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3 years ago

Write a system of linear equations.Write two-variable equations in slope-intercept form.

Mathematics

1 answer:

kolbaska11 [484]3 years ago

4 0

Answer:

A linear relation can be written in the slope-intercept form as:

y = a*x + b

Where a is the slope, and b is the y-intercept.

And if a line passes through the points (x₁, y₁) and (x₂, y₂), the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Now let's look at our lines.

The left one passes through the points (0, -3) and (-2, 0)

Then the slope of this line is:

a = (0 - (-3))/(-2 - 0) = 3/-2 = -(3/2)

Then the line will be something like:

y = -(3/2)*x + b

Knowing that this line passes through the point (0, -3), we know that when x = 0, we must have y = -3

Then:

-3 = (-3/2)*0 + b

-3 = b

So the first linear equation is:

y = -(3/2)*x - 3

Now let's look at the second line, this one passes through the points (0, 2) and (1, 0)

Then the slope of this line is:

a = (0 - 2)/(1 - 0) = -2

And we can write the line as:

y = -2*x + b

Knowing that this line passes through the point (0, 2), we know that when x = 0 we must have y = 0, replacing that we get:

2 = -2*0 + b

2 = b

Then the equation of this line is:

y = -2*x + 2

Now that we know both equations we can write our system as:

y = (-3/2)*x - 3

y = -2*x + 2

To solve it, we need to remember that y = y

then:

(-3/2)*x - 3 = y = -2*x + 2

(-3/2)*x - 3 = -2*x + 2

We can solve this for x.

2*x - (3/2)*x = 2 + 3

(1/2)*x = 5

x = 5((1/2) = 5*2 = 10

And to find the y-value, we need to input this x-value in one of the equations:

y = -2*10 + 2 = -20 + 2 = -18

Then the solution of the system is the point (10, -18)

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Pachacha [2.7K]

Answer: 3, "obtuse and scalene".

Step-by-step explanation:

Equilateral has all sides equal, eliminate 5.

Isosceles has two sides equal, eliminate 4.

Haven't seen the word scalene since 1966...

Sum of angles is 180°, right angle is 90°, obtuse angle is more than 90°, so there is no such thing as a right and obtuse triangle, eliminate 2. Think |_/.

Similarly, only one angle can be obtuse, think \_/, so every obtuse triangle has two acute angles. But I'm pretty sure "acute triangle" is defined to exclude triangles with an obtuse angle. In that case, "obtuse and acute" is contradictory. Eliminate 1.

That leaves 3, "obtuse and scalene." So now I remember a scalene triangle is one with all three sides different.

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3 years ago

Magnus purchased a new car for $35,865. It depreciates about 3.6% each year. What is the value of the car after 10 years?

Naddik [55]

1 year = 3.6 % depreciation
100-3.6=96.4

so you do 35,865 ×0.964 = 34,573.86

so the price after a year is £34,573.86

to find out what the price is after 10 years you do 34,573.86 (0.964) to the power of 10
which equals £23961.73

I hope that was helpful :)

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4 years ago

A function y(t) satisfies the differential equation dy dt = y4 − 9y3 + 20y2. (a) What are the constant solutions of the equation

Darya [45]

Answer:

a) y = 0, y = 4 and y = 5

b) y ⊂ (- ∞, 0) ∪ (0, 4) ∪ (5, ∞)

c) y ⊂ (4,5)

Step-by-step explanation:

Data provided in the question:

function y(t) satisfies the differential equation:

$\frac{dy}{dt}$ = y⁴ − 9y³ + 20y²

Now,

a) For constant solution

$\frac{dy}{dt}$ = 0

y⁴ − 9y³ + 20y² = 0

y² (y² - 9y + 20 ) = 0

y²(y² -4y - 5y + 20) = 0

y²( y(y - 4) -5(y - 4)) = 0

y²(y - 4)(y - 5) = 0

therefore, solutions are

y = 0, y = 4 and y = 5

b) for y increasing

$\frac{dy}{dt}$ > 0

y²(y - 4)(y - 5) > 0

y²

y ⊂ (- ∞, 0) ∪ (0, 4) ∪ (5, ∞)

c) for y decreasing

$\frac{dy}{dt}$ < 0

y²(y - 4)(y - 5) > 0

y²

y ⊂ (4,5)

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4 years ago

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and th

andrew11 [14]

Answer:

a) 0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.

b) 0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.

c) 0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 8.1 minutes and a standard deviation of 2.0 minutes.

This means that $\mu = 8.1, \sigma = 2$

a. between 5 and 10 min

This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5.

X = 10

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{10 - 8.1}{2}$

$Z = 0.95$

$Z = 0.95$ has a p-value of 0.8289

X = 5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5 - 8.1}{2}$

$Z = -1.55$

$Z = -1.55$ has a p-value of 0.0606

0.8289 - 0.0606 = 0.7683

0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.

b. less than 5 min

p-value of Z when X = 5, which, found from item a, is of 0.0606

0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.

c. more than 10 min

1 subtracted by the p-value of Z when X = 10, which, from item a, is of 0.8289

1 - 0.8289 = 0.1711

0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.

7 0

3 years ago

How many 1 4 cup servings are in 3 8 cups of pudding? (in simplest fraction form) A) 1 6 B) 2 3 C) 3 2 D) 3 8

SVETLANKA909090 [29]

Answer: is c 3/2

Step-by-step explanation:

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3 years ago