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.
Lucia bought a table and some chairs at a furniture store. The equation that models this situation is y = 40x + 55, where y is the amount of money she spent and x is the number of chairs she bought. What does the y-intercept mean in this situation?
A. She paid $40 for each chair.
B. She paid $55 for the table.
C. She paid $40 for the table.
D. She paid $55 for each chair.
Answer: C. She paid $40 for each chair.
Step-by-step explanation:
Will give brainlyiest answer if explained.
In the figure below, lines g and h are parallel and are cut by transversal j to form the angles shown. If the measure of <8 is 82, what is the measure of <1?
A. 180.
B. 98.
C. 82.
D. 8.
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?
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
.
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
...?
What is 6 1/2 as a decimal?
A restaurant manager recorded the number of people in different age groups who attended her food festival. She then created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
Which of the following statements best compares the height of the bars of the histogram?
There are twice as many participants in the 60–79 age group than in the 0–19 age group.
There are 3 times as many participants in the 40–59 age group than in the 0–19 age group.
There are more participants in the 40–59 age group than in the 0–19 and 60–79 groups combined.
There are more participants in the 60–79 age group than in the 0–19 and 20–39 groups combined.
Answer:
Option: B
There are three times as many participants in the 40-59 age group than in the 0-19 age group.
Step-by-step explanation:
From the histogram we have following observations:
Number of people in the age group 0-19= 20
Number of people in the age group 20-39=40
Number of people in the age group 40-59=60
Number of people in the age group 60-79=50
Hence, from the data we could say that there are three times as many participants in the 40-59 age group( which is 60) than in the 0-19 age group(which is 20).
Hence, option B is correct.
What are the x and y intercept of c = 0.75m + 2.25?
What is the 8th term in the sequence?
Note: Use the explicit rule.
an=25−3n
Enter your answer in the box.
a8=
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 inverse of the conditional statement " If a number is divisible by 6, then it is divisible by 3"?
A) If a number is divisible by 3, then it is divisible by 6.
B)If a number is not divisible by 6, then it is not divisible by 3.
C)If a number is not divisible by 3, then it is not divisible by 6.
D)If a number is not divisible by 6, then it is divisible by 3.
...?
Answer: I think its A.
what is 4/12 simplest form
Will upvote!
Graph −7y+8=21x−6
Two points that the line would go through is all I need.
Thanks!!
Given the two points (2,4) and (-3,2), what is the slope of the line that goes through both of these points?
What is the value of ∑n=13(17n−15)?
the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex] is indeed 1352.
To find the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex], we need to compute the sum of the expression 17n - 15 for n ranging from 1 to 13.
Using the formula for the sum of an arithmetic series, we can express this sum as:
[tex]\[ \sum_{n=1}^{13} (17n - 15) = \sum_{n=1}^{13} 17n - \sum_{n=1}^{13} 15 \][/tex]
We know that the sum of the first \(n\) natural numbers can be expressed as [tex]\( \sum_{n=1}^{N} n = \frac{N(N+1)}{2} \).[/tex]
So, the sum of [tex]\(17n\) from \(n=1\) to \(n=13\)[/tex] is:
[tex]\[ \sum_{n=1}^{13} 17n = 17 \sum_{n=1}^{13} n = 17 \cdot \frac{13 \cdot (13 + 1)}{2} \][/tex]
[tex]\[ = 17 \cdot \frac{13 \cdot 14}{2} = 17 \cdot 91 = 1547 \][/tex]
And the sum of 15, 13 times (since there are 13 terms) is[tex]\(15 \cdot 13 = 195\).[/tex]
Now, we can find the value of the given expression:
[tex]\[ \sum_{n=1}^{13} (17n - 15) = 1547 - 195 = 1352 \][/tex]
So, the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex] is indeed 1352.
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)
slope-intercept form .... slope=.25, x-intercept=24 ...?
Answer:
Step-by-step explanation:
Given : slope=.25, x-intercept=24 ...?
5/8 as a decimal and a percent
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.
if x=t^2-1 and y=t^4-2t^3, then when t=1 what's d^2y/dx^2? if x=t^2-1 and y=t^4-2t^3, then when t=1 what's d^2y/dx^2?
To find d^2y/dx^2 when t = 1, we need to first express y in terms of x. Then, differentiate y with respect to x to find dy/dx. Finally, differentiate dy/dx to find d^2y/dx^2 and substitute t = 1.
Explanation:Given the equations x = t^2 - 1 and y = t^4 - 2t^3, we can find d^2y/dx^2 when t = 1.
First, we need to express y in terms of x. From the equation x = t^2 - 1, we can solve for t as t = sqrt(x + 1). Substituting this into the equation y = t^4 - 2t^3, we get y = (sqrt(x + 1))^4 - 2(sqrt(x + 1))^3.
Next, we need to find the first derivative of y with respect to x: dy/dx. Then, we can find the second derivative d^2y/dx^2 by differentiating dy/dx. Finally, substitute t = 1 into d^2y/dx^2 to find the value.
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?
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
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
On the cube in the figure above, each of the following points is the same distance from
P as it is from Q
EXCEPT
(A) A (B) B (C) C (D) D (E) E
What is the expression in simplest radical form?
√384
If theres 3 apples and you take 2 away, how many do you have?
Divide. Express your answer in lowest terms
=15/16 + (-3/4)
please tell me how you got your answer after
What is the gcf for 36, 54 and 135?
K-X=V-W solve for the letter x
To solve for 'x' in the equation 'K - X = V - W', we rearrange the equation to isolate 'x', resulting in 'X = K - V + W'.
Explanation:To solve the equation for the letter x, you need to isolate x on one side of the equation. It's a simple process of rearranging the equation.
Here we start with the original equation:
K - X = V - W
First, to separate your desired variable, or in this case 'x', we add 'X' to both sides to cancel 'X' from the left hand side:
K = X + V - W
Finally, to isolate 'x', we just need to subtract 'V' and add 'W' to both sides
X = K - V + W
So, the solution to the equation when solved for the letter 'x' is X = K - V + W.
Learn more about Solving for a variable here:
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