What is the value of 2/3− (3/4) * (2)÷( -4/3 ) ?

Nitella [24]

$x = r cos \theta \\ \\ y = r sin \theta$

$x = (-2) cos (\pi/3) = (-2)(\frac{1}{2}) =-1 \\ \\ y=(-2) sin (\pi/3) = (-2)(\frac{\sqrt{3}}{2})=-\sqrt{3}$

The rectangular coordinates are:
$(-1,-\sqrt{3})$

4 0

3 years ago

Drag values to complete each equation.

kherson [118]

Answer:

$9^{-7}$ and $9^{-2}$

Step-by-step explanation:

using the rules of exponents

• $(a^m)^{n}$ = $a^{mn}$

• $a^{m}$ × $a^{n}$ = $a^{(m+n)}$

• $\frac{a^{m} }{a^{n} }$ = $a^{(m-n)}$

given ( $9^{5}$ × $9^{-9}$ ) / $9^{3}$

= $\frac{9^{5+(-9)} }{9^{3} }$ = $\frac{9^{-4} }{9^{3} }$ = $9^{-4-3}$ = $9^{-7}$

given $(9^4)^{3}$ × $9^{-14}$

= $9^{12}$ × $9^{-14}$

= $9^{12+(-14)}$ = $9^{-2}$

8 0

4 years ago

Read 2 more answers

What is the equation of the line

satela [25.4K]

Answer:

y=1/2x+2

Step-by-step explanation:

Slope Form: Mx+b

Rise/Run:1/2

Y-intercept: 2

3 0

3 years ago

Please answer this question fast in 2 minutes

Stolb23 [73]

Answer:

(-20, 19)

Step-by-step explanation:

We need to use the Midpoint Formula, which says that given two points $(x_1,y_1)$ and $(x_2,y_2)$ , the midpoint is $(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$ .

Here, we are given one of the endpoints and the midpoint:

endpoint S = (5, -8)

midpoint M = (-7.5, 5.5)

Plug these into the formula. In $\frac{x_1+x_2}{2}$ , x1 = 5, and this whole expression is equal to -7.5:

$\frac{x_1+x_2}{2}=\frac{5+x_2}{2} =-7.5$

Solve for x2:

5 + x2 = 2 * (-7.5) = -15

x2 = -15 - 5 = -20

Now, let's find y2. y1 is just -8, and the entire expression for the y-coordinate of the midpoint is equal to 5.5. So:

$\frac{y_1+y_2}{2}=\frac{-8+y_2}{2} =5.5$

Solve for y2:

-8 + y2 = 2 * 5.5

-8 + y2 = 11

y2 = 11 + 8 = 19

The coordinates of T are thus (-20, 19).

~ an aesthetics lover

5 0

3 years ago

Graph the system of inequalities presented here then use your graph to answer the following questions:

Nookie1986 [14]

Answer:

Part A) The graph in the attached figure (see the explanation)

Part B) The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)

Step-by-step explanation:

Part 1) Graph the system of inequalities

we have

$y> 5x+5$ ----> inequality A

The solution of the inequality A is the shaded area above the dashed line $y=5x+5$

The slope pf the dashed line A is positive m=5

The y-intercept of the dashed line A is (0,5)

The x-intercept of the dashed line A is (-1,0)

$y>-\frac{1}{2}x+1$ ----> inequality B

The solution of the inequality B is the shaded area above the dashed line $y=-\frac{1}{2}x+1$

The slope pf the dashed line B is negative m=-1/2

The y-intercept of the dashed line B is (0,1)

The x-intercept of the dashed line B is (2,0)

The solution of the system of inequalities is the shaded area above the dashed line A and above the dashed line B

using a graphing tool

see the attached figure

Part B) Is the point (-2, 5) included in the solution area for the system? Justify your answer mathematically

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

substitute the value of x and the value of y in each inequality

For x=-2, y=5

Verify inequality A

$5>5(-2)+5$

$5>-5$ ---> is true

so

The ordered pair satisfy inequality A

Verify inequality B

$5>-\frac{1}{2}(-2)+1$

$5>2$ ---> is true

so

The ordered pair satisfy inequality B

therefore

The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)

6 0

3 years ago