Answer:
is NOT the same for all ordered pairs
The graph does NOT go through the point (0,0
Step-by-step explanation:
TRUST me
Tell whether the orthocenter is inside, on, or outside the triangle. Then find the coordinates of the orthocenter.
L(0,5), M(3,1), N(8,1): Is it outside, inside or on?
The orthocenter is ( , )
Answer:
see explanation
Step-by-step explanation:
The orthocentre is
• Inside all acute triangles
• Outside all obtuse triangles
• On all right triangles
To determine if the triangle is any of the above, we require the lengths of the 3 sides of the triangle.
Calculate the lengths using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
L(0, 5) and M(3, 1)
LM = [tex]\sqrt{(3-0)^2+(1-5)^2}[/tex] = [tex]\sqrt{3^2+(-4)^2}[/tex] = [tex]\sqrt{9+16}[/tex] = [tex]\sqrt{25}[/tex] = 5
L(0, 5) and (N(8, 1)
LN = [tex]\sqrt{(8-0)^2+(1-5)^2}[/tex] = [tex]\sqrt{8^2+(-4)^2}[/tex] = [tex]\sqrt{64+16}[/tex] = [tex]\sqrt{80}[/tex] = 4[tex]\sqrt{5}[/tex]
M(3, 1) and (N(8, 1)
MN = [tex]\sqrt{(8-3)^2+(1-1)^2}[/tex] = [tex]\sqrt{5^2+0^2}[/tex] = [tex]\sqrt{25}[/tex] = 5
Given 3 sides of a triangle a, b, c where c is the longest side, then
• a² + b² = c² ⇒ right triangle
• a² + b² < c² ⇒ acute triangle
• a² + b² > c² ⇒ obtuse triangle
Here a = 5, b = 5, c = 4[tex]\sqrt{5}[/tex]
a² + b² = 5² + 5² = 25 + 25 = 50
c² = (4[tex]\sqrt{5}[/tex] )² = 80
Since a² + b² < c² then triangle is obtuse and the orthocentre is outside the triangle.
The orthocentre is the point of intersection of the 3 Altitudes of the triangle.
We only require to find the equation of 2 of the altitudes and solve them simultaneously to obtain the coordinates of the orthocentre.
An Altitude is a line from a vertex at right angles to the opposite side
Altitude from M to LN
Calculate the slope of LN using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] = [tex]\frac{1-5}{8-0}[/tex] = [tex]\frac{-4}{8}[/tex] = - [tex]\frac{1}{2}[/tex] ⇒ [tex]m_{perpendicular}[/tex] = 2
Equation of altitude
y - 1 = 2(x - 3)
y - 1 = 2x - 6
y = 2x - 5 → (1)
Altitude from N to LM
m = [tex]\frac{1-5}{3-0}[/tex] = - [tex]\frac{4}{3}[/tex] ⇒ [tex]m_{perpendicular }[/tex] = [tex]\frac{3}{4}[/tex]
Equation of altitude
y - 1 = [tex]\frac{3}{4}[/tex](x - 8)
y - 1 = [tex]\frac{3}{4}[/tex] x - 6
y = [tex]\frac{3}{4}[/tex] x - 5 → (2)
Equating (1) and (2)
2x - 5 = [tex]\frac{3}{4}[/tex] x - 5 ( multiply through by 4 )
8x - 20 = 3x - 20
5x - 20 = - 20 ( add 20 to both sides )
5x = 0 ⇒ x = 0
Substitute x = 0 into (1)
y = 0 - 5 = - 5
The orthocentre is (0, - 5 )
Answer:
The orthocenter is outside the triangle, at (0, -5)
Step-by-step explanation:
The orthocenter is the intersection of the altitudes. So let's find the slope-intercept equation of "LM" "MN" and "LN" then determine it's perpendicular:
LM: slope = m = 1-5/3-0 = -4/3, equation => y = -4/3x + 5, perpendicular => y = 3/4x + b
this line passes through the opposite point, (8, 1)...therefore we can find b:
y = 3/4x + b
1 = 3/4(8) + b, b = -5, equation => y = 3/4x - 5
______________________________________
MN: slope = m = 1-1/8-5 = 0, equation => y = 1, perpendicular => x = ?
the line passes through the opposite point (0, 5)...so we can find ? or b:
x = ?, equation => x = 0
______________________________________
LN: slope = m = 1-5/8-0 = -4/8 = -1/2, equation => y = -1/2x + 5, perpendicular => y = 2x + b
the line passes through the opposite point (3, 1)...so we can find b:
1 = 2(3) + b, b = 1-6 = -5, equation => y = 2x - 5
______________________________________
System of Equations:
[tex]\begin{bmatrix}y=\frac{3}{4}x-5\\ y=2x-5\\ x=0\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}y=\frac{3}{4}x-5: \begin{bmatrix}x=0\\ \frac{3}{4}x-5=2x-5\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}x=0: \begin{bmatrix}\frac{3}{4}\cdot \:0-5=2\cdot \:0-5\end{bmatrix}[/tex]
[tex]\mathrm{Simplify\:}: \begin{bmatrix}-5=-5\end{bmatrix}[/tex]
[tex]\mathrm{For\:}y=\frac{3}{4}x-5,\\\mathrm{Substitute\:}x=0,\\y=\frac{3}{4}\cdot \:0-5 = -5[/tex]
[tex]y=-5,\:x=0[/tex]
_____________________________________
The orthocenter is outside the triangle, at (0, -5)
A group of friends was working on a student film. They spent $330 on costumes, which was 55% of their total budget. What was the total budget for their student film?
Answer:
$600
Step-by-step explanation:
Let "x" represent their total budget for the film.
Amount spent on costumes = $330
Percent spent on costumes = 55%
Therefore:
55% of x = $330
55/100 × x = 330
55x/100 = 330
Cross multiply
55x = 100 × 330
55x = 33,000
Divide both sides by 55
x = 33,000/55
x = 600
Total budget = x = $600
An angle bisector and a perpendicular bisector both divide a
geometrical shape into two equal parts. True or False
Answer:
I think it would be true.
how many kilometers would we have travelled in 10 hours
Answer:
in 10 hours you will travel 800 km which is like 500 miles if you're driving
Step-by-step explanation:
PLEASE HELP IN ONE MINUTE WILL MARK BRAINLIST
Answer:
1,-2 | -2,7 ????
Step-by-step explanation:
Evaluate m + 7.5 when m = 8.6
Answer:
16.1
Step-by-step explanation:
Identify the independent variables A photo lab charges 0.15 per print
Answer:
i: number of prints
d: cost
Pls help!! i beg you
Answer:
fiesta size which is 5 times bigger than the normal size, and the fiesta size price is a little less than 3 times the normal price basicly if you bought 5 of those, you would get the same amount which. is a waist of money, therefore the fiesta size bag is a better deal to purchase
Hope It Helps!
on each of the following ellipses. (e) 4x2 + y2 = 64 (B) 9x2 + 4y2 = 36 Graph the vertices, foci, endpoints of the minor axis, and endpoints of the latera recta; then draw 2. the ellipse for each equation in problem 1. values for a, b, A (x, y) and B(x, y) from: AB is a chord of the partial ellipse with equation f(x)=a? - x . Find the length of AB using (b) 49x 2 + 625y2 = 30,625, A (15,f(15)), B(20,f(20)) + 4y (b) 25x + 6y? - 400 (d) 4x² + y² = 4 () x² + 4y = 36 h) 7x? + 8y = 112 = 360,000, A (15,f(15)), B(20,f(20)) 625y2 576x2 + (a) hthen find the equation of the allir inform
Answer:
the question is cutoff. please rewrite the question. please write exponents as 4x^2.
Find the tenth term of the geometric sequence with a1 = 3, and r = 2.
1377
1526
1659
1536
1500
General term of GP: a
1
r
n−1
10
th
term of GP =a
1
r
9
=45(0.2)
9
=23040×10
−9
=2.304×10
−5
Answer:
1536
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
Here a₁ = 3 and r = 2 , then
a₁₀ = 3 × [tex]2^{9}[/tex] = 3 × 512 = 1536
A coat at a store is originally priced at $85. The store marks the price down to $68. To the nearest percent, what is the percent markdown of the coat ?
Answer:
20%
Step-by-step explanation:
This is because the amount decreased is 17 and 17 is what percent of 85? The answer is 20%.
Start at 7. Create a pattern that has multiples by 7. Stop when you have 5 numbers
Answer:
7,14,21,28,35
Step-by-step explanation:
PLEASE HELP DUE SUPER SOON
Answer:
2 Blocks
Step-by-step explanation:
Answer:2/3
Step-by-step explanation: 2 blocks apart so just 1/3 times 2=2/3
10)
Which set of numbers is NOT in the solution set of the inequality x > 17?
A
(14, 15, 18, 25, 29)
B)
(18.21, 25, 27, 33)
D
(29.32, 35.40.55)
Answer:
a
Step-by-step explanation:
numbers all have to be greater than 17. 14 and 15 are both less than
2(3x+4y+5z) + 4(x-y)
Answer:
10x+4y+10z Hope I helped? :')
Steps for answer!
1. Expand by distributing terms.
6x+8y+10z+4(x-y)
2. Expand by distributing terms.
6x+8y+10z+4x-4y
3. Collect like terms.
(6x+4x)+(8y-4y)+10z
4. Simplify.
10x+4y+10z
Solve. You must factor first.
8n^2 29n + 15 = 0
Please show work
Answer: Multiply n299 by n by adding the exponents
Step-by-step explanation:
8n230+15=0
Which of the following events are disjoint?
O A student getting an A in Statistics and getting an A in Economics.
O An adult owning a dog and owning a cat.
O A child having brown hair and wearing glasses.
O A person being male and giving birth to a baby.
Answer:
a child having brown hair and wearing glasses
The table shows the number of goals scored by Number of goals Frequency
each of 22 footballers.
0
4
A bar chart showing this information has
1
5
been started below.
2
8
3
5
8
7
6
a) Fill in the label for the
horizontal axis.
Frequency
COOL -
b) Draw the remaining bars.
2
1
c) Give the bar chart a title.
0
0
3
1
2
Numberof goals
An appropriate label for the horizontal axis of this bar chart is "Number of goals" and its title should be "The number of goals scored by a team."
What is a bar graph?A bar chart is also known as bar graph and it can be defined as a type of chart that is used for the graphical representation of data (information), especially by using rectangular bars or vertical columns.
The appropriate label for the horizontal axis of this bar chart is "Number of goals" and its title should be "The number of goals scored by a team."
Read more on bar chart here: https://brainly.com/question/24741444
#SPJ1
A farmer sells 7.6 kilograms of apples and pears at the farmer's market. 4/5 of this weight is
apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's
market? )
Express your answer in fraction and decimal form.
Solve on paper. Then check your work on Zearn. )
The farmer sold
kg or
kg of pears.
8
9
Enter ✓
0
3
5
Answer:
1.52
Step-by-step explanation:
Write the fraction 46/90 in its simplest form
Steel alloys are formed by mixing certain ratios of iron, carbon, and possible other elements. The table shows the amount of carbon required to make certain amounts of a particular alloy. Find the missing value for the table.
Answer:
jjwwbdjcjxbskkvcbnsoskccbizoanabzoxna njznznb CA. jA c ziebbjnc nakcb
1. If 5x + 6 = 10, what is the value of 10x + 3?
Answer:
11
Step-by-step explanation:
5x+6=10
-6 -6
5x=4
-------
5 5
x=4/5
10(4/5)+3
8+3=11
is 15.09 less than 12.63
Answer: No
15.09 is greater than 12.63
I know how to do this but I am too lazy to do this . soooo plx you guys fo it .
Answer:
Lol what do I do?
Step-by-step explanation:
12345678910
what is 6 * 8/5 as a fraction
Answer:
48/5 or in simplified version its 9 3/5
Step-by-step explanation:
Answer:
9 3/5
Step-by-step explanation:
Which ones are like terms?
-1 and 4
3x and -6
5x and -1
5x and 4
For the proportion, find the unknown number n. 9.6/16 = n/3.2
Answer:
n = 1.92
Step-by-step explanation:
Multiply both sides of the equation by 3.2
[tex]3.2*\frac{2}{3.2} =3.2*\frac{9.6}{16}[/tex]
Simplify both sides of the equation.
n = 1.92
good luck, i hope this helps :)
Raj weighs a book and rounds the weights to the nearest tenth. Does this weight round to 1.5 pounds?
1.58
Answer:
False
Step-by-step explanation:
1.58 the 8 is above five so it would round up to 1.6
Which of the following will result in a rational answer?
O multiplying by a fraction
O adding the square root of a non perfect square to a whole number
adding the square root of a perfect square to
O multiplying à fraction by a repeating decimal.
Mark this and return
Save and Exit
Next
Submit
Answer:
multiplying by a fraction
Step-by-step explanation:
rational answers can be a fraction.
hope this helps :)
Write each expression as the product of its factor 24× ^2