Answers
The constant of variation for the given data is 1/4.
What is the constant of proportionality?If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Given that the data in the table is,
x f(x)
-8 -2
-4 -1
0 0
4 1
8 2
The constant of proportionality will be calculated as,
F(x) = kx
-2 = k x -8
k = -2 / -8
k = 1 / 4
Here, the proportionality constant will be 1/4.
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Related Questions
plsss help
For the given polynomial, determine which of the binomials listed are factors. Pick two.
f(x) = 2x3 + 9x2 + 13x + 6
A.x + 1
B.x – 1
C.x + 2
D.x – 2
E.x + 3
F.x – 3
Answers
The factors for the Polynomial are (x+1) and (x+2).
What is Factor Theorem?According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.
Given:
f(x) = 2x³ + 9x² + 13x + 6
Now, first (x+1) =0
x= -1
put x= -1 in f(x) as
f(-1) = 2(-1) + 9(1) + 13(-1) + 6
= -2 + 9 - 13 + 6
= 0
So, (x+1) is factor of f(x).
Now, second (x-1)= 0
x= 1
put x= 1 in f(x) as
f(1) = 2(1) + 9(1) + 13(1) + 6
= 2 + 9 + 13 + 6
= 31
So, (x-1) is not a factor of f(x).
Now, second (x+2)= 0
x= -2
put x= -2 in f(x) as
f(1) = 2(-2)³ + 9(-2)² + 13(-2) + 6
= -16 + 36 - 26 + 6
= 0
So, (x+2) is factor of f(x).
Now, second (x-2)= 0
x= 2
put x= 2 in f(x) as
f(1) = 2(2)³ + 9(2)² + 13(2) + 6
= 16 + 36 + 26 + 6
= 84
So, (x-2) is not a factor of f(x).
Now, second (x+3)= 0
x= -3
put x= -3 in f(x) as
f(1) = 2(-3)³ + 9(-3)² + 13(-3) + 6
= -54 + 81 - 39 + 6
= -6
So, (x+3) is not a factor of f(x).
Now, second (x-3)= 0
x= 3
put x= 3 in f(x) as
f(1) = 2(3)³ + 9(3)² + 13(3) + 6
= 54 + 81 + 39 + 6
= 180
So, (x-3) is not a factor of f(x).
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NEED HELP ASAP, VERY IMPORTANT PLEASE ANSWER CORRECTLY!!
Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range.
y=-5x^2+3x+10
Answers
Answer:
Is this what you wanted
Step-by-step explanation:
8
6
A
4
А
2
-8-6
4 -2
2
4
6
8
-2
B
4
-6
-8
a. Identify each transformation.
A to B:
B to C:
C to D:
Answers
Answer:
ansfhbshajsnshafakdkidbsbaga abfjdb
y=mx+b give the equation of the line in slope intercept form that runs through (-3,6) and (5,-2)
Answers
Answer:
y = -x +3
Step-by-step explanation:
You want the equation of the line through the points (-3, 6) and (5, -2) in slope-intercept form.
SlopeThe slope can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (-2 -6)/(5 -(-3)) = -8/8 = -1
InterceptThe y-intercept can be be found using the formula ...
b = y -mx
b = 6 -(-1)(-3) = 3
EquationThe equation in slope-intercept form is ...
y = mx +b
Using the found values, the equation is...
y = -x +3
<95141404393>
The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system.
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
Select the correct choice below and; if necessary; fill in the answer boxes to complete your choice A: The solution set has exactly one element; (Type integers or simplified fractions B. The solution set has infintely many elements C. The solution set is empty:
Answers
For the given Augmented Matrix ,the correct option is :
A) The solution set has exactly one element.
The exact solution is x = -25 , y = 2 and z = 2.
Augmented Matrix:
An augmented matrix is a means of solving simple linear equations. Coefficients and constant values of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.
Now, as given the Augmented matrix:
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
From this system we get:
y - z = 4 --------------------------- (1)
z = 2
and, z = 3
and, x + 7y + 3z =-5 ---------------- (2)
Now, Solving the equation with z = 2,
y - 2 = 4
⇒ y = 6
and, putting y = 6 and z = 2
x + 7× 6 + 3×2 = -5
⇒ x + 42 + 6 = -5
⇒ x +48 = -5
⇒ x = -53
Therefore, x = -53, y=6 and z =2
Now, for z = 3 in equation (1)
y - 3= 4
⇒ y = 7
Putting y =7 and z =3, we get:
x + 7 × 7 + 3×3 = -5
⇒ x + 49 + 9 =-5
⇒ x + 58 = -5
⇒ x = -63
Therefore, x = -63, y =7 and z =3
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Find QR - Will mark brainliest
Answers
Answer:
26
Step-by-step explanation:
Answer:
QR = 30
Step-by-step explanation:
GHI ~ PQR means that PQR is the same shape and length ratios as GHI but is a different size.
All of the leg lengths of GHI are multiplied by something to get the leg lengths of PQR.
You're given the leg lengths 12 and 20. So you need to find out what 12 is multiplied by to get to 20. 12 * 5/3 = 20.
So multiply 5/3 by the other leg length 18.
18 * 5/3 = 30
So QR = 30
Some girls are standing in a circle. The teacher makes them do a headcount. Bianca says one, her neighbour says two and so on. If they count in a clockwise direction, Antonia says five. If they count in an anticlockwise direction, Antonia says eight. How many girls are forming the circle?
Answers
Answer:
11
Step-by-step explanation:
See the attached image: the outer numbers count girls clockwise, showing Antonia at point J. The inner numbers show counting anticlockwise, showing Antonia as number 8, then continuing the count past her.
Aha! The inner and outer numbers always sum to 13.
But anticlockwise #12 really counted herself as #1 (she's being counted twice), so there aren't 12 girls, there are 11.
If you're not convinced, draw a picture with, say, 5 girls in it, number them counting both ways.
Please solve no links i will mark brailest
Answers
Answer:
oki! Mizuki here to help! 12 will be your answer!
Step-by-step explanation:
Soo... The ratio of blue to green is 4:3 right?
and there are 21 balloons!
4 + 3 is 7! So we divide 21 by 7 and get 3!
Then we multiply 3 by the number of blue balloons(aka 4) and get 12!
2 cm 10 cm 5 cm Find the area of the figure. 14 cm? 50 cm cm2 B) 60 cm2 Dj 64 cm? 12 if k = 62
Answers
Answer:
i believe it is B (๑ↀᆺↀ๑)
A fourth degree polynomial has real roots at 0, 3, a double real root at -1, and passes through the point
(2, 12). Write the particular equation of the function
Answers
Answer:
Step-by-step explanation:
y = a * x(x - 3)(x + 1)^2
2,12 is used to find the value of a
y = a (2)(2 - 3)(2 + 1)^2
12 = a (2)(-1)(3)^2
12 = a (2) (-1) (9)
12 = - 18*a
12/-18 = a
a = - 2/3
y = (-2/3)*x*(x - 3)(x + 1)^2
Please solve for the x. Thank you
Answers
The value of x will be;
⇒ x = 35
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
In Rectangle RSTW;
⇒ RZ = 3x + 6
⇒ SW = 7x - 23
Since, By the figure we conclude that;
⇒ 2 RZ = SW
Substitute the given values, we get;
⇒ 2 RZ = SW
⇒ 2 (3x + 6) = 7x - 23
⇒ 6x + 12 = 7x - 23
⇒ 12 + 23 = 7x - 6x
⇒ 35 = x
⇒ x= 35
Thus, The value of x = 35
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Line s passes through points (7, 10) and (2, 14). Line t is parallel to line s. What is the slope of line t?
Answers
Answer:
The slope of line t is -4/5.
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(14-10)/(2-7)
m=4/-5
Parallel lines have same slopes.
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answers
Answer:
[tex]A) \ \{ \dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2} \}[/tex]
Step-by-step explanation:
The quadratic equation to be solved is presented here as follows;
x² + 3·x - 5 = 0
The quadratic formula for a quadratic equation of the form, a·x²+b·x + c = 0, where 'a', 'b', and 'c' are constants and 'x' is unknown, is given as follows;
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4 \cdot a \cdot c} }{2 \cdot a}[/tex]
By comparison with the given equation, we have;
a = 1, b = 3, and c = -5
By plugging in the values, we get;
[tex]x = \dfrac{-3 \pm \sqrt{3^2 - 4 \times 1 \times (-5)} }{2 \times 1}[/tex]
Therefore;
[tex]x = \{\dfrac{-3 + \sqrt{9 + 20} }{2}, \dfrac{-3 - \sqrt{9 + 20} }{2}\} = \{\dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2}\}[/tex]
[tex]x= \{\dfrac{-3 + \sqrt{29} }{2}, \dfrac{-3 - \sqrt{29} }{2}\}[/tex]
4/9 = ?/?
+ 5/18 = ?/?
___________
?/?
Answers
Answer:
+6/27=?/?
Step-by-step explanation:
+6/27=?/? will be the next number as the patter keeps increasing the numerator by 1 and denominator by 9
Help Please i beg you
Answers
Please mark brainliest
Lia bought 4 3/5 pound of trail mix. She gave 3/5 of it to her iter. How much did give away?
Answers
Lia gave away 3/5 of the trail mix, which is equal to 2 2/5 pounds.
Lia bought 4 3/5 pounds of trail mix. She gave 3/5 of it to her iter.Since Lia bought 4 3/5 pounds of trail mix, we can express this as 4 + 3/5 pounds, or 9/5 pounds.
To find out how much trail mix Lia gave away, we can multiply 9/5 by 3/5.
3. 3/5 multiplied by 9/5 is equal to 27/25.
To simplify this fraction, we can divide both the numerator and denominator by 3.
27/25 can be simplified to 9/5 or 2 2/5 pounds.
Therefore, Lia gave away 2 2/5 pounds of the trail mix.
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PLEASE HELP ASAP!!!
ABCD is an isosceles trapezoid with legs ▁AB and ▁CD, and base ▁BC.
If the length of ▁AB = -3y+54, the length of ▁BC = 5y+ 2, and the length of ▁CD is 6y + 9, find the value of y.
Answers
The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.
What is Triangle ?
Triangle can be defined as which contains three sides, three angles and the sum of the angles is 180 degrees.
Given ,
ABCD is an isosceles trapezoid with legs AB and CD and base BC.
If the length of AB is (7y - 4),
the length of BC s (4y - 6),
and the length of CD is (8y - 18).
The two legs are of equal length In any isosceles trapezoid that means:
7y - 4 = 8y - 18
Add 18 on both sides in the above equation.
7y - 4 + 18 = 8y - 18 + 18
7y + 14 = 8y
Now, subtract 7y on both sides in the above equation.
7y + 14 - 7y = 8y - 7y
Simplify the above expression in order to get the value of 'y'.
y = 14
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Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
Answer: 18pi + 36 + (36-4.5pi)+4.5pi= 22.5pi + 36 + (36-4.5pi)
Step-by-step explanation:
CDEF is a square so all sides of CDEF are 6cm.
This tells us the area of CDEF which is 36cm squared
This tells us the radius of AE which is the side FE which we know is 6cm.
Area of a half circle= pi x r squared/2
Area of AE= pi x 36/2= 18pi
Now, look at the square with the half circle inside ABCF. If the half circle was part of the shaded square, the area would be 36cm squared. But since it isn't we need to minus the area of the half circle from 36cm square (area of ABCF)
Area of half circle BC= pi x 3 squared/2= pi x 9/2= 4.5pi.
So the area of ABCF is 36-4.5pi.
CD would also have an area of 4.5pi as it is the exact same half circle.
Area of AE=18pi cm squared
Area of CDEF= 36cm squared
Area of ABCF= 36-4.5pi
Area of CD= 4.5pi
18pi+36+(36-4.5pi)+4.5pi
simplified to:
22.5pi + 36 + (36-4.5pi)
What is the meaning of △?
Answers
Meaning of the △ is: the given symbol is the representation of the geometrical figure triangle.
Different symbols used to represent the different geometrical figures.The given symbol has three sides.Symbol also represents three interior angles.When three sides intersect with each other it represents the vertices.The triangle represents the 2 dimensional shape.Sum of all the measure of the three interior angles is equal to 180 degree.Symbol of triangle in the geometrical shape is given by △.There are different shape such as square, rectangle, circle and many more.Therefore, the meaning of the given symbol △ is the representation of the triangle.
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Explain why the triangles are similar and solve x and y
Answers
Answer:
x = 24
y = 26
Step-by-step explanation:
The triangle are similar because,
Each corresponding angles in the triangles are equal (AAA).
From the diagram,
5/10 = 12/x
Solving for x
x = (10×12)/5
x = 24
Also applying pythagoras theorem to get the hypotenuse of the larger side in the biggerr triangle.
y² = √(10²+24²)
a = √(100+576)
a = √(676)
a = 26.
help fast plss i have 0 brain cells to do this
Answers
Answer:
-3x3x-3x-3
Get yourself some braincells in the future, please.
William has 3 green shirts, 1 white shirt, and 2 blue shirts in his closet. William randomly selects 2 of these shirts from his closet. What is the probability of selecting a green shirt and a white shirt without replacement?
A. 1/9
B. 1/8
C. 1/12
D. 1/10
Answers
Answer:
d
Step-by-step explanation:
Richard has an account of -75 dollars. Which of the following equations accurately describes the size of Richards debt ?
(A.)Absolute value of (-75) meaning that Richard has a debt of 75 dollars
(B.) Absolute value of (-75) meaning that Richard has a debt of -75 dollars
(C.) -75=75 meaning that Richard has a debt of 75 dollars
(D.) Absolute value of (75)= -75 meaning that Richard has a debt of -75 dollars
Pls help me !!!!
Answers
Answer:
(A.) would be the answer.
Answer:
(A.)Absolute value of (-75) meaning that Richard has a debt of 75 dollars
Step-by-step explanation:
A produce manufacturer fills bags of baby carrots by weight. Each bag is supposed to have 12 ounces of baby carrots. Unfortunately, 3% of the baby carrots are discolored. Let X represent the number of discolored baby carrots in a bag.
Are the conditions for a binomial setting in this scenario met?
No, there is no fixed number of baby carrots.
Yes, all four conditions in BINS have been met.
No, we are sampling the carrots without replacement.
No, 3% is a very small probability, so we should not carry out a binomial procedure.
Answers
Answer:
It is A) No, There is no fixed number of baby carrots.
edge 100%
Step-by-step explanation:
Find the lope of a line parallel to the line whoe equation i 6xy=-36xy=−3. Fully implify your anwer
Answers
The line parallel to 6y = -36x -3 will have the same slope which will be -6.
What is Slope of a line ?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
The equation of the line is
6y = -36x -3
⇒y = -6x - 1/2
From slope intercept form of the equation we know that
equation of the line is y = mx + c
where m is the slope.
Therefore,
slope the line is -6
The line parallel to 6y = -36x -3 will have the same slope which will be -6.
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WILL GIVE BRAINLIEST PLZ HELP FAST!!! Jacque estimates the square root of 125 in the following way:
√125=5√25=5∙5=25
Explain why his reasoning is incorrect.
Approximate the square root of 125 using the perfect squares approximation method. Your answer should be a mixed fraction. Make sure to show your work.
Answers
Answer:
5Step-by-step explanation:
√125/5 = √25 since 125/5 = 25√25 = 5Hopes this helps. Mark as brainlest plz!Find the approximate volume of the figure. Round to the nearest tenth if
necessary. Use 3.14
Answers
Answer:
C. 267.9^3
Step-by-step explanation:
so if you use actual pi you get 268.08^3 since I use calculators... and since were using 3.14 instead of actual pi, it makes it so the answer has to be the third option.
I hope this helps :))
Stacy wants to buy a tree to decorate her apartment. Her living room has 8 foot high ceilings. The height of each tree she is interested in buying is given below. Which tree(s) can she buy so that they fit in her living room? Choose all that apply
A. 108 inches
B. 114 inches
C. 94 inches
D. 79 inches
or other you can type what you got
Answers
Answer:
C And D
Step-by-step explanation:
94 Inches Is 7.8 Feet Tall & 79 Inches is 6.5 Feet Tall
Answer:
C and D
Step-by-step explanation:
You should start by changing the inches to feet
(there are 12 inches in foot [ 12 inch = 1 foot ])
A. 9 foot
B. 9.5
C. about 7 feet
D. about 6 feet
C and D are correct. Hope this helps!
Tony bought a shirt for $40 and a second one at 50 percent off.
What was the total cost before taxes?
There was a 5percent tax. How much did Tony pay in total?
Answers
Do they give you an answer options??
HELP HELP HELP HELP HELP HELP ME PLEASE 20 POINTS
Answers
Answer:
Step-by-step explanation:
The y intercept is (0,5)
The slope is found from choosing 2 points on the line. My choice is (4,13) and (0,5)
x2 = 4
x1 = 0
y2 = 13
y1 = 5
slope = (y2 - y1)/(x2 - x1)
slope = (13 - 5)/(4 - 0) = 8/2 = 4
If I'm right answers A and D are both wrong. We don't know exactly what the 5 represents. I would say it is the beginning number of songs she knows when she starts graphing. In any event, B is not the answer.
That leaves C.
y = 2x + 5
x = 20
y = 2*20 + 5
y = 45
(20,45) is on the line