Answers
The correct statement regarding the relations in this problem is given as follows:
Only relation A could represent a linear relationship.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.From the first bullet point, we have that what classifies a linear relation is a constant rate of change.
For relation K, we have that it is not linear, as:
From x = -7 to x = -4, the rate of change is of 5/3.From x = -4 to x = -2, the rate of change is of 1/2. -> different to 5/3.For relation R, we have that it is linear, as it has a constant rate of change.
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Related Questions
In the figure, PA and PB are tangent to circle O and PD bisects BPA. The figure is not drawn to scale.
For m
Answers
The measure of ∠BPO is 48°.
How to find the measure of ∠BPO?Since PD bisects ∠BPA, we can say:
∠AOC = ∠BOC .
Thus, ∠ BOC = 42°
Since PB is tangent to the circle, PBO = 90°.
Looking at triangle PBO, we can say:
∠BPO + ∠PBO + ∠BOC = 180 (angles in a triangle add up to 180)
∠BPO + 90 + 42 = 180
∠BPO + 132 = 180
∠BPO = 180 - 32
∠BPO = 48°
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Complete Question
Check image attached
Solve the following for θ, in radians, where 0≤θ<2π.
−7cos2(θ)+4cos(θ)+6=0
Select all that apply:
1.07
3.96
0.31
2.32
1.68
2.43
Answers
Answer:correct answers are 3.96
2.32
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
-7u^2 + 4u + 6 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -7, b = 4, and c = 6. Substituting these values, we get:
u = (-4 ± sqrt(4^2 - 4(-7)(6))) / 2(-7)
u = (-4 ± sqrt(136)) / (-14)
u = (2 ± sqrt(34)) / 7
Therefore, either:
cos(θ) = (2 + sqrt(34)) / 7
or:
cos(θ) = (2 - sqrt(34)) / 7
Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse cosine function:
θ = arccos((2 + sqrt(34)) / 7)
θ = arccos((2 - sqrt(34)) / 7)
Using a calculator, we find:
In this figure, the two angles are complementary.
(2x + 6)°
(1/2x )°
What is the value of x?
Answers
Answer:
Step-by-step explanation:
Complementary means angles that add up to 90°
Based on that you can write and equation by adding the 2 angles and making equal to 90
2x+6+1/2x=90 combine like terms on left
5/2x+6=90 subtract both sides by 6
5/2x=84 multiply by the reciprocal of 5/2 => 2/5
x=168/5 or 33.6
Determine the relationship between the lengths of AB and BC. Please help
Answers
The relation between lengths of AB and BC are,
⇒ Lenght of AB and BC are different.
We have to given that;
Triangles ABD and BDC are given.
Here, All the angles of a triangle ABD are different from angles of BDC.
Hence, We get;
Both triangle ABD and BDC are congruent.
So, All the sides of ΔABD are different from the sides of different from ΔBDC.
Hence, Lenght of AB and BC are different.
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Find the values of x and y
Answers
Answer:
x = 8.4
y = 23.6
Step-by-step explanation:
tan31 = x/14
x = tan31(14) = 8.412
y² = (8.412)² + (22)² = 554.7626
y = √554.7626 = 23.55
A box has 7 blue and 7 green jelly beans. A bag has 6 blue and 4 green jelly beans. A jelly bean is selected at random from the box and placed in the bag. Then a jelly bean is selected at random from the bag. If a green jelly bean is selected from the bag, what is the probability that the transferred jelly bean was green? (Round your answer to three decimal places.)
Answers
The probability that the transferred jelly bean was green is P ( G ) = 0.636
Given data ,
Let the probability that the transferred jelly bean was green be P ( G )
Now , There are 7 blue and 7 green jelly beans in the box, so the probability of selecting a green jelly bean from the box is 7/(7+7) = 0.5, and the probability of selecting a blue jelly bean from the box is also 0.5
A jelly bean is chosen from the box and then put in the bag. Say someone chooses a green jelly bean from the package and puts it in the bag. Currently, there are 6 + 1 = 7 green jelly beans and 4 + 0 = 4 blue jelly beans in the bag.
Now , Since there are 7 green jelly beans and 4 blue jelly beans in the bag, the probability of selecting a green jelly bean from the bag is P ( G )
where P ( G ) = 7/(7+4)
P ( G ) = 0.636
Hence , the probability is 0.636
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Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = x + 2 Complete the table on your own paper, then select the value that is a solution to f(x) = g(x). (2 points) Group of answer choices x = 2 x = 3 x = 5 x = 6
Answers
f(x) = g(x)
-x^2 + 4x + 12 = x + 2
-x^2 + 3x + 10 = 0
Now we can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
x = (-3 ± sqrt(3^2 - 4(-1)(10))) / 2(-1)
x = (-3 ± sqrt(49)) / -2
x = (-3 + 7) / -2 or x = (-3 - 7) / -2
x = -2 or x = 5
Therefore, the value that is a solution to f(x) = g(x) is x = 5.
Find an equivalent equation in rectangular coordinates
Answers
Answer:
[tex]x^2+y^2 = 2x - 2y}[/tex]
Third answer option
Step-by-step explanation:
We are given the polar equation as
[tex]r = 2(\sin \theta - \cos \theta)[/tex]
and asked to convert it into rectangular form
We have the following equations which relate (r, θ) in polar form to (x, y) in rectangular form
[tex]\cos \theta=\dfrac{x}{r} \rightarrow x=r \cos\theta\\\\\sin \theta=\dfrac{y}{r} \rightarrow y=r \sin \theta\\\\[/tex]
[tex]r^2=x^2+y^2[/tex]
Original polar equation:
[tex]r = 2(\sin \theta - \cos \theta)[/tex]
Expand the right side:
[tex]r = 2\sin \theta - 2\cos \theta[/tex]
Substitute for sinθ and cosθ in terms of x and y
[tex]r & = 2\left(\dfrac{y}{r} - \dfrac{x}{r}\right)\\[/tex]
Multiply both sides by r:
[tex]r^2 = 2(x - y)\\r^2 = 2x - 2y\\[/tex]
Substitute [tex]r^2=x^2+y^2[/tex] on the left side:
[tex]\boxed{x^2+y^2 = 2x - 2y}[/tex]
This would be the third answer opton
f(x)=−7x^2+8x+2what is the value of the discriminant of f? how many x-intercepts does the graph of f have?
Answers
The discriminant value is 120 and 2 is the x - intercept will have the graph of f.
What is X Intercept?The intercept of a line is the point on a graph where the line crosses an axis. There can be both x and y intercepts on a graph. The x-axis is the horizontal line on the graph, therefore the x-intercept can also be referred to as the horizontal intercept. This is the point where the line crosses the x-axis. At this point, the value of y is zero. The y-axis is the vertical axis on a graph. The y-intercept is the point where the line crosses the y-axis and x has a value of zero.
The function, we have:
[tex]f(x) = -7x^2 + 8x + 2[/tex]
We have to find the value of the discriminant of f and how many x- intercepts of the graph?
Firstly, We have to find the value of discriminant is
[tex]b^2 -4ac[/tex]
[tex]where ,ax^2 +bx+c[/tex]
a= -7, b = 8, c=2
The discriminant is:
= [tex]8^2 - 4(-7) (2)[/tex]
= 64 +56
= 120
This will have 2 real x intercepts because 120 > 0
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IQR of 28 22 15 16 15 13 19 18
Answers
Answer: The IQR of this data set is 5.5
Step-by-step explanation: Ok so first you line the data set up in correct order.
Here's the correct order:
13, 15, 15, 16, 18, 19, 22, 28
Then you find the median and since there's even amount of numbers you add the two numbers in the middle which is 16 and 18 and divide that by 2 which is 17. So the median is 17. Then you split the data set into halves. The first quartile is 15 and the third quartile is 20.5. Then to find the IQR, you would minus 20.5 - 15 = 5.5. Hope this helps!
What is the answer to the question?
Answers
The solid that is produced rotating the triangle about the line m is given as follows:
A cylinder with height of 2 units.
What are the radius and the diameter of a cylinder?The cylinder has a circular base, hence we must start there, then we consider that;
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.The diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.Rotating the line, the features of the cylinder generated are given as follows:
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HELP ASAP!! ( failing my class lol pls help asappp )
What was the scale factor used?
Was the orientation preserved or changed?
Was congruence preserved or changed?
Answers
1) The scale factor of dilation is 1/3
2) The orientation is preserved in dilation of A to A'
3) The congruence is not preserved in dilation of A to A'
We know that the scale factor is nothing but the ratio of the size of the transformed image to the size of the original image.
Here from the attached graph we can observe that the square A is transformed to A'
The side length of square A is 18 units and the side length of square A' is 6
So, the scale factor would be,
r = A' / A
r = 6/18
r = 1/3
We know that a dilation preserves the shape and orientation of the figure, but changes the size of he figure.
So, the dilations do not preserve congruence, as it changes the size of a figure.
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Let u = 2i - 3j, and w=-i-6j. Find ||w - ul.
w-ul = (Type an exact answer, using radicals as needed.)
Answers
The value of ||w - u || = 3 sqrt 2
How to solveGiven:
u = 2i - 3j
w = - i - 6j
w - u = ( - i - 2i ) + ( - 6j - (-3j))
w - u = - 3i - 3j
|| w - u || = sqrt [ - 3^2 + - 3^2 ]
||w - u || = 3 sqrt 2
The concept of a radical in mathematics refers to the symbolic representation (√) of finding the roots of an expression or a number.
The widely known and frequently used kind is the square root (√), which reveals a positive value that, when multiplied by itself at once, generates the radicand.
Other forms may include cube roots (∛) or fourth roots (∜). To simplify radicals, one can factor out those factors within it that result in perfect cubes or squares from their corresponding radicands.
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Each week, Nursen saves $5 and shares $3.75. She also spends $4.95 on bus fare to get home from music lessons. This week she earned $24 babysitting. How much money does Nursen have left that she can spend?
Answers
Answer: In one week, Nursen saves $5 and shares $3.75, so she has $5 + $3.75 = $8.75 per week.
She spends $4.95 on bus fare, so she has $8.75 - $4.95 = $3.80 per week to spend.
This week, Nursen earned $24 babysitting, so she has an additional $24 to spend.
Therefore, Nursen has $3.80 + $24 = $27.80 to spend.
Step-by-step explanation:
Diego buys water bottles for his softball team, he buys 7 cases, each with t bottles. Diego buys a total of 168 bottles. Create an equation that models this situation, where t represents the number of bottles per case purchased
Answers
The sum of three consecutive integers is 108. What are the integers?
Answers
Answer:
Step-by-step explanation:
hello :
let : x ,x+1 ,x+2 three consecutive integers
x +x+1 +x+2 = 108
3x =105
x = 105/3
x = 35
35 , 36 , 37
What is the length of BD
Answers
The value of length BD is 3.0 units
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
since AC is a radius that joins a tangent, the angle between them is 90°. Therefore ∆ABC is a right triangle and Pythagoras theorem can be applied.
therefore c² = a²+b²
c² = 4.5²+6²
c²= 20.25+36
c²= 56.25
c = √7.5
AC = CD(radii of a circle)
therefore BD = BC -CD
= 7.5-4.5
= 3.0units
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Which function is a translation one unit right of the function f(x) = log x?
h(x) = log x + 1
g(x) = log x-1
j(x) = log(x + 1)
k(x) = log(x - 1)
Answers
Answer:
The function that is a translation one unit right of the function f(x) = log x is k(x) = log(x - 1).
When we shift a function f(x) one unit right, we replace x with (x - a) where "a" is the amount of the shift. In this case, "a" is equal to 1. Therefore, the function becomes:
f(x - 1) = log(x - 1)
This means that the function k(x) = log(x - 1) is obtained by shifting the function f(x) one unit to the right.
Brainliest and points if answered correct!!!!
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
Answers
since i don't see the graph ill go with... B The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
-24/6 = -4
Step-by-step explanation:
The slope of the line can be found using the formula:
slope = (change in y) / (change in x)
In this case, we can use the two given points on the line: (0, 24) and (6, 0).
Change in y = 0 - 24 = -24
Change in x = 6 - 0 = 6
Therefore, slope = -24/6 = -4
This means that for every minute that passes, the swimmer completes four laps. The swimmer's pace is steady and consistent throughout the race, gradually decreasing the number of laps remaining until they finish at 0 after six minutes.
Answer:
The slope of the line represents the rate of change in the number of laps remaining per unit of time (in this case, per minute). In other words, it tells us how quickly the swimmer is completing laps.
Since the slope of the line is -4, this means that the swimmer is completing 4 laps every minute. This could be interpreted as the swimmer's pace or speed in the race. The negative sign indicates that the number of laps remaining is decreasing over time, which is expected as the swimmer completes more and more laps.
It's worth noting that the slope is constant throughout the race, meaning that the swimmer is maintaining a consistent pace. This information could be useful for the swimmer and their coach in terms of planning and pacing the race.
If a =5 and b = 9, what is the following fraction in lowest terms? a+1/b
Answers
Answer:
2/3
Step-by-step explanation:
since a is 5 and b is 9.
so, 5+1( according to the expression given)/9
5+1/9 equals 6/9 and taking them down to the lowest terms that makes the answer 2/3
i need help asap!!!
Part C
Determine the meanmedianstandard deviation, and interquartile range for each data setThen, use the graphing tool to determine the value of the standard deviation
Answers
Using the statistical tool, the following were arrived at:
Standard Deviation = 4.68737.Mean = 9.6Median = 9IQR = IQR = Q3-Q1 = 12 - 7 = 5.What is the definition of Interquartile Range (IQR)?It should be noted that when arranged from lowest to highest, the IQR represents the central 50% of values.
Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).
These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.
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In circle N with � ∠ � � � = 12 4 ∘ m∠MNP=124 ∘ and � � = 13 MN=13, find the area of sector MNP. Round to the nearest hundredth.
Answers
If circle with center N with m∠MNP=124 ∘ and MN=13, the area of sector MNP is approximately equal to 194.86 square units.
To find the area of a sector of a circle, we need to use the formula:
Area of sector = (central angle/360°) x πr²
Where r is the radius of the circle.
In this problem, we know that the central angle m∠MNP is 124° and MN, which is also the radius of the circle, is 13. So we can substitute these values into the formula:
Area of sector = (124/360) x π(13)²
Area of sector ≈ 194.86
Therefore, the area of sector MNP is approximately equal to 194.86 square units.
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find the awnser to this question as fast as you can and make sure it’s right
Answers
The area of the polygon to the nearest tenth is 80.7 in²
What is area of a polygon?A polygon any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. Examples of polygon include ; triangle, quadrilateral, pentagon e.t.c
The area of a polygon is expressed as;
A = 1/2nsa
where n is the number of side
a is the apothem
s is the side length
Side length = apothem × 2tan(180/n)
n = 12
s = 5 × 2tan(180/12)
s = 5 × 2tan15
s = 2.679
Area = 1/2 × 12 × 5 ×2.679
= 80.7 in²(nearest tenth)
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A restaurant had 160 lunch customers last weekend. Of those, 90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both. There were 45 customers who ordered seltzer and a veggie sandwich. Eleven more people ordered a veggie sandwich than a tuna sandwich. Complete the two-way frequency table for the data.
Answers
The frequency table is plotted and the order for the restaurant is given
Given data ,
A restaurant had 160 lunch customers last weekend.
90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both.
There were 45 customers who ordered seltzer and a veggie sandwich.
Eleven more people ordered a veggie sandwich than a tuna sandwich.
On simplifying the equation , we get
A = 90 - 38 - 45 = 7
B = 75 - 38 = 37
E = 160-90 = 70
C = D + 11
D + 11 + D = 70-37
2D = 33-11
D=22/2
D=11
Thus C = 22
F = 45 + C
F = 45 + 22
F = 22
G = A + D = 18
Chicken Veggie Tuna Total
Seltzer 38 45 7 90
Iced Tea B 22 11 70
Total 75 67 18 160
Hence , the frequency is completed
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The complete question is attached below :
A restaurant had 160 lunch customers last weekend. Of those, 90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both. There were 45 customers who ordered seltzer and a veggie sandwich. Eleven more people ordered a veggie sandwich than a tuna sandwich. Complete the two-way frequency table for the data.
The circle with center O shown above has a 34° inscribed angle and a 42° central angle. What is the measure of minor arc ABC?
Answers
The measures of the three intercepted arcs from least to greatest are;
AC < BC < AB
We have,
We are given that
Angle ACB = 63 degrees
Arc BC is 118 degrees.
Now, from the Triangle angle sum theorem, we know that the sum of all interior angles of any triangle is always equal to 180 degrees.
Thus, the sum of the interior angles of the inscribed triangle given to us id also 180 degrees.
Now, since Angle ACB = 63 degrees
Then Arc AB = 63 * 2 = 126
Arc AC = 360 - (Arc BC + Arc AB)
We are given BC = 118 degrees
Thus;
Arc AC = 360 - (118 + 126)
Arc AC = 116°
Thus, the least arc angle is Arc AC while the greatest is Arc AB
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complete question:
Triangle ABC is inscribed in a circle centered at point O.
The figure shows triangle ABC is inscribed in a circle centered at point O and has an angle ACB is 63 degrees and arc BC is 118 degrees.
Order the measures of the three intercepted arcs from least to greatest.
Find and compare the domain and range of each function. f(x) = 5/8x + 1 g(x) = 2/3x^3 A. The domains and ranges of both functions are not restricted. B. The domain of f is restricted, but its range is not. The domain and range of g are not restricted. C. The range of f is restricted, but its domain is not. The domain and range of g are not restricted. D. Both the domain and range of f are restricted, but the domain and range of g are not.
Answers
A. The domains and ranges of both functions are not restricted.
For f(x) = 5/8x + 1, any real number can be plugged in for x, so the domain is (-∞, ∞). Similarly, any real number can be obtained by evaluating the function, so the range is also (-∞, ∞).
For g(x) = 2/3x^3, any real number can be plugged in for x, so the domain is (-∞, ∞). As x is cubed, the range can be negative or positive infinity, or any real number in between, so the range is also (-∞, ∞).
Therefore, both functions have unrestricted domains and ranges.
The correct answer is A.
PLEASE HELP (WILL GIVE BRAINLIEST
Answers
Answer:
cm^3 can be used to represent volume.
r(t) =
t2 − 36
i − j + ln(t − 1)k
(a)
Find the domain of r.
Answers
The domain of the vector function is : ( -6, -2) ∪ ( -2, 6)
The given vector function can be correctly expressed as:
r(t) = (t-2)i / (t+2) + sintj + ln(36-t²)k²
The domain of the given function can be determined by finding the domain of each respective component.
(t-2)i / (t+2)
Not defined, t = -2
Thus, the domain of the first component of the vector = (-∞, 2) ∪ (2, ∞)
The 2nd component = sin t
No restriction on t,
The 3rd component of the function is ㏑(36 - t²)
we know,
Natural number is defined for +ve numbers,
i.e.
36 - t² > 0
(6 + t) (6 - t) > 0
thus, it satisfies the inequality -6 < t < 6
The third domain = (-6,6)
Hence, the domain of the vector function is : ( -6, -2) ∪ ( -2, 6)
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John needs to paint one wall in his school. He knows that 1 can of paint covers 24 square feet.
Answers
Since John cannot buy a fraction of a can, he needs to round up to the nearest whole number. So, John needs at least 5 cans of paint to cover the entire wall as per the height and length.
To calculate the area of the wall, we need to multiply the height and the length of the wall.
From the diagram, we can see that the height of the wall is 2 meters and the length is 5 meters.
So the total area of the wall is:
Area = height x length
Area = 2 meters x 5 meters
Area = 10 square meters
To convert this to square feet, we can use the conversion factor:
1 square meter = 10.764 square feet
So:
Area = 10 square meters x 10.764 square feet/square meter
Area = 107.64 square feet
Since 1 can of paint covers 24 square feet, John needs:
Number of cans = Area ÷ Coverage per can
Number of cans = 107.64 square feet ÷ 24 square feet/can
Number of cans = 4.485 cans
Thus, John needs at least 5 cans of paint to cover the entire wall.
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Your question seems incomplete, the probable complete question is:
John needs to paint one wall in his school. He knows that 1 can of paint covers an area of 24 square feet.
John uses a meter stick to measure the dimensions of the wall as shown.
[1 meter = approximately 39 inches]
What is the fewest number of cans of paint John can use to paint the wall?
Look at image that is attached
Answers
Answer: Linear
Step-by-step explanation:
I can tell from the table because there is a difference of 4 between each y value.
I dont know what the other blanks will be because i cant see the options. But it shouldnt be too hard to fill out
