What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)?
Answers
Answer:
The perimeter of the polygon is 22.
Step-by-step explanation:
Let [tex]A(x,y) =(-3,1)[/tex], [tex]B(x,y) = (5,1)[/tex], [tex]C(x,y) = (-3, 4)[/tex] and [tex]D(x,y) =(5,4)[/tex] the vertices of the polygon. From Geometry we know that number of side of polygons equals their number of vertices, then we notice that a quadrilateral is here. In addition, we conclude that such quadrilateral is a rectangle:
1) [tex]x_{A} = x_{C}[/tex]
2) [tex]x_{B} = x_{D}[/tex]
3) [tex]y_{A} = y_{B}[/tex]
4) [tex]y_{C} = y_{D}[/tex]
Hence, we find that [tex]AB = CD[/tex] and [tex]AC = BD[/tex].
Then we find all lengths of the rectangle by Pythagorean Theorem:
[tex]AB = \sqrt{[5-(-3)]^{2}+(1-1)^{2}}[/tex]
[tex]AB =8[/tex]
[tex]AC = \sqrt{[(-3)-(-3)]^{2}+(4-1)^{2}}[/tex]
[tex]AC = 3[/tex]
By Geometry, we conclude that [tex]CD = 8[/tex] and [tex]BD = 3[/tex].
Then, the perimeter of the rectangle ([tex]p[/tex]), dimensionless, is defined by the following formula:
[tex]p = 2\cdot (s+l)[/tex] (Eq. 1)
Where:
[tex]s[/tex] - Shortest length, dimensionless.
[tex]l[/tex] - Longest length, dimensionless.
If we know that [tex]s = 3[/tex] and [tex]l = 8[/tex], then the perimeter of the rectangle is:
[tex]p = 2\cdot (3+8)[/tex]
[tex]p = 22[/tex]
The perimeter of the polygon is 22.
Related Questions
plzzzz help meeeeeeeeeeee
Answers
Answer:
The one on the left is your anwsers
Step-by-step explanation:
hey babies , help me pleaseee
Answers
Answer:
F can be at 19 or -5
Step-by-step explanation:
If F is on positive number line, F-E=12
F=12+7=19
If F is on negative number line, E-F=12
-F=12-7=5, F=-5
What is the solution: 5x + 17 = 3x + 53
Answers
Answer:
x=18
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
-3, square root of 31, square root of 11, 5.5, and -60/11 in least to greatest.
I already made a question about it, but it wont let me see the answer and i have no idea how to do it :(
Answers
Answer:
I think is a apple and stuff
Step-by-step explanation:
carrot
solve the equation
y=x²-2x-24
Answers
Answer:
when y is equal to 0
X will be equal to 6 & -4
[tex]5x + 15 \leqslant - 10 [/tex]
help me please.
Answers
Step-by-step explanation:
[tex]5x + 15 \leqslant - 10 \\ 5x \leqslant - 10 - 15 \\ 5x \leqslant - 25 \\ x \leqslant - 25 \div 5 \\ x \leqslant - 5[/tex]
how many foods need a rest time
Answers
Answer:
larger meats
Step-by-step explanation:
depends how long and howuch they weigh
Is my work right? Please tell me I’ll give brainliest !!!
Answers
Answer:
Yes Your Work Is correct.
James King
Hope This Helped
Have A Great Day
Answer:
it looks good to me!?
and your hand writing is amazing
Step-by-step explanation:
Veronica family is getting ready for a huge go cart race they only bought 15 gallons of gasoline though if each car needs 2 and 1/5 gallons of gas how many go carts can Be filled for the race
Answers
Hi! I believe your answer is 6 go-carts because 15 gallons divided by 2 and 1/5 gallons is 6 go-carts. I hope this helps you! Good luck and have a great day. ❤️
Simplify 5x +7 + 4(2x + 3)
Answers
Answer:
13x+19
Step-by-step explanation:
At president bushs inauguration in 2005 the news paper headlines stated there were about 400,000 people in attendance. If the newspaper rounded to the nearest ten thousand, what is the largest number and smallest number of people who could have been there
Answers
Answer: Largest = 404999
Smallest = 395,000.
Step-by-step explanation:
Given data:
Number of people in attendance = 400,000
Solution:
If we were to round off to the nearest ten thousand the greatest number we can get would be = 404999.
And following the same principle the smallest number we would be able to get would be = 395000
Therefore, the largest number of people who could have attended the inauguration would be 404999.
And the smallest number of people who could have attended would be 395000.
What is the slope of a line perpendicular to the line whose equation is
x + 2y = -14. Fully reduce your answer.
Answers
Answer:
Step-by-step explanation:
2
PLZ HELP I REALLY NEED IT FAST
what is 786 700 000 in scientific notation
Answers
Answer: 7.867 x 10^8
Step-by-step explanation:move the decimal forward and how many times you moved it is your exponent
You are given a 14 inch by 8 inch rectangular sheet of metal from which you are to construct a box. You are to cut a length, x, from each corner of the sheet of metal so that you can fold up the sides creating a box. Find the value of x that will yield the maximum volume of the box. Round your solution to the nearest hundredth.
Answers
Answer:
x = 1.639 in
Step-by-step explanation:
With these instructions, the length of the box would be (14-2x), the width would be (8-2x), and the height would be x, so the equation for volume would be width*length*height, or
[tex]V=(14-2x)(8-2x)(x)[/tex]
[tex]V=4x^3-44x^2+112[/tex]
Now we solve for dV/dx because we want to find maximum volume
[tex]\frac{dV}{dx} =12x^2-88x+112[/tex]
[tex]\frac{dV}{dx} =4(3x^2-22x+28)[/tex]
Now we let dV/dx equal zero to find critical values
[tex]0=4(3x^2-22x+28)[/tex]
[tex]0=3x^2-22x+28[/tex]
[tex]x=\frac{11+\sqrt{37} }{3}[/tex], [tex]x=\frac{11-\sqrt{37} }{3}[/tex]
Now we see where dV/dx changes signs:
dV/dx changes from positive to negative at [tex]\frac{11-\sqrt{37} }{3}[/tex]
and from negative to positive at [tex]\frac{11+\sqrt{37} }{3}[/tex]
so V(x) has a local maximum when x = [tex]\frac{11-\sqrt{37} }{3} = 1.639[/tex] in
Is the sum of the areas of two smaller squares equal to the area of a large square if the side lengths of the squares are 8 feet, 5 feet, and 3 feet? Note that the area of a square is s2, where s is the side length. Explain.
Answers
Answer:
No, the sum of the areas of two smaller squares is not equal to the area of a larger square if the lengths of sides of the squares are 8 feet, 5 feet and 3 feet.
Step-by-step explanation:
WE know that the area of a square is A = s² where s = length of side of the square. Now, since we have squares of varying sides of 8 feet, 5 feet and 3 feet respectively, we want to determine if the areas of the two smaller squares equals that of the larger square. Let A = area of 8 feet side square, A' = area of 5 feet side square and A" = area of 3 feet side square. We want to show if A = A' + A".
Now A = (8 ft)² = 64 ft²
A' = (5 ft)² = 25 ft² and
A" = (3 ft)² = 9 ft²
A' + A" = 25 ft² + 9 ft² = 36 ft²
Since L.H.S = 64 ft²and R.H.S = 36 ft²
So, 64 ft² ≠ 36 ft²
L.H.S ≠ R.H.S
So, the sum of the areas of two smaller squares is not equal to the area of a larger square if the lengths of sides of the squares are 8 feet, 5 feet and 3 feet.
Name the pair of angle and find the measure of angle b
Answers
three numbers have absolute values of 2, 4, and 6. The product of all the numbers is positive.
Find the product.
Answers
Answer:
i must say product means we have to multiple 2×4×6 that give 48
Step-by-step explanation:
happy Halloween
Please answer A.S.A.P
Answers
Answer:y=28
Step-by-step explanation:
2x – 8 + x = 3(x – 8) + 16
Answers
Answer:
0
Step-by-step explanation:
First, multiply
2x - 8 + x = 3x - 24 + 16
Combine like terms
6x -8 = -8
Add 8
6x = 0
so the answer should be 0
A system of linear equations that has no solution is a set of
equations
A) Consistent
B) Inconsistent
Answers
Answer:
Inconsistent
Step-by-step explanation:
A system of linear equations that has at least one solution is called consistent, whereas a system of linear equations that has no solutions is called inconsistent.
A system of linear equations that has no solution is a set of inconsistent equations.
The correct answer is an option (B)
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
What is system of equations?"It is a set of equations for which we find a common solution."
What is consistent system of equations?"A system of equations is consistent if there is at least one set of values that satisfies each equation in the system."
What is inconsistent system of equations?"A system of equations is inconsistent if there is no solution to the given system of equations."
From the definition, we can see that the system of equations is inconsistent if a system of equations has no solution.
Therefore, A system of linear equations that has no solution is a set of inconsistent equations.
The correct answer is an option (B)
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A thin wire 40 CM long is formed into a rectangle if the width of this rectangle is 8 CM what is length and area
Answers
Length of a wire = 40 cm.
Breadth of the rectangle formed = 8 cm.
Find:length and area of rectangle.
Solution:Length of a wire = 40 cm.
A rectangle is made from this wire.
That means,
Perimeter of the rectangle formed = length of the wire.
Also,
Breadth of the rectangle formed = 8 cm.
We know that,
Perimeter of a rectangle = 2(length + breadth).
Let the length of the rectangle be x cm.
Hence,
→ 2(x + 8) = 40
→ 2x + 16 = 40
→ 2x = 40 - 16
→ 2x = 24
→ x = 24/2
→ x = 12
Hence,
Length of the rectangle formed = x = 12 cm.
Now,
We know,
Area of a rectangle =length * breadth
→ Area of the rectangle = (12) * (8)
→ Area of the rectangle = 96 cm²
Therefore, the area of the rectangle formed is 96 cm².
I hope it will help you.
Regards.
Kerri earns $15 an hour tutoring. Last month she tutored for the following number or hours each week: 2 hours, 3 hours, and 4 hours
Answers
9 hours tutoring
15 * 9 = 135
The total amount of money earned by Kerri is $135.
Given that, Kerri earns $15 an hour tutoring.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the total amount of money earned by Kerri be x.
Now, total number of hours = 2+3+4=9 hours
Total money = Number of hours worked × Amount earned in an hour
x=9 × 15
⇒ x = 135
Therefore, the total amount of money earned by Kerri is $135.
To learn more about an equation visit:
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Liza needs help to solve this linear equation. 4(x – 5) + 2x = 9x – 2(4 + 2x) She has completed two steps, but now she's stuck. Examine her work. 1. 4x - 20 + 2x = 9x - 8 - 4x 2. 6x - 20 = 5x - 8 What could be the next step? Select all that apply. Add 8 to both sides. Add 5x to both sides. Subtract 6x from both sides. Subtract 20 from both sides. Divide both sides by –8. Divide both sides by –20
Answers
Answer:
Add 8 to both sides
Subtract 6x from both sides.
good luck i also did it on edge
To solve the given linear equation , next steps to be followed
1. Subtract 6x from both sides.
2. Add 8 to both sides.
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
Given linear equation
4(x – 5) + 2x = 9x – 2(4 + 2x)
Step 1: 4x - 20 + 2x = 9x - 8 - 4x
Step 2: 6x - 20 = 5x - 8
Next step is Subtract 6x from both sides.
Step 3: 6x - 20 - 6x = 5x - 8 - 6x
⇒ -20 = -x - 8
Next step is Add 8 to both sides.
Step 4: -20 + 8 = -x - 8 + 8
⇒ -12 = -x
⇒ x = 12
Hence,
To solve the given linear equation , next steps to be followed
1. Subtract 6x from both sides.
2. Add 8 to both sides.
Find out more information about linear equation here
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An angle measures 21.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answers
Answer:
angles 100.6 and 79.4 = 180 degrees
Step-by-step explanation:
supplementary angles add to 180
angles 100.6 and 79.4 = 180 degrees
100.6 -21.20= 79.4
x+ x-21.2 = 180
2x = 158.8
x= 79.4
79.4 + 21.2= 100.6
Avi’s dining room measures 124 square feet and is in the shape of a square. Which is the best estimate of the length of one side of the room, to the nearest tenth of a foot?
10.7 feet
10.9 feet
11.1 feet
11.4 feet
Answers
Answer:
11.1 feet
Step-by-step explanation:
because the formula for area of a square is A=L^2
so in this situation you would square root the 124 square feet, since all 4 sides are equal lenths
Answer:
The answer is C, 11.1 feet.
Step-by-step explanation:
To figure this out, you would estimate the square root of 124, since a square has sides of equal length. Your estimate would be closest to 11.1. I hope my answer helps, and if it does not, please leave a comment below, so that I can fix it.
Two sides of an isosceles triangle are 4 and 16, respectively. Find the length of the third side
Answers
Answer:
4 or 16.
Step-by-step explanation:
An isosceles triangle is one with two sides being the same sides, and the base a different one. If two of the lengths are 4 and 16, the last one has to be either of those.
I need to show my work to solve this equation and get an inequality at the end please help im confused
Answers
Answer:
You need to make $21 a day
Step-by-step explanation:
12d=250: you want $250 total, and you charge $12 for every delivery (d)
Divide 250 by 12, which is 20.83333... so thats 21
Which equation could be used to find the value of x in the triangle below?
4x + 10
6x - 10
А
12x + 20 = 180
B
12x = 180
С
12x - 20 = 180
D
8x - 10 = 4x + 10
Answers
Answer:
B
Step-by-step explanation:
4x+10+6x-10+2x=180°
4x+6x+2x=180°+10-10
12x/12=180°12
x=15° check :
4x+10+6x-10+2x=180° then x=15°
4*15+10+6*15-10+2*15=180°
60+10+90-10+30=180°
180°=180°
The equation representing the value of x is 12x + 20 = 180
What is a triangle?A triangle is a polygon with three edges and three vertices.
Given that, a triangle having interiors angles, 2x, 4x + 10 and 6x - 10
We know that, the sum of the interior angles of the triangle = 180°
Therefore,
2x + 4x + 10 + 6x - 10 = 180°
12x + 20 = 180°
Hence, the equation representing the value of x is 12x + 20 = 180
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The area in square feet of a rectangular field is x^2- 90x + 2000. The width, in feet, is x - 40. What is the length, in feet?
The length in foot
Answers
(X-40)(x-50) / (x-40)
Brainliest will be given
Answers
Answer:56i
Step-by-step explanation:the answer is 56i
Answer:
12x+-27
Step-by-step explanation:
3 times 4x is 12x then -9 times 3 is -27, and 12x-27 is the same as 12x+-27.