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2 years ago

What is the slope of the line on the graph?

Mathematics

1 answer:

Phoenix [80]2 years ago

6 0

Answer:

$m=-2$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-3, 6)

Point (3, -6)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute [SF]: $m=\frac{-6-6}{3+3}$
Subtract/Add: $m=\frac{-12}{6}$
Divide: $m=-2$

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Answer:

Height: 3/2 inches

Length: 12 inches

Width: 4 inches

Step-by-step explanation:

Let x is the side length of the square

The height of the box by cutting squares off :x

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The new width of the cardboard = 7 -2x (because we cut from 4 corners)

The new volume of it is:

V = (15 -2x) (7 -2x) x

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To maximum volume, we use the first derivative of the volume

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<=> $12x^2-88x+105=0$

<=> $\left(2x-3\right)\left(6x-35\right) = 0$

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To determine which value of x gives a maximum, we evaluate

$\dfrac{d^2V}{dx^2}$ = 24x -88

If x = 3/2, we have:

$\dfrac{d^2V}{dx^2}$ = 24(3/2) -88 = -52

If x = 35/6, we have:

$\dfrac{d^2V}{dx^2}$ = 24(35/6) -88 = 52

We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.

So the dimensions (in inches) of the box is:

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2 years ago

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Answer: The price of each small box is $4.8 and the price of each large box is $10.8.

Step-by-step explanation:

Let x = Price of each small box, y= price of each large box.

As per given,

3x+2y= 36 ...(i)

4x+y= 30 ...(ii)

Multiplying 2 to (ii), we get

8x+2y =60...(iii)

Subtract (i) from (iii), we get

5x= 24

x= 4.8

From (ii)

4(4.8)+y= 30

19.2+y=30

y= 10.8

Hence, the price of each small box is $4.8 and the price of each large box is $10.8.

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2 years ago

There were 200,000 animals of a certain species in 1980. Since then,this number has decreased by 4.5% each year. Approximately h

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Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

y = b(1 - r)^x

Where

y represents the population of animals after x years.

x represents the number of years.

b represents the initial population of animals.

r represents rate of decay.

From the information given,

b = 200000

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Therefore,

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The attached image shows an obtuse-angled triangle. We can note that measure ∠B is greater than 90°

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What is the slope of the line on the graph? ​

What is the slope of the line on the graph?