The KN is 21.4 rounded to the nearest tenth.
What is an orthocenter?The orthocenter of a triangle is the place where the perpendicular drawn from the vertices to the opposing sides of the triangle intersect each other. The orthocenter for a triangle with an acute angle is located within the triangle. The orthocenter for a triangle with an acute angle is outside the triangle.
Now we need to find the slope of JL.
From that we have to find the slope of the perpendicular line through B.
Slope of JL= (y₂ - y₁) / (x₂ - x₁)
J (7, 8) and L (5, 2)
here x₁= 7,y₁ = 8, x₂ = 5 and y₂ = 2
= -6 / -2
= 3
Slope of the altitude KM = -1/ slope of JL = -1/3
Equation of the altitude KM : (y - y₁) = m (x -x₁)
Here K(1,2);
(y - 2) = -1/3 (x -1)
(y - 2) = -x/3 +1/3
Now we need to find the slope of JK.
From that we have to find the slope of the perpendicular line through D.
Slope of KL= (y₂ - y₁) / (x₂ - x₁)
J(7,8) and K(1,2)
here x₁= 7,y₁ = 8, x₂ = 1 and y₂ = 2
= 1
Slope of the altitude JO = -1/ slope of JL
= -1
Equation of the altitude JO : (y - y₁) = m (x -x₁):
(y - 8) = -1 (x - 7)
Solving the equation, x = 21 and y = -6
So the orthocenter N is (21 , -6)
Now the distance of KN is = √(21 - 1)² + (-6 -2)²
=√464
= 21.5
Therefore, the KN is 21.5 rounded to the nearest tenth.
To learn more about the Orthocenter;
https://brainly.com/question/29576583
#SPJ1
Answer:6.3
Step-by-step explanation:
I got it correct on my test
two angles that are located between two coplanar lines on the same side of the transversal are called
When two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.
Alternate External Angles
The pairs of angles outside the two lines and on either side of a transversal that cuts two lines are referred to as the alternate external angles.
In the given diagram below, the alternate exterior angles are:
∠2 and ∠8
∠1 and ∠7
Hence, when two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.
To read more about Alternate External Angles.
https://brainly.com/question/26111088
#SPJ4
Can someone pls simplify 2x-1/x^2 -2x-3 + 1/x-3
The simplified form of (2x - 1)/(x² - 2x - 3 + 1)/(x - 3) is
(2x - 1)(x - 3)/(x - 1 - √3)(x - 1 + √3).
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, (2x - 1)/(x² - 2x - 3 + 1)/(x - 3).
= (2x - 1)/(x² - 2x - 2)/(x - 3).
= (2x - 1)/(x - 1 - √3)(x - 1 + √3)/(x - 3).
= (2x - 1)(x - 3)/(x - 1 - √3)(x - 1 + √3).
learn more about simplifying expressions here :
https://brainly.com/question/14083225
#SPJ1
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h (t) = 104t-16t^2. After how long will it reach its maximum height?
In a division question, when would you find the restrictions – before or after finding the
reciprocal? Explain your reasoning.
we find the restrictions after finding the reciprocal
What is Division?A division is a process of splitting a specific amount into equal parts.
The values that give a value of 0 in the denominator are the restrictions.
To divide rational expressions, multiply by the reciprocal of the divisor.
The restrictions to the domain of a product consist of the restrictions to the domain of each factor.
To solve this we changes to reciprocal
The reciprocal rule of division method is “Multiply the dividend by the reciprocal of the divisor”.
Hence, we find the restrictions after finding the reciprocal
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ1
1 cup equals 16 tablespoons. how many tablespoons would be 1/4 cup of sugar
Answer:4 tablespoons
Step-by-step explanation:
1 = 16 tablespoons
1/4 = 4 tablespoons
Take 16 divided by 4 = 4
2. The graph shows the number of feet a remote
control car travels every second.
How far does the remote control car travel per second?
A 1 foot
B 2 feet
C 3 feet
14 feet
Q#2:
E 6 feet
3. The graph of a linear function is shown.
The following points lie on the line: (0, 80) and (8, 60).
What is the equation of the function?
Remote Control Car Distance
y
Distance (in feet)
654321
-
0 1 2 3 456
Time (in seconds)
y
100
Sook 80
60
40
20
X
atsenil s to rigang
Holla
0 2 4 6 8 10
2. The distance traveled by the remote control car each second is given as follows: C. 3 feet.
3. The equation of the linear function is given as follows: y = -2.5x + 80.
How to obtain the distance traveled by the car each second?This distance is the rate of change of the output variable relative to the input variable of the linear function, hence it is the slope of the linear function.
Two points on the graph are given as follows:
(0,0) and (1,3).
Then the slope is calculated as the change in the output divided by the change in the input, as follows:
m = (3 - 0)/(1 - 0) = 3.
Meaning that option C is correct.
How to obtain the equation of the linear function?The linear function in this problem is defined in slope-intercept format, as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.When x = 0, y = 80, hence the intercept is given as follows:
b = 80.
When x increases by 8, y decayed by 20, hence the slope is calculated as follows:
m = -20/8 = -2.5.
This means that the equation is given as follows:
y = -2.5x + 80.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
the mean score on a college placement exam is 500 with a standard deviation of 100. ninety-five percent of the test takers score below what value?
The value for which test score is below 95% percent for the given mean and standard deviation on a college placement is equal to 696.
As given in the question,
Given : 95% of the test takers score are below z.
z-score is given by,
z=(x-μ)/σ
Mean of the score 'μ' = 500
Standard deviation of the score ' σ' = 100
Z = 95%
= 0.95
P(z<Z) = 1-0.95
= 0.05
The value of z which corresponds to 0.05 in the table is equal to 1.96.
Substitute all the values we get,
z=(x-μ)/σ
⇒1.96 = ( x - 500 ) / 100
Multiply by 100 both the sides we get,
⇒ 196 = ( x - 500 )
⇒ x = 696
Therefore, the value for which test score is below 95% percent for the given mean and standard deviation is equal to 696.
learn more about standard deviation here
brainly.com/question/23907081
#SPJ4
Vladas believes that an equation with a squared term is never a function of x. Which equation can be used to show vladas that his hypothesis is incorrect?.
The equation that shows that his hypothesis is wrong is:-
x²+ y²= 25
What is an equation in math?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
How do we solve equations?Remove parentheses from each side of the equation and combine similar terms to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
Vladas said that the equation with a squared term is never a function of x.
According to the Pythagorean Theorem, the square of two natural numbers is the third number. When these numbers are used to create a triangle, a right-angled triangle is formed, with a 90° angle between the two smaller sides.
Among the four provided hypotheses:
Option (C) is true since x2+y2=25.
To learn more about equations click the following link:-
https://brainly.com/question/4675274
#SPJ4
martin is considering the expressions 1/2(7x+48) and -(1/2x-3). he wants to know if one expression is greater than the other for all values of x. which statement about the relationship between the expressions is true
Part B how did u found your answer to part A
Answer:
2
Step-by-step explanation:
What is the length of sides of the square shown below?
45
90⁰
A
B. 4-2
C. 1
D. 2.2
E 2
OF. 4
Answer:
45
Step-by-step explanation:
it's very easy to do if u know
The ratio of yellow marbles to purple marbles was 13 to 4. If there were 102 marbles in the bag, how many were yellow marbles?
The number of yellow marbles based on the given ratio will be 78.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Suppose, the number of yellow marbles is Y while purple marbles are P.
As per the given,
The ratio Y/P = 13/4
Total Y + P = 102
(13/4)P + P = 102
13P + 4P = 408
17P = 408
P = 24
And, Y = 102 - 24 = 78
Hence "The number of yellow marbles based on the given ratio will be 78".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ1
Simplify.
21. 5t(2)(3)
24. 9(8n)
22. 7(a-b+5)
25. 3k+ 6k-12
23. 9y+ 15y-10y
26. 2t + 5m+7t-4m
The simplification of the following expression, are;
21. 5t(2)(3) = 30t
24. 9(8n)= 72n
22. 7(a-b+5)= 7a - 7b + 35
25. 3k+ 6k-12 = 9k - 12
23. 9y+ 15y-10y = 14y
26. 2t + 5m+7t-4m = m + 9t
What is simplification?The procedure in mathematics to utilize and analyze the function or expression to make the function or expression uncomplicated or more coherent is called simplifying and the process is called simplification.
We are given the following expression, we need to simplify all of them;
21. 5t(2)(3)
= 30 t
24. 9(8n)
= 72n
22. 7(a-b+5)
= 7a - 7b + 35
25. 3k+ 6k-12
= 9k - 12
23. 9y+ 15y-10y
= 14y
26. 2t + 5m+7t-4m
= m + 9t
Learn more about simplification;
https://brainly.com/question/17579585
#SPJ1
When Mr Norman turns 58, he will be two years older than twice the age his daughter will turn in January. How old is Nicole now?
How do I write down the equation?
Step-by-step explanation:
When Mr Norman turns 58, he will be two years older than twice the age his daughter will turn in January. How old is Nicole now?
equation: 58 = 2d + 2
58 = 2d + 2
subtract 2 from both sides:
56 = 2d
divide both sides by 2:
d = 28 , so his daughter is 28 years old.
Can some one show me what is 8.92×1.7 please
Answer: 15.164
Step-by-step explanation:
all this for brainiest and a lot of points
1.) how do you get from 10^8 to 10^4
2.) how do you get from 10^0 to 10^-1
3.) what is 10^-4 equivalent to
4.) what is 1/1000000 equivalent to
5.) look at the attached picture
Can you find the perimeter of each triangle and type the correct code? Please remember to type in ALL CAPS with no spaces.
Perimeter of triangles is 6x + 12, 18x + 12, 12x - 9 and 14x - 4.
What is perimeter of a triangle?
The perimeter of any two-dimensional figure is defined as the distance around the figure. Therefore, perimeter of a triangle is sum of three sides of a triangle.
According to the given question:
Perimeter of given triangles is
1) Sum of all sides of triangle 1
= (x + 6) + (3x + 2) + (2x + 4)
= 6x + 12
2) Sum of all sides of triangle 2
= (6x + 4) + (7x + 1) + (5x + 7)
= 18x + 12
3) Sum of all sides of triangle 3
= (4x - 3) + (3x) + (5x - 6)
= 12x - 9
4) Sum of all sides of triangle 4
= (6x - 8) + (3x + 7) + (5x - 3)
= 14x - 4
To know more about perimeter of triangle visit
https://brainly.com/question/29472908
#SPJ1
~Describe each transformation in words.
12.) _______________________.
The required transformations would carry reflection over the y-axis of the triangle in the given figure.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The figure is given in the question,
According to the given graph, the required transformations would be as:
In the above illustration, the needed transformations would convey reflection over the y-axis of the triangle.
Thus, the required transformations would carry reflection over the y-axis of the triangle in the given figure.
To learn more about the transformations click here :
https://brainly.com/question/28029674
#SPJ1
A student's course grade is related to class attendance. The grade can be modeled by the equation ý = 0. 66x +33. 3, where ŷ is the student's grade as a percentage
and x is the number of days that the student attended class. For a student who was in attendance for 90 days and has a grade of 94%, find and interpret the residual.
-1. 3; The regression line underpredicts the student's class average.
1. 3; The regression line overpredicts the student's class average.
-1. 3; The regression line overpredicts the student's class average.
1. 3; The regression line underpredicts the student's class average.
For the given modeled of equation ý = 0.66x + 33.3 the interpretation of the residual is given option D. 1.3 The regression line underpredicts the students class average.
As given in the question,
Equation to represents the grade of a students based on class attendance is given by :
ý = 0.66x + 33.3
Where ý is the grade of students in form of percentage.
And 'x' is the students attendance
Actual percentage = 94% when x = 90
Predicted percentage is,
ý = 0.66(90) + 33.3
= 92.7%
Residual = Actual - Predicted
= 94% - 92.7%
= 1.3
Actual > Predicted
Therefore, from the given equation the interpretation of the residual is given by Option D. 1.3 student's class average was underpredicted by the regression line.
Learn more about residual here
brainly.com/question/27864993
#SPJ4
Answer:
DDDDDDDDDD
Step-by-step explanation:
please mark as brainliest please!!!!!!!
what is the slope of the line?
The slope of the graph of the line is 40.
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
Taking any to points on the line point (5, 200) and (10, 400)
Slope = change in y-coordinates / change in x-coordinates
change in y-coordinate = 400 - 200 which is 200
change in x-coordinate = 10 - 5 = 5
slope = 200/5 which is 40
In conclusion the slope of the straight line graph is 40
Learn more about slope: https://brainly.com/question/1884491
#SPJ1
Which of the following constructions must you know how to do in order to construct a circumscribed circle for a given triangle?
angle bisector
inscribed quadrilateral
perpendicular bisector
duplicating a line segment
10000
The following constructions are crucial in drawing inscribed circles:
Construct an angle bisector
Construct perpendicular lines
What is the procedure to follow in drawing inscribed circles on an equilateral triangle?
An inscribed circle is a circle drawn in a triangle. An equilateral triangle is a triangle with three equal sides and angles.
The procedure to follow in drawing inscribed circles in such an equilateral triangle is as follows:
You need to construct an angle bisector at each angle of the triangle
Where they meet at the center, is the center of the inscribed circle.
Construct a straight perpendicular line, from the center to one side of the triangles
Set the compass just on the center point, you can change the length to where the perpendicular intersects the triangle to fit in, and construct your inscribed circle.
Learn more about drawing inscribed circles in an equilateral triangle here:
brainly.com/question/10132966
#SPJ1
Find nd the 10th term of the series attached.
Answer:
[tex]C) \ -2(2/3)^8[/tex]--------------------------
The nth term is visible in the sum:
[tex]t_n=3(-2/3)^{n-1}[/tex]Apply n = 10 to find the 10th term:
[tex]t_{10}=3(-2/3)^{10-1}[/tex][tex]t_{10}=3(-2/3)^9[/tex][tex]t_{10}=3(-2/3)^{8+1}[/tex][tex]t_{10}=3(-2/3)^8*(-2/3)[/tex][tex]t_{10}=-2(-2/3)^8[/tex][tex]t_{10}=-2(2/3)^8,\ since\ the\ power\ is\ even\ number[/tex]The matching choice is C.
(100 POINTS) Need some help with this (Detailed Explanation appreciated)
The addition of equality states that "if you add on one side, you must add the same number to the other side."
How do you appreciate someone for great work?To be aware of something, or to understand that something is valuable: [ + that clause ] I appreciate that this is a difficult decision for you. To appreciate something also means to be grateful for something: I appreciated your help very much.Coworker appreciation quotes for being dedicated“Wow thanks for working overtime today, I wouldn't have finished this report without your help! "Your dedication at work doesn't go unnoticed."Thank you for going above and beyond what's required of your job."“Thank you for always representing us with pride!Your answer would be C because 3x-1=26 because -1 and you're solving a math problem -1 would change to positive to cancel out the -1 add 1 to 26 which would be 27 then you would get 3x=27 which would then lead to 3/27 which is 9.3x = 27 This is true, for you add 1 to each side (doing the opposite of PEMDAS to isolate the x)C is your answerWe are summing the 3rd 4th and 5th terms because k goes from 3 to 5
The third term is
-2(3) +5 = -6+5 = -1
The fourth term is
-2(4) + 5 = -8+5 = -3
The fifth term is
-2(5) +5 = -10 +5 = -5
Add these 3 terms together
-1+-3+-5 = -9
To learn more about appreciated refer to:
https://brainly.com/question/11251332
#SPJ1
PLS HELP ASAP!!! 50 PTS Consider parallelogram ABCD with vertices A(-6,6), B(0,10), C(2,4), D(-4,0). Classify the parallelogram and select all that apply
ABCD is a square
ABCD is a rectangle
ABCD is a rhombus
ABCD is none of the above
1. Which subset of real numbers does
√3 belong to?
The subset of real numbers √3 belong to is irrational numbers
What is a subset ?
If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.
When all the components of Set A are also present in Set B, Set A is said to be a subset of Set B. Alternatively said, Set B contains Set A. Example: If set A contains X and Y and set B contains X, Y, and Z, then set A is a subset of set B because set B also contains X and Y.
As √3 is irrational number
∴it is a subset of real numbers √3 belong to is irrational numbers
To learn more about subset from the given link
https://brainly.com/question/13265691
#SPJ1
Josh rented a truck for one day there was a base fee fee of $12 and there was additional charge of 8 cents for each mile driven the total cost (c) for driving x miles is given by the following function
C(x)=12.00+0.08x
what is the total rental cost if Josh drive 20 miles?
Answer:
$13.60
Step-by-step explanation:
You want to evaluate the rental cost function C(x) = 12.00 +0.08x for x = 20.
EvaluationPut the value for x where x is in the cost function and do the arithmetic.
C(x) = 12.00 +0.08x
C(20) = 12.00 +0.08·20 = 12.00 +1.60
C(20) = 13.60
The total rental cost if Josh drives 20 miles is $13.60.
describe one situation where parametric equations can describe a physical situation where a standard relationship between two variables will not suffice
Consider presenting a particle moving through three dimensions as an illustration. Several x, y, and z-based equations could be used to describe its path.
Explain the term parametric equations?There are two kinds of parametric equations which are frequently encountered in practical applications.
The concept problem described the first as circular motion.Projectile motion is the second type.Circular Motion:
In parametric equations that model circular motion, sine and cosine have periodic functions for x and y.
Either x is a sine function and y is a cosine function, or vice versa.Thus, Consider presenting a particle moving through three dimensions as an illustration. Several x, y, and z-based equations could be used to describe its path.Projectile Motion:
The vertical component of projectile motion is quadratic, and the horizontal component is linear.
This is due to the fact that starting height, starting velocity, and gravitational force are the three variables that have the most impact on an object's location throughout flight. The vertical component has no bearing on the horizontal component.To know more about the parametric equations, here
https://brainly.com/question/28498229
#SPJ4
what is the probability that you are dealt with two queens as private cards? you need not simplify your answer.
The probability that we dealt with two queens as private cards is = 0.0046 .
In the question ,
it is given that ,
the two cards are drawn as private cards,
we have to find the probability that you are dealt with two queens .
the total number of cards in deck is = 52 ,
total number of queens in the deck is = 4 ,
So , the number of ways 2 queens can be drawn from 4 queens is = ⁴C₂ ways .
So , the total number of ways 2 cards can be drawn is = ⁵²C₂
So , the required probability is = ⁴C₂ / ⁵²C₂ .
= 6/1326
= 0.0046
Therefore , the required probability is 0.0046 .
Learn more about Probability here
https://brainly.com/question/28894419
#SPJ4
Find the quotient of (−2/9)÷(−21/3÷1/9).
Answer:
176366843 / 50000000000
Answer:
[tex]\frac{-2}{567}[/tex]
Step-by-step explanation:
Graph the arithmetic sequence. -15,0,15,30
To graph a sequence, let a term's position number [tex]n[/tex] in the sequence be [tex]x[/tex]value.
What is an arithmetic sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
Starting with a number and repeatedly adding a fixed constant (d) to it is an easy technique to create a series. An arithmetic sequence is this kind of sequence.
Definition: A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.
The term [tex]a_{n}[/tex] is the corresponding y value
Plot the ordered pairs
Make a table then plot the ordered pairs ([tex]n, a_{n}[/tex])
Position, [tex]n[/tex] Term, [tex]a_{n}[/tex] ([tex]n, a_{n}[/tex])
1 -15 (1, -15)
2 0 (2, 0)
3 15 (3, 15)
4 30 (4, 30)
To learn more about arithmetic sequence from given link
https://brainly.com/question/24205483
#SPJ1
−1/3(x+1 1/2)=−3 1/4
Responses
x=5 1/4
x equals 5 and 1 over 4
x=8 1/4
x equals 8 and 1 over 4
x=11 1/4
x equals 11 and 1 over 4
x=14 1/4
The value of x will be;
⇒ x = 8 1/4
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ - 1/3 (x + 1 1/2) = - 3 1/4
Now,
Since, The expression is,
⇒ - 1/3 (x + 1 1/2) = - 3 1/4
Solve for x as;
⇒ - 1/3 (x + 3/2) = - 13/4
⇒ x + 3/2 = 13/4 × 3/1
⇒ x + 3/2 = 39/4
⇒ x = 39/4 - 3/2
⇒ x = 39/4 - 6/4
⇒ x = 33/4
⇒ x = 8 1/4
Thus, The value of x will be;
⇒ x = 8 1/4
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1