What are the coordinates of the orthocenter of triangle ABC with vertices at A(1, 2), B(1, 6), and C(5, 6)?
Answers
The orthocenter of a triangle is the intersection of the triangle's three altitudes. This is shown below:
To find the orthocenter of the triangle, we need to find the equation of the lines of the triangle and find the lines perpendicular to each of them. We will only need to do this for two sides.
The equation of a line is given to be:
\(y=mx+b\)where m is the slope and b is the intercept.
The slope is calculated to be:
\(m=\frac{y_2-y_1}{x_2-x_1}\)Two lines are perpendicular if the product of their slopes is equal to -1, such that:
\(\begin{gathered} m_1\cdot m_2=-1 \\ or \\ m_1=-\frac{1}{m_2} \end{gathered}\)Therefore, the slopes of perpendicular lines are inverse reciprocals of each other.
Equation of Line AB:
\(\begin{gathered} A\to(x_1,y_1)=(1,2) \\ B\to(x_2,y_2)=(1,6) \end{gathered}\)The slope of the line is:
\(m=\frac{6-2}{1-1}=\frac{4}{0}\)This means that the line is a vertical line. Therefore, the equation of the line is
Related Questions
Question 6 of 10
What is the solution to the system of equations graphed below?
y = -2x + 4
y=x-5
Answers
Answer:
the solution to the system of equations is (x, y) = (3, -2).
Step-by-step explanation:
y = -2x + 4 (Equation 1)
y = x - 5 (Equation 2)
To solve for x, we can equate the right sides of the equations:
-2x + 4 = x - 5
Now, we can solve for x:
-2x - x = -5 - 4
-3x = -9
x = (-9) / (-3)
x = 3
Substituting the value of x back into Equation 2, we can solve for y:
y = 3 - 5
y = -2
Point A is located at (1, 2). Point B is located at (4, 6). Use this information to determine the length of the line, rounded to the nearest whole number.
Answers
If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.
To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.
Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:
d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5
Rounded to the nearest whole number, the length of the line is also 5 units.
In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.
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The average hourly wage of computer programmers with 2 years of experience has been $21.80.Because of high demand for computer programmers,it is believed there has been a significant increase in the average wage of computer programmers.To test whether or not there has been an increase,the correct hypotheses to be tested area. H0: μ < 21.80 Ha: μ >= 21.80b. H0: μ = 21.80 Ha: μ ≠ 21.80c. H0: μ > 21.80 Ha: μ =< 21.80d. H0: μ <= 21.80 Ha: μ > 21.80
Answers
Answer:
d. H0: μ <= 21.80 Ha: μ > 21.80
Step-by-step explanation:
We set the null hypothesis as what is already given . We are already informed that the average wage is equal to μ <= 21.80 against the claim that is required. It is required to test whether the average wage of the computer programmers is greater than μ > 21.80
So option d is the best answer.
Hypotheses testing is done using an observation and a claim. The observation is set as a null hypothesis and claim is set as an alternative hypothesis. The null and alternative hypotheses must be chosen wisely to get the correct results.
The critical region is dependent on the claim set.
Find the zeros of the function shown below
Answers
Answer:
x = - 5 , x = 2
Step-by-step explanation:
f(x) = x² + 3x - 10
to find the zeros let f(x) = 0 , that is
x² + 3x - 10 = 0
consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)
the factors are + 5 and - 2 , since
5 × - 2 = - 10 and 5 - 2 = + 3 , then
(x + 5)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 5 = 0 ( subtract 5 from both sides )
x = - 5
x - 2 = 0 ( add 2 to both sides )
x = 2
the zeros are x = - 5 , x = 2
Misty’s surgery lasted 214 hours. Convert the time to seconds.
Answers
Answer:
770,400
Step-by-step explanation:
770,400 seconds
Choose Yes or No to tell if each quadrilateral always has all sides equal in length and all right angles.
Answers
Answer:
No
Step-by-step explanation:
For example a trapezoid doesn't have all right angles. Also, only squares and rhombuses have equal sides. If you have an image for your question please show us.
whats the perimeter of this shape??
Answers
The perimeter of the shape is 10 inches.
How to calculate the perimeter?It's important to note that the perimeter of a shape or calculated by adding all the sides together.
In this case, this is a rectangle and the perimeter will be:
Perimeter = 2(length + width)
Length = 4 inches
Width = 1 inch
Perimeter = 2(length + width)
Perimeter = 2(4 + 1)
Perimeter = 10 inches.
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Does this graph represent a function? Why or why not?
Answers
Reason - it proves one output, y, for each unique input, x.
*Today's Assignment*
Design a salary slip for the month of March 2023 with information given below.
Fixed vs variable ratio- 70:30
Ctc - 18L
Basic- 50%
Hra- 20%
Da - 12%
Insurance - 2500
Incentive- 75% target completion
Pf 12%
Earned leaves - 2
LOP - 4
Calculate net pay
Answers
A salary slip for the month of March 2023 with information given below.
Salary Slip - March 2023
Employee Details:
Name: [Employee Name]
Employee ID: [Employee ID]
Designation: [Employee Designation]
Earnings:
Basic Salary: [Basic Salary]
House Rent Allowance (HRA): [HRA]
Dearness Allowance (DA): [DA]
Incentive: [Incentive]
Total Earnings: [Total Earnings]
Deductions:
Provident Fund (PF): [PF]
Insurance: [Insurance]
Loss of Pay (LOP): [LOP]
Total Deductions: [Total Deductions]
Net Pay: [Net Pay]
Breakdown:
Basic Salary: 50% of CTC (18L) = [Basic Salary]
HRA: 20% of Basic Salary = [HRA]
DA: 12% of Basic Salary = [DA]
Incentive: 75% of target completion = [Incentive]
Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]
PF: 12% of Basic Salary = [PF]
Insurance: Rs. 2500 = [Insurance]
LOP: [LOP]
Total Deductions = PF + Insurance + LOP = [Total Deductions]
Net Pay = Total Earnings - Total Deductions = [Net Pay]
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what is the value of the expression shown? 7 [(7 + 7) +7
Answers
Answer:
105
Step-by-step explanation:
7 (7x7) + 7 is the same as 7 x 14 + 7 so that would equal 105
Riley put £450 into a savings account which
gathered simple interest at a rate of 2% per month.
After 6 months, Riley used some of the money in
the account to buy a bike costing £480.
How much money did Riley have left?
Answers
Answer:
£26.77
Step-by-step explanation:
450(100% + 2%)^6
= 450 (1.02)^6
= 506.77.
506.77 - 480 - 26.77.
Riley had £26.77 left.
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answers
The steps peter could use in solving the quadratic equation is by applying the quadratic formula; x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
How to solve quadratic equation?8x² + 16x + 3 = 0
using Quadratic formula
The following steps are involved
\(x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)
\(x = \frac{ -16 \pm \sqrt{16^2 - 4(8)(3)}}{ 2(8) }\)
\(x = \frac{ -16 \pm \sqrt{256 - 96}}{ 16 }\)
\(x = \frac{ -16 \pm \sqrt{160}}{ 16 }\)
\(x = \frac{ -16 \pm 4\sqrt{10}\, }{ 16 }\)
\(x = \frac{ -16 }{ 16 } \pm \frac{4\sqrt{10}\, }{ 16 }\)
\(x = -1 \pm \frac{ \sqrt{10}\, }{ 4 }\)
\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)
\(x = -0.209431\)
or
\(x = -1.79057\)
Therefore, the steps peter could follow will give the result
\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)
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Select the equation that has a = 112 as its solution.
a−114=35
a+358=434
416+a=523
a×38=214
Answers
Answer:
none
Step-by-step explanation:
a-114=35 ⇒ a= 149
a+358=434⇒ a=76
416+a=523⇒ a=107
ax38=214⇒ a=5.63
The equation that has 112 as it's solution is not existing in the options.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given are four linear equations.
Check the solution of each equation.
a - 114 = 35
Adding both sides of the equation with 114,
⇒ a = 35 + 114 = 149
a + 358 = 434
Subtracting both sides of the equation with 358,
⇒ a = 434 - 358 = 76
416 + a = 523
Subtracting both sides of the equation with 416,
a = 523 - 416 = 107
a × 38 = 214
Dividing both sides of the equation with 38,
a = 214/38 = 5.63
Hence none of the equations have 112 as it's solution.
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Write the equation of a line that is parallel to {y=-0.75x}y=−0.75xy, equals, minus, 0, point, 75, x and that passes through the point {(8,0)}(8,0)left parenthesis, 8, comma, 0, right parenthesis.
Answers
Answer:
\(y = 0.75x - 6\)
Step-by-step explanation:
Given
Parallel to:
\(y = 0.75x\)
Passes through
\((8,0)\)
Required
The equation
The slope intercept form of an equation is:
\(y = mx + b\)
Where:
\(m \to\) slope
So, by comparison:
\(m = 0.75\)
For a line parallel to \(y = 0.75x\), it means they have the same slope of:
\(m = 0.75\)
The equation of the line is then calculated using:
\(y = m(x - x_1) + y_1\)
Where:
\(m = 0.75\)
\((x_1,y_1) = (8,0)\)
So, we have:
\(y = 0.75(x - 8) + 0\)
Open bracket
\(y = 0.75x - 6 + 0\)
\(y = 0.75x - 6\)
Which is an equation for the line that contains (-2,5) and has a slope of -7 ?
7x + y = 33
y=-7x+9
y=-7x-33
7y+y=-9
Answers
Answer:
y = -7x - 9Step-by-step explanation:
The standard from of equation of a line is expressed as;
y = mx+c
m is teh slope = -7
c is the intercept
Get the intercept by substituting m = -7 and the point (-2, 5) into the equation;
y = mx+c
5 = -7(-2) + c
5 = 14 + c
c = 5-14
c = -9
Substitute m = -7 and c = -9 into the expression y = mx+c
y = -7x - 9
Hence the required equation of the line is y = -7x - 9
Please if you know the answer tell me it and the steps also thank you.
Answers
Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.
Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..
A pistol is accidentally discharged vertically upward from a height of 3 feet above the ground. If the bullet has an initial velocity of 200 feet per second the path of the bullet is modeled by the equation h=-16t 2 +200t+3, what maximum height will it reach before it starts to fall back down to the ground?
Answers
Answer:
hmax = 628 ft
Step-by-step explanation:
The bullet will reach its maximum height when its velocity h'(t) becomes zero. The equation of motion is
h(t) = -16t^2 + 200t + 3
Taking the derivative of h(t) is
h'(t) = -32t + 200
Solving for t when h'(t) = 0, we get
t = 200/32 = 6.25 s
and this is the time it takes for the bullet to reach its maximum height. Using this value for t into h(t), we get
h = -16(6.25 s)^2 + 200(6.25 s) + 3
= 628 ft
if you are sliding right, your are..
a)adding
b)subtracting
Answers
Answer:
adding right is positive and left is subtracting.
Step-by-step explanation:
Answer:
adding
Step-by-step explanation:
-x is 5 units to the right of 0.
Use the drop-down menus to complete the statement about x.
x is () units to the () of 0
Answers
Answer:
-x=5 so x=-5 so x is 5 units to the left of 0
Step-by-step explanation:
Answer:
X=x is 13 units to the left of 0.
Use the drop-down menus to complete the statement about −x.
CLEAR CHECK
−x is
units to the
of 0.
Step-by-step explanation:
write and equation for the nth term of the geometric sequence for 2,8,32,128
then find a6 round to the nearest tenth if necessary.
Answers
The sixth term of the geometric sequence is 2048.
The given geometric sequence is 2, 8, 32, 128. We can observe that each term is obtained by multiplying the previous term by 4. Therefore, the common ratio (r) of the sequence is 4.
The formula for the nth term (an) of a geometric sequence is given by:
an = a1 * r^(n-1)
where a1 is the first term and r is the common ratio.
For this sequence, a1 = 2 and r = 4. Plugging in these values into the formula, we get:
an = 2 * 4^(n-1)
To find a6, we substitute n = 6 into the formula:
a6 = 2 * 4^(6-1)
= 2 * 4^5
= 2 * 1024
= 2048
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The Probable question may be:
Write an equation for the nth term of the geometric sequence 2, 8, 32, 128,
Then find a6. Round to the nearest tenth if necessary.
a = 5×4 X
a1 = n-1 X
how to solve this question?
Answers
The revised Doubtful Debts Provision should be, $4,555.
Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):
Net Debts x Provision Rate equals Adjusted PDD.
The computation would then be:
= $91,100 x 0.05
= $4,555 is the adjusted PDD.
Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,
= $4,555 - $3,500
= $1,055
Hence, The revised Doubtful Debts Provision should be $4,555.
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A fish starts at -9m and changes at 11m
Answers
Answer:
I don't really know what you were asking
In a game experience, the level of monsters, L, is measured by the formula L= 250M E, where M=number of monsters and E=experience of monsters. Solve the formula for E
Answers
The formula for E is given as E = L/250M
According to the question we have been given that the level of monsters is measured by as follows
L = 250M E (1)
where , M = number of monsters
E = experience of monsters.
Now we need to find the formula for E. For that we will solve equation (1) for E .
L = 250M E
Dividing both the sides by 250M we get
L/250M = E
or, E = L/250M
Thus above is the equation or the formula for E.
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someone help me
please and thank you
Answers
Answer: Answer C
Step-by-step explanation:
Because it is a reflection of the Y-axis, the X-coordinates would remain the same but the Y-coordinates would change.
On a map, 1 inch equals 20 miles. If two cities are 3 inches apart on the map, how far are they actually apart?
Answers
Answer: 60 miles
Step-by-step explanation:
1 in. times 3 = 3 in
20 mi times 3 = 60 mi.
This is just a question I had.
If Denny (random name) left to another country and he left the Tuesday of this week (June 20) and he left for a month, what day would he be back on? I though July 18 but I’m not sure. Pls help?
Answers
Answer:
Step-by-step explanation:
Well, since the length of a month can vary in the number of days, this answer can also vary.
For example, February is only 28 days long, while December is 31 days long.
That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back July 19th of July 20th.
I hope this helps!
A line passes through -8,5 and has a slope of 3/4 write the equation in slope intercept form
Answers
The equation of the line in slope-intercept form is y = (3/4)x.
To write the equation of a line in slope-intercept form, we need to use the slope-intercept form equation: y = mx + b,
where m is the slope and b is the y-intercept.
Given that the line passes through the point (-8, 5) and has a slope of 3/4, we can substitute the values into the equation to find the y-intercept (b).
First, let's find the value of b using the point-slope form equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Using (-8, 5) as the point and 3/4 as the slope, we have:
5 - 5 = (3/4)(-8 - x)
0 = (3/4)(-8 - x)
0 = (-3/4)(8 + x)
0 = -6 - (3/4)x
Next, we can solve for x:
(3/4)x = -6
x = -6 \(\times\) (4/3)
x = -8
Now that we have the value of x, we can substitute it back into the equation to find the value of b:
0 = -6 - (3/4)(-8)
0 = -6 + 6
0 = 0
So, the value of b is 0.
Finally, we can write the equation of the line in slope-intercept form:
y = (3/4)x + 0
y = (3/4)x.
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MISTERBRAINLYY!!
The paint in a certain container is sufficient to paint an area equal to 9.375m2. How many bricks of dimensions 22.5cm×10cm×7.5cm can be painted out of this container?
Answers
There are three area options for the number of bricks:
4165551250How many bricks can be painted out of a container?
The number of bricks that can be painted out is equal to the paint area (A), in square centimeters, divided to the area of a brick (A'), in square centimeters. That is:
n = A / A'
A' = w · h
Where:
w - Width of the brick, in centimeters.h - Height of the brick, in centimeters.There are three possible answers:
Case 1: A = 93750 cm², w = 22.5 cm, h = 10 cm
A' = 22.5 · 10
A' = 225
n = 93750 / 225
n = 416.667
n = 416
Case 2: A = 93750 cm², w = 22.5 cm, h = 7.5 cm
A' = 22.5 · 7.5
A' = 168.75
n = 93750 / 168.75
n = 555.556
n = 555
Case 3: A = 93750 cm², w = 10 cm, h = 7.5 cm
A' = 10 · 7.5
A = 75
n = 93750 / 75
n = 1250
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Nayeli sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below. 217 visitors purchased no costume. 113 visitors purchased exactly one costume. 36 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth.
Answers
The probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth is 0.443
Out of 217 visitors who came to Nayeli's website, none of them purchased a costume. Therefore, the number of visitors who may purchase a costume is 217 less than the total number of visitors:
Total visitors - No. of visitors who didn't purchase a costume = 217
Total visitors - 217 = No. of visitors who may purchase a costume
Total visitors = 113 + 217+36 = 336
Out of the remaining visitors, 113 purchased exactly one costume, and 36 purchased more than one costume. Therefore, the number of visitors who purchased one or more costumes is:
No. of visitors who purchased one or more costumes = 113 + 36 = 149
Therefore, the probability that the next person will purchase one or more costumes can be expressed as:
Probability = No. of visitors who purchased one or more costumes / Total visitors
Probability = 149 /336 = 0.443
The probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth is 0.443
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Answer:
Step-by-step explanation:
.44
Ms. April likes for the twenty students in her
class to have a carton of milk each day at break
time. She sends three of her students down to
the cafeteria to ask for the cartons of milk, but
she likes to mix things up a bit and wants to
send a different group of students down every
day. Will she have enough different groups of
three students in her class of twenty students to
send a different group every day of the school year? (There are 180 days in the school year)
Answers
Answer:
Ms. April will not have enough students.
Step-by-step explanation:
This is because 180 days of the year divided by 3 students per day = 60 students per year. The class only has 20 students, therefore, there is not enough students needed to collect milk.
Answer:
Ms. April will not have enough students.
Step-by-step explanation:
This is because 180 days of the year divided by 3 students per day = 60 students per year. The class only has 20 students, therefore, there is not enough students needed to collect milk.