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2 years ago

What is the slope-intercept form of the liner equation 2x + 3y = 6?

Mathematics

1 answer:

Romashka-Z-Leto [24]2 years ago

5 0

Answer: $y = -\frac{2}{3}x+2$

Check out the diagram below.

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Work Shown:

$2x + 3y = 6\\\\3y = 6-2x\\\\3y = -2x+6\\\\y = \frac{-2x+6}{3}\\\\y = \frac{-2x}{3}+\frac{6}{3}\\\\y = -\frac{2}{3}x+2\\\\$

The steps above show us subtracting 2x from both sides, then we divide both sides by 3 to fully isolate y.

The last equation is in $y = mx+b$ form with $m = -\frac{2}{3}$ as the slope and $b = 2$ as the y intercept.

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Write a function in any form that would match the graph shown below

ella [17]

Answers:

Vertex form: y = -2(x-1)^2 + 8
Standard form: y = -2x^2 + 4x + 6

Pick whichever form you prefer.

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

Explanation:

The vertex is the highest point in this case, which is located at (1,8).

In general, the vertex is (h,k). So we have h = 1 and k = 8.

One root of this parabola is (-1,0). So we'll plug x = -1 and y = 0 in as well. As an alternative, you can go for (x,y) = (3,0) instead.

Plug those four values mentioned into the equation below. Solve for 'a'.

y = a(x-h)^2 + k

0 = a(-1-1)^2+8

0 = a(-2)^2+8

0 = 4a+8

4a+8 = 0

4a = -8

a = -8/4

a = -2

The vertex form of this parabola is y = -2(x-1)^2+8

Expanding that out gets us the following

y = -2(x-1)^2+8

y = -2(x^2-2x+1)+8

y = -2x^2+4x-2+8

y = -2x^2+4x+6 .... equation in standard form

7 0

2 years ago

Find the reciprocal of the number. Multiply to check your answer.

Mars2501 [29]

To find the reciprocal of a fraction, you just need to "flip" it. To check your work, you multiply the fraction and the reciprocal to get 1.

the reciprocal if 2/3 is 3/2

$\frac{2}{3} * \frac{3}{2} = \frac{6}{6} = 1$

The answer is B

5 0

3 years ago

Read 2 more answers

F(x)=x^2 what is g(x)

Nonamiya [84]

Answer:

Step-by-step explanation:

You have to get 10 because g(x) means 5 so you multiply it by two.

6 0

3 years ago

Read 2 more answers

Prove the divisibility of the following numbers:

Brut [27]

Answer:

Step-by-step explanation:

To prove divisibility, we need to factor the divident such that one of its factors matches the divisor.

(I use the notation x|y to denote that x divides y)

(A)

$75^{30}|45^{45}\cdot15^{15}\\45^{45}\cdot15^{15}=3^{45}\cdot 15^{45}\cdot 15^{15}=\\=3^{45}\cdot 15^{60}=3^{45}\cdot 15^{30}\cdot 15^{30}=3^{45}\cdot (3\cdot5)^{30}\cdot 15^{30}=\\=3^{45}\cdot 3^{30}\cdot(5\cdot 15)^{30}=3^{45}\cdot 3^{30}\cdot(75)^{30}\\\implies\\75^{30}|3^{45}\cdot 3^{30}\cdot75^{30}$

(B)

$72^{63}|24^{54}\cdot 54^{24}\cdot2^{10}\\24^{54}\cdot 54^{24}\cdot2^{10}=(2^{162}\cdot 3^{54})\cdot(2^{24}\cdot 3^{72}) \cdot 2^{10}\\=2^{196}\cdot 3^{126}$

In this case, it is easier to also factor the divisor to primes:

$72^{63}=2^{189}\cdot 3^{126}$

Both of these factor must be matched in the dividend in order to prove divisibility, and that indeed turns out to be true:

$2^{189}\cdot 3^{126}|2^{196}\cdot 3^{126}\implies\\2^{189}|2^{196}\,\,\mbox{and}\,\,3^{126}|3^{126}$

6 0

3 years ago

What is the given value of the variable 7/8 times C for C equals eight

goldenfox [79]

7/8 * C

C = 8

7/8 * 8

56/8

7

6 0

3 years ago