The Mathalot Company makes and sells textbooks. They have one linear function that represents the cost of producing textbooks and another linear function that models how much income they get from those textbooks. Describe the key features that would determine if these linear functions ever intercepted.

Answers

Answer 1

Answer: The question is asking to explain or described the key features that would determine if the linear functions is ever intercepted base on the said equation and the function, I would say that the answer would be If two linear equations have different slopes, and are in the same plane, they WILL intersect at ONE point (they will have a unique solution).

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The perimeter of a rectangle is 70 cm. If its length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 cm2. Find the length and the width of the original rectangle.

Answers

x=length of the original rectangle. (in cm)
y=width o f the original rectangle. (in cm)

Perimeter of a rectangle=sum of the all sides.
Perimeter of the original rectangle=x+x+y+y=2x+2y

Area of a rectangle=length x width
Area of the original rectangle=xy

x-5=length decreased by 5 cm
y+5=width increase by 5 cm.

We can suggest this system of equations:
2x+2y=70
(x-5)(y+5)=xy+50

We solve this system of equations by susbstitution method:
2x+2y=70 ⇒x+y=35 ⇒ y=35-x

(x-5)(35-x+5)=x(35-x)+50
(x-5)(40-x)=35x-x²+50
40x-x²-200+5x=35x-x²+50
40x-35x+5x=200+50
10x=250
x=250/10
x=25

y=35-x
y=35-25
y=10

Answer: the lenght and the width of the original rectangle is :
lenght=25 cm
width=10 cm.

The length of the rectangle is 25cm and the width of the rectangle is 45cm and this can be determine by forming the linear equations.

Given :

Perimeter of a rectangle is 70 cm.

Rectangle length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 $\rm cm^2$ .

Let 'a' be the length of the rectangle and 'b' be the width of the rectangle. Than the perimrter of the rectangle will be:

a + b = 70 ---- (1)

Now, the area of the rectangle will be:

$\rm (a-5)(35-a+5)=a(35-a)+50$

$\rm 35a -a^2+5a-175+5a-25=35a-a^2+50$

$\rm10a -200=50$

a = 25

Now, put the value of 'a' in equation (1).

b = 70 - 25 = 45

b = 45

Therefore, the length of the rectangle is 25cm and the width of the rectangle is 45cm.

For more information, refer the link given below:

brainly.com/question/919810

Sam and Jeremy have ages that are consecutive odd integers.The product of their ages is 783. Which equation could be used to
find Jeremy’s age, j, if he is the younger man?
(1) j^2 + 2 = 783 (3) j^2 + 2j = 783
(2) j^2 - 2 = 783 (4) j^2 - 2j = 783

Answers

j, j+2 - consecutive odd integers
j - Jeremy's age
j+2 - Sam's age
The product of their ages is 783.

$j(j+2)=783 \nj^2+2j=783$

The answer is (3).

consecutive odd integers are 2 awya from each other
1,3,5,7,9...
since jeremy iis younger, he is 2 less than sam
j
s=j+2

sj=783
in terms of j
(j+2)j=783
distribute
j^2+2j=783

the answe ris the 3rd equation

After paying eight dollars for the pie, Mike has eighty - one dollars left, his friend has thirteen dollars. How much money did he have before buying the pie

Answers

Answer:

__ - 8=81

unsure if we're adding his friend but for this i assume no,

81+ 8 = 89

so its either 89 or

89+13=102

How to convert 1.86 m to feet

Answers

Answer:

5.905

Step-by-step explanation:

Formula

For an approximate result, multiply the length value by 3.281

1.8 × 3.281 = 5.905

-TheUnknownScientist

Find the vertex, focus, directrix, and focal width of the parabola. x = 4y2.

Answers

- Vertex : ( 0, 0 ).
- Focus: ( p/2, 0 );
y² = 1/4 x
y² = 2 p x ⇒ 2 p = 1/4
p = 1/8
p/2 = 1/16
F ( 1/16, 0)
- Directrix:
x = - p/2 x
x = - 1/16 x
- The focal length:
2 p = 2 · 1/8 = 1/4

Answer:

The vertex is (0,0), focus of the parabola is $((1)/(16),0)$ , directrix of the parabola is $y=-(1)/(16)$ , focal width is $(1)/(4)$ .

Step-by-step explanation:

The given equation of parabola is

$x=4y^2$

It can be written as

$y^2=(1)/(4)x$ ....(1)

The general equation of parabola is

$(y-k)^2=4p(x-h)$ ... (2)

Where, (h,k) is vertex, (h+p,k) is focus, y=h-p is directrix and |4p| is focal width.

On comparing (1) and (2), we get

$h=0,k=0$

The vertex is (0,0).

$4p=(1)/(4)$

$p=(1)/(16)$

Focus of the parabola is

$(h+p,k)=(0+(1)/(16),0)=((1)/(16),0)$

Therefore focus of the parabola is $((1)/(16),0)$ .

Directrix of the parabola is

$y=h-p=0-(1)/(16)=-(1)/(16)$

Directrix of the parabola is $y=-(1)/(16)$ .

Focal width is

$|4p|=|4* (1)/(16)|=(1)/(4)$

Focal width is $(1)/(4)$ .

A quadratic equation is shown below:x2 − 14x + 41 = 0

Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers? (5 points)

A:Add 8 to both sides of the equation
B:Add 9 to both sides of the equation
C:Subtract 8 from both sides of the equation
D:Subtract 9 from both sides of the equation

Answers

Since the desired equation is a perfect square binomial, it is necessary to obtain a constant term (in the case of the given equation, 41) that is also a perfect square. To determine the perfect square needed, take the coefficient of the second term (14x) and divide it by two, then square it. It should yield "49". To obtain 49 as the constant term, we have to add 8 to both sides of the equation. Among the choices, the correct answer is A.

The first correct step to write the above equation in the form id to subtract 49 from both sides of the equation