Find the coordinates of the orthocenter of each triangle with the given vertices. J(3,-2), K(5,6), L(9,-2)

The steps that could be part of the process of algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10 are

An algebraic equation is a mathematical statement that sets two expressions equal using variables, coefficients, and constants.

Algebraic equations are represented by the equal symbol (=).

y + 5x = x² + 10 and y = 4x – 10

Substitute y = 4x - 10:

4x – 10  + 5x = x² + 10

4x - 10 = x² – 5x + 10

Add 10 to both sides:

4x - 10 + 10 = x² - 5x + 20

4x = x² - 5x + 20

Subtract 4x from both sides:

4x - 4x = x² - 5x  - 4x + 20

0 = x² - 9x + 20

Solving, if x = 4:

x² - 9x + 20 = 0

4² - 9 (4) + 20 = 0

16 - 36 + 20 = 0

-20 + 20 = 0

Thus, the steps for algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10 are Options D and E.

Learn more about algebraic equations at https://brainly.com/question/4541471

#SPJ1

a) y = x2 + 5x + 10

b) y + 5x = x2 + 10 + 4x – 10

c) 0 = x2 – 9x

d) 0 = x2 – 9x + 20

e) One x-value of a solution to the system is 4.

Answer:

Step-by-step explanation:

what is 20 times 40 plus 67 minus 3

20 × 40 +  67 - 3 =   (remember PEMDAS)

800 + 64 =

864

Answer:864

Step-by-step explanation:

20 x 40 = 800 then you add 800 and 67 then you will get 867 then you subtract 3 that when you get 864

Answer:

a = j - g

Step-by-step explanation:

"solve for a" means to get a all by itself on one side of the equation. You can see the beginning of the answer that is provided on your screen says "a = "

We are starting with:

j = g + a

First, subtract g from both sides of the equation.

j - g = a

Now just trade the left and right sides of the equation.

a = j - g

Fill in your answer in the box: j - g

In the similar triangles given, the sum of AB and BD is: B. 4⅓.

The corresponding side lengths of two triangles that are similar to each other have equal ratio, that is, they are proportional in size.

Find AC:

AB/CD = AE/(8 - AC) [proportional sides of similar triangles]

AB = 3

CD = 2

AE = 8

Substitute

3/2 = 8/(8 - AC)

3(8 - AC) = 2(8)

24 - 3AC = 16

24 - 16 = 3AC

8 = 3AC

8/3 = AC

AC = 2⅔

Find BD:

AB/CD = BE/(5 - BD) [proportional sides of similar triangles]

BE = 5

AB = 3

CD = 2

Substitute

3/2 = 5/(5 - BD)

3(5 - BD) = 2(5)

15 - 3BD = 10

15 - 10 = 3BD

5 = 3BD

5/3 = BD

BD = 1⅔

AB + BD = 8/3 + 5/3

AB + BD = (8 + 5)/3

AB + BD = 13/3

AB + BD = 4⅓

Thus, in the similar triangles given, the sum of AB and BD is: B. 4⅓.

Learn more about similar triangles on:

https://brainly.com/question/11899908

#SPJ1

Answer:

The dimensions of the rectangular plot of the land is 17 × 12 square units.

Step-by-step explanation:

What is perimeter? The perimeter of a shape is the distance around the shape. It is the total length of the shape's sides.

What is the formula for the perimeter of rectangle?

Perimeter of rectangle = 2( length + width)

What is area?

The area can be defined as the space occupied by a flat shape or the surface of an object.

What is formula for the area of rectangle?

Area of rectangle = length × width

The answer is C cause it makes ore sense against the other answers

0.25 is the probability a bean bag lands closer to the center of the circle than to the edge of the circle.

What is the probability in simple terms?

Let the radius of the circle be r.

Now the distsnce of the edge of the circle from the center is r units.

Now for any point lying in the circle, the sum of the distance of that point

from the center and from the nearest edge of the circle is r.

Thus, the bag will land closer to the circle if it lies within r/2 distance from the center.

Now, the area of the inner circle with radius r/2 is =  [tex]\pi (\frac{r}{2})^{2} = \pi \frac{r^{2} }{4}[/tex]

The area of the actual circle = πr²

Thus, the bean bag will land closer to the center if it lies within the inner circle of area = π r²/4

Hence, the required probability = [tex]\pi r^{2} /4/ \pi r^{2}[/tex] = 1/4 = 0.25

Learn more about probability

brainly.com/question/11234923

#SPJ4

Solution:

The formula for the perimeter of a rectangle is, P = length + breadth + length + breadth.

As you stated the formula of a rectangle is P (perimeter) = 2W (the two widths added together) + 2L (the two lengths added together).

To solve this algebraically you need to define your variable, or unknown, which in this case is the width or "W".

Now set this same equation with any symbol you wish, "x" is often used, and solve for x.  You could keep W instead of X also if it makes it easier to work on the problem.

P= 2x + 2L

isolate the 2x by subtracting 2L from both sides.

P-2L=2x

Now isolate the x by dividing both sides by 2 and you have

P-2L/2=x

x will be W.  Just put in the numbers P and L and you will have solved for W.

One More Solution :

The perimeter of a rectangle is given by the following formula:    

P = 2W + 2L

To solve this formula for W, the goal is to isolate this variable to one side of the equation such that the width of the rectangle (W) can be solved when given its perimeter (P) and length (L).

P = 2W + 2L

subtract 2L from both sides of the equation

P - 2L = 2W + 2L - 2L

P - 2L = 2W

divide both sides of the equation by 2

(P - 2L)/2 = (2W)/2

(P - 2L)/2 = (2/2)W

(P - 2L)/2 = (1)W

(P - 2L)/2 = W

Thus, given that the perimeter (P) of a rectangle is defined by    P = 2W + 2L ,

then its width (W) is given by    W = (P - 2L)/2

more details : brainly.com/question/12612753

#SPJ9

Answer:

o na ain't no one answering that

Answer: D. Have a great day :3

Step-by-step explanation:

The constant of proportionality for the relationship of millimeters of rainwater to time in hours is 48 millimeter/hour.

Given that the measuring tool captures rain falling at a constant.The table shows the height of rainwater in the measuring tool and the number of minutes it rains as shown in attached image.

A ratio is a mathematical comparison between two numbers. In proportion, if two given sets of numbers increase or decrease by the same ratio then the given ratios are said to be proportional.

Now we will calculate the proportion by using the formula

Ratio=(r₂-r₁)/(t₂-t₁)

Here, r₁=4, r₂=8, t₁=5, t₂=10

So, r₂-r₁=8-4=4 and

t₂-t₁=10-5=5

Now, we will convert the time from min to hour by dividing it with 60, we get

t₂-t₁=5/60

Substitute this value in above equation, we get

Ratio=4/(5/60)

Ratio=(4×60)/5

Ratio=4×12

Ratio=48 mm/hr

Hence, the constant of proportionality for the relationship of millimeters of rainwater to time in hours by using the given table is 48 mm/hr.

Learn more about proportionality from here brainly.com/question/6283094

#SPJ9

If the tire says P235/65R17, the diameter of your wheel will be 17 inches.

The primary purposes of a car's tires are to carry the weight of the car, transmit traction and braking forces to the road surface, insulate against shocks from the road, and change and maintain the direction of motion.

It offers traction for braking and acceleration and reduces the number of road vibrations that reach the car's body.

It should be noted that the numbers that are written on the tire are vital in knowing the diameter that's illustrated.

In this case, when the tire says P235/65R17, the diameter of your wheel will be 17 inches.

In conclusion, it is 17 inches.

Learn more about diameter on:

brainly.com/question/23220731

#SPJ1

Answer:

1. p^10

2. p^24

Step-by-step explanation:

p^6 x p^4=p^(6+4)=p^10

(p^6)^4=p^(6x4)=p^24

Answer:

solve this

Step-by-step explanation:

260*9/4

Answer:

68%

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

calculate the sum for both classes

class 1

[tex]\frac{sum}{20}[/tex] = 64 ( multiply both sides by 20 )

sum = 1280

class 2

[tex]\frac{sum}{10}[/tex] = 76 ( multiply both sides by 10 )

sum = 760

combine the 2 sums and divide by count of both classes for overall mean

overall mean = [tex]\frac{1280+760}{30}[/tex] = [tex]\frac{2040}{30}[/tex] = 68%

The distance between the given parallel lines is

In the given statement is :

The equations of the pair of each parallel lines is:

y = 4x and y = 4x - 17

To find the distance between each pair of parallel lines.

Two lines a₁x +b₁y + c₁=0   and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.

As we know that distance between the parallel lines (d) is given as:-

d = [tex]\frac{c_{2} -c_{1} }{\sqrt{a^{2} +b^{2} } }[/tex]

Parallel lines equation as:

y - 4x = 0

y - 4x + 17 = 0

Here,

a = -4 , b = 1, c1 = 0, c2 = 17

Therefore, putting the values

d = [tex]\frac{17 -0}{\sqrt{-4^{2}+1^{2} } }[/tex]

d = [tex]\frac{17}{\sqrt{17} }[/tex]

d = root 17

d = 4.12 units

Hence, The distance between the given parallel lines is 4.12 units

Learn more about Parallel lines at:

https://brainly.com/question/28563054

#SPJ4

Answer:

B

Step-by-step explanation:

The rational form of 0.412 is 103/250.

According to the question,  to write the rational expression for the given link by removing the decimal. When the decimal is removed from the numerator then that many zeros will come in the denominator.

Therefore, the rational expression can be written as:

Required expression = 0.412 = 412/1000 = 103/250

Hence, the correct answer for this expression is 103/250.

What is rational expression?

The rational expression can be represented in the form of ratios which has two polynomials in the numerator as well as in the denominator. The value of the denominator term should never be zero.

To learn more about the rational expression from the given link:

https://brainly.com/question/2264785

#SPJ9

Answer:

b(x) = 4x + 1

Step-by-step explanation:

If x starts from 1, we can give the equation as follows:

b(x) = 4x + 1

Let's check it, for the first one

x = 1, b(x) = 5

for the second, x = 2, b(x) = 4(2)+1 =9

The average speed in miles per hour for the round trip is (D) 47.5.

To find the average speed:

Formula: Sum of terms/Number of terms

Therefore, the average speed in miles per hour for the round trip is (D) 47.5.

Know more about averages here:

https://brainly.com/question/20118982

#SPJ4

Answer:

The conditional statement is true.

Step-by-step explanation:

If a and b are negative, it doesn't matter what numbers they are; the sum will always be negative.

Answer:

write your full question.

The relationship between the number x of days and the total cost represent as piecewise function.

f(x) = -x < 0

      = x if x ≥ 0

The bike store charges $20 for the first day and $15 for each additional day. The relationship between the number x of days and the total cost represent as:

f(x) = 20 , if 0 < x ≤ 1

      = 35,  if 1 < x ≤ 2

      = 50,  if 2 < x ≤ 3

      = 65,  if 3 < x ≤ 4

The absolute value function f(x) = |x| can be written as a piecewise function.

f(x) = -x < 0

      = x if x ≥ 0

Piecewise functions: A piecewise function is made up of two or more functions, each defined on a specific domain. Piecewise functions follow the following format:

f(x)    ⇒ -x,   x < 0

               ⇒  0,  x = 0

                ⇒ x,  x > 0

The piecewise function above is the absolute value function. As you can see, piecewise functions include:

A curly bracket to indicate that the function is comprised of more than one subfunction

The subfunctions that make up the piecewise function

The subdomains corresponding to each subfunction

The domains of the subfunctions cannot overlap, but one function can end where another starts. If different functions were part of the same domain, the piecewise function would not be a function anymore!

To graph a piecewise function, graph each subfunction at the indicated domain. Be wary of the inequality symbols (< , ≤ , > , ≥) and whether they include or exclude the end of the subdomain. If they include the domain, draw a point and fill it in. If they exclude the domain, draw a point but do not fill it in.

To learn more about piecewise function visit here : brainly.com/question/12561612

#SPJ1

Answer: 15

Step-by-step explanation:

-15 is 15 units to zero (answer should always be positive)

According to the Alternate Exterior Angles Theorem, when two parallel lines are severed by a transversal, the resultant alternate exterior angles are congruent if and only if the transversal is itself parallel to the two parallel lines.

So, in the figure below, if k ∥ l then

∠1 ≅ ∠7 and ∠4 ≅ ∠6.

Proof.

Since k ∥ l by the Corresponding Angles Postulate,

∠1 ≅ ∠5.

Also, by the Vertical Angles Theorem,

∠5 ≅ ∠7

Then, by the Transitive Property of Congruence,

∠1 ≅ ∠7

You may use the same strategy to demonstrate that ∠4 and ∠6 are equivalent to establish that they are congruent.

It should also be noted that the opposite of this theorem is true; more specifically, if two lines, k, and l, are sliced by a transversal in such a way that the alternative exterior angles are congruent, then k∥l.

Learn more about alternative exterior angles-https://brainly.com/question/2398628

Answer:

y=61°

Step-by-step explanation:

(y-8°)+(y+15°)+(y-10°)=180°

y-8°+y+15°+y-10°=180°

3y-3°=180°

3y=180°+3°

3y=183°

3y÷3=183°÷3

y=61°

The value of y from the given triangle can be calculated using the angle sum property as 61.

Given that:

A triangle has three angles given.

The measures of the angles are y - 8°, y - 10°, and y + 15°.

The angle sum property of triangles is defined as the property which states that the sum of the angles of the triangle is 180°.

Equating the angle measures:

y - 8 + y - 10 + y + 15 = 180

Add the like terms together.

3y - 3 = 180

Take 3 as common.

3(y - 1) = 180

Divide both sides of the equation by 3.

y - 1 = 60

Add 1 on both sides.

y = 61

Hence, the value of y is 61.

Learn more about Angles here :

https://brainly.com/question/31186705

#SPJ6

Answer:

f(- 1) = 6

Step-by-step explanation:

substitute x = - 1 into f(x)

f(- 1) = 2(- 1)² + 4 = 2(1) + 4 = 2 + 4 = 6

The first term of the given sequence is a(1) = 128

The formula for the nth term of a geometric sequence is:

a(n) = a(1) . rⁿ⁻¹

In the above formula, a(1) refers to the first term while r refers to the common ratio.

Information from the problem.

a(9) = 1/2 and a(12) = 1/16

Substitute n = 9 into the formula, we get:

a(9) = a(1) . r⁸

1/2  = a(1) .  r⁸

Substitute n = 12 into the formula, we get:

a(12) = a(1) . r¹¹

1/16  = a(1) .  r¹¹

Divide a(12) by a(9):

1/16 : 1/2 = ( a(1) .  r¹¹ ) : (a(1) .  r⁸ )  

Since a(1) terms are cancelled out, we have:

2 : 16 = r¹¹ :  r⁸

1/8 = r³

r = 1/2

Substitute r = 1/2 into a(9) :

a(9) = a(1) . r⁸

1/2 = a(1) . (1/2)⁸

a(1) = 1/2 : (1/2)⁸ = (1/2)¹⁻⁸

       = (1/2)⁻⁷ = 2⁷

       = 128

Learn more about geometric sequence here:

https://brainly.com/question/11847927

#SPJ4

Answer:

x=3

Step-by-step explanation:

8*3 = 24

4*3=12

24-12=12

Answer:

x = 3

Step-by-step explanation:

8x - 12 = 4x ( subtract 4x from both sides )

4x - 12 = 0 ( add 12 to both sides )

4x = 12 ( divide both sides by 4 )

x = 3

the distance between the cars is 3 miles

By elimination, the solution of the system of equations, 20x + 5y = 120 and 10x + 7.5y = 80, is (5 , 4).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Multiply first equation 2 by 2.

10x + 7.5y = 80     (equation 2)

20x + 15y = 160

Subtracting the two equations will eliminate the variable x.

20x + 15y = 160     (equation 2)

20x +  5y = 120     (equation 1)

0x + 10y = 40

y = 4

Substitute the value of y to any of the two equations and solve for x.

20x + 5y = 120     (equation 1)

20x + 5(4) = 120

20x = 120 - 20

20x = 100

x = 5

Hence, the solution of the system of equations is (5 , 4).

Learn more about solving systems of equations by elimination here: https://brainly.com/question/28405823

#SPJ4