Answer:
(x-2)(x+2)(x^2 + 4)
Step-by-step explanation:
This can be done by difference of squares:
(x^2 - 4) (x^2 + 4)
And now (x^2 - 4) can be further factored:
(x-2)(x+2)(x^2 + 4) is your answer
Clearly, There are only 2 zeroes that we can get from this, 2 and -2
Hope this helps!
If you think I helped please mark brainliest! Would really appreciate!
Answer:
[tex]\large\boxed{x^4-16=(x^2+4)(x+2)(x-2)}[/tex]
[tex]\large\boxed{g(x)=x^4-16\ \text{has two real zeros}\ x=-2\ \text{and}\ x=2}[/tex]
Step-by-step explanation:
[tex]x^4-16=x^4-2^4=x^{(2)(2)}-2^{(2)(2)}\\\\\text{use}\ (a^n)^m=a^{(n)(m)}\\\\=(x^2)^2-(2^2)^2\\\\\text{use}\ a^2-b^2=(a+b)(a-b)\\\\=(x^2+2^2)(x^2-2^2)=(x^2+4)(x+2)(x-2)[/tex]
The zeros of g(x):
[tex]g(x)=x^2-16=(x^2+4)(x+2)(x-2)\\\\g(x)=0\iff(x^2+4)(x+2)(x-2)=0\iff x^2+4=0\ \vee\ x+2=0\ \vee\ x-2=0\\\\x^2+4=0\qquad\text{subtract 4 from both sides}\\x^2=-4\qquad\bold{FALSE}\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\boxed{x=-2}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}[/tex]
A bag contains purple marbles and white marbles, 34 in total. The number of purple marbles is 1 less than 4 times the number of white marbles. How many purple marbles are there?
There are 27 purple marbles
Step-by-step explanation:
Let p be the purple marbles
and
w be the white marbles
Then according to given statements
[tex]p+w = 34\ \ \ Eqn\ 1\\p = 4w-1\ \ \ Eqn 2[/tex]
Putting p = 4w-1 in equation 1
[tex]4w-1 +w = 34[/tex]
Adding one on both sides
[tex]5w-1+1 = 34+1\\5w = 35[/tex]
Dividing both sides by 5
[tex]\frac{5w}{5} = \frac{35}{5}\\w = 7[/tex]
Putting w = 7 in equation 2
[tex]p = 4(7)-1\\p = 28-1\\p = 27[/tex]
Hence,
There are 27 purple marbles
Keywords: Linear equation
Learn more about linear equations at:
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Leonard wants to save $100 in the next 2 months. He knows that in the
second month, he will be able to save $20 more than the first month.
How much should he save each month?
1 st
2nd
total
+
Answer:
$40,$60
Step-by-step explanation:
Let the money in the first month be x.
2x+20=100
x=40
PLZZ HELP!!! NEED ANSWER QUICKLY!!!!
Describe and correct the following error for evaluating the function g(x)=-5x+3 when x=-3.
g(-3)=(-5)(-3)+3=-3g+g=-6
plz show step by step how you solved it
Answer:
The value of g(x) at x = -3 is 18.
Step-by-step explanation:
Here, the given function is:
g(x) = - 5 x + 3
Now, for the value of x = -3 ,
g (-3) : Substitute the value of x = -3 in g(x) , we get
g (-3) = -5 (-3) + 3
= 15 + 3 = 18
or, g ( -3) = 18
Hence, the value of g(x) at x = -3 is 18.
find the area of the figure.
12 ft
18 ft
18 ft
36 ft
The area of the given figure is 864 square feet.
To find the area of the given figure, we can break it down into two rectangles and then sum their areas.
The figure consists of two rectangles with dimensions:
1. The first rectangle has a length of 36 ft and a width of 18 ft.
2. The second rectangle has a length of 12 ft and a width of 18 ft.
The area (A) of a rectangle is calculated using the formula: [tex]\(A = \text{length} \times \text{width}\).[/tex]
For the first rectangle:
[tex]\[ A_1 = 36 \, \text{ft} \times 18 \, \text{ft} = 648 \, \text{ft}^2 \][/tex]
For the second rectangle:
[tex]\[ A_2 = 12 \, \text{ft} \times 18 \, \text{ft} = 216 \, \text{ft}^2 \][/tex]
Now, add the areas of both rectangles to find the total area (A) of the figure:
[tex]\[ A = A_1 + A_2 = 648 \, \text{ft}^2 + 216 \, \text{ft}^2 = 864 \, \text{ft}^2 \][/tex]
The question probable maybe :-
Find the combined area of two rectangles with side 36 ft 18 ft ,12 ft
18 ft respectively .
In a different plan for area codes, the first digit could be any number from 0 through 6 , the second digit was either 7 or 8, and the third digit could be any number except 0 or 6. or 6. With this plan, how many different area codes are possible?
112 different area codes can be made.
Solution:Given, In a different plan for area codes, the first digit could be any number from 0 through 6 ,
So, total 7 digits are possible for 1st place (i.e. 0 1 2 3 4 5 6)
The second digit was either 7 or 8,
So, total 2 digits are possible for 2nd place (i.e. 7 8)
And the third digit could be any number except 0 or 6.
So, total possible digits are 8 for 3rd place (i.e. 1 2 3 4 5 7 8 9)
With this plan, we have to find how many different area codes are possible?
[tex]\text { total possible combinations }=7 \text { possibilities for } 1 \text { st place } \times 2 \text { for } 2 \text { nd place } \times 8 \text { for } 3 \text { rd place }[/tex]
[tex]\text { Total possible area codes }=7 \times 2 \times 8=14 \times 8=112[/tex]
Hence, 112 different area codes can be made.
Cos(theta)= -.9041, 180degress< theta <270degress
Answer:
[tex]\theta=205.298^o[/tex]
Step-by-step explanation:
We know
[tex]cos\theta=-.9041[/tex]
in the third quadrant [tex]180^o<\theta<270^o[/tex]
We use a scientific calculator to find the inverse cosine of -0.9041 to find
[tex]\theta=154.702^o[/tex]
Since this angle is not in the required quadrant we must find the other angle who has the same cosine. The required angle is equidistant from the found value from the 180 degrees angle, so our solution is
[tex]\theta=180^o+(180^o-154.702)=205.298^o[/tex]
12. What's
written as a fraction with a denominator of 42?
O C. 42/42
O D.742
Mark for review (Will be highlighted on the review page)
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Answer:
C.)
Step-by-step explanation:
Denominator is the bottom part of a fraction
2.c is anyone good with exponential and logarithmic?
Answer:
After 48 months the value will increase by 10 percent of the initial value.Step-by-step explanation:
Let's first find the rate of increase for each period which is 3 months here.
According to the table at month [tex]x=0[/tex] value is [tex]2000[/tex]dollars and at month [tex]x=3[/tex] value is [tex]2012[/tex]dollars.
∴[tex]2012=2000(1+\frac{r}{100} )^1[/tex]
⇒[tex]1+\frac{r}{100} =\frac{2012}{2000}=1.006[/tex]
⇒[tex]r=0.006*100[/tex]
⇒[tex]r=0.6[/tex]%
Now the question is to find how long it will take for the investment value to increase 10 percent.
[tex]y=2000(1+0.006)^\frac{x}{3}[/tex]
[tex]2000(1+0.1)=2000(1.006)^\frac{x}{3}[/tex]
⇒[tex](1.006)^\frac{x}{3} =1.1[/tex]
⇒[tex]\frac{x}{3}=\frac{log(1.1)}{log(1.006)}[/tex]
⇒[tex]x=3(\frac{log(1.1)}{log(1.006)} )[/tex]
⇒[tex]x=47.7979126....[/tex]
∴at [tex]x=48[/tex] the value will slightly cross 10 percent increase.
An employee of a car wash earns $12 for each car she washes. She always saves $50 of her weekly earnings. This week, she wants to have at least $100 in spending money. Write an inequality to find the fewest number of cars she must wash.
the inequality representing the fewest number of cars she must wash is [tex]\( x \geq 13 \).[/tex]
To find the fewest number of cars the employee must wash, we need to determine the minimum number of cars that will allow her to have at least $100 in spending money after saving $50.
Let's denote the number of cars she must wash as( x \).
Given:
- Earnings per car washed: $12
- Amount saved: $50
- Desired spending money: at least $100
Step 1: Calculate her earnings from washing cars:
The total earnings from washing cars will be ( 12x ) dollars.
Step 2: Calculate her spending money after saving:
She saves $50 of her weekly earnings, so her spending money will be her total earnings minus $50, which is \( 12x - 50 \) dollars.
Step 3: Write the inequality:
Since she wants to have at least $100 in spending money, we can write the inequality:
[tex]\[ 12x - 50 \geq 100 \][/tex]
This inequality states that her spending money after saving must be greater than or equal to $100.
Now, to solve for [tex]\( x \), we'll isolate \( x \)[/tex] on one side of the inequality.
Step 4: Solve the inequality:
[tex]\[ 12x - 50 \geq 100 \][/tex]
Add 50 to both sides:
[tex]\[ 12x \geq 150 \][/tex]
Now, divide both sides by 12:
[tex]\[ x \geq \frac{150}{12} \][/tex]
[tex]\[ x \geq 12.5 \][/tex]
Step 5: Interpret the result:
Since the number of cars washed must be a whole number (you can't wash half a car), the fewest number of cars she must wash to have at least $100 in spending money is 13.
So, the inequality representing the fewest number of cars she must wash is [tex]\( x \geq 13 \).[/tex]
What is 7225 / 8 with the remainder as a whole number
Answer:
903 1/8
Step-by-step explanation:
Just divide 7225 by 8. :) I put it in fraction form but decimal form is just 903.125. I hope this helps you out. :)
Answer:
its 903 with 1 left over
I need help with this math problem.
===============================================
Explanation:
The x intercept is (-2,0) which is where the graph crosses the x axis.
The y intercept is (0,-6) which is where the graph crosses the y axis.
-----
Find the slope of the line through those two points
m = (y2-y1)/(x2-x1)
m = (-6-0)/(0-(-2))
m = (-6-0)/(0+2)
m = -6/2
m = -3
-----
The y intercept (0,-6) leads to b = -6
Both m = -3 and b = -6 plug into y = mx+b to get
y = mx+b
y = -3x+(-6)
y = -3x-6
-----
Now add 3x to both sides
y = -3x-6
y+3x = -3x-6+3x
3x+y = -6
-----
Lastly, multiply both sides by -2 so that the "-6" on the right hand side turns into "12" (each answer choice has 12 on the right hand side)
3x+y = -6
-2(3x+y) = -2(-6)
-2(3x)-2(y) = 12
-6x-2y = 12
which is what choice B shows.
Make b the subject of the formula
[tex]a = \sqrt{b + 6} [/tex]
Answer:
a^2 -6
Step-by-step explanation:
use ur basic knowing of equations
One number is
= of another number. The sum of the two numbers is
12. Find the two numbers. Use a comma to separate your answers.
Answer:
Two such numbers are 10 , 2 .
Step-by-step explanation:
Here, the question is INCOMPLETE.
Here is the Complete question:
One number is 1/5 of another number. The sum of the two numbers is 12. Find the two numbers. Use a comma to separate your answers.
We can solve the given problem as follows:
Here, : One number is 1/5 of another number.
Let one such number = m
⇒ The other number = 1/5 (m)
Sum of both the given number = 12
[tex]\implies m + \frac{1}{5} m = 12\\\implies \frac{5m + m}{5} = 12\\\implies \frac{6m}{5} = 12[/tex]
or, 6 m = 12 x (5) = 60
or, m = 60 / 6 = 10
or, m = 1 0
Hence, the first number = m = 10
Second number is [tex]\frac{1}{5} m = \frac{1}{5} \times 10 = 2[/tex]
Hence, two such numbers are 10 , 2 .
Shawn is buying his first home. At closing he brought a check for $7570. The
closing costs were as follows:
Title Fee
Processing Fee
Appraisal
No. of Points
$545
$2100
$695
Based on this information, how much did the house cost?
Answer:It cost 2100 dollars
Step-by-step explanation:I did the math on calculator very very simple buddy
What is the volume of a sphere that has a 64 m radius
Answer:
V=349525.333*pi
Step-by-step explanation:
Volume of a sphere: V=(4/3)*pi*r^3 where r=radius.
r=64
V=(4/3)*pi*(64)^3=(4/3)(262144)pi=349525.333*pi
A scale has a percent error of 5%. The actual mass of a rock is 258 g.
Select from the drop-down menus to correctly complete the statement.
The scale is likely to show the mass is either [Choose...] g or [Choose...] g.
The scale is likely to show the mass is either 270.9g or 245.1g
Step-by-step explanation:
Actual mass = 258g
Percent error = 5% = ±0.05
Mass shown by scale = Actual mass*percent error
[tex]Mass\ shown\ by\ scale=258*(\±0.05)\\Mass\ shown\ by\ scale=\±12.9g[/tex]
Therefore,
Mass shown by scale = 258+12.9 , Mass shown by scale = 258-12.9
Mass shown by scale = 270.9g , Mass shown by scale = 245.1g
The scale is likely to show the mass is either 270.9g or 245.1g
Keywords: error, percentage
Learn more about percentages at:
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Answer:
A scale has a percent error of 5%. The actual mass of a rock is 258 g.
Select from the drop-down menus to correctly complete the statement.
The scale is likely to show the mass is either
245.1
g or
270.9
g.
Step-by-step explanation:
I copied an pasted from k-12
What is an equation of the line that passes through the points (0,2) and (5,8)
The equation of the line that passes through the points (0, 2) and (5, 8) will be y = (6/5)x + 2.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The point given that lie on the line are mentioned below.
(0, 2) and (5, 8)
Then the equation of the line that passes through the points (0, 2) and (5, 8) will be given as,
(y - 2) = [(8 - 2) / (5 - 0)](x - 0)
y - 2 = (6/5)x
y = (6/5)x + 2
The equation of the line that passes through the points (0, 2) and (5, 8) will be y = (6/5)x + 2.
More about the line passing through two points link is given below.
https://brainly.com/question/12740817
#SPJ3
Final answer:
To find the equation of the line passing through (0,2) and (5,8), we calculate the slope as 6/5 and use the y-intercept of 2 to write the equation as y = (6/5)x + 2.
Explanation:
To find an equation of the line that passes through the points (0,2) and (5,8), we need to calculate the slope and use one of the points to write the equation in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
First, let’s find the slope of the line using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (8 - 2) / (5 - 0), which simplifies to m = 6 / 5. This is the slope of the line.
Now, we can use the slope and one of the points to find the y-intercept. Since the line passes through (0,2), we know that the y-intercept b is 2. Therefore, the equation of the line is y = (6/5)x + 2.
Jordan can run a mile in 8.4 minutes. How long would it take to run 6.21 miles
Final answer:
To find how long it takes Jordan to run 6.21 miles, multiply the per-mile time (8.4 minutes) by the total miles (6.21), resulting in approximately 52.164 minutes.
Explanation:
To calculate how long it would take Jordan to run 6.21 miles based on the information that Jordan can run a mile in 8.4 minutes, we use the following steps:
Multiply the time it takes to run one mile by the total number of miles.Time for 1 mile = 8.4 minutes
Total distance = 6.21 miles
Total time = 8.4 minutes/mile × 6.21 miles
Total time = 52.164 minutes
Therefore, it would take Jordan approximately 52.164 minutes to run 6.21 miles. This straightforward multiplication provides a precise estimate, illustrating the application of the mile pace to calculate the overall running time for the specified distance.
) What number makes the equation true?
-5+__=7 1/3
In a triangle ABC, measure of angle B is 90 degrees. AB is 3x-2 units and BC is x+3. If the area of the triangle is 17 sq cm, form an equation in terms of x and solve it.
Answer:
[tex]x=\frac{8}{3}\ cm[/tex]
Step-by-step explanation:
we know that
The area of the right triangle ABC is equal to
[tex]A=\frac{1}{2}(AB)(BC)[/tex]
we have
[tex]A=17\ cm^2[/tex]
[tex]AB=(3x-2)\ cm[/tex]
[tex]BC=(x+3)\ cm[/tex]
substitute the values
[tex]17=\frac{1}{2}(3x-2)(x+3)[/tex]
[tex]34=(3x-2)(x+3)[/tex]
[tex]34=3x^2+9x-2x-6[/tex]
[tex]3x^2+7x-6-34=0[/tex]
[tex]3x^2+7x-40=0[/tex]
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]3x^2+7x-40=0[/tex]
so
[tex]a=3\\b=7\\c=-40[/tex]
substitute in the formula
[tex]x=\frac{-7(+/-)\sqrt{7^{2}-4(3)(-40)}} {2(3)}[/tex]
[tex]x=\frac{-7(+/-)\sqrt{529}} {6}[/tex]
[tex]x=\frac{-7(+/-)23} {6}[/tex]
[tex]x=\frac{-7(+)23} {6}=\frac{16}{6}=\frac{8}{3}[/tex]
[tex]x=\frac{-7(-)23} {6}=-5[/tex]
therefore
The solution is
[tex]x=\frac{8}{3}\ cm[/tex]
How do you answer this?
Answer:
The simplified form would be [tex]6x^5[/tex]
Step-by-step explanation:
Given:
[tex]\frac{(3x^4)(12x^2)}{6x}[/tex]
Now multiplying the numbers and variable we get,
[tex]\frac{(3x^4)(12x^2)}{6x}\\\\\frac{(36x^{2+4})}{6x}\\\\\frac{36x^6}{6x}[/tex]
Now Dividing 36 by 6 we get,
[tex]\frac{6x^6}{x}=6x^6\times x^{-1} = 6x^{6-1}= 6x^5[/tex]
Hence the simplified form would be [tex]6x^5[/tex]
Help with number 15 with the graph
Answer:
I believe it is 7
Step-by-step explanation:
SOS PLEASE HELP so I don't fail math
Answer:
2 years ago :/
Step-by-step explanation:
(5x)(-2x)(3x) is equal to?
Carlotta has 12 2/3 yd of ribbon to be divided among 19 girls in the cheerleading squad.how much ribbon will each girl get if it is divided equally among the 19 girls
Answer:
Each girl gets 2/3 yd of ribbon.
Step-by-step explanation:
12 2/3=38/3
(38/3)/19
(38/3)(1/19)
(2/3)(1/1)=2/3
A rectangle has an area of 24 sq. inches and a perimeter of 50 in. what are the dimensions of the rectangle
Final answer:
To find the dimensions of a rectangle with an area of 24 sq. inches and a perimeter of 50 inches, we set up a system of linear equations and solve for the length and width. The dimensions are found to be either 24 inches by 1 inch or 1 inch by 24 inches.
Explanation:
The question given by a student involves finding the dimensions of a rectangle given its area and perimeter. Given the area (24 sq. inches) and the perimeter (50 in.), we can set up two equations to solve for the length and width:
Area = length imes width = 24 sq. inches
Perimeter = 2 imes (length + width) = 50 inches
We can divide the perimeter by 2 to get the sum of the length and width:
25 = length + width
Since we have two equations, this forms a system of linear equations which we can solve simultaneously. First, assume the length is the larger dimension and let us represent it by 'L' and the width by 'W'. We have:
L imes W = 24
L + W = 25
To solve for L and W, we can use substitution or elimination methods. Let's assume we solve for W in terms of L using the first equation, W = 24/L, and then we substitute it into the second equation:
L + 24/L = 25
Multiplying both sides by L to clear the fraction, we get:
L² + 24 = 25L
Then we rearrange the terms to set the equation to zero:
L² - 25L + 24 = 0
Now we can factor this quadratic equation to find the values of L:
(L - 1)(L - 24) = 0
So, L can be either 1 inch or 24 inches. If L is 24 inches, then W will be 1 inch (since 24 imes 1 = 24), and if L is 1 inch, then W will be 24 inches. Either way, the dimensions that satisfy both the area and perimeter equations are 24 inches by 1 inch.
The dimensions of the rectangle are [tex]\( {24 \text{ inches} \text{ by } 1 \text{ inch}} \)[/tex].
To find the dimensions of the rectangle, let's denote the length by l and the width by w.
Given:
1. The area of the rectangle is 24 square inches:
[tex]\[ l \cdot w = 24 \][/tex]
2. The perimeter of the rectangle is 50 inches, which gives us the equation:
[tex]\[ 2l + 2w = 50 \][/tex]
Let's solve these equations step by step.
From the perimeter equation:
[tex]\[ 2l + 2w = 50 \][/tex]
Divide the entire equation by 2 to simplify:
[tex]\[ l + w = 25 \][/tex]
Now we have two equations:
[tex]\[ l + w = 25 \]\[ l \cdot w = 24 \][/tex]
Let's solve for l and w using substitution or elimination.
From ( l + w = 25 ), we can express l as:
[tex]\[ l = 25 - w \][/tex]
Substitute [tex]\( l = 25 - w \)[/tex] into [tex]\( l \cdot w = 24 \)[/tex]:
[tex]\[ (25 - w) \cdot w = 24 \][/tex]
Expand and rearrange the equation:
[tex]\[ 25w - w^2 = 24 \]\[ w^2 - 25w + 24 = 0 \][/tex]
Now, solve this quadratic equation using the quadratic formula [tex]\( w = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \)[/tex], where ( a = 1 ), ( b = -25 ), and ( c = 24 ):
[tex]\[ w = \frac{{-(-25) \pm \sqrt{{(-25)^2 - 4 \cdot 1 \cdot 24}}}}{{2 \cdot 1}} \]\[ w = \frac{{25 \pm \sqrt{{625 - 96}}}}{2} \]\[ w = \frac{{25 \pm \sqrt{{529}}}}{2} \]\[ w = \frac{{25 \pm 23}}{2} \][/tex]
So, we get two possible values for w:
[tex]\[ w = \frac{{25 + 23}}{2} = 24 \]\[ w = \frac{{25 - 23}}{2} = 1 \][/tex]
Now, find l for each value of w:
1. If ( w = 24 ):
[tex]\[ l = 25 - 24 = 1 \][/tex]
2. If ( w = 1 ):
[tex]\[ l = 25 - 1 = 24 \][/tex]
One-Step Equations:
1. x - 3.5 + 14.9
2. x - 2.8 = 9.5
3. x - 8.5 = -2.1
4. z - 9.4 = -3.6
5. -5/6 + x = -11/12
6. x - 1/9 = 5/18
7. x + 6 = -3
8. z - 7 = 11
9. -1 = x - 8
(I will be trying to figure these out as well)
What is 889 divided by 17
Answer:
The answer is 52.2
Step-by-step explanation:
The horizontal line segment at the top of the polygon on the grid below is how many units long?
Answer:
6 units long.
Step-by-step explanation:
Given:
A polygon drawn on a graph.
In order to determine the distance of the horizontal line at the top, we find the coordinates of the end points and then use distance formula to find the exact distance.
Let us label the polygon as ABCD as shown below. AB is the length of the horizontal line.
Coordinates of A are [tex](x_1,y_1)=(-3, 4)[/tex] as seen in the graph.
Coordinates of B are [tex](x_2,y_2)=( 3, 4)[/tex] as seen in the graph.
Now, distance formula for two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d_{AB}=\sqrt{(3-(-3))^2+(4-4)^2}\\d_{AB}=\sqrt{(3+3)^2+0}\\d_{AB}=\sqrt{36}=6\ units[/tex]
Therefore, the horizontal line at the top is 6 units long.
Answer:
6 units long
Step-by-step explanation:
brainly patrol what is wrong with that
Solve for k
7k+2m = kr + 4m + 3
Answer:
[tex]\large\boxed{k=\dfrac{2m+3}{7-r}\ \text{for}\ r\neq7}[/tex]
Step-by-step explanation:
[tex]7k+2m=kr+4m+3\qquad\text{subtract}\ 2m\ \text{from both sides}\\\\7k+2m-2m=kr+4m-2m+3\\\\7k=kr+2m+3\qquad\text{subtract}\ kr\ \text{from both sides}\\\\7k-kr=kr-kr+2m+3\\\\7k-kr=2m+3\qquad\text{distribute}\\\\k(7-r)=2m+3\qquad\text{divide both sides by}\ (7-r)\neq0\\\\k=\dfrac{2m+3}{7-r}[/tex]