Answer:
z=312 if you meant x=26
Step-by-step explanation:
Direct proportional means there is a constant k such that z=kr. k is called the constant of proportionality. The constant k will never change no matter your (x,z).
So using our equation z=kr with point (18,216) we will find k.
216=k(18)
Divide both sides by 18
216/18=k
k=216/18
Simplify
k=12
So we now know the equation fully that satisfies the given conditions of directly proportion and goes through (x,z)=(18,216).
It is z=12x.
Now we want to know the value of z if x=26.
Plug it in. z=12(26)=312
z=312
Rachel is making bouquets she has 72 carnations and 48 roses. Each bouquet has the same number of flowers, with no flowers left over. What is the greatest number of bouquets she can make?
There are 24 bouquets making by Rachel.
What is Factor?
A number which means to break it up into numbers that can be multiplied together to get the original number.
Now, To solve this problem,
Let us first lay out all the factors of each number.
72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
So, The greatest number of bouquets that can be made would be equal to the greatest common factor of the two numbers 72 and 48 will 24.
Hence, There are 2 bouquets making by Rachel.
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Rachel can make 24 bouquets with 72 carnations and 48 roses.
To determine the greatest number of bouquets Rachel can make with 72 carnations and 48 roses, we need to find the greatest common divisor (GCD) of 72 and 48. The GCD is the largest number that divides both 72 and 48 without leaving a remainder.
Here are the steps to find the GCD:
List the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72List the factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48Identify the common factors: 1, 2, 3, 4, 6, 8, 12, 24The greatest common factor is 24.The table below shows the cube roots of different numbers:
Number
(x) 8 27 64 125
Cube root
(y) 2 3 4 5
Part A: Does the table represent y as a function of x? Justify your answer. (5 points)
Part B: The total cost f(x), in dollars, for renting a bike for x hours is shown below:
f(x) = 10 + 20x
What is the value of f(100), and what does f(100) represent? (5 points)
part A)
[tex]\bf \begin{array}{|c|cccccc|ll} \cline{1-7} x&8&27&64&125&&x\\ \cline{1-7} y&\stackrel{\sqrt[3]{8}}{2}&\stackrel{\sqrt[3]{27}}{3}&\stackrel{\sqrt[3]{64}}{4}&\stackrel{\sqrt[3]{125}}{5}&&\sqrt[3]{x} \\ \cline{1-7} \end{array}~\hspace{10em}y = \sqrt[3]{x}[/tex]
part B)
f(x) = 10 + 20x
so if you rent the bike for a few hours that is
1 hr.............................10 + 20(1)
2 hrs..........................10 + 20(2)
3 hrs..........................10 + 20(3)
so the cost is really some fixed 10 + 20 bucks per hour, usually the 10 bucks is for some paperwork fee, so you go to the bike shop, and they'd say, ok is 10 bucks to set up a membership and 20 bucks per hour for using it, thereabouts.
f(100) = 10 + 20(100) => f(100) = 2010.
f(100), the cost of renting the bike for 100 hours.
Drag the correct steps into order to evaluate 27 – t • 3 for t = 6.
Answer:
Step-by-step explanation:
Step 1 : 27-t*3
Now put the value t=6
Step 2:
=27-6*3
According to the DMAS rule multiplication wll be solved first.
Step3:
=27-18
Step 4:
=9 ....
-f(3f-7)=0 solve equation
Answer:
F=0 or (7/3)
Step-by-step explanation:
When F is 0, the equation reads -0(3(0)-7)=0. The outside 0 will multiply by everything and make it equal 0. When F is 7/3, the inside of the parenthesis read 3(7/3)-7. This equals 7-7. It'll end up being (7/3)0, which equals 0.
NEED HELP ASAP PLEASE
Answer:
AAS theorem
Step-by-step explanation:
Angle SUT = Angle TVS (given)
Angle SRY = Angle TRV (vertically opposite angles)
SU = TV (given)
So, Triangle SUR is congruent to triangle TVR by AAS theorem.
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Consider the quadratic equation 2x2 + 3x + 5 = 0.
The discriminant of this quadratic equation is ________ zero.
This means the quadratic equation will have ________ real solution(s) and _______ complex solution(s).
Answer:
The discriminant of this quadratic equation is less than zero.
This means the quadratic equation will have no real solution(s) and two complex solution(s).
Step-by-step explanation:
The discriminant is found using the formula b^2 - 4ac.
Therefore, the discriminant is (3)^2 - 4(2)(5), which yields -31.
Since the discriminant is negative, there are no real solutions.
Answer: less then
No
Two distinct
Step-by-step explanation:
Consider the table of values for function f.
x: -1, 0, 1, 2, 3, 4, 5
f(x): 3.5, 4, 5, 7, 11, 19, 35
The function g is shown below:
g(x)=4x+5
In which of the following intervals is the average rate of change greater for f than for g?
A. [1,3]
B. [3,5]
C. [0,2]
D. [-1,0]
Answer:
B. [3,5]
Step-by-step explanation:
The rate of change of a function is the same as the slope between two given points from that same function,
Hence,
all we need to do is use the slope's equation, that is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
And eval it in every couple of ordered pairs given from the table we obtain the following>
x2 y2 x1 y1 m
0 4 -1 3,5 0,5
1 5 0 4 1
2 7 1 5 2
3 11 2 7 4
4 19 3 11 8
5 35 4 19 16
The rate of change from g(x) is 4 (its slope)
Hence, the interval when the rate of change of f(x) is greater than g(x) is from x=3 to x=5
Which statement best describes the polynomial -8x^4 ? first degree polynomial with two terms fourth degree polynomial with two terms fourth degree monomial second degree binomial
Answer:
fourth degree monomial
Step-by-step explanation:
-8x^4
There is one term so it is a monomial
The highest power is degree 4, so it would be a quartic
5. Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set, and P = {1, 3, 5, 7}. What is p'? (1
point)
{2, 4, 6, 8)
{1, 2, 3, 4, 5, 6, 7, 8
O {1, 3, 5, 7}
{1, 3, 5, 7, 8)
Answer:
p' = {2, 4, 6, 8}.
Step-by-step explanation:
The set p' has all the elements in the universal set U that are not in set p.
p' = {2, 4, 6, 8}.
Step-by-step answer:
U = universal set (all possible members)
P = given set
P' = complement of P, i.e. contains all members in U but NOT 1,3,5,7in P.
Thus, U=P or P'.
Here,
U={1,2,3,4,5,6,7,8}
P={1,3,5,7}
so P'={2,4,6,8}
Check: P or P' ={1,3,5,7} or {2,4,6,8} = {1,2,3,4,5,6,7,8} = U good !
What is the range of this relation (2,-3),(-4,2),(6,2),(-5,-3),(-3,0)
Answer:
Range of this relation = -3, 2
Step-by-step explanation:
We are given the following relation and we are to find its range:
[tex](2,-3),(-4,2),(6,2),(-5,-3),(-3,0)[/tex]
The set of all the possible dependent values a relation can produce from its values of domain are called its range. In simple words, it is the list of all possible inputs (without repeating any numbers).
Therefore, the range of this relation is: -3, 2
Answer: [tex]Range:[/tex]{[tex]-3,0,2[/tex]}
Step-by-step explanation:
The range of a relation is the set of y-coordinates of the ordered pairs (These are the second numbers of each ordered pair).
In this case you have the following relation:
[tex](2,-3),(-4,2),(6,2),(-5,-3),(-3,0)[/tex]
Therefore, based on the explained bofore, you can conclude that the rsnge of the given relation is the following:
[tex]Range:[/tex]{[tex]-3,0,2[/tex]}
(Notice that you do not need to write the same number twice)
A bag contains 5 blue, 3 red, and 8 green marbles. You choose a marble, do not replace it, and then choose another one. What is the probability that both marbles are red?
Answer:
1/40
Step-by-step explanation:
A bag contains 5 blue, 3 red, and 8 green marbles
You have (5+3+8=16) marbles
P(red 1) = red/total = 3/16
You do not replace it
A bag contains 5 blue, 2 red, and 8 green marbles
You have (5+2+8=15) marbles
P(red 2nd) = red/total = 2/15
P(red 1, red 2) = P (red 1)* P (red 2) = 3/16 * 2/15
=1/40
Find the domain of the graphed function.
-10
The domain is the X values.
There are two dots located at x = -4 and x = 9
The answer would be: D -4 < x < 9
The domain of the graphed function is - 4 ≤ x ≤ 9, that is option D. This can be obtained by finding all the x-values.
What is the domain of the graph?⇒Domain is all x-values of a function.
From the graph, we can say that the graph start from (-4,-4) to (8,9).
Thus x-values are from -4 to 9.
Since the endpoints are closed circles the points -4 and 9 are included.
∴The required domain is - 4 ≤ x ≤ 9
Hence the domain of the graphed function is - 4 ≤ x ≤ 9, that is option D.
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a plain takes off at an angel of 20 degree. assuming a constant speed and trajectory, by the time it has travelled 25 kilo meter horizontally, how h8gh it will be fly
Answer:
9.10 km to the nearest hundredth.
Step-by-step explanation:
We have a triangle whose adjacent side is 25 km and angle 20 degrees.
If h is the height we have the equation:
tan 20 = h / 25
h = 25 tan 20
= 9.099 km.
GCF of 32ab cubed and 40a squared
Answer:
8a.
Step-by-step explanation:
32 = 2*2*2*2*2
40 = 2*2*2* 5
Thus the GCF of 32 and 40 is 2*2*2 = 8.
The GCF of a and ab = a.
For this case we must find the GCF of the following expressions:
[tex]32ab ^ 3\\40a ^ 2[/tex]
By definition, the GCF is given by the largest factor that divides both numbers without leaving residue.
We look for the factors of 32 and 40:
32: 1,2,4,8,16
40: 1,2,4,5,8,10,20
Thus, the GCF is 8.
On the other hand, the GCF of [tex]ab ^ 3[/tex]and [tex]a ^ 2[/tex] is a.
Finally, the GFC of the expressions is:
[tex]8a[/tex]
Answer:
[tex]8a[/tex]
What is the sum of The square root of negative 2 and the square root of negative 18
Answer:
[tex]\large\boxed{\sqrt{-2}+\sqrt{-18}=4\sqrt2\ i}[/tex]
Step-by-step explanation:
[tex]\sqrt{-1}=i\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\===================\\\\\sqrt{-2}+\sqrt{-18}=\sqrt{(2)(-1)}+\sqrt{(9)(2)(-1)}\\\\=\sqrt2\cdot\sqrt{-1}+\sqrt9\cdot\sqrt2\cdot\sqrt{-1}\\\\=\sqrt2\cdot i+3\cdot\sqrt2\cdot i\\\\=i\sqrt2+3i\sqrt2=4i\sqrt2[/tex]
The sum of √-2 and √-18 is 4√2i.
What is the square root of -1?The square root of -1 is an imaginary number which is represented by i.
√-1=i
Here we have to calculate √-2+√-18
√-2+√-18
=√(-1).2+√(-1).18
=√(-1).√2+√(-1).√18
=i√2+i√18 (as √-1=i where i is imaginary number)
But √18=√(9*2)=√9*√2=3√2
(as √(ab)=√a.√b)
=i√2+i3√2
=√2(i+3i)
=√2*4i
=4√2i
Therefore the sum of √-2 and √-18 is 4√2i.
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all of the following expressions have the same value except... -4/5-1/5 -(4/5+1/5) -4/5+ -1/5 -4/5-(-1/5)
Answer:
-4/5-(-1/5)
Step-by-step explanation:
-4/5-1/5 is equivalent to -4/5+-1/5 which equals -1
-(4/5+1/5) when you add the expression in the parenthesis you get 1 and when you multiply that by -1 you get -1
-4/5+ -1/5 this is like the first choice so it equals -1
-4/5-(-1/5) this expression is the equivalent to -4/5+1/5 which gives you -3/5
The last option is -3/5 while the others are -1 which it the one with the different value
All of the expressions have the same value except -4/5 - (-1/5).
Explanation:In this case, all of the expressions have the same value except -4/5 - (-1/5).
To simplify each expression:
-4/5 - 1/5 can be simplified to -5/5 which is equal to -1.-(4/5 + 1/5) can be simplified to -5/5 which is also equal to -1.-4/5 + (-1/5) can be simplified to -5/5 which is still equal to -1.Finally, -4/5 - (-1/5) can be simplified to -4/5 + 1/5. Adding these fractions gives us -3/5.Therefore, the expression that has a different value is -4/5 - (-1/5).
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A 10 kg ball is traveling at the same speed as a 1 kg ball. Compared to the 10 kg ball, the 1 kg ball has...
Answer: The 1-kg ball has 1/10 as much kinetic energy as the 10-kg ball.
Step-by-step explanation:
Option (a) - "less momentum" - accurately describes the relationship between the momentum of the 1 kg ball compared to the 10 kg ball.
The momentum of an object is directly proportional to its mass. When comparing a 10 kg ball to a 1 kg ball traveling at the same speed, the 10 kg ball has more momentum due to its greater mass. Since momentum is determined by both mass and velocity, and the velocity is the same for both balls, the difference in momentum is solely due to the difference in mass. The 10 kg ball has ten times the mass of the 1 kg ball. Therefore, the 1 kg ball has less momentum compared to the 10 kg ball. In fact, it has one-tenth of the momentum of the 10 kg ball.
Complete question: A 10 kg ball is traveling at the same speed as a 1 kg ball. Compared with the 10 kg ball, the 1 kg ball has
a-less momentum.
b-twice momentum.
c-five times the momentum.
d-the same momentum.
Find the limit of the function by using direct substitution. (6 points) limit as x approaches zero of quantity x squared minus three.
Answer:
[tex]\lim_{x \to 0} x^2-3=-3[/tex]
Step-by-step explanation:
This limit can be written as follows
[tex]\lim_{x \to 0} x^2-3[/tex]
Direct substitution means that we substitute in the value for x to get our limit
[tex]\lim_{x \to 0} x^2-3\\\\0^2-3\\\\-3[/tex]
[tex]\displaystyle\\\lim_{x\to 0}(x^2-3)=0^2-3=-3[/tex]
f(x) = x^2-5
g(x) = 4x - 4
Find (f-g) (5)
Answer:
The correct answer option is: 4.
Step-by-step explanation:
We are given the following two functions and we are to find the value of [tex] ( f - g ) ( 5 ) [/tex]:
[tex]f(x) = x^2 - 5[/tex]
[tex]g(x) = 4x - 4[/tex]
Finding [tex] ( f - g ) ( x ) [/tex]:
[tex] ( f - g ) ( x ) [/tex] [tex]= (x^2-5)-(4x-4) = x^2-4x-5+4[/tex]
[tex]( f - g ) ( x ) = x^2-4x-1[/tex]
So, [tex]( f - g ) ( 5 ) = (5)^2-4(5)-1 = 4[/tex]
Use the grouping method to factor this polynomial completely.
4x3 + 8x2 + 3x+6
Answer:
(x + 2)(4x^2 + 3)
Step-by-step explanation:
The first two terms factor as follows: 4x^2(x + 2).
The last two factor as follows: 3(x + 2).
Thus, (x + 2) is a factor of 4x3 + 8x2 + 3x+6:
4x^2(x + 2) + 3(x + 2), or:
(x + 2)(4x^2 + 3).
Note that 4x^2 + 3 can be factored further, but doing so yields two complex roots.
Answer: (x + 2)(4x^2 + 3)
Step-by-step explanation:
4x3 + 8x2 + 3x+6 becomes 4x^2(x + 2) + 3(x + 2) and can also be written as (x + 2)(4x^2 + 3).
----------------------
Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!
- Cutiepatutie ☺❀❤
Which best describes the graph of the function f(x)=4x ?
Answer:
F
Step-by-step explanation:
The equation of a line in slope-intercept form is
y = mx + b
where m = slope, and b = y-intercept.
This line has equation
y = 4x
When we compare y = 4x with y = mx + b, we see that m = 4, and b = 0.
This line intersects the y-axis (the y-intercept) at y = 0, which is the origin. The slope is positive, so it slopes up to the right.
Answer: F
The function f(x) = 4x is a linear function, and when graphed, it will produce a straight line with a slope of 4. The graph demonstrates the dependence of y on x and it's an example of a line graph.
Explanation:The question asks for a description of the graph of the function f(x) = 4x.
The function f(x) = 4x is a linear function, which means it creates a straight line when graphed. The number 4 in the function is the slope of the line. This value indicates that for each increase by 1 in the x value, the y value will increase by 4.
This demonstrates the dependence of y on x. So, a graph of this function would be a straight line that slopes upward from left to right, starting at the origin (0,0) and increasing by 4 in the y direction for each step of 1 in the x direction. This is a typical representation of a linear function demonstrating the relationship between two variables on a line graph.
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In graphing the equation y<2x -5, the line is dotted and shaded below the line drawn.
True
False
Answer:
True.
Step-by-step explanation:
This is 'less than' so the area below the line is shaded.
It is a dotted line because the solution does not contain points on the line as the inequality sign is < NOT ≤.
Answer:
First option: True.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Given this inequality:
[tex]y<2x -5[/tex]
We know that the line is:
[tex]y=2x -5[/tex]
Whose slope is 2 and the y-intercept is -5
The symbol "<" provided in the inequalty, indicates that the shaded region must be below the line and the line must be dotted. Therefore, the answer is: TRUE.
An equation was used to predict the number of possible enrollments in an afterschool program for the first 6 months of the year. The actual enrollments are also listed.
Actual enrollment 55 80 95 100 115 90
Predicted enrollment 75 80 85 90 95 100
The sum of the residuals is ______.
Answer:
70
Step-by-step explanation:
75-55=20
95-85=10
100-90=10
115-95=20
100-90=10
sum of the differences is 70
Answer:
A: 10
Step-by-step explanation:
Let's add the actual enrollments all together. 55 + 80 + 95 + 100 + 115 + 90 all added together is 535. The predicted enrollments, all added together, is: 75 + 80 + 85 +90 +95 + 100 = 525.
535 - 525 = 10 residuals.
Find the first six terms of the sequence. a1 = 4, an = an-1 + 8
[tex]\bf \begin{array}{llll} term&\stackrel{a_{n-1}+8}{value}\\ \cline{1-2} a_1&4\\ a_2&\stackrel{4+8}{12}\\ a_3&\stackrel{12+8}{20}\\ a_4&\stackrel{20+8}{28}\\ a_5&\stackrel{28+8}{36}\\ a_6&\stackrel{36+8}{44} \end{array}[/tex]
Answer:
The first 6 terms are 4,12,20,28,36,44
Step-by-step explanation:
So we have the recursive sequence
[tex]a_n=a_{n-1}+8 \text{ with } a_1=4[/tex].
If you try to dissect what this really means, it becomes easy.
Pretend [tex]a_n[/tex] is a term in your sequence.
Then [tex]a_{n-1}[/tex] is the term right before or something like [tex]a_{n+1}[/tex] means the term right after.
So it is telling us to find a term all we have to is add eight to the previous term.
So the second term [tex]a_2[/tex] is 4+8=12.
The third term is [tex]a_3[/tex] is 12+8=20.
The fourth term is [tex]a_4[/tex] is 20+8=28.
The fifth term is [tex]a_5[/tex] is 28+8=36
The sixth term is [tex]a_6[/tex] is 36+8=44.
Now sometimes it isn't that easy to see the pattern from the recursive definition of a relation. Sometimes the easiest way is to just plug in. Let's do a couple of rounds of that just to see what it looks like.
[tex]a_n=a_{n-1}+8 \text{ with } a_1=4[/tex].
[tex]a_2=a_1+8=4+8=12[/tex]
[tex]a_3=a_2+8=12+8=20[/tex]
[tex]a_4=a_3+8=20+8=28[/tex]
[tex]a_5=a_4+8=28+8=36[/tex]
[tex]a_6=a_5+8=36+8=44[/tex]
Explain how to model the multiplication of –6 and 3 on a number line
Answer:
Multiplication is basically repeating addition
Step-by-step explanation:
So, on a numberline, start at 0 then add -6 three times (since you are multiplying it by three) and you should get -18
A ball has a surface area of 26.87 square feet. To the nearest tenth of a foot, what is the radius of the ball? Use π = 3.14.
Answer:
about 1.5 feet
Step-by-step explanation:
First we need to note the equation to find the surface area of a sphere. This is 4πr^2.
4πr^2=Surface Area
4πr^2=26.87
4(3.14)r^2=26.87 Substitute
r^2=26.87/(4*3.14) Divide
r^2=26.87/12.56 Simplify
r=√(26.87/12.56) Find square root of both sides
r≈1.5 Do the calculations
So the radius of the ball is about 1.5 feet.
Answer:1.5 ft
Step-by-step explanation:
Given
Surface area of ball=[tex]26.87 ft^2 [/tex]
And we know surface area of ball is =[tex]4\pi r^2[/tex]
Equating
[tex]26.87=4\times 3.14\times r^2 [/tex]
[tex]r^2=2.1393[/tex]
[tex]r=1.4626\approx 1.5 [/tex]
Which phrase matches the algebraic expression below?
2(x − 7) + 10
Answer:
Two times the difference of a number x and 7 plus 10.
Step-by-step explanation:
We are to write a phrase which matches the following algebraic expression below:
[tex] 2 ( x − 7 ) + 1 0 [/tex]
We can see that there is a bracket with a coefficient outside it so we can express it as:
'Two times the difference of a number x and 7'.
While + 10 can be added to it to complete the phrase:
Two times the difference of a number x and 7 plus 10.
What happens when you reflect a shape over the x-axis and then the y-axis. What is the one transformation that could have been performed to achieve the same result? A degree rotation.
Reflecting a shape over the x-axis and then the y-axis is equivalent to a 180-degree rotation around the origin.
When a shape is reflected over the x-axis, any point (x, y) on the shape will have its y-coordinate inverted, becoming (x, -y). If this reflected shape is then reflected over the y-axis, the x-coordinate is inverted, so (x, -y) becomes (-x, -y). The same final position of the shape could have been achieved by a single transformation: rotating the shape 180 degrees around the origin.
Mathematically, the combination of these two reflections can be represented by matrices and is equivalent to the composition of two reflection transformations. The reflection across the x-axis can be represented by a matrix that inverts the sign of the y-coordinate and reflection across the y-axis can be represented by a matrix inverting the x-coordinate. Together, these operations are equivalent to a 180-degree rotation around the origin.
Given the functions f(x) = x2 - 2x - 4 and g(x) = 2x - 4, at what values of x do f(x) and g(x) intersect?
Answer:
The values of x are 0 and 4
Step-by-step explanation:
we have
[tex]f(x)=x^{2}-2x-4[/tex] ------> equation A
[tex]g(x)=2x-4[/tex] ----> equation B
To find the values of x when f(x) and g(x) intersect
equate f(x) and g(x)
[tex]f(x)=g(x)[/tex]
[tex]x^{2}-2x-4=2x-4[/tex]
[tex]x^{2}-2x-4-2x+4=0[/tex]
[tex]x^{2}-4x=0[/tex]
Factor x
[tex]x(x-4)=0[/tex]
The solutions are
x=0 and x=4
Final answer:
The functions f(x) = x²- 2x - 4 and g(x) = 2x - 4 intersect at x = 0 and x = 4, found by setting the equations equal to each other and solving for x.
Explanation:
To find the intersection points of the functions f(x) = x2 - 2x - 4 and g(x) = 2x - 4, we need to set the two functions equal to each other and solve for x.
Set f(x) equal to g(x): x ²- 2x - 4 = 2x - 4.
Move all terms to one side to set the equation to zero: x² - 4x = 0.
Factor the quadratic equation: x(x - 4) = 0.
Find the solutions for x by setting each factor equal to zero: x = 0 and x - 4 = 0, which gives us x = 0 and x = 4.
Therefore, the functions f(x) and g(x) intersect at the values x = 0 and x = 4.
help me with the work
first off, let's check what's the slope of that line through those two points anyway
[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-(-2)}{7-5}\implies \cfrac{2+2}{7-5}\implies \cfrac{4}{2}\implies 2[/tex]
now, let's take a peek of what is the slope of that equation then
[tex]\bf -5y+kx=6-4x\implies -5y=6-4x-kx\implies -5y=6-x(4+k) \\\\\\ -5y=-x(4+k)+6\implies -5y=-(4+k)x+6\implies y=\cfrac{-(4+k)x+6}{-5}[/tex]
[tex]\bf y=\cfrac{(4+k)x-6}{5}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{(4+k)}{5}} x-\cfrac{6}{5}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{since both slopes are the same then}}{\cfrac{4+k}{5}=2\implies 4+k=10}\implies \blacktriangleright k=6 \blacktriangleleft[/tex]