Calculate the area of the right triangle that has the following coordinates:
A: (-2,-1)
B: (1, 1)
C: (3,-2)
You must show all calculations to earn any credit. I suggest that you sketch this
triangle on graph paper so that the visual can help you.
Answers
The area of right triangle is [tex]\frac{1}{15}[/tex].
The given coordinates are [tex](-2,-1), (1, 1), (3,-2)[/tex].
We have to find the area of right triangle.
To find the area we first draw the graph using that coordinate.
The graph of the coordinate is
To find the area we use the formula
[tex]\angle ABC=\frac{1}{2}(|AB|)(|AC|)[/tex]
We first find the value of [tex](|AB|)[/tex] and [tex](|AC|)[/tex].
e coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]B[/tex] is [tex](1,1)[/tex].
The slope of [tex](|AB|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AB|)=\frac{1-(-1)}{1-(-2)}[/tex]
The slope of [tex](|AB|)=\frac{1+1}{1+2}[/tex]
The slope of [tex](|AB|)=\frac{2}{3}[/tex]
The coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]C[/tex] is [tex](3,-2)[/tex].
The slope of [tex](|AC|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AC|)=\frac{(-2)-(-1)}{3-(-2)}[/tex]
The slope of [tex](|AC|)=\frac{-2+1}{3+2}[/tex]
The slope of [tex](|AC|)=-\frac{1}{5}[/tex]
Now finding the area of right triangle by putting the values.
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times(-\frac{1}{5})[/tex]
Area can't be negative so
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times\frac{1}{5}\\\angle ABC=\frac{2}{30}\\\angle ABC=\frac{1}{15}[/tex]
Hence, the area of right triangle is [tex]\frac{1}{15}[/tex].
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Related Questions
determine the orderd pair (8,-3)is a solytion to the linear pair
Answers
To answer this question, we need to evaluate if the ordered pair forms an identity with both equations. We need to substitute the values for x = 8, and y = -3 in both equations:
[tex]\frac{x}{2}+5y=-11\Rightarrow\frac{8}{2}+5(-3)=-11\Rightarrow4-15=-11\Rightarrow-11=-11[/tex]These values result in an equality in this equation. We need to evaluate the other equation:
[tex]6x-\frac{y}{6}=40\Rightarrow6\cdot(8)-(\frac{-3}{6})=40\Rightarrow48+\frac{1}{2}=\frac{97}{2}\ne-11[/tex]In this case, the values do not result in an equality in one of both equations.
Therefore, we have that the correct answer is the option B:
No, the proposed solution does not result in an equality in one of the two equations.
See attached for the problem
Answers
The areas and volumes are given as follows:
a) Area of the four sides to be painted: 2448 m².
b) Area to be covered with shingles: 1140 m².
c) Volume of concrete needed to pour a floor 16 cm deep: 174.72 m³.
d) Total surface area: 5878.4 m².
Area -> Four sides paintedThe sides painted are divided as follows:
Two rectangles of dimensions 26 m and 18 m.Two rectangles of dimensions 42 m and 18 m.Hence the total area to be painted is found as follows:
Total area = 2 x 26 x 18 + 2 x 42 x 18 = 2448 m².
(Area rectangle = base x height)
Area to be covered with shinglesThis part of the problem seems incomplete, however the answer is correct.
Volume of concreteThe volume is given by:
Volume = base area x height.
Hence:
The base area is a rectangle of dimensions 26 m and 42 m.The height is of 16 cm = 0.16 m.Hence the volume is given by:
V = 26 x 42 x 0.16 = 174.72 m³.
Surface areaThe base is a rectangular prism of dimensions 26 m, 42 m and 18m, hence:
Surface area base = 2 x (26 x 42 + 26 x 18 + 42 x 18) = 4632 m².
The top is composed by:
Two rectangles of dimensions 13.6 m and 42 m.Two triangles of base 26 m and height 4 m.Hence:
Surface area top = 2 x 13.6 x 42 + 2 x 0.5 x 26 x 4 = 1246.4 m².
Then the total surface area is:
Total surface area = 4632 + 1246.4 = 5878.4 m².
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May I get help, I know I have to multiply the possibilities, but I keep getting stuck
Answers
First we obtain each probability
The land has no oil
is a 45% chance that the land has oli , then the chance that the land has not oil is 55%
55% can be represented like 0.55
then the probability to the land has no oil is 0.55
The test shows that there is no oil
Kit claims to have an 80% of idicating oil, then the percent that there is no oil is 20%
20% can be represented like 0.2
the tne probability to shows that theere is no oil is 0.2
Finally
Multiply the probabilities to find the probability that say the land has no oil and the test shows that there is no oil
[tex]0.55\times0.2=0.11[/tex]then irhg toption is B
Which relation below is not a function
Answers
Answer:
0,0
Step-by-step explanation:
Two numbers can not equal another number
One factor of the polynomial x3 − 7x2 + 13x − 3 is (x − 3). What is the other factor of the polynomial? (Note: Use long or synthetic division.) A. (x2 + 4x − 1) B. (x2 − 4x + 1) C. (x − 4) D. (x + 4)
Answers
The other factor of the polynomial from what we have here is given as x² - 4x + 1 option B is correct.
How to solve the polynomialWe are required to divide x³ - 7x² + 13x - 3 by x -3
We have this as
x² - 4x + 1
-----------------
x-3 | x³ - 7x² + 13x - 3
we would have
x³ - 3x²
subtract this value by the one that we have above
then we would have
-4x² + 13x
-4x² + 12x
subtract these values from each other to get the value below.
x - 3
Hence the solution to the polynomial would be x² - 4x + 1.
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Find all solutions of the equation in the interval [0,2pi). csc =7/4 If there is more than one solution, separate them with commas.Do not round any intermediate computations. Give your answer(s) in radians, and round your answer(s) to the nearest hundredth
Answers
Since the cosecant is the inverse of the sine, we can write the following:
[tex]\begin{gathered} \csc (\theta)=\frac{7}{4} \\ \sin (\theta)=\frac{1}{\csc(\theta)}=\frac{1}{\frac{7}{4}}=\frac{4}{7} \end{gathered}[/tex]Then, using a calculator, we can calculate the angle that has a sine of 4/7:
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{4}{7})_{} \\ \theta=34.85\degree \end{gathered}[/tex]There is one more angle between 0 and 2π that has the same value of 4/7 for the sine, and it's the supplementary angle to the one we found:
[tex]\theta_2=180-\theta_1=180-34.85=145.15\degree[/tex]Therefore the answers are 34.85° and 145.15°.
Converting to radians, we have:
[tex]\begin{gathered} 34.85\cdot\frac{\pi}{180}=0.61 \\ 145.15\cdot\frac{\pi}{180}=2.53 \end{gathered}[/tex]So the final answer is 0.61 and 2.53.
In a right triangle, the hypotenuse is the longest side?
Answers
Okay, here we have this:
The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle. The other two sides are called the opposite and adjacent sides.
This mean that the statement is true.
You might need:CalculatorHiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 squaremeters left to paint.Let y represent the area (in square meters) left to paint after chours.Which of the following information about the graph of the relationship is given?
Answers
The graph is that of area painted against the number of hours. Given that he painted 8 square meters per hour, the slope is 8 square meters per hour because slope is known as unit rate.
After 3 hours of painting, he would have painted 8*3 = 24 square meters.
Since he has 28 meters left to paint, it means that the total rea of the room that
What type of number is - Choose all answers that apply:AWhole numberBIntegerRationalDIrratio
Answers
It is whole, integer, rational
Melanie went shopping and spent $18 on scarves. If she spent $77 total, what percentage did she spend on scarves? Round your answer to the nearest percent.
Answers
Answer:
23.4%
Step-by-step explanation:
[tex]\frac{18}{77} =\frac{x}{100}[/tex]
$18 divided by $77 is the equivalent of X(% spent on scarves) divided by 100. To find X you cross multiply and divide. [tex](18*100)/77=23.377...[/tex], rounded, X = 23.4
select the ordered pair that represent solutions of the system of inequalities A) (-1,3)B) (0,0)C) (-4,1)D) (0,2)E) (-5,0)F) ( -4,4)G) (-5,3)H) (-6,5)please answer fast
Answers
From the graph, the solution of the graph is given by the area of intersection of the two functions. The are under the area of the two functions are (-4, 1), (-5, 0), (-4, 4)
Trying to figure out this for my home work assignment
Answers
Given:
Choosing a even number from the numbers between 1 and 10.
The sample space is
[tex]\mleft\lbrace2,3,4,5,6,7,8,9\mright\rbrace[/tex]Let A be the event of choosing a even number.
There are 4 out comes in the experiment.
What is the explicit formula for the sequence?3,1,-1, -3, -5,...a,= -2n +5a, = 17-5an= 2n-5an= -2n + 3
Answers
We need the formula that gives us the values of the sequence
where n is the value of the position
using the formula
[tex]a_n=-2n+5[/tex][tex]\begin{gathered} a_1=-2(1)+5=3 \\ a_2=-2(2)+5=1 \\ a_3=-2(3)+5=-1 \\ a_4=-2(4)+5=-3 \\ a_5=-2(5)+5=-5 \end{gathered}[/tex]as we can see the formula is the correct formula because we obtain the values of the sequence
Calculate the value of each expression.
1) (-5)
/
4
2) (-5)-(-/-)
3)-20
4)-20
(-20)
(4)
5)
Answers
Answer:
1) -15/4 or -3.75
2) 15/4 or 3.75
3) 5
4) -5
5) -5
Step-by-step explanation:
I need help with this practice problem If you can, show your work step by step so I can take helpful notes
Answers
The given geometric series is
[tex]120-80+\frac{160}{3}-\frac{320}{9}+\cdots[/tex]In a geometric series, there is a common ratio between consecutive terms defined as
[tex]r=\frac{-80_{}}{120_{}}=-\frac{2}{3}[/tex]The sum of the first n terms of a geometric series is given by
[tex]S_n=\frac{a(1-r^n)}{1-r},r<1[/tex]Where a is the first term.
From the given series
a = 120
Hence, the sum of the first 8 terms is
[tex]S_8=\frac{120(1-(-\frac{2}{3})^8)}{1-(-\frac{2}{3})}[/tex]Simplify the brackets
[tex]S_8=\frac{120(1-\frac{2^8}{3^8}^{})}{1+\frac{2}{3}}[/tex]Simplify further
[tex]\begin{gathered} S_8=\frac{120(1-\frac{256}{6561})}{\frac{3+2}{3}} \\ S_8=\frac{120(\frac{6561-256}{6561})}{\frac{5}{3}} \\ S_8=\frac{120(\frac{6305}{6561})}{\frac{5}{3}} \\ S_8=\frac{120\times6305}{6561}\div\frac{5}{3} \\ S_8=\frac{120\times6305}{6561}\times\frac{3}{5} \\ S_8=\frac{120\times6305}{6561}\times\frac{3}{5} \\ S_8=\frac{8\times6305}{729} \\ S_8=\frac{50440}{729} \end{gathered}[/tex]Therefore, the sum of the first 8 terms is
[tex]\frac{50440}{729}[/tex]3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive? 0.475 0.038 0.525 0.905
Answers
ANSWER:
0.475
STEP-BY-STEP EXPLANATION:
The probability of a person has disease given the test is positive:
P (disease) = 3.8% = 0.038
P (positive | disease) = 93.9% = 0.939
P (positive | no disease) = 4.1% = 0.041
P (no disease) = 100% - 3.8% = 96.2% = 0.962
The probability that the person has the disease given that the test result is positive is calculated as follows:
[tex]\begin{gathered} \text{ P\lparen infected \mid test positive\rparen }=\frac{\text{ P\lparen positive \mid infected\rparen }\times\text{ \rbrack P \lparen infected\rparen}}{\text{ P \lparen positive\rparen}} \\ \\ \text{ P \lparen positive \mid infected\rparen }=\text{ P \lparen positive \mid disease\rparen = 0.939} \\ \\ \text{ P \lparen infected\rparen = P \lparen disease\rparen = 0.038} \\ \\ \text{ P \lparen positive\rparen = P \lparen positive \mid infected\rparen }\times\text{ P \lparen infected\rparen }+\text{ P \lparen positive \mid no infected\rparen}\times\text{ P \lparen no infected\rparen } \\ \\ \text{ P \lparen positive \mid infected\rparen =P \lparen positive \mid no disease\rparen = 0.041} \\ \\ \text{ P \lparen no infected\rparen = P \lparen no disease\rparen = 0.962} \\ \\ \text{ We replacing:} \\ \\ \text{ P \lparen positive\rparen = }0.038\cdot0.939+0.041\cdot0.962=0.075124 \\ \\ \text{ P\lparen infected \mid test positive\rparen }=\frac{0.038\cdot0.939}{0.075124} \\ \\ \text{ P\lparen infected \mid test positive\rparen = }\:0.47497=0.475 \end{gathered}[/tex]The correct answer is the first option: 0.475
pls help the hw is due today
Answers
Answer: the slope for the line is
y= -2x-4
(b) The area of a rectangular painting is 5568 cm².If the width of the painting is 58 cm, what is its length?Length of the painting:
Answers
Step 1: Problem
The area of a rectangular painting is 5568 cm².
If the width of the painting is 58 cm, what is its length?
Length of the painting:
Step 2: Concept
Area of a rectangle = Length x Width
Step 3: Method
Given data
Area = 5568 cm square
Width = 58 cm
Length = ?
Area of a rectangle = Length x Width
5568 = 58L
L = 5568/58
L = 96cm
Step 4: Final answer
Length of the painting = 96cm
a certain number was multiplied by 3. then, this product was divided by 10.2. finally, 12.4 was subtracted from this quotient, resulting in a difference of -8.4. what was this number
Answers
Answer:
13.6
Step-by-step explanation:
[tex] \frac{3x}{10.2} - 12.4 = - 8.4[/tex]
[tex] \frac{3x}{10.2} = 4[/tex]
[tex]3x = 40.8[/tex]
[tex]x = 13.6[/tex]
If tan=21/20,0
a. sin a/2
b. cos a/2
c. tan a/2
Answers
Using trigonometry we can conclude that the value is sin a/2=7/58, cos a/2= -3/√58, tan a/2= -7/3.
What is Trigonometry?A branch of mathematics called trigonometry looks at how triangle side lengths and angles relate to one another. Applications of geometry to astronomical research led to the development of the field in Hellenistic civilization during the third century BC.We are aware:
x=tan(a/2)And,
tan(a)=2tan(a/2)/1-tan²(a/2)=21/20= 2x/1x2⇒21−21x²=40x⇒21x²+40x−21=0⇒21x²+49x−9x−21=0⇒7x(3x+7)−3(3x+7)=0⇒(3x+7)(7x−3)=0Thus, x=7/3 or x=3/7
It is now given:
180<a<270⇒ 90<a/2<135The a/2 second quadrant.
As a result:
x = tan(a/2)negativeTherefore,
x = tan(a/2)= -7/3sin(a/2) => +veThis means that:
sin(a/2) = 1/cos(a/2) = 1/(1+cot²(a/2))= 1/(1+1/tan(a/2))=1/√(1+9/49)=7/√58The formula is now:
cos(a/2)=sin(a/2)/tan(a/2)=7/√58/ -7/3cos(a/2) = -3/√58Therefore, using trigonometry we can conclude that the value is sin a/2=7/58, cos a/2= -3/√58, tan a/2= -7/3.
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b) A survey on the nationality of the student in the St Thomas international school is conducted and the results are shown below:i) if two students are randomly selected, what is the probability that both of them are European (correct to 4 decimal places)ii) if one student is randomly selected, what is the probability that a student is not Asian. (correct to 4 decimal places)
Answers
Given:-
A survey on the nationality of the student in the St Thomas international school is conducted and the results are shown.
To find if two students are randomly selected, what is the probability that both of them are European and if one student is randomly selected, what is the probability that a student is not Asian.
So now the total number of students are,
[tex]230+110+85+25=450[/tex]So now the probability of getting European is,
[tex]\frac{110}{450}=\frac{11}{45}[/tex]So the probability is,
[tex]\frac{11}{45}[/tex]So now the probability is asian is,
[tex]\frac{230}{450}=\frac{23}{45}[/tex]So the probability that it is not asian is,
[tex]1-\frac{23}{45}=\frac{45-23}{45}=\frac{22}{45}[/tex]so the required probability is,
uhh im stuck and im stressed .. and i dont understand area model math..
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(5x + 6)(2x² + 3x + 8) = ?
Step 02:
Area Model
First, you must multiply the values in the rows by each of the values in the columns.
Then, you must add all the values resulting from the multiplications.
10x³
2x²
+ 12x²
15x²
18x
3x
40x
48
8
--------------------------------------------
10x³ + 29x² + 61x + 56
The answer is:
(5x + 6)(2x² + 3x + 8) = 10x³ + 29x² + 61x + 56
In a class of students, the following data table summarizes the gender of the studentsand whether they have an A in the class. What is the probability that a student whohas an A is a female?Female MaleHas an A24Does not have an A176
Answers
We are asked to find the probability that a student is female given that they have an A.
Since this is the case, we limit ourselves to observing the row "Has an A".
In said row, there is a total of 6 students who have an A. Out of those 6, 2 are female.
Thus, P(Female|A) = 2/6 = 1/3 = 33.33%.
The figure below shows a striaght line AB intersected by another straight line t: Write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3. (10 points)
Answers
Angles 1 and 3 are vertical angles, that is, are pairs of opposite angles made by intersecting lines. If 2 angles are vertical then they are congruent, in other words, they have the same measure.
What is the difference between the inverse function of quadratic and exponential
Answers
Answer:
Quadratic functions are those where their rate of change changes at a constant rate. Exponential functions are those where their rate of change is proportional to itself.
Step-by-step explanation:
An example of a quadratic function would be the shape that a ball makes when you throw it. Gravity causes a constant acceleration, the ball slows down as it is moving up, and then it speeds up as it comes down.
An example of an exponential function would be the population of a bacterium as long as there is enough space and nutrients or how your money grows with compound interest in a bank.
Write the equation of a quadratic in general form, given its solutions.x=4 ; x=-1
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The given solutions of the quadratic equation:
x = 4 and x = -1
First we make them factors of the equation:
x= 4 becomes:
[tex]x-4\text{ = 0}[/tex]and x = -1 becomes:
[tex]x\text{ + 1 = 0}[/tex]So (x-4) and (x+1) are the factors.
To get the general quadratic equation, we would expand the factors
[tex]\begin{gathered} (x-4)(x+1)\text{ = 0 } \\ x(x+1)\text{ -4(x+1) = 0} \\ x^2+x\text{ -4x-4 = 0} \end{gathered}[/tex][tex]\begin{gathered} Adding\text{ like terms} \\ x^2-3x-4\text{ = 0} \end{gathered}[/tex]The general quadratic equation:
[tex]x^2\text{ - 3x - 4 = 0}[/tex]4. If line segment AB has coordinates A(-2,4) and B(2,0) and line segment
CD has coordinates C(3,4)and D(-3,-2), how would you describe these two
line segments?
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These 2 lines perpendicular to each other on the graph.
What are perpendicular lines?The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I
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Find x rounded to the nearest whole degree. Be sure to round correctly!
Answers
answer: 36°
Course ListScore! OU TUUTUTZu anisweredQuestion 11In A XYZ, the sum of the measures of ZX and Y are 55°. What is the measure of ZZ?ZZ=?
Answers
To solve that question we must remember that the sum of all internal angles of a triangle is 180°, we can say that
[tex]\angle X+\angle Y+\angle Z=180[/tex]That's a rule! it's always true.
The problem says that
[tex]\angle X+\angle Y=55[/tex]Then let's use it in our equation!
[tex]\begin{gathered} \operatorname{\angle}X+\operatorname{\angle}Y+\operatorname{\angle}Z=180 \\ \\ 55+\operatorname{\angle}Z=180 \end{gathered}[/tex]Now we can solve it for Z
[tex]\begin{gathered} 55+\angle Z=180 \\ \\ \angle Z=180-55 \\ \\ \angle Z=125° \end{gathered}[/tex]Therefore the measure of Z is 125°
Consider the following expression-x + 8x2 - 9x?Step 2 of 2: Determine the degree and the leading coefficient of the polynomial.
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Solution
For this case we have the following polynomial:
[tex]-x+8x^2-9x[/tex]For this case the higher degree is 2 then the answer is:
Degree= 2
Leading Coefficient of the polynomial: 8
