Answer:
Question: What is the orthocenter of a triangle with the vertices (-1,2) (5,2) and (2,1)?
The coordinates of point A are (-1,2), point B are (5,2), and point C are (2,1).
The orthocent is the intersection of the three altitudes. An altitude goes from a vertex and is perpendicular to the line containing the opposite side.
In the coordinate plane the equations of the altitudes can be found and then a system of equations can be solved.
Altitude 1. From point C perpendicular to the line containing side AB.
Slope of line AB is 0 (horizontal line), a vertical line is perpendicular to a horizontal line. Thus, the equation of altitude 1 is x=2 .
Altitude 2. From point B perpendicular to the line containing side AC.
Slope of line AC is −13 , the slope of a line perpendicular to line AC is 3. The equation of altitude 2 is y=3x−13
Altitude 3. From point A perpendicular to the line containing side BC.
Slope of line BC is 13 , the slope of a line perpendicular to line BC is −3 . The equation of altitude 3 is y=−3x−1
The orthocenter is the point where all three altitudes intersect.
x=2
y=3x−13
y=−3x−1
Use substitution to solve the first two equations y=3(2)−13=−7
The orthocenter is the point (2,−7)
we did not need the third equation, but we can use it as a check, plug the coordinates into the third equation:
−7=−3(2)−1
−7=−6−1
−7=−7 it works.
What is the value of f(x) = 2 • 2x for f(–2)?
Answer:
0.0625
Step-by-step explanation:
because the other answer is wrong.
(and bad) :)
Solve the equation x2 + 4x − 11 = 0 by completing the square. Fill in the values of a and b to complete the solutions.
Answer:
x = - 2 -[tex]\sqrt{15\\[/tex]
x = - 2 + [tex]\sqrt{15[/tex]
Step-by-step explanation:
The given equation needs to be solved by completing the squares.
The required values are -2+√15, -2-√15
Completing the squaresThe given equation is [tex]x^2+4x-11=0[/tex]
The general form of a quadratic equaiton is [tex]ax^2+bx+c=0[/tex]
Comparing with the given equation we have
a = 1
b = 4
c = -11
Rearranging the equation
[tex]x^2+4x=11[/tex]
Finding (b/2)²
[tex](\dfrac{4}{2})^2=4[/tex]
Adding to both sides of the equation
[tex]x^2+4x+4=11+4\\\Rightarrow (x+2)^2=15\\\Rightarrow x+2=\pm\sqrt{15}\\\Rightarrow x=-2+\sqrt{15},-2-\sqrt{15}[/tex]
Learn more about completing the squares:
https://brainly.com/question/24860429
PLS HELP !!!!!!!!!!!!!!!!!!
pls show ur work
Answer:
The skier has a faster rate of speed.
Snowboarder: 15m/s
skier: 18 m/s
Step-by-step explanation:
plzzz help me with this math im so confused!!
Answer:
I have made it in above picture
Answer:
2 A.)
1) 3-4x+8x^2-6+2x-5x^2
2) 8x^2-5x^2-4x+2x+3-6
3) 3x^2-2x-3
B.) 3x-5-7x^2+2+6x^2+5x
Step-by-step explanation:
please mark brainiest
please give 5 stars
thank you
PLEASE ANSWER FAST AS POSSIBLE I HAVE 40 LESSONS DUE BY 12 PM :(
Answer: B
Step-by-step explanation: Skeletons serve as a scaffold which supports organs, anchors muscles, and protect organs such as, the brain, lung, heart, and spinal cord.
Kiran has 27 nickels and quarters in his pocket, worth a total of $2.75.
B. How many nickels and quarters are in Kiran's pocket? Show your reasoning.
Answer:
1.35 about 6 quarters
Step-by-step explanation:
2.75-1.35=1.40
1.40/0.25=about 6
Answer:
there will be 20 nickels and 7 quarters
Consider the rectangular prism.
8 cm
14 cm
6 cm
How many cubes with side lengths of a cm can fit inside the rectangular prism?
0672 cubes
1, 344 cubes
2,688 cubes
0 5,376 cubes
Answer:
672 cubes because 8×6×14 equals 672 I hope it helps
To rent a party room, customers
are charged an amount equal to the number
of hours they rent plus a $60 cleaning fee.
What is the cost of a 3-hour rental?
WILL MARK BRANLIEST !!
Answer:
78
Step-by-step explanation:
im not sure but i think is 78
60+18=78
sorry
HELP PLEAAAASEEE LOLOLOL
1.Find the slope of the line graphed below.
A. 1/2
B. 2
C. -1/2
D. -2
I REALLY NEED HELP! PLEASE HELP ME!!
A burger cost $10 while a hot dog cost $6. What is the ratio of the cost of burger to hot dog?
Answer:
5:3
Step-by-step explanation:
a burger cost 10 and a hot dog cost 6 so the ratio is literally 10:6 if u want a simplified answer divide both numbers by 2
5:3
Answer: 3:5
Step-by-step explanation:
100000x5000000+997890-8
Answer:
500,000,997,882
Step-by-step explanation:
fun fact: the average tree frog weighs 0.8 ounces
Answer:
500000997882
Step-by-step explanation:100000 5000000 times is 500000997882.
Loren made a scale map of his football field to prepare for the big game. The length
of the football field on his map was 3 in. In reality the football field is 100 yards long.
What is the scale factor?
Answer:
1200
Step-by-step explanation:
brainliest please :D
Pls someone answer these 2 questions ill mark you as brainliest pls pls asap
Pls help me with this answer
Answer:
3.3x10^4
Step-by-step explanation:
2. The two equations y = (x + 2)(x + 3) and y = x? + 5x + 6 are equivalent.
a. Which equation helps find the x-intercepts most efficiently?
b. Which equation helps find the y-intercept most efficiently?
Answer:
it b
Step-by-step explanation:
a) y = (x + 2)(x + 3) helps find the x-intercepts most efficiently.
b) y= [tex]x^{2} +5x+6[/tex] helps find the y-intercept most efficiently
What is intercepts?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Given that:
a) y= (x+2)(x+3)
i.e., x+2= 0 , x+3 = 0
x= -2 , x= -3
and, y = [tex]x^{2} +5x+6[/tex]
= (x+2)(x+3)
x= -2 and y= -3
y = (x + 2)(x + 3) helps to find the x-intercepts most efficiently
Now,
b) y=(x+2)(x+3)
x =0 , y = 2 x 3 =6
y= [tex]x^{2} +5x+6[/tex]
y= 0 +05 x 0 + 6
y= 6
So, for y-intercept use y= [tex]x^{2} +5x+6[/tex]
Learn more about intercepts here:
https://brainly.com/question/14180189
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pls answer it now!!
argatogozaimasu!!
Answer:
850 and 23
Step-by-step explanation:
Can someone please help me
Answer:
radius = 10
(x-5)² + (y-11)² = 100
Step-by-step explanation:
The circumference is given, we get r = 20π/2π = 10
∴Equation of circle is (x-5)² + (y-11)² = 100
Answer:
hiii
Step-by-step explanation:
A polynomial p has zeros when x = 5,2 = -1, and 2
1
4
What could be the equation of p?
Answer:
apolynomial p has zeros
Answer:
p(x)=(x-5)(x+1)(4x+1)
When n = 3, which of the expressions below will be greater than 50? Select all that apply. A) (8n2÷9)⋅7 B) 2n2⋅3 –4n C) 4n2–6n+12 D) 7n+(n⋅8)
Answer:
A
Step-by-step explanation:
a)
[tex](8(3)^{2} / 9) * 7[/tex]
8(9) / 9 = 8 x 7 = 56
b)
[tex]2(3)^{2} * 3 - 4(3)[/tex]
2(9) * 3 - 12
18 * 3 = 54 - 12 = 42
c)
[tex]4(3)^{2} - 6(3) + 12[/tex]
4(9) - 18 + 12
36 - 18 = 18 + 12 = 30
d)
[tex]7(3) + (3 * 8)[/tex]
21 + 24 = 45
Someone help me ASAP !
Answer:
31
Step-by-step explanation:
There are 40 students in The class. Nine of those students are girls. What is the number of boys in the class ?
Answer:
31 students
Step-by-step explanation:
Han wrote a proof that triangle BCD is congruent to triangle DAB. Han's proof is incomplete. Which step is missing some information? DC∥AB
Step 1: Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.
Step 2: Side DB is congruent to side BD because they're the same segment.
Step 3: Angle A is congruent to angle C because they're both right angles.
Step 4: By the Angle-Side-Angle Triangle Congruence Theorem, triangle BCD is congruent to triangle DAB .
and WHY?
Answer:
The answer is below
Step-by-step explanation:
From the image, we can see that DC is parallel to AB.
Step 1:
Alternate interior angles are angles formed at the inner corners of intersection on opposite sides of transversal when two parallel lines are intersected by a transversal.
Since Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.
Step 2:
DB ≅ BD (reflexive property of congruence)
Step 3:
∠A = ∠C = 90° (right angles, given). But to prove that both triangles are congruent, the correct step 3 is:
Since, ∠A = ∠C = 90° and angles CDB and ABD are congruent. This means that the third angles in the both triangles are also congruent. Hence, angle ADB and CBD are must be congruent.
Step 4:
BD = DB, angles CDB and ABD are congruent, angle ADB and CBD are congruent.
Therefore, By the Angle-Side-Angle Triangle Congruence Theorem, triangle BCD is congruent to triangle DAB .
Expand and simplify (y+3)-(y-2)
Answer:
5
Step-by-step explanation:
Given
(y + 3) - (y - 2) ← distribute parenthesis
= y + 3 - y + 2 ← collect like terms
= 5
PLZZZZZZ HEEEEEEEEELLLLLPPPPP
(will mark brainliest for correct answers)
Answer:
y=4
Step-by-step explanation:
3(9) +4y= 43
27+4y=43
4y=16
y=4
It says shade 3/4 of this figure
Answer:
I think you shade in 6 of the rectangles
help me please with my geometry
Answer: 47.86
Step-by-step explanation:
tan x =42/38
tan x= 1.105
x= 47.86
If these four countries trade only with each other, what is the difference between the highest balance of trade and the lowest
balance of trade within this group?
a €4,378,000,000
€2,797,000,000
€1,928,000,000
d €738,000,000
Answer:
€4,378,000,000
Step-by-step explanation: just took the test :)
Answer:
A
Step-by-step explanation:
Took the test
The number of people using an older version of a spreadsheet program decreases at a rate that is proportional at any time to the number of people still using the version at that time.
There were 10,000 people using the older version of the spreadsheet program when the new version first came out. The number of people still using the older version decreases by 20%, percent every 6 months.
Answer:
5842 people after 2 months
Step-by-step explanation:
Given
Initial Value: [tex]a =10000[/tex]
Rate: [tex]r = 20\%[/tex] every 6 months
Required
Number of people using it after 2 months
The function follows an exponential model.
So, we need to first write out the function.
If Rate: [tex]r = 20\%[/tex] every 6 months
Then
Rate: [tex]r = 40\%[/tex] after 1 year
[tex]r = 0.04[/tex]
The function is represented as:
[tex]y = ar^x[/tex]
So:
[tex]y = 10000 * 0.04^t[/tex]
For 2 months, we have:
[tex]t = 2\ months[/tex]
Convert to years
[tex]t = \frac{2}{12}[/tex]
[tex]t = 0.167[/tex]
[tex]y = 10000 * 0.04^t[/tex]
[tex]y = 10000 * 0.04^{0.167}[/tex]
[tex]y = 5842[/tex]
HELP ME PLZ !!!!!!!!
Answer:
LM=JM
Step-by-step explanation:
If Jk=Lk Maybe that K was not 90 This means that the triangles are not congruent if it was K = 90 maybe Jk ≠ Lk and that means the two triangles are not congruentif LM = GM و MK = MK It means that the two triangles are congruentNote: Enter your answer and show all the steps that you use to solve this problem in the space provided. Find the area of the parallelogram. A parallelogram has a lower side measuring 24 centimeters and a right side measuring 9 centimeters. A dashed vertical segment with endpoints on the upper and lower sides is 8 centimeters and meets the lower left vertex at a right angle.
Answer:
[tex]Area = 192cm^2[/tex]
Step-by-step explanation:
The given information can be interpreted as:
[tex]Base = 24cm[/tex] --- lower side
[tex]Slant\ Height = 9cm[/tex] --- right side
[tex]Height = 8cm[/tex] --- dashed line
Required
Determine the area
The area of parallelogram is:
[tex]Area = Base * Height[/tex]
[tex]Area = 24cm * 8cm[/tex]
[tex]Area = 192cm^2[/tex]
Answer:
she like
Step-by-step explanation:
faygo u gettin bigger