find the coordinates of the orthocenter for a triangle with vertices (1,3) , (1,12) , (8,10)

Answers

Answer 1
the orthocenter is (3,10) I think
Answer 2
For convenience, I'll name the three points: A(1, 3), B(1,12), C(8,10)

The orthocenter is where the three altitudes of the triangle meet. That is, where the perpendicular lines from each vertex to the opposite side meet.

the goal in this case is to find out where the perpendicular line from C to AB, the perpendicular line from B to AC, and the perpendicular line form A to BC meet.
It is enough to find two perpendicular lines.

step one: find the equation of two perpendicular lines

find the slope of AB: m=(12-3)/(1-1), notice the denominator is 0, so the slope doesn't exist, that means AB is a vertical line parallel to the y axis, so the perpendicular line has a slope of o, a horizontal line. this horizontal line goes through C(8,10), so the equation is y=10
use the same method, slope of AC: (10-3)/(8-1)=1, so the perpendicular line from B to AC has a slope of -1. y=-x+b
Now use the point B(1,12) to find b: 12=-1+b =>b=13

so the equation for this line is y=-x+13

Step two: solve the system of equations: y=10
                                                                  y=-x+13
we get x=3, y=10, which are the coordinates of the orthocenter.

I've also found the equation of the third line, which is y=(7/2)x-1/2, the point (3,10) is also on this line. So it works!

Related Questions

In softball, a batting average is the number of hits divided by the number of times at bat. Does Eva or Michelle have the higher batting average?

Player Hits At Bats
Eva 42 90
Michelle 38 80

Answers

Eva
42 / 90 = .46

Michelle
38 / 80 = .47

Michelle has the higher batting average.

Answer:

Michelle has a higher batting average with 0.475

Step-by-step explanation:

Batting average is equal to the number of hits divided by the number of times at bat:

First, we have to know the batting average of both players:

Eva:

Hits = 42

Times at bat = 90

Now we divide to get the batting average:

42/90 = 0.466

Michelle:

Hits = 38

Times at bat = 80

Now we divide to get the batting average:

38/80 = 0.475

Michelle has a batting average of 0.475 compared to Eva's which is a 0.466, so Michelle's has a higher batting average.

Distributive property of 96+80

Answers

(12*8)+(8*10) or (90+6)+(40+40)
(90 + 6) + (40 + 40)

Ella went to the zoo and saw cockroaches, spiders, and moths. She was there 3 hours. She saw 3 times as many spiders as cockroaches and twice as many moths as cockroaches. If Ella saw 5 cockroaches, how many bugs did she see altogether?

Answers

Ella saw 30 bugs altogether at the zoo.
Ella saw 30 bugs total
15+10+5= 30

what is the slope of the line with equation y-7=5(x-12)

Answers

Use the distributive property
y - 7 = 5x - 60

add 7
y=5x-53

5x is your slope
To find the slope we have to get it into slope intercept form.

To do this, first distribute the 5.

Now the equation is:

y-7=5x-60

Then add 7 to both sides to get y by itself.

So now the equation is y=5x-53
y=mx+b

m is the slope.

That means 5 is the slope.

Hope this helps!

How many minutes equal 4.8 days? Enter your answer in the box.

Answers

1hour=60min
24hour=?
24hour=1440 min

1d=1440 min
4.8d=?
4.8 days =6956      hope you like my explanation 





Answer:4.8 days =6956

Step-by-step explanation:

What may be a concern if you have an adjustable rate mortgage (ARM)?

Answers

Answer:

A.) After the initial fixed-rate period, your rate may increase.

Step-by-step explanation:

Due to the rate being adjustable, you may be forced to pay more than what you had originally hoped for after the fixed-rate period. This tends to usually be negative for you since you will have to pay more money, but will help you pay off the debt faster.

A concern with an adjustable-rate mortgage (ARM) is the potential increase in monthly payments over time as interest rates adjust to market rates after the initial fixed period, which can pose a cash flow problem for the homeowner.

A major concern if you have an adjustable-rate mortgage (ARM) is the potential for an increase in your mortgage payments over time. This type of mortgage allows the interest rate to vary in accordance with market interest rates, which often reflect changes in inflation. Initially, an ARM might have a lower interest rate than a fixed-rate mortgage, making it an attractive option. However, after a certain period, the interest rate may adjust based on a specific financial index, such as the U.S. Treasury Note, and can result in higher monthly payments.

In the case of a five-year ARM, for example, the mortgage might start with a lower interest rate compared to a thirty-year fixed mortgage, leading to lower initial payments. However, after the initial fixed period, the rate can adjust, potentially leading to increased payments and creating a cash flow problem for the borrower if the rates rise significantly.

Without changing the order of the numbers below, insert parentheses and/or addition signs so that the computation results in the number described below. 4 3 6 1 a. The number is a multiple of 5. b. The number is a factor of 36.

Answers

4,3,6,1

(a) multiple of 5 : 4(3 + 6 + 1) = 4(10) = 40
(b) factor of 36 : (4)(3) + (6)(1) = 12 + 6 = 18

m<2=34 find m<4 and explain how you know

Answers

Angle 4 equals 34 degrees since angle 2 and 4 are opposite angles and opposite angles are congruent

Final answer:

Given only that m<2 = 34, we can't find the value of m<4. More information about the relationship between these angles is needed to solve the problem.

Explanation:

The question asks to find the value of m<4 given that m<2=34.

It's important to note here that 'm<2' and 'm<4' are two different angle measures. Without more information about their relationship, such as them being supplementary, complementary or vertically opposite angles, it's impossible to find the measure of m<4 based on m<2 alone.

So, we can't find the value of m<4 using only the information provided. You might need to look back at the original problem or figure to see if there is additional information available about these angles.

Learn more about angles here:

https://brainly.com/question/33354646

#SPJ2

HELP PLEASEEEEE
Which biconditional is NOT a good definition?
A. A whole number is even if and only if it is divisible by 2.
B. A whole number is odd if and only if the number is not divisible by 2.
C. An angle is straight if and only if its measure is 180.
D. A ray is a bisector of an angle if and only if it splits the angle into two angles.

Answers

Answer:

Option D

Step-by-step explanation:

Given are the four options and we have to select the one which is not good defintion.

A)A whole number is even if and only if it is divisible by 2.

--- Is correct definition of even number.

B. A whole number is odd if and only if the number is not divisible by 2.  

---  Correct definition

C. An angle is straight if and only if its measure is 180.  

... correct definition

D. A ray is a bisector of an angle if and only if it splits the angle into two angles

...   This is incorrect because congruent/equal angles should be there

Correct definition is

A ray is a bisector of an angle if and only if it splits the angle into two congruent angles

Answer:

Option D.

Step-by-step explanation:

A biconditional statement are the statement in which both parts have the same truth value. It is written in the form of "p if and only if q".

First statement: A whole number is even if and only if it is divisible by 2.

This statement is a biconditional statement because it is the definition of even numbers and have the same truth value.

Second statement: A whole number is odd if and only if the number is not divisible by 2.

This statement is a biconditional statement because it is the definition of odd numbers and have the same truth value.

Third statement: An angle is straight if and only if its measure is 180.

This statement is a biconditional statement because it is the definition of straight angle and have the same truth value.

Fourth statement: A ray is a bisector of an angle if and only if it splits the angle into two angles.

This statement is not a biconditional statement because if a ray splits the angle into two angles, then it is not necessary that it is a bisector.

Definition of bisector: A ray is a bisector of an angle if and only if it splits the angle into two congruent angles.

Therefore, the correct option is D.

What is the mass of an object that requires a force of 30 N to accelerate at 5 m/s2?

Answers

well if their is a force of 30 N and accelerates 5m/s2.
F=ma
F=30 N

Step-by-step explanation:

if F=ma

therefore m will be equal to dividing a

f/a=m

therefore mass is force divided by acceleration.

An 8-kilogram bag of carrots costs $16.08. What is the unit price?

Answers

The Unit Price Is $2.01
The unit rate is $2.01

If y=4x + 3 find the value of y when x= -2

Answers

y=4(-2)+3
y= -8+3
y= -5
The correct answer is -5, cause you plug-in -2 * 4 which equals -8 and that +3 = -5

Can someone help !!!!

Answers

I got 397. Do you want an explanation as to why?

Please Help Quickly!

If the dimensions of the following cylinder are tripled, what will be the volume of the new cylinder?

15,260.4 cm
45,781.2 cm
61,041.6 cm
183,124.8 cm

Answers

45,781.2 I believe, I am not sure, but I think that is right.

Answer: [tex]45781.2\text{ cm}^3 [/tex]

Step-by-step explanation:

From the given picture, the diameter of the base of cylinder = 12 cm

i.e. the radius of the cylinder =[tex]r=\dfrac{12}{2}=6\ cm[/tex]

Height = 15 cm

If the dimensions of the following cylinder are tripled, then the radius of cylinder =[tex]3\times6=18\ cm[/tex]

Height=[tex]3\times15=45\ cm[/tex]

We know that the volume of a cylinder is given by :-

[tex]\text{Volume}=\pi r^2 h\\\\\Rightarrow\\text{Volume}=(3.14)(18)^2(45)\\\\\Rightarrow\text{Volume}=45781.2\text{ cm}^3 [/tex]

How do I solve 2q+10=7q

Answers

Final answer:

To solve the equation 2q + 10 = 7q, subtract 2q from both sides and then divide by 5, resulting in q = 2.

Explanation:

To solve the equation 2q + 10 = 7q, you need to isolate the variable q on one side. Here are the steps you should follow:

Subtract 2q from both sides to get all q terms on one side of the equation: 2q + 10 - 2q = 7q - 2q, which simplifies to 10 = 5q.

Divide both sides by 5 to solve for q: 10 / 5 = 5q / 5, resulting in q = 2.

Therefore, the value of q that solves the equation is 2.

a rectangular container is 15cm long by 25cm wide and contains 2.5 liters of water. find the height of the water level in the container (1 liter=1000cm

Answers

Since 1 liter is equivalent to 1000cm, you can convert the total amount of water in the container and get 2500[tex]cm^{3} [/tex] of water. since V=l*w*h or B*h, you can plug in 15cm and 25cm as well as the volume to get 2500=15*25*h, or 375*h. Dividing 2500 by 375 gives the height, of 6 2/3 cm or 20/3cm.

What is gcf of 18 and 24 with 18/24 in simplest form

Answers

The GCF is 6. To find this, we list out the factors of both ones, circle the common ones between them, and find the biggest one.
Now, we can use the GCF of 6 to find 18/24 in simplest form.
Divide both the numerator and denominator by 6 to get 3/4.
Hope this helps.

What is the slope of the line? y = 3x + 9

Question 3 options:
a)9
b) 3
c) 12
d) 6

Answers

the answer is 3..y=mx+b where m is the slope

Answer:

b 3

Step-by-step explanation:

3x is the lope

Am employer may conduct an aptitude test to check for what?

Answers

An aptitude test helps an employer to learn how a person might perform specific tasks and react to a range of different situations.

Answer:

The capacity to acquire certain skills

Step-by-step explanation:

yvonne runs three times as fast as xavier. what is an algebraic translation of this?
A y = 2x
B y = 3x
C y = 1/2x
D y = 1/3x

Answers

The answer is Y = 3X

Select all ratios equivalent to 6:9:

A)54:46
B)9:6
C)18:27

Answers

the answer would be c. hope that helped
c only 18:27 / 3 on each side will give you 6:9other no. Hope this helped

how to do RX - sx + y equals B plzz explain how to get the answer there all variables!!!!

Answers

rx - sx + y = b

WHEN SOLVING FOR X :

rx - sx + y = b

We must get x onto it's own side, so subtract y from both side.s

rx - sx = b - y

Then, factor out x.

x(r - s) = b - y

Then, divide both sides by (r - s).

x(r - s) ÷ (r - s) = b - y ÷ (r - s)

Simplify.

x = b - y / r - s → [tex]x = \frac{b-y}{r-s} [/tex]

WHEN SOLVING FOR Y :

rx - sx + y = b

We need to isolate y, so get rid of everything BUT y on the left side.

Subtract rx from both sides.

-sx + y = b - rx

Then, add sx to both sides.

y = b - rx + sx

~Hope I helped!~

Which problem will have the greater quotient, 376.0 divided by 93 OR 376 divided by 93.01 ? Explain how you know.

Answers

376/93 = 4.04301075

376/ 93.01 = 4.04257607. 

So 376 divided by 93 is greater because the higher the divisor, the lower the quotient. 

these are typical bowling scores for 16-20 year olds: 74, 88, 89, 95, 99, 100, 101, 106. What is the mean for the data?

Answers

Mean is 94.
Add all of them and then divide with add numbers and medain

Answer:

The answer is 94.

Step-by-step explanation:

In order to determine the answer, we have to know about the mean of a group of values. When we need to calculate the mean, first we have to sum all the values. Then, we have to divide this result by the amount of datas.

In this case, we have 8 datas of differents bowling scores.

The sum of all values is:

[tex]74+88+89+95+99+100+101+106=752[/tex]

Finally, the mean is:

[tex]Mean=\frac{752}{8}= 94[/tex]

The mean for the data is 94.

The ratio of the same side angles of two parallel lines is 1:14. Find all angles.

Answers

The angles that lie at the same side of parallel lines are known to be always supplement of each other. This means that when we add them together, the value is 180°. If we let x be the common factor for the measures of the angle, the equation that we could use to determine the answer is,
 
                x + 14x = 180°

The value of x from the equation is 12. Hence, the angles are,
       
              x = 12
            14(12) = 168

Answer: 12° and 168°

Answer:

the anwser would be 12 and 168

Michael earned $159 mowing lawns all summer. If he mowed 39 lawns, about how much did he make per lawn?

Answers

Michael made approximately $4.08 per lawn by dividing the total earnings of $159 by the total number of lawns 39 he mowed.

To find out how much Michael made per lawn, we need to divide the total amount of money he earned by the number of lawns he mowed. Michael earned $159 over the summer and mowed 39 lawns. Therefore, we calculate the earnings per lawn using the following equation:

Earnings per lawn = Total money earned \/ Number of lawns mowed

Earnings per lawn = $159 / 39

Now, let's do the calculation:

Earnings per lawn = $4.0769...

To provide an approximate value, we round the amount to the nearest cent, which gives us an answer of approximately $4.08 per lawn.

Ice is placed around a bowl of water to lower the temperature. The equation D=−7/5t+22 shows the time, t, measured in minutes and temperature, D, measured in degrees Celsius. Which statement is correct?


a)The temperature of the water decreases 5°C every 7 minutes.

b)The temperature of the water increases 7°C every 5 minutes.

c)The temperature of the ice that is around the bowl is 22°C

d)Before cooling begins, the temperature of the water is 22°C

Answers

C. Is the answer troll loll

Answer:

d)Before cooling begins, the temperature of the water is 22°C

Step-by-step explanation:

Given equation that shows the temperature of the bowl after t minutes,

[tex]D=-\frac{7}{5}t+22[/tex]

Initially ( when ice is not placed ) t = 0,

So, the temperature of the water,

[tex]D=(0) + 22 = 22^{\circ}[/tex]

i.e. Option d) is correct.

If t = 7 minutes,

The temperature would be,

[tex]D=-\frac{7}{5}\times 7+22[/tex]

[tex]=-\frac{49}{5}+22[/tex]

[tex]=-\frac{49+110}{5}[/tex]

[tex]=\frac{61}{5}[/tex]

[tex]=12.2^{\circ}C[/tex]

So, the change in temperature = 12.2° - 22° = -9.8°,

Thus, option a) is incorrect.

If x = 5 minutes,

The temperature would be,

[tex]D=-\frac{7}{5}\times 5+22=-7+22 = 15^{\circ}[/tex]

Change in temperature = 15° - 22° = -7°,

So, Option b) is incorrect.

∵ The temperature of the ice must be less than 22°,

Thus, option c) is incorrect.

you are going to get a new cell phone and need to choose between two cell phone companies, Bell Phone Company charges $40 per month. It costs $0.50 per minute after you have gone over the monthly number of minutes included in the plan

Please help and explain your reasoning, i need to do this for extra credit to bring up my grade.

Answers

$65-$60=$5    5/50=0.1
The Bell Phone Company have greater rate of change because you pay $0.50 for every minute you spend on the cell phone, while you only pay $0.10 for every minute you spend on the cell phone. $0.50 per minute is more increase than $0.10 per minute, which will involve in more change and increase.

It takes 63 minutes for 4 people to paint 9 walls.

How many minutes does it take 7 people to paint 4 walls?

Answers

63 / 9 = 7
7 / 4 = 1.75
It takes 1.75 minutes for 1 person to paint 1 wall...
1.75 * 4 = 7
7 * 7 = 49
It took 49 minutes for 7 people to paint 4 walls...

Answer:

7 people will take 16 minutes to paint 4 walls.

Step-by-step explanation:

Since, if [tex]x_1[/tex] people take [tex]n_1[/tex] times for [tex]w_1[/tex] work and in the same kind of work [tex]x_2[/tex] people take [tex]n_2[/tex] time for [tex]w_2[/tex] work,

Then,

[tex]\frac{x_1\times n_1}{w_1}=\frac{x_2\times n_2}{w_2}[/tex]

Here, [tex]x_1=4[/tex], [tex]n_1=63[/tex], [tex]w_1=9[/tex],

[tex]x_2=7[/tex], [tex]w_2=4[/tex]

By substituting the values in the above formula,

[tex]\frac{4\times 63}{9}=\frac{7n_2}{4}[/tex]

By the cross multiplication,

[tex]1008=63n_2[/tex]

[tex]\implies n_2=\frac{1008}{63}=16[/tex]

Hence, 7 people will take 16 minutes to paint 4 walls.

One fifth equals the quotient of a number and 10

Answers

You would have x/10 so then you would have 1/5=x/10 then you cross multiply. You would get x =2. So the number is 2
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