If the ends of the base of an isosceles triangle are at (2,0) & (0,1) & the eqn of one side is
x=2,
then the orthocentre of the triangle is
a) (3/2, 3/2)
b) (5/4, 1)
c) (3/4, 1)
d) (4/3, 7/12)
...?
Answers
such that xo=(2+0 + 2)/3, so xo= 4/3, so the answer must be
d) (4/3, 7/12)
Answer:
The orthocenter of the triangle is [tex](\frac{5}{4},1)[/tex] and option b is correct.
Step-by-step explanation:
The ends of the base of an isosceles triangle are at (2,0) & (0,1).
Orthocentre of the triangle is the intersection point of all three altitudes from its vertices.
First find any two altitudes, then find intersection point of altitudes.
The equation of a side is x=2, which is an vertical line. The opposite vertices of this side is (0,1), so the perpendicular line is a horizontal line. The equation of first altitude is
[tex]y=1[/tex] .... (1)
In an isosceles triangle, then attitude is the median of non-equal side. It means the altitude is passing through the midpoint of base side.
[tex]Midpoint=(\frac{2+0}{2},\frac{0+1}{2})=(1,0.5)[/tex]
Slope of base side is
[tex]m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{0-2}=-0.5[/tex]
The product of slopes of two perpendicular lines is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]-0.5\times m_2=-1[/tex]
[tex]m_2=2[/tex]
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is slope.
The slope of second altitude is 2 and it passing through the pint (1,0.5), therefore the equation of second altitude is
[tex]y-0.5=2(x-1)[/tex]
[tex]y=2x-1.5[/tex] ..... (2)
From equation (1) and (2), we get
[tex]x=\frac{5}{4}[/tex]
[tex]y=1[/tex]
Therefore the orthocenter of the triangle is [tex](\frac{5}{4},1)[/tex] and option b is correct.
Related Questions
How many faces, edges, and vertices does a triangular pyramid have?
A. 3 faces, 4 edges, 4 vertices
B. 3 faces, 3 edges, 3 vertices
C. 4 faces, 6 edges, 3 vertices
D. 4 faces, 6 edges, 4 vertices
Answers
A triangular pyramid has 3 faces, 4 edges, 4 vertices.
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Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .
Answers
A student is training for the track team during the first three months of the year by running for 30 minutes every day while averaging 5 miles each day. Select the graph that correctly shows the total miles ran during the time of his training program.
Answers
1 hour - 10 miles
10 hours - 100 miles ...
The independent value is plotted along the x- axis ( Hours ) and the dependent variable is plotted along the y-axis ( Miles ). Also:
3 months = 90 days
90 x 1/2 hours = 45 hours
Answer: The graph B ) ( or the second one ).
Answer:
Graph 2 :)
Step-by-step explanation:
The length of the rectangle is 2(x+1) meters and the perimeter is 60 meters. Find the length of the rectangle
Answers
1.) If P = 2l + 2w, the formula to find w is _____
A.) w=P-21
B.) w=P/2-21
C.) w=2(P-21)
D.) w=(P-21)/2
2.)If P is 30 units and l is 10 units, w is units_____
A.) 5
B.) 10
C.) 15
Answers
Answer:
d and a
Step-by-step explanation:
look for the horizontal asymptote of
(sin x)/(1 + cos x).
Answers
The horizontal asymptotes are the values to which the function approaches as x becomes larger and larger (+/- infinity).
Then you have to find the limits of the function for x -> + and - infinity.
If the limit does not exist then there is not horizontal asypmtotes.
Indeed the limit of that function when x goes to +/- infinity does not exist, because the denominator will continue fluctating between 1 and 2, and the numerator will be fluctuating between -1 and 1.
This function fluctuates periodically from negative infinity to positive infinity, it does not have a limit when x grows so it does not have horizontal asymptotes.
Convert pounds to ounces 12.6 pounds
Answers
hope this helps you
so 12.6 lbs = 201.6 oz
so 12.6 multiplied by 16 gives you the answer
What percent of 20 is 40??
Answers
x * 20 = 40
20x = 40
x = 40 / 20
x = 2
2*100 = 200%
An experiment consists of rolling two fair(not weighted) dice and adding the dots on the two sides facing up. Each die has the number 1 on two opposite faces, the number 2 on two opposite faces, and the number 3 on two opposite faces.
Compute the probability of obtaining the indicated sums in problem.
Answers
So, the answer would be
12/36=1/3
the rest can also be obtained by counting. the probability you get a sum of 2 is
4/36
So, for a sum of 6 and the probability you get a sum of 3 and the probability you get a sum of 5 is 8/36
Final answer:
The student is performing a probability calculation involving rolling two dice and must enumerate all possible outcomes. The probability of a specific sum is determined by dividing the number of ways to achieve that sum by the total number of possible outcomes, 36 in the case of rolling two dice.
Explanation:
The student's experiment consists of rolling two fair dice and adding the numbers that appear on the faces that land upwards. Each die in this scenario has the numbers 1, 2, and 3 on two opposite faces. When calculating the probability of specific sums resulting from this experiment, we need to consider all the possible outcomes (the sample space) and the number of ways to achieve the sum in question.
To find the probability of any particular sum, one must enumerate each distinct way that sum can occur. There are a total of 36 possible outcomes when rolling two dice (6 outcomes per die × 2 dice). For example, to calculate the probability of getting a sum of 4, we need to consider the possible dice combinations (1+3, 2+2, 3+1) that would result in that sum.
As for the probability of an event, it is the number of favorable outcomes over the total number of possible outcomes. If the event is 'rolling a sum of 4', and there are three combinations out of 36 total that yield that sum, the probability would be 3/36 or 1/12. Remember that we must count each die distinctly; although the numbers are the same (1, 2, 3), a roll of 1 on the first die and 3 on the second die is a different outcome from a roll of 3 on the first die and 1 on the second die.
What is the value of p in the equation x2 = 12y?
Answers
x^2=3.4.y
p=3
The Greens want to put an addition on their house 18 months from now. They will need to save $10,620 in order to achieve this goal. They set aside the same amount each month, and after a year discover they have saved $6,120. The Greens must adjust their plan in order to meet their goal, so they came up with the following optionsa.Only option A will allow them to meet their goal.b.Only option B will allow them to meet their goal.c.Both options A and B will allow them to meet their goal.d.Neither option A nor option B will allow them to meet their goal.
Answers
Using a new lawn mower, Abby can mow the lawn in 2 hours. Her sister Carla used an older lawn mower and takes 3 hours to mow the same lawn. How long will it take them if they work together?
Answers
So it would be:[tex] \frac{x}{3} + \frac{x}{2} = 1 [/tex] Then cross muitply.
2x + 3x = 6
5x=6
x= [tex] \frac{6}{5} hours[/tex]
Bill started west on road U.S. 50, riding a bicycle at an average rate of 9 mph. Four hours later Charles started after Bill on a motor cycle and overtook him in 2 hours. What was Charles' rate?
Which equation could be used to solve for Charles' rate if it is represented by x?
A.2x = 36
B.2x = 54
C.6x = 54
Answers
Answer: 2x = 54
I got this question correct on my lesson.
To find Charles' rate, we can set up an equation using the formula Distance = Rate x Time. The correct equation to solve for Charles' rate x is 2x = 36.
Explanation:To solve this problem, we can use the equation Distance = Rate x Time. Let's assume that Charles' rate is represented by x. When Charles overtakes Bill, they have traveled the same distance. Bill has been riding for 4 hours at a rate of 9 mph, so his distance is 9 x 4 = 36 miles. Charles overtakes Bill in 2 hours, so his distance is x x 2. Setting the two distances equal to each other, we have 36 = 2x, which simplifies to 2x = 36. Therefore, the correct equation to solve for Charles' rate x is option A, 2x = 36.
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Aditi has $50.00 in her wallet. She buys a shirt for $12.00 and also wants to buy some bracelets that are on sale for $0.60 each. The inequality below relates x, the number of bracelets she can buy, with her shirt purchase and the money in her wallet.
What is the greatest number of bracelets she could buy?
Answers
Answer:
The answer is 63.
Step-by-step explanation:
50-12=38 38/.6 is equal to 63.333 you can't buy .333 of a bracelet so she will be able to buy 63 and have little money left.
The greatest number of bracelets she could buy will be 63.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
Given data;
The total amount of money in my wallet = $50.00
Cost of shirt = $12.00
Price of bracelet per piece = $0.60
Let x is the no of the bracelet;
The equation obtained as;
⇒The total amount of money in my wallet = Cost of the shirt + Price of the bracelet per piece × No of the bracelet
⇒50 = 12 + 0.60 x
⇒0.60 x = 50-12
⇒x = 38/0.60
⇒x= 63.333 ≈ 63 bracelet
Hence the greatest number of bracelets she could buy will be 63.
To learn more about inequility, refer to https://brainly.com/question/20383699.
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how many solutions does the system of equations have 2x = -10y + 6 and x + 5y = 3
Answers
x=-5y+3 is the same as x+5y=3
what subset of real numbers does 26 belong to
Answers
this set does not include negative numbers or 0
whole numbers are natual numbers but including 0
integers are whole numbers and also negative numbers
rational numbers are numbers that can be written in form a/b where b≠0
irrational numbers can't be written in form a/b, examples are like pi
real numbers are all of the abovee and more
26 belongs to the natural numbers set
You have 10 fish, 5 drown, 3 come
back to life. How many fish do you have? ...?
Answers
Ravi is driving 440 miles to visit his grandma. if he drives at an average rate of 55miles per hour, how many hours will it take him to get 3/4 of the way there?
Answers
Answer:
Using formula:
[tex]\text{Time} = \frac{\text{Distance}}{\text{Speed}}[/tex]
As per the statement:
Ravi is driving 440 miles to visit his grandma. if he drives at an average rate of 55 miles per hour.
⇒Speed = 55 miles/hour and Distance = 440 miles.
We have to find how many hours will it take him to get 3/4 of the way there.
Distance to get 3/4 of the way there= [tex]\frac{3}{4} \cdot 440 = 3 \cdot 110 = 330[/tex] miles.
Substitute the given values we have;
[tex]\text{Time} = \frac{330}{55}[/tex]
Simplify:
Time = 6 hours.
Therefore, 6 hours will it take him to get 3/4 of the way there
Simplify √24
A 3√8
B 2√12
C 2√6
D 4√6
Answers
c)2√6
---------
4. In an A-frame house, the two congruent sides extend from the ground to form a 34° angle at the peak. What angle does each side form with the ground? (1 point)
156°
146°
73°
78°
True or False
5. All right triangles are isosceles. (1 point)
true
false
14. What does CPCTC represent and when would you use it? (4 points)
Answers
1) 2x + 35 = 180° so x= 180 - 35 / 2 =73°
the answer is 73°
2)
3) In geometry, "Corresponding parts of congruent triangles are congruent" (CPCTC) is a succinct statement of a theorem regarding congruent trigonometry, defined as triangles either of which is an isometry of the other. CPCTC states that if two or more triangles are congruent, then all of their corresponding angles and sides are congruent as well. CPCTC is useful in proving various theorems about triangles and other polygons.
If triangles ABC and DEF are congruent, denoted as
Final answer:
Each congruent side of the A-frame house forms a 73° angle with the ground, and the statement that all right triangles are isosceles is false. CPCTC is a geometric theorem that states corresponding parts of congruent triangles are congruent.
Explanation:
Angles in an A-frame house
The given A-frame house forms an isosceles triangle with a peak angle of 34°. Using the theorem that the sum of angles in a triangle is 180°, we can calculate the angles each side forms with the ground. Since the two congruent sides are equal, the angles they form with the ground are also equal. There are two steps to solve this:
Subtract the peak angle from 180° to find the sum of the two base angles: 180° - 34° = 146°.
Divide the sum of the base angles by 2 (since they are equal in an isosceles triangle): 146° / 2 = 73°.
Therefore, each side forms a 73° angle with the ground.
All right triangles are isosceles - True or False?
This statement is false. Not all right triangles are isosceles. A right triangle is defined as having one 90° angle, but it doesn't necessarily have two sides of equal length, which would make it isosceles.
What does CPCTC represent?
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It is a theorem used in geometry to conclude that the corresponding parts (angles or sides) of two triangles are congruent, given that the triangles themselves are proven to be congruent based on certain criteria like side-angle-side (SAS) or angle-side-angle (ASA).
What is the solution to the equation? 3q 5 = -2q 20
a. q = 3
b. q = 5
c. q = 15
d. q = 25
Answers
3q+5=-2q+20
5q = 15
q=3
3q-5=-2q-20
5q = -15
q = -3
3q+5=-2q-20
5q = -25
q = -5
3q-5=-2q+20
5q = 25
q = 5
Donte simplified the expression below.
4(1 + 3i) – (8 – 5i) = –4 + 8i
What mistake did Donte make?
A.He did not apply the distributive property correctly for 4(1 + 3i).
B.He did not distribute the subtraction sign correctly for 8 – 5i.
C.He added the real number and coefficient of i in 4(1 + 3i).
D.He added the two complex numbers instead of subtracted.
Answers
_____________________________________________
Explanation:
______________________
Note the distributive property of multiplication:
_____________________________
a*(b+c) = ab + ac.
____________________________
As such: 4*(1 + 3i) = (4*1) + (4*3i) = 4 + 12i ;
_____________________________________
Instead, Donte somehow incorrectly calculated:
_____________________________________
4*(1 + 3i) = (4*1) + 3i = 4 + 31; (and did the rest of the problem correctly);
Note: - (8 - 5i) = -8 + 5i (done correctly;
___________________________________
So if Donte did not apply the distributive property correctly for 4*(1+3i)—and incorrect got 4 + 3i (as mentioned above); but did the rest of the problem correctly, he would have got:
_____________________________
4+ 3i - 8 + 5i = -4 + 8i (the incorrect answer as stated in our original problem.
__________________
This corresponds to: "Answer choice: [A]: He did not apply the distributive property correctly for 4(1 + 3i)."
___________________________
4(1 + 3i) – (8 – 5i)
4+12i - 8 + 5i
17i-4
so, 4(1 + 3i) – (8 – 5i) should be equal to 17i - 4.
Hope this is the answer that you are looking for. Have a great day!
Jordan scores 6 points for every touchdown he makes. This season he has scored 18 touchdowns. Write a number sentence using the variable t to represent the number of points Joran scored this season.
Answers
Answer:
18 times 6= t
Step-by-step explanation:
Solve –2x2 – 16x – 44 = 0
answer please using quadtratic equation ...?
Answers
Answer: x=-4 + or - i square root of 6
turn 4√5 into an entire radical (unsimplify), the process
Answers
To turn 4√5 into an entire radical, the expression is rewritten as a single radical expression, √80, by identifying that 4 is a perfect square (4²), and multiplying it by the number inside the original radical (5) to get the product under one radical sign.
To turn 4√5 into an entire radical, we need to rewrite it as a single radical expression, effectively reversing the process of simplifying radicals. Let's start by recognizing that 4 is a perfect square and can be written as 4². So, we have 4 (the square root of 5), which can be expressed as √(4² × 5).
Here are the steps to convert 4√5 into an entire radical:
Identify the square of the number outside the radical: 4² = 16.
Multiply the square by the number inside the radical: 16 × 5 = 80.
Write the product under a single radical sign: √80.
Now, the expression 4√5 has been turned into an entire radical, √80.
What is the approximate circumference of the circle shown below?
A.102.4 cm
B. 63.4 cm
C. 25.6 cm
D. 51.2 cm
Answers
Answer
Formula
[tex]Circumference\ of\ circle = 2\pi r[/tex]
where r is the radius of a circle.
As shown in the image
Diameter of the circle = 16 .3 cm
[tex]Radius\ of\ the\ circle = \frac{16.3}{2}[/tex]
= 8.15 cm
Put in the formula
[tex]Circumference\ of\ circle = 2\pi\times 8.15[/tex]
As
[tex]\pi = 3.14[/tex]
[tex]Circumference\ of\ circle = 2\times 3.14\times 8.15[/tex]
= 51.2 cm (approx)
Therefore the circumference of a circle is 51.2cm (approx) .
Option (D) is correct .
The circumference of the circle [tex]\boxed{51.2{\text{ cm}}}.[/tex] Option (D) is correct.
Further explanation:
The formula for the circumference of the circle can be expressed as follows,
[tex]\boxed{{\text{Circumference of circle}} = 2\pi r}[/tex]
The formula for the area of the circle can be expressed as follows,
[tex]\boxed{{\text{Area of circle}} = \pi {r^2}}[/tex]
Here, “r” represents the radius of the circle.
The relationship between the radius and the diameter can be given by,
[tex]\boxed{r =\dfrac{d}{2}}[/tex]
Here, “d” represents the diameter of the circle.
Given:
The options are as follows.
A.[tex]102.4{\text{ cm}}[/tex]
B.[tex]63.4{\text{ cm}}[/tex]
C.[tex]25.6{\text{ cm}}[/tex]
D.[tex]51.2{\text{ cm}}[/tex]
Explanation:
The diameter of the circle is [tex]16.3{\text{ cm}}.[/tex]
The radius of the circle can be obtained as follows,
[tex]\begin{aligned}{\text{Radius}}&= \frac{{16.3}}{2}\\&= 8.15\\\end{aligned}[/tex]
The radius of the circle is [tex]8.15{\text{ cm}}.[/tex]
The circumference of the circle can be obtained as follows,
[tex]\begin{aligned}{\text{Circumference of circle}}&= 2\times\frac{{22}}{7}\times 8.15\\&=\frac{{44}}{7}\times 8.15\\&= 51.2\\\end{aligned}[/tex]
The circumference of the circle [tex]\boxed{51.2{\text{ cm}}}[/tex].Option (D) is correct.
Option (A) is not correct as the circumference of the circleis .
Option (B) is not correct as the circumference of the circle is .
Option (C) is not correct as the circumference of the circle is .
Option (D) is correct as the circumference of the circle is .
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Circle
Keywords: Circle, circumference, radius, diameter, area of the circle, angle, sector, arc, approximate.
The sum of two numbers is 26. When the second number is subtracted from the first number, the difference is 10. Find the two numbers.
Answers
Identify the explanatory and response variables in the following situation:
There is a strong positive correlation between latitude above the equator and number of hours of daylight on June 21.
A. Explanatory: Latitude
Response: Average temperature
B. Explanatory: Daylight hours
Response: Latitude
C. Explanatory: Time of year
Response: Daylight hours
D. Explanatory: Latitude
Response: Daylight hours
Answers
Response: Daylight hours
June 21 is the summer solstice where the amount of daylight in the northern hemisphere is 12 hours 8 minutes.
Factor completely 3x3 + 12x2 + 18x.
x2 + 4x + 6
3(x3 + 4x2 + 6x)
3x(x2 + 4x + 6)
x(3x2 + 12x + 18)
Answers
Factor of [tex]3x^{3} + 12x^{2} + 18x[/tex] is [tex]3x ( x^{2} +4x + 6 )[/tex].
Here,
We have to find factor of [tex]3x^{3} + 12x^{2} + 18x[/tex].
What is Factor?
A number or algebraic expression that divides another number or expression evenly with no remainder.
Now,
Factor of [tex]3x^{3} + 12x^{2} + 18x[/tex] is,
⇒[tex]3x^{3} + 12x^{2} + 18x = 3x (x^{2} + 4x + 6x)[/tex]
Hence,
Factor of [tex]3x^{3} + 12x^{2} + 18x[/tex] is [tex]3x ( x^{2} +4x + 6 )[/tex].
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What is √6/√5 in simplest radical form?
Answers
5√ cannot be reduced 5 cannot be reduced 5√≈2.23606797749979
Hi i know this is late like by 2 years but for future people the answer is
[tex]\frac{\sqrt{30} }{\sqrt{5} }[/tex]
hope this helps other ppl