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2 years ago

True or false? it is possible for a system of linear equations to have exactly two solutions.

Mathematics

2 answers:

maksim [4K]2 years ago

4 0

Answer: False

Systems of linear equations can only have 0, 1, or an infinite number of solutions. These two lines cannot intersect twice. The correct answer is that the system has one solution.

Step-by-step explanation:

Shkiper50 [21]2 years ago

4 0

False. Enjoy the holidays!

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2. Dr. Scott bought 3 pound of oranges for $1.50. How much would 7

n200080 [17]

Do 1.50 divided by 3 to get the unit price.

6 0

3 years ago

The graph of a linear function is shown on the grid

monitta

Answer: Choice A

y + 1 = -3(x+2)

=============================

Explanation:

Let's look through the answer choices.

Choices C and D show that the point (2,1) is on the line. But the graph does not show this. So we can rule out choices C and D.

With choice A, the slope is negative and choice B has a positive slope.

The answer must be choice A because the line is going downhill as we move from left to right.

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A common method is to pick two points on the line and compute the slope using the slope formula

m = (y2-y1)/(x2-x1)

Once you know the slope, you would use point slope form

y - y1 = m(x - x1)

4 0

2 years ago

Find gradient xe^y + 4 ln y = x² at (1, 1)

cricket20 [7]

$xe^y+4\ln y=x^2$

Differentiate both sides with respect to x, assuming y = y(x).

$\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}$

$\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x$

$\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

$e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

Solve for dy/dx :

$e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x$

$\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}$

If y ≠ 0, we can write

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}$

At the point (1, 1), the derivative is

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}$

4 0

3 years ago

Evaluate when n = 3. (244 − n)×n -3 9 55 72

HACTEHA [7]

Answer:

$(244 - n)n \\ n = 3 \\ (244 - 3) \times 3 \\ = (241) \times 3 \\ = 723$

3 0

2 years ago

Multiple choice. Use the Law of Sines to find the missing angle of the triangle. Find m angle C to the nearest tenth if c = 111

nalin [4]

Answer:

Both A and B are possible.

Step-by-step explanation:

It's both!

This is a might tricky. First you have to find the altitude. You have to determine if this is a real triangle.

Sin(22) = opposite / hypotenuse. The hypotenuse = 111. The angle is 22

opposite = hypotenuse * sin(22)

opposite = 111 * sin(22)

opposite = 41.58 and this is the altitude.

What have you learned?

Since 42 is larger than 41.58 you have 2 solutions to the triangle. One of the angles is acute, and the other one is obtuse. They are supplementary angles.

Sin(C) / c = Sin(A) / a

Sin(C) = c * Sin(22) / 42

Sin(C) = 111*sin(22)/ 42

Sin(C) = .99003

Sin(C) = 81.9

So that's your first answer. The second answer comes from Finding the supplement to this angle

supplement + 81.9 = 180

supplement = 180 - 81.9

supplement = 98.1

7 0

2 years ago