The orthocenter of the ΔABC is ( -1,5 ).
What is orthocenter?In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.
Given the co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).
To find the orthocenter using below steps:
1. First, we find the equations of AB and BC.
The general form of a line is y = mx + b
where m is the slope and b is the y-intercept.
Using the formula of slope given [tex]$m =\frac{y_2 - y_1}{x_2 - x_1}[/tex] , we will find the slope of AB and BC.
Now, slope of AB is m = (7-3/-1 + 3)
i.e. m = (4/2) = 2
Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,
y = mx + b
1 = 2 × (-1) + b
i.e. b = 3.
So, the equation of AB is y = 2x + 3.
Also, slope of BC is m=(3-7/3+1) i.e. m=-4/4 i.e. m--1
Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,
y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.
So, the equation of BC is y = -x.
2. We will find the slope of line perpendicular to AB and BC.
When two lines are perpendicular, then the product of their slopes is -1.
So, slope of line perpendicular to AB is [tex]m*2=-1[/tex] i.e. m = -1/2
So, slope of line perpendicular to BC is i.e.[tex]m*-1=-1[/tex] i.e. m = 1.
3. We will now find the equations of line perpendicular to AB and BC.
Using the slope of line perpendicular to AB m=-1/2 i.e. and the point opposite to AB
i.e. C(3, 3), we get,
y = mx + b
i.e. [tex]3=-1/2*3+b[/tex]
i.e. b = 9/2
So, the equation of line perpendicular to AB is
[tex]y=-x/2+9/2[/tex]
Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC
i.e. A( -3,3 ), we get,
y = mx + b
i.e. 3 = 1 × -3 + b
i.e. b = 6.
So, the equation of line perpendicular to BC is y = x+6
4. Finally, we will solve the obtained equations to find the value of (x, y).
As, we have y = x + 6 and y = -x/2 + 9/2
This gives, y = -x/2 + 9/2 → x + 6
y = -x/2 + 9/2
simplifying the above equation, we get
2x + 12 = -x + 9
3x = -3
x = -1.
So, y = x + 6
simplifying the above equation, we get
y = -1 + 6
y = 5.
The value of x = -1 and y = 5.
Hence, the orthocenter of the ΔABC is ( -1,5 ).
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Evaluate the expression 3(x-1) to the 2 power + 2x-7 For x = 3
The value of the function is x = 3 is 11
Function and valuesFunctions are expressions that consists of dependent and independent variables. This variables are represented using letters. For instance, f(x) is a function of x.
Given the function below
f(x) = 3(x-1)² + 2x - 7
Given that the value of x is 3, hence;
f(x) = 3(3-1)² + 2(3) - 7
Expand to have:
f(3) = 3(2)² + 2(3) - 7
f(3) = 3(4) + 6 - 7
f(3) = 12 - 1
f(3) = 11
Hence the value of the function is x = 3 is 11
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Two lines intersect at point P. If the measures of a pair of vertical angles are (2x-7)° and, (x+3)° determine x and the measures of the other two angles?
Answer:
x = 10
One angle is 13 and the other angle is 13
Step-by-step explanation:
Vertical angles have the same measurement, so set the angles equal to each other and solve for x.
2x - 7 = x + 3 Subtract x from both sides of the equation
x - 7 = 3 Add 7 to both sides of the equation
x = 10 Now use this to solve for both angles
2(10) - 7 =
20 - 7 =
13
x + 3
10 + 3 =
13
Please help I will give you 30 points
Step-by-step explanation:
520÷13=40..............
Answer:
The answer is C 40
Step-by-step explanation:
520/ 13 = 40
:) have a nice day
Express each fraction as a decimal to the nearest hundredth.
43/46
43/49= 0.93
To express each fraction into its decimal we need to bring 100 at the denominator.
Fraction = numerator\denominator
For example :
1> 4\5
= 4*20\ 5* 20
= 80\ 100
= 0.80
2> 1\4
= 1 *20\ 4 *20
= 20\ 100
= 0.20
3> 49/50
= 49*2/50*2
= 98/100
=0.98
There are some numbers where it is not possible to make the denominator 100
So by the process of division method, we can convert the fraction into decimal form
43/46
0.93
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Match the sequence to its equation
2, -4,-10, -16
Answer: 2, -4, -10. -16, ..., -6n+8 n=1, 2, 3, ...
Step-by-step explanation:
2, -4, -10, -16
a₁=2
a₂=-4
a₃=-10
a₄=-16
a₂-a₁=-4-2=-6
a₃-a₂=-10-(-4)=-6
a₄-a₃=-16-(-10)=-6
Hence, this is an arithmetic progression: a₁=2 d=-6
[tex]a_n=a₁+(n-1)d\\a_n=2+(n-1)(-6)\\a_n=2-6n+6\\a_n=-6n+8[/tex]
PROOF Write a coordinate proof for each statement.The measure of the segment that joins the vertex of the right angle in a right triangle to the midpoint of the hypotenuse is one-half the measure of the hypotenuse.
We have proved that PA = 1/2 PB using the SAS rule or Side Angle Side rule.
A right angle triangle is given.
We have to prove that measure of the segment that joins the vertex of the right angle in a right triangle to the midpoint of the hypotenuse is one-half the measure of the hypotenuse.
What is a triangle ?
A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.
As per the question ;
Let's assume P is the midpoint of the hypotenuse of the right angle △ABC and it is right angled at B. Also , D is the midpoint of AB.
Now ;
Draw a line parallel to BC from P meeting B at O and join PB.
Here ;
In △PAD and △PBD
∠PDA =∠PDB = 90°
and
PD = PD common)
AD = DB (As D is mid point of AB)
So ;
△ PAD ≅ PBD
by SAS rule
and
PA = 1/2 PB
Thus , we have proved that PA = 1/2 PB using the SAS rule or Side Angle Side rule.
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Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. (Lesson 3-1)
∠5 and ∠7
Answer:
Step-by-step explanation:
Use the Alternate Exterior Angles Theorem. If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.Solve by substituton
Solve the first equation for [tex]x[/tex].
[tex]x+3y = -2 \implies x = -3y - 2[/tex]
Substitute this into the second equation and solve for [tex]y[/tex].
[tex]-3(-3y-2) + y = 6 \implies 9y + 6 + y = 6 \implies 10y = 0 \implies y=0[/tex]
Now solve for the value of [tex]x[/tex].
[tex]x = -3\cdot0 - 2 = -2[/tex]
So the solution to the system is the point [tex](x,y) = \boxed{(-2,0)}[/tex]
Answer:
[tex]\left( \: \boxed{-2}\:, \: \boxed{0} \: \right)[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x+3y=-2\\-3x+y=6 \end{cases}[/tex]
To solve using the method of substitution, solve one equation for one of the variables.
Solving equation 2 for y:
[tex]\implies -3x+y=6[/tex]
[tex]\implies -3x+y+3x=3x+6[/tex]
[tex]\implies y=3x+6[/tex]
Substitute this expression into the other equation and solve for x:
[tex]\implies x+3y=-2[/tex]
[tex]\implies x+3(3x+6)=-2[/tex]
[tex]\implies x+9x+18=-2[/tex]
[tex]\implies 10x+18=-2[/tex]
[tex]\implies 10x+18-18=-2-18[/tex]
[tex]\implies 10x=-20[/tex]
[tex]\implies 10x \div 10=-20 \div 10[/tex]
[tex]\implies x=-2[/tex]
Substitute the found value of x into the expression for y, and solve for y:
[tex]\implies y=3x+6[/tex]
[tex]\implies y=3(-2)+6[/tex]
[tex]\implies y=-6+6[/tex]
[tex]\implies y=0[/tex]
Therefore, the solution to the given system of equations is:
[tex]\left( \: \boxed{-2}\:, \: \boxed{0} \: \right)[/tex]
|x-1| = |2x+3| ; solve for x
Answer: x=-2/3 x=-4
Step-by-step explanation:
[tex]|x-1|=|2x+3|\\[/tex]
Equate the submodular functions to zero:
x-1=0
x-1+1=0+1
x=1
2x+3=0
2x+3-3=0-3
2x=-3
Divide both parts of the equation by 2:
x=-1.5
Thus,
-∞____-1.5_____1____+∞
x∈[1,+∞)
x-1=2x+3
x-1-x-3=2x+3-x-3
-4=x∉[1,+∞)
x∈(-1.5,1)
-(x-1)=2x+3
-x+1=2x+3
-x+1+x-3=2x+3-x-3
-2=3x
Divide both parts of the equation by 3:
x=-2/3∈(-1.5,1)
x∈(-∞,-1.5]
-(x-1)=-(2x+3)
-x+1=-2x-3
-x+1+2x-1=-2x-3+2x-1
x=-4∈(-∞,-1.5]
I need to find out the quadrilateral of 78° k,L,N,M
Answer: ∠L = 102°
∠N = 78°
Step-by-step explanation:
Quadrilaterals can be classified into Parallelograms, Squares, Rectangles, and Rhombuses. Square, Rectangle, and Rhombus are also Parallelograms.
A quadrilateral is called a parallelogram, if both pairs of its opposite sides are parallel. AB ∥ DC and AD ∥ BC. So, ABCD is a parallelogram. A parallelogram having all sides equal, is called a rhombus.
Given data,
In □KLMN, side LM ∥ side KN, side KL ≅ side NM If ∠K = 78°
then find the measure of ∠L, and ∠N
side LM∥ side KN
Interior angles on the same side of the transversal are supplementary.
∠K + ∠L = 180°
78° + ∠L = 180°
∠L = 180° - 78°
∠L = 102°
Construction:
Draw LP ∥ MN
So, LM ∥ KN and LP ∥ MN
PLMN is a parallelogram
MN ≅ LP
Now MN = LP and MN = KL
LP = KL
∠LKP = ∠LPK = 78°
LP ∥ MN so,
∠MNP = ∠LPK = 78° (corresponding angles are equal)
∠L = 102°
∠N = 78°
Therefore,
∠L = 102°
∠N = 78°.
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Find the area of the polygon.
The area of the polygon is what?
Answer:
Area = 792 m
Step-by-step explanation:
You can cut the polygon into 2 rectangles.
Subtracting 18 from 60 can give you the length of rectangle A, so 42 will be the new length for rectangle A.
Multiply 6 and 42 to get 252 for the area of rectangle A.
Multiply 18 and 30 to get 540 for the area of rectangle B.
(You multiply to find the area.)
Lastly you add both areas, 252 + 540, and the final result is:
Area = 792 m
work out y=8x+5 when x=-2 1/2
Solve each equation. Check the solution. y/y+1 = 2/3
The solution of the given equation y/y+1 = 2/3 is calculated as (y = 2).
What is meant by cross multiplication?In cross-multiplication, the numerator of the first fraction is multiplied by the denominator of the second fraction, and the numerator of the second fraction is multiplied by the denominator of the first fraction.
Denominators are removed during cross multiplication. It's employed to make comparisons fraction sizes, solve proportional and percentage problems.A absent value or variable is common in proportion problems. After removing the denominators with cross multiplication, algebra skills are employed to solve again for missing variable. Percentage problems are solved in the same way that proportion problems are.Now, the given equation is as follows;
y/y+1 = 2/3
Cross-multiplying the values;
3y = 2(y + 1)
3 y = 2y + 2
Bring the variable on the single side and constants on the other.
3y - 2y = 2
y = 2
Therefore, the solution of the given equation y/y+1 = 2/3 is computed as (y = 2).
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Z is a standard normal random variable. what is the value of z if the areato the right of z is 0.0122?
As per question, ‘Z’ is a standard normal random variable. And the value of ‘z’ is [tex]0.9878.[/tex]
According to the question, the area to left of ‘z’ and the equation can be written as:
[tex]P(Z > z) =0.01222[/tex]
Therefore,[tex]P(Z < z) =1-0.01222=0.9878[/tex]
Now the desired z-score corresponding to z-table graph = [tex]2.25[/tex]
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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choose the definition for the function
Answer: C
Step-by-step explanation:
Since the inequalities for all 4 options are different, all you need to look at are the inequality signs.
For the line with a positive slope (bottom left to top right), the point it ends at is not filled in, so that point is not included meaning it is x > 1.
For the line with a negative slope (top left to bottom right), the point it ends at is filled in, so that point is included meaning it is x [tex]\leq[/tex] 1.
C. is the only one that has these inequalities.
Find the area of this shape.
6
13
Diagram NOT to scale
The units of the dimensions are m.
Give your answer in m².
m²
Answer:
78m
Step-by-step explanation:
6×13
78
not too sure tho
Leah walks 13 miles in 6 hours .lee walks 5 miles in 3 hours .Hercules walks 36 miles in 8 hours which Person had the fastest pace
Answer: Hercules has the fastest pace
Step-by-step explanation:
L=Leah. l=lee. H=Hercules
**Since the speeds are in fractions, make the denominators the same.
L=13/6
l=5/3
l=(5*2)/(3*2)
l=10/6
H=36/8
H=(36*6/8)/(8*6/8)
H=(216/8)/(48/8)
H=27/6
27/6 > 13/6 > 10/6
H>L>l
Hercules has the fastest pace
NEED NOW!!! WILL GIVE BRAINLIEST!!! 17-19!!!
For the given systems of equations, we have that:
17. The solution is: x = 3, y = 4.
18. The company can afford to promote 2 engineers to level II.
19. The substitution method was used, as writing x as a function of y in the given equation was quite straight forward, as was replacing into the second equation to find y.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For item 17, the system is:
3x + 2y = 17.4x - 2y = 4.Adding the equations, we can eliminate y and solve for x, hence:
7x = 21
x = 3.
Then the solution for y is given as follows:
3x + 2y = 17
3(3) + 2y = 17
2y = 8
y = 4.
For item 18, the variables are given as follows:
Variable x: number of level I engineers.Variable y: number of level II engineers.The company has 8 engineers, hence:
x + y = 8 -> x = 8 - y.
The company can afford to pay a total of $472,000 to the engineers, hence, considering the salaries(in thousands of dollars) of each:
56x + 68y = 472.
We want to solve for y, hence, since x = 8 - y:
56x + 68y = 472.
56(8 - y) + 68y = 472.
12y = 24.
y = 2.
The company can afford to promote 2 engineers to level II.
The substitution method was used, as writing x as a function of y in the given equation was quite straight forward, as was replacing into the second equation to find y.
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Answer:
This is my other account. I just needed 1+ answers togive brainliest for the other person. dont mind this
Step-by-step explanation:
A dog breeder charges a certain amount of money for litter of puppies along with a per puppy share. A litter with 6 puppies costs $172 and a littered with 10 puppies costs $220. Write an equation that could be used to calculate the cost, y, of any number of puppies, x.
Hint: y = mx + b
Given the task content, the cost, y, of any number of puppies, x is modeled by the equation y = mx + b where cost of any number of puppies is $12
EquationThere are three major types of equation. Namely,
Linear equationQuadratic equationSimultaneous equationAn equation can be solved through the following methods:
FactorizationGraphical methodCompleting the square methodSubstitution methodElimination methodGiven:
6 puppies costs $172
10 puppies costs $220
y = mx + b
Where,
y = total costx = number of puppiesm = cost of each litterb = fixed cost172 = m(6) + b
220 = m(10) + b
172 = 6m + b
220 = 10m + b
substract the equation48 = 4m
m = 48/4
m = 12
Substitute m = 12 into172 = 6m + b
172 = 6(12) + b
172 = 72 + b
172 - 72 = b
100 = b
Therefore, the cost of any number of puppies is $12
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raise y to the 2nd power, add the result to z, then double what you have
Answer:
2y²+2z
Step-by-step explanation:
y² raise y to the second power
y²+z add result to z
(y²+z)(2) double it
2y²+2ź
Simplify each complex fraction.
2/x + y / 3
The simplification of the given complex fraction 2/(x +y/3) is
6/(3x + y).
Accoring to the given question.
We have a complex fraction.
2/(x +y/3)
As we know that, complex fraction is a rational expression that has a fraction in its numerator, denominator or both.
For example: (2/3)/(4/6)
So, the above complex fraction can be simplified by
(2/3) × (6/4)
= (2/3) × (3/2)
= 1
Thereofore, the siplification of the complex fraction 2/(x +y/3) is given by
[tex]\frac{2}{x + \frac{y}{3} }[/tex]
= [tex]\frac{2}{\frac{3x+y}{3} }[/tex]
= 2(3)/(3x + y)
= 6/(3x + y)
Hence, the simplification of the given complex fraction 2/(x +y/3) is
6/(3x + y).
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Solve each equation. Check your answer.
2 x-5=17
Answer:
x = 11Step-by-step explanation:
Solve each equation. Check your answer.
2x - 5 = 17
2x = 12
x = 22 : 2
x = 11
------------------
check
2 * 11 - 5 = 17
22 - 5 = 17
17 = 17
the answer is good
Points!!!!!!!!!!!!!!!!
Simplify by combining like terms. 5 v-3(2-v)
The simplification by combining like terms of 5v-3(2 -v) is 8v - 6.
According to the given question.
We have an expression5v - 3(2 - v).
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression
5v - 3(2 - v).
Here 5v, and 3v both are the like terms.
So, we add coeffcients of v to simplify the given expression.
Therefore, the simplification of 5v -3 (2 -v ) is given by
5v - 3(2 - v)
= 5v - 6 + 3v
= 8v - 6
Hence, the simplification by combining like terms of 5v - 3(2 - v) is 8v - 6.
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Suppose you write and solve an equation to determine the amount of money m you have in your bank account after several weeks. You find that m=-36 . What does this solution mean?
Answer:
From the Soldier's point of view, the American Civil War was not a continuous battle. Instead, it was long monotonous marches and long residency in camps punctuated by the terror and chaos of combat. When winter set in and the campaigning season came to a close, most Soldiers counted on a long, cold stay in a winter camp. The four log cabins at the center of the Army Heritage Trail represent the types of buildings which Soldiers in both the Union and the Confederate Armies spent the long dreary months of winter. The cabins are modeled after images from the USAHEC collection, including the Army of the Potomac's winter camp at Brandy Station and the Confederate camp at Centerville
If Johnson & Johnson
sold $12,949,847 of hand
lotion in 2009 and $3,150,367
of that money was spent by
mothers of children who are
Hispanic, what percentage of
Johnson & Johnson's profits
were due to mothers who are
Hispanic? Round to the nearest
tenth
If Johnson & Johnson sold $12,949,847 of hand lotion in 2009 and $3,150,367 of the sales was spent by mothers of Hispanic children, the percentage of Johnson & Johnson's profits due to Hispanic mothers is 24.43%.
What is a percentage?A percentage is a ratio of one variable to the whole value or number.
Like ratios, probabilities, and proportions, percentages are expressed over 100.
Data and Calculations:The total sales revenue in 2009 = $12,949,847
The total sales revenue from Hispanic mothers = $3,150,367
The percentage of Hispanic sales over the total sales revenue = 24.43%($3,150,367/$12,949,847 x 100)
Thus, the percentage of Johnson & Johnson's profits due to Hispanic mothers is 24.43%.
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Suppose a trolley stops at a certain intersection every 14min . The first trolley of the day gets to the stop at 6: 43 A.M. How long do you have to wait for a trolley if you get to the stop at 8: 15 A.M.? At 3: 20 P.M.?
You will wait for 11 minutes
Find the number of minutes between 5:00am and 8:37am
60 mins in an hour.
8-5=3 hours
60x3=180+37=217 minutes
Divide 217 by 12 to see how many bus stops have already been made
217/12=18
18*12=216
217-216=1 minute
12-1=11 minutes
Therefore you will have to wait 11 minutes.
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Multiply Which it correct?
Answer:Your answer is the fourth one
Step-by-step explanation:Please give brainliest if right
Circle J has a radius of 10 units, ®K has a radius of 8 units, and BC = 5.4 units. Find the measure.
CK
If circle J has a radius of 10 units and BC = 5.4 units then the measure of CK is 2.6 units.
What is meant by the radius of a circle?A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length. The name is derived from the Latin radius, which means both rays and spoke of a chariot wheel.
The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.
Since the radius of K is 8 units, BK = 8.
CK + BC = BK
Where the value of BC = 5.4, we get
substitute the value of BC in the above equation, then we get
CK + 5.4 = 8
subtract 5.4 from both sides
CK + 5.4 - 5.4 = 8 - 5.4
simplifying the above equation,
CK = 2.6
Therefore, the measure of CK is 2.6 units.
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Simplify (4.3)(4.3^2)^4.
(4.3)^6
(4.3)^7
(4.3)^9
(4.3)^8
The simplified form of the given expression is 4.3⁹. The correct option is the third option (4.3)^9
Simplifying an ExpressionFrom the question, we are to simplify the given expression
The given expression is
(4.3)(4.3^2)^4
This can be written as
(4.3)(4.3²)⁴
Applying the law of exponents, we get
(4.3)(4.3² ˣ ⁴)
(4.3)(4.3⁸)
Then,
4.3 × 4.3⁸
NOTE: 4.3 = 4.3¹
Thus,
4.3¹ × 4.3⁸
Applying the multiplication law of indices, we get
4.3¹ ⁺ ⁸
= 4.3⁹
Hence, the simplified form of the given expression is 4.3⁹. The correct option is the third option (4.3)^9
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