All categories

3 years ago

Evaluate the problem below. Please show all your work for full credit. Highlight or -4 1/2+5 2/3

Mathematics

1 answer:

lubasha [3.4K]3 years ago

3 0

Answer:

$\frac{7}{6}$

Step-by-step explanation:

$-4\frac{1}{2} + 5\frac{2}{3} =$

For the first term you have to multiply 2x(-4) and add 1, for the second term you have to multiply 3x5 and add 2.

$\frac{2(-4)+1}{2} + \frac{3(5)+2}{3} =$

$-\frac{9}{2} +\frac{17}{3} =$

Now you need to find the lowest common multiple between the denominators, just cross multiply as it is shown:

$-\frac{9}{2} (\frac{3}{3} )+\frac{17}{3} (\frac{2}{2} )=$

$-\frac{27}{6} +\frac{34}{6} = \frac{7}{6}$

finally you get the result by doing a substraction = 7/6, or 1 $\frac{1}{6}$

You might be interested in

Taylor Scuff leased a new sports car and is certain she can keep under the 12,000 miles allowed a year. The $2,200 due at signin

damaskus [11]

Answer:

The answer would be 36 months

Step-by-step explanation:

3 0

3 years ago

Find an explicit solution of the given initial-value problem.dy/dx = ye^x^2, y(3) = 1.

tamaranim1 [39]

Answer:

$y=exp(\int\limits^x_4 {e^{-t^{2} } } \, dt)$

Step-by-step explanation:

This is a separable equation with an initial value i.e. y(3)=1.

Take y from right hand side and divide to left hand side ;Take dx from left hand side and multiply to right hand side:

$\frac{dy}{y} =e^{-x^{2} }dx$

Take t as a dummy variable, integrate both sides with respect to "t" and substituting x=t (e.g. dx=dt):

$\int\limits^x_3 {\frac{1}{y} } \, \frac{dy}{dt} dt=\int\limits^x_3 {e^{-t^{2} } } dt$

Integrate on both sides:

$ln(y(t))\left \{ {{t=x} \atop {t=3}} \right. =\int\limits^x_3 {e^{-t^{2} } } \, dt$

Use initial condition i.e. y(3) = 1:

$ln(y(x))-(ln1)=\int\limits^x_3 {e^{-t^{2} } } \, dt\\ln(y(x))=\int\limits^x_3 {e^{-t^{2} } } \, dt\\$

Taking exponents on both sides to remove "ln":

$y=exp (\int\limits^x_3 {e^{-t^{2} } } \, dt)$

7 0

3 years ago

a store sells boxes of juice in equal size packs. Garth bought 18 boxes, Rico bought 36 boxes, and Mai bought 45 boxes. what is

aniked [119]

Mai 45 boxes that is the answer simple

5 0

3 years ago

(Geometry) Question 2

Kruka [31]

Answer:

E = {0, 1, 2, 3)

Step-by-step explanation:

Integer: a number with no decimal or fractional part, from the set of negative and positive numbers, including zero
< means less than
> means more than

E = {0, 1, 2, 3)

6 0

2 years ago

Identify the standard form of the equation by completing the square.

OLEGan [10]

Answer:

$\dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Step-by-step explanation:

Given equation:

$4x^2-9y^2-8x+36y-68=0$

This is an equation for a horizontal hyperbola.

To complete the square for a hyperbola

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.

$\implies 4x^2-8x-9y^2+36y=68$

Factor out the coefficient of the x² term and the y² term.

$\implies 4(x^2-2x)-9(y^2-4y)=68$

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

$\implies 4\left(x^2-2x+\left(\dfrac{-2}{2}\right)^2\right)-9\left(y^2-4y+\left(\dfrac{-4}{2}\right)^2\right)=68+4\left(\dfrac{-2}{2}\right)^2-9\left(\dfrac{-4}{2}\right)^2$

$\implies 4\left(x^2-2x+1\right)-9\left(y^2-4y+4\right)=36$

Factor the two perfect trinomials on the left side:

$\implies 4(x-1)^2-9(y-2)^2=36$

Divide both sides by the number of the right side so the right side equals 1:

$\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}$

Simplify:

$\implies \dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Therefore, this is the standard equation for a horizontal hyperbola with:

center = (1, 2)
vertices = (-2, 2) and (4, 2)
co-vertices = (1, 0) and (1, 4)
$\textsf{Asymptotes}: \quad y = -\dfrac{2}{3}x+\dfrac{8}{3} \textsf{ and }y=\dfrac{2}{3}x+\dfrac{4}{3}$
$\textsf{Foci}: \quad (1-\sqrt{13}, 2) \textsf{ and }(1+\sqrt{13}, 2)$

4 0

2 years ago