Find the coordinates of the orthocenter of a triangle with vertices at each set of points on a coordinate plane. a. (0,0), (16,4), (4,6) b. (3,4), (11,12), (8,15)
Answer:
The answer is below
Step-by-step explanation:
a) The equation of a line passing through the point (0,0) and (16,4) is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-0=\frac{4-0}{16-4}(x-0)\\\\y=\frac{1}{4}x[/tex]
We have to find the equation of the line perpendicular to y = (1/4)x and passing through the point (4,6).
The line perpendicular to y = (1/4)x has a slope of -4 (product of their slope = -1).
Hence:
[tex]y- y_1=m(x-x_1)\\\\y-6=-4(x-4)\\\\y-6=-4x+16\\\\y=-4x+22[/tex]
The slope of a line passing through the point (16,4) and (4,6) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{6-4}{4-16}=-\frac{1}{6}[/tex]
We have to find the equation of the line perpendicular to the line with slope of -1/6 and passing through the point (0,0).
The line perpendicular to a line with slope -1/6 has a slope of 6
Hence:
[tex]y- y_1=m(x-x_1)\\\\y-0=6(x-0)\\\\y=6x[/tex]
Solving y = 6x and y = -4x + 22, gives:
x = 2.2, y = 13.2
Hence the orthocenter is at (2.2, 13.2)
b)
The slope of a line passing through the point (3,4) and (11,12) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{12-4}{11-3}=1[/tex]
We have to find the equation of the line perpendicular to the line with slope of 1 and passing through the point (8,15).
The line perpendicular to a line with slope 1 has a slope of -1
Hence:
[tex]y- y_1=m(x-x_1)\\\\y-15=-1(x-8)\\\\y=-x+8+15\\\\y=-x+23[/tex]
The slope of a line passing through the point (11,12) and (8,15) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{15-12}{8-11}=-1[/tex]
We have to find the equation of the line perpendicular to the line with slope of -1 and passing through the point (3,4).
The line perpendicular to a line with slope -1 has a slope of 1
Hence:
[tex]y- y_1=m(x-x_1)\\\\y-4=1(x-3)\\\\y=x-3+4\\\\y=x+1[/tex]
Solving y = -x + 23 and y = x + 1, gives:
x = 11, y = 12
Hence the orthocenter is at (11, 12)
Plz help me answer this
Answer:
(-2, -8)
x = -2
y = -8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
13x - 6y = 22
x = y + 6
Step 2: Solve for y
Substitution
Substitute in x: 13(y + 6) - 6y = 22Distribute 13: 13y + 78 - 6y = 22Combine like terms: 7y + 78 = 22Isolate y term: 7y = -56Isolate y: y = -8Step 3: Solve for x
Define original equation: x = y + 6Substitute in y: x = -8 + 6Add: x = -2Can you figure this out for me ? I’m having issues .
Answer:
71
you just had to add them
Step-by-step explanation:
For the linear model, y = -67.9x + 679 , the distance, in miles y, is a function of time, x, in hours. Use the model to calculate the total distance, in miles, at x = 5 hours.
cannot be determined
1,018.5 miles
339.5 miles
9.9 miles
Hey there!
x = 5
“y = -67.9(5) + 679”
-67.9(5) = -339.5
NEW EQUATION: “y = -339.5 + 679”
Solve above ^
Answer: y = 339.5 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Answer:
339.5 m
Step-by-step explanation:
AHHH PLEASE HELP! theres a pic
Answer:
A is Phosphourous, B is Oxygen
Step-by-step explanation:
The highest boiling point on the chart is 280 which belongs to Phosphouors, meaning that it has the highest boiling point. If you count it out, -183 you'd have to add 183 to get to 0, with 184 you would have to minus 184 to get to 0. So therefore oxygen's boiling point is closer to iodine.
pls help I really need this
Answer:
Rocks
Explanation:
I'm quite sure scientists have looked at rock mass to determine Earth's crusts.
Solve- x/2 + 1=5
A)8
B)9
C) 11
D) 2
Answer:
A. 8
Step-by-step explanation:
Answer:
A/8
Step-by-step explanation:
Since you need to get x by itself you have to subtract the one on both sides. Then the equation is x/2=4 Since x is being divided by the 2 you have to multiply by two on both sides. That leaves you with x=8
PLEASE PLEASE PLEASE HELP ME!!!!!! Determine whether the points (–2,3) and (0,–1) are in the solution set of the system of inequalities below. y > –x – 2 y < –5x + 2.
options
A)
Both points are in the solution set.
B)
Neither of the points is in the solution set.
C)
The point (–2,3) is not in the solution set, and the point (0,–1) is in the solution set.
D)
The point (–2,3) is in the solution set, and the point (0,–1) is not in the solution set.
Answer: the answer is A.
Step-by-step explanation:
I took the test
Jean picks peaches during her summer vacation. She gets paid $0.60 for each pound of peaches picked. Jean averages 45 pounds per hour.
a. How much can Jean earn in 16 hours?
b. How many hours would it take for Jean to earn $990?
12.2z + 19.4 = -2.7z + 93.9
Answer:
z=5
Step-by-step explanation:
12.2z+ 19.4 = -2.7z + 93.9
14.9z=74.5
z=5
Annabelle has $600 in a savings account that earns 2% simple interest for 6 years. Caroline has $400 in a savings account that earns 3% simple interest for 6 years. Whose account will have more money in it after the 6 years? How much more money will they have in their account?
Answer:
Step-by-step explanation:
Using the formula for calculating Amount;
Amount = Principal + Interest
Interest = Principal * Rate * time/100
For Annabelle:
Interest = 600*2*6/100
Interest = 6*2*6
Interest = $72
Amount after 6 years = $600 + $72 = $672
For Caroline:
Interest = 400*3*6/100
Interest = 4*3*6
Interest = $72
Amount after 6years = $400+$72 = $472
Hence Annabelle account will have more in it after 6 years.
Taking the difference in their amount = $672-$472 = $200
Hence Annabelle will have $200 more than Caroline in her account after 6 years
Simplify the following expression by showing any work
Answer:
4[tex]x^{4}[/tex][tex]y^{4}[/tex]z
what is the answer to 9x=y+8
Answer:
1
Step-by-step explanation:
Answer:
For X:
Divide each term by 9
and simplify.
x= y/9 + 8/9
For Y:
y= 9x−8
The bar diagram represents 24 hours in one day and shows a mark at 30%
If you sleep 30% of the day, how many hours do you sleep? Enter your answer in the box
24
Hours slept
Percent
0%
30%
100%
hours
Please help
Answer:
7.2 hours slept
Step-by-step explanation:
30%>.30
.30*24=7.2 hours
Hope this will help!
Help this confusing no matter how any times I do it
Answer:
The variable 8. Equation is 16 + 12x = 112.
Step-by-step explanation:
We know that she spent $16 dollars on magazines, so we can put it in the equation (16 + x= ?). We also know that the total is $112, so we can also add that (16+ x= 112). We don't know how many books she got, but we do know how much they cost (16 + 12x=112. So that makes the books the variable (X).
To find the variable we need to take out the magazines from the price. 112-16=96. Now we're left with 12x=96. Now all we have to do is divide 96 by 12, which equals 8.
Sorry everything is so long, I tried to make it short as possible
Factor completely 54x4 + 2x
Answer:
2x+216
Step-by-step explanation:
The answer was easy to get because to factor you would just multiply the two numbers together to get 54x4 = 216 and then add the 2x, so your answer is 216+2x
Does the graph represent a function ?
Answer:
Yes, it represents a function
Step-by-step explanation:
Doing the vertical line test, no point goes through the vertical line twice
What is the slope of the line that passes through the points (-9,10) and (21,15)
Answer:
1/6
Step-by-step explanation:
We can find the slope of the line using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 15 - 10)/( 21 - -9)
= ( 15-10) /( 21+9)
=5 / 30
= 1/6
What is the y-intercept of the graph?
Answer:
2
Step-by-step explanation:
The y-intercept is when the line intersects the y-axis. In this image, you can see that the line intersects at 2 on the y-axis.
Hope this helps! :)
HEELLLPPPP MEEE 100 POINTS!!!
Juan has a collection of 13 dice, 5 of which have eight sides. If Juan randomly rolls 4 dice, what is the probability that exactly 2 of the chosen dice have eight sides? Write your answer as a decimal rounded to four decimal places.
Answer:
38
Step-by-step explanation:
Whats the answer to #1
Answer:
-8/5 or 1.6
Step-by-step explanation:
if you get the 2 points on the graph and use slope formula you get the answer
what is 4/5 ÷ 1/3 =____
430 divided by 2 ____ remainder____
Answer:
215.
Step-by-step explanation:
I dotn think there is any remainder so put 0
Answer:
215 NO REMAINDER
Step-by-step explanation:
Graham paid $87.45 for a pair of jeans. This amount included a tax of 40%. What was the cost of the jeans before tax?
The final price is the cost plus the tax.
Since we know the tax and a percent, we can write this as
T = C(1+r)
T = what Graham paid = $87.45
C = cost before tax
r = tax rate expressed as a decimal = .40
Plugging in what we know
87.45 = C (1+.4)
87.45 = C(1.4)
Divide both sides by 1.4
C = $62.46
What would be the new ordered pair for point Q' given the following rule for the transformation?
(x,y)----}(-x,y)
Q=(-5, 7)
Answer:
The new ordered pair for point Q' are: Q' (5, 7)
Step-by-step explanation:
Q = (-5, 7)
The rule of translation is:
(x, y) → (-x,y)
According to this rule, the value of x is multiplied by -1, and the value of y remains the same.
Thus,
P(x, y) → P'(-x,y)
Q (-5, 7) → Q' (-(-5), 7) → Q' (5, 7)
Thus, the new ordered pair for point Q' are: Q' (5, 7)
[tex]\frac{x-c}{2} =d, for ( x)[/tex]
SHow your work!
What is the value of the function for x = 2? HELP!
Answer:
-2
Step-by-step explanation:
Follow you finger 2 marks on the x axis and then move your finger up or down to say the resulting y value
Solve correctly and I’ll give brainliest
50 50 23 start fraction, 23, divided by, 50, end fraction of Xander's friends prefer to stay home on Friday nights. What percent of Xander's friends prefer to stay home on Friday nights?
Answer:
Percent of Xander's friends that prefer to stay home on Friday nights = 46%
Step-by-step explanation:
23/50 of Xander's friends prefer to stay home on Friday nights.
What percent of Xander's friends prefer to stay home on Friday nights?
% of Xander's friends that prefer to stay home on Friday nights
= 23/50 × 100
= 0.46 × 100
= 46%
Percent of Xander's friends that prefer to stay home on Friday nights = 46%
X-3=x+13 solution or not