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3 years ago

How many solutions does 2x+4y=8 have

Mathematics

1 answer:

Sladkaya [172]3 years ago

6 0

Answer:

Infinitely many solutions

Step-by-step explanation:

2x + 4y = 8 is a linear equation in two variables.

A linear equation in two variables have infinitely many solutions.

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Macy's store received an order of 75 baseball caps of which nine were green if one of the 75 caps is selected at random, what is

Helga [31]

Less likely
because 5 is green you might pick one but more likey you wont

6 0

3 years ago

For f(x) = 3x +1 and g(x) = x² - 6, find<br> (f/g)(x)

Paha777 [63]

Answer:

Step-by-step explanation:

$\frac{f(x)}{g(x)} =\frac{3x+1}{x^{2}-6 }$

8 0

2 years ago

Integrala x la a treia ori ln la a doua dx va rog

Studentka2010 [4]

I don't speak Romanian, but the closest translation for this suggests you're trying to compute

$\displaystyle \int x^3 \ln(x)^2 \, dx$

Integrate by parts:

$\displaystyle \int x^3 \ln(x)^2 \, dx = uv - \int v \, du$

where

u = ln(x)² ⇒ du = 2 ln(x)/x dx

dv = x³ dx ⇒ v = 1/4 x⁴

$\implies \displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \int x^3 \ln(x) \, dx$

Integrate by parts again:

$\displaystyle \int x^3 \ln(x) \, dx = u'v' - \int v' du'$

where

u' = ln(x) ⇒ du' = dx/x

dv' = x³ dx ⇒ v' = 1/4 x⁴

$\implies \displaystyle \int x^3 \ln(x) \, dx = \frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx$

So, we have

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \left(\frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx \right)$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \int x^3 \, dx$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \left(\frac14 x^4\right) + C$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac1{32} x^4 + C$

$\boxed{\displaystyle \int x^3 \ln(x)^2 \, dx = \frac1{32} x^4 \left(8\ln(x)^2 - 4\ln(x) + 1\right) + C}$

3 0

2 years ago

A triangle has sides of lengths 4, 3, and 5. Is it a right triangle? Explain.

vlada-n [284]

Answer:

yes; 4² + 3² = 5²

Step-by-step explanation:

Pythagorean theorem.

In a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Hypotenuse is the longest side of the triangle.

4² + 3² = 5²

16 + 9 = 25

25 = 25

7 0

3 years ago

Can you simplify the equation 64x(squared)-112x+49

Leni [432]

Answer:

You cannot simply 64x^2-112x+ 49 further than it is already simplified.

Step-by-step explanation:

5 0

3 years ago