Given:
The three points are W(0,-2), I(2,0) and L(5,k).
To find:
The value of k for which the given points are collinear.
Solution:
We know that, three points are collinear if the area of the triangle formed by these three points is 0.
[tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=0[/tex]
[tex]x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0[/tex]
The three points are W(0,-2), I(2,0) and L(5,k). So,
[tex]0(0-k)+2(k-(-2))+5(-2-0)=0[/tex]
[tex]0+2(k+2)+5(-2)=0[/tex]
[tex]2k+4-10=0[/tex]
[tex]2k-6=0[/tex]
Adding 6 on both sides, we get
[tex]2k=6[/tex]
[tex]k=\dfrac{6}{2}[/tex]
[tex]k=3[/tex]
Therefore, the correct option is E.
Graph the logarithmic function f(x) = log2(x - 1) + 2.
anyone know this pls help
Answer:
I graphed it for you in the image below.
Step-by-step explanation:
Graph the logarithmic function f(x) = log2(x - 1) + 2 is attached below.
What is a function?The function is referred to as a particular kind of relationship, every value in the domain is associated with exactly one value in the range. They have a set perimeter and territory.
It is given that the logarithmic function is, f(x) = log2(x - 1) + 2.
The first step in graphing a logarithmic function is to locate some points on the exponential f. (x). The graph will look better as we plot more points, and we can flip the x and y values to get points on the opposite axis. locate the asymptote. The following logarithmic functions can be graphed. Specify the domain and the range.
Thus, the graph is attached below.
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Using Angle Relationships to Solve Equations
Answer:
8. x=19
9. 42
10. 23
Step-by-step explanation:
8.
x+x+4+3x-9 =90
5x-5=90
x= 19
9.
x=19
x+4= 23
19+23=42
10.
x+4=23
7/6 written as a mixed number
Answer:
1 1/6
Step-by-step explanation:
A mixed number is a proper fraction.
Answer:
[tex]1\frac{1}{6}[/tex]
Step-by-step explanation:
We are given the fraction of [tex]\frac{7}{6}[/tex].
There are enough parts to make one whole, with one remaining.
Six sixths for the whole, the fraction would be one-sixth.
[tex]\frac{7}{6}=1\frac{1}{6}[/tex]
Hope this helps.
What is an
equation of the line that passes through the points (-3,-2) and (3,6)?
Answer:
y = 4/3x + 2
Step-by-step explanation:
y2 - y1/ x2 - x1
6 - (-2)/ 3 - (-3)
= 8 / 6
= 4/3
y = 4/3x + b
6 = 4/3(3) + b
6 = 4 + b
2 = b
Can you please help!!
Farmers have learned how to grow watermelons
in the shape shown at the right. What
three-dimensional figure is the watermelon?
Answer:
it looks like a cube to me lol
Find the area of this shape
Answer:
433 m²
Step-by-step explanation:
Find the side length of the square first.
Apply Pythagoras Theorem on 1 of the triangles on the right, to find its remaining side.
[tex] \sqrt{ {12}^{2} - {9.6}^{2} } [/tex]
=[tex] \sqrt{51.84} [/tex]
= 7.2 m
Therefore the side of the square is
7.2 ×2
= 14.4 m
The area of the square
= 14.4²
= 207.36 m²
You are able to find the area if of the 2 triangles.
(7.2 × 9.6)÷2 ×2
= 69.12 m²
The height of the pentagon
= 25.4 - 7.2
= 18.2 m
The area of the pentagon
= (10+7.2) × 18.2 ÷ 2
= 156.52 m²
Add up the areas of the 3 polygons.
The area of the shape
= 207.36 + 69.12 + 156.52
= 433 m²
Find the value of x and then perimeter
Answer:
×= 4 and the perimeter is 18
Step-by-step explanation:
(x+3)(x-2)=14
x^2+x-6=14
x^2+x-20=0
(x+5)(x-4)=0
x=4
perimeter = 7(2)+2(2)=18
The perimeter of ABCD is 26 cm
The area of PQRS is 45 cm(squares)
Find the length of AB
what is summer academy help fr fr ☝️
Answer:
Summer school (or summer university) is a school, or a program generally sponsored by a school or a school district, or provided by a private company, that provides lessons and activities during the summer vacation.
Step-by-step explanation:
Answer:
Step-by-step explanation:
A television newscaster from a 24-hour news station wants to estimate the number of hours per day its viewers watch
programming on this channel
. The neviscaster randomly selects 100 viewers and asks them how many hours per day
they watch this station. The newscaster constructs an 85% confidence interval for the true mean number of hours
viewers watch this station. Which of the following would decrease the margin of error?
Answer:
This isn't the best worded question but from what I understand a larger sample size decreases the margin of error. If he would like a more accurate answer a larger sample size of the viewers will give more accurate answers.
Step-by-step explanation:
simplify 3/x-1 + 1/x-2
Answer:
4-3x over x or 4-3x/x
I'm not sure. but I hope it can help you:))
Select the correct answer from each drop-down menu.
The table shows the number of games a chess player won in professional competitions, based on the number of games played.
Games Played (x) 10 15 20 25 30
Games Won (y) 4 10 16 21 25
The line of best fit for the situation is
___.
If the chess player plays 40 games in the next competition, the expected number of games won would be approximately __.
???
Answer:
36 games won ...............
Answer:
y=1.06x-6
36
Step-by-step explanation:
HELP ME PLS
GIVING BRAINLIEST
Explanation:
The max is 2 ounces, as shown by the X mark at the very far right side. The min amount is 1 ounce, shown by the other endpoint. Subtracting the two leads to the range of max-min = 2-1 = 1 ounce. The range helps us determine how spread out the data set is.
Find the volume of the sphere. Round your answer to the nearest tenth.
Answer:
See below.
Step-by-step explanation:
The formula for the volume of a sphere
= 4/3 π r^3 where r = the radius.
So for number 1:
V = 4/3 π (5)^3
= 523 .60 mm^3 to nearest hundredth.
The others are solved in exactly the same way except where the diameter is given as in number 4 and 5 you get the radius r by dividing the diameter by 2. So in number 4, r = 30/2 = 15.
What is the definition of the slope of a line?
Help plz need answers less than 10 minutes
Answer:
the answer wouldbe 8585434930.123
Step-by-step explanation:
can anyone help me with these homework pages please i need them asap, thanks
Answer:
1. reflection
2. translation
3. rotation
4. dilation (enlargement)
5. dilation (reduction)
6. rotation
7. reflection
Hi guys please help me out I would appreciate it thank you so much
Answer:
D) Angle VUX
Step-by-step explanation:
Round to the nearest tenth
1. Find x.
Answer:
x= 25.5 not rounded x=25.51393657
Step-by-step explanation:
Decide what trig ration you need/want to use. The 27 degrees are opposite of the 13 and adjacent to the x which means your ratio should be o/a or 13/x. The trig ratio needed is Tangent. Now you can write the equation as tan(27)=13/x and start solving.
tan(27)=13/x multiply the x on both sides and you'll have x * tan(27)=13 and decide which to put into your calculator and you'll get x=25.51393657 rounded as 25.5
Solve for x if:
y = 30
x = y
- + 20
3
A) 25
B) 40
C) 50
D) 30
Answer:
30?
Step-by-step explanation:
If y is 30 and x = y. Then wouldn't x be 30 HOWEVER I'm unsure what the other part of the equation is.
Plz help i have been asking this question too much
Answer:
6
Step-by-step explanation:
1/6 of 36 is 6
2/3 of 36 is 24
6+24=30
36-30=6
<3
Answer:
if u search your question on brainly you'll see alot of answers! here is one of them!!!
A square sticky note has sides that are 7 centimeters long. What is the sticky note's area?
Answer:
side- 7
area of square - side x side
7 x 7 - 49² cm
square - all sides are the same length
area - length * width
7 * 7 = 49
49 cm^2Show that f(x) = x^2 and g(x) = 1000x^2 grow at the same rate.
Answer:
You do not use the first derivative to find the rate you need to take the limit ratio as x approaches positive infinity. We use positive and not negative infinity because our function is increasing and not decreasing. The ratio ends up being 1/1000 meaning that this a finite non zero number. Which proves that they grow at the same rate
Step-by-step explanation:
70/5.2 + 16-1 helppppp
Answer:
28.4615384615
28.46
Step-by-step explanation:
Answer:
28.46, if this help please subscribe to amiredagoat Yt i wanna change the world.
Step-by-step explanation:
8-50. What is the area of a regular decagon if the length of each side is 20 units? Show all your work.
Answer:
3077.68
Step-by-step explanation:
the Area of the regular decagon is 3077.68
The area of the decagon with side length of 20 units is -
A = 1000√(5 + 2√5) square units.
What is Area?Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write area -
V = ∫∫F(x, y) dx dy
Given is a regular decagon with length of each side is 20 units
The area of the regular decagon is -
A = (5/2)a²√(5 + 2√5)
We have {a} = 20. So, we can write that -
A = (5/2)(20)²√(5 + 2√5)
A = (5/2) x 400 x √(5 + 2√5)
A = 5 x 200 x √(5 + 2√5)
A = 1000√(5 + 2√5)
Therefore, the area of the decagon with side length of 20 units is -
A = 1000√(5 + 2√5) square units.
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Elizabeth is going to invest $480 and leave it in an account for 8 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Elizabeth to end up with $670?
Answer:
4.2
Step-by-step explanation:
took a bullet for the team
Elizabeth would need an interest rate of 4.25% to make a profit of $670, to the closest hundredth of a percent.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
Given, Elizabeth is going to invest $480 and leave it in an account for 8 years.
from the formula of compound interest
A = P(1 + r/n) ^nt
in our case,
A =670
P = 480
t = 8
Thus,
670 = 480(1 + r)^8
r = 4.25%
Therefore, an interest rate, to the nearest tenth of a percent, would be 4.25% required in order for Elizabeth to end up with $670
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5.
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
A. 1/150 dollars per day; the cost is $1 for 150 days.
B. 25/1 dollars per day; the cost is $25 for each day.
C. 1/25 dollars per day; the cost is $25 for each day.
D. 75/1 dollars per day; the cost is $75 for each day.
Answer:
B
Step-by-step explanation:
75 divided by 3 = 25
so 25 dollars each day
Answer:
B. 25/1 dollars per day; the cost is $25 for each day.
Step-by-step explanation:
Suppose the depth of the tide in a certain harbor can be modeled by y = 23 - 5 cos (6.), where y is the water depth in fect
and t is the time in hours. Consider a day in which t= 0 represents 12:00 midnight. For that day, when are high tide and
low tide and what is the depth of each?
a. high tide at 6:00 a.m. and 6:00 p.m., depth 28 ft
low tide at 12:00 noon and 12:00 midnight, depth 18 ft
b. high tide at 6:00 a.m. and 6:00 p.m., depth 23 ft
low tide at 12:00 noon and 12:00 midnight, depth 5 ft
c. high tide at 12:00 noon and 12:00 midnight, depth 28 ft
low tide at 6:00 a.m. and 6:00p.m., depth 18 ft
d. high tide at 12:00 noon, depth 23 ft
low tide at 6:00 a.m., depth 5 ft
High tide at 6:00 a.m. and 6:00 p.m., depth 23 ft low tide at 12:00 noon and 12:00 midnight, depth 5 ft. Therefore, option B is the correct answer.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given trigonometric function is y=23-5cos(πt/6).
The given equation is y=23-5cos(πt/6), where y is the water depth in feet and t is the time in hours.
To find the high and low tide depths, we need to find the maximum and minimum values of y.
The maximum value of y is obtained when cos(πt/6) = -1, which gives y = 23 - 5(-1) = 28 ft.
The minimum value of y is obtained when cos(πt/6) = 1, which gives y = 23 - 5(1) = 18 ft.
To find the time when high and low tide occur, we need to find the values of t when cos(πt/6) equals -1 and 1 respectively.
When cos(πt/6) = -1, we get πt/6 = 3π/2, which gives t = 12 hours.
When cos(πt/6) = 1, we get πt/6 = 0, which gives t = 0 hours.
Since t = 0 represents 12:00 midnight, we can conclude that high tide will occur at 6:00 a.m. and 6:00 p.m., with a depth of 28 ft, and low tide will occur at 12:00 noon and 12:00 midnight, with a depth of 18 ft.
Therefore, option B is the correct answer.
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Is this correct? Answer if you know the answer and correct me if I am wrong.
Answer: Is correct trust me.
Step-by-step explanation:
