Answers
a. The values of k for which points A, B, and C are collinear are k = 3 and k = -2.
b. The value of k for which AB is parallel to CD is k = 13.
How to calculate the valuea. slope AB = (k+4-9)/(k+1-0) = (k-5)/(k+1)
The slope of AC is:
slope AC = (k+3-9)/(2k-0) = (k-6)/(2k)
Since A, B, and C are collinear, slope AB = slope AC. Therefore, we have:
(k-5)/(k+1) = (k-6)/(2k)
2k(k-5) = (k+1)(k-6)
2k^2 - 10k = k² - 5k - 6
k = 3 or k = -2
(b) The slope of AB is:
= (k+4-9)/(k+1-0) = (k-5)/(k+1)
The slope of CD is:
= (k+6-k-3)/(2k+2-2k) = 3/2
Since AB is parallel to CD, slope AB = slope CD. Therefore, we have:
(k-5)/(k+1) = 3/2
2(k-5) = 3(k+1)
k = 13
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Related Questions
Calculator A cylinder has a height of 16 m and a volume of 16,228 m³. What is the radius of the cylinder? Round your answer to the nearest whole number. O 256 m O 50 m O 18 m O 16 m 3 4 5
Answers
Answer: 18m
Step-by-step explanation:
Volume of cylinder = area of base circle x height
16228 = [tex]\pi r^2[/tex] x 15
16228/15pi = r^2
.: r = [tex]\sqrt{\frac{16228}{15\pi} }[/tex]
r ≅ 19 m
the closest answer choice is 18m
Using the given graph of the function f, find the following.
(a) the intercepts, if any
(b) its domain and range
(c) the intervals on which it is increasing, decreasing, or constant
(d) whether it is even, odd, or neither
Answers
By using the given graph of the function f, the key features include the following:
(a) the y-intercept is (0, 10).
(b) its domain is [-∞, ∞] and the range is [0, ∞].
(c) it is increasing over the interval [-∞, ∞].
(d) The function is even.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, or growth rate.Based on the graph, we would calculate the value of a and b as follows;
f(x) = a(b)^x
10 = a(b)⁰
a = 10
Next, we would determine value of b as follows;
12 = 10(b)¹
12 = 10b
b = 12/10
b = 1.2
Therefore, the required exponential function is given by;
[tex]y = 10(1.2)^x[/tex]
Part a.
When x = 0, the y-intercept can be determined as follows;
[tex]y = 10(1.2)^0[/tex]
y = 10(1)
y = 10.
Part b.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-∞, ∞].
Range = [0, ∞] or {y | y ≥ 0}
Part c.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce that the exponential function is always increasing over the interval [-∞, ∞].
Part d.
In conclusion, this exponential function is an even function because it is symmetric with respect to the y-coordinate (y-axis).
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5. Find the length of KL shown in red below. Show all work.
M
162°
Mi
5 ft.
K
L
PREVI
Answers
Answer:
1.57ft
Step-by-step explanation:
The circumference is twice the radius times pi.
C=2πr
C=2·π·5
C=10π
C=31.4159265359
We know that KL is 18° of that (180-162).
So we get the formula
31.4159265359÷360x18=1.57
A triangular pane of glass has a height of 32 inches and an area of 352 square inches. What is the length of the base of the pane?
Answers
The required length of the base of the triangular pane of glass is 22 inches.
We know that the formula for the area of a triangle is:
Area = 1/2 * base * height
We are given that the height of the triangular pane of glass is 32 inches and the area is 352 square inches. Substituting these values into the formula, we get:
352 = 1/2 * base * 32
Multiplying both sides by 2 and dividing by 32, we get:
base = 22
Therefore, the length of the base of the triangular pane of glass is 22 inches.
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If i make 413 dollars a second, how much money would i have in 30 minutes?
Answers
Answer:
if you make 413 dollars a second, in 30 minutes you would make 743,400 dollars.
Step-by-step explanation:
If you make 413 dollars a second, in 30 minutes you would make:
30 minutes = 30 x 60 = 1800 seconds
So, the amount of money you would make in 30 minutes can be calculated as follows:
1800 seconds x 413 dollars/second = 743,400 dollars
Which of the following statements are true regarding the reflection of A(1 1/2,-2)? Select all that apply..
Answers
The correct statements are:
A) When this point is reflected across the x-axis, the x-coordinate stays the same and the y-coordinates are opposites.C) When this point is reflected across the y-axis, the x-coordinates are opposites and the y-coordinate stays the same.D) When this point is reflected across the x-axis, the x-coordinates are opposites and the y-coordinate stays the same.How to explain the statementsWhen a point is reflected across the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. Therefore, statement A) is true.
When a point is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate changes sign. Therefore, statement C) is true.
It should be noted that to represent the reflection of point A (1,-2) across the y-axis, we flip the sign of the x-coordinate to obtain the image point A' (-1,-2). Therefore, statement D) is true.
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What is the length of C,D?
lengths:
a (-9,-12)
b (6,-12)
c (9,3)
d (-6,3)
Answers
Answer:
the length of C is 6, the length of D is 9,
Step-by-step explanation:
Fill in the blank using the scaling factor that makes the number sentence true. 5.3 × > 5.3 0.886 or 1.00 or 1.003
Answers
The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.
The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:
5.3 × x > 5.3 ÷ 5.3 × k
We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:
5.3 ÷ 5.3 × k = k × 1 = k
Substituting this into our equation, we get:
5.3 × x > k
We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.
The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.
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Find the area of the region that lies inside both curves. r = 6sin(2θ), r = 6sin(θ)
Answers
The area of the region that lies inside both curves is 11π/3 - 9√3/2 square units.
The area of the region that lies inside both curves first need to find the points of intersection.
The two equations equal to each other and solve for θ:
6sin(2θ) = 6sin(θ)
Dividing both sides by 6 get:
sin(2θ) = sin(θ)
The identity sin(2θ) = 2sin(θ)cos(θ) can rewrite this as:
2sin(θ)cos(θ) = sin(θ)
Dividing both sides by sin(θ) we get:
2cos(θ) = 1
Solving for θ we get:
θ = π/3, 5π/3
The area of the region by integrating the function r with respect to θ from θ = π/3 to θ = 5π/3:
A = ∫[π/3, 5π/3] 1/2 r² dθ
r = 6sin(2θ) when 0 ≤ θ ≤ π and r = 6sin(θ) when π ≤ θ ≤ 2π.
Substituting the appropriate values of r and integrating, we get:
A = ∫[π/3, π] 1/2 (6sin(2θ))² dθ + ∫[π, 5π/3] 1/2 (6sin(θ))² dθ
= ∫[π/3, π] 27sin²(2θ) dθ + ∫[π, 5π/3] 18sin²(θ) dθ
= [9θ - 3/4 sin(4θ)]π/3π + [6θ - 9/2 cos(2θ)]π/5π
= (π/3)[9π/2 - 3√3] + (2π/3)[5 - 9√3/2]
= 11π/3 - 9√3/2
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Find the area of the parallelogram with vertices L(–5, –2, –4), M(–12, –2, –4), N(–12, –8, –10), and O(–5, –8, –10).
Answers
From the vertices provided, the area of the parallelogram is 42cm².
How do we calculate the area of a parallelogram with the vertices provided?The area of a parallelogram remain
Area = base×height
we need to start by creating two vectors using the given vertices. We can use LM and LN.
Vector LM = M - L = (-12, -2, -4) - (-5, -2, -4) = (-7, 0, 0)
Vector LN = N - L = (-12, -8, -10) - (-5, -2, -4) = (-7, -6, -6)
LM x LN = (0×(-6) - 0×(-6), 0×(-7) - (-7)×0, -7×(-6) - 0×0)
= (0, 0, 42)
Area = ||LM x LN|| =√(0² + 0² + 42²) = √(0 + 0 + 1764)
= √(1764) = 42 cm²
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Find out if the fractions are proportional. Show work
3/5 and 9/15
Answers
To find out if the fractions are proportional, we need to check if their cross-products are equal.Cross-product of 3/5 and 9/15:
3/5 × 9/15 = (3 × 9)/(5 × 15) = 27/75We can simplify 27/75 by dividing both the numerator and denominator by their greatest common factor, which is 3:
27/75 = (3 × 9)/(3 × 25) = 9/25Therefore, the cross-product of 3/5 and 9/15 is 9/25.Since the cross-products are not equal to each other, the fractions are not proportional.
a) On the occasion of Teej, the principal of a school organized a Teej program for her female staffs. She distributes 90 bangles and 108 sweets equally to the staffs including herself. If there are 20 male staffs in the school, find the maximum number of staffs of her school.
Answers
The maximum number of staff at the school, given the distribution of bangles and sweets, is 38 staff.
How to find the number of staff ?The principal has distributed 90 bangles and 108 sweets equally among her female staff includng herself. This means that the total number of female staff in the school is a number that can divide both 90 and 108 evenly, as each staff member must receve an integer number of bangles and sweets.
Find the greatest common divisor (GCD) of 90 and 108. The GCD of 90 and 108 is 18.
So, the princpal's school has 18 female staff including herself. In addition to the 20 male staff, this implies a maxmum of:
18 (female staff) + 20 (male staff) = 38 staff in total
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Will Give Brainliest Please Help!
Answers
Step-by-step explanation:
If the lines are parallel then 3x + 9x = 180 degrees
12 x = 180
x = 15
What is the equation for the data table with x values 1, 2, 3, 4, 5 and y values 2, 4, 8, 16, 32
Answers
The equation of the data table of values is y = 2ˣ
How to determine the equation of the data tableFrom the question, we have the following parameters that can be used in our computation:
The data table with the values
x values 1, 2, 3, 4, 5
y values 2, 4, 8, 16, 32
From the above, we can see that the relationship between x and y is that
The number 2 takes the variable x as its exponent to get the variable y
Mathematically, this can be expressed as
y = 2ˣ
This represents an exponential function with a base of 2
Hence, the equation of the data table is y = 2ˣ
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Height=5 cm
Radius=4 cm
answer to the nearest tenth
SA = arl + B
Answers
The nearest tenth, the surface area of the given cylinder is approximately 175.9 cm².
To find the surface area (SA) of a cylinder, we need to calculate the sum of the lateral surface area (arl) and the base area (B).
The formula for the lateral surface area of a cylinder is given by:
arl = 2πrh,
where r is the radius and h is the height of the cylinder.
The formula for the base area of a cylinder is given by:
B = πr^2.
Let's calculate the values:
Given:
Height (h) = 5 cm
Radius (r) = 4 cm
First, we calculate the lateral surface area (arl):
arl = 2πrh
= 2 * 3.14159 * 4 cm * 5 cm
≈ 125.66368 cm²
Next, we calculate the base area (B):
B = πr^2
= 3.14159 * (4 cm)^2
≈ 50.26544 cm²
Finally, we find the surface area (SA):
SA = arl + B
≈ 125.66368 cm² + 50.26544 cm²
≈ 175.92912 cm²
Rounded to the nearest tenth, the surface area of the given cylinder is approximately 175.9 cm².
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HELP FAST PLEASE!
I do not understand please help and explain which ordered pair of 4 options represents a function.
Answers
Answer:
third option represents a function.
Step-by-step explanation:
for the ordered pairs to represent a function.
each value of x must only map to one unique value of y
in the first option
(- 2, 0 ) and (- 2, 2 )
the same x- coordinate maps to 2 different values of y
thus not a function.
in the second option
every value of x = - 5 maps to 5 different values of y
thus not a function.
in the third option
each value of x maps to a unique value of y.
thus a function.
in the fourth option
(- 6, - 3 ) and (- 6, - 2 )
the same x value maps to 2 different values of y
thus not a function.
The first six terms in a geometric sequence are shown, where a1=-4
-4 -16 -64 -256 -1024 -4096
Based on this information, which equation can be used to find the nth term in the sequence, an?
Answers
The equation that can be used to find the nth term in the sequence, an, is: [tex]an = -4 \times 4^{(n-1)[/tex]
In a geometric sequence, each term is found by multiplying the previous term by a constant ratio.
Let's denote this ratio as "r."
Given that the first term, a₁, is -4, we can find the value of r by dividing the second term, a₂, by the first term, a₁.
a₁ = -4
a₂ = -16
r = a₂/a₁
Substituting the given values:
r = -16 / -4
r = 4
So, the common ratio, r, in this geometric sequence is 4.
To find the nth term, aₙ, in the sequence, we can use the formula:
[tex]a1= a{1 } \times r^{(n-1) }[/tex]
Substituting the given values:
[tex]a_n= -4 \times 4^{(n-1) }[/tex]
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One box has a surface area of 96 cm2 and a height of 4 cm. A second similar box
has a volume of 1728 cm3 and a surface area of 864 cm2 .
Find:
(a) the height of the larger box (b) the volume of the smaller box.
Answers
(a) The height of the larger box is determined as 2 cm.
(b) The volume of the smaller box is determined as 384 cm³.
What is the height of the larger box?The height of the larger box is calculated by applying the following formula as follows;
Volume = surface area x height
V = Ah
h = V / A
h = ( 1728 cm³ ) / ( 864 cm²2)
h = 2 cm
The volume of the smaller box is calculated by applying the following formula as follows;
V = Ah
where;
A is the surface area of the smaller boxh is the height of the smaller boxV = 96 cm² x 4 cm
V = 384 cm³
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12. The figure below shows a circle centre O, inscribed inside a quadrant centre P and radius 14 cm. Calculate the value of r, radius of the circle.
Answers
Answer:
Step-by-step explanation:
here is the solution of your problem i hope u enjoy
Drag each inequality to the column which is labeled with its solution.
( look at photo for reference )
Answers
Drag the solution of each inequality as shown below:
3(x - 5) + x < 13 : x<7
2(x + 8) > 4x + 2 : x<7
3x + 2(x - 8) > x : x > 4
2(x + 6) < 3x + 8 : x > 4
How to solve the inequalities?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4
3(x - 5) + x < 13
3x -15 + x < 13
4x -15 < 13
4x < 13 + 15
4x < 28
x < 28/4
x < 7
2(x + 8) > 4x + 2
2x + 16 > 4x + 2
2x - 4x > 2 - 16
-2x > -14
x < -14/(-2) (Note: Sign will change if you divide with negative numbers)
x < 7
3x + 2(x - 8) > x
3x + 2x -16 > x
5x - 16 > x
5x - x > 16
4x > 16
x > 16/4
x > 4
2(x + 6) < 3x + 8
2x + 12 < 3x + 8
2x - 3x < 8 - 12
-1x < -4
x > -4/(-1)
x > 4
Therefore, drag the solution of each inequality accordingly.
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pls help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The length of the other diagonal of the kite is: 50 cm
What is the Area of a Kite?We want to find the area of the given kite but It should be noted that:
The hypotenuse is usually the slanted line part in a triangle.
Area of a kite = pq/2
where:
p and q are diagonals
We are given:
Area of Kite = 180 cm²
Length of diagonal = 16 cm
Thus:
16q = 180
q = 180/16
q = 50 cm
This gives us the length of the other diagonal of the kite
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simplify
3x2 + 5x - 7x-3-5x²-2
Answers
The simplified expression is [tex]-2x^2 - 2x - 5.[/tex]
To simplify the expression, combine like terms:
[tex]3x^2 + 5x - 7x - 3 - 5x^2 - 2[/tex]
Combine the [tex]x^2[/tex] terms:
[tex](3x^2 - 5x^2) + 5x - 7x - 3 - 2[/tex]
Simplify the [tex]x^2[/tex] terms:
[tex]-2x^2 + 5x - 7x - 3 - 2[/tex]
Combine the x terms:
[tex]-2x^2 - 2x - 3[/tex]
This is the simplified form of the expression.
Therefore, the simplified expression is [tex]-2x^2 - 2x - 5.[/tex]
We have grouped the terms with similar variables together and performed the necessary arithmetic operations to obtain the simplified form.
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A coin is flipped 5200 times the coin land on heads 1352 times which statement best describes the fairness of the coin
Answers
The statement that best describes the fairness of the coin is the coin is biased
How to describes the fairness of the coinFrom the question, we have the following parameters that can be used in our computation:
Flipping of a coin
Number of times it lands on head = 1352
Number of times it was flipped = 5200
using the above as a guide, we have the following:
P(Head) = 1352/5200
So, we have
P(Head) = 26%
This value is far from 50%
Hence, the fairness of the coin is the coin is that it is biased
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2. A small ball is tossed from a tall building. The function, h given by
h(t) = 100+ 30t - 16t² shows the ball's height, in feet, t seconds after it was
dropped.
Select all statements that are true about the situation.
a. The value t=8 does not belong in the domain of h.
b. The domain of function h can be all real numbers.
c. The ball has hit the ground in 4 seconds.
d. The ball has hit the ground in 2 seconds.
e. The ball was tossed from the building at 30 feet.
Answers
Answer:
Step-by-step explanation:
Set h=0 for ground height, then solve for t
-16t^2 -20t +240 = 0
divide by -4
4t^2 +5t - 60 = 0
use the quadratic formula
t= -5/8 + or - (1/8)square root of (25 +4(4)(60)). Ignore the negative square root
=-5/8 + (1/8)sqr(960+25)
= -5/8 + (1/8)sqr(985)
=-5/8 + (1/8)sqr(5(197))= slightly less than -5/8 +(10/8)(sqr10) = about -5/8 +32/8 = 27/8 = 3.3 seconds
the ball's initial velocity is negative, meaning the ball was thrown downward. Then add the effect of gravity, and it should hit the ground in a short time, even when thrown from an initial height of 240 feet.
plug t=2 into the original equation for height. You should get slightly above ground, near zero
-16(2)^2 -20(2) +240 = -64 -40+240 = 136
try t=3
-16(9) -20(3) +240 = -144 -60 +240 = 36
try t=4
-16(16) -20(4) +240 =-256 -80 +240 =-96
the time to hit ground should be between t=3 and 4, but closer to t=3, maybe about 3 1/3 seconds
In a normal distribution, a data value located 1.5 standard deviations below the mean has Standard Score: z =
In a normal distribution, a data value located 1.7 standard deviations above the mean has Standard Score: z =
In a normal distribution, the mean has Standard Score: z =
Answers
Answer:
Step-by-step explanation:
let m = mean
s= standard deviation
to find zscore = (value-m)/s
1.)
((m-1.5s)-m)/s = -1.5
in fact, if it's n standard deviations ABOVE the mean, your zscore is n
if it's n standard deviations BELOW the mean, your zscore is -n
2.)
((m+1.7s)-m)/s= 1.7
3.)
(m-m)/s= 0
A car is traveling at a rate of 80 miles per hour. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 5 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers. Rate: Distance traveled in 5 hours:
Answers
The car will travel 640 kilometers in 5 hours.
We have,
To convert miles per hour to kilometers per hour, we need to multiply by the conversion factor of 1.6:
= 80 miles/hour x 1.6 kilometers/mile
= 128 kilometers/hour
So the car's rate is 128 kilometers per hour.
Now,
To find the distance the car will travel in 5 hours, we need to multiply the rate by the time:
= 128 kilometers/hour x 5 hours
= 640 kilometers
Thus,
The car will travel 640 kilometers in 5 hours.
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Javier trained for his first marathon for months. He learned to pace himself and to push through the pain. He developed blisters
and shin splints. It broke his heart not to finish.
Which revision below most effectively uses transitions to create coherence?
Javier trained for his first marathon for months after he learned to pace himself and to push through the pain. Additionally,
he developed blisters and shin splints. In the end, it broke his heart not to finish.
Javier trained for his first marathon for months. First, he learned to pace himself and to push through the pain. Next, he
developed blisters and shin splints. Finally, it broke his heart not to finish.
Javier trained for his first marathon for months. He leaned to pace himself and to push through the pain. But during the
race, he developed blisters and shin splints. Because of that he had to stop, and it broke his heart when he couldn't finish.
Javier trained for his first marathon for months. He learned to pace himself and to push through the pain. Also, he
developed blisters and shin splints. Similarly, it broke his heart not to finish.
Submit
Pass
Hold
Don't know answer Skip for now
Save and close
Answers
This revision uses transitional words (first, next, finally) to indicate a clear sequence of events helps to create coherence and improve the flow of the passage.
The revision that most effectively uses transitions to create coherence is:
Javier trained for his first marathon for months.
He learned to pace himself and to push through the pain.
He developed blisters and shin splints.
It broke his heart not to finish.
This revision uses transitional words (first, next, finally) to indicate a clear sequence of events helps to create coherence and improve the flow of the passage.
The use of these transitions also helps the reader understand the chronological order of events in the story.
In addition, the other options have some issues.
The first revision uses "after" to indicate a time sequence but it is not clear what event this refers to.
The second revision uses "finally" is a good transition but it does not provide any other transition words to clarify the order of events.
The third revision uses "but" to contrast the two events creates a bit of confusion as there is no clear cause-and-effect relationship between the two.
The fourth revision uses "also" to indicate a connection but it does not clearly indicate the sequence of events.
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Read the following prompt and type your response in the space provided.
Diana has a bag with 20 marbles in it. Some of the marbles are blue, some are green, and some are yellow.
She draws one marble at random, records the color, and returns it to the bag.
Here is her data after 1000 trials:
Blue Green Yellow
36 99 865
Estimate the probability that a marble drawn at random will be blue.
Estimate the probability that a marble drawn at random will be green.
Estimate the probability that a marble drawn at random will be yellow.
Express each probability estimate as a fraction with 20 in the denominator.
Answers
Answer:
0.72/20. 1.98/20. 17.3/20.
Step-by-step explanation:
1000/20 = 50
for blue:
36/1000. divide top and bottom by 50 to get 0.72/20
for green:
99/1000. divide top and bottom by 50 to get 1.98/20
for yellow:
865/1000. divide top and bottom by 50 to get 17.3/20
Si x es una variable aleatoria continua distribuida de forma normal con media de 18 y varianza de 6.25. Encontrar el valor de A tal que la probabilidad de A igual a 0.1814
Answers
Answer:
Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?
Step-by-step explanation:
Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?
PLEASE HELP!! Did I do this right.???
Answers
Answer: 5
Step-by-step explanation:45