What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
14.6 units
15.5 units
21.0 units
21.6 units
see the attached figure to better understand the problem
we know that the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Let
[tex]A(-3,3)\ B(3,4))\ C(3,-3)[/tex]
Step 1
Find the distance AB
[tex]A(-3,3)\ B(3,4)[/tex]
substitute in the formula
[tex]d=\sqrt{(4-3)^{2}+(3+3)^{2}}[/tex]
[tex]d=\sqrt{(1)^{2}+(6)^{2}}[/tex]
[tex]dAB=\sqrt{37}\ units[/tex]
Step 2
Find the distance BC
[tex]B(3,4))\ C(3,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-4)^{2}+(3-3)^{2}}[/tex]
[tex]d=\sqrt{(-7)^{2}+(0)^{2}}[/tex]
[tex]dBC=7\ units[/tex]
Step 3
Find the distance AC
[tex]A(-3,3)\ C(3,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-3)^{2}+(3+3)^{2}}[/tex]
[tex]d=\sqrt{(-6)^{2}+(6)^{2}}[/tex]
[tex]dAC=\sqrt{72}\ units[/tex]
Step 4
Find the perimeter of the triangle
we know that
the perimeter of the triangle is the sum of the length sides of the triangle
[tex]P=AB+BC+AC[/tex]
substitute the values
[tex]P=\sqrt{37}\ units+7\ units+\sqrt{72}\ units=21.6\ units[/tex]
therefore
the answer is
the perimeter of the triangle is [tex]21.6\ units[/tex]
to construct the midpoint of a segment, fold the paper so that the given line segment lies on itself and
Answer:
The endpoints of the line segment lie on each other
Explanation
To understand the question, follow the practical steps below
1. Take a sheet of plane paper
2. Label the edges of the top of the paper A and B
3. Fold the paper in such a way that edge A lies on B.
You'll notice the following;
1. The top of the paper lies in itself; hence, we can say that the line segment lies on itself
2. You have a new line at the centre of the paper. The point at the top of this center line is the midpoint of the line segment
3. The edges that lie on each other translates to the endpoints lying on each other.
Number (3) above is the required observation and the right answer.
In a triangle, two of the angles measure 78o and 56o. What is the measure of the third angle?
Tom has been given 35 chores to complete today. This morning he finished 7 of them. How many chores does he now have left to do?
28 chores he now has left to do.
What is subtraction?An arithmetic intelligence operation minus simulates the process of deleting items from either a collection. To subtract is to take something or something from a particular group. The group's total number of items decreased and became lower when people eliminated it. The components of a subtraction issue are the issues dealing with, forces at play, and differences. The negative symbol, or, denotes subtraction.
35 tasks have been assigned to Tom for today.
He accomplished 7 of them this morning.
The remaining days are:
= 35-7
= 28 chores
The remaing chores are 28.
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The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?
27°
36°
54°
72°
The measure of the vertex angle is 72 degrees
Isosceles triangleThe sum of the interior angle of a triangle is 180 degrees. Of the base angles are equal hence;
54 + 54 + x = 180
where
x is the vertex angles
Simplify
108 + x = 180
x = 180 - 108
x = 72 degrees
Hence the measure of the vertex angle is 72 degrees
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A man’s age is two years more than four times his son’s age. His son is now 8. How old is the man?
What is the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1) ?
Enter your answer in the box. Do not round any side lengths.
What is the area of a triangle with vertices at (0, −2) , (8, −2) , and (9, 1) ?
Enter your answer in the box.
What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?
Enter your answer in the box. Do not round any side lengths.
What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
15.3 units
20.4 units
30.6 units
52.0 units
(1) the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1)
To find area of rectangle we need to find the length and width
Length = distance between (−6, 3) and (−2, −1)
Distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-2-(-6))^2 + (-1-3)^2}[/tex]
= [tex]\sqrt{(4)^2 + (-4)^2}[/tex]=[tex]\sqrt{(16) + 16}[/tex] =[tex]\sqrt{32}[/tex]
width = Distance between (−6, 3) , (−3, 6)
Distance = [tex]\sqrt{(-3-(-6))^2 + (6-3)^2}[/tex]
=[tex]\sqrt{3^2+3^2}= \sqrt{18}[/tex]
Area = Length * width = [tex]\sqrt{32} *\sqrt{18} = \sqrt{576}= 24[/tex]
(2) the area of a triangle with vertices at (0, −2) , (8, −2) , and (9, 1)
Area of triangle = [tex]\frac{1}{2} * base * height[/tex]
base is the distance between (0,-2) and (8,-2)
Distance = [tex]\sqrt{(8-0)^2 + (-2-(-2))^2}[/tex] = 8
To find out height we take two vertices (8,-2) and (9,1)
Height is the change in y values = 1- (-2) = 3
base = 8 and height = 3
So area of triangle = [tex]\frac{1}{2} * 8 * 3 = 12[/tex]
(3) the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1)
To find perimeter we add the length of all the sides
Distance between (−2, 1) and (−2, 4) = [tex]\sqrt{(-2+2)^2 + (4-1)^2}[/tex]= 3
Distance between(−2, 4) and (2, 7) = [tex]\sqrt{(2+2)^2 + (7-4)^2}[/tex]= 5
Distance between (2, 7) and (6, 4) = [tex]\sqrt{(6 - 2)^2 + (4-7)^2}[/tex]= 5
Distance between (6, 4) and (6, 1) = [tex]\sqrt{(6 - 6)^2 + (1-4)^2}[/tex]= 3
Distance between (6, 1) and (−2, 1) = [tex]\sqrt{(-2-6)^2 + (1-1)^2}[/tex]= 8
Perimeter = 3 + 5 + 5 + 3 + 8 = 24
(4) four coordinates are (-7,-1) (-6,4) (3,-3) and (4,2)
Length = Distance between (3,-3) and (4,2) = [tex]\sqrt{(4-3)^2 + (2+3)^2}[/tex]= [tex]\sqrt{26}[/tex]
Width = Distance between (-6,4) and (4,2) = [tex]\sqrt{(4+6)^2 + (2-4)^2}[/tex]= [tex]\sqrt{104}[/tex]
Perimeter = 2(lenght + width) = 2*( [tex]\sqrt{26}[/tex]+[tex]\sqrt{104}[/tex] )
= 30.6 units
The area of the rectangle is [tex]24\;square\;units[/tex].
1. According to the question, the vertices of the rectagle are at [tex](-6, 3) ;(-3, 6) ;(1, 2)[/tex] , and [tex](-2, -1)[/tex].
The distance between two vertices on the coordinate plane is
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
So,
[tex]Length=D_1\\D_1=\sqrt{(6-3)^2+(-3+6)^2}\\D_1=\sqrt{9+9}\\D_1=3\sqrt 2 units[/tex]
Similarly,
[tex]Width=D_2\\D_2=\sqrt{(-2+6)^2+(-1-3)^2}\\D_2=\sqrt{16+16}\\D_2=16\sqrt 2\;units[/tex]
The area of the rectangle is equals to product of length and width of the rectabgle.
So,
[tex]Area=length\times width\\Area=3\sqrt{2}\times 4\sqrt{2}\\Area=24\;square\;units[/tex]
Hence, the area of the rectangle is [tex]24\;square\;units[/tex].
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What is the remainder when 314^162 is divided by 7?
Final answer:
To find the remainder of 314162 divided by 7, we use modular arithmetic and find that the powers of 314 mod 7 repeat every 3 powers. Since 162 is a multiple of 3, 314162 mod 7 equals 1.
Explanation:
The question asks for the remainder when 314162 is divided by 7. To solve this problem, we can use a concept known as modular arithmetic, which deals with the remainder upon division. The key here is to find a pattern in the powers of 314 modulo 7, because large numbers can be cumbersome to work with directly. A helpful property is that (a×b) mod n = [(a mod n)×(b mod n)] mod n.
Let's consider the powers of 314 mod 7:
3141 mod 7 = 2
3142 mod 7 = (314 × 314) mod 7 = (2 × 2) mod 7 = 4
3143 mod 7 = (3142 × 314) mod 7 = (4 × 2) mod 7 = 1
Since we reached 1 again, the sequence will repeat every 3 powers. Now, 162 is divisible by 3 (162 = 3 × 54). Therefore, we can conclude that 314162 mod 7 will have the same remainder as 3143 mod 7, which is 1.
Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 3t^2 + cos(t) and v(0) = 2.
v(t) = t^3 + sin(t) + 2
v(t) = t^3 - sin(t) + 3
v(t) = 6t - sin(t) + 2
v(t) = t^3 - sin(t) + 2
The velocity function of an object moving along the {x} - axis would be -
v{t} = sin(t) + t³ + 2.
What is instantaneous acceleration?The acceleration at any instant of time is called instantaneous acceleration. Mathematically -
a = dv/dt
dv = a dt
∫dv = ∫a dt
Given is the acceleration function as -
a(t) = 3t² + cos(t)
We know that -
a = dv/dt
dv = a dt
∫dv = ∫a dt
v{t} = ∫{3t² + cos(t)} dt
v(t) = sin(t) + t³ + C
Now -
v(0) = 2
sin(0) + 0 + C = 2
C = 2
So, we can write the velocity function as -
v{t} = sin(t) + t³ + 2
Therefore, the velocity function of an object moving along the {x} - axis would be -
v{t} = sin(t) + t³ + 2.
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Which expression represents the probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides?
The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.
What is the probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is determined in the following steps given below.
[tex]\rm Probability=\dfrac{10}{3}\times \left (\dfrac{1}{3} \right ) ^3\times \left (\dfrac{5}{6} \right ) ^7\\\\Probability= \dfrac{10}{3}\times \dfrac{1}{27} \times \dfrac{78125}{279936}\\\\Probability=0.034[/tex]
Hence, the probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.
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Yolanda is saving money to buy a game. so far she has saved $30 , which is five-sixths of the total cost of the game. how much does the game cost?
Final answer:
To find the total cost of the game based on Yolanda's savings of $30, which is five-sixths of the cost, multiply $30 by the reciprocal of 5/6, resulting in a total cost of $36.
Explanation:
The question asks how much a game would cost if Yolanda has already saved $30, which is five-sixths of the total cost of the game. To find the total cost of the game, we consider the amount saved ($30) as five-sixths of the total cost (which we'll call x).
So the equation to solve is 5/6 * x = $30. To find x, we divide $30 by 5/6, which is the same as multiplying $30 by the reciprocal of 5/6 (which is 6/5). Therefore, x = $30 * (6/5) = $36. Thus, the total cost of the game is $36.
Which linear equation has a slope of 3 and a y-intercept of –2?
y = 3x + 2
y = 3x – 2
y = –2x + 3
y = –2x – 3
Answer: y = 3x - 2
Step-by-step explanation:
Equation of a straight line is
y=mx + c
m is the slope and c is the intercept
comparing it with the equation
y=3x - 2
m = slope =3
and c= intercept= -2
If milk costs $1.97 per gallon and a bread recipe uses 6 fl. ounces, how much do those 6 fl. ounces cost?
Help me with this question plzzzz
Sine: the trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse.
What is the Sine of angle A?
3/4
4/3
3/5
4/5
You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $120 and you pay 80% of the manufacturer's recommended list price. Plan B offers an annual membership fee of $40 and you pay 90% of the manufacturer's recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?
An equation is formed when two equal expressions. The number of merchandise that you would have to purchase in a year to pay the same amount under both plans is 800.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that you are choosing between two plans at a discount warehouse.
The cost for x number of merchandise under plan A, which offers an annual membership fee of $120 and you pay 80% of the manufacturer's. Therefore, the cost will be,
Cost = 120 + 0.8x
The cost for x number of merchandise under plan B, which offers an annual membership fee of $40 and you pay 90% of the manufacturer's recommended list price. Therefore, the cost will be,
Cost = 40 + 0.9x
Now, in order to find the number of merchandise that you would have to purchase in a year to pay the same amount under both plans, you need to equate the two equations together. Therefore,
Cost from Plan A = Cost from Plan B
120 + 0.8x = 40 + 0.9x
120 - 40 = 0.9x - 0.8x
80 = 0.1x
x = 80 / 0.1
x = 800
Hence, the number of merchandise that you would have to purchase in a year to pay the same amount under both plans is 800.
Further, the cost for each plan for 800 merchandise can be written as,
PlanA,
Cost = 120 + 0.8(800)
= $760
Plan B,
Cost = 40 + 0.9(800)
= $760
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What is 7,433,654 to the nearest 10,000
The leukemia and lymphoma society sponsors a 5k race to raise money it receives $55 per race entry and $10000 in donations but it must spend $15 per race entry to cover the cost of the race write and solve an inequality to determine the number of race entries the charity needs to raise at least 55,000
The temperature in degrees Celsius, c, can be converted to degrees Fahrenheit, f, using the equation mc026-1.jpg. Which statement best describes the relation (c, f)? It is a function because –40°C is paired with –40°F. It is a function because every Celsius temperature is associated with only one Fahrenheit temperature. It is not a function because 0°C is not paired with 0°F. It is not a function because some Celsius temperatures cannot be associated with a Fahrenheit temperature.
Answer:
B
Step-by-step explanation:
edge
Ax + by = c find Y show steps
(4.5+7.6)-8*2.5 I really need help with this problem
if x-2m=p make m the subject. answer must be written as fraction.
To make m the subject of the equation x-2m=p, add 2m to both sides, subtract p, and divide by 2. The result is m as the subject of the equation, represented as the fraction (x - p)/2.
Explanation:To solve the equation x-2m=p for m as the subject, we want to isolate m on one side of the equation. Here is the step-by-step process:
Start with the original equation: x - 2m = p.Add 2m to both sides to get x = p + 2m.Subtract p from both sides to get x - p = 2m.Divide both sides by 2 to isolate m: m = (x - p)/2.Now m is the subject of the equation, and it is represented as a fraction as requested.
Determine which of the following terms is a function: a. (1,2) (2,4) (3,5) c. (1,2) (2,4) (2,6) b. (1,2) (2,3) (1,5) d. (1,2) (3,5) (3,7)
Answer:
A is the mofluffin answer
Step-by-step explanation:
What is the reason for each step in the solution of the inequality? −2(x+3)−4>4x+30 Select the reason for each step from the drop-down menus.
The reason for each step in the solution of the inequality must be mathematical operations such as; the distributive property
What is a solution set to inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality.
We have given that -2(x + 3) - 4 > 4x + 30
First, apply the distributive property
-2x - 6 - 4 > 4x + 30
Now combine like terms;
-2x - 10 > 4x + 30
Then subtraction property
-6x - 10 > 30
The addition property
-6x > 40
The division property
x < -20/3
Hence, we get the answer equal to x < -20/3.
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Convert 30 feet per second to miles per minute.
5280 ft = 1 mi
Round to the nearest hundredth.
Answer:
0.34 miles per minute
Step-by-step explanation:
We have to convert 30 feet per second to miles per minute.
1 minute = 60 seconds
Therefore, in one minute = 60 × 30 = 1800 feet
5280 feet = 1 mile
180 feet = [tex]\frac{1800}{5280}[/tex]
= 0.3409 ≈ 0.34 mile
Therefore, 0.34 mile per minute.
What’s the best answer
1.Which statement is true about this argument?
Premises:
If two lines are parallel, then the lines do not intersect.
Lines m and n do not intersect.
Conclusion:
Lines m and n are parallel.
Which statement is true about the argument?
The argument is not valid because the premises are not true.
The argument is valid by the law of syllogism.
The argument is valid by the law of detachment.
The argument is not valid because the conclusion does not follow from the premises.
2.Which statement is true about this argument?
Premises:
If a quadrilateral is a square, then the quadrilateral has four right angles.
Quadrilateral JKLM has four right angles.
Conclusion:
Quadrilateral JKLM is a square.
The argument is not valid because the premises are not true.
The argument is valid by the law of detachment.
The argument is not valid because the conclusion does not follow from the premises.
The argument is valid by the law of syllogism.
The argument is valid by the law of detachment.
The statements that are true about the arguments in the question are;
1) Option C; Law of detachment
2) Option B; Law of detachment
1) We are given the premise that;
If two lines are parallel, then the lines do not intersect.
This premise is true because we know from parallel and perpendicular lines property that parallel lines never intersect each other.
With that premise, we are now given a conclusion that; Lines m and n do not intersect.
This kind of condition is known as law of detachment which states that;
If x is true, then y is also true.
Thus, Option C is correct
2) We are given the premise that;
If a quadrilateral is a square, then the quadrilateral has four right angles.
The given premise is true because from the definition of a square, all sides must be equal and all angles must be right angles.
We are now given the conclusion that;
Quadrilateral JKLM has four right angles.
This conclusion is valid because it follows the given premise.
Again like in 1 above, this follows the law of detachment.
Option B is correct
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Petro had $15 dollars. He spent $9 dollars on a book. His friend had $12 how much money did pedro have left
Margaret is reading a book. the number of pages she has left to read is 276 - 35d, where d represents the number of days she has been reading.
what does each part of the expression represent?
(note - not all options may be used)
a) the number of pages she has read during 1 week
b) the total number of pages in the book
c) the number of pages in the book
d) the number of pages she has read during d days
Answer:
Option b , c and d are the part of the expression .
Step-by-step explanation:
We are given that the number of pages she has left to read is 276 - 35d
d represents the number of days she has been reading.
276 denotes the total number of pages
35 pages denotes the number of pages read per day
35 d represents the number of pages she has read during d days
276 - 35d represents teh reamining pages
So, Option b , c and d are the part of the expression .
Based on a poll, 5050% of adults believe in reincarnation. assume that 44 adults are randomly selected, and find the indicated probability. complete parts (a) through (d) below.
a. what is the probability that exactly 33 of the selected adults believe in reincarnation? the probability that exactly 33 of the 44 adults believe in reincarnation is
To solve this problem, we use the formula for binomial probability:
P = [n! / (n – r)! r!] p^r * q^(n – r)
where,
n = total number of adults = 4
r = number of adults who believe in reincarnation = 3
p = chance of believing in reincarnation = 50% = 0.50
q = 1 – p = 0.50
P = [4! / (4 – 3)! 3!] 0.50^3 * 0.50^(4 – 3)
P = 0.25 = 25%
Answer:
Answer is 0.096
Step-by-step explanation:
Here 44 adults are randomly selected.
Each adult selected is independent of the other to believe in reincarnation.
Also there are only two outcomes, probability for success in each trial = 0.50
Hence X no of adults who believe in reincarnation is binomial with n =50 and p = 0.50
[tex]a) P(X=23) = 50C23 (0.5)^{50} =0.096[/tex]
Working notes:
50C23 =108043253365600
0.5^50) = 8.8178x10^(-14)
Simplifying we get answer as 0.096