Find the perimeter and the area of the polygon with the given vertices. J (1,2), K (7,2), L (7,8), M (1,8)
Answers
recall, the perimeter is all sides summed up, and the area is just length * width.
Answer : The perimeter and the area of the polygon with the given vertices is, 24 unit and 36 unit² respectively.
Step-by-step explanation :
First we have to calculate the distance of JK, KL, LM and MJ.
Using distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where,
d = distance between the two coordinates
x and y are the coordinates.
To calculate the distance of JK:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(7-1)^2+(2-2)^2}[/tex]
[tex]d=\sqrt{(6)^2+(0)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of KL:
[tex]d=\sqrt{(x_3-x_2)^2+(y_3-y_2)^2}[/tex]
[tex]d=\sqrt{(7-7)^2+(8-2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(6)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of LM:
[tex]d=\sqrt{(x_4-x_3)^2+(y_4-y_3)^2}[/tex]
[tex]d=\sqrt{(1-7)^2+(8-8)^2}[/tex]
[tex]d=\sqrt{(-6)^2+(0)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of MJ:
[tex]d=\sqrt{(x_4-x_1)^2+(y_4-y_1)^2}[/tex]
[tex]d=\sqrt{(1-1)^2+(8-2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(6)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
The distance of JK, KL, LM and MJ is, 6, 6, 6 and 6.
Now we have to calculate the perimeter of the polygon.
Perimeter of polygon = JK + KL + LM + MJ
Perimeter of polygon = 6 + 6 + 6 + 6
Perimeter of polygon = 24 unit.
Now we have to calculate the area of polygon.
As the distance between the coordinates are equal that means the geometry will be square because in square the all four sides are equal.
Now we have to calculate the area of polygon by using area of square formula.
Area of polygon = Area of square = (side)²
Given: Side = 6
Area of polygon = Area of square = (6)²
Area of polygon = Area of square = 36 unit²
Thus, the area of polygon is, 36 unit²
Related Questions
A scout troop planned to take a bus for an overnight trip to a campground in a nearby state. The bus will cost $360 to rent. The bus company told them that if they could get 3 more troop members to join in the trip each person could pay $6 less to go on the trip. If the troop was able to find the 3 additional people to join the trip, which answer is the most reasonable for the number of members that went on the trip?
Answers
.. 360/x -6 = 360/(x +3)
.. 360*(x +3) -6x(x +3) = 360x . . . . . multiply by the product of denominators
.. 360x +1080 -6x^2 -18x = 360x
.. x^2 +3x -180 = 0
.. (x +15)(x -12) = 0
Solutions are x = {-15, 12}
12 members went on the trip.
_____
The problem wording does not make clear whether the original number (12) or the number suggested by the bus company (15) went on the trip. It would be most reasonable for 15 to go, if the troop had people who were willing.
Which equation is quadratic in form 2(x+5)^2+8x+5+6=0, x^6+6x^4+8=0, 7x^6+36x^3+5=0, 4x^9+20x^3+25=0?
Answers
Equation 2(x+5)² + 8x + 5 + 6 = 0 or 2x² + 28x + 61 = 0 is the equation in quadratic form.
What is a quadratic equation?A quadratic equation is an equation of second order. Quad implies the square power, it is also called equation of degree 2.
The standard form of a quadratic equation is ax² + bx + c = 0.
Where a, b and c are constants.
In the given equation,
2(x+5)² + 8x + 5 + 6 = 0
2 (x² + 25 + 10x) + 8x + 11 = 0
2x² + 50 + 20x + 8x + 11 = 0
2x² + 28x + 61 = 0
This is the quadratic equation.
Rest of the equation are in the higher degree power, only equation 2x² + 28x + 61 = 0 is second power equation.
Hence, 2x² + 28x + 61 = 0 is a quadratic equation.
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Joaquim is baking giant cookies for the school bake sale. They will be sold for $20 for one large cookie or $20 for three small cookies. Which offer is the better buy? Explain your reasoning.
Answers
Because sure the large is bigger but you get more with the small cookies
Three small cookies for $20 is a better buy than one large cookie for $20 because the cost per small cookie is cheaper ($6.67 per small cookie). You get more cookies for the same price.
To determine which offer is the better buy, let's compare the cost in terms of cookies:
One large cookie: $20 for 1 large cookie.Three small cookies: $20 for 3 small cookies.Next, let's find the cost per small cookie:
For the large cookie: $20 / 1 large cookie = $20 per large cookie.For the small cookies: $20 / 3 small cookies = $6.67 per small cookie (approximately).Therefore, since $6.67 per small cookie is less than $20 for 1 large cookie, the offer of three small cookies for $20 is the better buy. This way, you get three cookies for the same price as one large cookie.
∆ABC has side lengths of 10 units, 20 units, and 24 units. ∆XYZ is similar to ∆ABC, and the length of its longest side is 60 units. The perimeter of ∆XYZ is units. If the height of ∆ABC, with respect to its longest side being the base, is 8 units, the area of ∆XYZ is square units. NextReset
Answers
Final answer:
The perimeter of ΔXYZ is 25 units and the area of ΔXYZ is 40 square units.
Explanation:
In this problem, we are given that ΔABC has side lengths of 10 units, 20 units, and 24 units, and ΔXYZ is similar to ΔABC. We are also given the length of the longest side of ΔXYZ as 60 units. To find the perimeter of ΔXYZ, we need to add up the lengths of all its sides. Since the longest side of ΔABC is 24 units, and the longest side of ΔXYZ is 60 units, we can set up the following proportion:
24/10 = 60/x
Cross-multiplying gives us:
24x = 600
x = 600/24 = 25 units
Therefore, the perimeter of ΔXYZ is 25 units.
Now, to find the area of ΔXYZ, we can use the proportional relationship between the areas of similar triangles. Since the ratio of the longest sides is 60/24 = 5/2, the ratio of the areas will be (5/2)^2 = 25/4. Since the area of ΔABC is 1/2 times the base times the height, we can use the same formula for ΔXYZ with the corresponding measurements:
Area of ΔXYZ = (1/2) * 10 * 8 = 40 square units
Substitute
-3x-8y=4
-2x+7y=15
Answers
x=-7.5+3.5y
-3x-8y=4
-3(7.5+3.5y)-8y=4
-22.5-10.5y-8y=4
-22.5-18.5y=4
-18.5y=4+22.5
-18.5y=26.5
y=-53/35
the fraction might not be in lowest terms.
The product of x and 8 is less than or equal to 19
Answers
Which table of ordered pairs represents a proportional relationship
Answers
Answer:
The second table.Step-by-step explanation:
In this case, "a proportional relationship" refers to the presence of a constant of variation between variables, that is, variables must variate at the same rate, where such rate is call the constant of proportionality.
Notice that the second table fulfils this definion, because x-variable variates 2 units, while y-variable variates ten units. To find the constant of proportionality, we just need to divide
[tex]k=\frac{10}{2}=5[/tex]
Which means that y-variable represents five times x-variable, let's evalute to prove this
[tex]2 \times 5=10\\4 \times 5 = 20\\6 \times = 30[/tex]
Notice that we got all y-values.
Therefore, the right table is the second one, it presents a proportional relationship.
A certain species of tree grows an average of 3.1 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 400 centimeters tall.
Answers
Answer:
h = 400 + 3.1(n - 1)
Step-by-step explanation:
this is an arithmetic sequence so instead the answer would be
h = 400 + 3.1(n - 1)
where h is the height of the tree after n weeks
Solve.
0 = x² + 8x + 15
Enter your answers in the boxes.
The solutions are _____
and _____.
Answers
(x+5)(x+3)=0
The solutions are -3 and -5.
For this case we have the following polynomial:
[tex] 0 = x ^ 2 + 8x + 15
[/tex]
We can rewrite the polynomial by factoring the expression.
We have then:
[tex] (x + 3) (x + 5) = 0
[/tex]
From here, we look for the solutions of the polynomial.
We have then:
Solution 1:
[tex] x + 3 = 0
x = -3
[/tex]
Solution 2:
[tex] x + 5 = 0
x = -5
[/tex]
Answer:
The solutions of the polynomial are given by:
[tex] x = -3
x = -5 [/tex]
A grid map marks the plot of Harold’s garden in meters. The coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5). He wants to build a short fence around the garden. The perimeter of his garden is meters.
Answers
Answer:
46, i did the assignment on edge hope this helps! :)
Step-by-step explanation:
On a coordinate plane, quadrilateral D G A R is shown. Point G is at (negative 8, 3), point A is (4, 8), point R is at (10, 0), and point (negative 2, negative 5).
A grid map marks the plot of Harold’s garden in meters. The coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5). He wants to build a short fence around the garden.
The perimeter of his garden is meters. 46
The Perimeter of garden as shown in the quadrilateral 46 units
Distance
The distance between two points is the amount of space between the points. From the quadrilateral:
[tex]AG=\sqrt{(8-3)^2+(4-(-8))^2}=13 \ units\\\\AR=\sqrt{(8-0)^2+(4-10)^2}=10 \ units\\\\GD=\sqrt{(-5-3)^2+(-2-(-8))^2}=10 \ units\\\\RD=\sqrt{(-5-0)^2+(-2-10)^2}=13 \ units\\[/tex]
Perimeter of garden = AG + AR + GD + RD = 13 + 10 + 13 + 10 = 46 units
The Perimeter of garden as shown in the quadrilateral 46 units
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The ratio of the measures of the sides of a triangle is 9:15:5. If the perimeter of the triangle is 130 feet, find the measures of the sides.
Answers
29x = 130
x = 4.4827586207
So the triangle sides =
22.4137931034
40.3448275862
67.2413793103
whats the value of x??im really confused i thought it was 7 but that doesnt make sense can someone please help me!!!
Answers
16x -12 = 180
16x = 192
x = 192/16
x = 12
meaning they both add up to 180 because they are on a straight line
To solve:
(10x - 20) + (6x + 8) = 180
combine like terms
(10x + 6x ) + (-20 + 8) = 180
16x - 12 = 180
add 12 to both sides
16x = 192
divide both sides by 16
x = 12
To solve for the angles, you would just take x and plug it into the angle and solve XD
Hope this helps
The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (–3) = 6, find the absolute maximum value of f (x) over the interval [–3, 0].
Graph of line segments increasing from x equals negative 4 to x equals negative 3, decreasing from x equals negative 3 to x equals 0, increasing from x equals 0 to x equals 3, constant from x equals 2 to x equals 4 and decreases from x equals 4 to x equals 5. x intercepts at x equals negative 4, x equals 0, x equals 5.
3
4.5
6
10.5
Answers
Answer
10.5
Step-by-step explanation:
The other answer is correct until solving for C. f(-3) = 6, not -6. So C = 21/2. This makes f(0) = 10.5. Local Max should occur at x intercepts on the f'(x) graph.
Answer: 10.5
Step-by-step explanation: The other answer is correct until solving for C. f(-3) = 6, not -6. So C = 21/2. This makes f(0) = 10.5. Local Max should occur at x intercepts on the f'(x) graph. A fraction is a number that shows how many equal parts there are. When we write fractions, we show one number with a line above (or a slash next to) another number. For example, 14, 1⁄4 and 1/4.are different ways of writing the same fraction (in this case a quarter). The top number tells us how many parts there are, and the bottom number tells us the total number of parts. The top part of the fraction is called a numerator. The bottom part of the fraction is called a denominator. For example, for the fraction 14 the 1 is the numerator, and the 4 is the denominator.
SIMPLIFY the radical expression: square root of 75 + square root of 3
Answers
what is 9^21 can somebody please help me
Answers
9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9=
1.09418989e20 is the answer.
Decimal Form: 1.09418989 * [tex] 10^{20} [/tex]
4x-7+7x=3x-1
Please help hurry for crutal test.
Answers
4x-7+7x=3x-1
Combine like terms.
11x-7=3x-1
Add 7 to both sides.
11x= 3x+6
Subtract 3x on both sides.
8x=6
Divide 8 into both sides.
x=6/8 or 3/4. (.75)
I hope this helps!
~kaikers
The solution to the equation is [tex]x = \frac{3}{4}[/tex] .
We start by rewriting the equation:
4x-7+7x=3x-1
Combine the x terms on the left side:
11x - 7 = 3x - 1
Isolate the x terms on one side of the equation. To do this, we’ll move the 3x term from the right side to the left side by subtracting 3x from both sides:
11x - 3x - 7 = -1
Simplify:
8x - 7 = -1
Add 7 to both sides to get rid of the constant term on the left side:
8x = 6
Divide both sides by 8 to find the value of x:
[tex]x = \frac{6}{8} = \frac{3}{4}[/tex]
Therefore, the solution to the equation is [tex]x = \frac{3}{4}[/tex] .
PLEASE HELP
7.01
1. Find the first six terms of the sequence.
a1 = 4, an = an-1 + 8
A) 0, 8, 16, 24, 32, 40
B) 12, 20, 28, 36, 44, 52
C) 4, 12, 20, 28, 36, 44
D) 4, 8, 16, 24, 32, 40
2. Find the first six terms of the sequence.
a1 = -8, an = 5 an-1
A) -8, -40, -200, -1000, -5000, -25,000
B) -8, -40, -35, -30, -25, -20
C) 0, 5, -40, -35, -30, -25
D) -40, -200, -1000, -5000, -25,000, -125,000
3. Find an equation for the nth term of the arithmetic sequence.
8, 6, 4, 2, ...
A) an = 8 + -2(n)
B) an = 8 - 2
C) an = 8 + -2(n + 1)
D) an = 8 + -2(n - 1)
4. Find an equation for the nth term of the arithmetic sequence.
-17, -12, -7, -2, ...
A) an = -17 + 5(n + 2)
B) an = -17 + 5(n + 1)
C) an = -17 + 5(n - 1)
D) an = -17 x 5(n - 1)
5. Find an equation for the nth term of the arithmetic sequence.
a19 = -58, a21 = -164
A) an = 896 - 53(n - 2)
B) an = 896 - 53(n - 1)
C) an = 896 + 53(n + 1)
D) an = 896 - 53(n + 1)
6. A certain species of tree grows an average of 0.5 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall.
Answers
For this case, the first thing you should do is replace the values given one by one.
We have then:
a1 = 4
a2 = a1 + 8 = 4 + 8 = 12
a3 = a2 + 8 = 12 + 8 = 20
a4 = a3 + 8 = 20 + 8 = 28
a5 = a4 + 8 = 28 + 8 = 36
a6 = a5 + 8 = 36 + 8 = 44
Answer:
C) 4, 12, 20, 28, 36, 44
2. Find the first six terms of the sequence.
a1 = -8, an = 5 an-1
For this case, the first thing you should do is replace the values given one by one.
We have then:
a1 = -8,
a2 = 5 ^ (- 8) = -40
a3 = 5 ^ (- 40) = -200
a4 = 5 ^ (- 200) = -1000
a5 = 5 ^ (- 1000) = -5000
a6 = 5 ^ (- 5000) = -25000
answer:
A) -8, -40, -200, -1000, -5000, -25,000
3. Find an equation for the nth term of the arithmetic sequence.
8, 6, 4, 2, ...
What you must do for this case is to verify which sequence is best suited to the problem.
For this case we have:
8, 6, 4, 2,
The sequence is:
an = 8 + -2 (n - 1)
a1 = 8 + -2 (1 - 1) = 8
a2 = 8 + -2 (2 - 1) = 6
Answer:
An equation for the nth term of the arithmetic sequence is
D) an = 8 + -2 (n - 1)
4. Find an equation for the nth term of the arithmetic sequence.
-17, -12, -7, -2, ...
What you must do for this case is to verify which sequence is best suited to the problem.
For this case we have:
-17, -12, -7, -2,
The sequence is:
an = -17 + 5 (n - 1)
a1 = -17 + 5 (1 - 1) = - 17
a2 = -17 + 5 (2 - 1) = - 12
Answer:
Answer:
An equation for the nth term of the arithmetic sequence is
C) an = -17 + 5 (n - 1)
5. Find an equation for the nth term of the arithmetic sequence.
a19 = -58, a21 = -164
What you must do for this case is to verify which sequence is best suited to the problem.
For this case we have:
a19 = -58, a21 = -164
The sequence is:
an = 896 - 53 (n - 1)
a19 = 896 - 53 (19 - 1) = - 58
a21 = 896 - 53 (21 - 1) = - 164
Answer:
An equation for the nth term of the arithmetic sequence is
B) an = 896 - 53 (n - 1)
6. A certain species of tree grows an average of 0.5 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall.
For this case, what you should do is to write the equation step by step to find the correct result.
We have then:
the measurements begin when the tree is 200 centimeters tall
200
tree grows an average of 0.5 cm per week
200 + 0.5n
Where
n: number of weeks.
answer:
An equation for the sequence that represents the weekly height of this tree in centimeters is
an = 200 + 0.5n
The answers identified are: (C) for the first sequence question, (A) for the second sequence question, (D) for the arithmetic sequence with a start of 8 and difference -2, (C) for the arithmetic sequence starting from -17, (B) for the arithmetic sequence question with given a19 and a21, and finally an = 200 + 0.5n for the tree growth question.
Explanation:The correct answers are as follows:
For the first question, you start with 4 (a1 = 4) and each subsequent term is the previous term plus 8 (an = an-1 + 8). This gives the sequence 4, 12, 20, 28, 36, 44, which matches option (C).For the second question, starting at -8 (a1 = -8) and then multiplying the previous term by 5 gives you -8, -40, -200, -1000, -5000, -25,000, which matches option (A).For the third question, the common difference between consecutive terms is -2 and the first term is 8, which gives an = 8 - 2(n - 1) (option D)For the fourth question, the common difference is +5 and the first term is -17, so the equation for the nth term is an = -17 + 5(n - 1) (option C). For the fifth question, the common difference can be calculated from the problem as 53. Hence the equation for the nth term is an = 896 - 53(n - 1) (option B).For the last question, if the tree grows at a rate of 0.5 cm per week and the initial height is 200 cm, the height of the tree each week is represented by an = 200 + 0.5n.Learn more about Arithmetic Sequences here:https://brainly.com/question/35880655
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Which of the following is equal to the expression below?
(160 * 243)^1/5
A. [tex] 6 \sqrt[5]{5} [/tex]
B.96
C.80
D.5[tex] 5 \sqrt[5]{5}
[/tex]
Answers
(160 * 243)^1/5
To simplify the above expression first step is to factor the numbers. Therefore,
[tex] (160*243)^{\frac{1}{5}} = ((2*2*2*2*2*5)*)(3*3*3*3*3)^{\frac{1}{5}} [/tex]
=[tex] (2^5*5*3^5)^{\frac{1}{5}} [/tex]
= [tex] (2^5)^{\frac{1}{5}} *(5)^{\frac{1}{5}} *(3^5)^{\frac{1}{5}} [/tex]
=[tex] 2 * (5)^{\frac{1}{5}} *3 [/tex]
= [tex] 6*(5)^{\frac{1}{5}} [/tex]
= [tex] 6\sqrt[5]{5} [/tex]
So, correct choice is A.
Use the diagram of g | | h, with transversal f, to answer the questions.
A pair of corresponding angles is
a. angle 1 and angle 3
b. angle 4 and 2
c.angle 4 and angle 8
Angle 2 is blank angle 8.
a. greater than
b. less than
c. congruent to
A pair of same-side interior angles is......
a. angle 2 and angle 5
b. angle 4 and angle 7
c. angle 5 and angle 7
Answers
Answer:
1) Angle 4 and angle 8.
2) c. Congruent to.
3) a. Angle 2 and angle 5.
Step-by-step explanation:
1) When a transversal cuts the shown parallel lines, the angles that are in the same relative position are call correponding angles.
2) Angle 2 and 8 are Alternal internal angles, therefore they are congruent.
3) Angle 2 and angle 5 are on one side of the transversal, therefore, they are same-side interior angles.
559 tickets were sold 59 more student tickets were sold than adult tickets how many adult tickets were sold
Answers
We have the equation: s + a = 559 and s = 59 + a;
Then, we solve the equation: 59 + a + a = 559;
59 + 2a = 559;
2a = 500;
a = 500/2;
a = 250;
s = 59 + 250;
s = 309;
The number of adult tickets sold will be 250.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Suppose the number of student tickets is S while adult tickets are A.
As per the given,
59 more student tickets were sold than adult tickets.
S = A + 59
S - A = 59
Total tickets S + A = 559
Add both equations as
S - A + S + A = 559 + 59
2S = 618
S = 309
A = 309 - 59 = 250
Hence "The number of adult tickets sold will be 250".
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Write the equation of a circle with a center at (15, –35) and a diameter of 100.
(x – 15)2 + (y + 35)2 = 250
(x – 15)2 + (y + 35)2 = 50
(x – 15)2 + (y + 35)2 = 2500
(x – 15)2 + (y + 35)2 = 100
Answers
Show that all of the powers in the prime-power factorization of an integer n are even if and only if n is a perfect square
Answers
An airplane has a maximum capacity of 118 passengers. The flight attendant has loaded 40 passengers. Which inequality represents the solution set that shows the number of passengers, p, that can still load the plane? A) p ≥ 68 B) p ≤ 68 C) p ≤ 78 D) p ≥ 78
Answers
Answer:
Its C
Step-by-step explanation:
It is C because you can only load 78 more passengers
Answer:
c
Step-by-step explanation:
If p = the number of passengers that can still load the plane, then p + 40 ≤ 118.
Therefore,
p + 40 ≤ 118
p + 40 − 40 ≤ 118 − 40
p ≤ 78
If you have 240 homies and the Crips rolls up on your block poppin 128 of yo homies, how many homies do ya got left?
Answers
Answer:
You'll have 112 blood homies left
240b-128b=112b
112
In 2008 Melvin thought that he was making a sound investment by buying $100,000 worth of Alpha Biotechnology stock. Unfortunately, his investment has depreciated, losing 13% of its current value each year.
Answers
current value in percent=100-13=87%
The value of $100,000 investment will be:
87/100*100000
=$87,000
Given this proportion, what ratio completes the equivilent proportion a/8?
[tex] \frac{a}{b}= \frac{8}{15} [/tex]
Please show your work so that I know how to do this.
Answers
You have a/b=8/15, Then:
1. You must divide in both side of the given proportion by 8:
a/bx8=8/15x8
2. When you simplify, you obtain:
a/8b=1/15
3. Now, you must multiply both sides by "b", as below:
axb/8b=1xb/15
4. Finally, when you simplify, you have:
a/8=b/15
if a circle has a diameter of 24 inches, which expression gives its area in square inches?
Answers
Divide 24 by 2 to get the radius or r.
12 squared by pi or 2.14
12 squared = 144
144 times 2.14 = the area
A = 452.39
The main arena hall has dimensions 200 m by 85 m. On a large diagram on the office wall the scale is 1:40. What are the dimensions of the floor space on the diagram?
Answers
Answer:
500 cm by 212.5 cm
Step-by-step explanation:
Using the scale 1:40 on the 200 m dimension, we have 200/40 = 5 m. Each meter is 100 cm; this makes this 5(100) = 500 cm.
Using the scale on the 85 m dimension, we have 85/40 = 2.125 m. Each meter is 100 cm; this makes this 2.125(100) = 212.5 cm.
Answer:
500 cm by 212.5 cm
Step-by-step explanation:
Given :
The main arena hall has dimensions 200 m by 85 m.
On a large diagram on the office wall the scale is 1:40.
To Find: What are the dimensions of the floor space
Solution :
Length of arena hall = 200 m
Scale is 1:40
So, the length of the floor = [tex]\frac{200\times 1}{40}[/tex]
= [tex]5m[/tex]
Since 1 m = 100 cm
So, 5 m = 100*5 = 500 cm
Width of arena hall = 85 m
So, width of floor = [tex]\frac{85\times 1}{40}[/tex]
= [tex]2.125m[/tex]
Now 1 m = 100 cm
So, 2.125 m = 212.5 cm
Thus the dimensions of floor is 500 cm by 212.5 cm
What is the solution to the equation g(x) = 3?
x = 3
3 < x < 5
3 ≤ x ≤ 4
3 ≤ x < 5
Answers
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Given the geometric sequence where a_1 = 3 and r = √2 find a_9
A.] 48
B.] 48√2
C.] 64
D.] 64√2
Answers
where:
[tex]a_{n} [/tex] is the term we are looking for
[tex]a _{1} [/tex] is the first term
[tex]r[/tex] is the ratio
[tex]n[/tex] is the position of the number in the sequence
From the question we now that [tex]a _{1} =3[/tex], [tex]r= \sqrt{2} [/tex], and [tex]n=9[/tex]. Lets replace those values into our formula to get:
[tex]a _{9} =3( \sqrt{2} )^{9-1} [/tex]
[tex]a_{9} =3 \sqrt{2} ^{8} [/tex]
[tex]a_{9} =48[/tex]
We can conclude that in our geometric sequence [tex]a_{9} =48[/tex]; therefore, the answer is A.