By using distance formula the following results are obtained
a) Other value of k = 14
b) For k = 4, the equation of bisector of [tex]\angle ABC[/tex] is
[tex]y = \frac{1}{3}x + 4[/tex]
What is distance formula?
Distance formula is used to find the distance between two coordinates.
If the coordinates of one point be ([tex]x_1, y_1[/tex]) and coordinates of other point is ([tex]x_2, y_2[/tex]), then distance between the two points is
[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]
The points A, B and C have coordinates A(2, 8), B(9, 7) and C(k, k-2).
Length of AB =
[tex]\sqrt{(9 - 2)^2 + (7 - 8)^2}\\\\\sqrt{49 +1}\\\\\sqrt{50}[/tex]
Length of BC =
[tex]\sqrt{(k - 9)^2 + (k - 2 - 7)^2}\\\\\sqrt{(k - 9)^2 + (k - 9)^2}\\\\\sqrt{2(k-9)^2}\\\\(k-9) \sqrt{2}[/tex]
By the problem,
[tex](k-9)\sqrt{2} = \sqrt{50}\\k - 9 = \sqrt\frac{50}{2}}\\k - 9 = \sqrt{25}\\k - 9 = \pm 5\\k - 9 = 5 \ or \ k - 9 = -5\\k = 5 + 9 \ or \ k = 9 -5\\k = 14 \ or \ k = 4[/tex]
The other value of k is 14
b) When k = 4
Coordinate of C = (4, 2)
Since AB =AC , the bisector of [tex]\angle ABC[/tex] passes through the midpoint of AC
Midpoint of AC =
[tex](\frac{2 + 4}{2} , \frac{8+2}{2})\\(3, 5)[/tex]
The line also passes through (9, 7)
Slope of the bisector of [tex]\angle ABC[/tex] = [tex]\frac{7 -5}{9 - 3}[/tex]
= [tex]\frac{1}{3}[/tex]
Equation of the bisector of [tex]\angle ABC[/tex]
[tex]y - 5 = \frac{1}{3}(x - 3)\\\\y - 5 = \frac{1}{3}x -1\\\\y = \frac{1}{3} x - 1 + 5\\\\y = \frac{1}{3} x + 4[/tex]
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50 points help pls
Question: state whether the figure appears to have a line symmetry (write yes or no). If so, draw all lines of symmetry
Answer:
No, it doesn't have all lines of symmetry
Step-by-step explanation:
If you can see, the triangle's line of symmetry is from a vertex to the center of another line. So, draw a line from the bottom left vertex (corner) to the center of the right side/line. And then, draw another from the right corner to left center line.
third angles theorem find the x!
I truly don’t understand how to find it with exponents
solve the system of equations by the substitution method x+10y=17 3x+6y=3
Fiona's fashion store is world renowned for its buttoned uniforms. A collection of 363636 shirts and 424242 jackets contains 842842842 buttons. A collection of 666 shirts and 777 jackets contains 137137137 buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons. How many buttons are there in a fiona's fashion shirt, and how many buttons are there in a jacket?.
The value of an integer or any letter associated with a variable is known as its coefficient. In the expression 2x + 3y, for instance, the variable x has a coefficient of 2 and the variable y has a coefficient of 3.
There are 842 buttons in 36 shirts and 42 jackets if the number of buttons in each is equal to x.
Additionally, the collection of six shirts and seven jackets has 137 buttons.
It can be expressed using the following equations:
36 x + 42 y = 842 ------(1);
6 x + 7 y = 137 ------(2);
6 x + 36 x + 42 y = 822 ------(3).
Although the constant term on one side of equation is different, the x and y coefficients are the same in both of these equations. This indicates that neither equation has a solution.
I.e →a1/a2=b1/b2≠c1/c2
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3. Corey is playing a game in which he selects
all of the numbers that are less than -5 but
greater than -20. Shade the values that Corey
should choose.
-9
7 -5
6
-3 -11
-15
18
0
The numbers that will be chosen when Corey selects all of the numbers that are less than -5 but greater than -20 include -9, -11 and -15.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Based on the information, the inequality will be expressed as:
-20 < x < -5
In this case, the numbers have to be from -6 to -19. The numbers illustrated in the options are -9, -11 and -15.
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40 is what percent of 54?
Answer: The answer will be 74.07 percent.
According to the question, let the number be x
Then, x*54/100 = 40
x = 40 × 100 / 54
x = 74.07 (approx)
A cylinder has a height of 20 yards and a radius of 17 yards. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
The volume of the cylinder is 18149.2 yards³.
What is the volume?It is important to note that the volume of a cylinder is calculated as:
Volume = πr²h
Radius = 17
Height = 20
Therefore, the volume will be:
Volume = πr²h
Volume = 3.14 × 17² × 20
Volume = 18149.2
The volume is 18149.2 yards³.
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Noah borrows \$2000$2000dollar sign, 2000 from his father and agrees to repay the loan and any interest determined by his father as soon as he has the money. The relationship between the amount of money, aaa, in dollars that noah owes his father (including interest), and the elapsed time, ttt, in years, is modeled by the following equation. A=2000e^{0. 1t}a=2000e 0. 1t a, equals, 2000, e, start superscript, 0, point, 1, t, end superscript how long did it take noah to pay off his loan if the amount he paid to his father was equal to \$2450$2450dollar sign, 2450? give an exact answer expressed as a natural logarithm.
Two years , is the time in which Naoh had to pay off his loan when the ammount he paid to his father was equal to $2450.
In the question we have given,
Amount borrowed by Naoh from his father
= $2000
The relationship between amount of money A in dollars with interest and elapsed time t is
A = 2000 e⁽⁰·¹⁾ᵗ
let Naoh pay $2450 after elapsing "t" years .
that is A = $2450 after time t years of borrowing.
We shall calculate the time which elapsed after borrowed by Naoh for paying $2450.
So, putting A = 2450 in above equation we get
2450 = 2000 e⁽⁰·¹⁾ᵗ
=> e⁽⁰·¹⁾ᵗ= 2450/2000 = 49/40
Taking logarithm both sides
=> ln ( e⁽⁰·¹⁾ᵗ) = ln (49/40)
=> (0.1 )t = 0.203
=> t = 2.023 ~ 2
Hence, after 2 years , Naoh will pay $2450 with including interest to his father.
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A-1. Age of airline paenger: x = 85, μ = 49, σ = 14 (Round your anwer to 3 decimal place. )
Z-score of age of airline passenger is 2.571
Age of airline passenger when x = 85 , μ = 49 and σ = 14 .Find standardized z-score ?
Z- Score give an idea how far a data point is from mean .
z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .
Given , x = 85
mean = 49
standard deviation = 14
z-score = x- μ / σ
putting all the values ,
z-score = 85 - 49 / 14
= 36 / 14
= 2.571
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I need help with this question too here is the question.
Fiona has 212 stickers to put in her sticker book. Page holds 18 stickers. How many pages does Fiona need for all of her stickers?
Again, please give me a valid answer. And show your work. Thank you. Have a good night.
Answer:
Fiona would need 12 pages to hold all 212 stickers.
Step-by-step explanation:
Since each page holds 18 stickers, and Fiona has 212 stickers, we need to divide.
212 / 18 = 11.7777778 pages
Because that we cannot have .77777778 of a page, we round to the nearest page, getting us 12 pages.
Have a good night, I hope my answer helped you!
Tavon is asked to find EF. What error does Tavon make?
EF2= DF2 + DE2-2(DF)(DE) cos D
EP2-82+102-2(8) (10) cos 44*
EF264+100-160
0.7193
EF 48.91
X
44°
10
Select the correct choice below and fill in the answer box within your choice.
Q
The error that Travon makes is
(C) Tavon forgot to take the square root to find the final answer. The correct answer is about 6.99
What is a root in mathematics?
In mathematics, a number's "root" is a number that, when multiplied by itself, equals the original number; alternatively, a number's "root" can also be an equation's solution, which is typically presented as a number or an algebraic formula.
For instance, since 7*7=49, the square root of 49 is 7. In this instance, 7 is referred to as the square root of 49 since it must be multiplied twice to produce the number. 3 because 3*3*3=27 is the cube root of 27. Since 27 is obtained by multiplying 3 by three, we refer to this as a cube root, so 3 is the cube root of 27.
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A shopper needs 48 hot dogs
Answer:
According to sources on googIe, the average price of a hot dog would be $5.22.
If a shopper needs 48 hot dogs, they would need a total of $250.56 dollars to pay.
Step-by-step explanation:
48 x 5.22 = 250.56
13 out of 20 jellybeans are green what percent of jellybeans are green
Answer:
65
Step-by-step explanation:
Riley has saved $60 to buy a new scooter. This amount is 30% of what he needs to save. What is the total amount of money Riley needs to save to buy the new scooter?
The total amount of money Riley needs to save to buy the new scooter is $200.
What is Percentage?
Percentage is the number or ratio which is expressed as "100". It is denoted by "%". It indicates the hundredth parts of any quantity.
It is calculated by dividing the value by total value and multiplied by 100.
Formula for percentage is (Value/total value)*100
For given information,
Riley saved $60 which is 30% of the total amount.
For 1% it will be $2
So, the total amount will be $200
Thus, the total amount of money Riley needs to save to buy the new scooter is $200.
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Another problem I need help with
Answer:
x^4 times q^2
Step-by-step explanation:
Answer:
Step-by-step explanation:
this looks tough, but just remember that powers can be rewritten like this
[tex]\sqrt{x^{4} x^{2} q^{4} }[/tex]
then just break up the square root sign, which is another property of square roots
[tex]\sqrt{x^{4} }[/tex]*[tex]\sqrt{x^{2} }[/tex]*[tex]\sqrt{q^{4} }[/tex]
you could break the [tex]x^{4}[/tex] into two [tex]x^{2}[/tex] but I think you can see that it will just be [tex]x^{2}[/tex] once it's pulled out of the square root
[tex]x^{2} *x*q^{2}[/tex]
[tex]x^{3}[/tex]*[tex]q^{2}[/tex]
Does this all make sense?
Sarita showed the steps to solving the equation.
When Sarita tried to verify her answer, she found it was wrong. Which explains her mistake?
The option that explains Sarita's mistake is Sarita’s solution is correct. She made an error in her verification.
What was Sarita's mistake?The given equation is: 5(x - 3) + 7(x + 4) = 73
In order to determine the value of x, take the following steps:
1. Apply the Distributive property:
5x - 15 + 7x + 28 = 73
2. Add similar terms together:
12x + 13 = 73
3. Combine similar terms:
12x = 73 - 13
4. Add similar terms
12x = 60
5. Divide both sides of the equation by 12
x = 60 / 12
x = 5
In order to verify the answer, substitute for x in the given equation :
5(5 - 3) + 7(5 + 4) = 73
5(2) + 7(9) = 73
10 + 63 = 73
73 = 73
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THROUGH (-3,-1) perp to y=-1/2x+5
ANSWER IT
The equation of the perpendicular line that passes through the point (- 3, - 1) is y = 2 · x + 5.
What is the equation of the line perpendicular to another line?
In this question we must determine the equation of a line that is perpendicular to another line and pass through a given point. Mathematically speaking, lines are represented by the following equation:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variabley - Dependent variableAnd the slopes of two lines perpendicular to each other satisfy the following relationship:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.First, determine the slope of the perpendicular line by means of the slope relationship:
m = - 1 / 2
m' = - 1 / m
m' = - 1 / (- 1 / 2)
m' = 2
Second, find the intercept of the perpendicular line by the equation of the line:
b = y - m · x
b = - 1 - 2 · (- 3)
b = - 1 + 6
b = 5
Third, write the equation of resulting line:
y = 2 · x + 5
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If you select two different women at random, what’s the probability that:
A. At least one experienced IPV?
B. At least one did not experience IPV?
The probability of selecting at least one experienced IPV is 0.598 and at least one did not experience IPV is 0.866.
In the given question we have to find the probability of selecting at least one experienced IPV and at least one did not experience IPV
From the given table
Probability of experiencing IPV
P(Experienced IPV) = 366 / 1000 = 0.366
Probability of not experiencing IPV
Q(Not-experienced IPV) = 634 / 1000 = 0.634
Now when n samples are chosen from the population, the binomial probabilty distribution follows (P + Q)^n.
Here, n = 2,
So, (p +q)^2 = p^2 + 2pq + q^2
p^2 = Both experienced IPV
2pq = One has experienced IPV and other hasn’t
q^2 = None have experienced IPV.
A. Finding the probability of at least one experienced IPV.
P(At least one has experienced IPV) = P^2 + 2PQ
= (0.366)^2 + 2(0.366)(0.634)
=0.1339+0.4641
= 0.598
B. Finding the probability of at least one did not experienced IPV.
Q(At least one did not experienced IPV) = Q^2 + 2PQ
= (0.634)^2 + 2(0.366)(0.634)
=0.4019+0.4641
= 0.866
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a random sample of high school seniors were asked whether they were applying for college. the resulting confidence interval for the proportion of students applying for college is (0.65,0.69). what is the margin of error?
Using the confidence interval, the margin of error is 0.02.
In the given equation we have to find the margin of error.
The resulting confidence interval for the proportion of students applying for college is (0.65,0.69).
Let p = population proportion of students applying for college
P = Sample proportion of students applying for college
ME = margin of error
So the confidence interval
CI = (P-ME, P+ME)
From the given question;
(P-ME, P+ME) = (0.65,0.69)
So lower bound= P-ME = 0.65............................(1)
Upper Bound = P+ME = 0.69............................(2)
Simplifying the Equation 1 and 2
Add equation 1 and 2 we get
2P = 1.34
Divide by 2 on both side we get
P = 0.67
Putting the value of P in the equation 2
P+ME = 0.69
0.67+ME=0.69
Subtract 0.67 on both side we get
ME = 0.02
Hence, the margin of error is 0.02.
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A kicker licked a football 60 yards deep into the end zone the hang time on the ball was 8.5 seconds. What is the average speed of the ball
The speed of the football in the air is 7.1 yards per second
How to determine the speed of the ball in the air?From the question, the given parameters are:
Distance = 60 yards
Time to cover this distance = 8,5 seconds
The speed of the football in the air is calculated as
Speed = Distance/Time to cover this distance
Substitute the known values in the above equation
So, we have the following equation
Speed = 60/8.5
Evaluating the quotient in the above equation, we have
Speed = 7.1
Hence, the ball's speed in air is 7.1 yards per second
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verify that the function satisfies the three hypotheses of rolle's theorem on the given interval. then find all numbers c that satisfy the conclusion of rolle's theorem. (enter your answers as a comma-separated list.) f(x)
The c has only one number is c = 81/4 that satisfy the conclusion of rolle's theorem.
The three hypotheses of Rolle's theorem are:
(a) f(x) is continuous on [a,b]
(b) f(x) is differentiable on (a,b)
(c) f(a) = f(b)
i) If you graph f(x), you can see that it is continuous that is no breaks on the interval [0,81]
ii) f(x) is differentiable on (0,81)
f '(x) = 1/(2√x) - 1/9 which exists on the open interval (0,81)
iii) f(0) = f(81) = √81 - 81/9 = 9-9 = 0
Rolle's Conclusion:
f'(c) = 0
f'(c) = 1/(2√c) -1/9 = 0
(9 - 2√c)/(18√c) = 0
√c = 9/2
c = 81/4
There is one number c = 81/4, which satisfies f '(c) = 0.
Therefore the c has only one number is c = 81/4 that satisfy the conclusion of rolle's theorem.
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Full question:
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)
f(x) =x − 1/9 x, [0, 81].
if the domain of f(x) = 2x + 3 is {-3 ≤ x ≤ 0}, which number is not in the range -1,3,0, or 6?
Answer: 6
Step-by-step explanation:
If the domain is {-3 ≤ x ≤ 0}, then we will decide which of the given values is not in the range.
6 is not between, including the values of, -3 and 0, so the number not in the range is 6.
Determine which set of side measurements could be used to form a triangle. 4, 6, 12 5, 19, 24 6, 10, 17 8, 9, 15
The set of side measurements that could be used to form a triangle is 8, 9 and 15
If a, b and c are the sides of the triangle
Then a + b > c
b + c > a
c + a> b
The first set of sides are
4, 6, 12
4 + 6 > 12
10 < 12
It will not form a triangle
The second set of sides are
5, 19 and 24
5 + 19 > 24
24 = 24
It will not form a triangle
The third set of sides are
6, 10 and 17
6 + 10 > 17
16 <17
It will not form a triangle
The fourth set of sides are
8, 9 and 15
8 +9 > 15
17 > 15
8+15 > 9
23 > 9
9 + 15 > 8
24 > 8
It will from a triangle
Hence, the set of side measurements that could be used to form a triangle is 8, 9 and 15
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help pls i dont understand this
Answer:
Basically Mate you gotta make a perpendicular line from the letter your told make a line from and then thats for the 2 pages basically they want you to do the same thing that is done but you do it for the letter.
PLEASE GIVE BRAINLIEST THANK YOU!!!
Please help ASAP and answer the whole thing please and thank you
Neil has been running a tutoring business since 2005. He charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount. The table shows what Neil charged each customer for two given years of his business:
Year Annual Tutoring Fee
2005 $1200
2008 $1350
A. What is the rate of change and initial value for Neil's business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Neil charges each year. (10 points)
The equation in slope intercept form that represent the situation is y = 50x - 99050.
How represent linear equation in slope intercept form?Linear equation can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptNeil charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount.
Using the table that shows the amount he charged for tutoring each year. we can find the rate of change.
The rate of change is the slope.
Therefore, (2005, 1200)(2008, 1350)
m = slope = 1350 - 1200 / 3
slope = 150 / 3
slope = 50
Therefore, let's represent the equation in slope intercept form. We will have to find the y-intercept of the equation.
Hence, using (2005, 1200)
y = 50x + b
1200 = 50(2005) + b
b = 1200 - 100250
b = - 99050
Hence, the equation is y = 50x - 99050.
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graph the system of inequalities y+5<2x and 2y≥-2x+6
Using graphing calculator, the solution to the inequality is attached
Graph of InequalityAn inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line.
If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ or ≥ ), graph a solid line.
Using a graphing calculator;
Kindly find the attached graph as solution to the inequality
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Solve for x.
8x-3x=35
Simplify your answer as much as possible.
X =
Water i draining from a conical tank at the rate of 2 m3/min. The tank i 16 meter high and the top radiu i 4 meter. How fat i the water level falling when the water’ level i 12 meter high?
Answer:
7.07 cm/min
Step-by-step explanation:
You want the rate of change of water level in a conical tank 16 m high with radius 4 m when the level is 12 m and the water is draining at 2 m³/min.
Surface areaThe level of water in the tank is 12/16 = 3/4 of the height of the tank, so the radius of its surface is (3/4)(4 m) = 3 m. The surface area is ...
A = πr²
A = π(3 m)² = 9π m² ≈ 28.3 m²
Level changeThe rate of change of level is the rate of change of volume divided by the surface area:
V'/A = (-2 m³/min)/(9π m²) = -2/(9π) m/min ≈ -0.07074 m/min
The water level is falling at about 7.07 cm/min.
A student states that a triangle can be formed with side lengths 3 in, 5 in, and 9 in. Is the student correct? why, or why not? yes, because 3 + 5 < 9 yes, because 3 + 9 > 5 no, because 3 + 9 > 5 no, because 3 + 5 < 9.
Answer:
no, because 3 + 5 < 9
Step-by-step explanation:
given three sides of a triangle
For the sides to form a triangle the sum of any 2 must be greater than the third.
given sides 3, 5 and 9 , then
3 + 9 = 12 > 5
5 + 9 = 14 > 3
3 + 5 = 8 < 9
the 3 sides do not form a triangle since 3 + 5 < 9
Find the slope of the line shown on the graph to the right.
The slope of the line is 5/6.
From the graph:
Slope : a surface of which one end or side is at a higher level than another rising or falling surface.
Points are (-3,-2) and (3,3)
slope m = y2-y1 / x2-x1
= 3 - (-2) / 3 - (-3)
= 3 + 2 / 3 + 3
m = 5/6.
Therefore the slope of the line is 5/6.
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