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tatuchka [14]
3 years ago
15

9. What is the slope of the line through the points (-2, -1) and (4, 3)?

Mathematics
1 answer:
Fofino [41]3 years ago
4 0

Step-by-step explanation:

given points,

(-2, -1) and (4,3)

we know,

slope of line = y_2 - y_1/ x_2 - x_1

x_1 and y_1 = -2 , -1

x_2 and y_2 = 4 , 3

according to the formula

3 - (-1)/4 - (-2)

→ 3 + 1/4 + 2

→ 4/6

→ 2/3

or (2,3)

therefore, slope of the given line is (2,3).

Hope this answer helps you dear!

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Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt.
Oliga [24]

Answer:

(a) 0.288 kg/liter

(b) 0.061408 kg/liter

Step-by-step explanation:

(a) The mass of salt entering the tank per minute, x = 0.2 kg/L × 5 L/minute = 1 kg/minute

The mass of salt exiting the tank per minute = 5 × (5 + x)/500

The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;

Δ/dt = x - 5 × (5 + x)/500

The increase, in mass, Δ, after an increase in time, dt, is therefore;

Δ = (x - 5 × (5 + x)/500)·dt

Integrating with a graphing calculator, with limits 0, 10, gives;

Δ = (99·x - 5)/10

Substituting x = 1 gives

(99 × 1 - 5)/10 = 9.4 kg

The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank)

∴ The concentration of the salt and water in the tank after 10 minutes =  (5 + 9.4)/500 = (14.4)/500 = 0.288

The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter

(b) With the added leak, we now have;

Δ/dt = x - 6 × (14.4 + x)/500

Δ = x - 6 × (14.4 + x)/500·dt

Integrating with a graphing calculator, with limits 0, 20, gives;

Δ = 19.76·x -3.456 = 16.304

Where x = 1

The increase in mass after an increase in = 16.304 kg

The total mass = 16.304 + 14.4 = 30.704 kg

The concentration of the salt in the tank then becomes;

Concentration = 30.704/500 = 0.061408 kg/liter.

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3 years ago
In kite WXYZ, the measure of Measure of angle X = measure of angle Z = 86 degrees, and the Measure of angle Y = 72 degrees.
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Answer:

116

Step-by-step explanation:

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2 years ago
Someone help please
Masteriza [31]
Answer: C) 42.3 cm^2

formula for the area if a trapzoid:
A= .5*(b1+b2)*h

A= .5(5.6+8.5)*6
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3 years ago
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Determine the equation of the graph and select the correct answer (-4,-1)
Snowcat [4.5K]

Answer:

(-4,-1)

Step-by-step explanation:

Assuming the graph is the one shown in the attachment.

The forward sloping line has a slope of 1 and a y-intercept of 3.

The equation of this line is y=x+3

The horizontal line has a slope of 0 and y-intercept of -1.

It's equation is y=-1

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In Erica's class of 40 students, 45% of the students report that Art is their favorite subject. How many student
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45% of 40 is 18.

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