Solve a(x - b) - 2k = l for k

Answers

Answer 1

a(x - b) - 2k = l
ax - ab - 2k = l

Subtract ax, add ab to both sides

- 2k = l - ax + ab

Divide by - 2 to isolate variable K

k = (l - ax + ab) / - 2 or [tex]k = \frac{l - ax + ab}{-2} [/tex]

Related Questions

A package of cookies contains 6 cookies. Each package of cookies costs $1.49.

A function, f(x), is written to represent the cost of purchasing x packages of cookies.

What is the practical domain for the function f(x)?
A: all positive integers
B: all real numbers
C: all whole numbers that are multiples of 6
D: all whole numbers

Answers

Given are 6 cookies in a package.

Given that the cost of a package = 1.49 dollars.

Let's assume we purchase 'x' numbers of packages.

So, total cost of 'x' packages = '1.49x' dollars.

f(x) is the function that represents the cost of 'x' packages, i.e. f(x) = 1.49x

Since the number of packages can not be negative or can't be decimal numbers, so 'x' should be positive integral values.

So, the practical domain of f(x) would be "positive integral values".

Hence, option A is correct, i.e. "all positive integers".

A rectangular garden measures 40 yards by 35 yards. a lawn of uniform width surrounds the garden and has an area of 316 square yards. find the width of the lawn that surrounds the garden.

Answers

The lawn area of uniform width can be written as follows:
A = (40 + 2x) * (35 + 2x) - (40) * (35)
Where,
x: width of the lawn
Substituting the value of the area we have:
316 = (40 + 2x) * (35 + 2x) - (40) * (35)
Rewriting:
316 = 1400 + 80x + 70x + 4x ^ 2 - 1400
Rewriting we have:
4x ^ 2 + 150x - 316 = 0
Solving the polynomial we have:
x1 = - 79/2
x2 = 2
Taking the positive root we have that the grass width des:
x = 2 yards
Answer:
The width of the lawn that surrounds the garden is:
x = 2 yards

The width of the lawn surrounding the garden is 2 yards.

Let's denote the width of the lawn as "w" yards.

The dimensions of the garden are 40 yards by 35 yards. Including the lawn, the dimensions become:

Length: 40 + 2w yards

Width: 35 + 2w yards

The area of the rectangle including the garden and the lawn is:

(40 + 2w) × (35 + 2w) square yards

The area of the garden itself is:

40 × 35 = 1400 square yards

The area of the lawn alone is:

Total area - Area of the garden = 316 square yards

Therefore:

(40 + 2w) × (35 + 2w) - 1400 = 316

Expand the left side of the equation:

= (40 + 2w)(35 + 2w)

= 40 × 35 + 40 × 2w + 35 × 2w + 2w × 2w

= 1400 + 80w + 70w + 4w²

= 1400 + 150w + 4w²

Set up the equation:

= 1400 + 150w + 4w² - 1400 = 316

= 150w + 4w² = 316

Rearranging the equation:

4w² + 150w - 316 = 0

Solve this quadratic equation using the quadratic formula:

w = (-b ± √(b² - 4ac)) / 2a

Here, a = 4, b = 150, and c = -316

Calculate the discriminant:

= b² - 4ac

= 150² - 4 × 4 × (-316)

= 22500 + 5056

= 27556

√27556 ≈ 166

Therefore:

w = (-150 ± 166) / 8

This gives two potential solutions:

w = (16 / 8) = 2

w = (-316 / 8) (not valid as width cannot be negative)

An equation of a function y(t) is shown. y(t)=−t2+14t−40 Which of the following statements are true about the graph of y(t) for 6≤t≤8 and WHY? a. The value of y(t) increases over the interval 6≤t≤7. b. The value of y(t) increases over the interval 7≤t≤8. c. The average rate of change over the interval 6≤t≤8 is 0. d. The value of y(t) is constant over the interval 6≤t≤8. e. The average rate of changer over the interval 6≤t≤7 is the same as the average rate of change over the interval 7≤t≤8. Make sure you use complete sentences and capitalize!

Answers

from the given the function, y(t)=−t²+14t−40; From the graph, it is evident that between the intervals 6≤t≤8:The value of our function decreases over the given interval. so the answer is: a. The value of y(t) increases over the interval 6≤t≤7
Hope this helps :)

Jack's father let jack use a rectangular section of the back yard that had dimensions of 10 feet by 12 feet for his garden. he wanted to put a fence around the outside of the garden. how long should the piece of fencing he needs to buy be?

Answers

That would be 12*2 + 10*2 = 24 + 20 = 44 feet

if f(x) = x-1 and g(x) =2x-3 find the sum, difference, product and quotient of these two functions

Answers

We have the following functions:
f (x) = x-1
g (x) = 2x-3

For the sum we have:
f (x) + g (x) = (x-1) + (2x-3)
f (x) + g (x) = 3x - 4

For subtraction we have:
f (x) - g (x) = (x-1) - (2x-3)
f (x) - g (x) = -x + 2

For the product we have:
f (x) * g (x) = (x-1) * (2x-3)
f (x) * g (x) = 2x ^ 2 - 3x - 2x + 3
f (x) * g (x) = 2x ^ 2 - 5x + 3

For the quotient we have:
f (x) / g (x) = (x-1) / (2x-3)

Tammy and Wyatt are sales associates at the same used car dealership. Their supervisor is planning to promote the employee with the best sales numbers, on average. The box plots below show their sales, in thousands of dollars, for the past 2 weeks:

box plot labeled Tammy with min at 19, Q1 at 21, median at 25.5, Q3 at 26.75, max at 27.75. Box plot labeled Wyatt with min at 18.5, Q1 at 20.5, median at 24, Q3 at 27.5, max at 28.25

Who should get the promotion, and why?

A) Wyatt should get the promotion. His data is more evenly distributed, so his sales are more consistent.
B) Wyatt should get the promotion because he had the highest sales in a single day.
C) Tammy should get the promotion because her lowest value is higher than Wyatt's lowest value.
D) Tammy should get the promotion. She has a higher median with a smaller IQR, so her sales are better on average.

Answers

I think the answer is D. The other answers are unreasonable. Wyatt would not get the promotion and just because Tammy's lowest value is bigger than Wyatt's doesn't mean that Tammy gets the promotion. The only reasonable answer is D.

Answer:

Tammy should get the promotion. She has a higher median with a smaller IQR, so her sales are better on average.

Solve the equation.
left parenthesis x plus 4 right parenthesis left parenthesis x minus 9 right parenthesis equals 4 x
x =
nothing
(Use a comma to separate answers as needed.)

Answers

Final answer:

To solve the equation (x + 4)(x - 9) = 4x, expand and rearrange the terms. Then solve the quadratic equation by factoring or using the quadratic formula.

Explanation:

To solve the equation (x + 4)(x - 9) = 4x, we can expand the left side of the equation and then rearrange the terms:

x^2 - 5x - 36 = 4x

Next, we can move all the terms to one side of the equation:

x^2 - 9x - 36 = 0

Finally, we can solve this quadratic equation by factoring or using the quadratic formula to find the values of x.

A scatter plot has a correlation coefficient of -0.159. What does this suggest about the relationship between the two variables?

Answers

r = -0.159 is the correlation coefficient

the value of r is closer to 0 than it is to -1, so the data is very weakly linear associated. The scatter plot points are too spread out for one single line to be close to them all. A different curve (such as a parabola) may be a better fit.

The fact that r is negative suggests that there is negative association. What this means is that as x goes up, y goes down. As you move from left to right, you go downhill. The regression line will have a negative slope.

The ratio of height between Joey and his girlfriend is 8:7. If Joey is 72 inches tall, how tall is his girlfriend in inches

Answers

Ratio is Joey/girlfriend = 8/7=8x/7x.
8x is height of Joey.
8x=72
x=72/8=9

7x is height of Joey's girlfriend.
7x=7*9=63 in.
Answer: 63 in.

Joey : Girlfriend = 8 : 7

Multiply the ratio by 9:
Joey : Girlfriend = 8x9 : 7x9
Joey : Girlfriend = 72 : 63

Answer: His girlfriend is 63 inches tall.

What is the y-value of sin(x) when x = -90°?

Answers

-90 degrees = 270 degrees

You can use the unit circle to find this value, if you wish.

sin(-90) = -1

how many real solutions does y = (-x + 4)^2 have?

Answers

it has 2 solutions
1.y = -1
2.y = 4/3 = 1.333

Short answer 1

Comment
There are a couple of ways of doing this to show there there is just one solution. The most easily done way is to graph the quadratic. I have done that for you.

Notice that the quadratic touches the x axis, it does not cut it in two places or no places. When a quadratic just touches the x axis, it has only one solution.

Method 2
The quadratic is shown in the vertex form. If there was a number outside he bracket showing squares then you would get

y = (-x + 4)^2 + 4 (drawn in blue)
y = (-x + 4)^2 - 6 (drawn in green)

These two examples show what the vertex form would look like if the axis was cut in 2 places or no places and there would be no solution for the first one and 2 places for the second one.

If i walk 4 miles an hour how long will it take to walk 1 mile

Answers

Set up a ratio.

x= portion of 1 hour

4 miles/1 hour= 1 mile/ x hour
cross multiply
4 * x= 1 * 1
4x= 1
divide both sides by 4
x= 1/4 of an hour

To find number of minutes:

1 hour= 60 minutes

=1/4 of an hour * 60 minutes
=60/4
=15 minutes

ANSWER: It would take 1/4 of one hour ( or 15 minutes) to walk 1 mile.

Hope this helps! :)

Find an explicit formula for the sequence 30\,,\,150\,,\,750\,,\,3750,...30,150,750,3750,...30, space, comma, space, 150, space, comma, space, 750, space, comma, space, 3750, comma, point, point, point.

Answers

The series shown is an geometric series and the explicit formula is given by:
an=ar^(n-1)
where
a=first term
n=number of terms
r=common ratio
from the sequence:
a=30
r=5
thus the explicit formula will be:
an=30(5)^(n-1)
hence the answer is:
an=30(5)^(n-1)

Answer:750+3750=4,500

Step-by-step explanation:

HELP!!! - The lunch special at a diner is a bowl of soup with either a salad or a sandwich. The diner offers chicken noodle, potato, or lentil soup as part of the special. Which statement best describes how this tree diagram represents the number of different ways the lunch special can be ordered?

A: The diagram is flawed because it should show there are four different ways the special can be ordered.
B: The diagram is flawed because it should show there are five different ways the special can be ordered.
C: The diagram models the situation correctly, and it shows there are six different ways the special can be ordered.
D: The diagram models the situation correctly, and it shows there are nine different ways the special can be ordered.

Answers

The correct answer is C) The diagram models the situation correctly, and it shows there are six different ways the special can be ordered.

Answer:

C: The diagram models the situation correctly, and it shows there are six different ways the special can be ordered.

Step-by-step explanation:

How do I do this ??

Answers

the answer is b.) -12x^3+28x^2

-4x^2 * 3x = -12x^3
-4x^2 *-7 = +28x^2
So since you can’t add them together the answer is the second one

A circle is centered at (−8, −13) and has a radius of 13.

What is the equation of the circle?

Enter the equation in the box using lower case variables x and y.

Answers

we know that
the equation of a circle is
(x-h)²+(y-k)²=r²
where
(h,k) is the center
r is the radius
so
for a circle is centered at (−8, −13) and has a radius of 13
the equation is
(x+8)²+(y+13)²=13²--------------> (x+8)²+(y+13)²=169

the answer is
(x+8)²+(y+13)²=169

The answer is
(x+8)²+(y+13)²=169

Find the quotient. 6^8/6^6

Answers

The answer would be 1^2.

To find this, first you divide 6 (numerator) by 6 (denominator) to get 1. Then you subratct the power of 6, from the power of 8, to get 2. Thus getting a final answer of 1^2.

I hope this helps!

6^2
Because 8 - 6 = 2

A fish tank in the shape of a rectangular prism has these dimensions: length = 20 inches width = 10 inches height = 12 inches What is the volume of water in the tank when it is 45 full?

Answers

Final answer:

The volume of water in the fish tank when it is 45% full is 1080 cubic inches.

Explanation:

To find the volume of water in the tank when it is 45% full, we first need to calculate the volume of the tank.

The formula for the volume of a rectangular prism is length × width × height.

Given that the length is 20 inches, the width is 10 inches, and the height is 12 inches, we can substitute these values into the formula: 20 × 10 × 12 = 2400 cubic inches.

Next, we need to find 45% of this volume. To do this, we multiply the volume by 0.45: 2400 × 0.45 = 1080 cubic inches.

Therefore, the volume of water in the tank when it is 45% full is 1080 cubic inches.

Ross and 5 of his friends are going kayaking. They rented 6 kayaks for 420. then they brought food for all 6 people , which costs 144. if all 6 people shared the cost 144. if all 6 people shared the cost of the trip equally, how much did each person pay?
A. 70
B.76
C.88
D.94
please help me

Answers

I think the correct answer would be : $94
adding $420 + $144 = 564
then divide 564 and 6 to get 94.

Answer:

its $95

Step-by-step explanation:

i got it right

shawna and amanda are selling pies for a school fundraiser. customers can buy cherry pies and pumpkin pies. shawna sold 1 cherry pie and 3 pumpkin pies for a total of $55. amanda sold 3 cherry pies and 3 pumpkin pies for a total of $69. what is the cost of each one cherry pie and one pumpkin pie?
PLEASE SHOW WORK

Answers

Let the cherry pies be c and the pumpkin pies be p:
Shawna: c + 3p = 55
Amanda: 3c + 3p = 69
We want to find the cost of c + p. To do this, the easiest way is to divide the second equation by 3:
(3c + 3p)/3 = 69/3
c + p = 23
Therefore, 1 cherry pie & 1 pumpkin pie cost $23.

Ryan wants to use the Fermi process to estimate the number of basketballs that would fill a gymnasium. As part of the process, he needs to estimate the volume of a basketball. The diameter of a basketball is about 10 in.

Which estimate best approximates the volume of a basketball?

5×10^1 in³
5×10^2 in³
5×10^3 in³
5×10^4 in³

Answers

A basketball is the shape of a sphere.

The volume of a sphere is given by

[tex]V= \frac{4}{3} \pi r^3[/tex]

Given that the diameter of the basketball is 10 in., thus the radius is 10 / 2 = 5 in.

Thus, the volume of the basketball is given by

[tex]V= \frac{4}{3} \pi(5)^3 \\ \\ = \frac{4\times125}{3} \pi=523.6\ in^3[/tex]

Therefore, The best approximate of the volume of the basketball is [tex]5\times10^2\ in^3[/tex]

The volume of two spheres are 327\pi in^{3} and 8829\pi in^{3}

What is the ratio of their radii?

Answers

a dimension of a sphere is its radius, so it correlates with its volume, thus

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\ -----------------------------[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ %The volume of two spheres are 327\pi in^{3} and 8829\pi in^{3} \cfrac{small}{large}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{8829}}\qquad \begin{cases} 8829=3\cdot 3\cdot 3\cdot 327\\ \qquad 3^3\cdot 327 \end{cases}[/tex]

[tex]\bf \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{3^3\cdot 327}}\implies \cfrac{s}{s}=\cfrac{\underline{\sqrt[3]{327}}}{3\underline{\sqrt[3]{327}}}\implies \cfrac{s}{s}=\cfrac{1}{3}[/tex]

Baby Kelsey wants to arrange 12 blocks in a row. How many different arrangements can she make?

Answers

Final answer:

To find the number of arrangements Baby Kelsey can make with 12 blocks, we calculate 12 factorial (12!), which equals 479,001,600. This represents the total number of unique ways to arrange the blocks in a row.

Explanation:

The student has asked how many different arrangements can be made with 12 blocks in a row. To determine the number of different arrangements, we use the concept of factorial, which is represented by an exclamation mark (!). In this case, we want to find 12!, which represents the product of all positive integers from 1 to 12.

Specifically, the calculation is 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. This multiplication results in the number of unique ways to arrange the 12 blocks since each block is distinct and can be placed in any position within the arrangement.

Therefore, there are 479,001,600 different arrangements possible when organizing 12 unique blocks in a row, showcasing the vast number of combinations for even a small number of objects.

What is 40.15 divided by 7.3, written as a decimal?

Answers

the answer is 5.5.
hope this helps!!

Final answer:

To calculate 40.15 divided by 7.3, we can use long division. The final quotient is 5.5, and there is no remainder. Therefore, 40.15 divided by 7.3 written as a decimal is 5.5.

Explanation:

To calculate 40.15 divided by 7.3, we can use long division.

First, we write the division problem with 40.15 as the dividend and 7.3 as the divisor:

5.5

________

7.3 | 40.15

We start by dividing 40.15 by 7.3. The quotient is 5.5.

Next, we subtract 5.5 multiplied by 7.3 from 40.15:

5.5

________

7.3 | 40.15

- 36.5

________

37.65

Since the remainder, 37.65, is greater than the divisor, 7.3, we can continue dividing.

We bring down the next digit from the dividend, which is 0, and divide it by 7.3:

5.5

________

7.3 | 40.15

- 36.5

________

4.15

3.65

We repeat the process of dividing and subtracting until the remainder is less than the divisor:

5.5

________

7.3 | 40.15

- 36.5

________

4.15

3.65

5.5

The final quotient is 5.5, and there is no remainder. Therefore, 40.15 divided by 7.3 written as a decimal is 5.5.

Given the two expressions shown below:

A. \sqrt{3} +\sqrt{2}
B. \sqrt{3} +\sqrt{6}

Which statement best describes the two expressions?

Both are rational.
Both are irrational.
A is rational, but B is irrational.
A is irrational, but B is rational.

Answers

[tex]\sqrt3\ is\ irrational\\\\\sqrt2\ is\ irrational\\\\\sqrt6\ is\ irrational\\\\therefore\\\\A.\ \sqrt3+\sqrt2\ is\ irrational\ and\ B.\ \sqrt3+\sqrt6\ is\ irrational[/tex]
Answer: Both are irrational.

Find the volume of a right prism with height h=10 cm, if: a The base is equilateral triangle with side 4 cm, base altitude of ≈ 3.5 cm. Help me!!!

Answers

V=BA×h
A(triangle)=(4×3.5)/2=7cm²
V(prism)=7×10=70cm³

Hope this helped!

To find its Volume of Right prism we multiply the base of the triangle times the height and divide that by 2.Then, multiply the area times the length, or the depth, of the prism to find the volume.

Area of the equilateral triangle = [tex]\frac{1}{2}x4x3.5.[/tex]

Area of triangle = 7 square cm.

Volume of the right prism = Area of triangle x Height of prism = 7x10 =70 cubic cm.

Volume of right prism = 70 cubic cm.

What is the excluded value of
-2x/17
a. x=0
b. x=2
c. x=17
d. no excluded values

Answers

Answer is d: no excluded values.

There is only excluded values if the variable x is in the denominator.

Find 3 consecutive odd numbers where the product of the smaller two numbers is 46 less than the square of the largest number.

Answers

Answer: The numbers are: " 5, 7, and 9 " .
___________________________________________________

Explanation:
___________________________________________________
Let the "3 consecutive odd numbers" be represented by:
___________________________________________________
"x" ;
___________________________________________________
"x + 2 " ;
___________________________________________________
"x + 4 " ;
___________________________________________________
→ Solve for "x" ; and then solve for "(x + 2)" and "(x + 4)" .
___________________________________________________

The product of the smaller two numbers, is "46 less than" (the square of) the largest number:
___________________________________________________
→ " x* (x + 2) = (x + 4)² − 46 " ;
___________________________________________________
Note the "distributive property" of multiplication:
___________________________________________________
a(b + c) = ab + ac ;

a(b − c) = ab − ac .
___________________________________________________

Start with simplifying the "left-hand side" of the equation:
___________________________________________________

" x(x + 2)" = (x * x) + (x * 2 ) = (x² + 2x) ;
___________________________________________________
Then simplify the "right-hand side" of the equation:
___________________________________________________

" (x + 4)² − 46 " ;
___________________________________________________
→ (x + 4)² = (x + 4) (x + 4) ;

Note: " (a + b)(c + d) = ac + ad + bc + bd " .

→ (x + 4)² = (x + 4) (x + 4) = (x *x) + (x *4) + (4 *x) + (4 * 4) ;

= x² + 4x + 4x + 16 ;

= x² + 8x + 16;

→ Bring down the " − 46 " ;
___________________________________________________
→ x² + 8x + 16 − 46 ;

= x² + 8x + 16 − 46 ;

= x² + 8x − 30 ;
____________________________________________________
Now, rewrite the entire equation:
____________________________________________________

→ x² + 2x = x² + 8x − 30 ;

Subtract "x² " & "2x" from EACH SIDE of the equation:

→ x² + 2x − x² − 2x = x² + 8x − 30 − x² − 2x ;

to get:

→ 0 = 6x − 30 ;

→ 6x − 30 = 0 ;

Add "30" to each side of the equation:

→ 6x − 30 + 30 = 0 + 30 ;

→ 6x = 30 ;

Divide each side of the equation by "6" ;
to isolate "x" on each side of the equation; & to solve for "x" ;

→ 6x / 6 = 30 / 6 ;

to get;

→ x = 5 ;

→ "(x + 2)" = "(5 + 2)" = 7 ;

→ "(x + 4)" = "(5 + 4)" = 9 ;
______________________________________________________
Answer: The numbers are: " 5, 7, and 9 " .
______________________________________________________

What is the input to a trigonometric function?

a ratio
the x position of a point on the circle
a central angle of a circle
the y position of a point on the circle

Answers

The input to a trig function is definitely an angle (whether in degrees or expressed in radians). That angle is also "a central angle of a circle."

Answer: A central angle of a circle

Step-by-step explanation:

The trigonometric functions are also known as circular functions.

The two fundamental trigonometric functions are defined as the coordinates of a any point A travelling around on the unit circle of radius 1 .

The input variable in trigonometric functions is the central angle of the circle 'x' such that we get sin x and cos x which give the x and y coordinates of A.

Hence, the input to a trigonometric function is a central angle of a circle.

Which is closer to the x-axis (1.4 , 2.2) and (4.1 , 2.4) or (3.9) and (8,9) or (1 1/4 , 2) and 1 1/4 , 8)?

Answers

hope this helps you with your problem

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