Find the area of the triangle ABC with the coordinates of A(10, 15) B(15, 15) C(30, 9).
A= units^2
Answers
Check the picture below. so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}[/tex]
[tex](\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}[/tex]
Related Questions
y'all pls help im really confused on how to do this
A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of 50mph
70mph
Xmph
x=10MPH
x-5mph
Answers
The trip would have taken 6 hours.
(300 mi) / (50 mi/h) = 6 h
Solve the system of equations:
y=2x
y=x²-8
Answers
x^2 - 8 = 2x
x^2 - 2x - 8 = 0
Factor
(x - 4)(x + 2) = 0
x = 4 or x = -2
Plug in 4
y = 2x or y = x^2 - 8
y = 2(4) or y = 4^2 - 8
y = 8
Plug in -2
y = 2x or y = x^2 - 8
y = 2(-2) or y = (-2)^2 - 8
y = -4
There are two solutions
(4, 8) and (-2, -4)
How are statistical questions different from other questions?
Answers
Answer & explanation:
A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer. For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question.
Pls, choose me as brainliest!
Could you help me find X,
Answers
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{4}{x}~~ = ~~\cfrac{x}{9}\implies 36=x^2\implies \sqrt{36}=x\implies 6=x[/tex]
Lawyer Fees:
A lawyer charges a base (one time) fee of
$200 and $75 each hour for consulting with
her. What would be the equation to model the situation?
Answers
8 hours = $275 x 8
= 2,200
Please help mee I'm gonna have a mental break downnn
Answers
Answer:
y[tex]\leq[/tex]-2/5x + 2
Step-by-step explanation:
-2/5x + 2 would be the slope and y intercept of the line
The line is solid, so it has to be either less than or equal to or greater than or equal to
It is shaded below the line, which means it has to be less than. you can tell this by looking at the closed end of the inequality sign. If it points left, you shade below, if it points right, you shade above.
A rectangle has a length 10 more than its width. If the width is increased by 8
and the length by 4, the resulting rectangle has an area of 135 square units.
Part A
Write an equation to model the above scenario. Use the model to find the length
of the original rectangle?
powered by
esmos
Part B
What is the perimeter of the expanded rectangle?
Answers
Step-by-step explanation:
length = the original length
width = the original width
length = width + 10 or
width = length - 10
(length + 4) × (width + 8) = 135
A
now we are using the first equation in the second to solve then for length :
(length + 4) × (length - 10 + 8) = 135
(length + 4) × (length - 2) = 135
length² - 2×length + 4×length - 8 = 135
length² + 2×length = 143 or
length² + 2×length - 143 = 0
this is the equation to model the scenario.
solving in general such a quadratic equation :
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = length
a = 1
b = 2
c = -143
length = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =
= (-2 ± sqrt(4 + 572))/2 =
= (-2 ± sqrt(576))/2 =
= (-2 ± 24)/2 = (-1 ± 12)
length1 = -1 + 12 = 11
length2 = -1 - 12 = -13
a negative solution for a length is not applicable, so,
length = 11
width = length - 10 = 11 - 10 = 1
B
the expanded length = 11 + 4 = 15
the expanded width = 1 + 8 = 9
the expanded perimeter is then
2×15 + 2×9 = 30 + 18 = 48
Please help asap!! drag each tile to the correct box.
arrange the steps in the correct order to solve this trigonometric equation.
cos^2x = 3sin^2x
Answers
cos²(x) = 3 sin²(x)
1 - sin²(x) = 3 sin²(x)
1 = 4 sin²(x)
1/4 = sin²(x)
± √(1/4) = sin(x)
± 1/2 = sin(x)
sin(x) = 1/2 or sin(x) = -1/2
[x = arcsin(1/2) + 2nπ or x = π - arcsin(1/2) + 2nπ]
… … … or [x = arcsin(-1/2) + 2nπ or x = π - arcsin(-1/2) + 2nπ]
(where n is any integer)
[x = π/6 + 2nπ or x = 5π/6 + 2nπ]
… … … or [x = -π/6 + 2nπ or x = 7π/6 + 2nπ]
The height of lava fountains spewed from volcanoes cannot be measured directly. Instead, their height in meters can be found using the equation y=1/2 gt^2
where y represents the height, g is 9.8, and t represents the falling time of the lava rocks. Find the height in meters of a lava rock that falls for 5 seconds.
Answers
The height in meters of a lava rock that falls for 5 seconds is; 122.5 m.
How to calculate height from quadratic equations?
We are told that the height is modelled by the equation;
y = ¹/₂gt²
where;
y represents the height.
g is 9.8 m/s²
t represents the falling time of the lava rocks.
Thus, at t = 5, we have;
y(5) = ¹/₂(9.8)(5)²
y(5) = 122.5 m
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11. Find the coordinates of the point located six units behind the yz- plane, seven units to the right of the xz - plane, and eight units above the xy-plane. O x = -6, y = 7, z =-6 O x = -6, y = 7, z = 8 Ox=7, y = 7, z = 8 O x = 6, y= 7, z = 8
Answers
Answer: I think
Step-by-step explanation:Let the coordinate of the point be (x,y,z). Since the point is located 3 units behind the YZ− plane, 4 units to the right of XZ− plane and 5 units above the XY−plane ,x=−3,y=4 and z=5 Hence, coordinates of the required points are (−3,4,5)
what is the slope-intercept equation of the line that includes the points in the table?
Answers
Answer:y=5x+1
Step-by-step explanation:the y intercept is the y value when x=0 which we can read off as run. Slope =rise/run=(change in y value)/(change in x value) for any two points.
Which expression is equivalent to 12b + 3a? choices: a (a + b) x 12 b 3 (4b + a) c ab x 12 x 3 d (12 x 3) + (b x a)
Answers
Answer:
The answer to the equation is B.
Step-by-step explanation:
Answer:
i took the test and its B
Step-by-step explanation:
12. The mean number of boxes of cookies sold by
each girl scout in Emma's troop was 28 with a
standard deviation of 8. If Emma's z-score
was -1.5, how many boxes of cookies did she
sell?
Answer:
Answers
Answer:
16
Step-by-step explanation:
i hope this help you
Abby has 159 bonus coupons. She wants to staple them in groups of 30. How many complete groups of 30 can Abby make?
5 complete groups
6 complete groups
14 complete groups
59 complete groups
Answers
Abby can make 5 complete groups with 9 extra bonus coupons.
What is Division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Here, Abby has total number of coupons = 159
Number of coupons in a group = 30
Total number of groups = Total Coupons / coupons in a group
= 159 / 30
= 5.3
Thus, Abby can make 5 complete groups with 9 extra bonus coupons.
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Julia has 15 nails she uses 8 to build a birdhouse she substract to find the number of nails left.wich addition sentence can use to check her work
Answers
Answer:
8+7=15
Step-by-step explanation:
15-8=7
so if she adds 8 to 7 and she gets 15 she did it right.
Answer: Julia can use 7 + 8 = 15 to check her work.
Step-by-step explanation: As fifteen minus eight equals seven, Julia can check her work by performing the inverse operation of seven plus eight to check her work. This is true as when c - b = a, a + b = c.
Can y’all help with this?
Answers
Answer:
Quadrilateral: shape with 4 sides
Perpendicular means at right angles. Therefore, draw two sides at a right angles to each other. Mark this with a right angle symbol.
Draw 2 sides that are parallel. Mark these with arrows.
Please see attached diagrams.
4 Solve these inequalities. Show the solutions on the number lines.
a 4v-2 > 16
b 6 ≥ 2(w-7)
0
5 a Write as a recurring decimal.
b Convert 0.45 to a fraction.
(5 marks)
Answers
Answer:
a) v>4.5
b) w<6.5
a) 0.3 recurring
b) 5/11
for the function f(x) = x^2, what effect will be multiplying f(x) by 1/2 have on the graph?
Answers
3. a local sports store charges $22.33 for a football and 6% tax. how much
will the total price be to purchase the football? *
Answers
Given the charges for a football and the tax rate, the total price to purchase a football is $23.6698.
How much will the total price be to purchase the football?
Given that;
Charges for a football = $22.33Tax rate = 6%Total price to purchase football = ?First, we calculate the tax price on the football.
Tax price = Tax rate × Charges for the football
Tax price = 6% × $22.33
Pax price = 0.06 × $22.33
Tax price = $1.3398
Now, total price to purchase football will be;
Total price = Charges for a football + Tax price
Total price = $22.33 + $1.3398
Total price = $23.6698
Given the charges for a football and the tax rate, the total price to purchase a football is $23.6698.
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The measure of the base angle of an isosceles triangle is 52.
What is the measure of the vertex angle?
Answers
Answer:
76°
Step-by-step explanation:
The 2 base angles are equal so
52+52+vertex angle=180° (Angle Sum Property)
104+ vertex angle=180°
vertex angle= 180-104
vertex angle=76°
help please I really need help and thank you :))))
Answers
Answer:
14) x = 30°
15) x = 50°
Step-by-step explanation:
14) 60 + x = 90
x = 90 - 60
x = 30°
15) 130 + x = 180
x = 180 - 130
x = 50°
Hope this helps
Step-by-step explanation:
Is first image we are given a right angle and we know that right angle = 90°
So,
60 + x = 90
x = 90 - 60 = 30°
x = 30°
In the second image we are given a straight line and we know that on the 180° angle is a straight line.
so,
130 + x = 180
x = 180 - 130
x = 50°
Which point on the number line most closley represents 1.ModifyingAbove 6 with bar?
A number line going from negative 6 to positive 6. Point A is between negative 2 and negative 1, point B is between 0 and 1, point C is 1, point D is between 1 and 2.
A
B
C
D
Answers
The correct answer is option D.The point 1.6 with bar will be lies between 1 and 2.
The image of the question is attached with the answer below:-
What is a number line?The number line is the line on which real numbers are marked with the same interval between them. Number lines are used to mark any point of the real number on the line.
We can see in the image that A, B, C and D points are marked on the number line. The line is marked with real numbers that are integers.1.6 bar number will lie between 1 and 2 numbers.
Therefore the correct answer is option D.The point 1.6 with a bar will be lies between 1 and 2.
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Answer:
D
Step-by-step explanation:
What is the value of a in the equation? 22 = startfraction a over 11 endfraction 2 33 222 242
Answers
Answer:
D / 242
Step-by-step explanation:
hope this helps!
[tex]\sqrt{8+2\sqrt{15}[/tex] Simplify this equation! Please help ASAP
Answers
[tex] \sqrt{8 \: + \: 2 \sqrt{15} } [/tex]
Factor the indicated expression:[tex] \sqrt{( \sqrt{3 } \: + \: \sqrt{5} ) ^{2} } [/tex]
Simplified the index, the root and also the exponent using the number 2.[tex] \boxed{ \bold{\sqrt{3} \: + \: \sqrt{5} }}[/tex]
MissSpanishIf y varies inversely with x and y=2 when x=5, what is the value of x when y=3?
Answers
Answer:
Step-by-step explanation:
Method
Inversely in this sentence means
y = k/x
So you first step is to find the value of k. You do that by setting up an inverse relationship with y = 2 , x = 5
2 = k/5 Multiply both sides by 5
2*5 = 5*k/5
10 = k
Now you are able to answer the question.
k = 10y = 3x = ?y = 10/x
3= 10/x Multiply both sides by x
3*x = x * 10/x
3x = 10 Divide both sides by 3
3x/3 = 10/3
x = 3.33 or x = 3 1/3
Answer
x = 3.33 or x = 3 1/3
What is the length of line segment AB in the triangle shown below?
Answers
Answer:
the lenght of the segment ab is 15 inches
David Saw three ducks in a pond then he saw two more ducks on the path how many decks did David see all together
Answers
Answer:
5
Step-by-step explanation:
Cindy wants to put new carpet in her entryway. The entryway is 15ft. long and 7ft. wide. She wants to buy 10% extra carpet in case it is needed. How much carpet will she need to order?
Answers
Answer:
10.5
Step-by-step explanation:
quick math
URGENT
Christian installed an electric pump to pump water from a borehole into a 30 000 litre cement dam. If the water is pumped at a rate of 75 litres per minute. How long does it take to fill the dam? A 4 h
B. 6 h 40 min
C 6 h 20 min
D 3 h 40 min
Answers
30000 / 75 = 400
400 minutes put into hours is 6 hours 40 minutes
Select the correct answer.
What is the general form of the equation for the given circle centered at O(0, 0)?
A.
x2 + y2 + 41 = 0
B.
x2 + y2 − 41 = 0
C.
x2 + y2 + x + y − 41 = 0
D.
x2 + y2 + x − y − 41 = 0
Answers
The general form of the equation for the given circle centered at O(0, 0) is x² +y² - 41=0.
The correct option is (B).
What is equation of circle?The general equation for a circle is ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.
as, general equation for a circle is ( x - h )² + ( y - k )² = r²
Here, centered at O(0, 0).
So,
a =0 and b = 0
now, r² = (BO)²
r² = (4-0)² +(5-0)²
r² = 16+25
r² = 41
Hence, Center at the origin passing through B(4, 5) is x² +y² = 41.
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