Graph the following set of points: A B C (1,3), (-3, -3), (5,2). Find the area and perimeter of ∆ABC . Leave answer in two decimal places.
Answers
The perimeter of the triangle is 29.31 units and the area of the triangle is 38.87 units^2
Distance Between Points
To find the perimeter and area of the triangle, we have to use the formula of distance between two points.
A = (1, 3)B = (-3, -3)C = (5, 2)Distance between AB
[tex]d_a_b = \sqrt{(a_1+a_2)^2 + (b_1 + b_2)^2} \\d_a_b = \sqrt{(3+1)^2 + (-3-3)^2}\\ d_a_b = \sqrt{4^2 + 9^2} \\d_a_b = 9.85 units[/tex]
Distance between BC
[tex]d_b_c = \sqrt{(b_1+b_2)^2 + (c_1+c_2)^2}\\d_b_c = \sqrt{(-9)^2 + (7)^2}\\d_b_c = \sqrt{130} \\d_b_c = 11.40 units[/tex]
Distance between AC
[tex]d_a_c = \sqrt{(a+1_a_2)^2 + (c_1+c_2)^2} \\d_a_c = 8.06 units[/tex]
The perimeter of the triangle is equal to
[tex]p = 9.85 + 11.40 + 8.06 = 29.31 units[/tex]
The area of the triangle is 38.87 units^2
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Related Questions
Which exponential function has the greatest average rate of change over the interval [0,2]
Answers
Step 1
Given;
Step 2
A) The equation of the graph will be;
[tex]\begin{gathered} y=ab^x \\ x=1,y=6 \\ 6=ab^1---(1) \\ x=0 \\ y=4 \\ 4=ab^0-----(2) \\ a=4 \\ \end{gathered}[/tex][tex]\begin{gathered} From\text{ equation 1} \\ 6=4b \\ b=\frac{6}{4}=\frac{3}{2} \\ The\text{ function is} \\ y=4(1.5)^x \end{gathered}[/tex]At the interval [0,2]
[tex]\begin{gathered} y_1=4(1.5)^0 \\ y_1=4 \\ y_2=4(1.5)^2 \\ y_2=9 \\ Average\text{ rate of change=}\frac{f(b)-f(a)}{b-a}=\frac{9-4}{2-0}=2.5 \end{gathered}[/tex]B)
[tex]\begin{gathered} 1.5=a(2)^0 \\ a=1.5 \\ y=1.5(2)^x \\ f(b)=6 \\ f(a)=1.5 \end{gathered}[/tex][tex]Average\text{ rate of change=}\frac{6-1.5}{2-0}=2.25[/tex]C)
[tex]\begin{gathered} f(x)=3(1.6)^x \\ f(b)=7.68 \\ f(a)=3 \\ Average\text{ rate of change=}\frac{7.68-3}{2-0}=2.34 \end{gathered}[/tex]D)
[tex]Average\text{ rate of change=}\frac{\frac{25}{2}-8}{2-0}=2.25[/tex]Answer;
[tex]Option\text{ A}[/tex]Un laboratorio está diseñando una nueva bacteria que se supone ayude a limpiar los ríos contaminados. Cada hora que pasa, el número de bacterias se duplica, por lo que se requiere una expresión que permita determinar ese número. Expresa la cantidad de bacterias que habrá después de "x" horas como una potencia. Seleccione una:1. 2x 2. 2x3. x² 4. 2X
Answers
From the statement, we know that the bacteria population doubles every x hours. We write the population as a function of x as:
[tex]P(x)=P_0\cdot2^x.[/tex]Where:
• P₀ = initial population,
,• x = time in hours.
If we consider P₀ = 1, we get the following formula:
[tex]P(x)=2^x.[/tex]Answer[tex]2^x[/tex]Question 2
What is the definition of
congruence?
A) If two figures have the same shape, then they are congruent.
B) If two figures have the same area, then they are congruent.
C) If there is a sequence of transformations taking one figure to another, then they are congruent.
D) If there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.
Next Question
Answers
Answer:
A. If two figures have the same shape, then they are congruent.
–
100g+79g–4g–69g+41g=–
53
Answers
Answer:–
100g+79g–4g–69g+41g=–
53
Step-by-step explanation:
Twenty students participated in a psychology experiment which measured their heart rates in two different situations.
Which situation shows greater variability?
Answers
Twenty students participated in a psychology experiment which measured their heart rates in two different situations.[75,100] situation shows greater variability.
f(75)=1
f(80)=4
f(90)=5
f(95)=4
f(100)=1
The measure of center should be median as the data is a bit scattered whereas the measure of variability should be the range of it.
Mean should be the measure of center as the data is concentrated in the middle the most whereas the standard deviation should be the measure of variability.
How far apart points are from one another and from the center of a distribution or a data collection is shown by variability. Spread, scatter, and dispersion are other terms for variation.
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Find the y-intercept of the quadratic function: g(x)=2(x+3)^2+8
Answers
x-intercept:
(−3,0)
y-intercept:
(0,118098)
Something Is DIFFERENT about this problem..
I'm not sure what..
991 + 2 = ?
Answers
Answer: 993
Step-by-step explanation:
I BELIEVE THE ANSWER IS 993 BUT I'M NOT SURE !
It could be 10,000 i don't know but i'm pretty sure it's 993 !
Hope it helped !
A square has a perimeter of 40 m what is the length of each side
Answers
Answer:
10m
Step-by-step explanation:
Perimeter means adding up all of the sides of a shape.
One property of a square is that all lengths of a square are the same.
We also know squares have 4 sides.
Lets set up an expression to solve the length for each side with variable S representing the length of a side:
4 * S = 40
Divide each side by 4:
S = 10
Therefore, each side of the square has a length 10m
A store owner mixes 2 Ib of candy that costs x dollars per pound with 3 Ib of candy that costs $1.50 per pound. She sells the mix for $2.50 per pound.
Answers
On solving the linear equation 12.5 = 2x + 4.5, we find that cost of first type of candy is $4 per pound
What is an linear equation in one variable?Linear equation is an equation containing one unknown variable with power one and constants.
The standard form of an linear equation in one variable x is :
ax + b = 0 , where a, b are constants
x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting, multiplying, dividing same number to both sides.
Given that there are two types of candies one is of x dollars per pound
and one is of $1.50 per pound
Cost of 2lb of candy that costs x dollars per pound = 2 × x = $ 2x
Cost of 3lb of candy that costs $1.50 per pound = 3 × 1.5 = $ 4.5
2lb of one type of candy and 3lb of other type of candy are mixed to form a mix of weight 2lb + 3lb = 5lb
The cost of one pound of mixture = $2.50
The cost of 5lb of such mixture = $ 5× 2.50 = $ 12.5
Cost of 5lb mix = Cost of 2lb candy of first type + Cost of 3lb candy of second type
⇒ 12.5 = 2x + 4.5
Subtract 4.5 from both sides,
⇒ 12.5 - 4.5 = 2x
⇒ 8 = 2x
Divide both sides by 2
⇒ 4 = x
Therefore, the cost of first type of candy is $ 4 per pound
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Jabari is power washing houses for a summer job. For every job, he charges an initial fee plus a $30 sign, 30 for each hour of work. His total fee for a 4-hour job, for instance, is $170 sign, 170.
Jabari's total fee, f for a single job is a function of the number, t, of hours it takes him to complete the job.
Answers
The initial fee that Jabari collects is $50.
What is the initial fee?It should be noted that Jabari is power washing houses for a summer job and for every job, he charges an initial fee plus a $30.
In this case, the amount collected was $170 for a four hours job. Let the initial fee be represented as x.
Therefore, this will be illustrated as:
x + (30 × 4) = 170
where x = initial fee
x + 120 = 170
Collect like terms
x = 170 - 120
x = 50
The initial fee is $50.
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Jabari is power washing houses for a summer job. For every job, he charges an initial fee plus a $30 sign, 30 for each hour of work. His total fee for a 4-hour job, for instance, is $170 sign, 170.
Jabari's total fee, f for a single job is a function of the number, t, of hours it takes him to complete the job. What is the initial fee?
What is the quotient of (−84) ÷ (−7) ÷ 4? −48 −3 3 48
Answers
Answer: 3
Step-by-step explanation:
(−84) ÷ (−7) ÷ 4=
-84/(-7)/4=
(84/7)/4=
12/4=3
How many 1/4 inch pieces can be cut from a piece of ribbon 9/20 of an inch long
Answers
5/20
Meaning only one 1/4 inch pieces can be cut from 9/20 of an inch
What is the solution to the equation 3x-4 = 8?
x=8
x=4
x=1
x=6
Answers
B) x=4
Explanation:
=> 3x-4=8
=> 3x=8+4
=> 3x=12
=>x=12/3
=> x=4
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
A is not equivalent
Step-by-step explanation:
A is .15 while all the others are .75 in some way
Answer:
0.15
Step-by-step explanation:trust me
how do i multiply this and simplify (2x+6)^2
Answers
Answer:4x^2+24x+36
Step-by-step explanation:
when you have it squared it turns into (2x+6) (2x+6) then you distribute it which gives you 4x^2+12x +12x+36 when you simplify that you et 4x^2+24x+36
You expand the square
(2x+6)(2x+6)
4x^2+12x+12x+36
Simplify it
4x^2+24x+36
one of the longest commercial aircraft in use today is 144 feet in length. another airplane manufacturer decides to build an airplane that is approximately 41% of this length. use compatible numbers to estimate the length of the plane built by the other manufacturer.
Answers
The length of the other aircraft is 59.04ft.
Percentage of NumberTo solve this problem, we simply need to find the certain percentage of the length of aircraft which is given as 144ft.
let's calculate 41% of 144
[tex]41\% of 144[/tex]
This is given as
[tex]\frac{41}{100} = \frac{x}144}\\ 0.41 = \frac{x}{144} \\x = 0.41 * 144\\x = 59.04ft[/tex]
The length of the plane built by the other manufacturer is 59.04 ft.
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Determine which integer(s) from the set S:{−40, 2, 20, 42} will make the inequality three eighths m minus three is less than one fourth m plus 2 false.
Answers
Answer:
{-40, 2}
Step-by-step explanation:
Part A: -40/8 x 3/8 would be
120/8 but then we have to subtract it from 3
that would be 117/8 then we simplify it 14 -5/8.
Part B: first it would be 2 plus 2 and that's 4 and then make 4 into a fraction
4/4 we simplify that 1 0/4.
14 -5/8 < 1 0/4.
Hope This Helped!
Jina made $207 for 9 hours of work.
At the same rate, how much would she make for 13 hours of work?
Answers
Answer:
$299
Step-by-step explanation:
[tex](\frac{207}{9} )(13)=\frac{2691}{9}}} =299[/tex]
Hope this helps
The water level in a tank measures 15 inches and is decreasing 0.5 inches every minute. How many minutes, x, will it take for the water level to measure 9 inches deep?
Answers
12 minutes .
The tank takes 12 minute for the water level to measure 9 inches deep.
Explain two step problem?A two-step problem is a word problem that must be solved in two steps.While many of these problems have only one step, a two-step word problem necessitates the solution of two different equations. Two different operations (such as multiplication and addition) or two of the same operation may be used in the two-step word problem (like subtraction and subtraction).Given tank measurement = 15 inches .
it decreases 0.5 inches every minute.
We have to the minute at which water level reaches 9 inches deep,
Here the difference of inches is 6 inches .
15 inches - 6 inches = 9 inches
To find minute ,
6 / 0.5 = 12 minute .
The tank takes 12 minute to measure 9 inches deep.
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in the market for canadian dollars measured in us dollars, if the price of a us dollar is 1.10 canadian dollars, a canadian dollar is a.1.10 us dollars b.1 us dollar c.0.99 cents us d.0.91 cents us
Answers
The price of one canadian dollar in US dollars is 91 cents or 0.91 US dollars.
It is given that the price of a US dollar is 1.10 Canadian dollars in the market.
Thus we can say that,
1.10 Canadian Dollar = 1 US Dollar
∴ 1 Canadian Dollar = [tex]\frac{1}{1.10}[/tex] US Dollars
⇒ 1 Canadian Dollar = 0.91 US Dollars
Now we know that 1 US Dollar = 100 cents
∴ 0.91 US Dollars = 0.91 x 100 = 91 cents
Hence the value of 1 Canadian Dollar is 0.91 US Dollars or 91 cents.
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If * = 8 units, y= 13 units, and h= 11 units, then what is the area of the parallelogram shown above?
Answers
The area of the figure shown below is equivalent to 88 square units.
Properties of a parallelogramA parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.
The opposite sides of a parallelogram are congruent and the sum of their adjacent side is equivalent to 180 degrees.
The formula for calculating the area of a parallelogram is expressed as;
Area = length * breadth
Area = x * h
Area = 8 * 11
Area = 88 square units
Hence the area of the parallelogram above is 88 square units.
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Evaluate. Write your answer as a whole number or as a simplified fraction.
3-1.9-¹ =
Answers
Answer:
27^-1
Step-by-step explanation:
1/3 ×1/9=1/27=27^-1
A store sells 12 cans of fruitcocktail for $21.How much would it cost you to buy 7 cans of fruit cocktail?
Answers
Answer:
$189
Step-by-step explanation:
you would take 27 × 7 and multiply the two numbers, then get your answer.
Answer:
$12.25
Step-by-step explanation:
The unit rate would be[tex]\frac{21}{12}[/tex] 1.75 a can
7 x 1.75 = 12.25
I’ve been stuck on this problem for a while & I have an SHSAT practice test tomorrow, can someone please tell me how to solve this
Answers
The number of ways of different platters will be 360 ways.
How to illustrate the information?From the information, it should be noted that the salad bar offers 6 different vegetables and it was illustrated that Selena wants to get exactly 2 different vegetables in the platter.
The number of different platters that she can create will be:
= nCr
n = total vegetables
r = amount needed
= 6! / 2!
= 6 × 5 × 4 × 3 × 2 / 2
= 360 ways.
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At an important meet Hassan won the mens 800 meters in 106.72 seconds Hassan ran at an average of blank meters per second
Answers
To find the average rate at which Hassan ran in meters per second, divide the distance of 800 meters over the 106.72 seconds that it took for Hassan to run that distance:
[tex]\frac{800m}{106.72s}=7.496251874...\frac{m}{s}\approx7.50\frac{m}{s}[/tex]Therefore, Hassan ran at an average of 7.50 meters per second.
The boca grande causeway in florida is about 1 4/9 times as long as the golden gate bridge in san francisco golden gate bridge is about 9000 feet long about how long is the boca grande causeway
Answers
The length of the Boca Grande Causeway = 13,000 feet.
When do we use multiplication ?Repeated addition of the same number is made easier by multiplying the numbers. When we need to merge groups of similar sizes, we employ it. For instance, if there are 5 baskets, each containing 4 apples, we can use multiplication to get the total number of apples, which is 5 x 4 = 20 apples.
We can rapidly determine the total number of things by multiplying. When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group.
Given: The boca grande causeway in florida = 1 4/9 times golden gate bridge
Length of the Golden Gate Bridge = 9000 feet
Thus the length of the Boca grande causeway = 1 4/9 × 9000
= 13/9 × 9000
On further solving we get
= 13 × 1000
= 13,000 feet .
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3) A group of students were testing the walking capability of a newly created robot. Using the graph, what can
you interpret about point A?
Answers
Answer:
The robot walked 2 meters in 8 seconds. Time is seconds on the x-axis since it's an independent variable and distance in meters on the y-axis.
Exterior angle, theorem, and triangle, some theorem
Answers
Answer:
? = 94°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
143° is an exterior angle of the triangle , then
? + 49° = 143° ( subtract 49° from both sides )
? = 94°
hurry plssssssssssssss
Answers
Answer:
So the answer would be
D
Step-by-step explanation:
Use the formula an=a1rn−1 to identify the geometric sequence an=81⋅2n−13n−1
I think this is right but I'm not 100% sure
I'm like 75% sure sorry
2x+3y=5x−y
Complete the missing value in the solution to the equation
( ,0)
Answers
Answer:dsafdf
Step-by-step explanation's