluate the value of K.
[tex]-5=K(0-2)(0-3)(0-5)[/tex]
[tex]5=30K[/tex]
[tex]K = \dfrac{1}{6}[/tex]
Therefore the cubic polynomial equation is given by:
[tex]y = \dfrac{1}{6}(x-2)(x-3)(x-5)[/tex]
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what is the product? 4k+2/k^2-4*k-2/2k+1
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Describe how you would estimate the square root of a number that is not a perfect square without using a calculator. lets say n was the imperfect square number and the square root is w. the square root of n = n+w squared/ 2w.
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√X =√S +(X-S)2√S
Where, X = the number you want the square roof of, and S is the closest square you know to x.
For example 75 is an imperfect square
Thus, X=75 and thus the nearest number S = 81, this ,means √81 =9.
Putting this into the formula;
√75= 9+(75-81)/2/2(9)
= 9 + -6/18
= 9-0.33333 = 8.667
= 8.667, thus the square root of 75 is 8.66
Select all that apply.
(xyz)2 = _____
The expression without exponents is?
xyz⋅xyz
x•x•y•y•z•z
x2 •y2 •z2
xy•xy•xy
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Answer:
xyz⋅xyz
x•x•y•y•z•z
Step-by-step explanation:
Select all that apply.
(xyz)2 = _____
The expression without exponents is?
xyz⋅xyz
x•x•y•y•z•z
x2 •y2 •z2
xy•xy•xy
Odyssey
What value of x makes the denominator of the function equal zero? y = 6/4x-40
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Perhaps you intend
.. y = 6/(4x -40)
Then x=10 will make the denominator zero.
Please help on these questions for 5 stars and brainliest!!
1. Suppose the equation of the axis of symmetry for a quadratic function is x = -3
and one of the x-intercepts is -8.
What is the other x-intercept?
2. If the equation of the axis of symmetry of a quadratic function is x = 0,
and one of the x-intercept is -4, what is the other x-intercept?
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===
x=0 is the y axis. So the other x intercept is a mirror image of x = - 4.
x = 4 is the other x value for the intercept.
(4,0) is the other intercept. <<==== answer.
One
===
Axis of symmetry is x = - 3
One of the intercepts is (- 8,0) That is 5 units to the left of (-3,0) so now yo much go 5 units to the right of (-3,0)
That will take you to -3 + 5 = 2
(2,0) is the other intercept <<<<< ===== answer.
A jar of dimes and quarters contains $15.25. there are 103 coins in all. how many quarters are in the jar?
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**HELP!**
El Generico public high school got a new flag pole. But they completely forgot to buy a cord and NO ONE knows how tall the flagpole is! To find out, they decided to use similar figures! As the sun was setting, Bob the janoitor set up a 5-foot stick next to the flagpole and compared shadows. The 5 foot stick cast an 8-foot shadow. The shadow of the flagpole was 32-feet long.
Use rules of similar polygons to figure out how tall the flagpole is! HINT: this will involve proportions!
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Thus, 8/32 =5/x
8x = 160
x = 20 feet
Therefore, the length of the flag pole was 20 feet long
Domingo works 40 hours per week as a tire store manager . If he made $29640 last year. how much he made per hour
A. $14.25
B. $16.50
C. $12.25
D.$11.00
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Domingo made $14.25 per hour last year by dividing his annual income of $29640 by the total hours worked in the year, which is 2080 hours (40 hours/week imes 52 weeks).
Explanation:To calculate how much Domingo made per hour, divide his annual income by the total number of hours worked in a year. Domingo works 40 hours per week, and there are 52 weeks in a year, so the total hours worked in a year is 40 hours/week imes 52 weeks/year = 2080 hours/year.
The formula to find the hourly wage is:
Hourly Wage = Annual Income / Total Hours Worked
Thus, Domingo's hourly wage would be:
$29640 / 2080 hours = $14.25 per hour.
Therefore, the correct answer is A. $14.25.
BRAINIEST WILL BE GIVEN------ University Law School accepts 2 out of every 15 applicants. If the school accepts 180 students, find how many applicants they received.
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2/15=180/x
cross multiply
180*15=2*x
2700=2x
x=1350
Step 1: Assign variable for the unknown that we need to find.
Let ' x ' be the number of applicants received by University Law School.
Step 2: Set up an equation based on the information given.
"University Law School accepts 2 out of every 15 applicants. If the school accepts 180 students, find how many applicants they received"
[tex] \frac{Accepted \; application}{Applied \; applicants} =\frac{2}{15} =\frac{180}{x} [/tex]
Step 3: Solving the equation
[tex] \frac{2}{15} =\frac{180}{x} \\ Cross \; Multiply\\ \\ 2x=15(180)\\ 2x=2700\\ Divide\; by\; 2\; on\; both\; sides\\ \\ \frac{2x}{2} =\frac{2700}{2} \\ Simplifying\; fraction\; on\; both\; sides\\ \\ x=1350 [/tex]
Conclusion:
The number of applicants received by University Law School is 1350.
If Chloe has $3,200 in weekly sales, she will earn more money with
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we know that
weekly sales------------> $3200
8% weekly sales--------> 0.08*3200=$256
Option 1---------> salary=$600 per week
Option 2---------> salary=$350+$256=$606 per week
Option 2> Option 1
then
she will earn more money with the option 2
the answer part A) is option 2
Part B)
If x represents Chloe’s weekly sales
equation option 1---------> 600
equation option 2---------> 350+0.08*x
the equation can be used to determine which option will benefit her the most is making the two options equal
600= 350+0.08*x
the answer Part B) is 600= 350+0.08*x
Part C)
she will earn more money with Option 1 when
600 > 350+0.08*x------------> (600-350) > 0.08*x-------> 250 > 0.08*x
250/0.08 > x------> 3125 > x---------> x < $3125
the answer Part C) is x < $3125
Sabastian is driving 400 miles to meet his friend. He travels 100 miles in the first two hours of his trip. If he continues at the same rate, how long will it take to drive the remaining distance?
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.. (300 mi)/(50 mi/h) = 6 h
A dad has two daughters – wendy and julia. wendy is twice as old as julia. the man is now five times as old as wendy, and in 4 years he will be six times as old as julia. find the present age of the father.
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2x = age of Wendy
10x = age of dad (because dad is five times as old as Wendy)
(x+4)*6=10x+4 (because in four years, that's why I added 4 to both sides, dad's age will be now 10x+4 and Julia's age x+4, now dad is 6 times as old and I multiplied Julia's age by six) ==> 6x+24=10x+4, now subtract 4 from both sides:
6x+20=10x, let's subtract 6x from both sides
20=4x ==> x=5
because age of father is 10x, we substitute x value and we get
10*5=50
Answer: 50
Step-by-step explanation:
The volume of the cylinder is 392 cm cubed work out the length
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B • h = Pi r ^2 • h = 392 cm^3.
H = 392/Pi r^2.
This is the height or length.
Write a complete sentence that states the type of transformation that was performed and explains the transformation in detail. Quadrilateral EFGH is the image.
ABCD A(-4,-1)B(-1,-4)C(-2,-8)D(-5,-4)
EFGH
E(0,-6)F(3,-9)G(2,-13)H(-1,-9)
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the equation for the translation mentioned is;
T4, -5(x,y)
this means that every point in the image has moved down by 5 units and moved to the right by 4 units.
Point A to Point E
Point A - (-4,-1)
after translation (x+4, y-5) = (-4+4,-1-5)
= (0,-6) these are the coordinates of point E.
the other three points too have moved the same distance and direction as point A did.
which definitions or properties would you use to simplify the expression
[tex]( {4}^{8} \times {4}^{ - 4} {)}^{ - 2} [/tex]
explain
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Exponent Addition: a^b * a^c = a^(b + c)
Exponent Multiplication: (a^ d) ^ e = a ^ (d * e)
Multiplication of 4^8 * 4^(-4) is the same as adding exponents together:
4^(8 - 4)
Which makes the expression simplify to (4^4). This expression is now to another exponent which is equivalent to multiplying exponents together:
(4^4)^-2 = 4^ (4 * -2) = 4 ^ -8
The expression has been reduced to its simplest form.
A rectangular prism has a length of 212 centimeters, a width of 212 centimeters, and a height of 5 centimeters. Justin has a storage container for the prism that has a volume of 35 cubic centimeters. What is the difference between the volume of the prism and the volume of the storage container?
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We have then:
V = (l) * (w) * (h)
Where,
l: long
w: width
h: height
Substituting the values we have:
V = (2 1/2) * (2 1/2) * (5)
V = 31.25 cm ^ 3
The difference between the container and the prism is:
35-31.25 = 3.75 cm ^ 3
Answer:
the difference between the volume of the prism and the volume of the storage container is:
3.75 cm ^ 3
.help me please thank you.
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A bag contains 3 red marbles and 4 blue marbles.A marble is taken out from the bag and replaced. Another marble is taken from the bag. Work out the probability that the two marbles taken from the bag are the same colour.
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Total number of marbles in the bag is 3 + 4 = 7.The problem asks for the probability of (RR) or (BB).It's worthy to note we are replacing the balls after each draw, which means we always have 7 to draw fromSince each draw is independent, we take the product of each event for the total event probability.
P(RR) = 3/7 * 3/7 = 9/49
P(BB) = 4/7 * 4/7 = 16/49
We want to know P(RR) + P(BB)
P(RR) + P(BB) = 9/49 + 16/49 = 25/49
Explain why 0.04 divided by 3.6 has the same answer as 4 divided by 360
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Hope that helped
Can someone help me with this please!!
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1. Okay, so there are 3 terms in the polynomial, which makes it a trinomial. That eliminates A, C, and D, because those answers do not say trinomials. The degree in the trinomial is 2, because that's the highest exponent in any of the terms. That is a quadratic trinomial. The answer is B.
2. Alright. So like the previous question, there are 3 terms in the polynomial. That eliminates answer choices C and D. The degree is 3, which makes it cubic. This is a cubic trinomial. The answer is A.
3. The degree is as stated above, the highest exponent in the polynomial out of the terms. 2 and 4 are not the degrees in this polynomial, so those answers are crossed out. It seems like the degree is 5. However, there is a monomial where two exponent amounts are together. In this case, we will combine the exponents by adding. 2 + 4 is 6. There. The degree is 6. The answer is D.
Note: Keep in mind that linear is where the highest degree is 1, quadratic is where the highest degree si 2, cubic is where the highest degree is 3, quartic is where the highest degree is 4, quintic is where the highest degree is 5. Quadratic and Quartic are not the same, and are easy to get mixed up due to the spelling. Be careful not to make an error on which is which, when it comes to those two.
The sales tax in New York is 8.25%. About how much will a $65.95 of shoes cost, including sales tax? A) $84 B)$7 C)$73 D)$59
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The shoes would cost about $73.
Leyla drops a penny from a height of 150m.
How long will it take for the penny to hit the ground? Round to the nearest tenth of a second.
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https://brainly.com/question/9071599
Answer:
5.5
Step-by-step explanation:
3.8 is misinformation
Lou Harris is guaranteed a minimum $275 weekly salary plus 5.25% of his total sales. What were his total sales for a week in which his gross pay was $700?
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let's say "x" is the total amount for the sales, namely the 100%, but we also know that 5.25% of that is 425, the leftover from the 700 bucks minus his salary, what is "x" anyway?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 425&5.25 \end{array}\implies \cfrac{x}{425}=\cfrac{100}{5.25}\implies x=\cfrac{425\cdot 100}{5.25}[/tex]
find p(-3) and p(5) for the function p(x)=4x^4+8x^3-2x^2+13x+10
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.. p(-3) = 61
.. p(5) = 3525
Please help !! Thank you :)
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.. (x, y) = (-√2, √2)
This does not match any of the offered choices.
If Rachel starts 2 mi NE of her house, then selection D is appropriate.
Anna started a race at 9:30am. She ran for 3 hours and 47 minutes. What time did she finish her race?
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9:03+3h47=12h50
so the race ends at 12h50 (noon)
The solution is, the race ends at 12h50 (noon)
What is addition?It can be stated as, Addition is a way of combining things and counting them together as one large group.We know that, Addition in math is a process of combining two or more numbers.
here, we have,
Anna started a race at 9:30am. She ran for 3 hours and 47 minutes.
so we know the time she start and how many time the race was so let's add them together to get the end time
now,
9:03+3h47
=12h50
so the race ends at 12h50 (noon)
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