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)
...?
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.
Hexagon DEFGHI is translated 8 units down and 3 units to the right. If the coordinates of the pre-image of point F are
(–9, 2), what are the coordinates of F'?
(–17, 5)
(–6, –6)
(–17, –1)
(–12, –6)
Similar triangles. Solve for x
A boardwalk that is x feet wide is built around a rectangular pond. The combined area of the pond and the boardwalk is 4x^2+140x+1200 square feet. What are the dimensions of the pool?
a. 100 ft by 60 ft c. 55 ft by 70 ft
b. 30 ft by 40 ft d. 15 ft by 80 ft
...?
A meteorological office keeps records of the annual precipitation in different cities. For one city, the mean annual precipitation is 15.3 and the standard deviation of the annual precipitation amounts is 4.2. Let x represent the annual precipitation in that city. Determine the standardized version of x.
To find the standardized version of x in a given city's annual precipitation data, use Z = (x - mean) / standard deviation.
Explanation:The standardized version of x (annual precipitation in a city) can be calculated using the formula: Z = (x - mean) / standard deviation. Substituting the given values, Z = (x - 15.3) / 4.2. This helps in determining how many standard deviations a particular precipitation amount is from the mean.
Which represents the empirical formula for A3B9?
AB3
AB2
A3B9
A9B27
Answer:
[tex]AB_{3}[/tex]
Step-by-step explanation:
Given : [tex]A_{3}B_{9}[/tex]
To Find : Which represents the empirical formula for[tex]A_{3}B_{9}[/tex]?
Solution:
Definition of Empirical Formula - A formula that gives the simplest whole-number ratio of atoms in a compound.
[tex]A_{3}B_{9}[/tex]
To reduce it in simplest form
Divide the subscript numbers by 3
So, the resultant : [tex]AB_{3}[/tex]
Thus the empirical formula for [tex]A_{3}B_{9}[/tex] :
[tex]AB_{3}[/tex]
One number is six times another number. their difference is 35. what are the two numbers? 5 and 30 8 and 48 7 and 42 6 and 41
Answer: The answer is (c) 7 and 42.
Step-by-step explanation: We are given that one number is six times another number and their difference is 35. We are to find the two numbers.
Let 'x' and 'y' be the two numbers. Then, we have
[tex]y=6x,\\\\y-x=35.[/tex]
Substituting the value of 'y' from first equation in the second, we have
[tex]6x-x=35\\\\\Rightarrow 5x=35\\\\\Rightarrow x=7,[/tex]
and
[tex]y=6\times 7=42.[/tex]
Therefore, the numbers are 7 and 42.
Thus, the answer is (c) 7 and 42.
1. Choose the correct solution in roster form.
S is the set of prime numbers that are less than 15.
A.{2,3,5,7,11,13}
B.{2,3,5,7,9,11,13}
C.{1,3,5,7,9,11,13}
D.{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
Answer:
A. {2,3,5,7,11,13}
Step-by-step explanation:
Since, prime numbers are the whole numbers which have only two multiple which are 1 and itself.
Thus, the prime numbers are,
2, 3, 5, 7, 11, 13, 17, 19, 23, ..................
Note : 1 is not a prime number because it has only one multiple i.e. 1.
or it does not satisfy the definition of prime number.
Thus, the prime numbers that are less than 15,
2, 3, 5, 7, 11, 13
Which are the elements of the set S,
Hence, S = { 2, 3, 5, 7, 11, 13 }
OPTION A is correct.
Will upvote!
Graph −7y+8=21x−6
Two points that the line would go through is all I need.
Thanks!!
Michael breeds chickens and ducks. last month, he sold 50 chickens and 30 ducks for $550. this month, he sold 44 chickens and 36 ducks for $532. how much does a chicken cost, and how much does a duck cost?
write y=2x+3 using function notation
Answer:
[tex]f(x) = 2x+3[/tex]
Step-by-step explanation:
The function f(x) is the another way of representing the y-values in the function
i.e
[tex]y=f(x)[/tex]
Then y-axis be labeled with f(x)
Also; the ordered pair is written as: (x, f(x)) instead of (x, y)
Given the equation:
[tex]y = 2x+3[/tex]
replace y = f(x)
then;
[tex]f(x) = 2x+3[/tex]
therefore, the equation y=2x+3 using function notation is, [tex]f(x) = 2x+3[/tex]
S=(1 r)
c. find c if s = r 174 and r= 45%
Expand 3(-5q + 4).
A.5q + 12
B.-15q + 4
C.-15q + 12
D. 5q + 12
If theres 3 apples and you take 2 away, how many do you have?
What is the solution of the system?
Use the substitution method.
{y+7=3x
{6x−2y=12
A) (14, 12)
B) (12, 14)
C)There is no solution.
D)There are an infinite number of solutions.
When working with the square root of a number, when would you have only a positive answer and when would you have both a positive and negative answer?
A recipe calls for 6 quarts of water. Michael put 1 gallon of water in the bowl and realized that he made a mistake. Michael should ___.
-Remove 2 cups.
-Add 1 gallon.
-Add 2 quarts.
-Add 2 pints.
-Add 2 quarts. Michael incorrectly used gallons instead of quarts for his recipe. Since 1 gallon equals 4 quarts, he simply needs to add 2 more quarts to the existing gallon to meet the recipe's requirement of 6 quarts.
Explanation:The question involves unit conversion between gallons and quarts. Since the recipe calls for 6 quarts of water and Michael has already put 1 gallon (which is 4 quarts) into the bowl, he needs to add more water to reach the required amount.
A gallon is equivalent to 4 quarts, so Michael should add 2 quarts more to the 4 quarts he already has, totaling the 6 quarts needed for the recipe.
Given the two points (2,4) and (-3,2), what is the slope of the line that goes through both of these points?
In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours (h < 7) or after working more than 9 hours (h >9). How can these inequalities be written as one statement?
a. 7 < h < 9
b. 7 > h > 9
c. h < 7 or h > 9
d. h > 7 or h < 9
which method could be used to prove triangle PVU is congruent to triangle QVS?
5/8 as a decimal and a percent
slope-intercept form .... slope=.25, x-intercept=24 ...?
Answer:
Step-by-step explanation:
Given : slope=.25, x-intercept=24 ...?
A triangle inscribed in a semicircle can be identified as a/an _______ triangle.
A triangle inscribed in a semicircle can be identified as a right triangle.
Explanation:A triangle inscribed in a semicircle can be identified as a right triangle.
To see why, consider that when a triangle is inscribed in a semicircle, one of its sides will coincide with the diameter of the circle. Since the diameter of a circle is always a straight line, it forms a right angle (90 degrees) with the semicircle's arc. Therefore, the triangle that is inscribed in the semicircle has a right angle as one of its angles, making it a right triangle.
whats 9+10? PLZ HELP !!!!
So if we add 9 slices to pizza, and 10 more...We get...0 because I ate them all
19
A high school athletic department bought 40 soccer uniforms at a cost of$3,000. after soccer season, they returned some of the uniforms but only received $40 per uniform. what was the difference between what they paid for each uniform and what they returned
25 m equals how many feet
In circle A shown below, m arc BC is 61° and m Arc EF is 76°.
What is m∡FDE?
Answer
76°
38°
30.5°
68.5°
Answer:
68.5°
Step-by-step explanation:
Here is the solution:
m<FDE = 1/2( Arc BC + Arc 76)
m<FDE = 1/2 (61° + 76°)
m<FDE = 137/2 = 68.5°
So the answer is 68.5°
What is the y-intercept of y=1.5x?
What is the length of one side of a square if its area is 100 square centimeters?
a. 100 cm
b. 40 cm
c. 25 cm
d. 10 cm user: the cost of one textbook is $14.90. which expression below can be used to compute the cost of 8 textbooks?
a. 8($15.00 $0.90)
b. 8($15.00 $0.10)
c. 8($15.00 – $0.90)
d. 8($15.00 – $0.10)
Answer:
The anser is D. I just had this question
You are playing a game of Scrabble and have the 5 A tiles, 3 E tiles, 1 Z tile, 2 M tiles, 3 L tiles, and 1 Y tile to choose from. What is the probability that you choose E or Y on your next draw
Answer:
4/15
Step-by-step explanation:
To find the probability we use the mutually exclusive probability formula P(A) + P(B). The probability of picking a E tile is
1
5
and the probability of picking a Y tile is
1
15
. The sum is
4
15
.