The following graph shows a proportional relationship.
What is the constant of proportionality between yyy and xxx in the graph?
Answers
Answer:
The constant of proportionality is thus 1
Step-by-step explanation:
Note that the green line passes through (6, 6) and has a y-intercept of 0. Thus, the equation of the line is y = (6/6)x + 0, or y = x, or y = 1x.
The constant of proportionality is thus 1, which is also the slope of this line.
Related Questions
find x,y,z : 4x^2+2y^2+2z^2-4xy-4xz+2yz-2y+6z+10=0
Answers
I hope this helps.
Answer:-
∴x−3y−4z=0
Explanation:
First we rearrange the equation of the surface into the form f(x,y,z)=0
x2+2z2=y2
∴x2−y2+2z2=0
And so we have our function:
f(x,y,z)=x2−y2+2z2
In order to find the normal at any particular point in vector space we use the Del, or gradient operator:
∇f(x,y,z)=∂f∂xˆi+∂f∂yˆj+∂f∂zˆk
remember when partially differentiating that we differentiate wrt the variable in question whilst treating the other variables as constant. And so:
∇f=(∂∂x(x2−y2+2z2))ˆi+
(∂∂y(x2−y2+2z2))ˆj+
(∂∂z(x2−y2+2z2))ˆk
=2xˆi−2yˆj+4zˆk
So for the particular point (1,3,−2) the normal vector to the surface is given by:
∇f(1,3,−2)=2ˆi−6ˆj−8ˆk
So the tangent plane to the surface x2+2z2=y2 has this normal vector and it also passes though the point (1,3,−2). It will therefore have a vector equation of the form:
→r⋅→n=→a⋅→n
Where →r=⎛⎜⎝xyz⎞⎟⎠; →n=⎛⎜⎝2−6−8⎞⎟⎠, is the normal vector and a is any point in the plane
Hence, the tangent plane equation is:
⎛⎜⎝xyz⎞⎟⎠⋅⎛⎜⎝2−6−8⎞⎟⎠=⎛⎜⎝13−2⎞⎟⎠⋅⎛⎜⎝2−6−8⎞⎟⎠
∴(x)(2)+(y)(−6)+(z)(−2)=(1)(2)+(3)(−6)+(−2)(−8)
∴2x−6y−8z=2−18+16
∴2x−6y−8z=0
∴x−3y−4z=0
The ground temperature at an airport is 14 "C. The temperature decreases by 6.2 "C for every increase of 1 kllometer above the ground. What is the temperature outside a plane flying at an altitude of 5 kilometers?
Answers
Answer:
-17 C
Step-by-step explanation:
14 - 5(6.2) = 14 - 31 = -17 C
Solve the equations.
[tex]3(x+4)^{2} =10x+32\\(x+4)^{2} =3x+40\\\frac{x^{2} -1}{2} -11x=11[/tex]
Answers
Answer:
a) x = {-2 2/3, -2}
b) x = {-8, 3}
c) x = {-1, 23}
Step-by-step explanation:
If all you want are solutions, a graphing calculator can give them to you easily. The attachment shows the solutions as x-intercepts when the equation is rearranged to the form f(x) = 0.
__
In general, it can be convenient to write the equation in standard form with integer coefficients. Common factors among the coefficients should be removed.
a)3(x+4)^2 = 10x +32 . . . . . given
3(x^2 +8x +16) -10x -32 = 0
3x^2 +14x +16 = 0
To factor this, we're looking for factors of 3·16 that total 14.
48 = 1·48 = 2·24 = 3·16 = 4·12 = 6·8
The last pair of factors has a total of 14, so we can rewrite the equation as ...
(3x +6)(3x +8)/3 = 0
(x +2)(3x +8) = 0
The solutions are the values of x that make the factors zero:
x = -2, x = -8/3
__
b)(x +4)^2 = 3x +40 . . . . . . . . given
x^2 +8x +16 -3x -40 = 0 . . . . subtract the right side
x^2 +5x -24 = 0 . . . . . . . . simplify
(x +8)(x -3) = 0 . . . . . . factor
The solutions are the values of x that make the factors zero:
x = -8, x = 3
__
c)(x^2 -1)/2 -11x = 11 . . . . . given
x^2 -1 -22x -22 = 0 . . . . . . multiply by 2, subtract the right side
x^2 -22x -23 = 0 . . . . . . simplify
(x -23)(x +1) = 0 . . . . . . factor
x = 23, x = -1
_____
Additional comment
Factoring often gets to the solution with the least fuss when the solutions are rational. There are several ways factoring can be done when the leading coefficient is not 1. One of them is illustrated in (a) above. We will show two other methods that give the same result.
factoring by pairs
We have identified the factors of 3·16 = 48 that have a total of 14. We can use those factors to rewrite the 14x term in the equation.
3x^2 +6x +8x +16 = 0
Now, we can group the terms in pairs, and factor each pair. It does not matter which of the factors (6 or 8) you write first. You will end with the same result.
(3x^2 +6x) +(8x +16) = 0
3x(x +2) +8(x +2) = 0
(3x +8)(x +2) = 0 ⇒ x = -8/3, x = -2
__
factoring using the X method
This method is usually shown using a large graphic X. In the top quadrant is written the product of the leading coefficient and the constant: 3·16 = 48.
In the bottom quadrant is written the coefficient of the x-term: 14.
If one or the other, or both, of these top/bottom values is negative, be sure to keep the sign.
The side quadrants are then filled with values that have a product equal to the top number, and a sum equal to the bottom number. (Pay attention to the signs.) Further, in each of those quadrants, the number written is divided by the leading coefficient, and the fraction reduced to lowest terms.
Here, we would have 6/3 = 2 on one side, and 8/3 on the other side. Now the factors are written as (bx+a), where the reduced fraction on either side is a/b. In our example, the factors are (x+2) and (3x+8)
__
alternate X method
This starts off in the same way the X method does, as described above. However, the factors on either side of the X are not divided by the leading coefficient (a). If those side values are 'p' and 'q', the quadratic is written in factored form as ...
(ax +p)(ax +q)/a = 0
You will notice we used this form above: (3x +6)(3x +8)/3 = 0.
Now, the divisor 'a' can be used to reduce either or both of the numerator factors. Here, the entire factor of 3 can be removed from (3x+6) to make the factorization be ...
(x +2)(3x +8) = 0
__
Sometimes, one factor of the divisor will be removed from one term, and the other factor of it will be removed from the other term. An example of this might be ...
[tex]\dfrac{(6x+3)(6x+2)}{6}=\dfrac{6x+3}{3}\cdot\dfrac{6x+2}{2}=(2x+1)(3x+1)[/tex]
3x - 7 = 3x + 9; x =
Please can someone help me and show me the answers step by steps
Answers
Answer:
i think probably x∉∅
Step-by-step explanation:
3x-7 = 3x+9
-7 = 9
so x∉∅
Answer:
0 = 16 or No Solution
Step-by-step explanation:
1) Add 7 to both sides of the equation
3x - 7 + 7 = 3x + 9 + 7
2) Simplify
A. Add the numbers
3x = 3x + 9 + 7
B. Add the numbers
3x = 3x + 16
3) Subtract 3x from both sides of the equation
3x - 3x = 3x + 16 - 3x
4) Simplify
A. Combine like terms
0 = 3x + 16 - 3x
B. Combine like terms
0 = 16
10 x + 2 y . Find P when: x = 3 and y = 6
help pleaseee
Answers
Answer:
42
Step-by-step explanation:
(10x3) + (2x6)
= 30 + 12
= 42
10x + 2 y = (10.3) +(2.6) = 30+12=42
Our answer is 42
y=-2x2+12x-26
Rewrite the equation in vertex form and identify the vertex, the axis of symmetry, and the y-intercept.
Answers
Answer:
y = 12x - 22
Step-by-step explanation:
If we first write the equation in vertex form and we identify it (I think you meant to simplify y) we get y = 12x - 22 as your answer!
a store is handing out scratch-off cards to its customers .for each card a customer wins either a coupon or a free t-shirt .the ratio of coupon cards to t-shrits is 9:2 .the total of 8,250 cards how many of the cards are t-shirts cards
Answers
Step-by-step explanation:
Ratio 9:2, therefore total number of shares is 11.
because 9+2 = 11
total cards = 8,250
8,250/11 = 750
This is the value for one of the shares.
As the ratio is 9:2 we can find:
9 X 750 : 2 X 750
To see what everyone has won.
T-shirts : 2 X 750 = 1,500.
Hope you understand how it's done, if not leave a comment and I'll try to be more thorough
What the vertex of y=4(x-3)^2+3
Answers
Answer:
(3,3)
Step-by-step explanation:
we rewrite in vertex form and use this form to find the vertex (h,k)
Solve the following system of equations.
4x + 7y= 18
- 7x - 8y = -23
X =
y =
Answers
im lazy to solve in my paper hope it helps
What is the length of the mid segment AB??
Answers
Answer:
14.5
Step-by-step explanation:
AB is halfway between MN and PO. this means it would be the distance halfway between 9 units (length of MN) and 20 units (length of PO). to find this, find the average of 20 and 9. 20+9= 29. 29/2= 14.5
which is a better deal? 5 pens for $1.85 OR 8 pens for $3.12 ? find the unit rate
Answers
Answer:
5 pens
Step-by-step explanation:
1.85 divided by 5 is .37
3.12 divided by 8 is .39
so 1.85 is a better deal
plsss help mee i donot now the answer
Activity 1: Identifying Hypothesis and Conclusion Directions: Identify the hypothesis and the conclusion for each of the following statements.
1. If you live in Manila, then you live in the Philippines.
2. If a triangle is a right triangle, then one of its interior angle is a 90-degree angle.
3. A square is not a triangle.
4. An even number is divisible by 2.
5. The measure of an acute angle is less than 90.
Answers
Answer:
1. If you live in Manila(hypothesis) then you live in the Philippines ( conclusion)
2. If a triangle is a right triangle (hypothesis), then one of its interior angle is a 90-degree angle ( conclusion)
3. A square is not a triangle (conclusion)
4. An even number is divisible by 2. (conclusion)
5. The measure of an acute angle is less than 90. (conclusion)
Given the function f(x) x^2-2x/x^3 +9x^2-10x Find any holes, vertical asymptotes, and horizontal asymptotes there may be.
Answers
Answer:
See below
Step-by-step explanation:
I assume you mean [tex]f(x)=\frac{x^2-2x}{x^3+9x^2-10x}[/tex]:
Holes: Since [tex]f(x)=\frac{x^2-2x}{x^3+9x^2-10x}[/tex] reduces to [tex]f(x)=\frac{x(x-2)}{x(x^2+9x-10)}[/tex], then there is a hole at [tex]x=0[/tex] as [tex]x[/tex] exists in both the numerator and denominator (however, its limit as x approaches 0 is 1/5).
Vertical Asymptotes: If we further reduce [tex]f(x)=\frac{x(x-2)}{x(x^2+9x-10)}[/tex] to [tex]f(x)=\frac{x-2}{(x+10)(x-1)}[/tex], then we see that there are vertical asymptotes at [tex]x=-10[/tex] and [tex]x=1[/tex]
Horizontal Asymptotes: As the degree of the numerator is less than the degree of the numerator ([tex]2<3[/tex]), then there is a horizontal asymptote at [tex]y=0[/tex]
23.15 – [ 115 + ( 12 - 25)]
Answers
Answer:
-78.85
Step-by-step explanation:
Using Order of Operations (PEDMAS):
23.15 – [ 115 + ( 12 - 25)]
= 23.15 – [ 115 + (-13)]
= 23.15 – [ 115 - 13]
= 23.15 - 102
= -78.85
Maija is bicycling north on a straight path. She bicycles for
17.
4
kilometers when she realizes she is
thirsty. Maija remembers passing a water fountain
2 kilometers earlier By rounding to the nearest
whole number, estimate the distance from the beginning of Maija's ride to the water fountain
Answers
Answer:
The awnser is 19 Kilometers
Can i get some help ?:
Answers
Answer:
7 + 3² - 2.5 / 4 - 1.2 > ( 3/4 + 1/8 ) ÷ 1/8 - 2²
Step-by-step explanation:
7 + 3² - 2.5 / 4 - 1.2 = 4.82142857
( 3/4 + 1/8 ) ÷ 1/8 - 2² = 3
Which means :
7 + 3² - 2.5 / 4 - 1.2 > ( 3/4 + 1/8 ) ÷ 1/8 - 2²
What does point G represent in the context of this situation?
Answers
Answer:
The famous point G that everyone enjoys... of course it represents a point of a graph! What else could it be? G stands for graph.
Use the quadratic formula to solve for x.
9x^2-3x=1
Round the answer to the nearest hundredth
Last question.
Answers
X= 1-5/6
The probability of event A is 0.53 and the probability of event B is 0.17. The probability of A and B occurring is 0.901. Which statement accurately describes these two events?
Answers
Explanation:
We're given that
P(A) = 0.53P(B) = 0.17P(A and B) = 0.901Note that P(A)*P(B) = 0.53*0.17 = 0.0901 which is somewhat similar to 0.901 but not entirely the same. We have an extra zero between the decimal point and the nine. So this indicates that [tex]P(A)*P(B) \ne P(\text{A and B})[/tex]. Therefore, events A and B are not independent. We consider them dependent.
Can someone please give me the (Answers) to this? ... please ...
Answers
b.) We are given two triangles with a pair of corresponding, congruent sides. We need to have a pair of corresponding, congruent angles, another pair of corresponding, congruent sides to follow SAS. Therefore, we would need to know the angle measures of angles UVW and KVM. We know that they are vertical angles, so they are indeed congruent. Now, we would need to know the side lengths of sides WV and VM. If those sides are congruent, then we have a pair of corresponding, congruent sides, a pair of corresponding, congruent angles, and another pair of corresponding, congruent sides, making SAS.
c.) The Angle Side Angle Postulate states that if there is a pair of corresponding, congruent angles, a pair of corresponding, congruent sides, and another pair of corresponding, congruent angles in two triangles, then the two triangles are congruent. We have a pair of corresponding, congruent angles, a pair of corresponding, congruent sides, but we need another pair of congruent, corresponding angles. Therefore, we would need to know the angle measures of angles MLK and STU. Then we would have a a pair of corresponding, congruent angles, a pair of corresponding, congruent sides, and another pair of corresponding, congruent angles.
Please give Brainliest! This took a lot of time!
Answer:
To be congruent at b. no. UV= VK,V=V,UW=KM.
To be congruent at C no. M=S,LM=ST,LK=TU.
Why is the slope the same on a line when different points are used to identify the slope?
Answers
Therefore the slope is the same because the line passes through both those points.
Different points can be used to identify the slope as follows -
We have a straight line.
We have to investigate why is the slope same on a line when different points are used to identify the slope.
What is Slope of a Line ?The slope of a line is denoted by m and is defined as the change in y coordinate with respect to the change in x coordinate.
According to question -
Different points can be used to identify the slope provided that they all lie on the same straight line. Line is a collection of points and these set of points can be used top determine the rate of change of y with respect to x. The slope of a line can also be found out using y - intercept of the line using the general equation of straight line -
y = mx + c.
Hence, the slope is same on a line provided that they all lie on the same straight line
To solve more questions on Slope of lines, visit the link below -
https://brainly.com/question/10623813
#SPJ2
2a- 1-4 1/3a+ 7-a consider the linear expression what are the like terms in the expression simplify the linear expression
Answers
Answer:
2a7-1
Step-by-step explanation:
Anybody know the answer !!
Answers
Answer:
17.08
Step-by-step explanation:
When it reaches its maximum, suppose that y = 0
Therefore you will need to factorise and solve
-16x^2 + 267 x + 107 = 0
Here you can use the quadratic equation[tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
Where you will get x = -0.39 seconds or 17.08 seconds (rounded to 2 decimal places according to the question
Because -0.39 is negative, this answer can be deleted
Leacing x = 17.08 seconds
Solve for x.
(−19)2=x
Answers
Answer:
Step-by-step explanation:
Answer:
x=-38
Step-by-step explanation:
-19*2=-38
Hope this helps! Pls give brainliest! Also sub to kgir633 on yt.
what expressions are equivalent to 7 ^ 8 x 7 ^ -4
Answers
Answer:
7^4
Step-by-step explanation:
The equivalent expression 7^8 x 7^-4 using a single exponent is 7^4
How to write the expression using a single exponent.From the question, we have the following parameters that can be used in our computation:
7 ^ 8 x 7 ^ -4
This means that
7^8 x 7^-4
Apply the law of indices
So, we have
7^8 x 7^-4 = 7^(8 - 4)
This gives
7^8 x 7^-4 = 7^4
Hence, the solution is 7^8 x 7^-4 = 7^4
Read more about expressions at
brainly.com/question/30492964
#SPJ3
can anyone plz help me with this math problem
Answers
A music store purchases a grand
piano, wholesale, for $5,000.
They markup the retail price 65%.
What is the retail price?
Answers
Answer: 8250
Step-by-step explanation:
Answer:
8548
Step-by-step explanation:
what is the approximate value of a local maximum for the polynomial
Answers
Answer:
D) 2.5
Aaliyah- ツ
Oscar has baskets that each contain 25 apples. Each day 2 apples are
eaten from each basket. Oscar has (25 – 2d) apples left afterd days in
one basket. If Oscar has 7 baskets of apples, how many apples are left
after d days?
Answers
Answer:
175 -14d
Step-by-step explanation:
There will be 7 times as many as in one basket.
7(25 -2d) = 175 -14d . . . . total apples left
Last week, you finished Level 2 of a video game in 32 minutes. Today, you finish Level 2in 28 minutes. What is your percent of change
Answers
Answer:
12.5% decrease
Step-by-step explanation:
[(V2 - V1) / V1] x 100 = Percent Change