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2 years ago

Most linear graphs are direct variation, unless they go through the origin.

1 answer:

5 0

False

A linear graph that is a direct variation is in the form y=kx, so it has a y-intercept at (0,0). This means it passes through the origin if it is a direct variation.

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What is the difference between microeconomics and macroeconomics?

Citrus2011 [14]

The major thing that differentiate microeconomics from macroeconomics is the object of study. Microeconomics refers to the study of economics at individual, group or business level while macroeconomics involves the study of economics on the national scale, that is the study of the economy of a nation. The economics of a nation is the combination of all the individuals, businesses, households, etc in a country.

4 0

2 years ago

A quadratic equation is shown below:

Valentin [98]

Part A)

The given equation is:

$25 x^{2} +10x+1=0$

The radicand or discriminant(d) of the equation will be:

$d=(10)^{2}-4(25)(1) \\ \\ 
d=100-100 \\ \\ 
d=0$

Since the discriminant is equal to 0, the given quadratic equation has only 1 root. In other words we can say the the given equation is a perfect square.

Part B)

The given equation is:

$4 x^{2} -4x+1=0$

We can solve this expression by factorization. Factors of middle term are to be made in such a way that their product equals the product of first and third term and sum is equal to the middle term i.e. product should be 4x² and sum should be -4x.
So the two such terms are -2x and -2x. Using the factors and simplifying the equation by taking common we get:

$4 x^{2} -2x-2x+1=0 \\ \\ 
2x(2x-1)-1(2x-1)=0 \\ \\ 
(2x-1)(2x-1)=0 \\ \\ 
(2x-1) ^{2}=0 \\ \\ 
2x-1=0 \\ \\ 
x= \frac{1}{2}$

4 0

3 years ago

Does anyone know how to solve this? It’s really starting to stress me out.

bekas [8.4K]

Answer:

π − 12

Step-by-step explanation:

lim(x→2) (sin(πx) + 8 − x³) / (x − 2)

If we substitute x = u + 2:

lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)

lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u

Distribute the cube:

lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u

lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u

lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u

Using angle sum formula:

lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u

lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u

Divide:

lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]

lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)

lim(u→0) (sin(πu) / u) − 12

Multiply and divide by π.

lim(u→0) (π sin(πu) / (πu)) − 12

π lim(u→0) (sin(πu) / (πu)) − 12

Use special identity, lim(x→0) ((sin x) / x ) = 1.

π (1) − 12

π − 12

3 0

3 years ago

Help me on this one please

shepuryov [24]

Answer:

The equation is set up wrong

Step-by-step explanation:

$9^{2} +b^{2} =15^{2}$

3 0

2 years ago

What’s the correct answer for this question?

weqwewe [10]

Answer:

Last answer choice

Step-by-step explanation:

The AAS congruence theorem uses two adjacent angles, followed by a side length on the side (not in between the angles.) Therefore, the first answer is ruled out (because it deals with angles and not sides), and the second answer is ruled out because it involves side lengths between angles. LP=MO may be true, but it does not compare the two triangles that we are interested in. However, the last answer choice is correct, because a midpoint divides a line exactly in half, meaning that both halves are the same length and therefore congruent. Therefore, the last answer choice is correct. Hope this helps!

7 0

3 years ago