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3 years ago

Find the slope of the line represented by the data below

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

7 0

Answer:

Slope = -4

Step-by-step explanation:

Let us solve the question

∵ The slope of the line is m = Δy/Δx

∵ Δy is the change of y ⇒ Δy = y2 - y1

∵ Δx is the change of x ⇒ Δx = x2 - x1

→ Choose from the table x1, y1 and x2, y2

∵ x1 = -3 and y1 = 12

∵ x2 = -2 and y2 = 8

→ Use them to find Δx and Δy

∵ Δx = -2 - (-3) = -2 + 3 = 1

∴ Δx = 1

∵ Δy = 8 - 12 = -4

∴ Δy = -4

→ Use them to find the slope

∵ m = Δy/Δx

∴ m = $\frac{-4}{1}$

∴ m = -4

∵ m is the slope of the line

∴ The slope of the line is -4

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The quantity demanded x for a certain brand of MP3 players is 100 units when the unit price p is set at $80. The quantity demand

Cerrena [4.2K]

Answer:p = (2100 - x)/25

Step-by-step explanation:

According to the law of demand, when the price,p of the brand of MP3 players is is high, the quantity,x of the brand of MP3 players demanded would be low and when the price,p of the brand of MP3 players is is low, the quantity,x of the brand of MP3 players demanded would be high.

To derive the demand equation, we would apply the slope intercept form of equation which is expressed as

y = mx + c

Where

m = slope

c = intercept

The slope, m would be

(y2 - y1)/(x2 - x1)

Slope = (1100 - 100)/(40 - 80) = 1000/-40

Slope = - 25

To find the y intercept, we would substitute m = - 25, y = 1100 and x = 40 into y = mx + c. It becomes

1100 = - 25 × 40 + c

1100 = - 1000 + c

c = 1100 + 1000 = 2100

y = - 25x + 2100

Therefore, the demand equation is

x = - 25p + 2100

25p = 2100 - x

p = (2100 - x)/25

4 0

3 years ago

True or False: The following relation is a function.

AysviL [449]

Answer:

Step-by-step explanation:

true

6 0

3 years ago

Read 2 more answers

Solve each of these equations. 1. 2(x+5)=3x+1 2. 3y−4=6−2y 3. 3(n+2)=9(6−n)

Anastasy [175]

Answer:

1. x=9

2. y=2

3. n=4

hello just helping out!

6 0

3 years ago

Length of the base of the given triangle is (x+3) units and the perpendicular height is (x-1)units. If the area of the triangle

Lana71 [14]

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, in our case we know this is 10 :

(x+3)(x-1)/2 = 10

(x+3)(x-1) = 20

x² - x + 3x - 3 = 20

x² + 2x - 23 = 0

that is exactly the provided equation. so, yes, x satisfies it.

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 2

c = -23

x = (-2 ± sqrt(2² - 4×1×-23))/(2×1) =

= (-2 ± sqrt(4 + 92))/2 = (-2 ± sqrt(96))/2 =

= (-2 ± sqrt(16×6))/2 = (-2 ± 4×sqrt(6))/2 =

= -1 ± 2×sqrt(6)

x1 = -1 + 2×sqrt(6) = 3.898979486... ≈ 4

or using sqrt(6) ≈ 2.45

= -1 + 2×2.45 = -1 + 4.9 = 3.9 ≈ 4

x2 = -1 - 2×sqrt(6) = -5.898979486... ≈ -6

or using sqrt(6) ≈ 2.45

= -1 - 2×2.45 = -1 - 4.9 = -5.9 ≈ -6

x2 would give us negative lengths for the triangle, which does not make sense.

so, x = 4 is our solution.

and that makes the height x-1 = 4-1 = 3 units.

7 0

2 years ago

Solve the inequality: 4k-(5+3k)>2

Elanso [62]

Answer:

k > 7

Step-by-step explanation:

Given the inequality statement: 4k - (5 + 3k) > 2

Distribute -1 into (5 + 3k):

4k -5 - 3k > 2

Next, add like terms:

k - 5 > 2

Add 5 to both sides of the inequality:

k - 5 + 5 > 2 + 5

k > 7

Please mark my answers as the Brainliest if you find my explanations helpful :)

5 0

2 years ago

Read 2 more answers