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2 years ago

An inequality is shown: −np − 4 ≤ 2(c − 3) Which of the following solves for n?

Mathematics

1 answer:

sesenic [268]2 years ago

6 0

Answer:

$\huge\boxed{n\leq\dfrac{2-2c}{p}\ \text{for}\ p0}$

Step-by-step explanation:

$-np-4\leq2(c-3)\qquad\text{use the distributive property}\\\\-np-4\leq2c-6\qquad\text{add 4 to both sides}\\\\-np\leq2c-2\qquad\text{change the signs}\\\\np\geq2-2c\qquad\text{divide both sides by}\ p\neq0\\\\\text{If}\ p0 ,\ \text{then}\\\boxed{n\geq\dfrac{2-2c}{p}}$

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BIG POINTS Please solve. Thanks!

Nitella [24]

9^1/3 * 3^x = 27^4/5

Rewrite 9 as 3^2

(3^2)^1/3 * 3^x = 27^4/5

Multiply the exponents in the first term:

3^2/3 * 3^x = 27^4/5

Use power rule to combine exponents:

3^(2/3 +x) = 27^4/5

Rewrite the 2nd term:

3^(2/3 +x) = (3^3)^4/5

Set the exponents only to equal:

2/3 + x = 3(4/5)

Solve for x:

simplify the right side:

2/3 + x = 12/5

Subtract 2/3 from both sides:

x = 26/15

3 0

2 years ago

The height, h, in feet of a gold ball above the ground after being hit into the air is given by the equation. H=-16t2+64t, where

stiv31 [10]

Answer:

4 seconds

Step-by-step explanation:

Given : $H = -16t^{2} +64t$

To Find: How many seconds does it take for the golf ball to hit the ground?

Solution :

Since we are given an equation : $H = -16t^{2} +64t$

Where H denotes height

t denotes the number of seconds elapsed since the ball was hit.

When he golf ball to hit the ground at that time the height becomes 0

So, put H = 0 in the equation

$H = - 16t^{2} +64t$

$0 = - 16t^{2} +64t$

$16t^{2} = 64t$

$16t = 64$

$t =\frac{64}{16}$

$t =4$

Thus it take 4 seconds for the golf ball to hit the ground

4 0

2 years ago

Help please I'm trying to graduate (Only #3)

lesya [120]

The pieces shown are like all of 8 slices of a pizza.

the area of cirlce = area of the rectangle formed by rearranging the pizza slices.
= (pi*r)*r

5 0

2 years ago

Line p has an equation of y=-8x+6. Line q, which is perpendicular to line p, includes the point (2,–2). What is the equation of

Arturiano [62]

Answer:

$y = \frac{1}{8} x - 2 \frac{1}{4}$

Step-by-step explanation:

<u>Slope-intercept </u><u>form</u>

y= mx +c, where m is the slope and c is the y-intercept

Line p: y= -8x +6

slope= -8

The product of the slopes of perpendicular lines is -1. Let the slope of line q be m.

m(-8)= -1

m= -1 ÷(-8)

m= ⅛

Substitute m= ⅛ into the equation:

y= ⅛x +c

To find the value of c, substitute a pair of coordinates that the line passes through into the equation.

When x= 2, y= -2,

-2= ⅛(2) +c

$- 2 = \frac{1}{4} + c$

$c = - 2 - \frac{1}{4}$

$c = - 2 \frac{1}{4}$

Thus, the equation of line q is $y = \frac{1}{8} x - 2 \frac{1}{4}$ .

4 0

2 years ago

Assuming that a soap bubble is a perfect sphere, what is the diameter of a bubble containing 1,000 cm3 of air? Round to the near

Minchanka [31]

Answer:

17.85 cm

Step-by-step explanation:

1) Area of a sphere formula: $A=4\pi r^{2}$

2) Plug in A: 1000 = $4\pi r^{2}$

3) Simplify: 1000 = 12.56 $r^{2}$

4) Divide Each Side By 12.56: 79.61783439 = $r^{2}$

5) Take the Square Root of 79.61783439 to Solve for $r$ : 8.922882628 = $r$

6) Double $r$ to get the diameter: 8.922882628*2= 17.84576486

7) Round to the Nearest Tenth: 17.85 cm

8 0

2 years ago