Which inequality has the solution n <5?A. 4n + 11 > -9
B. 4n + 11 < -9
C. -4n +11 < -9
D. -4n + 11 > -9

(Please show your work:) )

Answers

Answer 1

Answer: Not A because:
(Subtract 11 from both sides)
4n > -20
(Divide both sides by 4)
n > -5

Because we have found that dividing the negative number by 4 does not work, we know B is also wrong.

Not C because:
(Subtract 11 from both sides)
-4n < -20
(Divide each side by -4)
(Reverse inequality sign because you are dividing by a negative number)
n > 5

So, it must be D!
Here's why:
(Subtract 11 from both sides)
-4n > -20
(Divide each side by -4)
(Reverse inequality sign because you are dividing by a negative number)
n < 5

Hope this helps!

Answer 2

Answer: Let's just pick each and solve

4n + 11 > -9

4n > -9 - 11

4n > -20

n > -20/4

n > -5

This does not give the required solution of n < -5

B would give n < -5, this would also not be correct.

Let us try option C

-4n + 11 < -9

-4n < -9 -11

-4n < -20

n > -20/-4 since we divided by -ve, the sign changes.

n > 5 this does not give the answer as well.

-4n + 11 > -9

-4n > -9 -11

-4n > -20

Divide both sides by 4 and the sign changes.

-4n/4 < -20/-4

n < 5

This is the required solution. So option D gives that solution.

Hope this helps.

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Order the fractions -1/2, 5/2, -12/4, 1/6, and 7/8 from least to greatest

Answers

-12/4 then -1/2 then 1/6 then 7/8 then 5/2
Hope I helped :)

Which equation does the graph below represent?
y=1/3+x
y=1/3x
y=3+x
y=3x

Answers

Lets find 2 points, one obvious one is (0,0), another point is (12,4)

$Slope = (4-0)/(12-0) =(4)/(12) = (4* 1)/(4* 3) = (1)/(3)$

y = mx + b

m is the slope

we got m = 1/3

We can eliminate answer choices C and D.

y = 1/3x + b

we need to solve for b

Plug in the point (0,0) and solve for b

0 = 1/3(0) + b

0 = 0 + b

b = 0

The equation of the line is y = 1/3x + 0, or y = 1/3x

Your answer is B.

Add or subtract mentally 16.9+ 12.1

Answers

Well, just add or subtract it form the back and work your way to the front, and you have to remember what the digit was.

16.9 + 12.1 = 29
16.9 - 12.1 = 4.8

When you add it mentally you'd get 29
When you subtract it mentally you'd get 4.8

To the nearest hundredth, what is the area of a circle with a radius of 5 units?

Answers

Answer: 78. 571 unit²

Step-by-step explanation:

To find the area of a circle, we simple use the formular;

area of a circle = Πr²

The value of π = 22/7

r= radius of the circle = 5

area of a circle = Πr²

= 22/7 × 5 ×5

=550 / 7

= 78. 57143

=78. 571 unit² to the nearest hundredth

Therefore area of the circle with radius 5cm is 78. 571 unit²

Answer would be: 78.5. best i got

When the width of a rectangle with a length of 3/5 foot was decreased by 1/3 foot, the area of the rectangle became 7/25. Find the original width of the rectangle.

Answers

Answer:

$\large\boxed{\text{The original width}\ =(4)/(5)\ ft}$

Step-by-step explanation:

$\text{The dimensions of rectangle:}\ (3)/(5)* w.\n\n\text{The dimensions of new rectangel:}\ (3)/(5)*\left(w-(1)/(3)\right)\n\n\text{The area of the new rectangle:}\ A=(7)/(25)\ ft^2\n\n\text{We have the equation:}\n\n(3)/(5)\left(w-(1)/(3)\right)=(7)/(25)\qquad\text{multiply both sides by 25}\n\n25\!\!\!\!\!\diagup^5\cdot(3)/(5\!\!\!\!\diagup_1)\left(w-(1)/(3)\right)=25\!\!\!\!\!\diagup^1\cdot(7)/(25\!\!\!\!\!\diagup_1)$

$15\left(w-(1)/(3)\right)=7\qquad\text{use the distributive property}\n\n15w-15\!\!\!\!\!\diagup^5\cdot(1)/(3\!\!\!\!\diagup_1)=7\n\n15w-5=7\qquad\text{add 5 to both sides}\n\n15w=12\qquad\text{divide both sides by 15}\n\nw=(12:3)/(15:3)\n\nw=(4)/(5)$

Answer:

The original width is 4/5

Step-by-step explanation:

To find this, note that the new dimensions of the rectangle and 3/5 (lengths) and x - 1/3 (width), in which x is the original width. Now we multiply them together and set equal to 7/25

3/5(x - 1/3) = 7/25

3/5x - 1/5 = 7/25

3/5x = 12/25

x = 4/5

Meghan counted the candies she had in a jar. She discovered that half of the candies were red. If she had 50 red candies, in which equation does x represent the total number candies in the jar?