Jason knows that AK←→⊥KB←→ , AK←→∥EF←→ , and AK←→∥CB←→ .
Which other facts can Jason conclude are true?
Select each correct answer.
m∠EJM=90°
KB←→⊥CB←→
m∠JFB=90°
KB←→∥DM←→−
Answers
The corresponding angles between parallel lines and their common transversal are congruent
The other facts Jason can conclude are true are:
1) [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
2) m∠JFB = 90°
The reason why the above selected options are correct are:
The relationships between the lines Jason knows are:
Segment AK is perpendicular to KB: [tex]\underset{AK}{\leftrightarrow}[/tex] ⊥ [tex]\underset{KB}{\leftrightarrow}[/tex]
Segment AK is parallel to EF: [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex]
Segment AK is parallel to CB: [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex]
m∠DKF = 90°
The required information:
The facts that Jason can conclude are true
Method:
Find the other relationships between the lines based on the relationships Jason knows
Solution:
We have;
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{EF}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex], and [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{EF}{\leftrightarrow}}[/tex] ║ [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex]
The relationship, [tex]\underset{EF}{\leftrightarrow}[/tex] ⊥ [tex]\underset{KB}{\leftrightarrow}[/tex], gives m∠JFB = 90°
Therefore;
The correct options for the facts Jason can conclude are;
1) [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
2) m∠JFB = 90°
Learn more about the angle formed between parallel lines here:
https://brainly.com/question/10623667
https://brainly.com/question/1588620
Related Questions
Which function below is the inverse of f(x)=x^2-25
Answers
f(x) = x^2-25
inverse:
y = x^2-25
x = y^2-25
y = sqrt(5 +25)
Answer is B
What numbers below belong to the solution set of the inequality... x+16>51
38
35
16
80
55
34
Answers
The coordinate plane below represents a town. Points A through F are farms in the town.Part A: Using the graph above, create a system of inequalities that only contains points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points) Part B: Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A.
(3 points)
Answers
y > = x + 4
y > = 4.......this is a horizontal line with a y int of 4.....so go to 4 on ur y axis, and draw a line going horizontal...all the way across....and since it is greater then, shade above the line...and since there is an equal sign, the line should be solid.
y > = x + 4....this has a y int of 4 or (0,4).....the slope is 1....the x int is (-4,0)....since it is greater, it will be shaded above the line...and since there is an equal sign, the line will be solid.
D and E are solutions because when u graph these lines, they both fall into the shaded region and are therefore solutions
Nonstandard dice can produce interesting distributions of outcomes. you have two balanced, six-sided dice. one is a standard die, with faces having 1, 2, 3, 4, 5, and 6 spots. the other die has three faces with 0 spots and three faces with 6 spots. what are the possible values for the total number of spots y on the up-faces when you roll these two dice?
Answers
One die can show the values 1-6, while the other die can only show 0 or 6. So the possible totals are 1 through 6 plus 0 and 1 through 6 plus 6. Written out, one-by-one, this gives: 1+0 = 1 2+0 = 2 3+0 = 3 4+0 = 4 5+0 = 5 6+0 = 6 1+6 = 7 2+6 = 8 3+6 = 9 4+6 = 10 5+6 = 11 6+6 = 12
When rolling a standard die and another die with faces having either 0 or 6 spots, the possible total values y range from 1 to 12, excluding the numbers 5 and 6 twice due to the unique nature of the second die.
Explanation:The question asks about the possible values for the total number of spots y on the up-faces when you roll two nonstandard dice: a standard six-sided die with faces having 1, 2, 3, 4, 5, and 6 spots, and another die with three faces having 0 spots and three faces having 6 spots. To find y, we need to consider all the possible outcomes of rolling these two dice and summing the numbers of spots on the up-faces.
If the standard die shows a 1, y can be 1+0=1 or 1+6=7.If it shows a 2, y can be 2+0=2 or 2+6=8.If it shows a 3, y can be 3+0=3 or 3+6=9.If it shows a 4, y can be 4+0=4 or 4+6=10.If it shows a 5, y can be 5+0=5 or 5+6=11.If it shows a 6, y can be 6+0=6 or 6+6=12.Therefore, the possible values for y are 1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 11, and 12.
The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
Solve for a.
Answers
multiply both sides by 2 to get
2A = (a+b)*h
divide both sides by h
to get 2A/h = a+b
subtract b from both sides to get a = 2A/h -b
3rd choice is correct
Option C - a = [tex]$\frac{2A-bh}{h}[/tex] is the correct alternative.
We have the formula for a trapezoid that relates the area - A, the two bases - a and b and the height - h as follows -
[tex]$A=\frac{(a+b)}{2} h[/tex]
We have to solve for ' a '.
Solve for x : x ( 1 + 2 + 3 + .... + n) = πOn solving -
x( 1 + 2 + 3 + .... + n) = π
[tex]\frac{xn(n+1)}{2} =\pi[/tex]
[tex]x =\frac{2\pi }{n(n+1)}[/tex]
According to the question, we have -
[tex]$A=\frac{(a+b)}{2} h[/tex]
2A = (a + b)h
2A = ah + bh
2A - bh = ah
a = [tex]$\frac{2A-bh}{h}[/tex]
Hence, Option C is the correct alternative.
To solve more questions on Rearranging expressions, visit the link below-
brainly.com/question/8864600
#SPJ2
Enid got a job through an employment agency that charges a fee equal to 40% of the first five weeks’ pay. The job pays $315 per week. How much does Enid have to pay the employment agency?
Answers
(-7,8)(-9,10)(-6,11) reflected over x-axis What are the new coordinates
Answers
So
(-7,8) is now (-7, -8)
(-9,10) is now (-9, -10)
(-6,11) is now (-6, -11)
Hope this helps!
Three variable 2x-5y+z=5 3x+2y-z=17 4x-3y+2z=17
Answers
Triangle MNO is an equilateral triangle with sides measuring units. What is the height of the triangle? NR units
Answers
Answer:24
Step-by-step explanation:
What is 3x-2 if x=-1/3
Answers
Givens
x = - 1/3
y = 3x - 2
Problem solve for y
y = 3(-1/3) - 2
but 3 * (1/3) = 1
and 3 * (- 1/3) = - 1
So y = -1 - 2
y = - 3
Think of this as a money question. If you are one dollar in the whole and you spend 2 more, you are not 3 in the whole which is minus 3.
Find two consecutive integers whose sum is 101
Answers
A rectangular rug covers the floor in a living room one of the walls in the same living room is painted blue. Are the rug and the blue wall parallel
Answers
Please help me with this graphing problem
Answers
Anyway....
A domain of all real numbers means that a function will have an infinite amount of x-values. As g(x) and f(x) both are line segments, p(x) is the only function with a domain of all real numbers.
(17+4) + 9 = 17 + (4+9)
Answers
it is normally written as
(a+b)+c=a+(b+c)
which is like what you have
(17+4)+9=17+(4+9)
What is the equation of a horizontal line passing through the point (−3, 8)?
x = −3
y = 8
x = 5
y = −11
Answers
The equation of a horizontal line passing through the point (−3, 8) is y= 8
How to determine the equation of a horizontal line passing through the point (−3, 8)
From the question, we have the following parameters that can be used in our computation:
The point (−3, 8)
The equation of a horizontal line is of the form
y = c, where
c is a constant.
Since the line is horizontal, the value of y is constant for all points on the line.
In this case, the line passes through the point (−3,8), so the equation of the horizontal line is y = 8.
Did I do number 2 right?
Answers
y = a*(x-p)*(x-q)
2 = a*(x-0)*(x-1)
2 = a*(2-0)*(2-1)
2 = a*(2)*(1)
2 = 2a
2a = 2
2a/2 = 2/2
a = 1
So the equation
y = a(x-0)(x-1)
updates to
y = 1(x-0)(x-1)
and that simplifies to
y = x(x-1)
The next step is to distribute the x through to get this final answer
y = x^2-x
Find b given that p(b,2) is equidistant from a(5,4) and b(2,5)
Answers
PA = PB or PA² = PB²
(5-b)²+(4-2)² = (2-b)² + (5-2)²
(5-b)²+4 = (2-b)² + 9
25 -10b +b² + 4 = 4 -4b+b² +9
-6b = -16
b = 8/3
If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f*g) (x)?
Answers
(f*g) (x) = 3x^3 + 3x + 2x^2 + 2
(f*g) (x) = 3x^3 + 2x^2 + 3x + 2
Answer: The required expression is [tex]3x^3+2x^2+3x+2.[/tex]
Step-by-step explanation: We are given the following two functions :
[tex]f(x)=3x+2\\\\g(x)=x^2+1.[/tex]
We are to find the expression equivalent to [tex](f*g)(x).[/tex]
We know that
for any two functions p(x) and q(x), we have
[tex](p*q)(x)=p(x)\times q(x).[/tex]
Therefore, we get
[tex](f*g)(x)\\\\=f(x)\times g(x)\\\\=(3x+2)(x^2+1)\\\\=x^2(3x+2)+1(3x+2)\\\\=3x^3+2x^2+3x+2.[/tex]
Thus, the required expression is [tex]3x^3+2x^2+3x+2.[/tex]
-4=g+1
A. g=-4
B. g=4
C. g=-5
D. g=-3
Answers
At an annual salary of 55000 per year what is the amount of semi monthly paychecks
Answers
4583.33 / 2 = 2291.665 simi per month or if we round 2291.67
The answers is 2291.665
The answer if we round is 2291.67
If someone gets 55,000 salary annually or 12 months, he will get 55,000/24 = 2291.67 per 2 times per month(semi-monthly).
Ans: 2291.7.
Brooke buys a toothbrush and toothpaste for 2.95. If the toothbrush costs .65 less than the toothpaste. How much is the toothbrush
Answers
Given the information, we can determine that the cost of the toothbrush is $1.15. To arrive at this, we created an equation based on the given information and solved for the unknown, which in this case is the cost of the toothbrush.
Explanation:If Brooke buys a toothbrush and toothpaste for $2.95, and the toothbrush costs $.65 less than the toothpaste, we have to use the information to solve for the cost of the toothbrush.
Let's define the cost of the toothpaste as x. Therefore, the cost of the toothbrush would be x - $0.65 (since the toothbrush costs $0.65 less than the toothpaste).
The combined cost of the toothbrush and toothpaste is $2.95, so we can set up the equation: x + (x - $0.65) = $2.95
If we simplify and solve this equation, we get x = $1.80. That's the cost of the toothpaste. The cost of the toothbrush would therefore be $1.80 - $0.65 = $1.15.
So, the toothbrush costs $1.15.
Learn more about Basic Algebra here:https://brainly.com/question/36762717
#SPJ2
Sammy and David were selling waterbottles to raise money for new football uniforms Sammy sold 5 for every 3 waterbottles David sold together they sold 160 waterbottles how many did each boy sell
Answers
160 divide by 8 = 20 sets
20 X 5 = 100 ( Sammy)
20 X 3 = 15 ( David )
Rhinestone Cowboy Dreadlock Holiday MacArthur Park Total Republican B 33 C 90 Democrat A 24 34 E Total 61 D 53 171 Which of the following can be determined from the table above? A. 2004-06-03-06-00_files/i0290000.jpg B. 2004-06-03-06-00_files/i0290001.jpg C. 2004-06-03-06-00_files/i0290002.jpg D. 2004-06-03-06-00_files/i0290003.jpg
Answers
B) On e2020 at least
Hope I helped!
The values that can be determined from the table are:
A = 23, B = 38, C = 19, D = 57 and E = 81
What are equations?Equations are expressions that have equal values, and they are represented by the "=" sign
How to determine the values of A to EThe table entries are given as:
Rhinestone Cowboy Dreadlock Holiday MacArthur Park Total
Republican B 33 C 90
Democrat A 24 34 E
Total 61 D 53 171
From the table, we have the following equations
[tex]B + 33 + C = 90[/tex]
[tex]A + 24 + 34 = E[/tex]
[tex]61 + D + 53 = 171[/tex]
The above equations become:
[tex]B + 33 + C = 90[/tex]
[tex]B + C = 57[/tex]
[tex]A + 24 + 34 = E[/tex]
[tex]A + 58 = E[/tex]
[tex]61 + D + 53 = 171[/tex]
[tex]D= 57[/tex]
Also from the table, we have the following equations
[tex]B + A = 61[/tex]
[tex]C + 34 = 53[/tex]
[tex]90 + E = 171[/tex]
Solve for C and E in the above equations
[tex]C + 34 = 53[/tex]
[tex]C = 19[/tex]
[tex]90 + E = 171[/tex]
[tex]E = 81[/tex]
Recall that:
[tex]A + 58 = E[/tex]
So, we have:
[tex]A + 58 = 81[/tex]
[tex]A = 23[/tex]
Recall that:
[tex]B + A = 61[/tex]
So, we have:
[tex]B + 23 = 61[/tex]
[tex]B = 38[/tex]
Hence, the values that can be determined from the table are:
A = 23, B = 38, C = 19, D = 57 and E = 81
Read more about tables and equations at:
https://brainly.com/question/13196178
Find the area of triangle.
Answers
The base is 6 and the height is 5 (remember that height must be perpendicular to the base and that the red lines aren't actually a part of the figure).
6*5=30
30/2=15
Final answer: 15 yd^2
Four times a number, x, plus 3 times a number, y, equals 75. Five times x minus 3 times y equals 6. Find the numbers by setting up a system of linear equations and solving the system using the elimination method.
Answers
4x+3y=75;5x−3y=6
Step: Solve4x+3y=75for x:
4x+3y+−3y=75+−3y(Add -3y to both sides)
I don't know how to do this
Answers
2(6-7x) = -8(x+6)
multiply the numbers inside the parenthesis with the numbers outside of them:
12 -14x = -8x-48
add 12 to each side:
-14x =-8x -36
add 8x to both sides
-6x = -36
divide both sides by-6
x = 6
What is 4 pi cubed divided by 3
Answers
P=21+2w the answer is w=p-21/2 I need the work to go along with it
Answers
P=21+2w
minus 21 both sides
P-21=2w
divide both sides by 2
[tex]\frac{P-21}{2}=w[/tex]
[tex]w=\frac{P-21}{2}[/tex]
A dependent variable is a. directly changed by the experimenter. b. manipulated by changes to the independent variable. c. a variable that is kept constant. d. a variable that is used as a control.
Answers
A dependent variable is one that is changed, when the independent variable changes.
For example, if we wanted to calculate how many dollars we've earned in a given amount of time, time would be the independant variable, because it is a constant and is not affected by how much many we earn. The amount of money we earned is directly affected by the independent variable, time.
Your answer is b.
Hope I helped!
Be sure to leave a "Brainliest" if I was helpful. Or not lol. I really don't care tbh XD
Answer:- Option b. is the right answer. A dependent variable is manipulated by changes to the independent variable.
Explanation:-
In mathematical modelling or scientific research a variable is defined as a term that has a quantity that varies. There are two kinds of variables:- 1) dependent variables 2) independent variables.
A independent variable can be change by the experimenter to check the effects on dependent variables which is observed by the him in a scientific experiment.
Thus, A dependent variable is manipulated by changes to the independent variable.
the table shows the annual profits (in thousands of dollars) of a county fair from 2008 to 2012. What must the 2012 profit be (in hundreds of dollars) to break even over the five-year period?
Answers
Let the 2012 profit be x, then
2.5 + 1.75 + (-3.3) + (-1.4) + x = 0
4.25 - 3.3 - 1.4 + x = 0
-0.45 + x = 0
x = 0.45
Therefore, the 2012 profit must be 0.45 thousand dollars = 4.5 hundred dollars to break even over the five-year period.
The 2012 profit must be 0.45 thousand dollars is equal to 4.5 hundred dollars to break even over the five-year period.
It is required to find the profit in 2012.
What is break even point?The break-even point is the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business. It tells an owner the amount of revenue needed to cover all expenses, including fixed costs.
Given:
The break-even point is the point in which a business makes no gain and no loss.
According to given question we have
Let the 2012 profit be x, then
2.5 + 1.75 + (-3.3) + (-1.4) + x = 0
4.25 - 3.3 - 1.4 + x = 0
-0.45 + x = 0
x = 0.45
Therefore, the 2012 profit must be 0.45 thousand dollars is equal to 4.5 hundred dollars to break even over the five-year period.
Learn more about break even point here:
https://brainly.com/question/15356272
#SPJ2